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GitHub

API Reference

This page lists the public API of MathOptAI.

Info

This page is an unstructured list of the MathOptAI API. For a more structured overview, read the Manual or Tutorial parts of this documentation.

Load all of the public the API into the current scope with:

using MathOptAI

Alternatively, load only the module with:

import MathOptAI

and then prefix all calls with MathOptAI. to create MathOptAI.<NAME>.

AbstractPredictor

add_predictor

MathOptAI.add_predictor — Function
add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::AbstractPredictor,
+    x::Vector,
+)::Vector

Return a Vector representing y such that y = predictor(x).

The element type of x is deliberately unspecified. The vector x may contain any mix of scalar constants, JuMP decision variables, and scalar JuMP functions like AffExpr, QuadExpr, or NonlinearExpr.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.Affine([2.0, 3.0])
+Affine(A, b) [input: 2, output: 1]
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Affine[1]
+
+julia> formulation
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ 2 x[1] + 3 x[2] - moai_Affine[1] = 0
source

build_predictor

Affine

MathOptAI.Affine — Type
Affine(
+    A::Matrix{T},
+    b::Vector{T} = zeros(T, size(A, 1)),
+) where {T} <: AbstractPredictor

An AbstractPredictor that represents the relationship:

\[y = A x + b\]

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, 0 <= x[i in 1:2] <= i);
+
+julia> f = MathOptAI.Affine([2.0 3.0], [4.0])
+Affine(A, b) [input: 2, output: 1]
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Affine[1]
+
+julia> formulation
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [3]
+  ├ moai_Affine[1] ≥ 4
+  ├ moai_Affine[1] ≤ 12
+  └ 2 x[1] + 3 x[2] - moai_Affine[1] = -4
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+1-element Vector{AffExpr}:
+ 2 x[1] + 3 x[2] + 4
+
+julia> formulation
+ReducedSpace(Affine(A, b) [input: 2, output: 1])
+├ variables [0]
+└ constraints [0]
source

BinaryDecisionTree

MathOptAI.BinaryDecisionTree — Type
BinaryDecisionTree{K,V}(
+    feat_id::Int,
+    feat_value::K,
+    lhs::Union{V,BinaryDecisionTree{K,V}},
+    rhs::Union{V,BinaryDecisionTree{K,V}},
+)

An AbstractPredictor that represents a binary decision tree.

  • If x[feat_id] <= feat_value, then return lhs
  • If x[feat_id] > feat_value, then return rhs

Example

To represent the tree x[1] <= 0.0 ? -1 : (x[1] <= 1.0 ? 0 : 1), do:

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:1]);
+
+julia> f = MathOptAI.BinaryDecisionTree{Float64,Int}(
+           1,
+           0.0,
+           -1,
+           MathOptAI.BinaryDecisionTree{Float64,Int}(1, 1.0, 0, 1),
+       )
+BinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_BinaryDecisionTree_value
+
+julia> formulation
+BinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]
+├ variables [4]
+│ ├ moai_BinaryDecisionTree_value
+│ ├ moai_BinaryDecisionTree_z[1]
+│ ├ moai_BinaryDecisionTree_z[2]
+│ └ moai_BinaryDecisionTree_z[3]
+└ constraints [7]
+  ├ moai_BinaryDecisionTree_z[1] + moai_BinaryDecisionTree_z[2] + moai_BinaryDecisionTree_z[3] = 1
+  ├ moai_BinaryDecisionTree_z[1] --> {x[1] ≤ 0}
+  ├ moai_BinaryDecisionTree_z[2] --> {x[1] ≥ 0}
+  ├ moai_BinaryDecisionTree_z[2] --> {x[1] ≤ 1}
+  ├ moai_BinaryDecisionTree_z[3] --> {x[1] ≥ 0}
+  ├ moai_BinaryDecisionTree_z[3] --> {x[1] ≥ 1}
+  └ moai_BinaryDecisionTree_z[1] - moai_BinaryDecisionTree_z[3] + moai_BinaryDecisionTree_value = 0
source

GrayBox

MathOptAI.GrayBox — Type
GrayBox(
+    output_size::Function,
+    callback::Function;
+    has_hessian::Bool = false,
+) <: AbstractPredictor

An AbstractPredictor that represents the relationship:

\[y = f(x)\]

as a user-defined nonlinear operator.

Arguments

  • output_size(x::Vector):Int: given an input vector x, return the dimension of the output vector
  • callback(x::Vector)::NamedTuple -> (;value, jacobian[, hessian]): given an input vector x, return a NamedTuple that computes the primal value and Jacobian of the output value with respect to the input. jacobian[j, i] is the partial derivative of value[j] with respect to x[i].
  • has_hessian: if true, the callback additionally contains a field hessian, which is an N × N × M matrix, where hessian[i, j, k] is the partial derivative of value[k] with respect to x[i] and x[j].

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.GrayBox(
+           x -> 2,
+           x -> (value = x.^2, jacobian = [2 * x[1] 0.0; 0.0 2 * x[2]]),
+       );
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_GrayBox[1]
+ moai_GrayBox[2]
+
+julia> formulation
+GrayBox
+├ variables [2]
+│ ├ moai_GrayBox[1]
+│ └ moai_GrayBox[2]
+└ constraints [2]
+  ├ op_##330(x[1], x[2]) - moai_GrayBox[1] = 0
+  └ op_##331(x[1], x[2]) - moai_GrayBox[2] = 0
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ op_##332(x[1], x[2])
+ op_##333(x[1], x[2])
+
+julia> formulation
+ReducedSpace(GrayBox)
+├ variables [0]
+└ constraints [0]
source

Pipeline

MathOptAI.Pipeline — Type
Pipeline(layers::Vector{AbstractPredictor}) <: AbstractPredictor

An AbstractPredictor that represents the relationship:

\[y = (l_1 \circ \ldots \circ l_N)(x)\]

where $l_i$ are a list of other AbstractPredictors.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.Pipeline(
+           MathOptAI.Affine([1.0 2.0], [0.0]),
+           MathOptAI.ReLUQuadratic(),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 2, output: 1]
+ * ReLUQuadratic()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_ReLU[1]
+
+julia> formulation
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ x[1] + 2 x[2] - moai_Affine[1] = 0
+ReLUQuadratic()
+├ variables [2]
+│ ├ moai_ReLU[1]
+│ └ moai_z[1]
+└ constraints [4]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_z[1] ≥ 0
+  ├ moai_Affine[1] - moai_ReLU[1] + moai_z[1] = 0
+  └ moai_ReLU[1]*moai_z[1] = 0
source

PytorchModel

MathOptAI.PytorchModel — Type
PytorchModel(filename::String)

A wrapper struct for loading a PyTorch model.

The only supported file extension is .pt, where the .pt file has been created using torch.save(model, filename).

Example

julia> using PythonCall, MathOptAI
+
+julia> predictor = PytorchModel("model.pt");
source

Quantile

MathOptAI.Quantile — Type
Quantile{D}(distribution::D, quantiles::Vector{Float64}) where {D}

An AbstractPredictor that represents the quantiles of distribution.

Example

julia> using JuMP, Distributions, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, 1 <= x <= 2);
+
+julia> predictor = MathOptAI.Quantile([0.1, 0.9]) do x
+           return Distributions.Normal(x, 3 - x)
+       end
+Quantile(_, [0.1, 0.9])
+
+julia> y, formulation = MathOptAI.add_predictor(model, predictor, [x]);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_quantile[1]
+ moai_quantile[2]
+
+julia> formulation
+Quantile(_, [0.1, 0.9])
+├ variables [2]
+│ ├ moai_quantile[1]
+│ └ moai_quantile[2]
+└ constraints [2]
+  ├ moai_quantile[1] - op_quantile_0.1(x) = 0
+  └ moai_quantile[2] - op_quantile_0.9(x) = 0
source

ReducedSpace

MathOptAI.ReducedSpace — Type
ReducedSpace(predictor::AbstractPredictor)

A wrapper type for other predictors that implement a reduced-space formulation.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> predictor = MathOptAI.ReducedSpace(MathOptAI.ReLU());
+
+julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ max(0.0, x[1])
+ max(0.0, x[2])
source

ReLU

MathOptAI.ReLU — Type
ReLU() <: AbstractPredictor

An AbstractPredictor that represents the relationship:

\[y = \max\{0, x\}\]

as a non-smooth nonlinear constraint.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, -1 <= x[i in 1:2] <= i);
+
+julia> f = MathOptAI.ReLU()
+ReLU()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_ReLU[1]
+ moai_ReLU[2]
+
+julia> formulation
+ReLU()
+├ variables [2]
+│ ├ moai_ReLU[1]
+│ └ moai_ReLU[2]
+└ constraints [6]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[1] ≤ 1
+  ├ moai_ReLU[2] ≥ 0
+  ├ moai_ReLU[2] ≤ 2
+  ├ moai_ReLU[1] - max(0.0, x[1]) = 0
+  └ moai_ReLU[2] - max(0.0, x[2]) = 0
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ max(0.0, x[1])
+ max(0.0, x[2])
+
+julia> formulation
+ReducedSpace(ReLU())
+├ variables [0]
+└ constraints [0]
source

ReLUBigM

MathOptAI.ReLUBigM — Type
ReLUBigM(M::Float64) <: AbstractPredictor

An AbstractPredictor that represents the relationship:

\[y = \max\{0, x\}\]

via the big-M MIP reformulation:

\[\begin{aligned} +y \ge 0 \\ +y \ge x \\ +y \le M z \\ +y \le x + M(1 - z) \\ +z \in\{0, 1\} +\end{aligned}\]

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, -3 <= x[i in 1:2] <= i);
+
+julia> f = MathOptAI.ReLUBigM(100.0)
+ReLUBigM(100.0)
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_ReLU[1]
+ moai_ReLU[2]
+
+julia> formulation
+ReLUBigM(100.0)
+├ variables [4]
+│ ├ moai_ReLU[1]
+│ ├ moai_ReLU[2]
+│ ├ moai_z[1]
+│ └ moai_z[2]
+└ constraints [12]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[1] ≤ 1
+  ├ moai_ReLU[2] ≥ 0
+  ├ moai_ReLU[2] ≤ 2
+  ├ moai_z[1] binary
+  ├ -x[1] + moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[1] - moai_z[1] ≤ 0
+  ├ -x[1] + moai_ReLU[1] + 3 moai_z[1] ≤ 3
+  ├ moai_z[2] binary
+  ├ -x[2] + moai_ReLU[2] ≥ 0
+  ├ moai_ReLU[2] - 2 moai_z[2] ≤ 0
+  └ -x[2] + moai_ReLU[2] + 3 moai_z[2] ≤ 3
source

ReLUQuadratic

MathOptAI.ReLUQuadratic — Type
ReLUQuadratic() <: AbstractPredictor

An AbstractPredictor that represents the relationship:

\[y = \max\{0, x\}\]

by the reformulation:

\[\begin{aligned} +x = y - z \\ +y \cdot z = 0 \\ +y, z \ge 0 +\end{aligned}\]

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, -1 <= x[i in 1:2] <= i);
+
+julia> f = MathOptAI.ReLUQuadratic()
+ReLUQuadratic()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_ReLU[1]
+ moai_ReLU[2]
+
+julia> formulation
+ReLUQuadratic()
+├ variables [4]
+│ ├ moai_ReLU[1]
+│ ├ moai_ReLU[2]
+│ ├ moai_z[1]
+│ └ moai_z[2]
+└ constraints [12]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[1] ≤ 1
+  ├ moai_ReLU[2] ≥ 0
+  ├ moai_ReLU[2] ≤ 2
+  ├ moai_z[1] ≥ 0
+  ├ moai_z[1] ≤ 1
+  ├ moai_z[2] ≥ 0
+  ├ moai_z[2] ≤ 1
+  ├ x[1] - moai_ReLU[1] + moai_z[1] = 0
+  ├ x[2] - moai_ReLU[2] + moai_z[2] = 0
+  ├ moai_ReLU[1]*moai_z[1] = 0
+  └ moai_ReLU[2]*moai_z[2] = 0
source

ReLUSOS1

MathOptAI.ReLUSOS1 — Type
ReLUSOS1() <: AbstractPredictor

An AbstractPredictor that represents the relationship:

\[y = \max\{0, x\}\]

by the reformulation:

\[\begin{aligned} +x = y - z \\ +[y, z] \in SOS1 \\ +y, z \ge 0 +\end{aligned}\]

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, -1 <= x[i in 1:2] <= i);
+
+julia> f = MathOptAI.ReLUSOS1()
+ReLUSOS1()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_ReLU[1]
+ moai_ReLU[2]
+
+julia> formulation
+ReLUSOS1()
+├ variables [4]
+│ ├ moai_ReLU[1]
+│ ├ moai_ReLU[2]
+│ ├ moai_z[1]
+│ └ moai_z[2]
+└ constraints [10]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[1] ≤ 1
+  ├ moai_ReLU[2] ≥ 0
+  ├ moai_ReLU[2] ≤ 2
+  ├ moai_z[1] ≤ 1
+  ├ moai_z[2] ≤ 1
+  ├ x[1] - moai_ReLU[1] + moai_z[1] = 0
+  ├ x[2] - moai_ReLU[2] + moai_z[2] = 0
+  ├ [moai_ReLU[1], moai_z[1]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])
+  └ [moai_ReLU[2], moai_z[2]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])
source

Scale

MathOptAI.Scale — Type
Scale(
+    scale::Vector{T},
+    bias::Vector{T},
+) where {T} <: AbstractPredictor

An AbstractPredictor that represents the relationship:

\[y = Diag(scale)x + bias\]

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, 0 <= x[i in 1:2] <= i);
+
+julia> f = MathOptAI.Scale([2.0, 3.0], [4.0, 5.0])
+Scale(scale, bias)
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_Scale[1]
+ moai_Scale[2]
+
+julia> formulation
+Scale(scale, bias)
+├ variables [2]
+│ ├ moai_Scale[1]
+│ └ moai_Scale[2]
+└ constraints [6]
+  ├ moai_Scale[1] ≥ 4
+  ├ moai_Scale[1] ≤ 6
+  ├ moai_Scale[2] ≥ 5
+  ├ moai_Scale[2] ≤ 11
+  ├ 2 x[1] - moai_Scale[1] = -4
+  └ 3 x[2] - moai_Scale[2] = -5
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{AffExpr}:
+ 2 x[1] + 4
+ 3 x[2] + 5
+
+julia> formulation
+ReducedSpace(Scale(scale, bias))
+├ variables [0]
+└ constraints [0]
source

Sigmoid

MathOptAI.Sigmoid — Type
Sigmoid() <: AbstractPredictor

An AbstractPredictor that represents the relationship:

\[y = \frac{1}{1 + e^{-x}}\]

as a smooth nonlinear constraint.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, -1 <= x[i in 1:2] <= i);
+
+julia> f = MathOptAI.Sigmoid()
+Sigmoid()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_Sigmoid[1]
+ moai_Sigmoid[2]
+
+julia> formulation
+Sigmoid()
+├ variables [2]
+│ ├ moai_Sigmoid[1]
+│ └ moai_Sigmoid[2]
+└ constraints [6]
+  ├ moai_Sigmoid[1] ≥ 0.2689414213699951
+  ├ moai_Sigmoid[1] ≤ 0.7310585786300049
+  ├ moai_Sigmoid[2] ≥ 0.2689414213699951
+  ├ moai_Sigmoid[2] ≤ 0.8807970779778823
+  ├ moai_Sigmoid[1] - (1.0 / (1.0 + exp(-x[1]))) = 0
+  └ moai_Sigmoid[2] - (1.0 / (1.0 + exp(-x[2]))) = 0
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ 1.0 / (1.0 + exp(-x[1]))
+ 1.0 / (1.0 + exp(-x[2]))
+
+julia> formulation
+ReducedSpace(Sigmoid())
+├ variables [0]
+└ constraints [0]
source

SoftMax

MathOptAI.SoftMax — Type
SoftMax() <: AbstractPredictor

An AbstractPredictor that represents the relationship:

\[y = \frac{e^{x}}{||e^{x}||_1}\]

as a smooth nonlinear constraint.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.SoftMax()
+SoftMax()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_SoftMax[1]
+ moai_SoftMax[2]
+
+julia> formulation
+SoftMax()
+├ variables [3]
+│ ├ moai_SoftMax_denom
+│ ├ moai_SoftMax[1]
+│ └ moai_SoftMax[2]
+└ constraints [8]
+  ├ moai_SoftMax[1] ≥ 0
+  ├ moai_SoftMax[1] ≤ 1
+  ├ moai_SoftMax[2] ≥ 0
+  ├ moai_SoftMax[2] ≤ 1
+  ├ moai_SoftMax_denom ≥ 0
+  ├ moai_SoftMax_denom - (0.0 + exp(x[2]) + exp(x[1])) = 0
+  ├ moai_SoftMax[1] - (exp(x[1]) / moai_SoftMax_denom) = 0
+  └ moai_SoftMax[2] - (exp(x[2]) / moai_SoftMax_denom) = 0
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ exp(x[1]) / moai_SoftMax_denom
+ exp(x[2]) / moai_SoftMax_denom
+
+julia> formulation
+ReducedSpace(SoftMax())
+├ variables [1]
+│ └ moai_SoftMax_denom
+└ constraints [2]
+  ├ moai_SoftMax_denom ≥ 0
+  └ moai_SoftMax_denom - (0.0 + exp(x[2]) + exp(x[1])) = 0
source

SoftPlus

MathOptAI.SoftPlus — Type
SoftPlus(; beta = 1.0) <: AbstractPredictor

An AbstractPredictor that represents the relationship:

\[y = \frac{1}{\beta} \log(1 + e^{\beta x})\]

as a smooth nonlinear constraint.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, -1 <= x[i in 1:2] <= i);
+
+julia> f = MathOptAI.SoftPlus(; beta = 2.0)
+SoftPlus(2.0)
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_SoftPlus[1]
+ moai_SoftPlus[2]
+
+julia> formulation
+SoftPlus(2.0)
+├ variables [2]
+│ ├ moai_SoftPlus[1]
+│ └ moai_SoftPlus[2]
+└ constraints [6]
+  ├ moai_SoftPlus[1] ≥ 0.0634640055214863
+  ├ moai_SoftPlus[1] ≤ 1.0634640055214863
+  ├ moai_SoftPlus[2] ≥ 0.0634640055214863
+  ├ moai_SoftPlus[2] ≤ 2.0090749639589047
+  ├ moai_SoftPlus[1] - (log(1.0 + exp(2 x[1])) / 2.0) = 0
+  └ moai_SoftPlus[2] - (log(1.0 + exp(2 x[2])) / 2.0) = 0
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ log(1.0 + exp(2 x[1])) / 2.0
+ log(1.0 + exp(2 x[2])) / 2.0
+
+julia> formulation
+ReducedSpace(SoftPlus(2.0))
+├ variables [0]
+└ constraints [0]
source

Tanh

MathOptAI.Tanh — Type
Tanh() <: AbstractPredictor

An AbstractPredictor that represents the relationship:

\[y = \tanh(x)\]

as a smooth nonlinear constraint.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, -1 <= x[i in 1:2] <= i);
+
+julia> f = MathOptAI.Tanh()
+Tanh()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_Tanh[1]
+ moai_Tanh[2]
+
+julia> formulation
+Tanh()
+├ variables [2]
+│ ├ moai_Tanh[1]
+│ └ moai_Tanh[2]
+└ constraints [6]
+  ├ moai_Tanh[1] ≥ -0.7615941559557649
+  ├ moai_Tanh[1] ≤ 0.7615941559557649
+  ├ moai_Tanh[2] ≥ -0.7615941559557649
+  ├ moai_Tanh[2] ≤ 0.9640275800758169
+  ├ moai_Tanh[1] - tanh(x[1]) = 0
+  └ moai_Tanh[2] - tanh(x[2]) = 0
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ tanh(x[1])
+ tanh(x[2])
+
+julia> formulation
+ReducedSpace(Tanh())
+├ variables [0]
+└ constraints [0]
source

AbstractFormulation

Formulation

MathOptAI.Formulation — Type
struct Formulation{P<:AbstractPredictor} <: AbstractFormulation
+    predictor::P
+    variables::Vector{Any}
+    constraints::Vector{Any}
+end

Fields

  • predictor: the predictor object used to build the formulation
  • variables: a vector of new decision variables added to the model
  • constraints: a vector of new constraints added to the model

Check the docstring of the predictor for an explanation of the formulation and the order of the elements in .variables and .constraints.

source

PipelineFormulation

MathOptAI.PipelineFormulation — Type
struct PipelineFormulation{P<:AbstractPredictor} <: AbstractFormulation
+    predictor::P
+    layers::Vector{Any}
+end

Fields

  • predictor: the predictor object used to build the formulation
  • layers: the formulation associated with each of the layers in the pipeline
source

Extensions

MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::MathOptAI.Quantile{<:AbstractGPs.PosteriorGP},
+    x::Vector,
+)

Add the quantiles of a trained Gaussian Process from AbstractGPs.jl to model.

Example

julia> using JuMP, MathOptAI, AbstractGPs
+
+julia> x_data = 2π .* (0.0:0.1:1.0);
+
+julia> y_data = sin.(x_data);
+
+julia> fx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.1);
+
+julia> p_fx = AbstractGPs.posterior(fx, y_data);
+
+julia> model = Model();
+
+julia> @variable(model, 1 <= x[1:1] <= 6, start = 3);
+
+julia> predictor = MathOptAI.Quantile(p_fx, [0.1, 0.9]);
+
+julia> y, _ = MathOptAI.add_predictor(model, predictor, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_quantile[1]
+ moai_quantile[2]
+
+julia> @objective(model, Max, y[2] - y[1])
+moai_quantile[2] - moai_quantile[1]
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::Union{DecisionTree.Root,DecisionTree.DecisionTreeClassifier},
+    x::Vector,
+)

Add a binary decision tree from DecisionTree.jl to model.

Example

julia> using JuMP, MathOptAI, DecisionTree
+
+julia> truth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)
+truth (generic function with 1 method)
+
+julia> features = abs.(sin.((1:10) .* (3:4)'));
+
+julia> size(features)
+(10, 2)
+
+julia> labels = truth.(Vector.(eachrow(features)));
+
+julia> predictor = DecisionTree.build_tree(labels, features)
+Decision Tree
+Leaves: 3
+Depth:  2
+
+julia> model = Model();
+
+julia> @variable(model, 0 <= x[1:2] <= 1);
+
+julia> y, _ = MathOptAI.add_predictor(model, predictor, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_BinaryDecisionTree_value
source
MathOptAI.build_predictor — Method
MathOptAI.build_predictor(predictor::DecisionTree.Root)

Convert a binary decision tree from DecisionTree.jl to a BinaryDecisionTree.

Example

julia> using MathOptAI, DecisionTree
+
+julia> truth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)
+truth (generic function with 1 method)
+
+julia> features = abs.(sin.((1:10) .* (3:4)'));
+
+julia> size(features)
+(10, 2)
+
+julia> labels = truth.(Vector.(eachrow(features)));
+
+julia> tree = DecisionTree.build_tree(labels, features)
+Decision Tree
+Leaves: 3
+Depth:  2
+
+julia> predictor = MathOptAI.build_predictor(tree)
+BinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::Flux.Chain,
+    x::Vector;
+    config::Dict = Dict{Any,Any}(),
+    reduced_space::Bool = false,
+    gray_box::Bool = false,
+)

Add a trained neural network from Flux.jl to model.

Supported layers

  • Flux.Dense
  • Flux.Scale
  • Flux.softmax

Supported activation functions

  • Flux.relu
  • Flux.sigmoid
  • Flux.softplus
  • Flux.tanh

Keyword arguments

  • config: a dictionary that maps supported Flux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Flux.sigmoid => MathOptAI.Sigmoid() or Flux.relu => MathOptAI.QuadraticReLU().
  • gray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by Flux.withjacobian.

Example

julia> using JuMP, Flux, MathOptAI
+
+julia> chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));
+
+julia> model = Model();
+
+julia> @variable(model, x[1:1]);
+
+julia> y, _ = MathOptAI.add_predictor(
+           model,
+           chain,
+           x;
+           config = Dict(Flux.relu => MathOptAI.ReLU()),
+       );
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Affine[1]
source
MathOptAI.build_predictor — Method
MathOptAI.build_predictor(
+    predictor::Flux.Chain;
+    config::Dict = Dict{Any,Any}(),
+    gray_box::Bool = false,
+    gray_box_hessian::Bool = false,
+)

Convert a trained neural network from Flux.jl to a Pipeline.

Supported layers

  • Flux.Dense
  • Flux.Scale
  • Flux.softmax

Supported activation functions

  • Flux.relu
  • Flux.sigmoid
  • Flux.softplus
  • Flux.tanh

Keyword arguments

  • config: a dictionary that maps supported Flux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Flux.sigmoid => MathOptAI.Sigmoid() or Flux.relu => MathOptAI.QuadraticReLU().
  • gray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by Flux.withjacobian.
  • gray_box_hessian: if true, the gray box additionally computes the Hessian of the output using Flux.hessian.

Example

julia> using Flux, MathOptAI
+
+julia> chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));
+
+julia> MathOptAI.build_predictor(
+           chain;
+           config = Dict(Flux.relu => MathOptAI.ReLU()),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 1, output: 16]
+ * ReLU()
+ * Affine(A, b) [input: 16, output: 1]
+
+julia> MathOptAI.build_predictor(
+           chain;
+           config = Dict(Flux.relu => MathOptAI.ReLUQuadratic()),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 1, output: 16]
+ * ReLUQuadratic()
+ * Affine(A, b) [input: 16, output: 1]
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::GLM.GeneralizedLinearModel{
+        GLM.GlmResp{Vector{Float64},GLM.Bernoulli{Float64},GLM.LogitLink},
+    },
+    x::Vector;
+    sigmoid::AbstractPredictor = MathOptAI.Sigmoid(),
+    reduced_space::Bool = false,
+)

Add a trained logistic regression model from GLM.jl to model.

Keyword arguments

  • sigmoid: the predictor to use for the sigmoid layer.

Example

julia> using GLM, JuMP, MathOptAI
+
+julia> X, Y = rand(10, 2), rand(Bool, 10);
+
+julia> predictor = GLM.glm(X, Y, GLM.Bernoulli());
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> y, _ = MathOptAI.add_predictor(
+           model,
+           predictor,
+           x;
+           sigmoid = MathOptAI.Sigmoid(),
+       );
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Sigmoid[1]
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::GLM.LinearModel,
+    x::Vector;
+    reduced_space::Bool = false,
+)

Add a trained linear model from GLM.jl to model.

Example

julia> using GLM, JuMP, MathOptAI
+
+julia> X, Y = rand(10, 2), rand(10);
+
+julia> predictor = GLM.lm(X, Y);
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> y, _ = MathOptAI.add_predictor(model, predictor, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Affine[1]
source
MathOptAI.build_predictor — Method
MathOptAI.build_predictor(
+    predictor::GLM.GeneralizedLinearModel{
+        GLM.GlmResp{Vector{Float64},GLM.Bernoulli{Float64},GLM.LogitLink},
+    };
+    sigmoid::MathOptAI.AbstractPredictor = MathOptAI.Sigmoid(),
+)

Convert a trained logistic model from GLM.jl to a Pipeline layer.

Keyword arguments

  • sigmoid: the predictor to use for the sigmoid layer.

Example

julia> using GLM, MathOptAI
+
+julia> X, Y = rand(10, 2), rand(Bool, 10);
+
+julia> model = GLM.glm(X, Y, GLM.Bernoulli());
+
+julia> predictor = MathOptAI.build_predictor(model)
+Pipeline with layers:
+ * Affine(A, b) [input: 2, output: 1]
+ * Sigmoid()
source
MathOptAI.build_predictor — Method
MathOptAI.build_predictor(predictor::GLM.LinearModel)

Convert a trained linear model from GLM.jl to an Affine layer.

Example

julia> using GLM, MathOptAI
+
+julia> X, Y = rand(10, 2), rand(10);
+
+julia> model = GLM.lm(X, Y);
+
+julia> predictor = MathOptAI.build_predictor(model)
+Affine(A, b) [input: 2, output: 1]
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::Tuple{<:Lux.Chain,<:NamedTuple,<:NamedTuple},
+    x::Vector;
+    config::Dict = Dict{Any,Any}(),
+    reduced_space::Bool = false,
+)

Add a trained neural network from Lux.jl to model.

Supported layers

  • Lux.Dense
  • Lux.Scale

Supported activation functions

  • Lux.relu
  • Lux.sigmoid
  • Lux.softplus
  • Lux.softmax
  • Lux.tanh

Keyword arguments

  • config: a dictionary that maps supported Lux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Lux.sigmoid => MathOptAI.Sigmoid() or Lux.relu => MathOptAI.QuadraticReLU().

Example

julia> using JuMP, Lux, MathOptAI, Random
+
+julia> rng = Random.MersenneTwister();
+
+julia> chain = Lux.Chain(Lux.Dense(1 => 16, Lux.relu), Lux.Dense(16 => 1))
+Chain(
+    layer_1 = Dense(1 => 16, relu),     # 32 parameters
+    layer_2 = Dense(16 => 1),           # 17 parameters
+)         # Total: 49 parameters,
+          #        plus 0 states.
+
+julia> parameters, state = Lux.setup(rng, chain);
+
+julia> predictor = (chain, parameters, state);
+
+julia> model = Model();
+
+julia> @variable(model, x[1:1]);
+
+julia> y, _ = MathOptAI.add_predictor(
+           model,
+           predictor,
+           x;
+           config = Dict(Lux.relu => MathOptAI.ReLU()),
+       );
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Affine[1]
source
MathOptAI.build_predictor — Method
MathOptAI.build_predictor(
+    predictor::Tuple{<:Lux.Chain,<:NamedTuple,<:NamedTuple};
+    config::Dict = Dict{Any,Any}(),
+)

Convert a trained neural network from Lux.jl to a Pipeline.

Supported layers

  • Lux.Dense
  • Lux.Scale

Supported activation functions

  • Lux.relu
  • Lux.sigmoid
  • Lux.softplus
  • Lux.softmax
  • Lux.tanh

Keyword arguments

  • config: a dictionary that maps supported Lux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Lux.sigmoid => MathOptAI.Sigmoid() or Lux.relu => MathOptAI.QuadraticReLU().

Example

julia> using Lux, MathOptAI, Random
+
+julia> rng = Random.MersenneTwister();
+
+julia> chain = Lux.Chain(Lux.Dense(1 => 16, Lux.relu), Lux.Dense(16 => 1))
+Chain(
+    layer_1 = Dense(1 => 16, relu),     # 32 parameters
+    layer_2 = Dense(16 => 1),           # 17 parameters
+)         # Total: 49 parameters,
+          #        plus 0 states.
+
+julia> parameters, state = Lux.setup(rng, chain);
+
+julia> predictor = MathOptAI.build_predictor(
+           (chain, parameters, state);
+           config = Dict(Lux.relu => MathOptAI.ReLU()),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 1, output: 16]
+ * ReLU()
+ * Affine(A, b) [input: 16, output: 1]
+
+julia> MathOptAI.build_predictor(
+           (chain, parameters, state);
+           config = Dict(Lux.relu => MathOptAI.ReLUQuadratic()),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 1, output: 16]
+ * ReLUQuadratic()
+ * Affine(A, b) [input: 16, output: 1]
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::MathOptAI.PytorchModel,
+    x::Vector;
+    config::Dict = Dict{Any,Any}(),
+    reduced_space::Bool = false,
+    gray_box::Bool = false,
+    gray_box_hessian::Bool = false,
+    gray_box_device::String = "cpu",
+)

Add a trained neural network from PyTorch via PythonCall.jl to model.

Supported layers

  • nn.Linear
  • nn.ReLU
  • nn.Sequential
  • nn.Sigmoid
  • nn.Softplus
  • nn.Tanh

Keyword arguments

  • config: a dictionary that maps Symbols to AbstractPredictors that control how the activation functions are reformulated. For example, :Sigmoid => MathOptAI.Sigmoid() or :ReLU => MathOptAI.QuadraticReLU(). The supported Symbols are :ReLU, :Sigmoid, :SoftPlus, and :Tanh.
  • gray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by torch.func.jacrev.
  • gray_box_hessian: if true, the gray box additionally computes the Hessian of the output using torch.func.hessian.
  • gray_box_device: device used to construct PyTorch tensors, e.g. "cuda" to run on an Nvidia GPU.
source
MathOptAI.build_predictor — Method
MathOptAI.build_predictor(
+    predictor::MathOptAI.PytorchModel;
+    config::Dict = Dict{Any,Any}(),
+    gray_box::Bool = false,
+    gray_box_hessian::Bool = false,
+    gray_box_device::String = "cpu",
+)

Convert a trained neural network from PyTorch via PythonCall.jl to a Pipeline.

Supported layers

  • nn.Linear
  • nn.ReLU
  • nn.Sequential
  • nn.Sigmoid
  • nn.Softplus
  • nn.Tanh

Keyword arguments

  • config: a dictionary that maps Symbols to AbstractPredictors that control how the activation functions are reformulated. For example, :Sigmoid => MathOptAI.Sigmoid() or :ReLU => MathOptAI.QuadraticReLU(). The supported Symbols are :ReLU, :Sigmoid, :SoftPlus, and :Tanh.
  • gray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by torch.func.jacrev.
  • gray_box_hessian: if true, the gray box additionally computes the Hessian of the output using torch.func.hessian.
  • gray_box_device: device used to construct PyTorch tensors, e.g. "cuda" to run on an Nvidia GPU.
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::StatsModels.TableRegressionModel,
+    x::DataFrames.DataFrame;
+    kwargs...,
+)

Add a trained regression model from StatsModels.jl to model, using the DataFrame x as input.

In most cases, predictor should be a GLM.jl predictor supported by MathOptAI, but trained using @formula and a DataFrame instead of the raw matrix input.

In general, x may have some columns that are constant (Float64) and some columns that are JuMP decision variables.

Keyword arguments

All keyword arguments are passed to the corresponding add_predictor of the GLM extension.

Example

julia> using DataFrames, GLM, JuMP, MathOptAI
+
+julia> train_df = DataFrames.DataFrame(x1 = rand(10), x2 = rand(10));
+
+julia> train_df.y = 1.0 .* train_df.x1 + 2.0 .* train_df.x2 .+ rand(10);
+
+julia> predictor = GLM.lm(GLM.@formula(y ~ x1 + x2), train_df);
+
+julia> model = Model();
+
+julia> test_df = DataFrames.DataFrame(
+           x1 = rand(6),
+           x2 = @variable(model, [1:6]),
+       );
+
+julia> test_df.y, _ = MathOptAI.add_predictor(model, predictor, test_df);
+
+julia> test_df.y
+6-element Vector{VariableRef}:
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
source
diff --git a/dev/assets/documenter.js b/dev/assets/documenter.js new file mode 100644 index 00000000..82252a11 --- /dev/null +++ b/dev/assets/documenter.js @@ -0,0 +1,1064 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on( + "click", + ".docstring .docstring-article-toggle-button", + function () { + let articleToggleTitle = "Expand docstring"; + const parent = $(this).parent(); + + debounce(() => { + if (parent.siblings("section").is(":visible")) { + parent + .find("a.docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + parent + .find("a.docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + parent + .children(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + parent.siblings("section").slideToggle(); + }); + } +); + +$(document).on("click", ".docs-article-toggle-button", function (event) { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + let animationSpeed = event.noToggleAnimation ? 0 : 400; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $("a.docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(animationSpeed); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $("a.docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(animationSpeed); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-xmark"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-xmark"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let meta = $("div[data-docstringscollapsed]").data(); + + if (meta?.docstringscollapsed) { + $("#documenter-article-toggle-button").trigger({ + type: "click", + noToggleAnimation: true, + }); + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +/* +To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +PSEUDOCODE: + +Searching happens automatically as the user types or adjusts the selected filters. +To preserve responsiveness, as much as possible of the slow parts of the search are done +in a web worker. Searching and result generation are done in the worker, and filtering and +DOM updates are done in the main thread. The filters are in the main thread as they should +be very quick to apply. This lets filters be changed without re-searching with minisearch +(which is possible even if filtering is on the worker thread) and also lets filters be +changed _while_ the worker is searching and without message passing (neither of which are +possible if filtering is on the worker thread) + +SEARCH WORKER: + +Import minisearch + +Build index + +On message from main thread + run search + find the first 200 unique results from each category, and compute their divs for display + note that this is necessary and sufficient information for the main thread to find the + first 200 unique results from any given filter set + post results to main thread + +MAIN: + +Launch worker + +Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results) + +On text update + if worker is not running, launch_search() + +launch_search + set worker_is_running to true, set last_search_text to the search text + post the search query to worker + +on message from worker + if last_search_text is not the same as the text in the search field, + the latest search result is not reflective of the latest search query, so update again + launch_search() + otherwise + set worker_is_running to false + + regardless, display the new search results to the user + save the unfiltered_results as a global + update_search() + +on filter click + adjust the filter selection + update_search() + +update_search + apply search filters by looping through the unfiltered_results and finding the first 200 + unique results that match the filters + + Update the DOM +*/ + +/////// SEARCH WORKER /////// + +function worker_function(documenterSearchIndex, documenterBaseURL, filters) { + importScripts( + "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js" + ); + + let data = documenterSearchIndex.map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; + }); + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", + ]); + + let index = new MiniSearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + + word = word.toLowerCase(); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not + // find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + prefix: true, + boost: { title: 100 }, + fuzzy: 2, + }, + }); + + index.addAll(data); + + /** + * Used to map characters to HTML entities. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const htmlEscapes = { + "&": "&", + "<": "<", + ">": ">", + '"': """, + "'": "'", + }; + + /** + * Used to match HTML entities and HTML characters. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const reUnescapedHtml = /[&<>"']/g; + const reHasUnescapedHtml = RegExp(reUnescapedHtml.source); + + /** + * Escape function from lodash + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + function escape(string) { + return string && reHasUnescapedHtml.test(string) + ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr]) + : string || ""; + } + + /** + * RegX escape function from MDN + * Refer: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping + */ + function escapeRegExp(string) { + return string.replace(/[.*+?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string + } + + /** + * Make the result component given a minisearch result data object and the value + * of the search input as queryString. To view the result object structure, refer: + * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ + function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + searchstring = escapeRegExp(querystring); + let textindex = new RegExp(`${searchstring}`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + text = text.length ? escape(text) : ""; + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`${escape(searchstring)}`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${escape(result.title)}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+ + ${search_divider} + `; + + return result_div; + } + + self.onmessage = function (e) { + let query = e.data; + let results = index.search(query, { + filter: (result) => { + // Only return relevant results + return result.score >= 1; + }, + combineWith: "AND", + }); + + // Pre-filter to deduplicate and limit to 200 per category to the extent + // possible without knowing what the filters are. + let filtered_results = []; + let counts = {}; + for (let filter of filters) { + counts[filter] = 0; + } + let present = {}; + + for (let result of results) { + cat = result.category; + cnt = counts[cat]; + if (cnt < 200) { + id = cat + "---" + result.location; + if (present[id]) { + continue; + } + present[id] = true; + filtered_results.push({ + location: result.location, + category: cat, + div: make_search_result(result, query), + }); + } + } + + postMessage(filtered_results); + }; +} + +// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript! +const filters = [ + ...new Set(documenterSearchIndex["docs"].map((x) => x.category)), +]; +const worker_str = + "(" + + worker_function.toString() + + ")(" + + JSON.stringify(documenterSearchIndex["docs"]) + + "," + + JSON.stringify(documenterBaseURL) + + "," + + JSON.stringify(filters) + + ")"; +const worker_blob = new Blob([worker_str], { type: "text/javascript" }); +const worker = new Worker(URL.createObjectURL(worker_blob)); + +/////// SEARCH MAIN /////// + +// Whether the worker is currently handling a search. This is a boolean +// as the worker only ever handles 1 or 0 searches at a time. +var worker_is_running = false; + +// The last search text that was sent to the worker. This is used to determine +// if the worker should be launched again when it reports back results. +var last_search_text = ""; + +// The results of the last search. This, in combination with the state of the filters +// in the DOM, is used compute the results to display on calls to update_search. +var unfiltered_results = []; + +// Which filter is currently selected +var selected_filter = ""; + +$(document).on("input", ".documenter-search-input", function (event) { + if (!worker_is_running) { + launch_search(); + } +}); + +function launch_search() { + worker_is_running = true; + last_search_text = $(".documenter-search-input").val(); + worker.postMessage(last_search_text); +} + +worker.onmessage = function (e) { + if (last_search_text !== $(".documenter-search-input").val()) { + launch_search(); + } else { + worker_is_running = false; + } + + unfiltered_results = e.data; + update_search(); +}; + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + selected_filter = ""; + } else { + selected_filter = $(this).text().toLowerCase(); + } + + // This updates search results and toggles classes for UI: + update_search(); +}); + +/** + * Make/Update the search component + */ +function update_search() { + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + if (selected_filter == "") { + results = unfiltered_results; + } else { + results = unfiltered_results.filter((result) => { + return selected_filter == result.category.toLowerCase(); + }); + } + + let search_result_container = ``; + let modal_filters = make_modal_body_filters(); + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + for (var i = 0, n = results.length; i < n && count < 200; ++i) { + let result = results[i]; + if (result.location && !links.includes(result.location)) { + search_results += result.div; + count++; + links.push(result.location); + } + } + + if (count == 1) { + count_str = "1 result"; + } else if (count == 200) { + count_str = "200+ results"; + } else { + count_str = count + " results"; + } + let result_count = `
${count_str}
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
+
No result found!
+ `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(` +
Type something to get started!
+ `); + } +} + +/** + * Make the modal filter html + * + * @returns string + */ +function make_modal_body_filters() { + let str = filters + .map((val) => { + if (selected_filter == val.toLowerCase()) { + return `${val}`; + } else { + return `${val}`; + } + }) + .join(""); + + return ` +
+ Filters: + ${str} +
`; +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); + }); + // Close the dialog if X is clicked + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); + }); + // Close dialog if ESC is pressed + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let search_modal_header = ` +
+
+

+ + + + +

+
+
+ +
+
+ `; + + let initial_search_body = ` +
Type something to get started!
+ `; + + let search_modal_footer = ` + + `; + + $(document.body).append( + ` + + ` + ); + + document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); + }); + + document + .querySelector(".close-search-modal") + .addEventListener("click", () => { + closeModal(); + }); + + $(document).on("click", ".search-result-link", function () { + closeModal(); + }); + + document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; + }); + + // Functions to open and close a modal + function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); + } + + function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
Type something to get started!
+ `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); + } + + document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function () { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { + ev.preventDefault(); + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind("click", function (ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); + } + }); +}); + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function () { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css("max-width"), 10); + var L0 = e.width(); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on("orientationchange", resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function () { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if (typeof active !== "undefined") { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Theme picker setup +$(document).ready(function () { + // onchange callback + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); + } + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function () { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== "undefined") { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $( + "" + ); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}); + +}) diff --git a/dev/assets/themes/catppuccin-frappe.css b/dev/assets/themes/catppuccin-frappe.css new file mode 100644 index 00000000..32e3f008 --- /dev/null +++ b/dev/assets/themes/catppuccin-frappe.css @@ -0,0 +1 @@ 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html.theme--catppuccin-frappe .content kbd.button.is-outlined{background-color:transparent;border-color:#414559;box-shadow:none;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-frappe .content 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.button.is-link.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#8caaee}html.theme--catppuccin-frappe .button.is-link.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-link.is-outlined{background-color:transparent;border-color:#8caaee;color:#8caaee}html.theme--catppuccin-frappe .button.is-link.is-outlined:hover,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-link.is-outlined:focus,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-focused{background-color:#8caaee;border-color:#8caaee;color:#fff}html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading::after{border-color:transparent transparent #8caaee #8caaee !important}html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe 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.button.is-link.is-inverted.is-outlined.is-focused{background-color:#fff;color:#8caaee}html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #8caaee #8caaee !important}html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-link.is-light{background-color:#edf2fc;color:#153a8e}html.theme--catppuccin-frappe .button.is-link.is-light:hover,html.theme--catppuccin-frappe .button.is-link.is-light.is-hovered{background-color:#e2eafb;border-color:transparent;color:#153a8e}html.theme--catppuccin-frappe .button.is-link.is-light:active,html.theme--catppuccin-frappe .button.is-link.is-light.is-active{background-color:#d7e1f9;border-color:transparent;color:#153a8e}html.theme--catppuccin-frappe .button.is-info{background-color:#81c8be;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info:hover,html.theme--catppuccin-frappe .button.is-info.is-hovered{background-color:#78c4b9;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info:focus,html.theme--catppuccin-frappe .button.is-info.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info:focus:not(:active),html.theme--catppuccin-frappe .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(129,200,190,0.25)}html.theme--catppuccin-frappe .button.is-info:active,html.theme--catppuccin-frappe .button.is-info.is-active{background-color:#6fc0b5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info{background-color:#81c8be;border-color:#81c8be;box-shadow:none}html.theme--catppuccin-frappe .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted:hover,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-info.is-outlined{background-color:transparent;border-color:#81c8be;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-outlined:hover,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-info.is-outlined:focus,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-focused{background-color:#81c8be;border-color:#81c8be;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #81c8be #81c8be !important}html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-outlined{background-color:transparent;border-color:#81c8be;box-shadow:none;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #81c8be #81c8be !important}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-light{background-color:#f1f9f8;color:#2d675f}html.theme--catppuccin-frappe .button.is-info.is-light:hover,html.theme--catppuccin-frappe .button.is-info.is-light.is-hovered{background-color:#e8f5f3;border-color:transparent;color:#2d675f}html.theme--catppuccin-frappe .button.is-info.is-light:active,html.theme--catppuccin-frappe .button.is-info.is-light.is-active{background-color:#dff1ef;border-color:transparent;color:#2d675f}html.theme--catppuccin-frappe 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.button.is-success{background-color:#a6d189;border-color:#a6d189;box-shadow:none}html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-focused{background-color:#a6d189;border-color:#a6d189;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-light{background-color:#f4f9f0;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:hover,html.theme--catppuccin-frappe .button.is-success.is-light.is-hovered{background-color:#edf6e7;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:active,html.theme--catppuccin-frappe .button.is-success.is-light.is-active{background-color:#e6f2de;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-warning{background-color:#e5c890;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:hover,html.theme--catppuccin-frappe .button.is-warning.is-hovered{background-color:#e3c386;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:focus,html.theme--catppuccin-frappe .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:focus:not(:active),html.theme--catppuccin-frappe .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(229,200,144,0.25)}html.theme--catppuccin-frappe .button.is-warning:active,html.theme--catppuccin-frappe .button.is-warning.is-active{background-color:#e0be7b;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning{background-color:#e5c890;border-color:#e5c890;box-shadow:none}html.theme--catppuccin-frappe .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-outlined:hover,html.theme--catppuccin-frappe 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.button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e5c890 #e5c890 !important}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-light{background-color:#fbf7ee;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:hover,html.theme--catppuccin-frappe .button.is-warning.is-light.is-hovered{background-color:#f9f2e4;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:active,html.theme--catppuccin-frappe .button.is-warning.is-light.is-active{background-color:#f6edda;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-danger{background-color:#e78284;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:hover,html.theme--catppuccin-frappe .button.is-danger.is-hovered{background-color:#e57779;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:focus,html.theme--catppuccin-frappe .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:focus:not(:active),html.theme--catppuccin-frappe .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(231,130,132,0.25)}html.theme--catppuccin-frappe .button.is-danger:active,html.theme--catppuccin-frappe .button.is-danger.is-active{background-color:#e36d6f;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger{background-color:#e78284;border-color:#e78284;box-shadow:none}html.theme--catppuccin-frappe .button.is-danger.is-inverted{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-frappe .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-focused{background-color:#e78284;border-color:#e78284;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-light{background-color:#fceeee;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:hover,html.theme--catppuccin-frappe .button.is-danger.is-light.is-hovered{background-color:#fae3e4;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:active,html.theme--catppuccin-frappe .button.is-danger.is-light.is-active{background-color:#f8d8d9;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-frappe .button.is-small:not(.is-rounded),html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .button.is-normal{font-size:1rem}html.theme--catppuccin-frappe .button.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .button.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .button[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button{background-color:#737994;border-color:#626880;box-shadow:none;opacity:.5}html.theme--catppuccin-frappe .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-frappe .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-frappe .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-frappe .button.is-static{background-color:#292c3c;border-color:#626880;color:#838ba7;box-shadow:none;pointer-events:none}html.theme--catppuccin-frappe .button.is-rounded,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-frappe .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-frappe .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-frappe .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-frappe .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-frappe .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-frappe .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-frappe .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-frappe .buttons.has-addons .button:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-frappe .buttons.has-addons .button:focus,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused,html.theme--catppuccin-frappe .buttons.has-addons .button:active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-frappe .buttons.has-addons .button:focus:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-frappe .buttons.has-addons .button:active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-frappe .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .buttons.is-centered{justify-content:center}html.theme--catppuccin-frappe .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-frappe .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-frappe .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-frappe .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-frappe .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-frappe .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-frappe .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-frappe .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-frappe .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-frappe .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-frappe .content li+li{margin-top:0.25em}html.theme--catppuccin-frappe .content p:not(:last-child),html.theme--catppuccin-frappe .content dl:not(:last-child),html.theme--catppuccin-frappe .content ol:not(:last-child),html.theme--catppuccin-frappe .content ul:not(:last-child),html.theme--catppuccin-frappe .content blockquote:not(:last-child),html.theme--catppuccin-frappe .content pre:not(:last-child),html.theme--catppuccin-frappe .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-frappe .content h1,html.theme--catppuccin-frappe .content h2,html.theme--catppuccin-frappe .content h3,html.theme--catppuccin-frappe .content h4,html.theme--catppuccin-frappe .content h5,html.theme--catppuccin-frappe .content h6{color:#c6d0f5;font-weight:600;line-height:1.125}html.theme--catppuccin-frappe .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-frappe .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-frappe .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-frappe .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-frappe .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-frappe .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-frappe .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-frappe .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-frappe .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-frappe .content blockquote{background-color:#292c3c;border-left:5px solid #626880;padding:1.25em 1.5em}html.theme--catppuccin-frappe .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-frappe .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-frappe .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-frappe .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-frappe .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-frappe .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-frappe .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-frappe .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-frappe .content ul ul ul{list-style-type:square}html.theme--catppuccin-frappe .content dd{margin-left:2em}html.theme--catppuccin-frappe .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-frappe .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-frappe .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-frappe .content figure img{display:inline-block}html.theme--catppuccin-frappe .content figure figcaption{font-style:italic}html.theme--catppuccin-frappe .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-frappe .content sup,html.theme--catppuccin-frappe .content sub{font-size:75%}html.theme--catppuccin-frappe .content table{width:100%}html.theme--catppuccin-frappe .content table td,html.theme--catppuccin-frappe .content table th{border:1px solid #626880;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-frappe .content table th{color:#b0bef1}html.theme--catppuccin-frappe .content table th:not([align]){text-align:inherit}html.theme--catppuccin-frappe .content table thead td,html.theme--catppuccin-frappe .content table thead th{border-width:0 0 2px;color:#b0bef1}html.theme--catppuccin-frappe .content table tfoot td,html.theme--catppuccin-frappe .content table tfoot th{border-width:2px 0 0;color:#b0bef1}html.theme--catppuccin-frappe .content table tbody tr:last-child td,html.theme--catppuccin-frappe .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-frappe .content .tabs li+li{margin-top:0}html.theme--catppuccin-frappe .content.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-frappe .content.is-normal{font-size:1rem}html.theme--catppuccin-frappe .content.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .content.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-frappe .icon.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-frappe .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-frappe .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-frappe .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-frappe .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-frappe .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--catppuccin-frappe .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--catppuccin-frappe div.icon-text{display:flex}html.theme--catppuccin-frappe .image,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--catppuccin-frappe .image img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--catppuccin-frappe .image img.is-rounded,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--catppuccin-frappe .image.is-fullwidth,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--catppuccin-frappe .image.is-square img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--catppuccin-frappe .image.is-square .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--catppuccin-frappe .image.is-1by1 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--catppuccin-frappe .image.is-1by1 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--catppuccin-frappe .image.is-5by4 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--catppuccin-frappe .image.is-5by4 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--catppuccin-frappe .image.is-4by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--catppuccin-frappe .image.is-4by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--catppuccin-frappe .image.is-3by2 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--catppuccin-frappe .image.is-3by2 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--catppuccin-frappe .image.is-5by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--catppuccin-frappe .image.is-5by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--catppuccin-frappe .image.is-16by9 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--catppuccin-frappe .image.is-16by9 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--catppuccin-frappe .image.is-2by1 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--catppuccin-frappe .image.is-2by1 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--catppuccin-frappe .image.is-3by1 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--catppuccin-frappe .image.is-3by1 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by1 .has-ratio,html.theme--catppuccin-frappe .image.is-4by5 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by5 img,html.theme--catppuccin-frappe .image.is-4by5 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by5 .has-ratio,html.theme--catppuccin-frappe .image.is-3by4 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by4 img,html.theme--catppuccin-frappe .image.is-3by4 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by4 .has-ratio,html.theme--catppuccin-frappe .image.is-2by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by3 img,html.theme--catppuccin-frappe .image.is-2by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by3 .has-ratio,html.theme--catppuccin-frappe .image.is-3by5 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--catppuccin-frappe .image.is-3by5 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--catppuccin-frappe .image.is-9by16 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--catppuccin-frappe .image.is-9by16 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-9by16 .has-ratio,html.theme--catppuccin-frappe .image.is-1by2 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by2 img,html.theme--catppuccin-frappe .image.is-1by2 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by2 .has-ratio,html.theme--catppuccin-frappe .image.is-1by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by3 img,html.theme--catppuccin-frappe .image.is-1by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by3 .has-ratio{height:100%;width:100%}html.theme--catppuccin-frappe .image.is-square,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-square,html.theme--catppuccin-frappe .image.is-1by1,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by1{padding-top:100%}html.theme--catppuccin-frappe .image.is-5by4,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by4{padding-top:80%}html.theme--catppuccin-frappe .image.is-4by3,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by3{padding-top:75%}html.theme--catppuccin-frappe 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.modal-card{display:flex;flex-direction:column;max-height:calc(100vh - 40px);overflow:hidden;-ms-overflow-y:visible}html.theme--catppuccin-frappe .modal-card-head,html.theme--catppuccin-frappe .modal-card-foot{align-items:center;background-color:#292c3c;display:flex;flex-shrink:0;justify-content:flex-start;padding:20px;position:relative}html.theme--catppuccin-frappe .modal-card-head{border-bottom:1px solid #626880;border-top-left-radius:8px;border-top-right-radius:8px}html.theme--catppuccin-frappe .modal-card-title{color:#c6d0f5;flex-grow:1;flex-shrink:0;font-size:1.5rem;line-height:1}html.theme--catppuccin-frappe .modal-card-foot{border-bottom-left-radius:8px;border-bottom-right-radius:8px;border-top:1px solid #626880}html.theme--catppuccin-frappe .modal-card-foot .button:not(:last-child){margin-right:.5em}html.theme--catppuccin-frappe 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rgba(245,245,245,0.25)}html.theme--catppuccin-latte .button.is-light:active,html.theme--catppuccin-latte .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light{background-color:#f5f5f5;border-color:#f5f5f5;box-shadow:none}html.theme--catppuccin-latte .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-inverted:hover,html.theme--catppuccin-latte .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-outlined:hover,html.theme--catppuccin-latte .button.is-light.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-light.is-outlined:focus,html.theme--catppuccin-latte .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark,html.theme--catppuccin-latte .content kbd.button{background-color:#ccd0da;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark:hover,html.theme--catppuccin-latte .content kbd.button:hover,html.theme--catppuccin-latte .button.is-dark.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-hovered{background-color:#c5c9d5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark:focus,html.theme--catppuccin-latte .content kbd.button:focus,html.theme--catppuccin-latte .button.is-dark.is-focused,html.theme--catppuccin-latte .content kbd.button.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark:focus:not(:active),html.theme--catppuccin-latte .content kbd.button:focus:not(:active),html.theme--catppuccin-latte .button.is-dark.is-focused:not(:active),html.theme--catppuccin-latte .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(204,208,218,0.25)}html.theme--catppuccin-latte .button.is-dark:active,html.theme--catppuccin-latte .content kbd.button:active,html.theme--catppuccin-latte .button.is-dark.is-active,html.theme--catppuccin-latte .content kbd.button.is-active{background-color:#bdc2cf;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark[disabled],html.theme--catppuccin-latte .content kbd.button[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button{background-color:#ccd0da;border-color:#ccd0da;box-shadow:none}html.theme--catppuccin-latte .button.is-dark.is-inverted,html.theme--catppuccin-latte .content kbd.button.is-inverted{background-color:rgba(0,0,0,0.7);color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted:hover,html.theme--catppuccin-latte .content kbd.button.is-inverted:hover,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-inverted[disabled],html.theme--catppuccin-latte .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-inverted,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-loading::after,html.theme--catppuccin-latte .content kbd.button.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-dark.is-outlined,html.theme--catppuccin-latte .content kbd.button.is-outlined{background-color:transparent;border-color:#ccd0da;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-outlined:hover,html.theme--catppuccin-latte .content kbd.button.is-outlined:hover,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-dark.is-outlined:focus,html.theme--catppuccin-latte .content kbd.button.is-outlined:focus,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-focused,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-focused{background-color:#ccd0da;border-color:#ccd0da;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #ccd0da #ccd0da !important}html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-dark.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-outlined{background-color:transparent;border-color:#ccd0da;box-shadow:none;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ccd0da #ccd0da !important}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte 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.docstring>section>a.button.is-inverted.docs-sourcelink{background-color:#fff;color:#1e66f5}html.theme--catppuccin-latte .button.is-primary.is-inverted:hover,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-inverted.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-hovered.docs-sourcelink{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-primary.is-inverted[disabled],html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.docs-sourcelink[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-primary.is-inverted,fieldset[disabled] html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.docs-sourcelink{background-color:#fff;border-color:transparent;box-shadow:none;color:#1e66f5}html.theme--catppuccin-latte .button.is-primary.is-loading::after,html.theme--catppuccin-latte .docstring>section>a.button.is-loading.docs-sourcelink::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-primary.is-outlined,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.docs-sourcelink{background-color:transparent;border-color:#1e66f5;color:#1e66f5}html.theme--catppuccin-latte .button.is-primary.is-outlined:hover,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-outlined.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.is-hovered.docs-sourcelink,html.theme--catppuccin-latte .button.is-primary.is-outlined:focus,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.docs-sourcelink:focus,html.theme--catppuccin-latte .button.is-primary.is-outlined.is-focused,html.theme--catppuccin-latte 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.docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.is-hovered.docs-sourcelink,html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink:focus,html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined.is-focused,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.is-focused.docs-sourcelink{background-color:#fff;color:#1e66f5}html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--catppuccin-latte 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.button.is-primary.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-primary.is-light,html.theme--catppuccin-latte .docstring>section>a.button.is-light.docs-sourcelink{background-color:#ebf2fe;color:#0a52e1}html.theme--catppuccin-latte .button.is-primary.is-light:hover,html.theme--catppuccin-latte .docstring>section>a.button.is-light.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-light.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-light.is-hovered.docs-sourcelink{background-color:#dfe9fe;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-primary.is-light:active,html.theme--catppuccin-latte .docstring>section>a.button.is-light.docs-sourcelink:active,html.theme--catppuccin-latte .button.is-primary.is-light.is-active,html.theme--catppuccin-latte .docstring>section>a.button.is-light.is-active.docs-sourcelink{background-color:#d3e1fd;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-link{background-color:#1e66f5;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-link:hover,html.theme--catppuccin-latte .button.is-link.is-hovered{background-color:#125ef4;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-link:focus,html.theme--catppuccin-latte .button.is-link.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-link:focus:not(:active),html.theme--catppuccin-latte .button.is-link.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(30,102,245,0.25)}html.theme--catppuccin-latte .button.is-link:active,html.theme--catppuccin-latte .button.is-link.is-active{background-color:#0b57ef;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-link[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-link{background-color:#1e66f5;border-color:#1e66f5;box-shadow:none}html.theme--catppuccin-latte .button.is-link.is-inverted{background-color:#fff;color:#1e66f5}html.theme--catppuccin-latte .button.is-link.is-inverted:hover,html.theme--catppuccin-latte .button.is-link.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-link.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-link.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#1e66f5}html.theme--catppuccin-latte .button.is-link.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-link.is-outlined{background-color:transparent;border-color:#1e66f5;color:#1e66f5}html.theme--catppuccin-latte .button.is-link.is-outlined:hover,html.theme--catppuccin-latte .button.is-link.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-link.is-outlined:focus,html.theme--catppuccin-latte .button.is-link.is-outlined.is-focused{background-color:#1e66f5;border-color:#1e66f5;color:#fff}html.theme--catppuccin-latte .button.is-link.is-outlined.is-loading::after{border-color:transparent transparent #1e66f5 #1e66f5 !important}html.theme--catppuccin-latte .button.is-link.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-link.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-link.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-link.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-link.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-link.is-outlined{background-color:transparent;border-color:#1e66f5;box-shadow:none;color:#1e66f5}html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-focused{background-color:#fff;color:#1e66f5}html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #1e66f5 #1e66f5 !important}html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-link.is-light{background-color:#ebf2fe;color:#0a52e1}html.theme--catppuccin-latte .button.is-link.is-light:hover,html.theme--catppuccin-latte .button.is-link.is-light.is-hovered{background-color:#dfe9fe;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-link.is-light:active,html.theme--catppuccin-latte .button.is-link.is-light.is-active{background-color:#d3e1fd;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-info{background-color:#179299;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-info:hover,html.theme--catppuccin-latte .button.is-info.is-hovered{background-color:#15878e;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-info:focus,html.theme--catppuccin-latte .button.is-info.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-info:focus:not(:active),html.theme--catppuccin-latte .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(23,146,153,0.25)}html.theme--catppuccin-latte .button.is-info:active,html.theme--catppuccin-latte .button.is-info.is-active{background-color:#147d83;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-info[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info{background-color:#179299;border-color:#179299;box-shadow:none}html.theme--catppuccin-latte .button.is-info.is-inverted{background-color:#fff;color:#179299}html.theme--catppuccin-latte .button.is-info.is-inverted:hover,html.theme--catppuccin-latte .button.is-info.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#179299}html.theme--catppuccin-latte .button.is-info.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-info.is-outlined{background-color:transparent;border-color:#179299;color:#179299}html.theme--catppuccin-latte .button.is-info.is-outlined:hover,html.theme--catppuccin-latte .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-info.is-outlined:focus,html.theme--catppuccin-latte .button.is-info.is-outlined.is-focused{background-color:#179299;border-color:#179299;color:#fff}html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #179299 #179299 !important}html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info.is-outlined{background-color:transparent;border-color:#179299;box-shadow:none;color:#179299}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-focused{background-color:#fff;color:#179299}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #179299 #179299 !important}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-info.is-light{background-color:#edfcfc;color:#1cb2ba}html.theme--catppuccin-latte .button.is-info.is-light:hover,html.theme--catppuccin-latte .button.is-info.is-light.is-hovered{background-color:#e2f9fb;border-color:transparent;color:#1cb2ba}html.theme--catppuccin-latte .button.is-info.is-light:active,html.theme--catppuccin-latte .button.is-info.is-light.is-active{background-color:#d7f7f9;border-color:transparent;color:#1cb2ba}html.theme--catppuccin-latte .button.is-success{background-color:#40a02b;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:hover,html.theme--catppuccin-latte .button.is-success.is-hovered{background-color:#3c9628;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:focus,html.theme--catppuccin-latte .button.is-success.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:focus:not(:active),html.theme--catppuccin-latte .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(64,160,43,0.25)}html.theme--catppuccin-latte .button.is-success:active,html.theme--catppuccin-latte .button.is-success.is-active{background-color:#388c26;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success{background-color:#40a02b;border-color:#40a02b;box-shadow:none}html.theme--catppuccin-latte .button.is-success.is-inverted{background-color:#fff;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted:hover,html.theme--catppuccin-latte .button.is-success.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-success.is-outlined{background-color:transparent;border-color:#40a02b;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-outlined:hover,html.theme--catppuccin-latte .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-success.is-outlined:focus,html.theme--catppuccin-latte .button.is-success.is-outlined.is-focused{background-color:#40a02b;border-color:#40a02b;color:#fff}html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #40a02b #40a02b !important}html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-outlined{background-color:transparent;border-color:#40a02b;box-shadow:none;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-focused{background-color:#fff;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #40a02b #40a02b !important}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-success.is-light{background-color:#f1fbef;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:hover,html.theme--catppuccin-latte .button.is-success.is-light.is-hovered{background-color:#e8f8e5;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:active,html.theme--catppuccin-latte .button.is-success.is-light.is-active{background-color:#e0f5db;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:hover,html.theme--catppuccin-latte .button.is-warning.is-hovered{background-color:#d4871c;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus,html.theme--catppuccin-latte .button.is-warning.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus:not(:active),html.theme--catppuccin-latte .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(223,142,29,0.25)}html.theme--catppuccin-latte .button.is-warning:active,html.theme--catppuccin-latte .button.is-warning.is-active{background-color:#c8801a;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:#df8e1d;box-shadow:none}html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-focused{background-color:#df8e1d;border-color:#df8e1d;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-light{background-color:#fdf6ed;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:hover,html.theme--catppuccin-latte .button.is-warning.is-light.is-hovered{background-color:#fbf1e2;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:active,html.theme--catppuccin-latte .button.is-warning.is-light.is-active{background-color:#faebd6;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:hover,html.theme--catppuccin-latte .button.is-danger.is-hovered{background-color:#c60e36;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus,html.theme--catppuccin-latte .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus:not(:active),html.theme--catppuccin-latte .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(210,15,57,0.25)}html.theme--catppuccin-latte .button.is-danger:active,html.theme--catppuccin-latte .button.is-danger.is-active{background-color:#ba0d33;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:#d20f39;box-shadow:none}html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-focused{background-color:#d20f39;border-color:#d20f39;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-light{background-color:#feecf0;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:hover,html.theme--catppuccin-latte .button.is-danger.is-light.is-hovered{background-color:#fde0e6;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:active,html.theme--catppuccin-latte .button.is-danger.is-light.is-active{background-color:#fcd4dd;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-latte .button.is-small:not(.is-rounded),html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .button.is-normal{font-size:1rem}html.theme--catppuccin-latte .button.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .button.is-large{font-size:1.5rem}html.theme--catppuccin-latte .button[disabled],fieldset[disabled] html.theme--catppuccin-latte .button{background-color:#9ca0b0;border-color:#acb0be;box-shadow:none;opacity:.5}html.theme--catppuccin-latte .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-latte .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-latte .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-latte .button.is-static{background-color:#e6e9ef;border-color:#acb0be;color:#8c8fa1;box-shadow:none;pointer-events:none}html.theme--catppuccin-latte .button.is-rounded,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-latte .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-latte .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-latte .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-latte .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-latte .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-latte .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-latte .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-latte .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-latte .buttons.has-addons .button:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-latte .buttons.has-addons .button:focus,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused,html.theme--catppuccin-latte .buttons.has-addons .button:active,html.theme--catppuccin-latte .buttons.has-addons .button.is-active,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-latte .buttons.has-addons .button:focus:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-latte .buttons.has-addons .button:active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-latte .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .buttons.is-centered{justify-content:center}html.theme--catppuccin-latte .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-latte .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-latte .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-latte .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-latte .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-latte .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-latte .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-latte .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-latte .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-latte .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-latte .content li+li{margin-top:0.25em}html.theme--catppuccin-latte .content p:not(:last-child),html.theme--catppuccin-latte .content dl:not(:last-child),html.theme--catppuccin-latte .content ol:not(:last-child),html.theme--catppuccin-latte .content ul:not(:last-child),html.theme--catppuccin-latte .content blockquote:not(:last-child),html.theme--catppuccin-latte .content pre:not(:last-child),html.theme--catppuccin-latte .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-latte .content h1,html.theme--catppuccin-latte .content h2,html.theme--catppuccin-latte .content h3,html.theme--catppuccin-latte .content h4,html.theme--catppuccin-latte .content h5,html.theme--catppuccin-latte .content h6{color:#4c4f69;font-weight:600;line-height:1.125}html.theme--catppuccin-latte .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-latte .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-latte .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-latte .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-latte .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-latte .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-latte .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-latte .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-latte .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-latte .content blockquote{background-color:#e6e9ef;border-left:5px solid #acb0be;padding:1.25em 1.5em}html.theme--catppuccin-latte .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-latte .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-latte .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-latte .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-latte .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-latte .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-latte .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-latte .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-latte .content ul ul ul{list-style-type:square}html.theme--catppuccin-latte .content dd{margin-left:2em}html.theme--catppuccin-latte .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-latte .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-latte .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-latte .content figure img{display:inline-block}html.theme--catppuccin-latte .content figure figcaption{font-style:italic}html.theme--catppuccin-latte .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-latte .content sup,html.theme--catppuccin-latte .content sub{font-size:75%}html.theme--catppuccin-latte .content table{width:100%}html.theme--catppuccin-latte .content table td,html.theme--catppuccin-latte .content table th{border:1px solid #acb0be;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-latte .content table th{color:#41445a}html.theme--catppuccin-latte .content table th:not([align]){text-align:inherit}html.theme--catppuccin-latte .content table thead td,html.theme--catppuccin-latte .content table thead th{border-width:0 0 2px;color:#41445a}html.theme--catppuccin-latte .content table tfoot td,html.theme--catppuccin-latte .content table tfoot th{border-width:2px 0 0;color:#41445a}html.theme--catppuccin-latte .content table tbody tr:last-child td,html.theme--catppuccin-latte .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-latte .content .tabs li+li{margin-top:0}html.theme--catppuccin-latte .content.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-latte .content.is-normal{font-size:1rem}html.theme--catppuccin-latte .content.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .content.is-large{font-size:1.5rem}html.theme--catppuccin-latte .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-latte .icon.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-latte .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-latte .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-latte .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-latte .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-latte .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--catppuccin-latte .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--catppuccin-latte div.icon-text{display:flex}html.theme--catppuccin-latte .image,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--catppuccin-latte .image img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--catppuccin-latte .image img.is-rounded,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--catppuccin-latte .image.is-fullwidth,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--catppuccin-latte .image.is-square img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--catppuccin-latte .image.is-square .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--catppuccin-latte .image.is-1by1 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--catppuccin-latte .image.is-1by1 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--catppuccin-latte .image.is-5by4 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--catppuccin-latte .image.is-5by4 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--catppuccin-latte .image.is-4by3 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--catppuccin-latte .image.is-4by3 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--catppuccin-latte .image.is-3by2 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--catppuccin-latte .image.is-3by2 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--catppuccin-latte .image.is-5by3 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--catppuccin-latte .image.is-5by3 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--catppuccin-latte .image.is-16by9 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--catppuccin-latte .image.is-16by9 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--catppuccin-latte .image.is-2by1 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--catppuccin-latte .image.is-2by1 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--catppuccin-latte .image.is-3by1 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--catppuccin-latte .image.is-3by1 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by1 .has-ratio,html.theme--catppuccin-latte .image.is-4by5 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-4by5 img,html.theme--catppuccin-latte .image.is-4by5 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-4by5 .has-ratio,html.theme--catppuccin-latte .image.is-3by4 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by4 img,html.theme--catppuccin-latte .image.is-3by4 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by4 .has-ratio,html.theme--catppuccin-latte .image.is-2by3 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-2by3 img,html.theme--catppuccin-latte .image.is-2by3 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-2by3 .has-ratio,html.theme--catppuccin-latte .image.is-3by5 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--catppuccin-latte .image.is-3by5 .has-ratio,html.theme--catppuccin-latte 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.button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-black:hover,html.theme--catppuccin-macchiato .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-black:focus,html.theme--catppuccin-macchiato .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-black:focus:not(:active),html.theme--catppuccin-macchiato .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--catppuccin-macchiato .button.is-black:active,html.theme--catppuccin-macchiato .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-black[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--catppuccin-macchiato .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-macchiato .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-black.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-light{background-color:#f5f5f5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light:hover,html.theme--catppuccin-macchiato .button.is-light.is-hovered{background-color:#eee;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light:focus,html.theme--catppuccin-macchiato .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light:focus:not(:active),html.theme--catppuccin-macchiato .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(245,245,245,0.25)}html.theme--catppuccin-macchiato .button.is-light:active,html.theme--catppuccin-macchiato .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-light{background-color:#f5f5f5;border-color:#f5f5f5;box-shadow:none}html.theme--catppuccin-macchiato .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-macchiato .button.is-light.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-macchiato .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--catppuccin-macchiato .button.is-light.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-light.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-macchiato 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.content kbd.button{background-color:#363a4f;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-dark:hover,html.theme--catppuccin-macchiato .content kbd.button:hover,html.theme--catppuccin-macchiato .button.is-dark.is-hovered,html.theme--catppuccin-macchiato .content kbd.button.is-hovered{background-color:#313447;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-dark:focus,html.theme--catppuccin-macchiato .content kbd.button:focus,html.theme--catppuccin-macchiato .button.is-dark.is-focused,html.theme--catppuccin-macchiato .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-dark:focus:not(:active),html.theme--catppuccin-macchiato .content kbd.button:focus:not(:active),html.theme--catppuccin-macchiato .button.is-dark.is-focused:not(:active),html.theme--catppuccin-macchiato .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(54,58,79,0.25)}html.theme--catppuccin-macchiato .button.is-dark:active,html.theme--catppuccin-macchiato .content kbd.button:active,html.theme--catppuccin-macchiato .button.is-dark.is-active,html.theme--catppuccin-macchiato .content kbd.button.is-active{background-color:#2c2f40;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-dark[disabled],html.theme--catppuccin-macchiato .content kbd.button[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-dark,fieldset[disabled] html.theme--catppuccin-macchiato .content kbd.button{background-color:#363a4f;border-color:#363a4f;box-shadow:none}html.theme--catppuccin-macchiato .button.is-dark.is-inverted,html.theme--catppuccin-macchiato .content kbd.button.is-inverted{background-color:#fff;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted:hover,html.theme--catppuccin-macchiato .content kbd.button.is-inverted:hover,html.theme--catppuccin-macchiato 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.button.is-dark.is-outlined:hover,html.theme--catppuccin-macchiato .content kbd.button.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-hovered,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-dark.is-outlined:focus,html.theme--catppuccin-macchiato .content kbd.button.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-focused,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-focused{background-color:#363a4f;border-color:#363a4f;color:#fff}html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #363a4f #363a4f !important}html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-dark.is-outlined[disabled],html.theme--catppuccin-macchiato .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-macchiato .content kbd.button.is-outlined{background-color:transparent;border-color:#363a4f;box-shadow:none;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-macchiato .content 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.button.is-info.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-info.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-focused{background-color:#8bd5ca;border-color:#8bd5ca;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #8bd5ca #8bd5ca !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-outlined{background-color:transparent;border-color:#8bd5ca;box-shadow:none;color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #8bd5ca #8bd5ca !important}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-light{background-color:#f0faf8;color:#276d62}html.theme--catppuccin-macchiato .button.is-info.is-light:hover,html.theme--catppuccin-macchiato .button.is-info.is-light.is-hovered{background-color:#e7f6f4;border-color:transparent;color:#276d62}html.theme--catppuccin-macchiato .button.is-info.is-light:active,html.theme--catppuccin-macchiato .button.is-info.is-light.is-active{background-color:#ddf3f0;border-color:transparent;color:#276d62}html.theme--catppuccin-macchiato .button.is-success{background-color:#a6da95;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:hover,html.theme--catppuccin-macchiato .button.is-success.is-hovered{background-color:#9ed78c;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:focus,html.theme--catppuccin-macchiato .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:focus:not(:active),html.theme--catppuccin-macchiato .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,218,149,0.25)}html.theme--catppuccin-macchiato .button.is-success:active,html.theme--catppuccin-macchiato .button.is-success.is-active{background-color:#96d382;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success{background-color:#a6da95;border-color:#a6da95;box-shadow:none}html.theme--catppuccin-macchiato .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined{background-color:transparent;border-color:#a6da95;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-success.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-focused{background-color:#a6da95;border-color:#a6da95;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6da95 #a6da95 !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-outlined{background-color:transparent;border-color:#a6da95;box-shadow:none;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6da95 #a6da95 !important}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-light{background-color:#f2faf0;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:hover,html.theme--catppuccin-macchiato .button.is-success.is-light.is-hovered{background-color:#eaf6e6;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:active,html.theme--catppuccin-macchiato .button.is-success.is-light.is-active{background-color:#e2f3dd;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:hover,html.theme--catppuccin-macchiato .button.is-warning.is-hovered{background-color:#eccf94;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus,html.theme--catppuccin-macchiato .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus:not(:active),html.theme--catppuccin-macchiato .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(238,212,159,0.25)}html.theme--catppuccin-macchiato .button.is-warning:active,html.theme--catppuccin-macchiato .button.is-warning.is-active{background-color:#eaca89;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:#eed49f;box-shadow:none}html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-focused{background-color:#eed49f;border-color:#eed49f;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-light{background-color:#fcf7ee;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:hover,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-hovered{background-color:#faf2e3;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:active,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-active{background-color:#f8eed8;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:hover,html.theme--catppuccin-macchiato .button.is-danger.is-hovered{background-color:#eb7c8c;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus,html.theme--catppuccin-macchiato .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus:not(:active),html.theme--catppuccin-macchiato .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(237,135,150,0.25)}html.theme--catppuccin-macchiato .button.is-danger:active,html.theme--catppuccin-macchiato .button.is-danger.is-active{background-color:#ea7183;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:#ed8796;box-shadow:none}html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-macchiato .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-focused{background-color:#ed8796;border-color:#ed8796;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-light{background-color:#fcedef;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:hover,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-hovered{background-color:#fbe2e6;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:active,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-active{background-color:#f9d7dc;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-small:not(.is-rounded),html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-macchiato .button.is-normal{font-size:1rem}html.theme--catppuccin-macchiato .button.is-medium{font-size:1.25rem}html.theme--catppuccin-macchiato .button.is-large{font-size:1.5rem}html.theme--catppuccin-macchiato .button[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button{background-color:#6e738d;border-color:#5b6078;box-shadow:none;opacity:.5}html.theme--catppuccin-macchiato .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-macchiato .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-macchiato .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-macchiato .button.is-static{background-color:#1e2030;border-color:#5b6078;color:#8087a2;box-shadow:none;pointer-events:none}html.theme--catppuccin-macchiato .button.is-rounded,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-macchiato .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-macchiato .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-macchiato .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-macchiato .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-macchiato .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-macchiato .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-macchiato .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-macchiato .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-macchiato .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-macchiato .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-macchiato .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-macchiato .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-macchiato .buttons.has-addons .button:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-macchiato .buttons.has-addons .button:focus,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-focused,html.theme--catppuccin-macchiato .buttons.has-addons .button:active,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-active,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-macchiato .buttons.has-addons .button:focus:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button:active:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-macchiato .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-macchiato .buttons.is-centered{justify-content:center}html.theme--catppuccin-macchiato .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-macchiato 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kbd.button.is-hovered{background-color:#2c2d3d;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-dark:focus,html.theme--catppuccin-mocha .content kbd.button:focus,html.theme--catppuccin-mocha .button.is-dark.is-focused,html.theme--catppuccin-mocha .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-dark:focus:not(:active),html.theme--catppuccin-mocha .content kbd.button:focus:not(:active),html.theme--catppuccin-mocha .button.is-dark.is-focused:not(:active),html.theme--catppuccin-mocha .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(49,50,68,0.25)}html.theme--catppuccin-mocha .button.is-dark:active,html.theme--catppuccin-mocha .content kbd.button:active,html.theme--catppuccin-mocha .button.is-dark.is-active,html.theme--catppuccin-mocha .content kbd.button.is-active{background-color:#262735;border-color:transparent;color:#fff}html.theme--catppuccin-mocha 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kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#313244}html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #313244 #313244 !important}html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined[disabled],html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-primary,html.theme--catppuccin-mocha .docstring>section>a.button.docs-sourcelink{background-color:#89b4fa;border-color:transparent;color:#fff}html.theme--catppuccin-mocha 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html.theme--catppuccin-mocha .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-link.is-light{background-color:#ebf3fe;color:#063c93}html.theme--catppuccin-mocha .button.is-link.is-light:hover,html.theme--catppuccin-mocha .button.is-link.is-light.is-hovered{background-color:#dfebfe;border-color:transparent;color:#063c93}html.theme--catppuccin-mocha .button.is-link.is-light:active,html.theme--catppuccin-mocha .button.is-link.is-light.is-active{background-color:#d3e3fd;border-color:transparent;color:#063c93}html.theme--catppuccin-mocha .button.is-info{background-color:#94e2d5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:hover,html.theme--catppuccin-mocha .button.is-info.is-hovered{background-color:#8adfd1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:focus,html.theme--catppuccin-mocha 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.button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-info.is-outlined{background-color:transparent;border-color:#94e2d5;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-outlined:hover,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-info.is-outlined:focus,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-focused{background-color:#94e2d5;border-color:#94e2d5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #94e2d5 #94e2d5 !important}html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-outlined{background-color:transparent;border-color:#94e2d5;box-shadow:none;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #94e2d5 #94e2d5 !important}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-light{background-color:#effbf9;color:#207466}html.theme--catppuccin-mocha .button.is-info.is-light:hover,html.theme--catppuccin-mocha .button.is-info.is-light.is-hovered{background-color:#e5f8f5;border-color:transparent;color:#207466}html.theme--catppuccin-mocha .button.is-info.is-light:active,html.theme--catppuccin-mocha .button.is-info.is-light.is-active{background-color:#dbf5f1;border-color:transparent;color:#207466}html.theme--catppuccin-mocha .button.is-success{background-color:#a6e3a1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:hover,html.theme--catppuccin-mocha .button.is-success.is-hovered{background-color:#9de097;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:focus,html.theme--catppuccin-mocha .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:focus:not(:active),html.theme--catppuccin-mocha .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,227,161,0.25)}html.theme--catppuccin-mocha .button.is-success:active,html.theme--catppuccin-mocha .button.is-success.is-active{background-color:#93dd8d;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success{background-color:#a6e3a1;border-color:#a6e3a1;box-shadow:none}html.theme--catppuccin-mocha .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted:hover,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-success.is-outlined{background-color:transparent;border-color:#a6e3a1;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-outlined:hover,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-success.is-outlined:focus,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-focused{background-color:#a6e3a1;border-color:#a6e3a1;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-outlined{background-color:transparent;border-color:#a6e3a1;box-shadow:none;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-light{background-color:#f0faef;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:hover,html.theme--catppuccin-mocha .button.is-success.is-light.is-hovered{background-color:#e7f7e5;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:active,html.theme--catppuccin-mocha .button.is-success.is-light.is-active{background-color:#def4dc;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:hover,html.theme--catppuccin-mocha .button.is-warning.is-hovered{background-color:#f8dea3;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus,html.theme--catppuccin-mocha .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus:not(:active),html.theme--catppuccin-mocha .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(249,226,175,0.25)}html.theme--catppuccin-mocha .button.is-warning:active,html.theme--catppuccin-mocha .button.is-warning.is-active{background-color:#f7d997;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:#f9e2af;box-shadow:none}html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-focused{background-color:#f9e2af;border-color:#f9e2af;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-light{background-color:#fef8ec;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:hover,html.theme--catppuccin-mocha .button.is-warning.is-light.is-hovered{background-color:#fdf4e0;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:active,html.theme--catppuccin-mocha .button.is-warning.is-light.is-active{background-color:#fcf0d4;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:hover,html.theme--catppuccin-mocha .button.is-danger.is-hovered{background-color:#f27f9f;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus,html.theme--catppuccin-mocha .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus:not(:active),html.theme--catppuccin-mocha .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(243,139,168,0.25)}html.theme--catppuccin-mocha .button.is-danger:active,html.theme--catppuccin-mocha .button.is-danger.is-active{background-color:#f17497;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:#f38ba8;box-shadow:none}html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-mocha .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-focused{background-color:#f38ba8;border-color:#f38ba8;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-light{background-color:#fdedf1;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:hover,html.theme--catppuccin-mocha .button.is-danger.is-light.is-hovered{background-color:#fce1e8;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:active,html.theme--catppuccin-mocha .button.is-danger.is-light.is-active{background-color:#fbd5e0;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-mocha .button.is-small:not(.is-rounded),html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .button.is-normal{font-size:1rem}html.theme--catppuccin-mocha .button.is-medium{font-size:1.25rem}html.theme--catppuccin-mocha .button.is-large{font-size:1.5rem}html.theme--catppuccin-mocha .button[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button{background-color:#6c7086;border-color:#585b70;box-shadow:none;opacity:.5}html.theme--catppuccin-mocha .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-mocha .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-mocha .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-mocha .button.is-static{background-color:#181825;border-color:#585b70;color:#7f849c;box-shadow:none;pointer-events:none}html.theme--catppuccin-mocha .button.is-rounded,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-mocha .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-mocha .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-mocha .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-mocha .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-mocha .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-mocha .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-mocha .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-mocha .buttons.has-addons .button:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-mocha .buttons.has-addons .button:focus,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused,html.theme--catppuccin-mocha .buttons.has-addons .button:active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-mocha .buttons.has-addons 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html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-light{background-color:#ecf0f1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:hover,html.theme--documenter-dark .button.is-light.is-hovered{background-color:#e5eaec;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:focus,html.theme--documenter-dark .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:focus:not(:active),html.theme--documenter-dark .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(236,240,241,0.25)}html.theme--documenter-dark .button.is-light:active,html.theme--documenter-dark .button.is-light.is-active{background-color:#dde4e6;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark 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html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content 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.button.is-link.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-link.is-outlined{background-color:transparent;border-color:#1abc9c;color:#1abc9c}html.theme--documenter-dark .button.is-link.is-outlined:hover,html.theme--documenter-dark .button.is-link.is-outlined.is-hovered,html.theme--documenter-dark .button.is-link.is-outlined:focus,html.theme--documenter-dark .button.is-link.is-outlined.is-focused{background-color:#1abc9c;border-color:#1abc9c;color:#fff}html.theme--documenter-dark .button.is-link.is-outlined.is-loading::after{border-color:transparent transparent #1abc9c #1abc9c !important}html.theme--documenter-dark .button.is-link.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-link.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-link.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-link.is-outlined{background-color:transparent;border-color:#1abc9c;box-shadow:none;color:#1abc9c}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-focused{background-color:#fff;color:#1abc9c}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #1abc9c #1abc9c !important}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-link.is-light{background-color:#edfdf9;color:#15987e}html.theme--documenter-dark .button.is-link.is-light:hover,html.theme--documenter-dark .button.is-link.is-light.is-hovered{background-color:#e2fbf6;border-color:transparent;color:#15987e}html.theme--documenter-dark .button.is-link.is-light:active,html.theme--documenter-dark .button.is-link.is-light.is-active{background-color:#d7f9f3;border-color:transparent;color:#15987e}html.theme--documenter-dark .button.is-info{background-color:#3c5dcd;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-info:hover,html.theme--documenter-dark .button.is-info.is-hovered{background-color:#3355c9;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-info:focus,html.theme--documenter-dark .button.is-info.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-info:focus:not(:active),html.theme--documenter-dark .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(60,93,205,0.25)}html.theme--documenter-dark .button.is-info:active,html.theme--documenter-dark .button.is-info.is-active{background-color:#3151bf;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-info[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-info{background-color:#3c5dcd;border-color:#3c5dcd;box-shadow:none}html.theme--documenter-dark .button.is-info.is-inverted{background-color:#fff;color:#3c5dcd}html.theme--documenter-dark .button.is-info.is-inverted:hover,html.theme--documenter-dark .button.is-info.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-info.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#3c5dcd}html.theme--documenter-dark .button.is-info.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-info.is-outlined{background-color:transparent;border-color:#3c5dcd;color:#3c5dcd}html.theme--documenter-dark .button.is-info.is-outlined:hover,html.theme--documenter-dark .button.is-info.is-outlined.is-hovered,html.theme--documenter-dark .button.is-info.is-outlined:focus,html.theme--documenter-dark .button.is-info.is-outlined.is-focused{background-color:#3c5dcd;border-color:#3c5dcd;color:#fff}html.theme--documenter-dark .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #3c5dcd #3c5dcd !important}html.theme--documenter-dark .button.is-info.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-info.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-info.is-outlined{background-color:transparent;border-color:#3c5dcd;box-shadow:none;color:#3c5dcd}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-focused{background-color:#fff;color:#3c5dcd}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #3c5dcd #3c5dcd !important}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-info.is-light{background-color:#eff2fb;color:#3253c3}html.theme--documenter-dark .button.is-info.is-light:hover,html.theme--documenter-dark .button.is-info.is-light.is-hovered{background-color:#e5e9f8;border-color:transparent;color:#3253c3}html.theme--documenter-dark .button.is-info.is-light:active,html.theme--documenter-dark .button.is-info.is-light.is-active{background-color:#dae1f6;border-color:transparent;color:#3253c3}html.theme--documenter-dark .button.is-success{background-color:#259a12;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-success:hover,html.theme--documenter-dark .button.is-success.is-hovered{background-color:#228f11;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-success:focus,html.theme--documenter-dark .button.is-success.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-success:focus:not(:active),html.theme--documenter-dark .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(37,154,18,0.25)}html.theme--documenter-dark .button.is-success:active,html.theme--documenter-dark .button.is-success.is-active{background-color:#20830f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-success[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success{background-color:#259a12;border-color:#259a12;box-shadow:none}html.theme--documenter-dark .button.is-success.is-inverted{background-color:#fff;color:#259a12}html.theme--documenter-dark .button.is-success.is-inverted:hover,html.theme--documenter-dark .button.is-success.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#259a12}html.theme--documenter-dark .button.is-success.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-success.is-outlined{background-color:transparent;border-color:#259a12;color:#259a12}html.theme--documenter-dark .button.is-success.is-outlined:hover,html.theme--documenter-dark .button.is-success.is-outlined.is-hovered,html.theme--documenter-dark .button.is-success.is-outlined:focus,html.theme--documenter-dark .button.is-success.is-outlined.is-focused{background-color:#259a12;border-color:#259a12;color:#fff}html.theme--documenter-dark .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #259a12 #259a12 !important}html.theme--documenter-dark .button.is-success.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-outlined{background-color:transparent;border-color:#259a12;box-shadow:none;color:#259a12}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-focused{background-color:#fff;color:#259a12}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #259a12 #259a12 !important}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-success.is-light{background-color:#effded;color:#2ec016}html.theme--documenter-dark .button.is-success.is-light:hover,html.theme--documenter-dark .button.is-success.is-light.is-hovered{background-color:#e5fce1;border-color:transparent;color:#2ec016}html.theme--documenter-dark .button.is-success.is-light:active,html.theme--documenter-dark .button.is-success.is-light.is-active{background-color:#dbfad6;border-color:transparent;color:#2ec016}html.theme--documenter-dark .button.is-warning{background-color:#f4c72f;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning:hover,html.theme--documenter-dark .button.is-warning.is-hovered{background-color:#f3c423;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning:focus,html.theme--documenter-dark .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning:focus:not(:active),html.theme--documenter-dark .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(244,199,47,0.25)}html.theme--documenter-dark .button.is-warning:active,html.theme--documenter-dark .button.is-warning.is-active{background-color:#f3c017;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning{background-color:#f4c72f;border-color:#f4c72f;box-shadow:none}html.theme--documenter-dark .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-inverted:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#f4c72f;color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-outlined.is-focused{background-color:#f4c72f;border-color:#f4c72f;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #f4c72f #f4c72f !important}html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#f4c72f;box-shadow:none;color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f4c72f #f4c72f !important}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning.is-light{background-color:#fefaec;color:#8c6e07}html.theme--documenter-dark .button.is-warning.is-light:hover,html.theme--documenter-dark .button.is-warning.is-light.is-hovered{background-color:#fdf7e0;border-color:transparent;color:#8c6e07}html.theme--documenter-dark .button.is-warning.is-light:active,html.theme--documenter-dark .button.is-warning.is-light.is-active{background-color:#fdf3d3;border-color:transparent;color:#8c6e07}html.theme--documenter-dark .button.is-danger{background-color:#cb3c33;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:hover,html.theme--documenter-dark .button.is-danger.is-hovered{background-color:#c13930;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:focus,html.theme--documenter-dark .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:focus:not(:active),html.theme--documenter-dark .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(203,60,51,0.25)}html.theme--documenter-dark .button.is-danger:active,html.theme--documenter-dark .button.is-danger.is-active{background-color:#b7362e;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger{background-color:#cb3c33;border-color:#cb3c33;box-shadow:none}html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-inverted:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#cb3c33;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-outlined.is-focused{background-color:#cb3c33;border-color:#cb3c33;color:#fff}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #cb3c33 #cb3c33 !important}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#cb3c33;box-shadow:none;color:#cb3c33}html.theme--documenter-dark 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html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fbefef;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#f8e6e5;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#f6dcda;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark 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.button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark 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h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark 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GitHub

Design principles

This project is inspired by two existing projects:

OMLT is a framework built around Pyomo, and gurobi-machinelearning is a framework build around gurobipy.

These projects served as inspiration, but we also departed from them in some carefully considered ways.

All of our design decisions were guided by two principles:

  1. To be simple
  2. To leverage Julia's Pkg extensions and multiple dispatch.

Terminology

Because the field is relatively new, there is no settled choice of terminology.

MathOptAI chooses to use "predictor" as the synonym for the machine learning model. Hence, we have AbstractPredictor, add_predictor, and build_predictor.

In contrast, gurobi-machinelearning tends to use "regression model" and OMLT uses "formulation."

We choose "predictor" because all models we implement are of the form $y = f(x)$.

We do not use "machine learning model" because we have support for the linear and logistic regression models of classical statistical fitting. We could have used "regression model," but we find that models like neural networks and binary decision trees are not commonly thought of as regression models.

Inputs are vectors

MathOptAI assumes that all inputs $x$ and outputs $y$ to $y = predictor(x)$ are Base.Vectors.

We make this choice for simplicity.

In our opinion, Julia libraries often take a laissez-faire approach to the types that they support. In the optimistic case, this can lead to novel behavior by combining two packages that the package author had previously not considered or tested. In the pessimistic case, this can lead to incorrect results or cryptic error messages.

Exceptions to the Vector rule will be carefully considered and tested.

Currently, there are two exceptions:

  1. If x is a Matrix, then the columns of x are interpreted as independent observations, and the output y will be a Matrix with the same number of columns
  2. The StatsModels extension allows x to be a DataFrames.DataFrame, if the predictor is a StatsModels.TableRegressionModel.

Exceptions 1 and 2 are combined in the StatsModels exception, so that the predictor is mapped over the rows of the DataFrames.DataFrame (which we assume will be a common use-case).

We choose to interpret the rows as input variables and columns as independent observations (rather than the more traditional table-based approach where columns are the input variables and rows are observations) because Julia uses column-major ordering in Matrix. Another justification follows from the Affine predictor, $f(x) = Ax + b$, where passing in a Matrix as x with column observations naturally leads to a Matrix output for y of the appropriate dimensions.

We choose to make y a Vector, even for scalar outputs, to simplify code that works generically for many different predictors. Without this principle, there will inevitably be cases where a scalar and length-1 vector are confused.

If you want to use a predictor that does not take Vector input (for example, it is an image as input to a neural network), the first preprocessing step should be to vec the input into a single Vector.

Inputs are provided, outputs are returned

The main job of MathOptAI is to embed models of the form y = predictor(x) into a JuMP model. A key design decision is how to represent the input x and output y.

gurobi-machinelearning

gurobi-machinelearning implements an API of the following general form:

pred_constr = add_predictor_constr(model, predictor, x, y)

Here, both the input x and the output y must be created and provided by the user, and a new object pred_constr is returned.

The benefit of this design is that pred_constr can contain statistics about the reformulation (for example, the number of variables that were added), and it can be used to delete a predictor from model.

The downside is that the user must ensure that the shape and size of y is correct.

OMLT

OMLT implements an API of the following general form:

model.pred_constr = OmltBlock()
+model.pred_constr.build_formulation(predictor)
+x, y = model.pred_constr.inputs, model.pred_constr.outputs

First, a new OmltBlock() is created. Then the formulation is built inside the block, and both the input and output are provided to the user.

The benefit of this design is that pred_constr can contain statistics about the reformulation (for example, the number of variables that were added), and it can be used to delete a predictor from model.

The downside is that the user must often write additional constraints to connect the input and output of the OmltBlock to their existing decision variables:

#connect pyomo model input and output to the neural network
+@model.Constraint()
+def connect_input(mdl):
+    return mdl.input == mdl.nn.inputs[0]
+
+@model.Constraint()
+def connect_output(mdl):
+    return mdl.output == mdl.nn.outputs[0]

A second downside is that the predictor must describe the input and output dimension; these cannot be inferred automatically. As one example, this means that it cannot do the following:

# Not possible because dimension not given
+model.pred_constr.build_formulation(ReLU())

In the context of MathOptAI, something like ReLU() is useful so that we can map generic layers like Flux.relu => MathOptAI.ReLU(), and so that we do not duplicate required dimension information in input and predictor (see the MathOptAI section below).

MathOptAI

The main entry-point to MathOptAI is add_predictor:

y, formulation = MathOptAI.add_predictor(model, predictor, x)

The user provides the input x, and the output y is returned.

The main benefit of this approach is simplicity.

First, the user probably already has the input x as decision variables or an expression in the model, so we do not need the connect_input constraint, and because we use a full-space formulation by default, the output y will always be a vector of decision variables, which avoids the need for a connect_output constraint.

Second, predictors do not need to store dimension information, so we can have:

y, formulation = MathOptAI.add_predictor(model, MathOptAI.ReLU(), x)

for any size of x.

Activations are predictors

OMLT makes a distinction between layers, like full_space_dense_layer, and elementwise activation functions, like sigmoid_activation_function.

The downside to this approach is that it treats activation functions as special, leading to issues such as OMLT#125.

In contrast, MathOptAI treats activation functions as a vector-valued predictor like any other:

y, formulation = MathOptAI.add_predictor(model, MathOptAI.ReLU(), x)

This means that we can pipeline them to create predictors such as:

function LogisticRegression(A)
+    return MathOptAI.Pipeline(MathOptAI.Affine(A), MathOptAI.Sigmoid())
+end

Controlling transformations

Many predictors have multiple ways that they can be formulated in an optimization model. For example, ReLU implements the non-smooth nonlinear formulation $y = \max\{x, 0\}$, while ReLUQuadratic implements a the complementarity formulation $x = y - slack; y, slack \ge 0; y * slack = 0$.

Choosing the appropriate formulation for the combination of model and solver can have a large impact on the performance.

Because gurobi-machinelearning is specific to the Gurobi solver, they have a limited ability for the user to choose and implement different formulations.

OMLT is more general, in that it has multiple ways of formulating layers such as ReLU. However, these are hard-coded into complete formulations such as omlt.neuralnet.nn_formulation.ReluBigMFormulation or omlt.neuralnet.nn_formulation.ReluComplementarityFormulation.

In contrast, MathOptAI tries to take a maximally modular approach, where the user can control how the layers are formulated at runtime, including using a custom formulation that is not defined in MathOptAI.jl.

Currently, we achieve this with a config dictionary, which maps the various neural network layers to an AbstractPredictor. For example:

chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));
+config = Dict(Flux.relu => MathOptAI.ReLU())
+predictor = MathOptAI.build_predictor(chain; config)

Please open a GitHub issue if you have a suggestion for a better API.

Full-space or reduced-space

OMLT has two ways that it can formulate neural networks: full-space and reduced-space.

The full-space formulations add intermediate variables to represent the output of all layers.

For example, in a Flux.Dense(2, 3, Flux.relu) layer, a full-space formulation will add an intermediate y_tmp variable to represent the output of the affine layer prior to the ReLU:

layer = Flux.Dense(2, 3, Flux.relu)
+model_full_space = Model()
+@variable(model_full_space, x[1:2])
+@variable(model_full_space, y_tmp[1:3])
+@variable(model_full_space, y[1:3])
+@constraint(model_full_space, y_tmp == layer.A * x + layer.b)
+@constraint(model_full_space, y .== max.(0, y_tmp))

In contrast, a reduced-space formulation encodes the input-output relationship as a single nonlinear constraint:

layer = Flux.Dense(2, 3, Flux.relu)
+model_reduced_space = Model()
+@variable(model_reduced_space, x[1:2])
+@variable(model_reduced_space, y[1:3])
+@constraint(model_reduced_space, y .== max.(0, layer.A * x + layer.b))

In general, the full-space formulations have more variables and constraints but simpler nonlinear expressions, whereas the reduced-space formulations have fewer variables and constraints but more complicated nonlinear expressions.

MathOptAI.jl implements the full-space formulation by default, but some layers support the reduced-space formulation with the ReducedSpace wrapper.

diff --git a/dev/index.html b/dev/index.html new file mode 100644 index 00000000..8f0d8b3a --- /dev/null +++ b/dev/index.html @@ -0,0 +1,30 @@ + +MathOptAI.jl · MathOptAI.jl
GitHub

MathOptAI.jl

MathOptAI.jl is a JuMP extension for embedding trained AI, machine learning, and statistical learning models into a JuMP optimization model.

License

MathOptAI.jl is provided under a BSD-3 license as part of the Optimization and Machine Learning Toolbox project, O4806.

See LICENSE.md for details.

Despite the name similarity, this project is not affiliated with OMLT, the Optimization and Machine Learning Toolkit.

Installation

Install MathOptAI.jl using the Julia package manager:

import Pkg
+Pkg.add("MathOptAI")

Getting started

Here's an example of using MathOptAI to embed a trained neural network from Flux into a JuMP model. The vector of JuMP variables x is fed as input to the neural network. The output y is a vector of JuMP variables that represents the output layer of the neural network. The formulation object stores the additional variables and constraints that were added to model.

julia> using JuMP, MathOptAI, Flux
+
+julia> predictor = Flux.Chain(
+           Flux.Dense(28^2 => 32, Flux.sigmoid),
+           Flux.Dense(32 => 10),
+           Flux.softmax,
+       );
+
+julia> #= Train the Flux model. Code not shown for simplicity =#
+
+julia> model = JuMP.Model();
+
+julia> JuMP.@variable(model, 0 <= x[1:28^2] <= 1);
+
+julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
+
+julia> y
+10-element Vector{VariableRef}:
+ moai_SoftMax[1]
+ moai_SoftMax[2]
+ moai_SoftMax[3]
+ moai_SoftMax[4]
+ moai_SoftMax[5]
+ moai_SoftMax[6]
+ moai_SoftMax[7]
+ moai_SoftMax[8]
+ moai_SoftMax[9]
+ moai_SoftMax[10]

Getting help

This package is under active development. For help, questions, comments, and suggestions, please open a GitHub issue.

Inspiration

This project is mainly inspired by two existing projects:

Other works, from which we took less inspiration, include:

The 2024 paper of López-Flores et al. is an excellent summary of the state of the field at the time that we started development of MathOptAI.

López-Flores, F.J., Ramírez-Márquez, C., Ponce-Ortega J.M. (2024). Process Systems Engineering Tools for Optimization of Trained Machine Learning Models: Comparative and Perspective. Industrial & Engineering Chemistry Research, 63(32), 13966-13979. DOI: 10.1021/acs.iecr.4c00632

diff --git a/dev/manual/AbstractGPs/index.html b/dev/manual/AbstractGPs/index.html new file mode 100644 index 00000000..413b2b3d --- /dev/null +++ b/dev/manual/AbstractGPs/index.html @@ -0,0 +1,6 @@ + +AbstractGPs.jl · MathOptAI.jl
GitHub

AbstractGPs.jl

AbstractGPs.jl is a library for fitting Gaussian Processes in Julia.

Basic example

Here is an example:

julia> using JuMP, MathOptAI, AbstractGPs
julia> x_data = 2π .* (0.0:0.1:1.0);
julia> y_data = sin.(x_data);
julia> fx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.1);
julia> p_fx = AbstractGPs.posterior(fx, y_data);
julia> model = Model();
julia> @variable(model, 1 <= x[1:1] <= 6, start = 3);
julia> predictor = MathOptAI.Quantile(p_fx, [0.1, 0.9]);
julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
julia> y2-element Vector{JuMP.VariableRef}:
+ moai_quantile[1]
+ moai_quantile[2]
julia> formulationQuantile(_, [0.1, 0.9])
+├ variables [0]
+└ constraints [0]
julia> @objective(model, Max, y[2] - y[1])moai_quantile[2] - moai_quantile[1]
diff --git a/dev/manual/DecisionTree/index.html b/dev/manual/DecisionTree/index.html new file mode 100644 index 00000000..0cebbdda --- /dev/null +++ b/dev/manual/DecisionTree/index.html @@ -0,0 +1,18 @@ + +DecisionTree.jl · MathOptAI.jl
GitHub

DecisionTree.jl

DecisionTree.jl is a library for fitting decision trees in Julia.

Basic example

Here is an example:

julia> using JuMP, MathOptAI, DecisionTree
julia> truth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)truth (generic function with 1 method)
julia> features = abs.(sin.((1:10) .* (3:4)'));
julia> size(features)(10, 2)
julia> labels = truth.(Vector.(eachrow(features)));
julia> predictor = DecisionTree.build_tree(labels, features)Decision Tree
+Leaves: 3
+Depth:  2
julia> model = Model();
julia> @variable(model, 0 <= x[1:2] <= 1);
julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_BinaryDecisionTree_value
julia> formulationBinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]
+├ variables [4]
+│ ├ moai_BinaryDecisionTree_value
+│ ├ moai_BinaryDecisionTree_z[1]
+│ ├ moai_BinaryDecisionTree_z[2]
+│ └ moai_BinaryDecisionTree_z[3]
+└ constraints [7]
+  ├ moai_BinaryDecisionTree_z[1] + moai_BinaryDecisionTree_z[2] + moai_BinaryDecisionTree_z[3] = 1
+  ├ moai_BinaryDecisionTree_z[1] --> {x[1] ≤ 0.4743457016210958}
+  ├ moai_BinaryDecisionTree_z[2] --> {x[1] ≥ 0.4743457016210958}
+  ├ moai_BinaryDecisionTree_z[2] --> {x[2] ≤ 0.41966499895337794}
+  ├ moai_BinaryDecisionTree_z[3] --> {x[1] ≥ 0.4743457016210958}
+  ├ moai_BinaryDecisionTree_z[3] --> {x[2] ≥ 0.41966499895337794}
+  └ 2 moai_BinaryDecisionTree_z[1] - 3 moai_BinaryDecisionTree_z[2] - 4 moai_BinaryDecisionTree_z[3] + moai_BinaryDecisionTree_value = 0
diff --git a/dev/manual/Flux/index.html b/dev/manual/Flux/index.html new file mode 100644 index 00000000..c713e2a7 --- /dev/null +++ b/dev/manual/Flux/index.html @@ -0,0 +1,69 @@ + +Flux.jl · MathOptAI.jl
GitHub

Flux.jl

Flux.jl is a library for machine learning in Julia.

The upstream documentation is available at https://fluxml.ai/Flux.jl/stable/.

Supported layers

MathOptAI supports embedding a Flux model into JuMP if it is a Flux.Chain composed of:

Basic example

Use MathOptAI.add_predictor to embed a Flux.Chain into a JuMP model:

julia> using JuMP, Flux, MathOptAI
julia> predictor = Flux.Chain(Flux.Dense(1 => 2, Flux.relu), Flux.Dense(2 => 1));
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_Affine[1]
julia> formulationAffine(A, b) [input: 1, output: 2]
+├ variables [2]
+│ ├ moai_Affine[1]
+│ └ moai_Affine[2]
+└ constraints [2]
+  ├ -0.4923129379749298 x[1] - moai_Affine[1] = 0
+  └ 1.2562174797058105 x[1] - moai_Affine[2] = 0
+MathOptAI.ReLU()
+├ variables [2]
+│ ├ moai_ReLU[1]
+│ └ moai_ReLU[2]
+└ constraints [4]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[2] ≥ 0
+  ├ moai_ReLU[1] - max(0.0, moai_Affine[1]) = 0
+  └ moai_ReLU[2] - max(0.0, moai_Affine[2]) = 0
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ 0.6359503865242004 moai_ReLU[1] - 0.8882789015769958 moai_ReLU[2] - moai_Affine[1] = 0

Reduced-space

Use the reduced_space = true keyword to formulate a reduced-space model:

julia> using JuMP, Flux, MathOptAI
julia> predictor = Flux.Chain(Flux.Dense(1 => 2, Flux.relu), Flux.Dense(2 => 1));
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> y, formulation =
+           MathOptAI.add_predictor(model, predictor, x; reduced_space = true);
julia> y1-element Vector{JuMP.NonlinearExpr}:
+ ((+(0.0) + (0.06276053190231323 * max(0.0, -1.29595947265625 x[1]))) + (-0.5483795404434204 * max(0.0, 0.43275389075279236 x[1]))) + 0.0
julia> formulationReducedSpace(Affine(A, b) [input: 1, output: 2])
+├ variables [0]
+└ constraints [0]
+ReducedSpace(MathOptAI.ReLU())
+├ variables [0]
+└ constraints [0]
+ReducedSpace(Affine(A, b) [input: 2, output: 1])
+├ variables [0]
+└ constraints [0]

Gray-box

Use the gray_box = true keyword to embed the network as a nonlinear operator:

julia> using JuMP, Flux, MathOptAI
julia> predictor = Flux.Chain(Flux.Dense(1 => 2, Flux.relu), Flux.Dense(2 => 1));
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> y, formulation =
+           MathOptAI.add_predictor(model, predictor, x; gray_box = true);
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_GrayBox[1]
julia> formulationGrayBox
+├ variables [1]
+│ └ moai_GrayBox[1]
+└ constraints [1]
+  └ op_##1221(x[1]) - moai_GrayBox[1] = 0

Change how layers are formulated

Pass a dictionary to the config keyword that maps Flux activation functions to a MathOptAI predictor:

julia> using JuMP, Flux, MathOptAI
julia> predictor = Flux.Chain(Flux.Dense(1 => 2, Flux.relu), Flux.Dense(2 => 1));
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> y, formulation = MathOptAI.add_predictor(
+           model,
+           predictor,
+           x;
+           config = Dict(Flux.relu => MathOptAI.ReLUSOS1()),
+       );
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_Affine[1]
julia> formulationAffine(A, b) [input: 1, output: 2]
+├ variables [2]
+│ ├ moai_Affine[1]
+│ └ moai_Affine[2]
+└ constraints [2]
+  ├ 1.3536356687545776 x[1] - moai_Affine[1] = 0
+  └ -0.6924732327461243 x[1] - moai_Affine[2] = 0
+MathOptAI.ReLUSOS1()
+├ variables [4]
+│ ├ moai_ReLU[1]
+│ ├ moai_ReLU[2]
+│ ├ moai_z[1]
+│ └ moai_z[2]
+└ constraints [6]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[2] ≥ 0
+  ├ moai_Affine[1] - moai_ReLU[1] + moai_z[1] = 0
+  ├ moai_Affine[2] - moai_ReLU[2] + moai_z[2] = 0
+  ├ [moai_ReLU[1], moai_z[1]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])
+  └ [moai_ReLU[2], moai_z[2]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ 1.188759207725525 moai_ReLU[1] - 0.8120986223220825 moai_ReLU[2] - moai_Affine[1] = 0
diff --git a/dev/manual/GLM/index.html b/dev/manual/GLM/index.html new file mode 100644 index 00000000..823cab4d --- /dev/null +++ b/dev/manual/GLM/index.html @@ -0,0 +1,28 @@ + +GLM.jl · MathOptAI.jl
GitHub

GLM.jl

GLM.jl is a library for fitting generalized linear models in Julia.

MathOptAI.jl supports embedding two types of regression models from GLM:

  • GLM.lm(X, Y)
  • GLM.glm(X, Y, GLM.Bernoulli())

Linear regression

The input x to add_predictor must be a vector with the same number of elements as columns in the training matrix. The return is a vector of JuMP variables with a single element.

julia> using GLM, JuMP, MathOptAI
julia> X, Y = rand(10, 2), rand(10);
julia> predictor = GLM.lm(X, Y);
julia> model = Model();
julia> @variable(model, x[1:2]);
julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_Affine[1]
julia> formulationAffine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ -0.14231172919360008 x[1] + 0.9996847313760107 x[2] - moai_Affine[1] = 0

Logistic regression

The input x to add_predictor must be a vector with the same number of elements as columns in the training matrix. The return is a vector of JuMP variables with a single element.

julia> using GLM, JuMP, MathOptAI
julia> X, Y = rand(10, 2), rand(Bool, 10);
julia> predictor = GLM.glm(X, Y, GLM.Bernoulli());
julia> model = Model();
julia> @variable(model, x[1:2]);
julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_Sigmoid[1]
julia> formulationAffine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ 6.874780525948348 x[1] - 1.9173931361902363 x[2] - moai_Affine[1] = 0
+MathOptAI.Sigmoid()
+├ variables [1]
+│ └ moai_Sigmoid[1]
+└ constraints [3]
+  ├ moai_Sigmoid[1] ≥ 0
+  ├ moai_Sigmoid[1] ≤ 1
+  └ moai_Sigmoid[1] - (1.0 / (1.0 + exp(-moai_Affine[1]))) = 0

DataFrames

DataFrames.jl can be used with GLM.jl.

The input x to add_predictor must be a DataFrame with the same feature columns as the training DataFrame. The return is a vector of JuMP variables, with one element for each row in the DataFrame.

julia> using DataFrames, GLM, JuMP, MathOptAI
julia> train_df = DataFrames.DataFrame(x1 = rand(10), x2 = rand(10));
julia> train_df.y = 1.0 .* train_df.x1 + 2.0 .* train_df.x2 .+ rand(10);
julia> predictor = GLM.lm(GLM.@formula(y ~ x1 + x2), train_df);
julia> model = Model();
julia> test_df = DataFrames.DataFrame(
+           x1 = rand(6),
+           x2 = @variable(model, [1:6]),
+       );
julia> test_df.y, _ = MathOptAI.add_predictor(model, predictor, test_df);
julia> test_df.y6-element Vector{JuMP.VariableRef}:
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
diff --git a/dev/manual/Lux/index.html b/dev/manual/Lux/index.html new file mode 100644 index 00000000..8f75c377 --- /dev/null +++ b/dev/manual/Lux/index.html @@ -0,0 +1,76 @@ + +Lux.jl · MathOptAI.jl
GitHub

Lux.jl

Lux.jl is a library for machine learning in Julia.

The upstream documentation is available at https://lux.csail.mit.edu/stable/.

Supported layers

MathOptAI supports embedding a Lux model into JuMP if it is a Lux.Chain composed of:

Basic example

Use MathOptAI.add_predictor to embed a tuple (containing the Lux.Chain, the parameters, and the state) into a JuMP model:

julia> using JuMP, Lux, MathOptAI, Random
julia> rng = Random.MersenneTwister();
julia> chain = Lux.Chain(Lux.Dense(1 => 2, Lux.relu), Lux.Dense(2 => 1))Chain(
+    layer_1 = Dense(1 => 2, relu),      # 4 parameters
+    layer_2 = Dense(2 => 1),            # 3 parameters
+)         # Total: 7 parameters,
+          #        plus 0 states.
julia> parameters, state = Lux.setup(rng, chain);
julia> predictor = (chain, parameters, state);
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_Affine[1]
julia> formulationAffine(A, b) [input: 1, output: 2]
+├ variables [2]
+│ ├ moai_Affine[1]
+│ └ moai_Affine[2]
+└ constraints [2]
+  ├ 1.332558274269104 x[1] - moai_Affine[1] = 0
+  └ -0.6588695049285889 x[1] - moai_Affine[2] = 0
+MathOptAI.ReLU()
+├ variables [2]
+│ ├ moai_ReLU[1]
+│ └ moai_ReLU[2]
+└ constraints [4]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[2] ≥ 0
+  ├ moai_ReLU[1] - max(0.0, moai_Affine[1]) = 0
+  └ moai_ReLU[2] - max(0.0, moai_Affine[2]) = 0
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ 0.8753094673156738 moai_ReLU[1] - 0.9528286457061768 moai_ReLU[2] - moai_Affine[1] = 0

Reduced-space

Use the reduced_space = true keyword to formulate a reduced-space model:

julia> using JuMP, Lux, MathOptAI, Random
julia> rng = Random.MersenneTwister();
julia> chain = Lux.Chain(Lux.Dense(1 => 2, Lux.relu), Lux.Dense(2 => 1))Chain(
+    layer_1 = Dense(1 => 2, relu),      # 4 parameters
+    layer_2 = Dense(2 => 1),            # 3 parameters
+)         # Total: 7 parameters,
+          #        plus 0 states.
julia> parameters, state = Lux.setup(rng, chain);
julia> predictor = (chain, parameters, state);
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> y, formulation =
+           MathOptAI.add_predictor(model, predictor, x; reduced_space = true);
julia> y1-element Vector{JuMP.NonlinearExpr}:
+ ((+(0.0) + (0.10877224802970886 * max(0.0, -0.3746817708015442 x[1]))) + (-0.7371025085449219 * max(0.0, 0.7540135383605957 x[1]))) + 0.0
julia> formulationReducedSpace(Affine(A, b) [input: 1, output: 2])
+├ variables [0]
+└ constraints [0]
+ReducedSpace(MathOptAI.ReLU())
+├ variables [0]
+└ constraints [0]
+ReducedSpace(Affine(A, b) [input: 2, output: 1])
+├ variables [0]
+└ constraints [0]

Gray-box

The Lux extension does not yet support the gray_box keyword argument.

Change how layers are formulated

Pass a dictionary to the config keyword that maps Lux activation functions to a MathOptAI predictor:

julia> using JuMP, Lux, MathOptAI, Random
julia> rng = Random.MersenneTwister();
julia> chain = Lux.Chain(Lux.Dense(1 => 2, Lux.relu), Lux.Dense(2 => 1))Chain(
+    layer_1 = Dense(1 => 2, relu),      # 4 parameters
+    layer_2 = Dense(2 => 1),            # 3 parameters
+)         # Total: 7 parameters,
+          #        plus 0 states.
julia> parameters, state = Lux.setup(rng, chain);
julia> predictor = (chain, parameters, state);
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> y, formulation = MathOptAI.add_predictor(
+           model,
+           predictor,
+           x;
+           config = Dict(Lux.relu => MathOptAI.ReLUSOS1()),
+       );
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_Affine[1]
julia> formulationAffine(A, b) [input: 1, output: 2]
+├ variables [2]
+│ ├ moai_Affine[1]
+│ └ moai_Affine[2]
+└ constraints [2]
+  ├ -1.1883398294448853 x[1] - moai_Affine[1] = 0
+  └ 1.126004934310913 x[1] - moai_Affine[2] = 0
+MathOptAI.ReLUSOS1()
+├ variables [4]
+│ ├ moai_ReLU[1]
+│ ├ moai_ReLU[2]
+│ ├ moai_z[1]
+│ └ moai_z[2]
+└ constraints [6]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[2] ≥ 0
+  ├ moai_Affine[1] - moai_ReLU[1] + moai_z[1] = 0
+  ├ moai_Affine[2] - moai_ReLU[2] + moai_z[2] = 0
+  ├ [moai_ReLU[1], moai_z[1]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])
+  └ [moai_ReLU[2], moai_z[2]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [2]
+  ├ moai_Affine[1] ≤ 0
+  └ -0.9932889342308044 moai_ReLU[1] - 0.7215462923049927 moai_ReLU[2] - moai_Affine[1] = 0
diff --git a/dev/manual/PyTorch/index.html b/dev/manual/PyTorch/index.html new file mode 100644 index 00000000..2495bd3f --- /dev/null +++ b/dev/manual/PyTorch/index.html @@ -0,0 +1,76 @@ + +PyTorch · MathOptAI.jl
GitHub

PyTorch

PyTorch is a library for machine learning in Python.

The upstream documentation is available at https://pytorch.org/docs/stable/.

Supported layers

MathOptAI supports embedding a PyTorch models into JuMP if it is a nn.Sequential composed of:

File format

Use torch.save to save a trained PyTorch model to a .pt file:

#!/usr/bin/python3
+import torch
+model = torch.nn.Sequential(
+    torch.nn.Linear(1, 2),
+    torch.nn.ReLU(),
+    torch.nn.Linear(2, 1),
+)
+torch.save(model, "saved_pytorch_model.pt")

Python integration

MathOptAI uses PythonCall.jl to call from Julia into Python.

See CondaPkg.jl for more control over how to link Julia to an existing Python environment. For example, if you have an existing Python installation (with PyTorch installed), and it is available in the current Conda environment, set:

ENV["JULIA_CONDAPKG_BACKEND"] = "Current"

before importing PythonCall.jl. If the Python installation can be found on the path and it is not in a Conda environment, set:

ENV["JULIA_CONDAPKG_BACKEND"] = "Null"

If python is not on your path, you may additionally need to set JULIA_PYTHONCALL_EXE, for example, to:

ENV["JULIA_PYTHONCALL_EXE"] = "python3"

Basic example

Use MathOptAI.add_predictor to embed a PyTorch model into a JuMP model:

julia> using JuMP, MathOptAI
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> predictor = MathOptAI.PytorchModel("saved_pytorch_model.pt");
julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_Affine[1]
julia> formulationAffine(A, b) [input: 1, output: 2]
+├ variables [2]
+│ ├ moai_Affine[1]
+│ └ moai_Affine[2]
+└ constraints [2]
+  ├ 0.7473132610321045 x[1] - moai_Affine[1] = 0.27370238304138184
+  └ -0.8237636089324951 x[1] - moai_Affine[2] = 0.08490216732025146
+MathOptAI.ReLU()
+├ variables [2]
+│ ├ moai_ReLU[1]
+│ └ moai_ReLU[2]
+└ constraints [4]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[2] ≥ 0
+  ├ moai_ReLU[1] - max(0.0, moai_Affine[1]) = 0
+  └ moai_ReLU[2] - max(0.0, moai_Affine[2]) = 0
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ -0.4644489884376526 moai_ReLU[1] + 0.5382549166679382 moai_ReLU[2] - moai_Affine[1] = 0.5698285102844238

Reduced-space

Use the reduced_space = true keyword to formulate a reduced-space model:

julia> using JuMP, MathOptAI
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> predictor = MathOptAI.PytorchModel("saved_pytorch_model.pt");
julia> y, formulation =
+           MathOptAI.add_predictor(model, predictor, x; reduced_space = true);
julia> y1-element Vector{JuMP.NonlinearExpr}:
+ ((+(0.0) + (-0.4644489884376526 * max(0.0, 0.7473132610321045 x[1] - 0.27370238304138184))) + (0.5382549166679382 * max(0.0, -0.8237636089324951 x[1] - 0.08490216732025146))) + -0.5698285102844238
julia> formulationReducedSpace(Affine(A, b) [input: 1, output: 2])
+├ variables [0]
+└ constraints [0]
+ReducedSpace(MathOptAI.ReLU())
+├ variables [0]
+└ constraints [0]
+ReducedSpace(Affine(A, b) [input: 2, output: 1])
+├ variables [0]
+└ constraints [0]

Gray-box

Use the gray_box = true keyword to embed the network as a nonlinear operator:

julia> using JuMP, MathOptAI
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> predictor = MathOptAI.PytorchModel("saved_pytorch_model.pt");
julia> y, formulation =
+           MathOptAI.add_predictor(model, predictor, x; gray_box = true);
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_GrayBox[1]
julia> formulationGrayBox
+├ variables [1]
+│ └ moai_GrayBox[1]
+└ constraints [1]
+  └ op_##1242(x[1]) - moai_GrayBox[1] = 0

Change how layers are formulated

Pass a dictionary to the config keyword that maps the Symbol name of each PyTorch layer to a MathOptAI predictor:

julia> using JuMP, MathOptAI
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> predictor = MathOptAI.PytorchModel("saved_pytorch_model.pt");
julia> y, formulation = MathOptAI.add_predictor(
+           model,
+           predictor,
+           x;
+           config = Dict(:ReLU => MathOptAI.ReLUSOS1()),
+       );
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_Affine[1]
julia> formulationAffine(A, b) [input: 1, output: 2]
+├ variables [2]
+│ ├ moai_Affine[1]
+│ └ moai_Affine[2]
+└ constraints [2]
+  ├ 0.7473132610321045 x[1] - moai_Affine[1] = 0.27370238304138184
+  └ -0.8237636089324951 x[1] - moai_Affine[2] = 0.08490216732025146
+MathOptAI.ReLUSOS1()
+├ variables [4]
+│ ├ moai_ReLU[1]
+│ ├ moai_ReLU[2]
+│ ├ moai_z[1]
+│ └ moai_z[2]
+└ constraints [6]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[2] ≥ 0
+  ├ moai_Affine[1] - moai_ReLU[1] + moai_z[1] = 0
+  ├ moai_Affine[2] - moai_ReLU[2] + moai_z[2] = 0
+  ├ [moai_ReLU[1], moai_z[1]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])
+  └ [moai_ReLU[2], moai_z[2]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ -0.4644489884376526 moai_ReLU[1] + 0.5382549166679382 moai_ReLU[2] - moai_Affine[1] = 0.5698285102844238
diff --git a/dev/manual/predictors/index.html b/dev/manual/predictors/index.html new file mode 100644 index 00000000..9baac358 --- /dev/null +++ b/dev/manual/predictors/index.html @@ -0,0 +1,2 @@ + +Predictors · MathOptAI.jl
GitHub

Predictors

The main entry point for embedding prediction models into JuMP is add_predictor.

All methods use the form y, formulation = MathOptAI.add_predictor(model, predictor, x) to add the relationship y = predictor(x) to model.

Supported predictors

The following predictors are supported. See their docstrings for details:

PredictorRelationshipDimensions
Affine$f(x) = Ax + b$$M \rightarrow N$
BinaryDecisionTreeA binary decision tree$M \rightarrow 1$
GrayBox$f(x)$$M \rightarrow N$
Pipeline$f(x) = (l_1 \circ \ldots \circ l_N)(x)$$M \rightarrow N$
QuantileThe quantiles of a distribution$M \rightarrow N$
ReLU$f(x) = \max.(0, x)$$M \rightarrow M$
ReLUBigM$f(x) = \max.(0, x)$$M \rightarrow M$
ReLUQuadratic$f(x) = \max.(0, x)$$M \rightarrow M$
ReLUSOS1$f(x) = \max.(0, x)$$M \rightarrow M$
Scale$f(x) = scale .* x .+ bias$$M \rightarrow M$
Sigmoid$f(x) = \frac{1}{1 + e^{-x}}$$M \rightarrow M$
SoftMax$f(x) = \frac{e^x}{\sum e^{x_i}}$$M \rightarrow M$
SoftPlus$f(x) = \frac{1}{\beta} \log(1 + e^{\beta x})$$M \rightarrow M$
Tanh$f(x) = \tanh.(x)$$M \rightarrow M$

Note that some predictors, such as the ReLU ones, offer multiple formulations of the same mathematical relationship. The ''right'' choice is solver- and problem-dependent.

ReLU

There are a number of different mathematical formulations for the rectified linear unit (ReLU).

  • ReLU: requires the solver to support the max nonlinear operator.
  • ReLUBigM: requires the solver to support mixed-integer linear programs, and requires the user to have prior knowledge of a suitable value for the "big-M" parameter.
  • ReLUQuadratic: requires the solver to support quadratic equality constraints
  • ReLUSOS1: requires the solver to support SOS-I constraints.

The correct choice for which ReLU formulation to use is problem- and solver-dependent.

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zz#BKM=3ObS?n+i+a17|Zf9X!Q&kd|+_GomjNqYLfm6=`?$jCr+z8_FsA4a`ieFtq?LEn} zS9_k<8z!*&=|}MOHS|wO9}6=com~>i1&kTgp)lnReO7_YKi}RCI#j=P)uy!%-YSn@ zmKM~Z=&{s8*|1oznqR|-)txw)+4aa1q^ds^4T93{RyjcGjPip*&7B}f)$Phba({jW z#2u6o0eS6Mc}B}Yub7XH2OQJf)C@!%bgCWuxT+nCi3b^T5bCw-q`Z?Jr33tD81+s= z&;N^HN0<$F>G=*Ga&rF&ruwJDcOBGSMWG{<-?GE4!+ez=Up1O^RefJM2$o&z|0N 2, Flux.relu), Flux.Dense(2 => 1));\nmodel = Model();\n@variable(model, x[1:1]);\ny, formulation = MathOptAI.add_predictor(model, predictor, x);\ny\nformulation","category":"page"},{"location":"manual/Flux/#Reduced-space","page":"Flux.jl","title":"Reduced-space","text":"","category":"section"},{"location":"manual/Flux/","page":"Flux.jl","title":"Flux.jl","text":"Use the reduced_space = true keyword to formulate a reduced-space model:","category":"page"},{"location":"manual/Flux/","page":"Flux.jl","title":"Flux.jl","text":"using JuMP, Flux, MathOptAI\npredictor = Flux.Chain(Flux.Dense(1 => 2, Flux.relu), Flux.Dense(2 => 1));\nmodel = Model();\n@variable(model, x[1:1]);\ny, formulation =\n MathOptAI.add_predictor(model, predictor, x; reduced_space = true);\ny\nformulation","category":"page"},{"location":"manual/Flux/#Gray-box","page":"Flux.jl","title":"Gray-box","text":"","category":"section"},{"location":"manual/Flux/","page":"Flux.jl","title":"Flux.jl","text":"Use the gray_box = true keyword to embed the network as a nonlinear operator:","category":"page"},{"location":"manual/Flux/","page":"Flux.jl","title":"Flux.jl","text":"using JuMP, Flux, MathOptAI\npredictor = Flux.Chain(Flux.Dense(1 => 2, Flux.relu), Flux.Dense(2 => 1));\nmodel = Model();\n@variable(model, x[1:1]);\ny, formulation =\n MathOptAI.add_predictor(model, predictor, x; gray_box = true);\ny\nformulation","category":"page"},{"location":"manual/Flux/#Change-how-layers-are-formulated","page":"Flux.jl","title":"Change how layers are formulated","text":"","category":"section"},{"location":"manual/Flux/","page":"Flux.jl","title":"Flux.jl","text":"Pass a dictionary to the config keyword that maps Flux activation functions to a MathOptAI predictor:","category":"page"},{"location":"manual/Flux/","page":"Flux.jl","title":"Flux.jl","text":"using JuMP, Flux, MathOptAI\npredictor = Flux.Chain(Flux.Dense(1 => 2, Flux.relu), Flux.Dense(2 => 1));\nmodel = Model();\n@variable(model, x[1:1]);\ny, formulation = MathOptAI.add_predictor(\n model,\n predictor,\n x;\n config = Dict(Flux.relu => MathOptAI.ReLUSOS1()),\n);\ny\nformulation","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"EditURL = \"mnist.jl\"","category":"page"},{"location":"tutorials/mnist/#Adversarial-machine-learning-with-Flux.jl","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"","category":"section"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"The purpose of this tutorial is to explain how to embed a neural network model from Flux.jl into JuMP.","category":"page"},{"location":"tutorials/mnist/#Required-packages","page":"Adversarial machine learning with Flux.jl","title":"Required packages","text":"","category":"section"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"This tutorial requires the following packages","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"using JuMP\nimport Flux\nimport Ipopt\nimport MathOptAI\nimport MLDatasets\nimport Plots","category":"page"},{"location":"tutorials/mnist/#Data","page":"Adversarial machine learning with Flux.jl","title":"Data","text":"","category":"section"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"This tutorial uses images from the MNIST dataset.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"We load the predefined train and test splits:","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"train_data = MLDatasets.MNIST(; split = :train)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"test_data = MLDatasets.MNIST(; split = :test)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Since the data are images, it is helpful to plot them. (This requires a transpose and reversing the rows to get the orientation correct.)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"function plot_image(x::Matrix; kwargs...)\n return Plots.heatmap(\n x'[size(x, 1):-1:1, :];\n xlims = (1, size(x, 2)),\n ylims = (1, size(x, 1)),\n aspect_ratio = true,\n legend = false,\n xaxis = false,\n yaxis = false,\n kwargs...,\n )\nend\n\nfunction plot_image(instance::NamedTuple)\n return plot_image(instance.features; title = \"Label = $(instance.targets)\")\nend\n\nPlots.plot([plot_image(train_data[i]) for i in 1:6]...; layout = (2, 3))","category":"page"},{"location":"tutorials/mnist/#Training","page":"Adversarial machine learning with Flux.jl","title":"Training","text":"","category":"section"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"We use a simple neural network with one hidden layer and a sigmoid activation function. (There are better performing networks; try experimenting.)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"predictor = Flux.Chain(\n Flux.Dense(28^2 => 32, Flux.sigmoid),\n Flux.Dense(32 => 10),\n Flux.softmax,\n)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Here is a function to load our data into the format that predictor expects:","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"function data_loader(data; batchsize, shuffle = false)\n x = reshape(data.features, 28^2, :)\n y = Flux.onehotbatch(data.targets, 0:9)\n return Flux.DataLoader((x, y); batchsize, shuffle)\nend","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"and here is a function to score the percentage of correct labels, where we assign a label by choosing the label of the highest softmax in the final layer.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"function score_model(predictor, data)\n x, y = only(data_loader(data; batchsize = length(data)))\n y_hat = predictor(x)\n is_correct = Flux.onecold(y) .== Flux.onecold(y_hat)\n p = round(100 * sum(is_correct) / length(is_correct); digits = 2)\n println(\"Accuracy = $p %\")\n return\nend","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"The accuracy of our model is only around 10% before training:","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"score_model(predictor, train_data)\nscore_model(predictor, test_data)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Let's improve that by training our model.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"note: Note\nIt is not the purpose of this tutorial to explain how Flux works; see the documentation at https://fluxml.ai for more details. Changing the number of epochs or the learning rate can improve the loss.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"begin\n train_loader = data_loader(train_data; batchsize = 256, shuffle = true)\n optimizer_state = Flux.setup(Flux.Adam(3e-4), predictor)\n for epoch in 1:30\n loss = 0.0\n for (x, y) in train_loader\n loss_batch, gradient = Flux.withgradient(predictor) do model\n return Flux.crossentropy(model(x), y)\n end\n Flux.update!(optimizer_state, predictor, only(gradient))\n loss += loss_batch\n end\n loss = round(loss / length(train_loader); digits = 4)\n print(\"Epoch $epoch: loss = $loss\\t\")\n score_model(predictor, test_data)\n end\nend","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Here are the first eight predictions of the test data:","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"function plot_image(predictor, x::Matrix)\n score, index = findmax(predictor(vec(x)))\n title = \"Predicted: $(index - 1) ($(round(Int, 100 * score))%)\"\n return plot_image(x; title)\nend\n\nplots = [plot_image(predictor, test_data[i].features) for i in 1:8]\nPlots.plot(plots...; size = (1200, 600), layout = (2, 4))","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"We can also look at the best and worst four predictions:","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"x, y = only(data_loader(test_data; batchsize = length(test_data)))\nlosses = Flux.crossentropy(predictor(x), y; agg = identity)\nindices = sortperm(losses; dims = 2)[[1:4; end-3:end]]\nplots = [plot_image(predictor, test_data[i].features) for i in indices]\nPlots.plot(plots...; size = (1200, 600), layout = (2, 4))","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"There are still some fairly bad mistakes. Can you change the model or training parameters improve to improve things?","category":"page"},{"location":"tutorials/mnist/#JuMP","page":"Adversarial machine learning with Flux.jl","title":"JuMP","text":"","category":"section"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Now that we have a trained machine learning model, we can embed it in a JuMP model.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Here's a function which takes a test case and returns an example that maximizes the probability of the adversarial example.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"function find_adversarial_image(test_case; adversary_label, δ = 0.05)\n model = Model(Ipopt.Optimizer)\n set_silent(model)\n @variable(model, 0 <= x[1:28, 1:28] <= 1)\n @constraint(model, -δ .<= x .- test_case.features .<= δ)\n # Note: we need to use `vec` here because `x` is a 28-by-28 Matrix, but our\n # neural network expects a 28^2 length vector.\n y, _ = MathOptAI.add_predictor(model, predictor, vec(x))\n @objective(model, Max, y[adversary_label+1] - y[test_case.targets+1])\n optimize!(model)\n @assert is_solved_and_feasible(model)\n return value.(x)\nend","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Let's try finding an adversarial example to the third test image. The image on the left is our input image. The network thinks this is a 1 with probability 99%. The image on the right is the adversarial image. The network thinks this is a 7, although it is less confident.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"x_adversary = find_adversarial_image(test_data[3]; adversary_label = 7);\nPlots.plot(\n plot_image(predictor, test_data[3].features),\n plot_image(predictor, Float32.(x_adversary)),\n)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"This page was generated using Literate.jl.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"EditURL = \"student_enrollment.jl\"","category":"page"},{"location":"tutorials/student_enrollment/#Logistic-regression-with-GLM.jl","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"","category":"section"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The purpose of this tutorial is to explain how to embed a logistic regression model from GLM.jl into JuMP.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The data and example in this tutorial comes from the paper: David Bergman, Teng Huang, Philip Brooks, Andrea Lodi, Arvind U. Raghunathan (2021) JANOS: An Integrated Predictive and Prescriptive Modeling Framework. INFORMS Journal on Computing 34(2):807-816. https://doi.org/10.1287/ijoc.2020.1023","category":"page"},{"location":"tutorials/student_enrollment/#Required-packages","page":"Logistic regression with GLM.jl","title":"Required packages","text":"","category":"section"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"This tutorial uses the following packages.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"using JuMP\nimport CSV\nimport DataFrames\nimport Downloads\nimport GLM\nimport Ipopt\nimport MathOptAI\nimport Statistics","category":"page"},{"location":"tutorials/student_enrollment/#Data","page":"Logistic regression with GLM.jl","title":"Data","text":"","category":"section"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Here is a function to load the data directly from the JANOS repository:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"function read_df(filename)\n url = \"https://raw.githubusercontent.com/INFORMSJoC/2020.1023/master/data/\"\n data = Downloads.download(url * filename)\n return CSV.read(data, DataFrames.DataFrame)\nend","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"There are two important files. The first, college_student_enroll-s1-1.csv, contains historical admissions data on anonymized students, their SAT score, their GPA, their merit scholarships, and whether the enrolled in the college.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"train_df = read_df(\"college_student_enroll-s1-1.csv\")","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The second, college_applications6000.csv, contains the SAT and GPA data of students who are currently applying:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"evaluate_df = read_df(\"college_applications6000.csv\")","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"There are 6,000 prospective students:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"n_students = size(evaluate_df, 1)","category":"page"},{"location":"tutorials/student_enrollment/#Prediction-model","page":"Logistic regression with GLM.jl","title":"Prediction model","text":"","category":"section"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The first step is to train a logistic regression model to predict the Boolean enroll column based on the SAT, GPA, and merit columns.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"predictor = GLM.glm(\n GLM.@formula(enroll ~ 0 + SAT + GPA + merit),\n train_df,\n GLM.Bernoulli(),\n)","category":"page"},{"location":"tutorials/student_enrollment/#Decision-model","page":"Logistic regression with GLM.jl","title":"Decision model","text":"","category":"section"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Now that we have a trained logistic regression model, we want a decision model that chooses the optimal merit scholarship for each student in","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"evaluate_df","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Here's an empty JuMP model to start:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"model = Model()","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"First, we add a new column to evaluate_df, with one JuMP decision variable for each row. It is important the .merit column name in evaluate_df matches the name in train_df.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"evaluate_df.merit = @variable(model, 0 <= x_merit[1:n_students] <= 2.5);\nevaluate_df","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Then, we use MathOptAI.add_predictor to embed predictor into the JuMP model. MathOptAI.add_predictor returns a vector of variables, one for each row inn evaluate_df, corresponding to the output enroll of our logistic regression.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"evaluate_df.enroll, _ = MathOptAI.add_predictor(model, predictor, evaluate_df);\nevaluate_df","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The .enroll column name in evaluate_df is just a name. It doesn't have to match the name in train_df.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The objective of our problem is to maximize the expected number of students who enroll:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"@objective(model, Max, sum(evaluate_df.enroll))","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Subject to the constraint that we can spend at most 0.2 * n_students on merit scholarships:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"@constraint(model, sum(evaluate_df.merit) <= 0.2 * n_students)","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Because logistic regression involves a Sigmoid layer, we need to use a smooth nonlinear optimizer. A common choice is Ipopt. Solve and check the optimizer found a feasible solution:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"set_optimizer(model, Ipopt.Optimizer)\nset_silent(model)\noptimize!(model)\n@assert is_solved_and_feasible(model)\nsolution_summary(model)","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Let's store the solution in evaluate_df for analysis:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"evaluate_df.merit_sol = value.(evaluate_df.merit);\nevaluate_df.enroll_sol = value.(evaluate_df.enroll);\nevaluate_df","category":"page"},{"location":"tutorials/student_enrollment/#Solution-analysis","page":"Logistic regression with GLM.jl","title":"Solution analysis","text":"","category":"section"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"We expect that just under 2,500 students will enroll:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"sum(evaluate_df.enroll_sol)","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"We awarded merit scholarships to approximately 1 in 6 students:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"count(evaluate_df.merit_sol .> 1e-5)","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The average merit scholarship was worth just over $1,000:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"1_000 * Statistics.mean(evaluate_df.merit_sol[evaluate_df.merit_sol.>1e-5])","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"This page was generated using Literate.jl.","category":"page"},{"location":"manual/GLM/#GLM.jl","page":"GLM.jl","title":"GLM.jl","text":"","category":"section"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"GLM.jl is a library for fitting generalized linear models in Julia.","category":"page"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"MathOptAI.jl supports embedding two types of regression models from GLM:","category":"page"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"GLM.lm(X, Y)\nGLM.glm(X, Y, GLM.Bernoulli())","category":"page"},{"location":"manual/GLM/#Linear-regression","page":"GLM.jl","title":"Linear regression","text":"","category":"section"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"The input x to add_predictor must be a vector with the same number of elements as columns in the training matrix. The return is a vector of JuMP variables with a single element.","category":"page"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"using GLM, JuMP, MathOptAI\nX, Y = rand(10, 2), rand(10);\npredictor = GLM.lm(X, Y);\nmodel = Model();\n@variable(model, x[1:2]);\ny, formulation = MathOptAI.add_predictor(model, predictor, x);\ny\nformulation","category":"page"},{"location":"manual/GLM/#Logistic-regression","page":"GLM.jl","title":"Logistic regression","text":"","category":"section"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"The input x to add_predictor must be a vector with the same number of elements as columns in the training matrix. The return is a vector of JuMP variables with a single element.","category":"page"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"using GLM, JuMP, MathOptAI\nX, Y = rand(10, 2), rand(Bool, 10);\npredictor = GLM.glm(X, Y, GLM.Bernoulli());\nmodel = Model();\n@variable(model, x[1:2]);\ny, formulation = MathOptAI.add_predictor(model, predictor, x);\ny\nformulation","category":"page"},{"location":"manual/GLM/#DataFrames","page":"GLM.jl","title":"DataFrames","text":"","category":"section"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"DataFrames.jl can be used with GLM.jl.","category":"page"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"The input x to add_predictor must be a DataFrame with the same feature columns as the training DataFrame. The return is a vector of JuMP variables, with one element for each row in the DataFrame.","category":"page"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"using DataFrames, GLM, JuMP, MathOptAI\ntrain_df = DataFrames.DataFrame(x1 = rand(10), x2 = rand(10));\ntrain_df.y = 1.0 .* train_df.x1 + 2.0 .* train_df.x2 .+ rand(10);\npredictor = GLM.lm(GLM.@formula(y ~ x1 + x2), train_df);\nmodel = Model();\ntest_df = DataFrames.DataFrame(\n x1 = rand(6),\n x2 = @variable(model, [1:6]),\n);\ntest_df.y, _ = MathOptAI.add_predictor(model, predictor, test_df);\ntest_df.y","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"CurrentModule = MathOptAI","category":"page"},{"location":"developers/design_principles/#Design-principles","page":"Design principles","title":"Design principles","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"This project is inspired by two existing projects:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"OMLT\ngurobi-machinelearning","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"OMLT is a framework built around Pyomo, and gurobi-machinelearning is a framework build around gurobipy.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"These projects served as inspiration, but we also departed from them in some carefully considered ways.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"All of our design decisions were guided by two principles:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"To be simple\nTo leverage Julia's Pkg extensions and multiple dispatch.","category":"page"},{"location":"developers/design_principles/#Terminology","page":"Design principles","title":"Terminology","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Because the field is relatively new, there is no settled choice of terminology.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"MathOptAI chooses to use \"predictor\" as the synonym for the machine learning model. Hence, we have AbstractPredictor, add_predictor, and build_predictor.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In contrast, gurobi-machinelearning tends to use \"regression model\" and OMLT uses \"formulation.\"","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"We choose \"predictor\" because all models we implement are of the form y = f(x).","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"We do not use \"machine learning model\" because we have support for the linear and logistic regression models of classical statistical fitting. We could have used \"regression model,\" but we find that models like neural networks and binary decision trees are not commonly thought of as regression models.","category":"page"},{"location":"developers/design_principles/#Inputs-are-vectors","page":"Design principles","title":"Inputs are vectors","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"MathOptAI assumes that all inputs x and outputs y to y = predictor(x) are Base.Vectors.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"We make this choice for simplicity.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In our opinion, Julia libraries often take a laissez-faire approach to the types that they support. In the optimistic case, this can lead to novel behavior by combining two packages that the package author had previously not considered or tested. In the pessimistic case, this can lead to incorrect results or cryptic error messages.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Exceptions to the Vector rule will be carefully considered and tested.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Currently, there are two exceptions:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"If x is a Matrix, then the columns of x are interpreted as independent observations, and the output y will be a Matrix with the same number of columns\nThe StatsModels extension allows x to be a DataFrames.DataFrame, if the predictor is a StatsModels.TableRegressionModel.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Exceptions 1 and 2 are combined in the StatsModels exception, so that the predictor is mapped over the rows of the DataFrames.DataFrame (which we assume will be a common use-case).","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"We choose to interpret the rows as input variables and columns as independent observations (rather than the more traditional table-based approach where columns are the input variables and rows are observations) because Julia uses column-major ordering in Matrix. Another justification follows from the Affine predictor, f(x) = Ax + b, where passing in a Matrix as x with column observations naturally leads to a Matrix output for y of the appropriate dimensions.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"We choose to make y a Vector, even for scalar outputs, to simplify code that works generically for many different predictors. Without this principle, there will inevitably be cases where a scalar and length-1 vector are confused.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"If you want to use a predictor that does not take Vector input (for example, it is an image as input to a neural network), the first preprocessing step should be to vec the input into a single Vector.","category":"page"},{"location":"developers/design_principles/#Inputs-are-provided,-outputs-are-returned","page":"Design principles","title":"Inputs are provided, outputs are returned","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The main job of MathOptAI is to embed models of the form y = predictor(x) into a JuMP model. A key design decision is how to represent the input x and output y.","category":"page"},{"location":"developers/design_principles/#gurobi-machinelearning","page":"Design principles","title":"gurobi-machinelearning","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"gurobi-machinelearning implements an API of the following general form:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"pred_constr = add_predictor_constr(model, predictor, x, y)","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Here, both the input x and the output y must be created and provided by the user, and a new object pred_constr is returned.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The benefit of this design is that pred_constr can contain statistics about the reformulation (for example, the number of variables that were added), and it can be used to delete a predictor from model.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The downside is that the user must ensure that the shape and size of y is correct.","category":"page"},{"location":"developers/design_principles/#OMLT","page":"Design principles","title":"OMLT","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"OMLT implements an API of the following general form:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"model.pred_constr = OmltBlock()\nmodel.pred_constr.build_formulation(predictor)\nx, y = model.pred_constr.inputs, model.pred_constr.outputs","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"First, a new OmltBlock() is created. Then the formulation is built inside the block, and both the input and output are provided to the user.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The benefit of this design is that pred_constr can contain statistics about the reformulation (for example, the number of variables that were added), and it can be used to delete a predictor from model.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The downside is that the user must often write additional constraints to connect the input and output of the OmltBlock to their existing decision variables:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"#connect pyomo model input and output to the neural network\n@model.Constraint()\ndef connect_input(mdl):\n return mdl.input == mdl.nn.inputs[0]\n\n@model.Constraint()\ndef connect_output(mdl):\n return mdl.output == mdl.nn.outputs[0]","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"A second downside is that the predictor must describe the input and output dimension; these cannot be inferred automatically. As one example, this means that it cannot do the following:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"# Not possible because dimension not given\nmodel.pred_constr.build_formulation(ReLU())","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In the context of MathOptAI, something like ReLU() is useful so that we can map generic layers like Flux.relu => MathOptAI.ReLU(), and so that we do not duplicate required dimension information in input and predictor (see the MathOptAI section below).","category":"page"},{"location":"developers/design_principles/#MathOptAI","page":"Design principles","title":"MathOptAI","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The main entry-point to MathOptAI is add_predictor:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"y, formulation = MathOptAI.add_predictor(model, predictor, x)","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The user provides the input x, and the output y is returned.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The main benefit of this approach is simplicity.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"First, the user probably already has the input x as decision variables or an expression in the model, so we do not need the connect_input constraint, and because we use a full-space formulation by default, the output y will always be a vector of decision variables, which avoids the need for a connect_output constraint.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Second, predictors do not need to store dimension information, so we can have:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"y, formulation = MathOptAI.add_predictor(model, MathOptAI.ReLU(), x)","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"for any size of x.","category":"page"},{"location":"developers/design_principles/#Activations-are-predictors","page":"Design principles","title":"Activations are predictors","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"OMLT makes a distinction between layers, like full_space_dense_layer, and elementwise activation functions, like sigmoid_activation_function.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The downside to this approach is that it treats activation functions as special, leading to issues such as OMLT#125.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In contrast, MathOptAI treats activation functions as a vector-valued predictor like any other:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"y, formulation = MathOptAI.add_predictor(model, MathOptAI.ReLU(), x)","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"This means that we can pipeline them to create predictors such as:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"function LogisticRegression(A)\n return MathOptAI.Pipeline(MathOptAI.Affine(A), MathOptAI.Sigmoid())\nend","category":"page"},{"location":"developers/design_principles/#Controlling-transformations","page":"Design principles","title":"Controlling transformations","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Many predictors have multiple ways that they can be formulated in an optimization model. For example, ReLU implements the non-smooth nonlinear formulation y = maxx 0, while ReLUQuadratic implements a the complementarity formulation x = y - slack y slack ge 0 y * slack = 0.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Choosing the appropriate formulation for the combination of model and solver can have a large impact on the performance.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Because gurobi-machinelearning is specific to the Gurobi solver, they have a limited ability for the user to choose and implement different formulations.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"OMLT is more general, in that it has multiple ways of formulating layers such as ReLU. However, these are hard-coded into complete formulations such as omlt.neuralnet.nn_formulation.ReluBigMFormulation or omlt.neuralnet.nn_formulation.ReluComplementarityFormulation.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In contrast, MathOptAI tries to take a maximally modular approach, where the user can control how the layers are formulated at runtime, including using a custom formulation that is not defined in MathOptAI.jl.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Currently, we achieve this with a config dictionary, which maps the various neural network layers to an AbstractPredictor. For example:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));\nconfig = Dict(Flux.relu => MathOptAI.ReLU())\npredictor = MathOptAI.build_predictor(chain; config)","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Please open a GitHub issue if you have a suggestion for a better API.","category":"page"},{"location":"developers/design_principles/#Full-space-or-reduced-space","page":"Design principles","title":"Full-space or reduced-space","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"OMLT has two ways that it can formulate neural networks: full-space and reduced-space.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The full-space formulations add intermediate variables to represent the output of all layers.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"For example, in a Flux.Dense(2, 3, Flux.relu) layer, a full-space formulation will add an intermediate y_tmp variable to represent the output of the affine layer prior to the ReLU:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"layer = Flux.Dense(2, 3, Flux.relu)\nmodel_full_space = Model()\n@variable(model_full_space, x[1:2])\n@variable(model_full_space, y_tmp[1:3])\n@variable(model_full_space, y[1:3])\n@constraint(model_full_space, y_tmp == layer.A * x + layer.b)\n@constraint(model_full_space, y .== max.(0, y_tmp))","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In contrast, a reduced-space formulation encodes the input-output relationship as a single nonlinear constraint:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"layer = Flux.Dense(2, 3, Flux.relu)\nmodel_reduced_space = Model()\n@variable(model_reduced_space, x[1:2])\n@variable(model_reduced_space, y[1:3])\n@constraint(model_reduced_space, y .== max.(0, layer.A * x + layer.b))","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In general, the full-space formulations have more variables and constraints but simpler nonlinear expressions, whereas the reduced-space formulations have fewer variables and constraints but more complicated nonlinear expressions.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"MathOptAI.jl implements the full-space formulation by default, but some layers support the reduced-space formulation with the ReducedSpace wrapper.","category":"page"},{"location":"manual/DecisionTree/#DecisionTree.jl","page":"DecisionTree.jl","title":"DecisionTree.jl","text":"","category":"section"},{"location":"manual/DecisionTree/","page":"DecisionTree.jl","title":"DecisionTree.jl","text":"DecisionTree.jl is a library for fitting decision trees in Julia.","category":"page"},{"location":"manual/DecisionTree/#Basic-example","page":"DecisionTree.jl","title":"Basic example","text":"","category":"section"},{"location":"manual/DecisionTree/","page":"DecisionTree.jl","title":"DecisionTree.jl","text":"Here is an example:","category":"page"},{"location":"manual/DecisionTree/","page":"DecisionTree.jl","title":"DecisionTree.jl","text":"using JuMP, MathOptAI, DecisionTree\ntruth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)\nfeatures = abs.(sin.((1:10) .* (3:4)'));\nsize(features)\nlabels = truth.(Vector.(eachrow(features)));\npredictor = DecisionTree.build_tree(labels, features)\nmodel = Model();\n@variable(model, 0 <= x[1:2] <= 1);\ny, formulation = MathOptAI.add_predictor(model, predictor, x);\ny\nformulation","category":"page"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"CurrentModule = MathOptAI","category":"page"},{"location":"manual/predictors/#Predictors","page":"Predictors","title":"Predictors","text":"","category":"section"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"The main entry point for embedding prediction models into JuMP is add_predictor.","category":"page"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"All methods use the form y, formulation = MathOptAI.add_predictor(model, predictor, x) to add the relationship y = predictor(x) to model.","category":"page"},{"location":"manual/predictors/#Supported-predictors","page":"Predictors","title":"Supported predictors","text":"","category":"section"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"The following predictors are supported. See their docstrings for details:","category":"page"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"Predictor Relationship Dimensions\nAffine f(x) = Ax + b M rightarrow N\nBinaryDecisionTree A binary decision tree M rightarrow 1\nGrayBox f(x) M rightarrow N\nPipeline f(x) = (l_1 circ ldots circ l_N)(x) M rightarrow N\nQuantile The quantiles of a distribution M rightarrow N\nReLU f(x) = max(0 x) M rightarrow M\nReLUBigM f(x) = max(0 x) M rightarrow M\nReLUQuadratic f(x) = max(0 x) M rightarrow M\nReLUSOS1 f(x) = max(0 x) M rightarrow M\nScale f(x) = scale * x + bias M rightarrow M\nSigmoid f(x) = frac11 + e^-x M rightarrow M\nSoftMax f(x) = frace^xsum e^x_i M rightarrow M\nSoftPlus f(x) = frac1beta log(1 + e^beta x) M rightarrow M\nTanh f(x) = tanh(x) M rightarrow M","category":"page"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"Note that some predictors, such as the ReLU ones, offer multiple formulations of the same mathematical relationship. The ''right'' choice is solver- and problem-dependent.","category":"page"},{"location":"manual/predictors/#ReLU","page":"Predictors","title":"ReLU","text":"","category":"section"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"There are a number of different mathematical formulations for the rectified linear unit (ReLU).","category":"page"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"ReLU: requires the solver to support the max nonlinear operator.\nReLUBigM: requires the solver to support mixed-integer linear programs, and requires the user to have prior knowledge of a suitable value for the \"big-M\" parameter.\nReLUQuadratic: requires the solver to support quadratic equality constraints\nReLUSOS1: requires the solver to support SOS-I constraints.","category":"page"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"The correct choice for which ReLU formulation to use is problem- and solver-dependent.","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"CurrentModule = MathOptAI","category":"page"},{"location":"api/#API-Reference","page":"API Reference","title":"API Reference","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"This page lists the public API of MathOptAI.","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"info: Info\nThis page is an unstructured list of the MathOptAI API. For a more structured overview, read the Manual or Tutorial parts of this documentation.","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Load all of the public the API into the current scope with:","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"using MathOptAI","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Alternatively, load only the module with:","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"import MathOptAI","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"and then prefix all calls with MathOptAI. to create MathOptAI..","category":"page"},{"location":"api/#AbstractPredictor","page":"API Reference","title":"AbstractPredictor","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"AbstractPredictor","category":"page"},{"location":"api/#MathOptAI.AbstractPredictor","page":"API Reference","title":"MathOptAI.AbstractPredictor","text":"abstract type AbstractPredictor end\n\nAn abstract type representing different types of prediction models.\n\nMethods\n\nAll subtypes must implement:\n\nadd_predictor\nbuild_predictor\n\n\n\n\n\n","category":"type"},{"location":"api/#add_predictor","page":"API Reference","title":"add_predictor","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"add_predictor","category":"page"},{"location":"api/#MathOptAI.add_predictor","page":"API Reference","title":"MathOptAI.add_predictor","text":"add_predictor(\n model::JuMP.AbstractModel,\n predictor::AbstractPredictor,\n x::Vector,\n)::Vector\n\nReturn a Vector representing y such that y = predictor(x).\n\nThe element type of x is deliberately unspecified. The vector x may contain any mix of scalar constants, JuMP decision variables, and scalar JuMP functions like AffExpr, QuadExpr, or NonlinearExpr.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.Affine([2.0, 3.0])\nAffine(A, b) [input: 2, output: 1]\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Affine[1]\n\njulia> formulation\nAffine(A, b) [input: 2, output: 1]\n├ variables [1]\n│ └ moai_Affine[1]\n└ constraints [1]\n └ 2 x[1] + 3 x[2] - moai_Affine[1] = 0\n\n\n\n\n\n","category":"function"},{"location":"api/#build_predictor","page":"API Reference","title":"build_predictor","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"build_predictor(predictor::AbstractPredictor; kwargs...)","category":"page"},{"location":"api/#MathOptAI.build_predictor-Tuple{MathOptAI.AbstractPredictor}","page":"API Reference","title":"MathOptAI.build_predictor","text":"build_predictor(extension; kwargs...)::AbstractPredictor\n\nA uniform interface to convert various extension types to an AbstractPredictor.\n\nSee the various extension docstrings for details.\n\n\n\n\n\n","category":"method"},{"location":"api/#Affine","page":"API Reference","title":"Affine","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Affine","category":"page"},{"location":"api/#MathOptAI.Affine","page":"API Reference","title":"MathOptAI.Affine","text":"Affine(\n A::Matrix{T},\n b::Vector{T} = zeros(T, size(A, 1)),\n) where {T} <: AbstractPredictor\n\nAn AbstractPredictor that represents the relationship:\n\ny = A x + b\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, 0 <= x[i in 1:2] <= i);\n\njulia> f = MathOptAI.Affine([2.0 3.0], [4.0])\nAffine(A, b) [input: 2, output: 1]\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Affine[1]\n\njulia> formulation\nAffine(A, b) [input: 2, output: 1]\n├ variables [1]\n│ └ moai_Affine[1]\n└ constraints [3]\n ├ moai_Affine[1] ≥ 4\n ├ moai_Affine[1] ≤ 12\n └ 2 x[1] + 3 x[2] - moai_Affine[1] = -4\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n1-element Vector{AffExpr}:\n 2 x[1] + 3 x[2] + 4\n\njulia> formulation\nReducedSpace(Affine(A, b) [input: 2, output: 1])\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#BinaryDecisionTree","page":"API Reference","title":"BinaryDecisionTree","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"BinaryDecisionTree","category":"page"},{"location":"api/#MathOptAI.BinaryDecisionTree","page":"API Reference","title":"MathOptAI.BinaryDecisionTree","text":"BinaryDecisionTree{K,V}(\n feat_id::Int,\n feat_value::K,\n lhs::Union{V,BinaryDecisionTree{K,V}},\n rhs::Union{V,BinaryDecisionTree{K,V}},\n)\n\nAn AbstractPredictor that represents a binary decision tree.\n\nIf x[feat_id] <= feat_value, then return lhs\nIf x[feat_id] > feat_value, then return rhs\n\nExample\n\nTo represent the tree x[1] <= 0.0 ? -1 : (x[1] <= 1.0 ? 0 : 1), do:\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:1]);\n\njulia> f = MathOptAI.BinaryDecisionTree{Float64,Int}(\n 1,\n 0.0,\n -1,\n MathOptAI.BinaryDecisionTree{Float64,Int}(1, 1.0, 0, 1),\n )\nBinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_BinaryDecisionTree_value\n\njulia> formulation\nBinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]\n├ variables [4]\n│ ├ moai_BinaryDecisionTree_value\n│ ├ moai_BinaryDecisionTree_z[1]\n│ ├ moai_BinaryDecisionTree_z[2]\n│ └ moai_BinaryDecisionTree_z[3]\n└ constraints [7]\n ├ moai_BinaryDecisionTree_z[1] + moai_BinaryDecisionTree_z[2] + moai_BinaryDecisionTree_z[3] = 1\n ├ moai_BinaryDecisionTree_z[1] --> {x[1] ≤ 0}\n ├ moai_BinaryDecisionTree_z[2] --> {x[1] ≥ 0}\n ├ moai_BinaryDecisionTree_z[2] --> {x[1] ≤ 1}\n ├ moai_BinaryDecisionTree_z[3] --> {x[1] ≥ 0}\n ├ moai_BinaryDecisionTree_z[3] --> {x[1] ≥ 1}\n └ moai_BinaryDecisionTree_z[1] - moai_BinaryDecisionTree_z[3] + moai_BinaryDecisionTree_value = 0\n\n\n\n\n\n","category":"type"},{"location":"api/#GrayBox","page":"API Reference","title":"GrayBox","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"GrayBox","category":"page"},{"location":"api/#MathOptAI.GrayBox","page":"API Reference","title":"MathOptAI.GrayBox","text":"GrayBox(\n output_size::Function,\n callback::Function;\n has_hessian::Bool = false,\n) <: AbstractPredictor\n\nAn AbstractPredictor that represents the relationship:\n\ny = f(x)\n\nas a user-defined nonlinear operator.\n\nArguments\n\noutput_size(x::Vector):Int: given an input vector x, return the dimension of the output vector\ncallback(x::Vector)::NamedTuple -> (;value, jacobian[, hessian]): given an input vector x, return a NamedTuple that computes the primal value and Jacobian of the output value with respect to the input. jacobian[j, i] is the partial derivative of value[j] with respect to x[i].\nhas_hessian: if true, the callback additionally contains a field hessian, which is an N × N × M matrix, where hessian[i, j, k] is the partial derivative of value[k] with respect to x[i] and x[j].\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.GrayBox(\n x -> 2,\n x -> (value = x.^2, jacobian = [2 * x[1] 0.0; 0.0 2 * x[2]]),\n );\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_GrayBox[1]\n moai_GrayBox[2]\n\njulia> formulation\nGrayBox\n├ variables [2]\n│ ├ moai_GrayBox[1]\n│ └ moai_GrayBox[2]\n└ constraints [2]\n ├ op_##330(x[1], x[2]) - moai_GrayBox[1] = 0\n └ op_##331(x[1], x[2]) - moai_GrayBox[2] = 0\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n op_##332(x[1], x[2])\n op_##333(x[1], x[2])\n\njulia> formulation\nReducedSpace(GrayBox)\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#Pipeline","page":"API Reference","title":"Pipeline","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Pipeline","category":"page"},{"location":"api/#MathOptAI.Pipeline","page":"API Reference","title":"MathOptAI.Pipeline","text":"Pipeline(layers::Vector{AbstractPredictor}) <: AbstractPredictor\n\nAn AbstractPredictor that represents the relationship:\n\ny = (l_1 circ ldots circ l_N)(x)\n\nwhere l_i are a list of other AbstractPredictors.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.Pipeline(\n MathOptAI.Affine([1.0 2.0], [0.0]),\n MathOptAI.ReLUQuadratic(),\n )\nPipeline with layers:\n * Affine(A, b) [input: 2, output: 1]\n * ReLUQuadratic()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_ReLU[1]\n\njulia> formulation\nAffine(A, b) [input: 2, output: 1]\n├ variables [1]\n│ └ moai_Affine[1]\n└ constraints [1]\n └ x[1] + 2 x[2] - moai_Affine[1] = 0\nReLUQuadratic()\n├ variables [2]\n│ ├ moai_ReLU[1]\n│ └ moai_z[1]\n└ constraints [4]\n ├ moai_ReLU[1] ≥ 0\n ├ moai_z[1] ≥ 0\n ├ moai_Affine[1] - moai_ReLU[1] + moai_z[1] = 0\n └ moai_ReLU[1]*moai_z[1] = 0\n\n\n\n\n\n","category":"type"},{"location":"api/#PytorchModel","page":"API Reference","title":"PytorchModel","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"PytorchModel","category":"page"},{"location":"api/#MathOptAI.PytorchModel","page":"API Reference","title":"MathOptAI.PytorchModel","text":"PytorchModel(filename::String)\n\nA wrapper struct for loading a PyTorch model.\n\nThe only supported file extension is .pt, where the .pt file has been created using torch.save(model, filename).\n\nExample\n\njulia> using PythonCall, MathOptAI\n\njulia> predictor = PytorchModel(\"model.pt\");\n\n\n\n\n\n","category":"type"},{"location":"api/#Quantile","page":"API Reference","title":"Quantile","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Quantile","category":"page"},{"location":"api/#MathOptAI.Quantile","page":"API Reference","title":"MathOptAI.Quantile","text":"Quantile{D}(distribution::D, quantiles::Vector{Float64}) where {D}\n\nAn AbstractPredictor that represents the quantiles of distribution.\n\nExample\n\njulia> using JuMP, Distributions, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, 1 <= x <= 2);\n\njulia> predictor = MathOptAI.Quantile([0.1, 0.9]) do x\n return Distributions.Normal(x, 3 - x)\n end\nQuantile(_, [0.1, 0.9])\n\njulia> y, formulation = MathOptAI.add_predictor(model, predictor, [x]);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_quantile[1]\n moai_quantile[2]\n\njulia> formulation\nQuantile(_, [0.1, 0.9])\n├ variables [2]\n│ ├ moai_quantile[1]\n│ └ moai_quantile[2]\n└ constraints [2]\n ├ moai_quantile[1] - op_quantile_0.1(x) = 0\n └ moai_quantile[2] - op_quantile_0.9(x) = 0\n\n\n\n\n\n","category":"type"},{"location":"api/#ReducedSpace","page":"API Reference","title":"ReducedSpace","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"ReducedSpace","category":"page"},{"location":"api/#MathOptAI.ReducedSpace","page":"API Reference","title":"MathOptAI.ReducedSpace","text":"ReducedSpace(predictor::AbstractPredictor)\n\nA wrapper type for other predictors that implement a reduced-space formulation.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> predictor = MathOptAI.ReducedSpace(MathOptAI.ReLU());\n\njulia> y, formulation = MathOptAI.add_predictor(model, predictor, x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n max(0.0, x[1])\n max(0.0, x[2])\n\n\n\n\n\n","category":"type"},{"location":"api/#ReLU","page":"API Reference","title":"ReLU","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"ReLU","category":"page"},{"location":"api/#MathOptAI.ReLU","page":"API Reference","title":"MathOptAI.ReLU","text":"ReLU() <: AbstractPredictor\n\nAn AbstractPredictor that represents the relationship:\n\ny = max0 x\n\nas a non-smooth nonlinear constraint.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, -1 <= x[i in 1:2] <= i);\n\njulia> f = MathOptAI.ReLU()\nReLU()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_ReLU[1]\n moai_ReLU[2]\n\njulia> formulation\nReLU()\n├ variables [2]\n│ ├ moai_ReLU[1]\n│ └ moai_ReLU[2]\n└ constraints [6]\n ├ moai_ReLU[1] ≥ 0\n ├ moai_ReLU[1] ≤ 1\n ├ moai_ReLU[2] ≥ 0\n ├ moai_ReLU[2] ≤ 2\n ├ moai_ReLU[1] - max(0.0, x[1]) = 0\n └ moai_ReLU[2] - max(0.0, x[2]) = 0\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n max(0.0, x[1])\n max(0.0, x[2])\n\njulia> formulation\nReducedSpace(ReLU())\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#ReLUBigM","page":"API Reference","title":"ReLUBigM","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"ReLUBigM","category":"page"},{"location":"api/#MathOptAI.ReLUBigM","page":"API Reference","title":"MathOptAI.ReLUBigM","text":"ReLUBigM(M::Float64) <: AbstractPredictor\n\nAn AbstractPredictor that represents the relationship:\n\ny = max0 x\n\nvia the big-M MIP reformulation:\n\nbeginaligned\ny ge 0 \ny ge x \ny le M z \ny le x + M(1 - z) \nz in0 1\nendaligned\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, -3 <= x[i in 1:2] <= i);\n\njulia> f = MathOptAI.ReLUBigM(100.0)\nReLUBigM(100.0)\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_ReLU[1]\n moai_ReLU[2]\n\njulia> formulation\nReLUBigM(100.0)\n├ variables [4]\n│ ├ moai_ReLU[1]\n│ ├ moai_ReLU[2]\n│ ├ moai_z[1]\n│ └ moai_z[2]\n└ constraints [12]\n ├ moai_ReLU[1] ≥ 0\n ├ moai_ReLU[1] ≤ 1\n ├ moai_ReLU[2] ≥ 0\n ├ moai_ReLU[2] ≤ 2\n ├ moai_z[1] binary\n ├ -x[1] + moai_ReLU[1] ≥ 0\n ├ moai_ReLU[1] - moai_z[1] ≤ 0\n ├ -x[1] + moai_ReLU[1] + 3 moai_z[1] ≤ 3\n ├ moai_z[2] binary\n ├ -x[2] + moai_ReLU[2] ≥ 0\n ├ moai_ReLU[2] - 2 moai_z[2] ≤ 0\n └ -x[2] + moai_ReLU[2] + 3 moai_z[2] ≤ 3\n\n\n\n\n\n","category":"type"},{"location":"api/#ReLUQuadratic","page":"API Reference","title":"ReLUQuadratic","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"ReLUQuadratic","category":"page"},{"location":"api/#MathOptAI.ReLUQuadratic","page":"API Reference","title":"MathOptAI.ReLUQuadratic","text":"ReLUQuadratic() <: AbstractPredictor\n\nAn AbstractPredictor that represents the relationship:\n\ny = max0 x\n\nby the reformulation:\n\nbeginaligned\nx = y - z \ny cdot z = 0 \ny z ge 0\nendaligned\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, -1 <= x[i in 1:2] <= i);\n\njulia> f = MathOptAI.ReLUQuadratic()\nReLUQuadratic()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_ReLU[1]\n moai_ReLU[2]\n\njulia> formulation\nReLUQuadratic()\n├ variables [4]\n│ ├ moai_ReLU[1]\n│ ├ moai_ReLU[2]\n│ ├ moai_z[1]\n│ └ moai_z[2]\n└ constraints [12]\n ├ moai_ReLU[1] ≥ 0\n ├ moai_ReLU[1] ≤ 1\n ├ moai_ReLU[2] ≥ 0\n ├ moai_ReLU[2] ≤ 2\n ├ moai_z[1] ≥ 0\n ├ moai_z[1] ≤ 1\n ├ moai_z[2] ≥ 0\n ├ moai_z[2] ≤ 1\n ├ x[1] - moai_ReLU[1] + moai_z[1] = 0\n ├ x[2] - moai_ReLU[2] + moai_z[2] = 0\n ├ moai_ReLU[1]*moai_z[1] = 0\n └ moai_ReLU[2]*moai_z[2] = 0\n\n\n\n\n\n","category":"type"},{"location":"api/#ReLUSOS1","page":"API Reference","title":"ReLUSOS1","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"ReLUSOS1","category":"page"},{"location":"api/#MathOptAI.ReLUSOS1","page":"API Reference","title":"MathOptAI.ReLUSOS1","text":"ReLUSOS1() <: AbstractPredictor\n\nAn AbstractPredictor that represents the relationship:\n\ny = max0 x\n\nby the reformulation:\n\nbeginaligned\nx = y - z \ny z in SOS1 \ny z ge 0\nendaligned\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, -1 <= x[i in 1:2] <= i);\n\njulia> f = MathOptAI.ReLUSOS1()\nReLUSOS1()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_ReLU[1]\n moai_ReLU[2]\n\njulia> formulation\nReLUSOS1()\n├ variables [4]\n│ ├ moai_ReLU[1]\n│ ├ moai_ReLU[2]\n│ ├ moai_z[1]\n│ └ moai_z[2]\n└ constraints [10]\n ├ moai_ReLU[1] ≥ 0\n ├ moai_ReLU[1] ≤ 1\n ├ moai_ReLU[2] ≥ 0\n ├ moai_ReLU[2] ≤ 2\n ├ moai_z[1] ≤ 1\n ├ moai_z[2] ≤ 1\n ├ x[1] - moai_ReLU[1] + moai_z[1] = 0\n ├ x[2] - moai_ReLU[2] + moai_z[2] = 0\n ├ [moai_ReLU[1], moai_z[1]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])\n └ [moai_ReLU[2], moai_z[2]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])\n\n\n\n\n\n","category":"type"},{"location":"api/#Scale","page":"API Reference","title":"Scale","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Scale","category":"page"},{"location":"api/#MathOptAI.Scale","page":"API Reference","title":"MathOptAI.Scale","text":"Scale(\n scale::Vector{T},\n bias::Vector{T},\n) where {T} <: AbstractPredictor\n\nAn AbstractPredictor that represents the relationship:\n\ny = Diag(scale)x + bias\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, 0 <= x[i in 1:2] <= i);\n\njulia> f = MathOptAI.Scale([2.0, 3.0], [4.0, 5.0])\nScale(scale, bias)\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_Scale[1]\n moai_Scale[2]\n\njulia> formulation\nScale(scale, bias)\n├ variables [2]\n│ ├ moai_Scale[1]\n│ └ moai_Scale[2]\n└ constraints [6]\n ├ moai_Scale[1] ≥ 4\n ├ moai_Scale[1] ≤ 6\n ├ moai_Scale[2] ≥ 5\n ├ moai_Scale[2] ≤ 11\n ├ 2 x[1] - moai_Scale[1] = -4\n └ 3 x[2] - moai_Scale[2] = -5\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{AffExpr}:\n 2 x[1] + 4\n 3 x[2] + 5\n\njulia> formulation\nReducedSpace(Scale(scale, bias))\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#Sigmoid","page":"API Reference","title":"Sigmoid","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Sigmoid","category":"page"},{"location":"api/#MathOptAI.Sigmoid","page":"API Reference","title":"MathOptAI.Sigmoid","text":"Sigmoid() <: AbstractPredictor\n\nAn AbstractPredictor that represents the relationship:\n\ny = frac11 + e^-x\n\nas a smooth nonlinear constraint.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, -1 <= x[i in 1:2] <= i);\n\njulia> f = MathOptAI.Sigmoid()\nSigmoid()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_Sigmoid[1]\n moai_Sigmoid[2]\n\njulia> formulation\nSigmoid()\n├ variables [2]\n│ ├ moai_Sigmoid[1]\n│ └ moai_Sigmoid[2]\n└ constraints [6]\n ├ moai_Sigmoid[1] ≥ 0.2689414213699951\n ├ moai_Sigmoid[1] ≤ 0.7310585786300049\n ├ moai_Sigmoid[2] ≥ 0.2689414213699951\n ├ moai_Sigmoid[2] ≤ 0.8807970779778823\n ├ moai_Sigmoid[1] - (1.0 / (1.0 + exp(-x[1]))) = 0\n └ moai_Sigmoid[2] - (1.0 / (1.0 + exp(-x[2]))) = 0\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n 1.0 / (1.0 + exp(-x[1]))\n 1.0 / (1.0 + exp(-x[2]))\n\njulia> formulation\nReducedSpace(Sigmoid())\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#SoftMax","page":"API Reference","title":"SoftMax","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"SoftMax","category":"page"},{"location":"api/#MathOptAI.SoftMax","page":"API Reference","title":"MathOptAI.SoftMax","text":"SoftMax() <: AbstractPredictor\n\nAn AbstractPredictor that represents the relationship:\n\ny = frace^xe^x_1\n\nas a smooth nonlinear constraint.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.SoftMax()\nSoftMax()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_SoftMax[1]\n moai_SoftMax[2]\n\njulia> formulation\nSoftMax()\n├ variables [3]\n│ ├ moai_SoftMax_denom\n│ ├ moai_SoftMax[1]\n│ └ moai_SoftMax[2]\n└ constraints [8]\n ├ moai_SoftMax[1] ≥ 0\n ├ moai_SoftMax[1] ≤ 1\n ├ moai_SoftMax[2] ≥ 0\n ├ moai_SoftMax[2] ≤ 1\n ├ moai_SoftMax_denom ≥ 0\n ├ moai_SoftMax_denom - (0.0 + exp(x[2]) + exp(x[1])) = 0\n ├ moai_SoftMax[1] - (exp(x[1]) / moai_SoftMax_denom) = 0\n └ moai_SoftMax[2] - (exp(x[2]) / moai_SoftMax_denom) = 0\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n exp(x[1]) / moai_SoftMax_denom\n exp(x[2]) / moai_SoftMax_denom\n\njulia> formulation\nReducedSpace(SoftMax())\n├ variables [1]\n│ └ moai_SoftMax_denom\n└ constraints [2]\n ├ moai_SoftMax_denom ≥ 0\n └ moai_SoftMax_denom - (0.0 + exp(x[2]) + exp(x[1])) = 0\n\n\n\n\n\n","category":"type"},{"location":"api/#SoftPlus","page":"API Reference","title":"SoftPlus","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"SoftPlus","category":"page"},{"location":"api/#MathOptAI.SoftPlus","page":"API Reference","title":"MathOptAI.SoftPlus","text":"SoftPlus(; beta = 1.0) <: AbstractPredictor\n\nAn AbstractPredictor that represents the relationship:\n\ny = frac1beta log(1 + e^beta x)\n\nas a smooth nonlinear constraint.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, -1 <= x[i in 1:2] <= i);\n\njulia> f = MathOptAI.SoftPlus(; beta = 2.0)\nSoftPlus(2.0)\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_SoftPlus[1]\n moai_SoftPlus[2]\n\njulia> formulation\nSoftPlus(2.0)\n├ variables [2]\n│ ├ moai_SoftPlus[1]\n│ └ moai_SoftPlus[2]\n└ constraints [6]\n ├ moai_SoftPlus[1] ≥ 0.0634640055214863\n ├ moai_SoftPlus[1] ≤ 1.0634640055214863\n ├ moai_SoftPlus[2] ≥ 0.0634640055214863\n ├ moai_SoftPlus[2] ≤ 2.0090749639589047\n ├ moai_SoftPlus[1] - (log(1.0 + exp(2 x[1])) / 2.0) = 0\n └ moai_SoftPlus[2] - (log(1.0 + exp(2 x[2])) / 2.0) = 0\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n log(1.0 + exp(2 x[1])) / 2.0\n log(1.0 + exp(2 x[2])) / 2.0\n\njulia> formulation\nReducedSpace(SoftPlus(2.0))\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#Tanh","page":"API Reference","title":"Tanh","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Tanh","category":"page"},{"location":"api/#MathOptAI.Tanh","page":"API Reference","title":"MathOptAI.Tanh","text":"Tanh() <: AbstractPredictor\n\nAn AbstractPredictor that represents the relationship:\n\ny = tanh(x)\n\nas a smooth nonlinear constraint.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, -1 <= x[i in 1:2] <= i);\n\njulia> f = MathOptAI.Tanh()\nTanh()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_Tanh[1]\n moai_Tanh[2]\n\njulia> formulation\nTanh()\n├ variables [2]\n│ ├ moai_Tanh[1]\n│ └ moai_Tanh[2]\n└ constraints [6]\n ├ moai_Tanh[1] ≥ -0.7615941559557649\n ├ moai_Tanh[1] ≤ 0.7615941559557649\n ├ moai_Tanh[2] ≥ -0.7615941559557649\n ├ moai_Tanh[2] ≤ 0.9640275800758169\n ├ moai_Tanh[1] - tanh(x[1]) = 0\n └ moai_Tanh[2] - tanh(x[2]) = 0\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n tanh(x[1])\n tanh(x[2])\n\njulia> formulation\nReducedSpace(Tanh())\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#AbstractFormulation","page":"API Reference","title":"AbstractFormulation","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"AbstractFormulation","category":"page"},{"location":"api/#MathOptAI.AbstractFormulation","page":"API Reference","title":"MathOptAI.AbstractFormulation","text":"abstract type AbstractFormulation end\n\nAn abstract type representing different formulations.\n\n\n\n\n\n","category":"type"},{"location":"api/#Formulation","page":"API Reference","title":"Formulation","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Formulation","category":"page"},{"location":"api/#MathOptAI.Formulation","page":"API Reference","title":"MathOptAI.Formulation","text":"struct Formulation{P<:AbstractPredictor} <: AbstractFormulation\n predictor::P\n variables::Vector{Any}\n constraints::Vector{Any}\nend\n\nFields\n\npredictor: the predictor object used to build the formulation\nvariables: a vector of new decision variables added to the model\nconstraints: a vector of new constraints added to the model\n\nCheck the docstring of the predictor for an explanation of the formulation and the order of the elements in .variables and .constraints.\n\n\n\n\n\n","category":"type"},{"location":"api/#PipelineFormulation","page":"API Reference","title":"PipelineFormulation","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"PipelineFormulation","category":"page"},{"location":"api/#MathOptAI.PipelineFormulation","page":"API Reference","title":"MathOptAI.PipelineFormulation","text":"struct PipelineFormulation{P<:AbstractPredictor} <: AbstractFormulation\n predictor::P\n layers::Vector{Any}\nend\n\nFields\n\npredictor: the predictor object used to build the formulation\nlayers: the formulation associated with each of the layers in the pipeline\n\n\n\n\n\n","category":"type"},{"location":"api/#Extensions","page":"API Reference","title":"Extensions","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Modules = [\n Base.get_extension(MathOptAI, :MathOptAIAbstractGPsExt),\n Base.get_extension(MathOptAI, :MathOptAIDecisionTreeExt),\n Base.get_extension(MathOptAI, :MathOptAIFluxExt),\n Base.get_extension(MathOptAI, :MathOptAIGLMExt),\n Base.get_extension(MathOptAI, :MathOptAILuxExt),\n Base.get_extension(MathOptAI, :MathOptAIPythonCallExt),\n Base.get_extension(MathOptAI, :MathOptAIStatsModelsExt),\n]","category":"page"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, MathOptAI.Quantile{<:AbstractGPs.PosteriorGP}, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::MathOptAI.Quantile{<:AbstractGPs.PosteriorGP},\n x::Vector,\n)\n\nAdd the quantiles of a trained Gaussian Process from AbstractGPs.jl to model.\n\nExample\n\njulia> using JuMP, MathOptAI, AbstractGPs\n\njulia> x_data = 2π .* (0.0:0.1:1.0);\n\njulia> y_data = sin.(x_data);\n\njulia> fx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.1);\n\njulia> p_fx = AbstractGPs.posterior(fx, y_data);\n\njulia> model = Model();\n\njulia> @variable(model, 1 <= x[1:1] <= 6, start = 3);\n\njulia> predictor = MathOptAI.Quantile(p_fx, [0.1, 0.9]);\n\njulia> y, _ = MathOptAI.add_predictor(model, predictor, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_quantile[1]\n moai_quantile[2]\n\njulia> @objective(model, Max, y[2] - y[1])\nmoai_quantile[2] - moai_quantile[1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, Union{DecisionTree.DecisionTreeClassifier, DecisionTree.Root}, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::Union{DecisionTree.Root,DecisionTree.DecisionTreeClassifier},\n x::Vector,\n)\n\nAdd a binary decision tree from DecisionTree.jl to model.\n\nExample\n\njulia> using JuMP, MathOptAI, DecisionTree\n\njulia> truth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)\ntruth (generic function with 1 method)\n\njulia> features = abs.(sin.((1:10) .* (3:4)'));\n\njulia> size(features)\n(10, 2)\n\njulia> labels = truth.(Vector.(eachrow(features)));\n\njulia> predictor = DecisionTree.build_tree(labels, features)\nDecision Tree\nLeaves: 3\nDepth: 2\n\njulia> model = Model();\n\njulia> @variable(model, 0 <= x[1:2] <= 1);\n\njulia> y, _ = MathOptAI.add_predictor(model, predictor, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_BinaryDecisionTree_value\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.build_predictor-Tuple{DecisionTree.Root}","page":"API Reference","title":"MathOptAI.build_predictor","text":"MathOptAI.build_predictor(predictor::DecisionTree.Root)\n\nConvert a binary decision tree from DecisionTree.jl to a BinaryDecisionTree.\n\nExample\n\njulia> using MathOptAI, DecisionTree\n\njulia> truth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)\ntruth (generic function with 1 method)\n\njulia> features = abs.(sin.((1:10) .* (3:4)'));\n\njulia> size(features)\n(10, 2)\n\njulia> labels = truth.(Vector.(eachrow(features)));\n\njulia> tree = DecisionTree.build_tree(labels, features)\nDecision Tree\nLeaves: 3\nDepth: 2\n\njulia> predictor = MathOptAI.build_predictor(tree)\nBinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, Flux.Chain, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::Flux.Chain,\n x::Vector;\n config::Dict = Dict{Any,Any}(),\n reduced_space::Bool = false,\n gray_box::Bool = false,\n)\n\nAdd a trained neural network from Flux.jl to model.\n\nSupported layers\n\nFlux.Dense\nFlux.Scale\nFlux.softmax\n\nSupported activation functions\n\nFlux.relu\nFlux.sigmoid\nFlux.softplus\nFlux.tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps supported Flux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Flux.sigmoid => MathOptAI.Sigmoid() or Flux.relu => MathOptAI.QuadraticReLU().\ngray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by Flux.withjacobian.\n\nExample\n\njulia> using JuMP, Flux, MathOptAI\n\njulia> chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));\n\njulia> model = Model();\n\njulia> @variable(model, x[1:1]);\n\njulia> y, _ = MathOptAI.add_predictor(\n model,\n chain,\n x;\n config = Dict(Flux.relu => MathOptAI.ReLU()),\n );\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Affine[1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.build_predictor-Tuple{Flux.Chain}","page":"API Reference","title":"MathOptAI.build_predictor","text":"MathOptAI.build_predictor(\n predictor::Flux.Chain;\n config::Dict = Dict{Any,Any}(),\n gray_box::Bool = false,\n gray_box_hessian::Bool = false,\n)\n\nConvert a trained neural network from Flux.jl to a Pipeline.\n\nSupported layers\n\nFlux.Dense\nFlux.Scale\nFlux.softmax\n\nSupported activation functions\n\nFlux.relu\nFlux.sigmoid\nFlux.softplus\nFlux.tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps supported Flux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Flux.sigmoid => MathOptAI.Sigmoid() or Flux.relu => MathOptAI.QuadraticReLU().\ngray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by Flux.withjacobian.\ngray_box_hessian: if true, the gray box additionally computes the Hessian of the output using Flux.hessian.\n\nExample\n\njulia> using Flux, MathOptAI\n\njulia> chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));\n\njulia> MathOptAI.build_predictor(\n chain;\n config = Dict(Flux.relu => MathOptAI.ReLU()),\n )\nPipeline with layers:\n * Affine(A, b) [input: 1, output: 16]\n * ReLU()\n * Affine(A, b) [input: 16, output: 1]\n\njulia> MathOptAI.build_predictor(\n chain;\n config = Dict(Flux.relu => MathOptAI.ReLUQuadratic()),\n )\nPipeline with layers:\n * Affine(A, b) [input: 1, output: 16]\n * ReLUQuadratic()\n * Affine(A, b) [input: 16, output: 1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, GLM.GeneralizedLinearModel{GLM.GlmResp{Vector{Float64}, Distributions.Bernoulli{Float64}, GLM.LogitLink}}, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::GLM.GeneralizedLinearModel{\n GLM.GlmResp{Vector{Float64},GLM.Bernoulli{Float64},GLM.LogitLink},\n },\n x::Vector;\n sigmoid::AbstractPredictor = MathOptAI.Sigmoid(),\n reduced_space::Bool = false,\n)\n\nAdd a trained logistic regression model from GLM.jl to model.\n\nKeyword arguments\n\nsigmoid: the predictor to use for the sigmoid layer.\n\nExample\n\njulia> using GLM, JuMP, MathOptAI\n\njulia> X, Y = rand(10, 2), rand(Bool, 10);\n\njulia> predictor = GLM.glm(X, Y, GLM.Bernoulli());\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> y, _ = MathOptAI.add_predictor(\n model,\n predictor,\n x;\n sigmoid = MathOptAI.Sigmoid(),\n );\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Sigmoid[1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, GLM.LinearModel, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::GLM.LinearModel,\n x::Vector;\n reduced_space::Bool = false,\n)\n\nAdd a trained linear model from GLM.jl to model.\n\nExample\n\njulia> using GLM, JuMP, MathOptAI\n\njulia> X, Y = rand(10, 2), rand(10);\n\njulia> predictor = GLM.lm(X, Y);\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> y, _ = MathOptAI.add_predictor(model, predictor, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Affine[1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.build_predictor-Tuple{GLM.GeneralizedLinearModel{GLM.GlmResp{Vector{Float64}, Distributions.Bernoulli{Float64}, GLM.LogitLink}}}","page":"API Reference","title":"MathOptAI.build_predictor","text":"MathOptAI.build_predictor(\n predictor::GLM.GeneralizedLinearModel{\n GLM.GlmResp{Vector{Float64},GLM.Bernoulli{Float64},GLM.LogitLink},\n };\n sigmoid::MathOptAI.AbstractPredictor = MathOptAI.Sigmoid(),\n)\n\nConvert a trained logistic model from GLM.jl to a Pipeline layer.\n\nKeyword arguments\n\nsigmoid: the predictor to use for the sigmoid layer.\n\nExample\n\njulia> using GLM, MathOptAI\n\njulia> X, Y = rand(10, 2), rand(Bool, 10);\n\njulia> model = GLM.glm(X, Y, GLM.Bernoulli());\n\njulia> predictor = MathOptAI.build_predictor(model)\nPipeline with layers:\n * Affine(A, b) [input: 2, output: 1]\n * Sigmoid()\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.build_predictor-Tuple{GLM.LinearModel}","page":"API Reference","title":"MathOptAI.build_predictor","text":"MathOptAI.build_predictor(predictor::GLM.LinearModel)\n\nConvert a trained linear model from GLM.jl to an Affine layer.\n\nExample\n\njulia> using GLM, MathOptAI\n\njulia> X, Y = rand(10, 2), rand(10);\n\njulia> model = GLM.lm(X, Y);\n\njulia> predictor = MathOptAI.build_predictor(model)\nAffine(A, b) [input: 2, output: 1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, Tuple{Lux.Chain, NamedTuple, NamedTuple}, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::Tuple{<:Lux.Chain,<:NamedTuple,<:NamedTuple},\n x::Vector;\n config::Dict = Dict{Any,Any}(),\n reduced_space::Bool = false,\n)\n\nAdd a trained neural network from Lux.jl to model.\n\nSupported layers\n\nLux.Dense\nLux.Scale\n\nSupported activation functions\n\nLux.relu\nLux.sigmoid\nLux.softplus\nLux.softmax\nLux.tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps supported Lux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Lux.sigmoid => MathOptAI.Sigmoid() or Lux.relu => MathOptAI.QuadraticReLU().\n\nExample\n\njulia> using JuMP, Lux, MathOptAI, Random\n\njulia> rng = Random.MersenneTwister();\n\njulia> chain = Lux.Chain(Lux.Dense(1 => 16, Lux.relu), Lux.Dense(16 => 1))\nChain(\n layer_1 = Dense(1 => 16, relu), # 32 parameters\n layer_2 = Dense(16 => 1), # 17 parameters\n) # Total: 49 parameters,\n # plus 0 states.\n\njulia> parameters, state = Lux.setup(rng, chain);\n\njulia> predictor = (chain, parameters, state);\n\njulia> model = Model();\n\njulia> @variable(model, x[1:1]);\n\njulia> y, _ = MathOptAI.add_predictor(\n model,\n predictor,\n x;\n config = Dict(Lux.relu => MathOptAI.ReLU()),\n );\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Affine[1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.build_predictor-Tuple{Tuple{Lux.Chain, NamedTuple, NamedTuple}}","page":"API Reference","title":"MathOptAI.build_predictor","text":"MathOptAI.build_predictor(\n predictor::Tuple{<:Lux.Chain,<:NamedTuple,<:NamedTuple};\n config::Dict = Dict{Any,Any}(),\n)\n\nConvert a trained neural network from Lux.jl to a Pipeline.\n\nSupported layers\n\nLux.Dense\nLux.Scale\n\nSupported activation functions\n\nLux.relu\nLux.sigmoid\nLux.softplus\nLux.softmax\nLux.tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps supported Lux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Lux.sigmoid => MathOptAI.Sigmoid() or Lux.relu => MathOptAI.QuadraticReLU().\n\nExample\n\njulia> using Lux, MathOptAI, Random\n\njulia> rng = Random.MersenneTwister();\n\njulia> chain = Lux.Chain(Lux.Dense(1 => 16, Lux.relu), Lux.Dense(16 => 1))\nChain(\n layer_1 = Dense(1 => 16, relu), # 32 parameters\n layer_2 = Dense(16 => 1), # 17 parameters\n) # Total: 49 parameters,\n # plus 0 states.\n\njulia> parameters, state = Lux.setup(rng, chain);\n\njulia> predictor = MathOptAI.build_predictor(\n (chain, parameters, state);\n config = Dict(Lux.relu => MathOptAI.ReLU()),\n )\nPipeline with layers:\n * Affine(A, b) [input: 1, output: 16]\n * ReLU()\n * Affine(A, b) [input: 16, output: 1]\n\njulia> MathOptAI.build_predictor(\n (chain, parameters, state);\n config = Dict(Lux.relu => MathOptAI.ReLUQuadratic()),\n )\nPipeline with layers:\n * Affine(A, b) [input: 1, output: 16]\n * ReLUQuadratic()\n * Affine(A, b) [input: 16, output: 1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, MathOptAI.PytorchModel, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::MathOptAI.PytorchModel,\n x::Vector;\n config::Dict = Dict{Any,Any}(),\n reduced_space::Bool = false,\n gray_box::Bool = false,\n gray_box_hessian::Bool = false,\n gray_box_device::String = \"cpu\",\n)\n\nAdd a trained neural network from PyTorch via PythonCall.jl to model.\n\nSupported layers\n\nnn.Linear\nnn.ReLU\nnn.Sequential\nnn.Sigmoid\nnn.Softplus\nnn.Tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps Symbols to AbstractPredictors that control how the activation functions are reformulated. For example, :Sigmoid => MathOptAI.Sigmoid() or :ReLU => MathOptAI.QuadraticReLU(). The supported Symbols are :ReLU, :Sigmoid, :SoftPlus, and :Tanh.\ngray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by torch.func.jacrev.\ngray_box_hessian: if true, the gray box additionally computes the Hessian of the output using torch.func.hessian.\ngray_box_device: device used to construct PyTorch tensors, e.g. \"cuda\" to run on an Nvidia GPU.\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.build_predictor-Tuple{MathOptAI.PytorchModel}","page":"API Reference","title":"MathOptAI.build_predictor","text":"MathOptAI.build_predictor(\n predictor::MathOptAI.PytorchModel;\n config::Dict = Dict{Any,Any}(),\n gray_box::Bool = false,\n gray_box_hessian::Bool = false,\n gray_box_device::String = \"cpu\",\n)\n\nConvert a trained neural network from PyTorch via PythonCall.jl to a Pipeline.\n\nSupported layers\n\nnn.Linear\nnn.ReLU\nnn.Sequential\nnn.Sigmoid\nnn.Softplus\nnn.Tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps Symbols to AbstractPredictors that control how the activation functions are reformulated. For example, :Sigmoid => MathOptAI.Sigmoid() or :ReLU => MathOptAI.QuadraticReLU(). The supported Symbols are :ReLU, :Sigmoid, :SoftPlus, and :Tanh.\ngray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by torch.func.jacrev.\ngray_box_hessian: if true, the gray box additionally computes the Hessian of the output using torch.func.hessian.\ngray_box_device: device used to construct PyTorch tensors, e.g. \"cuda\" to run on an Nvidia GPU.\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, StatsModels.TableRegressionModel, DataFrames.DataFrame}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::StatsModels.TableRegressionModel,\n x::DataFrames.DataFrame;\n kwargs...,\n)\n\nAdd a trained regression model from StatsModels.jl to model, using the DataFrame x as input.\n\nIn most cases, predictor should be a GLM.jl predictor supported by MathOptAI, but trained using @formula and a DataFrame instead of the raw matrix input.\n\nIn general, x may have some columns that are constant (Float64) and some columns that are JuMP decision variables.\n\nKeyword arguments\n\nAll keyword arguments are passed to the corresponding add_predictor of the GLM extension.\n\nExample\n\njulia> using DataFrames, GLM, JuMP, MathOptAI\n\njulia> train_df = DataFrames.DataFrame(x1 = rand(10), x2 = rand(10));\n\njulia> train_df.y = 1.0 .* train_df.x1 + 2.0 .* train_df.x2 .+ rand(10);\n\njulia> predictor = GLM.lm(GLM.@formula(y ~ x1 + x2), train_df);\n\njulia> model = Model();\n\njulia> test_df = DataFrames.DataFrame(\n x1 = rand(6),\n x2 = @variable(model, [1:6]),\n );\n\njulia> test_df.y, _ = MathOptAI.add_predictor(model, predictor, test_df);\n\njulia> test_df.y\n6-element Vector{VariableRef}:\n moai_Affine[1]\n moai_Affine[1]\n moai_Affine[1]\n moai_Affine[1]\n moai_Affine[1]\n moai_Affine[1]\n\n\n\n\n\n","category":"method"},{"location":"manual/AbstractGPs/#AbstractGPs.jl","page":"AbstractGPs.jl","title":"AbstractGPs.jl","text":"","category":"section"},{"location":"manual/AbstractGPs/","page":"AbstractGPs.jl","title":"AbstractGPs.jl","text":"AbstractGPs.jl is a library for fitting Gaussian Processes in Julia.","category":"page"},{"location":"manual/AbstractGPs/#Basic-example","page":"AbstractGPs.jl","title":"Basic example","text":"","category":"section"},{"location":"manual/AbstractGPs/","page":"AbstractGPs.jl","title":"AbstractGPs.jl","text":"Here is an example:","category":"page"},{"location":"manual/AbstractGPs/","page":"AbstractGPs.jl","title":"AbstractGPs.jl","text":"using JuMP, MathOptAI, AbstractGPs\nx_data = 2π .* (0.0:0.1:1.0);\ny_data = sin.(x_data);\nfx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.1);\np_fx = AbstractGPs.posterior(fx, y_data);\nmodel = Model();\n@variable(model, 1 <= x[1:1] <= 6, start = 3);\npredictor = MathOptAI.Quantile(p_fx, [0.1, 0.9]);\ny, formulation = MathOptAI.add_predictor(model, predictor, x);\ny\nformulation\n@objective(model, Max, y[2] - y[1])","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"EditURL = \"pytorch.jl\"","category":"page"},{"location":"tutorials/pytorch/#Function-fitting-with-PyTorch","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"","category":"section"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"The purpose of this tutorial is to explain how to embed a neural network model from PyTorch into JuMP.","category":"page"},{"location":"tutorials/pytorch/#Python-integration","page":"Function fitting with PyTorch","title":"Python integration","text":"","category":"section"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"MathOptAI uses PythonCall.jl to call from Julia into Python.","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"See CondaPkg.jl for more control over how to link Julia to an existing Python environment. For example, if you have an existing Python installation (with PyTorch installed), and it is available in the current Conda environment, set:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"ENV[\"JULIA_CONDAPKG_BACKEND\"] = \"Current\"","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"before importing PythonCall.jl. If the Python installation can be found on the path and it is not in a Conda environment, set:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"ENV[\"JULIA_CONDAPKG_BACKEND\"] = \"Null\"","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"If python is not on your path, you may additionally need to set JULIA_PYTHONCALL_EXE, for example, to:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"ENV[\"JULIA_PYTHONCALL_EXE\"] = \"python3\"","category":"page"},{"location":"tutorials/pytorch/#Required-packages","page":"Function fitting with PyTorch","title":"Required packages","text":"","category":"section"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"This tutorial requires the following packages","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"using JuMP\nusing Test\nimport Ipopt\nimport MathOptAI\nimport Plots","category":"page"},{"location":"tutorials/pytorch/#Training-a-model","page":"Function fitting with PyTorch","title":"Training a model","text":"","category":"section"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"The following script builds and trains a simple neural network in PyTorch. For simplicity, we do not evaluate out-of-sample test performance, or use a batched data loader. In general, you should train your model in Python, and then use torch.save(model, filename) to save it to a .pt file for later use in Julia.","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"The model is unimportant, but for this example, we are trying to fit noisy observations of the function f(x) = x^2 - 2x.","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"In Python, we ran:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"#!/usr/bin/python3\nimport torch\nmodel = torch.nn.Sequential(\n torch.nn.Linear(1, 16),\n torch.nn.ReLU(),\n torch.nn.Linear(16, 1),\n)\n\nn = 1024\nx = torch.arange(-2, 2 + 4 / (n - 1), 4 / (n - 1)).reshape(n, 1)\nloss_fn = torch.nn.MSELoss()\noptimizer = torch.optim.Adam(model.parameters(), lr=0.01)\nfor epoch in range(100):\n optimizer.zero_grad()\n N = torch.normal(torch.zeros(n, 1), torch.ones(n, 1))\n y = x ** 2 -2 * x + 0.1 * N\n loss = loss_fn(model(x), y)\n loss.backward()\n optimizer.step()\n\ntorch.save(model, \"model.pt\")","category":"page"},{"location":"tutorials/pytorch/#JuMP-model","page":"Function fitting with PyTorch","title":"JuMP model","text":"","category":"section"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"Our goal for this JuMP model is to load the Neural Network from PyTorch into the objective function, and then minimize the objective for different fixed values of x to recreate the function that the Neural Network has learned to approximate.","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"First, create a JuMP model:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"model = Model(Ipopt.Optimizer)\nset_silent(model)\n@variable(model, x)","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"Then, load the model from PyTorch using MathOptAI.PytorchModel:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"predictor = MathOptAI.PytorchModel(joinpath(@__DIR__, \"model.pt\"))\ny, _ = MathOptAI.add_predictor(model, predictor, [x])\n@objective(model, Min, only(y))","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"Now, visualize the fitted function y = predictor(x) by repeatedly solving the optimization problem for different fixed values of x:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"X, Y = -2:0.1:2, Float64[]\n@constraint(model, c, x == 0.0)\nfor xi in X\n set_normalized_rhs(c, xi)\n optimize!(model)\n @test is_solved_and_feasible(model)\n push!(Y, objective_value(model))\nend\nPlots.plot(x -> x^2 - 2x, X; label = \"Truth\", linestype = :dot)\nPlots.plot!(X, Y; label = \"Fitted\")","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"This page was generated using Literate.jl.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"EditURL = \"decision_trees.jl\"","category":"page"},{"location":"tutorials/decision_trees/#Classification-problems-with-DecisionTree.jl","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"","category":"section"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The purpose of this tutorial is to explain how to embed a decision tree model from DecisionTree.jl into JuMP.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The data and example in this tutorial comes from the paper: David Bergman, Teng Huang, Philip Brooks, Andrea Lodi, Arvind U. Raghunathan (2021) JANOS: An Integrated Predictive and Prescriptive Modeling Framework. INFORMS Journal on Computing 34(2):807-816. https://doi.org/10.1287/ijoc.2020.1023","category":"page"},{"location":"tutorials/decision_trees/#Required-packages","page":"Classification problems with DecisionTree.jl","title":"Required packages","text":"","category":"section"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"This tutorial uses the following packages.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"using JuMP\nimport CSV\nimport DataFrames\nimport Downloads\nimport DecisionTree\nimport HiGHS\nimport MathOptAI\nimport Statistics","category":"page"},{"location":"tutorials/decision_trees/#Data","page":"Classification problems with DecisionTree.jl","title":"Data","text":"","category":"section"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Here is a function to load the data directly from the JANOS repository:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"function read_df(filename)\n url = \"https://raw.githubusercontent.com/INFORMSJoC/2020.1023/master/data/\"\n data = Downloads.download(url * filename)\n return CSV.read(data, DataFrames.DataFrame)\nend","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"There are two important files. The first, college_student_enroll-s1-1.csv, contains historical admissions data on anonymized students, their SAT score, their GPA, their merit scholarships, and whether the enrolled in the college.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"train_df = read_df(\"college_student_enroll-s1-1.csv\")","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The second, college_applications6000.csv, contains the SAT and GPA data of students who are currently applying:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"evaluate_df = read_df(\"college_applications6000.csv\")","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"There are 6,000 prospective students:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"n_students = size(evaluate_df, 1)","category":"page"},{"location":"tutorials/decision_trees/#Prediction-model","page":"Classification problems with DecisionTree.jl","title":"Prediction model","text":"","category":"section"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The first step is to train a logistic regression model to predict the Boolean enroll column based on the SAT, GPA, and merit columns.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"train_features = Matrix(train_df[:, [:SAT, :GPA, :merit]])\ntrain_labels = train_df[:, :enroll]\npredictor = DecisionTree.DecisionTreeClassifier(; max_depth = 3)\nDecisionTree.fit!(predictor, train_features, train_labels)\nDecisionTree.print_tree(predictor)","category":"page"},{"location":"tutorials/decision_trees/#Decision-model","page":"Classification problems with DecisionTree.jl","title":"Decision model","text":"","category":"section"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Now that we have a trained decision tree, we want a decision model that chooses the optimal merit scholarship for each student in:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"evaluate_df","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Here's an empty JuMP model to start:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"model = Model()","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"First, we add a new column to evaluate_df, with one JuMP decision variable for each row. It is important the .merit column name in evaluate_df matches the name in train_df.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"evaluate_df.merit = @variable(model, 0 <= x_merit[1:n_students] <= 2.5);\nevaluate_df","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Then, we use MathOptAI.add_predictor to embed model_ml into the JuMP model. MathOptAI.add_predictor returns a vector of variables, one for each row in evaluate_df, corresponding to the output enroll of our logistic regression.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"evaluate_features = Matrix(evaluate_df[:, [:SAT, :GPA, :merit]])\nevaluate_df.enroll = mapreduce(vcat, 1:size(evaluate_features, 1)) do i\n y, _ = MathOptAI.add_predictor(model, predictor, evaluate_features[i, :])\n return y\nend\nevaluate_df","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The .enroll column name in evaluate_df is just a name. It doesn't have to match the name in train_df.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The objective of our problem is to maximize the expected number of students who enroll:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"@objective(model, Max, sum(evaluate_df.enroll))","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Subject to the constraint that we can spend at most 0.2 * n_students on merit scholarships:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"@constraint(model, sum(evaluate_df.merit) <= 0.2 * n_students)","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Because logistic regression involves a Sigmoid layer, we need to use a smooth nonlinear optimizer. A common choice is Ipopt. Solve and check the optimizer found a feasible solution:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"set_optimizer(model, HiGHS.Optimizer)\nset_silent(model)\noptimize!(model)\n@assert is_solved_and_feasible(model)","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Let's store the solution in evaluate_df for analysis:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"evaluate_df.merit_sol = value.(evaluate_df.merit);\nevaluate_df.enroll_sol = value.(evaluate_df.enroll);\nevaluate_df","category":"page"},{"location":"tutorials/decision_trees/#Solution-analysis","page":"Classification problems with DecisionTree.jl","title":"Solution analysis","text":"","category":"section"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"We expect that just under 2,500 students will enroll:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"sum(evaluate_df.enroll_sol)","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"We awarded merit scholarships to approximately 1 in 6 students:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"count(evaluate_df.merit_sol .> 1e-5)","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The average merit scholarship was worth just under $1,000:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"1_000 * Statistics.mean(evaluate_df.merit_sol[evaluate_df.merit_sol.>1e-5])","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"This page was generated using Literate.jl.","category":"page"},{"location":"manual/Lux/#Lux.jl","page":"Lux.jl","title":"Lux.jl","text":"","category":"section"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"Lux.jl is a library for machine learning in Julia.","category":"page"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"The upstream documentation is available at https://lux.csail.mit.edu/stable/.","category":"page"},{"location":"manual/Lux/#Supported-layers","page":"Lux.jl","title":"Supported layers","text":"","category":"section"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"MathOptAI supports embedding a Lux model into JuMP if it is a Lux.Chain composed of:","category":"page"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"Lux.Dense\nLux.Scale\nLux.relu\nLux.sigmoid\nLux.softmax\nLux.softplus\nLux.tanh","category":"page"},{"location":"manual/Lux/#Basic-example","page":"Lux.jl","title":"Basic example","text":"","category":"section"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"Use MathOptAI.add_predictor to embed a tuple (containing the Lux.Chain, the parameters, and the state) into a JuMP model:","category":"page"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"using JuMP, Lux, MathOptAI, Random\nrng = Random.MersenneTwister();\nchain = Lux.Chain(Lux.Dense(1 => 2, Lux.relu), Lux.Dense(2 => 1))\nparameters, state = Lux.setup(rng, chain);\npredictor = (chain, parameters, state);\nmodel = Model();\n@variable(model, x[1:1]);\ny, formulation = MathOptAI.add_predictor(model, predictor, x);\ny\nformulation","category":"page"},{"location":"manual/Lux/#Reduced-space","page":"Lux.jl","title":"Reduced-space","text":"","category":"section"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"Use the reduced_space = true keyword to formulate a reduced-space model:","category":"page"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"using JuMP, Lux, MathOptAI, Random\nrng = Random.MersenneTwister();\nchain = Lux.Chain(Lux.Dense(1 => 2, Lux.relu), Lux.Dense(2 => 1))\nparameters, state = Lux.setup(rng, chain);\npredictor = (chain, parameters, state);\nmodel = Model();\n@variable(model, x[1:1]);\ny, formulation =\n MathOptAI.add_predictor(model, predictor, x; reduced_space = true);\ny\nformulation","category":"page"},{"location":"manual/Lux/#Gray-box","page":"Lux.jl","title":"Gray-box","text":"","category":"section"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"The Lux extension does not yet support the gray_box keyword argument.","category":"page"},{"location":"manual/Lux/#Change-how-layers-are-formulated","page":"Lux.jl","title":"Change how layers are formulated","text":"","category":"section"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"Pass a dictionary to the config keyword that maps Lux activation functions to a MathOptAI predictor:","category":"page"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"using JuMP, Lux, MathOptAI, Random\nrng = Random.MersenneTwister();\nchain = Lux.Chain(Lux.Dense(1 => 2, Lux.relu), Lux.Dense(2 => 1))\nparameters, state = Lux.setup(rng, chain);\npredictor = (chain, parameters, state);\nmodel = Model();\n@variable(model, x[1:1]);\ny, formulation = MathOptAI.add_predictor(\n model,\n predictor,\n x;\n config = Dict(Lux.relu => MathOptAI.ReLUSOS1()),\n);\ny\nformulation","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"EditURL = \"mnist_lux.jl\"","category":"page"},{"location":"tutorials/mnist_lux/#Adversarial-machine-learning-with-Lux.jl","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"","category":"section"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"The purpose of this tutorial is to explain how to embed a neural network model from Lux.jl into JuMP.","category":"page"},{"location":"tutorials/mnist_lux/#Required-packages","page":"Adversarial machine learning with Lux.jl","title":"Required packages","text":"","category":"section"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"This tutorial requires the following packages","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"using JuMP\nimport Lux\nimport Ipopt\nimport MathOptAI\nimport MLDatasets\nimport MLUtils\nimport OneHotArrays\nimport Optimisers\nimport Plots\nimport Random\nimport Zygote","category":"page"},{"location":"tutorials/mnist_lux/#Data","page":"Adversarial machine learning with Lux.jl","title":"Data","text":"","category":"section"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"This tutorial uses images from the MNIST dataset.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"We load the predefined train and test splits:","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"train_data = MLDatasets.MNIST(; split = :train)","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"test_data = MLDatasets.MNIST(; split = :test)","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Since the data are images, it is helpful to plot them. (This requires a transpose and reversing the rows to get the orientation correct.)","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"function plot_image(x::Matrix; kwargs...)\n return Plots.heatmap(\n x'[size(x, 1):-1:1, :];\n xlims = (1, size(x, 2)),\n ylims = (1, size(x, 1)),\n aspect_ratio = true,\n legend = false,\n xaxis = false,\n yaxis = false,\n kwargs...,\n )\nend\n\nfunction plot_image(instance::NamedTuple)\n return plot_image(instance.features; title = \"Label = $(instance.targets)\")\nend\n\nPlots.plot([plot_image(train_data[i]) for i in 1:6]...; layout = (2, 3))","category":"page"},{"location":"tutorials/mnist_lux/#Training","page":"Adversarial machine learning with Lux.jl","title":"Training","text":"","category":"section"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"We use a simple neural network with one hidden layer and a sigmoid activation function. (There are better performing networks; try experimenting.)","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"chain = Lux.Chain(\n Lux.Dense(28^2 => 32, Lux.sigmoid),\n Lux.Dense(32 => 10),\n Lux.softmax,\n)\nrng = Random.MersenneTwister();\nparameters, state = Lux.setup(rng, chain)\npredictor = (chain, parameters, state);\nnothing #hide","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Here is a function to load our data into the format that predictor expects:","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"function data_loader(data; batchsize, shuffle = false)\n x = reshape(data.features, 28^2, :)\n y = OneHotArrays.onehotbatch(data.targets, 0:9)\n return MLUtils.DataLoader((x, y); batchsize, shuffle)\nend","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"and here is a function to score the percentage of correct labels, where we assign a label by choosing the label of the highest softmax in the final layer.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"function score_model(predictor, data)\n chain, parameters, state = predictor\n x, y = only(data_loader(data; batchsize = length(data)))\n y_hat, _ = chain(x, parameters, state)\n is_correct = OneHotArrays.onecold(y) .== OneHotArrays.onecold(y_hat)\n p = round(100 * sum(is_correct) / length(is_correct); digits = 2)\n println(\"Accuracy = $p %\")\n return\nend","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"The accuracy of our model is only around 10% before training:","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"score_model(predictor, train_data)\nscore_model(predictor, test_data)","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Let's improve that by training our model.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"note: Note\nIt is not the purpose of this tutorial to explain how Lux works; see the documentation at https://lux.csail.mit.edu for more details. Changing the number of epochs or the learning rate can improve the loss.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"begin\n train_loader = data_loader(train_data; batchsize = 256, shuffle = true)\n optimizer_state = Optimisers.setup(Optimisers.Adam(0.0003f0), parameters)\n for epoch in 1:30\n loss = 0.0\n for (x, y) in train_loader\n global state\n (loss_batch, state), pullback = Zygote.pullback(parameters) do p\n y_model, new_state = chain(x, p, state)\n return Lux.CrossEntropyLoss()(y_model, y), new_state\n end\n gradients = only(pullback((one(loss), nothing)))\n Optimisers.update!(optimizer_state, parameters, gradients)\n loss += loss_batch\n end\n loss = round(loss / length(train_loader); digits = 4)\n print(\"Epoch $epoch: loss = $loss\\t\")\n score_model(predictor, test_data)\n end\nend","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Here are the first eight predictions of the test data:","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"function plot_image(predictor, x::Matrix)\n y, _ = chain(vec(x), parameters, state)\n score, index = findmax(y)\n title = \"Predicted: $(index - 1) ($(round(Int, 100 * score))%)\"\n return plot_image(x; title)\nend\n\nplots = [plot_image(predictor, test_data[i].features) for i in 1:8]\nPlots.plot(plots...; size = (1200, 600), layout = (2, 4))","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"We can also look at the best and worst four predictions:","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"x, y = only(data_loader(test_data; batchsize = length(test_data)))\ny_model, _ = chain(x, parameters, state)\nlosses = Lux.CrossEntropyLoss(; agg = identity)(y_model, y)\nindices = sortperm(losses; dims = 2)[[1:4; end-3:end]]\nplots = [plot_image(predictor, test_data[i].features) for i in indices]\nPlots.plot(plots...; size = (1200, 600), layout = (2, 4))","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"There are still some fairly bad mistakes. Can you change the model or training parameters improve to improve things?","category":"page"},{"location":"tutorials/mnist_lux/#JuMP","page":"Adversarial machine learning with Lux.jl","title":"JuMP","text":"","category":"section"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Now that we have a trained machine learning model, we can embed it in a JuMP model.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Here's a function which takes a test case and returns an example that maximizes the probability of the adversarial example.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"function find_adversarial_image(test_case; adversary_label, δ = 0.05)\n model = Model(Ipopt.Optimizer)\n set_silent(model)\n @variable(model, 0 <= x[1:28, 1:28] <= 1)\n @constraint(model, -δ .<= x .- test_case.features .<= δ)\n # Note: we need to use `vec` here because `x` is a 28-by-28 Matrix, but our\n # neural network expects a 28^2 length vector.\n y, _ = MathOptAI.add_predictor(model, predictor, vec(x))\n @objective(model, Max, y[adversary_label+1] - y[test_case.targets+1])\n optimize!(model)\n @assert is_solved_and_feasible(model)\n return value.(x)\nend","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Let's try finding an adversarial example to the third test image. The image on the left is our input image. The network thinks this is a 1 with probability 99%. The image on the right is the adversarial image. The network thinks this is a 7, although it is less confident.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"x_adversary = find_adversarial_image(test_data[3]; adversary_label = 7);\nPlots.plot(\n plot_image(predictor, test_data[3].features),\n plot_image(predictor, Float32.(x_adversary)),\n)","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"This page was generated using Literate.jl.","category":"page"},{"location":"manual/PyTorch/#PyTorch","page":"PyTorch","title":"PyTorch","text":"","category":"section"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"PyTorch is a library for machine learning in Python.","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"The upstream documentation is available at https://pytorch.org/docs/stable/.","category":"page"},{"location":"manual/PyTorch/#Supported-layers","page":"PyTorch","title":"Supported layers","text":"","category":"section"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"MathOptAI supports embedding a PyTorch models into JuMP if it is a nn.Sequential composed of:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"nn.Linear\nnn.ReLU\nnn.Sigmoid\nnn.Softplus\nnn.Tanh","category":"page"},{"location":"manual/PyTorch/#File-format","page":"PyTorch","title":"File format","text":"","category":"section"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"Use torch.save to save a trained PyTorch model to a .pt file:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"#!/usr/bin/python3\nimport torch\nmodel = torch.nn.Sequential(\n torch.nn.Linear(1, 2),\n torch.nn.ReLU(),\n torch.nn.Linear(2, 1),\n)\ntorch.save(model, \"saved_pytorch_model.pt\")","category":"page"},{"location":"manual/PyTorch/#Python-integration","page":"PyTorch","title":"Python integration","text":"","category":"section"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"MathOptAI uses PythonCall.jl to call from Julia into Python.","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"See CondaPkg.jl for more control over how to link Julia to an existing Python environment. For example, if you have an existing Python installation (with PyTorch installed), and it is available in the current Conda environment, set:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"ENV[\"JULIA_CONDAPKG_BACKEND\"] = \"Current\"","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"before importing PythonCall.jl. If the Python installation can be found on the path and it is not in a Conda environment, set:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"ENV[\"JULIA_CONDAPKG_BACKEND\"] = \"Null\"","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"If python is not on your path, you may additionally need to set JULIA_PYTHONCALL_EXE, for example, to:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"ENV[\"JULIA_PYTHONCALL_EXE\"] = \"python3\"","category":"page"},{"location":"manual/PyTorch/#Basic-example","page":"PyTorch","title":"Basic example","text":"","category":"section"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"Use MathOptAI.add_predictor to embed a PyTorch model into a JuMP model:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"using JuMP, MathOptAI\nmodel = Model();\n@variable(model, x[1:1]);\npredictor = MathOptAI.PytorchModel(\"saved_pytorch_model.pt\");\ny, formulation = MathOptAI.add_predictor(model, predictor, x);\ny\nformulation","category":"page"},{"location":"manual/PyTorch/#Reduced-space","page":"PyTorch","title":"Reduced-space","text":"","category":"section"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"Use the reduced_space = true keyword to formulate a reduced-space model:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"using JuMP, MathOptAI\nmodel = Model();\n@variable(model, x[1:1]);\npredictor = MathOptAI.PytorchModel(\"saved_pytorch_model.pt\");\ny, formulation =\n MathOptAI.add_predictor(model, predictor, x; reduced_space = true);\ny\nformulation","category":"page"},{"location":"manual/PyTorch/#Gray-box","page":"PyTorch","title":"Gray-box","text":"","category":"section"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"Use the gray_box = true keyword to embed the network as a nonlinear operator:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"using JuMP, MathOptAI\nmodel = Model();\n@variable(model, x[1:1]);\npredictor = MathOptAI.PytorchModel(\"saved_pytorch_model.pt\");\ny, formulation =\n MathOptAI.add_predictor(model, predictor, x; gray_box = true);\ny\nformulation","category":"page"},{"location":"manual/PyTorch/#Change-how-layers-are-formulated","page":"PyTorch","title":"Change how layers are formulated","text":"","category":"section"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"Pass a dictionary to the config keyword that maps the Symbol name of each PyTorch layer to a MathOptAI predictor:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"using JuMP, MathOptAI\nmodel = Model();\n@variable(model, x[1:1]);\npredictor = MathOptAI.PytorchModel(\"saved_pytorch_model.pt\");\ny, formulation = MathOptAI.add_predictor(\n model,\n predictor,\n x;\n config = Dict(:ReLU => MathOptAI.ReLUSOS1()),\n);\ny\nformulation","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"(Image: )","category":"page"},{"location":"#MathOptAI.jl","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"","category":"section"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"MathOptAI.jl is a JuMP extension for embedding trained AI, machine learning, and statistical learning models into a JuMP optimization model.","category":"page"},{"location":"#License","page":"MathOptAI.jl","title":"License","text":"","category":"section"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"MathOptAI.jl is provided under a BSD-3 license as part of the Optimization and Machine Learning Toolbox project, O4806.","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"See LICENSE.md for details.","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"Despite the name similarity, this project is not affiliated with OMLT, the Optimization and Machine Learning Toolkit.","category":"page"},{"location":"#Installation","page":"MathOptAI.jl","title":"Installation","text":"","category":"section"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"Install MathOptAI.jl using the Julia package manager:","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"import Pkg\nPkg.add(\"MathOptAI\")","category":"page"},{"location":"#Getting-started","page":"MathOptAI.jl","title":"Getting started","text":"","category":"section"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"Here's an example of using MathOptAI to embed a trained neural network from Flux into a JuMP model. The vector of JuMP variables x is fed as input to the neural network. The output y is a vector of JuMP variables that represents the output layer of the neural network. The formulation object stores the additional variables and constraints that were added to model.","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"julia> using JuMP, MathOptAI, Flux\n\njulia> predictor = Flux.Chain(\n Flux.Dense(28^2 => 32, Flux.sigmoid),\n Flux.Dense(32 => 10),\n Flux.softmax,\n );\n\njulia> #= Train the Flux model. Code not shown for simplicity =#\n\njulia> model = JuMP.Model();\n\njulia> JuMP.@variable(model, 0 <= x[1:28^2] <= 1);\n\njulia> y, formulation = MathOptAI.add_predictor(model, predictor, x);\n\njulia> y\n10-element Vector{VariableRef}:\n moai_SoftMax[1]\n moai_SoftMax[2]\n moai_SoftMax[3]\n moai_SoftMax[4]\n moai_SoftMax[5]\n moai_SoftMax[6]\n moai_SoftMax[7]\n moai_SoftMax[8]\n moai_SoftMax[9]\n moai_SoftMax[10]","category":"page"},{"location":"#Getting-help","page":"MathOptAI.jl","title":"Getting help","text":"","category":"section"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"This package is under active development. For help, questions, comments, and suggestions, please open a GitHub issue.","category":"page"},{"location":"#Inspiration","page":"MathOptAI.jl","title":"Inspiration","text":"","category":"section"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"This project is mainly inspired by two existing projects:","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"OMLT\ngurobi-machinelearning","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"Other works, from which we took less inspiration, include:","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"JANOS\nMeLOn\nENTMOOT\nreluMIP\nOptiCL\nPySCIPOpt-ML","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"The 2024 paper of López-Flores et al. is an excellent summary of the state of the field at the time that we started development of MathOptAI.","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"López-Flores, F.J., Ramírez-Márquez, C., Ponce-Ortega J.M. (2024). Process Systems Engineering Tools for Optimization of Trained Machine Learning Models: Comparative and Perspective. Industrial & Engineering Chemistry Research, 63(32), 13966-13979. DOI: 10.1021/acs.iecr.4c00632","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"EditURL = \"gaussian.jl\"","category":"page"},{"location":"tutorials/gaussian/#Function-fitting-with-AbstractGPs","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"","category":"section"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"The purpose of this tutorial is to explain how to embed a Gaussian Process from AbstractGPs into JuMP.","category":"page"},{"location":"tutorials/gaussian/#Required-packages","page":"Function fitting with AbstractGPs","title":"Required packages","text":"","category":"section"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"This tutorial requires the following packages","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"using JuMP\nusing Test\nimport AbstractGPs\nimport Ipopt\nimport MathOptAI\nimport Plots","category":"page"},{"location":"tutorials/gaussian/#Prediction-model","page":"Function fitting with AbstractGPs","title":"Prediction model","text":"","category":"section"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"Assume that we have some true underlying univariate function:","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"x_domain = 0:0.01:2π\ntrue_function(x) = sin(x)\nPlots.plot(x_domain, true_function.(x_domain); label = \"truth\")","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"We don't know the function, but we have access to a limited set of noisy sample points:","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"N = 20\nx_data = rand(x_domain, N)\nnoisy_sampler(x) = true_function(x) + 0.25 * (2rand() - 1)\ny_data = noisy_sampler.(x_data)\nPlots.scatter!(x_data, y_data; label = \"data\")","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"Using the data, we want to build a predictor y = predictor(x). One choice is a Gaussian Process:","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"fx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.4)\np_fx = AbstractGPs.posterior(fx, y_data)\nPlots.plot!(x_domain, p_fx; label = \"GP\", fillalpha = 0.1)","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"Gaussian Processes fit a mean and variance function:","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"AbstractGPs.mean_and_var(p_fx, [π / 2])","category":"page"},{"location":"tutorials/gaussian/#Decision-model","page":"Function fitting with AbstractGPs","title":"Decision model","text":"","category":"section"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"Our goal for this JuMP model is to embed the Gaussian Process from AbstractGPs into the model and then solve for different fixed values of x to recreate the function that the Gaussian Process has learned to approximate.","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"First, create a JuMP model:","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"model = Model(Ipopt.Optimizer)\nset_silent(model)\n@variable(model, x)","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"Since a Gaussian Process is a infinite dimensional object (its prediction is a distribution), we need some way of converting the Gaussian Process into a finite set of scalar values. For this, we use the Quantile predictor:","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"predictor = MathOptAI.Quantile(p_fx, [0.25, 0.75]);\ny, _ = MathOptAI.add_predictor(model, predictor, [x])","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"Now, visualize the fitted function y = predictor(x) by repeatedly solving the optimization problem for different fixed values of x. Each value of y has two elements: one for the 25th percentile and one for the 75th.","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"X, Y = range(0, 2π; length = 20), Any[]\n@constraint(model, c, x == 0.0)\nfor xi in X\n set_normalized_rhs(c, xi)\n optimize!(model)\n if is_solved_and_feasible(model)\n push!(Y, value.(y))\n else\n push!(Y, [NaN, NaN])\n end\nend\nPlots.plot!(X, reduce(hcat, Y)'; label = [\"P25\" \"P75\"], linewidth = 3)","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"This page was generated using Literate.jl.","category":"page"}] +} diff --git a/dev/siteinfo.js b/dev/siteinfo.js new file mode 100644 index 00000000..33434919 --- /dev/null +++ b/dev/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "dev"; diff --git a/dev/tutorials/decision_trees.jl b/dev/tutorials/decision_trees.jl new file mode 100644 index 00000000..7eabb4ea --- /dev/null +++ b/dev/tutorials/decision_trees.jl @@ -0,0 +1,138 @@ +# Copyright (c) 2024: Oscar Dowson and contributors #src +# Copyright (c) 2024: Triad National Security, LLC #src +# #src +# Use of this source code is governed by a BSD-style license that can be #src +# found in the LICENSE.md file. #src + +# # Classification problems with DecisionTree.jl + +# The purpose of this tutorial is to explain how to embed a decision tree +# model from [DecisionTree.jl](https://github.com/JuliaAI/DecisionTree.jl) into +# JuMP. + +# The data and example in this tutorial comes from the paper: David Bergman, +# Teng Huang, Philip Brooks, Andrea Lodi, Arvind U. Raghunathan (2021) JANOS: An +# Integrated Predictive and Prescriptive Modeling Framework. INFORMS Journal on +# Computing 34(2):807-816. +# [https://doi.org/10.1287/ijoc.2020.1023](https://doi.org/10.1287/ijoc.2020.1023) + +# ## Required packages + +# This tutorial uses the following packages. + +using JuMP +import CSV +import DataFrames +import Downloads +import DecisionTree +import HiGHS +import MathOptAI +import Statistics + +# ## Data + +# Here is a function to load the data directly from the JANOS repository: + +function read_df(filename) + url = "https://raw.githubusercontent.com/INFORMSJoC/2020.1023/master/data/" + data = Downloads.download(url * filename) + return CSV.read(data, DataFrames.DataFrame) +end + +# There are two important files. The first, `college_student_enroll-s1-1.csv`, +# contains historical admissions data on anonymized students, their SAT score, +# their GPA, their merit scholarships, and whether the enrolled in the college. + +train_df = read_df("college_student_enroll-s1-1.csv") + +# The second, `college_applications6000.csv`, contains the SAT and GPA data of +# students who are currently applying: + +evaluate_df = read_df("college_applications6000.csv") + +# There are 6,000 prospective students: + +n_students = size(evaluate_df, 1) + +# ## Prediction model + +# The first step is to train a logistic regression model to predict the Boolean +# `enroll` column based on the `SAT`, `GPA`, and `merit` columns. + +train_features = Matrix(train_df[:, [:SAT, :GPA, :merit]]) +train_labels = train_df[:, :enroll] +predictor = DecisionTree.DecisionTreeClassifier(; max_depth = 3) +DecisionTree.fit!(predictor, train_features, train_labels) +DecisionTree.print_tree(predictor) + +# ## Decision model + +# Now that we have a trained decision tree, we want a decision model that +# chooses the optimal merit scholarship for each student in: + +evaluate_df + +# Here's an empty JuMP model to start: + +model = Model() + +# First, we add a new column to `evaluate_df`, with one JuMP decision variable +# for each row. It is important the `.merit` column name in `evaluate_df` +# matches the name in `train_df`. + +evaluate_df.merit = @variable(model, 0 <= x_merit[1:n_students] <= 2.5); +evaluate_df + +# Then, we use [`MathOptAI.add_predictor`](@ref) to embed `model_ml` into the +# JuMP `model`. [`MathOptAI.add_predictor`](@ref) returns a vector of variables, +# one for each row in `evaluate_df`, corresponding to the output `enroll` of +# our logistic regression. + +evaluate_features = Matrix(evaluate_df[:, [:SAT, :GPA, :merit]]) +evaluate_df.enroll = mapreduce(vcat, 1:size(evaluate_features, 1)) do i + y, _ = MathOptAI.add_predictor(model, predictor, evaluate_features[i, :]) + return y +end +evaluate_df + +# The `.enroll` column name in `evaluate_df` is just a name. It doesn't have to +# match the name in `train_df`. + +# The objective of our problem is to maximize the expected number of students +# who enroll: + +@objective(model, Max, sum(evaluate_df.enroll)) + +# Subject to the constraint that we can spend at most `0.2 * n_students` on +# merit scholarships: + +@constraint(model, sum(evaluate_df.merit) <= 0.2 * n_students) + +# Because logistic regression involves a [`Sigmoid`](@ref) layer, we need to use +# a smooth nonlinear optimizer. A common choice is Ipopt. Solve and check the +# optimizer found a feasible solution: + +set_optimizer(model, HiGHS.Optimizer) +set_silent(model) +optimize!(model) +@assert is_solved_and_feasible(model) + +# Let's store the solution in `evaluate_df` for analysis: + +evaluate_df.merit_sol = value.(evaluate_df.merit); +evaluate_df.enroll_sol = value.(evaluate_df.enroll); +evaluate_df + +# ## Solution analysis + +# We expect that just under 2,500 students will enroll: + +sum(evaluate_df.enroll_sol) + +# We awarded merit scholarships to approximately 1 in 6 students: + +count(evaluate_df.merit_sol .> 1e-5) + +# The average merit scholarship was worth just under \$1,000: + +1_000 * Statistics.mean(evaluate_df.merit_sol[evaluate_df.merit_sol.>1e-5]) diff --git a/dev/tutorials/decision_trees/index.html b/dev/tutorials/decision_trees/index.html new file mode 100644 index 00000000..53473b74 --- /dev/null +++ b/dev/tutorials/decision_trees/index.html @@ -0,0 +1,246 @@ + +Classification problems with DecisionTree.jl · MathOptAI.jl
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Classification problems with DecisionTree.jl

The purpose of this tutorial is to explain how to embed a decision tree model from DecisionTree.jl into JuMP.

The data and example in this tutorial comes from the paper: David Bergman, Teng Huang, Philip Brooks, Andrea Lodi, Arvind U. Raghunathan (2021) JANOS: An Integrated Predictive and Prescriptive Modeling Framework. INFORMS Journal on Computing 34(2):807-816. https://doi.org/10.1287/ijoc.2020.1023

Required packages

This tutorial uses the following packages.

julia> using JuMP
julia> import CSV
julia> import DataFrames
julia> import Downloads
julia> import DecisionTree
julia> import HiGHS
julia> import MathOptAI
julia> import Statistics

Data

Here is a function to load the data directly from the JANOS repository:

julia> function read_df(filename)
+           url = "https://raw.githubusercontent.com/INFORMSJoC/2020.1023/master/data/"
+           data = Downloads.download(url * filename)
+           return CSV.read(data, DataFrames.DataFrame)
+       endread_df (generic function with 1 method)

There are two important files. The first, college_student_enroll-s1-1.csv, contains historical admissions data on anonymized students, their SAT score, their GPA, their merit scholarships, and whether the enrolled in the college.

julia> train_df = read_df("college_student_enroll-s1-1.csv")20000×6 DataFrame
+   Row │ Column1  StudentID  SAT    GPA      merit    enroll 
+       │ Int64    Int64      Int64  Float64  Float64  Int64  
+───────┼─────────────────────────────────────────────────────
+     1 │       1          1   1507     3.72     1.64       0
+     2 │       2          2   1532     3.93     0.52       0
+     3 │       3          3   1487     3.77     1.67       0
+     4 │       4          4   1259     3.05     1.21       1
+     5 │       5          5   1354     3.39     1.65       1
+     6 │       6          6   1334     3.22     0.0        0
+     7 │       7          7   1125     2.73     1.68       1
+     8 │       8          8   1180     2.82     0.0        1
+   ⋮   │    ⋮         ⋮        ⋮       ⋮        ⋮       ⋮
+ 19994 │   19994      19994   1185     3.09     1.16       1
+ 19995 │   19995      19995   1471     3.7      1.05       0
+ 19996 │   19996      19996   1139     3.03     1.21       1
+ 19997 │   19997      19997   1371     3.39     1.26       0
+ 19998 │   19998      19998   1424     3.72     0.85       0
+ 19999 │   19999      19999   1170     3.01     0.73       1
+ 20000 │   20000      20000   1389     3.57     0.55       0
+                                           19985 rows omitted

The second, college_applications6000.csv, contains the SAT and GPA data of students who are currently applying:

julia> evaluate_df = read_df("college_applications6000.csv")6000×3 DataFrame
+  Row │ StudentID  SAT    GPA     
+      │ Int64      Int64  Float64 
+──────┼───────────────────────────
+    1 │         1   1240     3.22
+    2 │         2   1206     2.87
+    3 │         3   1520     3.74
+    4 │         4   1238     3.11
+    5 │         5   1142     2.74
+    6 │         6   1086     2.77
+    7 │         7   1367     3.28
+    8 │         8   1034     2.41
+  ⋮   │     ⋮        ⋮       ⋮
+ 5994 │      5994   1121     2.96
+ 5995 │      5995   1564     4.1
+ 5996 │      5996   1332     3.14
+ 5997 │      5997   1228     2.95
+ 5998 │      5998   1165     2.81
+ 5999 │      5999   1400     3.43
+ 6000 │      6000   1097     2.65
+                 5985 rows omitted

There are 6,000 prospective students:

julia> n_students = size(evaluate_df, 1)6000

Prediction model

The first step is to train a logistic regression model to predict the Boolean enroll column based on the SAT, GPA, and merit columns.

julia> train_features = Matrix(train_df[:, [:SAT, :GPA, :merit]])20000×3 Matrix{Float64}:
+ 1507.0  3.72  1.64
+ 1532.0  3.93  0.52
+ 1487.0  3.77  1.67
+ 1259.0  3.05  1.21
+ 1354.0  3.39  1.65
+ 1334.0  3.22  0.0
+ 1125.0  2.73  1.68
+ 1180.0  2.82  0.0
+ 1098.0  2.91  0.0
+ 1116.0  2.95  0.0
+    ⋮
+ 1048.0  2.51  0.73
+ 1157.0  2.79  2.11
+ 1185.0  3.09  1.16
+ 1471.0  3.7   1.05
+ 1139.0  3.03  1.21
+ 1371.0  3.39  1.26
+ 1424.0  3.72  0.85
+ 1170.0  3.01  0.73
+ 1389.0  3.57  0.55
julia> train_labels = train_df[:, :enroll]20000-element Vector{Int64}:
+ 0
+ 0
+ 0
+ 1
+ 1
+ 0
+ 1
+ 1
+ 1
+ 1
+ ⋮
+ 1
+ 1
+ 1
+ 0
+ 1
+ 0
+ 0
+ 1
+ 0
julia> predictor = DecisionTree.DecisionTreeClassifier(; max_depth = 3)DecisionTreeClassifier
+max_depth:                3
+min_samples_leaf:         1
+min_samples_split:        2
+min_purity_increase:      0.0
+pruning_purity_threshold: 1.0
+n_subfeatures:            0
+classes:                  nothing
+root:                     nothing
julia> DecisionTree.fit!(predictor, train_features, train_labels)DecisionTreeClassifier
+max_depth:                3
+min_samples_leaf:         1
+min_samples_split:        2
+min_purity_increase:      0.0
+pruning_purity_threshold: 1.0
+n_subfeatures:            0
+classes:                  [0, 1]
+root:                     Decision Tree
+Leaves: 8
+Depth:  3
julia> DecisionTree.print_tree(predictor)Feature 1 < 1228.0 ?
+├─ Feature 2 < 3.125 ?
+    ├─ Feature 1 < 1214.0 ?
+        ├─ 1 : 7336/7336
+        └─ 1 : 334/361
+    └─ Feature 3 < 0.255 ?
+        ├─ 0 : 161/220
+        └─ 1 : 121/121
+└─ Feature 1 < 1412.0 ?
+    ├─ Feature 3 < 1.005 ?
+        ├─ 0 : 3600/4046
+        └─ 1 : 1603/2338
+    └─ Feature 3 < 1.865 ?
+        ├─ 0 : 4530/4530
+        └─ 0 : 947/1048

Decision model

Now that we have a trained decision tree, we want a decision model that chooses the optimal merit scholarship for each student in:

julia> evaluate_df6000×3 DataFrame
+  Row │ StudentID  SAT    GPA     
+      │ Int64      Int64  Float64 
+──────┼───────────────────────────
+    1 │         1   1240     3.22
+    2 │         2   1206     2.87
+    3 │         3   1520     3.74
+    4 │         4   1238     3.11
+    5 │         5   1142     2.74
+    6 │         6   1086     2.77
+    7 │         7   1367     3.28
+    8 │         8   1034     2.41
+  ⋮   │     ⋮        ⋮       ⋮
+ 5994 │      5994   1121     2.96
+ 5995 │      5995   1564     4.1
+ 5996 │      5996   1332     3.14
+ 5997 │      5997   1228     2.95
+ 5998 │      5998   1165     2.81
+ 5999 │      5999   1400     3.43
+ 6000 │      6000   1097     2.65
+                 5985 rows omitted

Here's an empty JuMP model to start:

julia> model = Model()A JuMP Model
+├ solver: none
+├ objective_sense: FEASIBILITY_SENSE
+├ num_variables: 0
+├ num_constraints: 0
+└ Names registered in the model: none

First, we add a new column to evaluate_df, with one JuMP decision variable for each row. It is important the .merit column name in evaluate_df matches the name in train_df.

julia> evaluate_df.merit = @variable(model, 0 <= x_merit[1:n_students] <= 2.5);
julia> evaluate_df6000×4 DataFrame
+  Row │ StudentID  SAT    GPA      merit         
+      │ Int64      Int64  Float64  GenericV…     
+──────┼──────────────────────────────────────────
+    1 │         1   1240     3.22  x_merit[1]
+    2 │         2   1206     2.87  x_merit[2]
+    3 │         3   1520     3.74  x_merit[3]
+    4 │         4   1238     3.11  x_merit[4]
+    5 │         5   1142     2.74  x_merit[5]
+    6 │         6   1086     2.77  x_merit[6]
+    7 │         7   1367     3.28  x_merit[7]
+    8 │         8   1034     2.41  x_merit[8]
+  ⋮   │     ⋮        ⋮       ⋮           ⋮
+ 5994 │      5994   1121     2.96  x_merit[5994]
+ 5995 │      5995   1564     4.1   x_merit[5995]
+ 5996 │      5996   1332     3.14  x_merit[5996]
+ 5997 │      5997   1228     2.95  x_merit[5997]
+ 5998 │      5998   1165     2.81  x_merit[5998]
+ 5999 │      5999   1400     3.43  x_merit[5999]
+ 6000 │      6000   1097     2.65  x_merit[6000]
+                                5985 rows omitted

Then, we use MathOptAI.add_predictor to embed model_ml into the JuMP model. MathOptAI.add_predictor returns a vector of variables, one for each row in evaluate_df, corresponding to the output enroll of our logistic regression.

julia> evaluate_features = Matrix(evaluate_df[:, [:SAT, :GPA, :merit]])6000×3 Matrix{JuMP.AffExpr}:
+ 1240  3.22  x_merit[1]
+ 1206  2.87  x_merit[2]
+ 1520  3.74  x_merit[3]
+ 1238  3.11  x_merit[4]
+ 1142  2.74  x_merit[5]
+ 1086  2.77  x_merit[6]
+ 1367  3.28  x_merit[7]
+ 1034  2.41  x_merit[8]
+ 1547  3.82  x_merit[9]
+ 1453  3.65  x_merit[10]
+ ⋮
+ 1299  3.16  x_merit[5992]
+ 1400  3.59  x_merit[5993]
+ 1121  2.96  x_merit[5994]
+ 1564  4.1   x_merit[5995]
+ 1332  3.14  x_merit[5996]
+ 1228  2.95  x_merit[5997]
+ 1165  2.81  x_merit[5998]
+ 1400  3.43  x_merit[5999]
+ 1097  2.65  x_merit[6000]
julia> evaluate_df.enroll = mapreduce(vcat, 1:size(evaluate_features, 1)) do i
+           y, _ = MathOptAI.add_predictor(model, predictor, evaluate_features[i, :])
+           return y
+       end6000-element Vector{JuMP.VariableRef}:
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ ⋮
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
julia> evaluate_df6000×5 DataFrame
+  Row │ StudentID  SAT    GPA      merit          enroll                       ⋯
+      │ Int64      Int64  Float64  GenericV…      GenericV…                    ⋯
+──────┼─────────────────────────────────────────────────────────────────────────
+    1 │         1   1240     3.22  x_merit[1]     moai_BinaryDecisionTree_valu ⋯
+    2 │         2   1206     2.87  x_merit[2]     moai_BinaryDecisionTree_valu
+    3 │         3   1520     3.74  x_merit[3]     moai_BinaryDecisionTree_valu
+    4 │         4   1238     3.11  x_merit[4]     moai_BinaryDecisionTree_valu
+    5 │         5   1142     2.74  x_merit[5]     moai_BinaryDecisionTree_valu ⋯
+    6 │         6   1086     2.77  x_merit[6]     moai_BinaryDecisionTree_valu
+    7 │         7   1367     3.28  x_merit[7]     moai_BinaryDecisionTree_valu
+    8 │         8   1034     2.41  x_merit[8]     moai_BinaryDecisionTree_valu
+  ⋮   │     ⋮        ⋮       ⋮           ⋮                      ⋮              ⋱
+ 5994 │      5994   1121     2.96  x_merit[5994]  moai_BinaryDecisionTree_valu ⋯
+ 5995 │      5995   1564     4.1   x_merit[5995]  moai_BinaryDecisionTree_valu
+ 5996 │      5996   1332     3.14  x_merit[5996]  moai_BinaryDecisionTree_valu
+ 5997 │      5997   1228     2.95  x_merit[5997]  moai_BinaryDecisionTree_valu
+ 5998 │      5998   1165     2.81  x_merit[5998]  moai_BinaryDecisionTree_valu ⋯
+ 5999 │      5999   1400     3.43  x_merit[5999]  moai_BinaryDecisionTree_valu
+ 6000 │      6000   1097     2.65  x_merit[6000]  moai_BinaryDecisionTree_valu
+                                                  1 column and 5985 rows omitted

The .enroll column name in evaluate_df is just a name. It doesn't have to match the name in train_df.

The objective of our problem is to maximize the expected number of students who enroll:

julia> @objective(model, Max, sum(evaluate_df.enroll))moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + [[...5940 terms omitted...]] + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value

Subject to the constraint that we can spend at most 0.2 * n_students on merit scholarships:

julia> @constraint(model, sum(evaluate_df.merit) <= 0.2 * n_students)x_merit[1] + x_merit[2] + x_merit[3] + x_merit[4] + x_merit[5] + x_merit[6] + x_merit[7] + x_merit[8] + x_merit[9] + x_merit[10] + x_merit[11] + x_merit[12] + x_merit[13] + x_merit[14] + x_merit[15] + x_merit[16] + x_merit[17] + x_merit[18] + x_merit[19] + x_merit[20] + x_merit[21] + x_merit[22] + x_merit[23] + x_merit[24] + x_merit[25] + x_merit[26] + x_merit[27] + x_merit[28] + x_merit[29] + x_merit[30] + [[...5940 terms omitted...]] + x_merit[5971] + x_merit[5972] + x_merit[5973] + x_merit[5974] + x_merit[5975] + x_merit[5976] + x_merit[5977] + x_merit[5978] + x_merit[5979] + x_merit[5980] + x_merit[5981] + x_merit[5982] + x_merit[5983] + x_merit[5984] + x_merit[5985] + x_merit[5986] + x_merit[5987] + x_merit[5988] + x_merit[5989] + x_merit[5990] + x_merit[5991] + x_merit[5992] + x_merit[5993] + x_merit[5994] + x_merit[5995] + x_merit[5996] + x_merit[5997] + x_merit[5998] + x_merit[5999] + x_merit[6000] ≤ 1200

Because logistic regression involves a Sigmoid layer, we need to use a smooth nonlinear optimizer. A common choice is Ipopt. Solve and check the optimizer found a feasible solution:

julia> set_optimizer(model, HiGHS.Optimizer)
julia> set_silent(model)
julia> optimize!(model)
julia> @assert is_solved_and_feasible(model)

Let's store the solution in evaluate_df for analysis:

julia> evaluate_df.merit_sol = value.(evaluate_df.merit);
julia> evaluate_df.enroll_sol = value.(evaluate_df.enroll);
julia> evaluate_df6000×7 DataFrame
+  Row │ StudentID  SAT    GPA      merit          enroll                       ⋯
+      │ Int64      Int64  Float64  GenericV…      GenericV…                    ⋯
+──────┼─────────────────────────────────────────────────────────────────────────
+    1 │         1   1240     3.22  x_merit[1]     moai_BinaryDecisionTree_valu ⋯
+    2 │         2   1206     2.87  x_merit[2]     moai_BinaryDecisionTree_valu
+    3 │         3   1520     3.74  x_merit[3]     moai_BinaryDecisionTree_valu
+    4 │         4   1238     3.11  x_merit[4]     moai_BinaryDecisionTree_valu
+    5 │         5   1142     2.74  x_merit[5]     moai_BinaryDecisionTree_valu ⋯
+    6 │         6   1086     2.77  x_merit[6]     moai_BinaryDecisionTree_valu
+    7 │         7   1367     3.28  x_merit[7]     moai_BinaryDecisionTree_valu
+    8 │         8   1034     2.41  x_merit[8]     moai_BinaryDecisionTree_valu
+  ⋮   │     ⋮        ⋮       ⋮           ⋮                      ⋮              ⋱
+ 5994 │      5994   1121     2.96  x_merit[5994]  moai_BinaryDecisionTree_valu ⋯
+ 5995 │      5995   1564     4.1   x_merit[5995]  moai_BinaryDecisionTree_valu
+ 5996 │      5996   1332     3.14  x_merit[5996]  moai_BinaryDecisionTree_valu
+ 5997 │      5997   1228     2.95  x_merit[5997]  moai_BinaryDecisionTree_valu
+ 5998 │      5998   1165     2.81  x_merit[5998]  moai_BinaryDecisionTree_valu ⋯
+ 5999 │      5999   1400     3.43  x_merit[5999]  moai_BinaryDecisionTree_valu
+ 6000 │      6000   1097     2.65  x_merit[6000]  moai_BinaryDecisionTree_valu
+                                                 3 columns and 5985 rows omitted

Solution analysis

We expect that just under 2,500 students will enroll:

julia> sum(evaluate_df.enroll_sol)3530.0

We awarded merit scholarships to approximately 1 in 6 students:

julia> count(evaluate_df.merit_sol .> 1e-5)1278

The average merit scholarship was worth just under $1,000:

julia> 1_000 * Statistics.mean(evaluate_df.merit_sol[evaluate_df.merit_sol.>1e-5])938.6854460093895

This page was generated using Literate.jl.

diff --git a/dev/tutorials/gaussian.jl b/dev/tutorials/gaussian.jl new file mode 100644 index 00000000..3bf78e90 --- /dev/null +++ b/dev/tutorials/gaussian.jl @@ -0,0 +1,87 @@ +# Copyright (c) 2024: Oscar Dowson and contributors #src +# Copyright (c) 2024: Triad National Security, LLC #src +# #src +# Use of this source code is governed by a BSD-style license that can be #src +# found in the LICENSE.md file. #src + +# # Function fitting with AbstractGPs + +# The purpose of this tutorial is to explain how to embed a Gaussian Process +# from [AbstractGPs](https://github.com/JuliaGaussianProcesses/AbstractGPs.jl) +# into JuMP. + +# ## Required packages + +# This tutorial requires the following packages + +using JuMP +using Test +import AbstractGPs +import Ipopt +import MathOptAI +import Plots + +# ## Prediction model + +# Assume that we have some true underlying univariate function: + +x_domain = 0:0.01:2π +true_function(x) = sin(x) +Plots.plot(x_domain, true_function.(x_domain); label = "truth") + +# We don't know the function, but we have access to a limited set of noisy +# sample points: + +N = 20 +x_data = rand(x_domain, N) +noisy_sampler(x) = true_function(x) + 0.25 * (2rand() - 1) +y_data = noisy_sampler.(x_data) +Plots.scatter!(x_data, y_data; label = "data") + +# Using the data, we want to build a predictor `y = predictor(x)`. One choice is +# a Gaussian Process: + +fx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.4) +p_fx = AbstractGPs.posterior(fx, y_data) +Plots.plot!(x_domain, p_fx; label = "GP", fillalpha = 0.1) + +# Gaussian Processes fit a mean and variance function: + +AbstractGPs.mean_and_var(p_fx, [π / 2]) + +# ## Decision model + +# Our goal for this JuMP model is to embed the Gaussian Process from AbstractGPs +# into the model and then solve for different fixed values of `x` to recreate +# the function that the Gaussian Process has learned to approximate. + +# First, create a JuMP model: + +model = Model(Ipopt.Optimizer) +set_silent(model) +@variable(model, x) + +# Since a Gaussian Process is a infinite dimensional object (its prediction is a +# distribution), we need some way of converting the Gaussian Process into a +# finite set of scalar values. For this, we use the [`Quantile`](@ref) +# predictor: + +predictor = MathOptAI.Quantile(p_fx, [0.25, 0.75]); +y, _ = MathOptAI.add_predictor(model, predictor, [x]) + +# Now, visualize the fitted function `y = predictor(x)` by repeatedly solving +# the optimization problem for different fixed values of `x`. Each value of `y` +# has two elements: one for the 25th percentile and one for the 75th. + +X, Y = range(0, 2π; length = 20), Any[] +@constraint(model, c, x == 0.0) +for xi in X + set_normalized_rhs(c, xi) + optimize!(model) + if is_solved_and_feasible(model) + push!(Y, value.(y)) + else + push!(Y, [NaN, NaN]) + end +end +Plots.plot!(X, reduce(hcat, Y)'; label = ["P25" "P75"], linewidth = 3) diff --git a/dev/tutorials/gaussian/0a432f4f.svg b/dev/tutorials/gaussian/0a432f4f.svg new file mode 100644 index 00000000..6fc527a1 --- /dev/null +++ b/dev/tutorials/gaussian/0a432f4f.svg @@ -0,0 +1,76 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/dev/tutorials/gaussian/a91833ac.svg b/dev/tutorials/gaussian/a91833ac.svg new file mode 100644 index 00000000..f245effd --- /dev/null +++ b/dev/tutorials/gaussian/a91833ac.svg @@ -0,0 +1,50 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/dev/tutorials/gaussian/b7d134a7.svg b/dev/tutorials/gaussian/b7d134a7.svg new file mode 100644 index 00000000..34832d2a --- /dev/null +++ b/dev/tutorials/gaussian/b7d134a7.svg @@ -0,0 +1,80 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/dev/tutorials/gaussian/c02934ec.svg b/dev/tutorials/gaussian/c02934ec.svg new file mode 100644 index 00000000..a42fbeab --- /dev/null +++ b/dev/tutorials/gaussian/c02934ec.svg @@ -0,0 +1,71 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/dev/tutorials/gaussian/index.html b/dev/tutorials/gaussian/index.html new file mode 100644 index 00000000..8cc0fd69 --- /dev/null +++ b/dev/tutorials/gaussian/index.html @@ -0,0 +1,31 @@ + +Function fitting with AbstractGPs · MathOptAI.jl
GitHub

Function fitting with AbstractGPs

The purpose of this tutorial is to explain how to embed a Gaussian Process from AbstractGPs into JuMP.

Required packages

This tutorial requires the following packages

using JuMP
+using Test
+import AbstractGPs
+import Ipopt
+import MathOptAI
+import Plots

Prediction model

Assume that we have some true underlying univariate function:

x_domain = 0:0.01:2π
+true_function(x) = sin(x)
+Plots.plot(x_domain, true_function.(x_domain); label = "truth")
Example block output

We don't know the function, but we have access to a limited set of noisy sample points:

N = 20
+x_data = rand(x_domain, N)
+noisy_sampler(x) = true_function(x) + 0.25 * (2rand() - 1)
+y_data = noisy_sampler.(x_data)
+Plots.scatter!(x_data, y_data; label = "data")
Example block output

Using the data, we want to build a predictor y = predictor(x). One choice is a Gaussian Process:

fx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.4)
+p_fx = AbstractGPs.posterior(fx, y_data)
+Plots.plot!(x_domain, p_fx; label = "GP", fillalpha = 0.1)
Example block output

Gaussian Processes fit a mean and variance function:

AbstractGPs.mean_and_var(p_fx, [π / 2])
([1.0370856314540664], [0.14953967972147553])

Decision model

Our goal for this JuMP model is to embed the Gaussian Process from AbstractGPs into the model and then solve for different fixed values of x to recreate the function that the Gaussian Process has learned to approximate.

First, create a JuMP model:

model = Model(Ipopt.Optimizer)
+set_silent(model)
+@variable(model, x)

\[ x \]

Since a Gaussian Process is a infinite dimensional object (its prediction is a distribution), we need some way of converting the Gaussian Process into a finite set of scalar values. For this, we use the Quantile predictor:

predictor = MathOptAI.Quantile(p_fx, [0.25, 0.75]);
+y, _ = MathOptAI.add_predictor(model, predictor, [x])
(JuMP.VariableRef[moai_quantile[1], moai_quantile[2]], Quantile(_, [0.25, 0.75])
+├ variables [0]
+└ constraints [0])

Now, visualize the fitted function y = predictor(x) by repeatedly solving the optimization problem for different fixed values of x. Each value of y has two elements: one for the 25th percentile and one for the 75th.

X, Y = range(0, 2π; length = 20), Any[]
+@constraint(model, c, x == 0.0)
+for xi in X
+    set_normalized_rhs(c, xi)
+    optimize!(model)
+    if is_solved_and_feasible(model)
+        push!(Y, value.(y))
+    else
+        push!(Y, [NaN, NaN])
+    end
+end
+Plots.plot!(X, reduce(hcat, Y)'; label = ["P25" "P75"], linewidth = 3)
Example block output

This page was generated using Literate.jl.

diff --git a/dev/tutorials/mnist.jl b/dev/tutorials/mnist.jl new file mode 100644 index 00000000..e1dbab52 --- /dev/null +++ b/dev/tutorials/mnist.jl @@ -0,0 +1,171 @@ +# Copyright (c) 2024: Oscar Dowson and contributors #src +# Copyright (c) 2024: Triad National Security, LLC #src +# #src +# Use of this source code is governed by a BSD-style license that can be #src +# found in the LICENSE.md file. #src + +# # Adversarial machine learning with Flux.jl + +# The purpose of this tutorial is to explain how to embed a neural network model +# from [Flux.jl](https://github.com/FluxML/Flux.jl) into JuMP. + +# ## Required packages + +# This tutorial requires the following packages + +using JuMP +import Flux +import Ipopt +import MathOptAI +import MLDatasets +import Plots + +# ## Data + +# This tutorial uses images from the MNIST dataset. + +# We load the predefined train and test splits: + +train_data = MLDatasets.MNIST(; split = :train) + +#- + +test_data = MLDatasets.MNIST(; split = :test) + +# Since the data are images, it is helpful to plot them. (This requires a +# transpose and reversing the rows to get the orientation correct.) + +function plot_image(x::Matrix; kwargs...) + return Plots.heatmap( + x'[size(x, 1):-1:1, :]; + xlims = (1, size(x, 2)), + ylims = (1, size(x, 1)), + aspect_ratio = true, + legend = false, + xaxis = false, + yaxis = false, + kwargs..., + ) +end + +function plot_image(instance::NamedTuple) + return plot_image(instance.features; title = "Label = $(instance.targets)") +end + +Plots.plot([plot_image(train_data[i]) for i in 1:6]...; layout = (2, 3)) + +# ## Training + +# We use a simple neural network with one hidden layer and a sigmoid activation +# function. (There are better performing networks; try experimenting.) + +predictor = Flux.Chain( + Flux.Dense(28^2 => 32, Flux.sigmoid), + Flux.Dense(32 => 10), + Flux.softmax, +) + +# Here is a function to load our data into the format that `predictor` expects: +function data_loader(data; batchsize, shuffle = false) + x = reshape(data.features, 28^2, :) + y = Flux.onehotbatch(data.targets, 0:9) + return Flux.DataLoader((x, y); batchsize, shuffle) +end + +# and here is a function to score the percentage of correct labels, where we +# assign a label by choosing the label of the highest `softmax` in the final +# layer. + +function score_model(predictor, data) + x, y = only(data_loader(data; batchsize = length(data))) + y_hat = predictor(x) + is_correct = Flux.onecold(y) .== Flux.onecold(y_hat) + p = round(100 * sum(is_correct) / length(is_correct); digits = 2) + println("Accuracy = $p %") + return +end + +# The accuracy of our model is only around 10% before training: + +score_model(predictor, train_data) +score_model(predictor, test_data) + +# Let's improve that by training our model. + +# !!! note +# It is not the purpose of this tutorial to explain how Flux works; see the +# documentation at [https://fluxml.ai](https://fluxml.ai) for more details. +# Changing the number of epochs or the learning rate can improve the loss. + +begin + train_loader = data_loader(train_data; batchsize = 256, shuffle = true) + optimizer_state = Flux.setup(Flux.Adam(3e-4), predictor) + for epoch in 1:30 + loss = 0.0 + for (x, y) in train_loader + loss_batch, gradient = Flux.withgradient(predictor) do model + return Flux.crossentropy(model(x), y) + end + Flux.update!(optimizer_state, predictor, only(gradient)) + loss += loss_batch + end + loss = round(loss / length(train_loader); digits = 4) + print("Epoch $epoch: loss = $loss\t") + score_model(predictor, test_data) + end +end + +# Here are the first eight predictions of the test data: + +function plot_image(predictor, x::Matrix) + score, index = findmax(predictor(vec(x))) + title = "Predicted: $(index - 1) ($(round(Int, 100 * score))%)" + return plot_image(x; title) +end + +plots = [plot_image(predictor, test_data[i].features) for i in 1:8] +Plots.plot(plots...; size = (1200, 600), layout = (2, 4)) + +# We can also look at the best and worst four predictions: + +x, y = only(data_loader(test_data; batchsize = length(test_data))) +losses = Flux.crossentropy(predictor(x), y; agg = identity) +indices = sortperm(losses; dims = 2)[[1:4; end-3:end]] +plots = [plot_image(predictor, test_data[i].features) for i in indices] +Plots.plot(plots...; size = (1200, 600), layout = (2, 4)) + +# There are still some fairly bad mistakes. Can you change the model or training +# parameters improve to improve things? + +# ## JuMP + +# Now that we have a trained machine learning model, we can embed it in a JuMP +# model. + +# Here's a function which takes a test case and returns an example that +# maximizes the probability of the adversarial example. + +function find_adversarial_image(test_case; adversary_label, δ = 0.05) + model = Model(Ipopt.Optimizer) + set_silent(model) + @variable(model, 0 <= x[1:28, 1:28] <= 1) + @constraint(model, -δ .<= x .- test_case.features .<= δ) + ## Note: we need to use `vec` here because `x` is a 28-by-28 Matrix, but our + ## neural network expects a 28^2 length vector. + y, _ = MathOptAI.add_predictor(model, predictor, vec(x)) + @objective(model, Max, y[adversary_label+1] - y[test_case.targets+1]) + optimize!(model) + @assert is_solved_and_feasible(model) + return value.(x) +end + +# Let's try finding an adversarial example to the third test image. The image on +# the left is our input image. The network thinks this is a `1` with probability +# 99%. The image on the right is the adversarial image. The network thinks this +# is a `7`, although it is less confident. + +x_adversary = find_adversarial_image(test_data[3]; adversary_label = 7); +Plots.plot( + plot_image(predictor, test_data[3].features), + plot_image(predictor, Float32.(x_adversary)), +) diff --git a/dev/tutorials/mnist/621cac01.svg b/dev/tutorials/mnist/621cac01.svg new file mode 100644 index 00000000..ae55b196 --- /dev/null +++ b/dev/tutorials/mnist/621cac01.svg @@ -0,0 +1,1221 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/dev/tutorials/mnist/9a9b4b30.svg b/dev/tutorials/mnist/9a9b4b30.svg new file mode 100644 index 00000000..55a42020 --- /dev/null +++ b/dev/tutorials/mnist/9a9b4b30.svg @@ -0,0 +1,327 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/dev/tutorials/mnist/e622c77d.svg b/dev/tutorials/mnist/e622c77d.svg new file mode 100644 index 00000000..a2831e2c --- /dev/null +++ b/dev/tutorials/mnist/e622c77d.svg @@ -0,0 +1,511 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/dev/tutorials/mnist/fa219281.svg b/dev/tutorials/mnist/fa219281.svg new file mode 100644 index 00000000..30360286 --- /dev/null +++ b/dev/tutorials/mnist/fa219281.svg @@ -0,0 +1,1199 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/dev/tutorials/mnist/index.html b/dev/tutorials/mnist/index.html new file mode 100644 index 00000000..a0584566 --- /dev/null +++ b/dev/tutorials/mnist/index.html @@ -0,0 +1,125 @@ + +Adversarial machine learning with Flux.jl · MathOptAI.jl
GitHub

Adversarial machine learning with Flux.jl

The purpose of this tutorial is to explain how to embed a neural network model from Flux.jl into JuMP.

Required packages

This tutorial requires the following packages

using JuMP
+import Flux
+import Ipopt
+import MathOptAI
+import MLDatasets
+import Plots

Data

This tutorial uses images from the MNIST dataset.

We load the predefined train and test splits:

train_data = MLDatasets.MNIST(; split = :train)
dataset MNIST:
+  metadata  =>    Dict{String, Any} with 3 entries
+  split     =>    :train
+  features  =>    28×28×60000 Array{Float32, 3}
+  targets   =>    60000-element Vector{Int64}
test_data = MLDatasets.MNIST(; split = :test)
dataset MNIST:
+  metadata  =>    Dict{String, Any} with 3 entries
+  split     =>    :test
+  features  =>    28×28×10000 Array{Float32, 3}
+  targets   =>    10000-element Vector{Int64}

Since the data are images, it is helpful to plot them. (This requires a transpose and reversing the rows to get the orientation correct.)

function plot_image(x::Matrix; kwargs...)
+    return Plots.heatmap(
+        x'[size(x, 1):-1:1, :];
+        xlims = (1, size(x, 2)),
+        ylims = (1, size(x, 1)),
+        aspect_ratio = true,
+        legend = false,
+        xaxis = false,
+        yaxis = false,
+        kwargs...,
+    )
+end
+
+function plot_image(instance::NamedTuple)
+    return plot_image(instance.features; title = "Label = $(instance.targets)")
+end
+
+Plots.plot([plot_image(train_data[i]) for i in 1:6]...; layout = (2, 3))
Example block output

Training

We use a simple neural network with one hidden layer and a sigmoid activation function. (There are better performing networks; try experimenting.)

predictor = Flux.Chain(
+    Flux.Dense(28^2 => 32, Flux.sigmoid),
+    Flux.Dense(32 => 10),
+    Flux.softmax,
+)
Chain(
+  Dense(784 => 32, σ),                  # 25_120 parameters
+  Dense(32 => 10),                      # 330 parameters
+  NNlib.softmax,
+)                   # Total: 4 arrays, 25_450 parameters, 99.617 KiB.

Here is a function to load our data into the format that predictor expects:

function data_loader(data; batchsize, shuffle = false)
+    x = reshape(data.features, 28^2, :)
+    y = Flux.onehotbatch(data.targets, 0:9)
+    return Flux.DataLoader((x, y); batchsize, shuffle)
+end
data_loader (generic function with 1 method)

and here is a function to score the percentage of correct labels, where we assign a label by choosing the label of the highest softmax in the final layer.

function score_model(predictor, data)
+    x, y = only(data_loader(data; batchsize = length(data)))
+    y_hat = predictor(x)
+    is_correct = Flux.onecold(y) .== Flux.onecold(y_hat)
+    p = round(100 * sum(is_correct) / length(is_correct); digits = 2)
+    println("Accuracy = $p %")
+    return
+end
score_model (generic function with 1 method)

The accuracy of our model is only around 10% before training:

score_model(predictor, train_data)
+score_model(predictor, test_data)
Accuracy = 8.49 %
+Accuracy = 9.19 %

Let's improve that by training our model.

Note

It is not the purpose of this tutorial to explain how Flux works; see the documentation at https://fluxml.ai for more details. Changing the number of epochs or the learning rate can improve the loss.

begin
+    train_loader = data_loader(train_data; batchsize = 256, shuffle = true)
+    optimizer_state = Flux.setup(Flux.Adam(3e-4), predictor)
+    for epoch in 1:30
+        loss = 0.0
+        for (x, y) in train_loader
+            loss_batch, gradient = Flux.withgradient(predictor) do model
+                return Flux.crossentropy(model(x), y)
+            end
+            Flux.update!(optimizer_state, predictor, only(gradient))
+            loss += loss_batch
+        end
+        loss = round(loss / length(train_loader); digits = 4)
+        print("Epoch $epoch: loss = $loss\t")
+        score_model(predictor, test_data)
+    end
+end
Epoch 1: loss = 1.7601	Accuracy = 81.14 %
+Epoch 2: loss = 1.1097	Accuracy = 85.49 %
+Epoch 3: loss = 0.8151	Accuracy = 87.49 %
+Epoch 4: loss = 0.6516	Accuracy = 89.05 %
+Epoch 5: loss = 0.5494	Accuracy = 90.04 %
+Epoch 6: loss = 0.4803	Accuracy = 90.4 %
+Epoch 7: loss = 0.4311	Accuracy = 90.9 %
+Epoch 8: loss = 0.3949	Accuracy = 91.22 %
+Epoch 9: loss = 0.3663	Accuracy = 91.54 %
+Epoch 10: loss = 0.3439	Accuracy = 91.75 %
+Epoch 11: loss = 0.3254	Accuracy = 91.97 %
+Epoch 12: loss = 0.3104	Accuracy = 92.16 %
+Epoch 13: loss = 0.2968	Accuracy = 92.42 %
+Epoch 14: loss = 0.2858	Accuracy = 92.66 %
+Epoch 15: loss = 0.2754	Accuracy = 92.81 %
+Epoch 16: loss = 0.2667	Accuracy = 92.99 %
+Epoch 17: loss = 0.2584	Accuracy = 93.18 %
+Epoch 18: loss = 0.2512	Accuracy = 93.19 %
+Epoch 19: loss = 0.2445	Accuracy = 93.29 %
+Epoch 20: loss = 0.2381	Accuracy = 93.39 %
+Epoch 21: loss = 0.2324	Accuracy = 93.5 %
+Epoch 22: loss = 0.227	Accuracy = 93.61 %
+Epoch 23: loss = 0.2218	Accuracy = 93.71 %
+Epoch 24: loss = 0.2176	Accuracy = 93.89 %
+Epoch 25: loss = 0.2127	Accuracy = 93.97 %
+Epoch 26: loss = 0.2087	Accuracy = 94.07 %
+Epoch 27: loss = 0.2047	Accuracy = 94.09 %
+Epoch 28: loss = 0.2009	Accuracy = 94.22 %
+Epoch 29: loss = 0.1972	Accuracy = 94.31 %
+Epoch 30: loss = 0.1938	Accuracy = 94.35 %

Here are the first eight predictions of the test data:

function plot_image(predictor, x::Matrix)
+    score, index = findmax(predictor(vec(x)))
+    title = "Predicted: $(index - 1) ($(round(Int, 100 * score))%)"
+    return plot_image(x; title)
+end
+
+plots = [plot_image(predictor, test_data[i].features) for i in 1:8]
+Plots.plot(plots...; size = (1200, 600), layout = (2, 4))
Example block output

We can also look at the best and worst four predictions:

x, y = only(data_loader(test_data; batchsize = length(test_data)))
+losses = Flux.crossentropy(predictor(x), y; agg = identity)
+indices = sortperm(losses; dims = 2)[[1:4; end-3:end]]
+plots = [plot_image(predictor, test_data[i].features) for i in indices]
+Plots.plot(plots...; size = (1200, 600), layout = (2, 4))
Example block output

There are still some fairly bad mistakes. Can you change the model or training parameters improve to improve things?

JuMP

Now that we have a trained machine learning model, we can embed it in a JuMP model.

Here's a function which takes a test case and returns an example that maximizes the probability of the adversarial example.

function find_adversarial_image(test_case; adversary_label, δ = 0.05)
+    model = Model(Ipopt.Optimizer)
+    set_silent(model)
+    @variable(model, 0 <= x[1:28, 1:28] <= 1)
+    @constraint(model, -δ .<= x .- test_case.features .<= δ)
+    # Note: we need to use `vec` here because `x` is a 28-by-28 Matrix, but our
+    # neural network expects a 28^2 length vector.
+    y, _ = MathOptAI.add_predictor(model, predictor, vec(x))
+    @objective(model, Max, y[adversary_label+1] - y[test_case.targets+1])
+    optimize!(model)
+    @assert is_solved_and_feasible(model)
+    return value.(x)
+end
find_adversarial_image (generic function with 1 method)

Let's try finding an adversarial example to the third test image. The image on the left is our input image. The network thinks this is a 1 with probability 99%. The image on the right is the adversarial image. The network thinks this is a 7, although it is less confident.

x_adversary = find_adversarial_image(test_data[3]; adversary_label = 7);
+Plots.plot(
+    plot_image(predictor, test_data[3].features),
+    plot_image(predictor, Float32.(x_adversary)),
+)
Example block output

This page was generated using Literate.jl.

diff --git a/dev/tutorials/mnist_lux.jl b/dev/tutorials/mnist_lux.jl new file mode 100644 index 00000000..cd41799e --- /dev/null +++ b/dev/tutorials/mnist_lux.jl @@ -0,0 +1,186 @@ +# Copyright (c) 2024: Oscar Dowson and contributors #src +# Copyright (c) 2024: Triad National Security, LLC #src +# #src +# Use of this source code is governed by a BSD-style license that can be #src +# found in the LICENSE.md file. #src + +# # Adversarial machine learning with Lux.jl + +# The purpose of this tutorial is to explain how to embed a neural network model +# from [Lux.jl](https://github.com/SciML/Lux.jl) into JuMP. + +# ## Required packages + +# This tutorial requires the following packages + +using JuMP +import Lux +import Ipopt +import MathOptAI +import MLDatasets +import MLUtils +import OneHotArrays +import Optimisers +import Plots +import Random +import Zygote + +# ## Data + +# This tutorial uses images from the MNIST dataset. + +# We load the predefined train and test splits: + +train_data = MLDatasets.MNIST(; split = :train) + +#- + +test_data = MLDatasets.MNIST(; split = :test) + +# Since the data are images, it is helpful to plot them. (This requires a +# transpose and reversing the rows to get the orientation correct.) + +function plot_image(x::Matrix; kwargs...) + return Plots.heatmap( + x'[size(x, 1):-1:1, :]; + xlims = (1, size(x, 2)), + ylims = (1, size(x, 1)), + aspect_ratio = true, + legend = false, + xaxis = false, + yaxis = false, + kwargs..., + ) +end + +function plot_image(instance::NamedTuple) + return plot_image(instance.features; title = "Label = $(instance.targets)") +end + +Plots.plot([plot_image(train_data[i]) for i in 1:6]...; layout = (2, 3)) + +# ## Training + +# We use a simple neural network with one hidden layer and a sigmoid activation +# function. (There are better performing networks; try experimenting.) + +chain = Lux.Chain( + Lux.Dense(28^2 => 32, Lux.sigmoid), + Lux.Dense(32 => 10), + Lux.softmax, +) +rng = Random.MersenneTwister(); +parameters, state = Lux.setup(rng, chain) +predictor = (chain, parameters, state); + +# Here is a function to load our data into the format that `predictor` expects: +function data_loader(data; batchsize, shuffle = false) + x = reshape(data.features, 28^2, :) + y = OneHotArrays.onehotbatch(data.targets, 0:9) + return MLUtils.DataLoader((x, y); batchsize, shuffle) +end + +# and here is a function to score the percentage of correct labels, where we +# assign a label by choosing the label of the highest `softmax` in the final +# layer. + +function score_model(predictor, data) + chain, parameters, state = predictor + x, y = only(data_loader(data; batchsize = length(data))) + y_hat, _ = chain(x, parameters, state) + is_correct = OneHotArrays.onecold(y) .== OneHotArrays.onecold(y_hat) + p = round(100 * sum(is_correct) / length(is_correct); digits = 2) + println("Accuracy = $p %") + return +end + +# The accuracy of our model is only around 10% before training: + +score_model(predictor, train_data) +score_model(predictor, test_data) + +# Let's improve that by training our model. + +# !!! note +# It is not the purpose of this tutorial to explain how Lux works; see the +# documentation at [https://lux.csail.mit.edu](https://lux.csail.mit.edu/stable/) +# for more details. Changing the number of epochs or the learning rate can +# improve the loss. + +begin + train_loader = data_loader(train_data; batchsize = 256, shuffle = true) + optimizer_state = Optimisers.setup(Optimisers.Adam(0.0003f0), parameters) + for epoch in 1:30 + loss = 0.0 + for (x, y) in train_loader + global state + (loss_batch, state), pullback = Zygote.pullback(parameters) do p + y_model, new_state = chain(x, p, state) + return Lux.CrossEntropyLoss()(y_model, y), new_state + end + gradients = only(pullback((one(loss), nothing))) + Optimisers.update!(optimizer_state, parameters, gradients) + loss += loss_batch + end + loss = round(loss / length(train_loader); digits = 4) + print("Epoch $epoch: loss = $loss\t") + score_model(predictor, test_data) + end +end + +# Here are the first eight predictions of the test data: + +function plot_image(predictor, x::Matrix) + y, _ = chain(vec(x), parameters, state) + score, index = findmax(y) + title = "Predicted: $(index - 1) ($(round(Int, 100 * score))%)" + return plot_image(x; title) +end + +plots = [plot_image(predictor, test_data[i].features) for i in 1:8] +Plots.plot(plots...; size = (1200, 600), layout = (2, 4)) + +# We can also look at the best and worst four predictions: + +x, y = only(data_loader(test_data; batchsize = length(test_data))) +y_model, _ = chain(x, parameters, state) +losses = Lux.CrossEntropyLoss(; agg = identity)(y_model, y) +indices = sortperm(losses; dims = 2)[[1:4; end-3:end]] +plots = [plot_image(predictor, test_data[i].features) for i in indices] +Plots.plot(plots...; size = (1200, 600), layout = (2, 4)) + +# There are still some fairly bad mistakes. Can you change the model or training +# parameters improve to improve things? + +# ## JuMP + +# Now that we have a trained machine learning model, we can embed it in a JuMP +# model. + +# Here's a function which takes a test case and returns an example that +# maximizes the probability of the adversarial example. + +function find_adversarial_image(test_case; adversary_label, δ = 0.05) + model = Model(Ipopt.Optimizer) + set_silent(model) + @variable(model, 0 <= x[1:28, 1:28] <= 1) + @constraint(model, -δ .<= x .- test_case.features .<= δ) + ## Note: we need to use `vec` here because `x` is a 28-by-28 Matrix, but our + ## neural network expects a 28^2 length vector. + y, _ = MathOptAI.add_predictor(model, predictor, vec(x)) + @objective(model, Max, y[adversary_label+1] - y[test_case.targets+1]) + optimize!(model) + @assert is_solved_and_feasible(model) + return value.(x) +end + +# Let's try finding an adversarial example to the third test image. The image on +# the left is our input image. The network thinks this is a `1` with probability +# 99%. The image on the right is the adversarial image. The network thinks this +# is a `7`, although it is less confident. + +x_adversary = find_adversarial_image(test_data[3]; adversary_label = 7); +Plots.plot( + plot_image(predictor, test_data[3].features), + plot_image(predictor, Float32.(x_adversary)), +) diff --git a/dev/tutorials/mnist_lux/1892610b.svg b/dev/tutorials/mnist_lux/1892610b.svg new file mode 100644 index 00000000..735bd861 --- /dev/null +++ b/dev/tutorials/mnist_lux/1892610b.svg @@ -0,0 +1,511 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/dev/tutorials/mnist_lux/b796493e.svg b/dev/tutorials/mnist_lux/b796493e.svg new file mode 100644 index 00000000..b99f042f --- /dev/null +++ b/dev/tutorials/mnist_lux/b796493e.svg @@ -0,0 +1,1195 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/dev/tutorials/mnist_lux/ed85ee8c.svg b/dev/tutorials/mnist_lux/ed85ee8c.svg new file mode 100644 index 00000000..c872cd25 --- /dev/null +++ b/dev/tutorials/mnist_lux/ed85ee8c.svg @@ -0,0 +1,1199 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/dev/tutorials/mnist_lux/f3b0d0d2.svg b/dev/tutorials/mnist_lux/f3b0d0d2.svg new file mode 100644 index 00000000..f44db0c1 --- /dev/null +++ b/dev/tutorials/mnist_lux/f3b0d0d2.svg @@ -0,0 +1,327 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/dev/tutorials/mnist_lux/index.html b/dev/tutorials/mnist_lux/index.html new file mode 100644 index 00000000..27146251 --- /dev/null +++ b/dev/tutorials/mnist_lux/index.html @@ -0,0 +1,135 @@ + +Adversarial machine learning with Lux.jl · MathOptAI.jl
GitHub

Adversarial machine learning with Lux.jl

The purpose of this tutorial is to explain how to embed a neural network model from Lux.jl into JuMP.

Required packages

This tutorial requires the following packages

using JuMP
+import Lux
+import Ipopt
+import MathOptAI
+import MLDatasets
+import MLUtils
+import OneHotArrays
+import Optimisers
+import Plots
+import Random
+import Zygote

Data

This tutorial uses images from the MNIST dataset.

We load the predefined train and test splits:

train_data = MLDatasets.MNIST(; split = :train)
dataset MNIST:
+  metadata  =>    Dict{String, Any} with 3 entries
+  split     =>    :train
+  features  =>    28×28×60000 Array{Float32, 3}
+  targets   =>    60000-element Vector{Int64}
test_data = MLDatasets.MNIST(; split = :test)
dataset MNIST:
+  metadata  =>    Dict{String, Any} with 3 entries
+  split     =>    :test
+  features  =>    28×28×10000 Array{Float32, 3}
+  targets   =>    10000-element Vector{Int64}

Since the data are images, it is helpful to plot them. (This requires a transpose and reversing the rows to get the orientation correct.)

function plot_image(x::Matrix; kwargs...)
+    return Plots.heatmap(
+        x'[size(x, 1):-1:1, :];
+        xlims = (1, size(x, 2)),
+        ylims = (1, size(x, 1)),
+        aspect_ratio = true,
+        legend = false,
+        xaxis = false,
+        yaxis = false,
+        kwargs...,
+    )
+end
+
+function plot_image(instance::NamedTuple)
+    return plot_image(instance.features; title = "Label = $(instance.targets)")
+end
+
+Plots.plot([plot_image(train_data[i]) for i in 1:6]...; layout = (2, 3))
Example block output

Training

We use a simple neural network with one hidden layer and a sigmoid activation function. (There are better performing networks; try experimenting.)

chain = Lux.Chain(
+    Lux.Dense(28^2 => 32, Lux.sigmoid),
+    Lux.Dense(32 => 10),
+    Lux.softmax,
+)
+rng = Random.MersenneTwister();
+parameters, state = Lux.setup(rng, chain)
+predictor = (chain, parameters, state);

Here is a function to load our data into the format that predictor expects:

function data_loader(data; batchsize, shuffle = false)
+    x = reshape(data.features, 28^2, :)
+    y = OneHotArrays.onehotbatch(data.targets, 0:9)
+    return MLUtils.DataLoader((x, y); batchsize, shuffle)
+end
data_loader (generic function with 1 method)

and here is a function to score the percentage of correct labels, where we assign a label by choosing the label of the highest softmax in the final layer.

function score_model(predictor, data)
+    chain, parameters, state = predictor
+    x, y = only(data_loader(data; batchsize = length(data)))
+    y_hat, _ = chain(x, parameters, state)
+    is_correct = OneHotArrays.onecold(y) .== OneHotArrays.onecold(y_hat)
+    p = round(100 * sum(is_correct) / length(is_correct); digits = 2)
+    println("Accuracy = $p %")
+    return
+end
score_model (generic function with 1 method)

The accuracy of our model is only around 10% before training:

score_model(predictor, train_data)
+score_model(predictor, test_data)
Accuracy = 16.84 %
+Accuracy = 17.02 %

Let's improve that by training our model.

Note

It is not the purpose of this tutorial to explain how Lux works; see the documentation at https://lux.csail.mit.edu for more details. Changing the number of epochs or the learning rate can improve the loss.

begin
+    train_loader = data_loader(train_data; batchsize = 256, shuffle = true)
+    optimizer_state = Optimisers.setup(Optimisers.Adam(0.0003f0), parameters)
+    for epoch in 1:30
+        loss = 0.0
+        for (x, y) in train_loader
+            global state
+            (loss_batch, state), pullback = Zygote.pullback(parameters) do p
+                y_model, new_state = chain(x, p, state)
+                return Lux.CrossEntropyLoss()(y_model, y), new_state
+            end
+            gradients = only(pullback((one(loss), nothing)))
+            Optimisers.update!(optimizer_state, parameters, gradients)
+            loss += loss_batch
+        end
+        loss = round(loss / length(train_loader); digits = 4)
+        print("Epoch $epoch: loss = $loss\t")
+        score_model(predictor, test_data)
+    end
+end
Epoch 1: loss = 1.8592	Accuracy = 72.93 %
+Epoch 2: loss = 1.2231	Accuracy = 82.72 %
+Epoch 3: loss = 0.9036	Accuracy = 86.19 %
+Epoch 4: loss = 0.7129	Accuracy = 88.19 %
+Epoch 5: loss = 0.591	Accuracy = 89.21 %
+Epoch 6: loss = 0.5093	Accuracy = 89.92 %
+Epoch 7: loss = 0.4518	Accuracy = 90.48 %
+Epoch 8: loss = 0.4104	Accuracy = 90.88 %
+Epoch 9: loss = 0.3784	Accuracy = 91.14 %
+Epoch 10: loss = 0.3537	Accuracy = 91.51 %
+Epoch 11: loss = 0.3333	Accuracy = 91.69 %
+Epoch 12: loss = 0.3165	Accuracy = 91.91 %
+Epoch 13: loss = 0.3023	Accuracy = 92.22 %
+Epoch 14: loss = 0.2904	Accuracy = 92.4 %
+Epoch 15: loss = 0.2789	Accuracy = 92.61 %
+Epoch 16: loss = 0.2694	Accuracy = 92.75 %
+Epoch 17: loss = 0.2609	Accuracy = 93.0 %
+Epoch 18: loss = 0.253	Accuracy = 93.08 %
+Epoch 19: loss = 0.2456	Accuracy = 93.18 %
+Epoch 20: loss = 0.239	Accuracy = 93.29 %
+Epoch 21: loss = 0.2328	Accuracy = 93.39 %
+Epoch 22: loss = 0.2274	Accuracy = 93.62 %
+Epoch 23: loss = 0.2215	Accuracy = 93.57 %
+Epoch 24: loss = 0.2169	Accuracy = 93.76 %
+Epoch 25: loss = 0.212	Accuracy = 93.81 %
+Epoch 26: loss = 0.2077	Accuracy = 93.97 %
+Epoch 27: loss = 0.2034	Accuracy = 94.02 %
+Epoch 28: loss = 0.1996	Accuracy = 94.17 %
+Epoch 29: loss = 0.1958	Accuracy = 94.17 %
+Epoch 30: loss = 0.1923	Accuracy = 94.25 %

Here are the first eight predictions of the test data:

function plot_image(predictor, x::Matrix)
+    y, _ = chain(vec(x), parameters, state)
+    score, index = findmax(y)
+    title = "Predicted: $(index - 1) ($(round(Int, 100 * score))%)"
+    return plot_image(x; title)
+end
+
+plots = [plot_image(predictor, test_data[i].features) for i in 1:8]
+Plots.plot(plots...; size = (1200, 600), layout = (2, 4))
Example block output

We can also look at the best and worst four predictions:

x, y = only(data_loader(test_data; batchsize = length(test_data)))
+y_model, _ = chain(x, parameters, state)
+losses = Lux.CrossEntropyLoss(; agg = identity)(y_model, y)
+indices = sortperm(losses; dims = 2)[[1:4; end-3:end]]
+plots = [plot_image(predictor, test_data[i].features) for i in indices]
+Plots.plot(plots...; size = (1200, 600), layout = (2, 4))
Example block output

There are still some fairly bad mistakes. Can you change the model or training parameters improve to improve things?

JuMP

Now that we have a trained machine learning model, we can embed it in a JuMP model.

Here's a function which takes a test case and returns an example that maximizes the probability of the adversarial example.

function find_adversarial_image(test_case; adversary_label, δ = 0.05)
+    model = Model(Ipopt.Optimizer)
+    set_silent(model)
+    @variable(model, 0 <= x[1:28, 1:28] <= 1)
+    @constraint(model, -δ .<= x .- test_case.features .<= δ)
+    # Note: we need to use `vec` here because `x` is a 28-by-28 Matrix, but our
+    # neural network expects a 28^2 length vector.
+    y, _ = MathOptAI.add_predictor(model, predictor, vec(x))
+    @objective(model, Max, y[adversary_label+1] - y[test_case.targets+1])
+    optimize!(model)
+    @assert is_solved_and_feasible(model)
+    return value.(x)
+end
find_adversarial_image (generic function with 1 method)

Let's try finding an adversarial example to the third test image. The image on the left is our input image. The network thinks this is a 1 with probability 99%. The image on the right is the adversarial image. The network thinks this is a 7, although it is less confident.

x_adversary = find_adversarial_image(test_data[3]; adversary_label = 7);
+Plots.plot(
+    plot_image(predictor, test_data[3].features),
+    plot_image(predictor, Float32.(x_adversary)),
+)
Example block output

This page was generated using Literate.jl.

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For example, if you +# have an existing Python installation (with PyTorch installed), and it is +# available in the current Conda environment, set: +# +# ```julia +# ENV["JULIA_CONDAPKG_BACKEND"] = "Current" +# ``` +# +# before importing PythonCall.jl. If the Python installation can be found on +# the path and it is not in a Conda environment, set: +# +# ```julia +# ENV["JULIA_CONDAPKG_BACKEND"] = "Null" +# ``` +# +# If `python` is not on your path, you may additionally need to set +# `JULIA_PYTHONCALL_EXE`, for example, to: +# +# ```julia +# ENV["JULIA_PYTHONCALL_EXE"] = "python3" +# ``` + +# ## Required packages + +# This tutorial requires the following packages + +using JuMP +using Test +import Ipopt +import MathOptAI +import Plots + +# ## Training a model + +# The following script builds and trains a simple neural network in PyTorch. +# For simplicity, we do not evaluate out-of-sample test performance, or use +# a batched data loader. In general, you should train your model in Python, +# and then use `torch.save(model, filename)` to save it to a `.pt` file for +# later use in Julia. + +# The model is unimportant, but for this example, we are trying to fit noisy +# observations of the function ``f(x) = x^2 - 2x``. + +# In Python, we ran: +# ```python +# #!/usr/bin/python3 +# import torch +# model = torch.nn.Sequential( +# torch.nn.Linear(1, 16), +# torch.nn.ReLU(), +# torch.nn.Linear(16, 1), +# ) +# +# n = 1024 +# x = torch.arange(-2, 2 + 4 / (n - 1), 4 / (n - 1)).reshape(n, 1) +# loss_fn = torch.nn.MSELoss() +# optimizer = torch.optim.Adam(model.parameters(), lr=0.01) +# for epoch in range(100): +# optimizer.zero_grad() +# N = torch.normal(torch.zeros(n, 1), torch.ones(n, 1)) +# y = x ** 2 -2 * x + 0.1 * N +# loss = loss_fn(model(x), y) +# loss.backward() +# optimizer.step() +# +# torch.save(model, "model.pt") +# ``` + +# ## JuMP model + +# Our goal for this JuMP model is to load the Neural Network from PyTorch into +# the objective function, and then minimize the objective for different fixed +# values of `x` to recreate the function that the Neural Network has learned to +# approximate. + +# First, create a JuMP model: + +model = Model(Ipopt.Optimizer) +set_silent(model) +@variable(model, x) + +# Then, load the model from PyTorch using [`MathOptAI.PytorchModel`](@ref): + +predictor = MathOptAI.PytorchModel(joinpath(@__DIR__, "model.pt")) +y, _ = MathOptAI.add_predictor(model, predictor, [x]) +@objective(model, Min, only(y)) + +# Now, visualize the fitted function `y = predictor(x)` by repeatedly solving +# the optimization problem for different fixed values of `x`: + +X, Y = -2:0.1:2, Float64[] +@constraint(model, c, x == 0.0) +for xi in X + set_normalized_rhs(c, xi) + optimize!(model) + @test is_solved_and_feasible(model) + push!(Y, objective_value(model)) +end +Plots.plot(x -> x^2 - 2x, X; label = "Truth", linestype = :dot) +Plots.plot!(X, Y; label = "Fitted") diff --git a/dev/tutorials/pytorch/f786293e.svg b/dev/tutorials/pytorch/f786293e.svg new file mode 100644 index 00000000..8ecc300b --- /dev/null +++ b/dev/tutorials/pytorch/f786293e.svg @@ -0,0 +1,48 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/dev/tutorials/pytorch/index.html b/dev/tutorials/pytorch/index.html new file mode 100644 index 00000000..2371ebad --- /dev/null +++ b/dev/tutorials/pytorch/index.html @@ -0,0 +1,39 @@ + +Function fitting with PyTorch · MathOptAI.jl
GitHub

Function fitting with PyTorch

The purpose of this tutorial is to explain how to embed a neural network model from PyTorch into JuMP.

Python integration

MathOptAI uses PythonCall.jl to call from Julia into Python.

See CondaPkg.jl for more control over how to link Julia to an existing Python environment. For example, if you have an existing Python installation (with PyTorch installed), and it is available in the current Conda environment, set:

ENV["JULIA_CONDAPKG_BACKEND"] = "Current"

before importing PythonCall.jl. If the Python installation can be found on the path and it is not in a Conda environment, set:

ENV["JULIA_CONDAPKG_BACKEND"] = "Null"

If python is not on your path, you may additionally need to set JULIA_PYTHONCALL_EXE, for example, to:

ENV["JULIA_PYTHONCALL_EXE"] = "python3"

Required packages

This tutorial requires the following packages

using JuMP
+using Test
+import Ipopt
+import MathOptAI
+import Plots

Training a model

The following script builds and trains a simple neural network in PyTorch. For simplicity, we do not evaluate out-of-sample test performance, or use a batched data loader. In general, you should train your model in Python, and then use torch.save(model, filename) to save it to a .pt file for later use in Julia.

The model is unimportant, but for this example, we are trying to fit noisy observations of the function $f(x) = x^2 - 2x$.

In Python, we ran:

#!/usr/bin/python3
+import torch
+model = torch.nn.Sequential(
+    torch.nn.Linear(1, 16),
+    torch.nn.ReLU(),
+    torch.nn.Linear(16, 1),
+)
+
+n = 1024
+x = torch.arange(-2, 2 + 4 / (n - 1), 4 / (n - 1)).reshape(n, 1)
+loss_fn = torch.nn.MSELoss()
+optimizer = torch.optim.Adam(model.parameters(), lr=0.01)
+for epoch in range(100):
+    optimizer.zero_grad()
+    N = torch.normal(torch.zeros(n, 1), torch.ones(n, 1))
+    y = x ** 2 -2 * x + 0.1 * N
+    loss = loss_fn(model(x), y)
+    loss.backward()
+    optimizer.step()
+
+torch.save(model, "model.pt")

JuMP model

Our goal for this JuMP model is to load the Neural Network from PyTorch into the objective function, and then minimize the objective for different fixed values of x to recreate the function that the Neural Network has learned to approximate.

First, create a JuMP model:

model = Model(Ipopt.Optimizer)
+set_silent(model)
+@variable(model, x)

\[ x \]

Then, load the model from PyTorch using MathOptAI.PytorchModel:

predictor = MathOptAI.PytorchModel(joinpath(@__DIR__, "model.pt"))
+y, _ = MathOptAI.add_predictor(model, predictor, [x])
+@objective(model, Min, only(y))

\[ moai\_Affine_{1} \]

Now, visualize the fitted function y = predictor(x) by repeatedly solving the optimization problem for different fixed values of x:

X, Y = -2:0.1:2, Float64[]
+@constraint(model, c, x == 0.0)
+for xi in X
+    set_normalized_rhs(c, xi)
+    optimize!(model)
+    @test is_solved_and_feasible(model)
+    push!(Y, objective_value(model))
+end
+Plots.plot(x -> x^2 - 2x, X; label = "Truth", linestype = :dot)
+Plots.plot!(X, Y; label = "Fitted")
Example block output

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diff --git a/dev/tutorials/student_enrollment.jl b/dev/tutorials/student_enrollment.jl new file mode 100644 index 00000000..af0574d7 --- /dev/null +++ b/dev/tutorials/student_enrollment.jl @@ -0,0 +1,134 @@ +# Copyright (c) 2024: Oscar Dowson and contributors #src +# Copyright (c) 2024: Triad National Security, LLC #src +# #src +# Use of this source code is governed by a BSD-style license that can be #src +# found in the LICENSE.md file. #src + +# # Logistic regression with GLM.jl + +# The purpose of this tutorial is to explain how to embed a logistic regression +# model from [GLM.jl](https://github.com/JuliaStats/GLM.jl) into JuMP. + +# The data and example in this tutorial comes from the paper: David Bergman, +# Teng Huang, Philip Brooks, Andrea Lodi, Arvind U. Raghunathan (2021) JANOS: An +# Integrated Predictive and Prescriptive Modeling Framework. INFORMS Journal on +# Computing 34(2):807-816. +# [https://doi.org/10.1287/ijoc.2020.1023](https://doi.org/10.1287/ijoc.2020.1023) + +# ## Required packages + +# This tutorial uses the following packages. + +using JuMP +import CSV +import DataFrames +import Downloads +import GLM +import Ipopt +import MathOptAI +import Statistics + +# ## Data + +# Here is a function to load the data directly from the JANOS repository: + +function read_df(filename) + url = "https://raw.githubusercontent.com/INFORMSJoC/2020.1023/master/data/" + data = Downloads.download(url * filename) + return CSV.read(data, DataFrames.DataFrame) +end + +# There are two important files. The first, `college_student_enroll-s1-1.csv`, +# contains historical admissions data on anonymized students, their SAT score, +# their GPA, their merit scholarships, and whether the enrolled in the college. + +train_df = read_df("college_student_enroll-s1-1.csv") + +# The second, `college_applications6000.csv`, contains the SAT and GPA data of +# students who are currently applying: + +evaluate_df = read_df("college_applications6000.csv") + +# There are 6,000 prospective students: + +n_students = size(evaluate_df, 1) + +# ## Prediction model + +# The first step is to train a logistic regression model to predict the Boolean +# `enroll` column based on the `SAT`, `GPA`, and `merit` columns. + +predictor = GLM.glm( + GLM.@formula(enroll ~ 0 + SAT + GPA + merit), + train_df, + GLM.Bernoulli(), +) + +# ## Decision model + +# Now that we have a trained logistic regression model, we want a decision model +# that chooses the optimal merit scholarship for each student in + +evaluate_df + +# Here's an empty JuMP model to start: + +model = Model() + +# First, we add a new column to `evaluate_df`, with one JuMP decision variable +# for each row. It is important the `.merit` column name in `evaluate_df` +# matches the name in `train_df`. + +evaluate_df.merit = @variable(model, 0 <= x_merit[1:n_students] <= 2.5); +evaluate_df + +# Then, we use [`MathOptAI.add_predictor`](@ref) to embed `predictor` into the +# JuMP `model`. [`MathOptAI.add_predictor`](@ref) returns a vector of variables, +# one for each row inn `evaluate_df`, corresponding to the output `enroll` of +# our logistic regression. + +evaluate_df.enroll, _ = MathOptAI.add_predictor(model, predictor, evaluate_df); +evaluate_df + +# The `.enroll` column name in `evaluate_df` is just a name. It doesn't have to +# match the name in `train_df`. + +# The objective of our problem is to maximize the expected number of students +# who enroll: + +@objective(model, Max, sum(evaluate_df.enroll)) + +# Subject to the constraint that we can spend at most `0.2 * n_students` on +# merit scholarships: + +@constraint(model, sum(evaluate_df.merit) <= 0.2 * n_students) + +# Because logistic regression involves a [`Sigmoid`](@ref) layer, we need to use +# a smooth nonlinear optimizer. A common choice is Ipopt. Solve and check the +# optimizer found a feasible solution: + +set_optimizer(model, Ipopt.Optimizer) +set_silent(model) +optimize!(model) +@assert is_solved_and_feasible(model) +solution_summary(model) + +# Let's store the solution in `evaluate_df` for analysis: + +evaluate_df.merit_sol = value.(evaluate_df.merit); +evaluate_df.enroll_sol = value.(evaluate_df.enroll); +evaluate_df + +# ## Solution analysis + +# We expect that just under 2,500 students will enroll: + +sum(evaluate_df.enroll_sol) + +# We awarded merit scholarships to approximately 1 in 6 students: + +count(evaluate_df.merit_sol .> 1e-5) + +# The average merit scholarship was worth just over \$1,000: + +1_000 * Statistics.mean(evaluate_df.merit_sol[evaluate_df.merit_sol.>1e-5]) diff --git a/dev/tutorials/student_enrollment/index.html b/dev/tutorials/student_enrollment/index.html new file mode 100644 index 00000000..ec7be7a8 --- /dev/null +++ b/dev/tutorials/student_enrollment/index.html @@ -0,0 +1,162 @@ + +Logistic regression with GLM.jl · MathOptAI.jl
GitHub

Logistic regression with GLM.jl

The purpose of this tutorial is to explain how to embed a logistic regression model from GLM.jl into JuMP.

The data and example in this tutorial comes from the paper: David Bergman, Teng Huang, Philip Brooks, Andrea Lodi, Arvind U. Raghunathan (2021) JANOS: An Integrated Predictive and Prescriptive Modeling Framework. INFORMS Journal on Computing 34(2):807-816. https://doi.org/10.1287/ijoc.2020.1023

Required packages

This tutorial uses the following packages.

julia> using JuMP
julia> import CSV
julia> import DataFrames
julia> import Downloads
julia> import GLM
julia> import Ipopt
julia> import MathOptAI
julia> import Statistics

Data

Here is a function to load the data directly from the JANOS repository:

julia> function read_df(filename)
+           url = "https://raw.githubusercontent.com/INFORMSJoC/2020.1023/master/data/"
+           data = Downloads.download(url * filename)
+           return CSV.read(data, DataFrames.DataFrame)
+       endread_df (generic function with 1 method)

There are two important files. The first, college_student_enroll-s1-1.csv, contains historical admissions data on anonymized students, their SAT score, their GPA, their merit scholarships, and whether the enrolled in the college.

julia> train_df = read_df("college_student_enroll-s1-1.csv")20000×6 DataFrame
+   Row │ Column1  StudentID  SAT    GPA      merit    enroll 
+       │ Int64    Int64      Int64  Float64  Float64  Int64  
+───────┼─────────────────────────────────────────────────────
+     1 │       1          1   1507     3.72     1.64       0
+     2 │       2          2   1532     3.93     0.52       0
+     3 │       3          3   1487     3.77     1.67       0
+     4 │       4          4   1259     3.05     1.21       1
+     5 │       5          5   1354     3.39     1.65       1
+     6 │       6          6   1334     3.22     0.0        0
+     7 │       7          7   1125     2.73     1.68       1
+     8 │       8          8   1180     2.82     0.0        1
+   ⋮   │    ⋮         ⋮        ⋮       ⋮        ⋮       ⋮
+ 19994 │   19994      19994   1185     3.09     1.16       1
+ 19995 │   19995      19995   1471     3.7      1.05       0
+ 19996 │   19996      19996   1139     3.03     1.21       1
+ 19997 │   19997      19997   1371     3.39     1.26       0
+ 19998 │   19998      19998   1424     3.72     0.85       0
+ 19999 │   19999      19999   1170     3.01     0.73       1
+ 20000 │   20000      20000   1389     3.57     0.55       0
+                                           19985 rows omitted

The second, college_applications6000.csv, contains the SAT and GPA data of students who are currently applying:

julia> evaluate_df = read_df("college_applications6000.csv")6000×3 DataFrame
+  Row │ StudentID  SAT    GPA     
+      │ Int64      Int64  Float64 
+──────┼───────────────────────────
+    1 │         1   1240     3.22
+    2 │         2   1206     2.87
+    3 │         3   1520     3.74
+    4 │         4   1238     3.11
+    5 │         5   1142     2.74
+    6 │         6   1086     2.77
+    7 │         7   1367     3.28
+    8 │         8   1034     2.41
+  ⋮   │     ⋮        ⋮       ⋮
+ 5994 │      5994   1121     2.96
+ 5995 │      5995   1564     4.1
+ 5996 │      5996   1332     3.14
+ 5997 │      5997   1228     2.95
+ 5998 │      5998   1165     2.81
+ 5999 │      5999   1400     3.43
+ 6000 │      6000   1097     2.65
+                 5985 rows omitted

There are 6,000 prospective students:

julia> n_students = size(evaluate_df, 1)6000

Prediction model

The first step is to train a logistic regression model to predict the Boolean enroll column based on the SAT, GPA, and merit columns.

julia> predictor = GLM.glm(
+           GLM.@formula(enroll ~ 0 + SAT + GPA + merit),
+           train_df,
+           GLM.Bernoulli(),
+       )StatsModels.TableRegressionModel{GLM.GeneralizedLinearModel{GLM.GlmResp{Vector{Float64}, Distributions.Bernoulli{Float64}, GLM.LogitLink}, GLM.DensePredChol{Float64, LinearAlgebra.CholeskyPivoted{Float64, Matrix{Float64}, Vector{Int64}}}}, Matrix{Float64}}
+
+enroll ~ 0 + SAT + GPA + merit
+
+Coefficients:
+──────────────────────────────────────────────────────────────────────────
+             Coef.   Std. Error      z  Pr(>|z|)    Lower 95%    Upper 95%
+──────────────────────────────────────────────────────────────────────────
+SAT     0.00243882  0.000309312   7.88    <1e-14   0.00183258   0.00304506
+GPA    -1.09868     0.123796     -8.87    <1e-18  -1.34132     -0.856045
+merit   0.248294    0.0191086    12.99    <1e-37   0.210842     0.285747
+──────────────────────────────────────────────────────────────────────────

Decision model

Now that we have a trained logistic regression model, we want a decision model that chooses the optimal merit scholarship for each student in

julia> evaluate_df6000×3 DataFrame
+  Row │ StudentID  SAT    GPA     
+      │ Int64      Int64  Float64 
+──────┼───────────────────────────
+    1 │         1   1240     3.22
+    2 │         2   1206     2.87
+    3 │         3   1520     3.74
+    4 │         4   1238     3.11
+    5 │         5   1142     2.74
+    6 │         6   1086     2.77
+    7 │         7   1367     3.28
+    8 │         8   1034     2.41
+  ⋮   │     ⋮        ⋮       ⋮
+ 5994 │      5994   1121     2.96
+ 5995 │      5995   1564     4.1
+ 5996 │      5996   1332     3.14
+ 5997 │      5997   1228     2.95
+ 5998 │      5998   1165     2.81
+ 5999 │      5999   1400     3.43
+ 6000 │      6000   1097     2.65
+                 5985 rows omitted

Here's an empty JuMP model to start:

julia> model = Model()A JuMP Model
+├ solver: none
+├ objective_sense: FEASIBILITY_SENSE
+├ num_variables: 0
+├ num_constraints: 0
+└ Names registered in the model: none

First, we add a new column to evaluate_df, with one JuMP decision variable for each row. It is important the .merit column name in evaluate_df matches the name in train_df.

julia> evaluate_df.merit = @variable(model, 0 <= x_merit[1:n_students] <= 2.5);
julia> evaluate_df6000×4 DataFrame
+  Row │ StudentID  SAT    GPA      merit         
+      │ Int64      Int64  Float64  GenericV…     
+──────┼──────────────────────────────────────────
+    1 │         1   1240     3.22  x_merit[1]
+    2 │         2   1206     2.87  x_merit[2]
+    3 │         3   1520     3.74  x_merit[3]
+    4 │         4   1238     3.11  x_merit[4]
+    5 │         5   1142     2.74  x_merit[5]
+    6 │         6   1086     2.77  x_merit[6]
+    7 │         7   1367     3.28  x_merit[7]
+    8 │         8   1034     2.41  x_merit[8]
+  ⋮   │     ⋮        ⋮       ⋮           ⋮
+ 5994 │      5994   1121     2.96  x_merit[5994]
+ 5995 │      5995   1564     4.1   x_merit[5995]
+ 5996 │      5996   1332     3.14  x_merit[5996]
+ 5997 │      5997   1228     2.95  x_merit[5997]
+ 5998 │      5998   1165     2.81  x_merit[5998]
+ 5999 │      5999   1400     3.43  x_merit[5999]
+ 6000 │      6000   1097     2.65  x_merit[6000]
+                                5985 rows omitted

Then, we use MathOptAI.add_predictor to embed predictor into the JuMP model. MathOptAI.add_predictor returns a vector of variables, one for each row inn evaluate_df, corresponding to the output enroll of our logistic regression.

julia> evaluate_df.enroll, _ = MathOptAI.add_predictor(model, predictor, evaluate_df);
julia> evaluate_df6000×5 DataFrame
+  Row │ StudentID  SAT    GPA      merit          enroll          
+      │ Int64      Int64  Float64  GenericV…      GenericV…       
+──────┼───────────────────────────────────────────────────────────
+    1 │         1   1240     3.22  x_merit[1]     moai_Sigmoid[1]
+    2 │         2   1206     2.87  x_merit[2]     moai_Sigmoid[1]
+    3 │         3   1520     3.74  x_merit[3]     moai_Sigmoid[1]
+    4 │         4   1238     3.11  x_merit[4]     moai_Sigmoid[1]
+    5 │         5   1142     2.74  x_merit[5]     moai_Sigmoid[1]
+    6 │         6   1086     2.77  x_merit[6]     moai_Sigmoid[1]
+    7 │         7   1367     3.28  x_merit[7]     moai_Sigmoid[1]
+    8 │         8   1034     2.41  x_merit[8]     moai_Sigmoid[1]
+  ⋮   │     ⋮        ⋮       ⋮           ⋮               ⋮
+ 5994 │      5994   1121     2.96  x_merit[5994]  moai_Sigmoid[1]
+ 5995 │      5995   1564     4.1   x_merit[5995]  moai_Sigmoid[1]
+ 5996 │      5996   1332     3.14  x_merit[5996]  moai_Sigmoid[1]
+ 5997 │      5997   1228     2.95  x_merit[5997]  moai_Sigmoid[1]
+ 5998 │      5998   1165     2.81  x_merit[5998]  moai_Sigmoid[1]
+ 5999 │      5999   1400     3.43  x_merit[5999]  moai_Sigmoid[1]
+ 6000 │      6000   1097     2.65  x_merit[6000]  moai_Sigmoid[1]
+                                                 5985 rows omitted

The .enroll column name in evaluate_df is just a name. It doesn't have to match the name in train_df.

The objective of our problem is to maximize the expected number of students who enroll:

julia> @objective(model, Max, sum(evaluate_df.enroll))moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + [[...5940 terms omitted...]] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1]

Subject to the constraint that we can spend at most 0.2 * n_students on merit scholarships:

julia> @constraint(model, sum(evaluate_df.merit) <= 0.2 * n_students)x_merit[1] + x_merit[2] + x_merit[3] + x_merit[4] + x_merit[5] + x_merit[6] + x_merit[7] + x_merit[8] + x_merit[9] + x_merit[10] + x_merit[11] + x_merit[12] + x_merit[13] + x_merit[14] + x_merit[15] + x_merit[16] + x_merit[17] + x_merit[18] + x_merit[19] + x_merit[20] + x_merit[21] + x_merit[22] + x_merit[23] + x_merit[24] + x_merit[25] + x_merit[26] + x_merit[27] + x_merit[28] + x_merit[29] + x_merit[30] + [[...5940 terms omitted...]] + x_merit[5971] + x_merit[5972] + x_merit[5973] + x_merit[5974] + x_merit[5975] + x_merit[5976] + x_merit[5977] + x_merit[5978] + x_merit[5979] + x_merit[5980] + x_merit[5981] + x_merit[5982] + x_merit[5983] + x_merit[5984] + x_merit[5985] + x_merit[5986] + x_merit[5987] + x_merit[5988] + x_merit[5989] + x_merit[5990] + x_merit[5991] + x_merit[5992] + x_merit[5993] + x_merit[5994] + x_merit[5995] + x_merit[5996] + x_merit[5997] + x_merit[5998] + x_merit[5999] + x_merit[6000] ≤ 1200

Because logistic regression involves a Sigmoid layer, we need to use a smooth nonlinear optimizer. A common choice is Ipopt. Solve and check the optimizer found a feasible solution:

julia> set_optimizer(model, Ipopt.Optimizer)
julia> set_silent(model)
julia> optimize!(model)
julia> @assert is_solved_and_feasible(model)
julia> solution_summary(model)* Solver : Ipopt
+
+* Status
+  Result count       : 1
+  Termination status : LOCALLY_SOLVED
+  Message from the solver:
+  "Solve_Succeeded"
+
+* Candidate solution (result #1)
+  Primal status      : FEASIBLE_POINT
+  Dual status        : FEASIBLE_POINT
+  Objective value    : 2.48820e+03
+  Dual objective value : -4.91918e+02
+
+* Work counters
+  Solve time (sec)   : 6.01563e+00
+  Barrier iterations : 142

Let's store the solution in evaluate_df for analysis:

julia> evaluate_df.merit_sol = value.(evaluate_df.merit);
julia> evaluate_df.enroll_sol = value.(evaluate_df.enroll);
julia> evaluate_df6000×7 DataFrame
+  Row │ StudentID  SAT    GPA      merit          enroll           merit_sol   ⋯
+      │ Int64      Int64  Float64  GenericV…      GenericV…        Float64     ⋯
+──────┼─────────────────────────────────────────────────────────────────────────
+    1 │         1   1240     3.22  x_merit[1]     moai_Sigmoid[1]  6.37389e-7  ⋯
+    2 │         2   1206     2.87  x_merit[2]     moai_Sigmoid[1]  1.08151
+    3 │         3   1520     3.74  x_merit[3]     moai_Sigmoid[1]  1.03717e-6
+    4 │         4   1238     3.11  x_merit[4]     moai_Sigmoid[1]  1.06046e-6
+    5 │         5   1142     2.74  x_merit[5]     moai_Sigmoid[1]  1.13489     ⋯
+    6 │         6   1086     2.77  x_merit[6]     moai_Sigmoid[1]  1.0759e-6
+    7 │         7   1367     3.28  x_merit[7]     moai_Sigmoid[1]  2.33948e-6
+    8 │         8   1034     2.41  x_merit[8]     moai_Sigmoid[1]  0.735482
+  ⋮   │     ⋮        ⋮       ⋮           ⋮               ⋮             ⋮       ⋱
+ 5994 │      5994   1121     2.96  x_merit[5994]  moai_Sigmoid[1]  6.26387e-7  ⋯
+ 5995 │      5995   1564     4.1   x_merit[5995]  moai_Sigmoid[1]  3.58792e-7
+ 5996 │      5996   1332     3.14  x_merit[5996]  moai_Sigmoid[1]  1.03863
+ 5997 │      5997   1228     2.95  x_merit[5997]  moai_Sigmoid[1]  1.21941
+ 5998 │      5998   1165     2.81  x_merit[5998]  moai_Sigmoid[1]  1.21872     ⋯
+ 5999 │      5999   1400     3.43  x_merit[5999]  moai_Sigmoid[1]  1.33971e-6
+ 6000 │      6000   1097     2.65  x_merit[6000]  moai_Sigmoid[1]  1.17865
+                                                  1 column and 5985 rows omitted

Solution analysis

We expect that just under 2,500 students will enroll:

julia> sum(evaluate_df.enroll_sol)2488.1951671444017

We awarded merit scholarships to approximately 1 in 6 students:

julia> count(evaluate_df.merit_sol .> 1e-5)1152

The average merit scholarship was worth just over $1,000:

julia> 1_000 * Statistics.mean(evaluate_df.merit_sol[evaluate_df.merit_sol.>1e-5])1041.6622990671967

This page was generated using Literate.jl.

diff --git a/index.html b/index.html new file mode 100644 index 00000000..6a5afc30 --- /dev/null +++ b/index.html @@ -0,0 +1,2 @@ + + diff --git a/stable b/stable new file mode 120000 index 00000000..7a5e833e --- /dev/null +++ b/stable @@ -0,0 +1 @@ +v0.1.4 \ No newline at end of file diff --git a/v0.1 b/v0.1 new file mode 120000 index 00000000..7a5e833e --- /dev/null +++ b/v0.1 @@ -0,0 +1 @@ +v0.1.4 \ No newline at end of file diff --git a/v0.1.2/.documenter-siteinfo.json b/v0.1.2/.documenter-siteinfo.json new file mode 100644 index 00000000..d84fb8ad --- /dev/null +++ b/v0.1.2/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-10-23T01:06:11","documenter_version":"1.7.0"}} \ No newline at end of file diff --git a/v0.1.2/api/index.html b/v0.1.2/api/index.html new file mode 100644 index 00000000..ad6ae0fb --- /dev/null +++ b/v0.1.2/api/index.html @@ -0,0 +1,944 @@ + +API Reference · MathOptAI.jl
GitHub

API Reference

This page lists the public API of MathOptAI.

Info

This page is an unstructured list of the MathOptAI API. For a more structured overview, read the Manual or Tutorial parts of this documentation.

Load all of the public the API into the current scope with:

using MathOptAI

Alternatively, load only the module with:

import MathOptAI

and then prefix all calls with MathOptAI. to create MathOptAI.<NAME>.

AbstractPredictor

add_predictor

MathOptAI.add_predictor — Function
add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::AbstractPredictor,
+    x::Vector,
+)::Vector

Return a Vector representing y such that y = predictor(x).

The element type of x is deliberately unspecified. The vector x may contain any mix of scalar constants, JuMP decision variables, and scalar JuMP functions like AffExpr, QuadExpr, or NonlinearExpr.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.Affine([2.0, 3.0])
+Affine(A, b) [input: 2, output: 1]
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Affine[1]
+
+julia> formulation
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ 2 x[1] + 3 x[2] - moai_Affine[1] = 0
source

build_predictor

MathOptAI.build_predictor — Function
MathOptAI.build_predictor(predictor::DecisionTree.Root)

Convert a binary decision tree from DecisionTree.jl to a BinaryDecisionTree.

Example

julia> using MathOptAI, DecisionTree
+
+julia> truth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)
+truth (generic function with 1 method)
+
+julia> features = abs.(sin.((1:10) .* (3:4)'));
+
+julia> size(features)
+(10, 2)
+
+julia> labels = truth.(Vector.(eachrow(features)));
+
+julia> ml_model = DecisionTree.build_tree(labels, features)
+Decision Tree
+Leaves: 3
+Depth:  2
+
+julia> MathOptAI.build_predictor(ml_model)
+BinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]
source
build_predictor(extension; kwargs...)::AbstractPredictor

A uniform interface to convert various extension types to an AbstractPredictor.

See the various extension docstrings for details.

source
MathOptAI.build_predictor(
+    predictor::Tuple{<:Lux.Chain,<:NamedTuple,<:NamedTuple};
+    config::Dict = Dict{Any,Any}(),
+)

Convert a trained neural network from Lux.jl to a Pipeline.

Supported layers

  • Lux.Dense
  • Lux.Scale

Supported activation functions

  • Lux.relu
  • Lux.sigmoid
  • Lux.softplus
  • Lux.softmax
  • Lux.tanh

Keyword arguments

  • config: a dictionary that maps supported Lux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Lux.sigmoid => MathOptAI.Sigmoid() or Lux.relu => MathOptAI.QuadraticReLU().

Example

julia> using Lux, MathOptAI, Random
+
+julia> rng = Random.MersenneTwister();
+
+julia> chain = Lux.Chain(Lux.Dense(1 => 16, Lux.relu), Lux.Dense(16 => 1))
+Chain(
+    layer_1 = Dense(1 => 16, relu),     # 32 parameters
+    layer_2 = Dense(16 => 1),           # 17 parameters
+)         # Total: 49 parameters,
+          #        plus 0 states.
+
+julia> parameters, state = Lux.setup(rng, chain);
+
+julia> predictor = MathOptAI.build_predictor(
+           (chain, parameters, state);
+           config = Dict(Lux.relu => MathOptAI.ReLU()),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 1, output: 16]
+ * ReLU()
+ * Affine(A, b) [input: 16, output: 1]
+
+julia> MathOptAI.build_predictor(
+           (chain, parameters, state);
+           config = Dict(Lux.relu => MathOptAI.ReLUQuadratic()),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 1, output: 16]
+ * ReLUQuadratic()
+ * Affine(A, b) [input: 16, output: 1]
source
MathOptAI.build_predictor(predictor::GLM.LinearModel)

Convert a trained linear model from GLM.jl to an Affine layer.

Example

julia> using GLM, MathOptAI
+
+julia> X, Y = rand(10, 2), rand(10);
+
+julia> model_glm = GLM.lm(X, Y);
+
+julia> MathOptAI.build_predictor(model_glm)
+Affine(A, b) [input: 2, output: 1]
source
MathOptAI.build_predictor(
+    predictor::GLM.GeneralizedLinearModel{
+        GLM.GlmResp{Vector{Float64},GLM.Bernoulli{Float64},GLM.LogitLink},
+    };
+    sigmoid::MathOptAI.AbstractPredictor = MathOptAI.Sigmoid(),
+)

Convert a trained logistic model from GLM.jl to a Pipeline layer.

Keyword arguments

  • sigmoid: the predictor to use for the sigmoid layer.

Example

julia> using GLM, MathOptAI
+
+julia> X, Y = rand(10, 2), rand(Bool, 10);
+
+julia> model_glm = GLM.glm(X, Y, GLM.Bernoulli());
+
+julia> MathOptAI.build_predictor(model_glm)
+Pipeline with layers:
+ * Affine(A, b) [input: 2, output: 1]
+ * Sigmoid()
source
MathOptAI.build_predictor(
+    predictor::MathOptAI.PytorchModel;
+    config::Dict = Dict{Any,Any}(),
+    gray_box::Bool = false,
+    gray_box_hessian::Bool = false,
+)

Convert a trained neural network from PyTorch via PythonCall.jl to a Pipeline.

Supported layers

  • nn.Linear
  • nn.ReLU
  • nn.Sequential
  • nn.Sigmoid
  • nn.Softplus
  • nn.Tanh

Keyword arguments

  • config: a dictionary that maps Symbols to AbstractPredictors that control how the activation functions are reformulated. For example, :Sigmoid => MathOptAI.Sigmoid() or :ReLU => MathOptAI.QuadraticReLU(). The supported Symbols are :ReLU, :Sigmoid, :SoftPlus, and :Tanh.
  • gray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by torch.func.jacrev.
  • gray_box_hessian: if true, the gray box additionally computes the Hessian of the output using torch.func.hessian.
source
MathOptAI.build_predictor(
+    predictor::Flux.Chain;
+    config::Dict = Dict{Any,Any}(),
+    gray_box::Bool = false,
+    gray_box_hessian::Bool = false,
+)

Convert a trained neural network from Flux.jl to a Pipeline.

Supported layers

  • Flux.Dense
  • Flux.Scale
  • Flux.softmax

Supported activation functions

  • Flux.relu
  • Flux.sigmoid
  • Flux.softplus
  • Flux.tanh

Keyword arguments

  • config: a dictionary that maps supported Flux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Flux.sigmoid => MathOptAI.Sigmoid() or Flux.relu => MathOptAI.QuadraticReLU().
  • gray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by Flux.withjacobian.
  • gray_box_hessian: if true, the gray box additionally computes the Hessian of the output using Flux.hessian.

Example

julia> using Flux, MathOptAI
+
+julia> chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));
+
+julia> MathOptAI.build_predictor(
+           chain;
+           config = Dict(Flux.relu => MathOptAI.ReLU()),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 1, output: 16]
+ * ReLU()
+ * Affine(A, b) [input: 16, output: 1]
+
+julia> MathOptAI.build_predictor(
+           chain;
+           config = Dict(Flux.relu => MathOptAI.ReLUQuadratic()),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 1, output: 16]
+ * ReLUQuadratic()
+ * Affine(A, b) [input: 16, output: 1]
source

Affine

MathOptAI.Affine — Type
Affine(
+    A::Matrix{T},
+    b::Vector{T} = zeros(T, size(A, 1)),
+) where {T} <: AbstractPredictor

An AbstractPredictor that represents the affine relationship:

\[f(x) = A x + b\]

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.Affine([2.0 3.0], [4.0])
+Affine(A, b) [input: 2, output: 1]
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Affine[1]
+
+julia> formulation
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ 2 x[1] + 3 x[2] - moai_Affine[1] = -4
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+1-element Vector{AffExpr}:
+ 2 x[1] + 3 x[2] + 4
+
+julia> formulation
+ReducedSpace(Affine(A, b) [input: 2, output: 1])
+├ variables [0]
+└ constraints [0]
source

BinaryDecisionTree

MathOptAI.BinaryDecisionTree — Type
BinaryDecisionTree{K,V}(
+    feat_id::Int,
+    feat_value::K,
+    lhs::Union{V,BinaryDecisionTree{K,V}},
+    rhs::Union{V,BinaryDecisionTree{K,V}},
+)

An AbstractPredictor that represents a binary decision tree.

  • If x[feat_id] <= feat_value, then return lhs
  • If x[feat_id] > feat_value, then return rhs

Example

To represent the tree x[1] <= 0.0 ? -1 : (x[1] <= 1.0 ? 0 : 1), do:

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:1]);
+
+julia> f = MathOptAI.BinaryDecisionTree{Float64,Int}(
+           1,
+           0.0,
+           -1,
+           MathOptAI.BinaryDecisionTree{Float64,Int}(1, 1.0, 0, 1),
+       )
+BinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_BinaryDecisionTree_value
+
+julia> formulation
+BinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]
+├ variables [4]
+│ ├ moai_BinaryDecisionTree_value
+│ ├ moai_BinaryDecisionTree_z[1]
+│ ├ moai_BinaryDecisionTree_z[2]
+│ └ moai_BinaryDecisionTree_z[3]
+└ constraints [7]
+  ├ moai_BinaryDecisionTree_z[1] + moai_BinaryDecisionTree_z[2] + moai_BinaryDecisionTree_z[3] = 1
+  ├ moai_BinaryDecisionTree_z[1] --> {x[1] ≤ 0}
+  ├ moai_BinaryDecisionTree_z[2] --> {x[1] ≥ 0}
+  ├ moai_BinaryDecisionTree_z[2] --> {x[1] ≤ 1}
+  ├ moai_BinaryDecisionTree_z[3] --> {x[1] ≥ 0}
+  ├ moai_BinaryDecisionTree_z[3] --> {x[1] ≥ 1}
+  └ moai_BinaryDecisionTree_z[1] - moai_BinaryDecisionTree_z[3] + moai_BinaryDecisionTree_value = 0
source

GrayBox

MathOptAI.GrayBox — Type
GrayBox(
+    output_size::Function,
+    callback::Function;
+    has_hessian::Bool = false,
+) <: AbstractPredictor

An AbstractPredictor that represents the function $f(x)$ as a user-defined nonlinear operator.

Arguments

  • output_size(x::Vector):Int: given an input vector x, return the dimension of the output vector
  • callback(x::Vector)::NamedTuple -> (;value, jacobian[, hessian]): given an input vector x, return a NamedTuple that computes the primal value and Jacobian of the output value with respect to the input. jacobian[j, i] is the partial derivative of value[j] with respect to x[i].
  • has_hessian: if true, the callback additionally contains a field hessian, which is an N × N × M matrix, where hessian[i, j, k] is the partial derivative of value[k] with respect to x[i] and x[j].

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.GrayBox(
+           x -> 2,
+           x -> (value = x.^2, jacobian = [2 * x[1] 0.0; 0.0 2 * x[2]]),
+       );
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_GrayBox[1]
+ moai_GrayBox[2]
+
+julia> formulation
+GrayBox
+├ variables [2]
+│ ├ moai_GrayBox[1]
+│ └ moai_GrayBox[2]
+└ constraints [2]
+  ├ op_##330(x[1], x[2]) - moai_GrayBox[1] = 0
+  └ op_##331(x[1], x[2]) - moai_GrayBox[2] = 0
+
+julia> y, formulation = MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ op_##332(x[1], x[2])
+ op_##333(x[1], x[2])
+
+julia> formulation
+ReducedSpace(GrayBox)
+├ variables [0]
+└ constraints [0]
source

Pipeline

MathOptAI.Pipeline — Type
Pipeline(layers::Vector{AbstractPredictor}) <: AbstractPredictor

An AbstractPredictor that represents a pipeline (composition) of nested layers:

\[f(x) = (l_1 \cdots (l_N(x))\]

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.Pipeline(
+           MathOptAI.Affine([1.0 2.0], [0.0]),
+           MathOptAI.ReLUQuadratic(),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 2, output: 1]
+ * ReLUQuadratic()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_ReLU[1]
+
+julia> formulation
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ x[1] + 2 x[2] - moai_Affine[1] = 0
+ReLUQuadratic()
+├ variables [2]
+│ ├ moai_ReLU[1]
+│ └ moai_z[1]
+└ constraints [2]
+  ├ moai_Affine[1] - moai_ReLU[1] + moai_z[1] = 0
+  └ moai_ReLU[1]*moai_z[1] = 0
source

PytorchModel

MathOptAI.PytorchModel — Type
PytorchModel(filename::String)

A wrapper struct for loading a PyTorch model.

The only supported file extension is .pt, where the .pt file has been created using torch.save(model, filename).

Example

julia> using PythonCall, MathOptAI
+
+julia> ml_model = PytorchModel("model.pt");
source

Quantile

MathOptAI.Quantile — Type
Quantile(distribution, quantiles::Vector{Float64})

An AbstractPredictor that represents the quantiles of distribution.

Example

julia> using JuMP, Distributions, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, 1 <= x <= 2);
+
+julia> predictor = MathOptAI.Quantile([0.1, 0.9]) do x
+           return Distributions.Normal(x, 3 - x)
+       end
+Quantile(_, [0.1, 0.9])
+
+julia> y, formulation = MathOptAI.add_predictor(model, predictor, [x]);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_quantile[1]
+ moai_quantile[2]
source

ReducedSpace

MathOptAI.ReducedSpace — Type
ReducedSpace(predictor::AbstractPredictor)

A wrapper type for other predictors that implement a reduced-space formulation.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> predictor = MathOptAI.ReducedSpace(MathOptAI.ReLU());
+
+julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ max(0.0, x[1])
+ max(0.0, x[2])
source

ReLU

MathOptAI.ReLU — Type
ReLU() <: AbstractPredictor

An AbstractPredictor that implements the ReLU constraint $y = \max\{0, x\}$ as a non-smooth nonlinear constraint.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.ReLU()
+ReLU()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_ReLU[1]
+ moai_ReLU[2]
+
+julia> formulation
+ReLU()
+├ variables [2]
+│ ├ moai_ReLU[1]
+│ └ moai_ReLU[2]
+└ constraints [4]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[2] ≥ 0
+  ├ moai_ReLU[1] - max(0.0, x[1]) = 0
+  └ moai_ReLU[2] - max(0.0, x[2]) = 0
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ max(0.0, x[1])
+ max(0.0, x[2])
+
+julia> formulation
+ReducedSpace(ReLU())
+├ variables [0]
+└ constraints [0]
source

ReLUBigM

MathOptAI.ReLUBigM — Type
ReLUBigM(M::Float64) <: AbstractPredictor

An AbstractPredictor that implements the ReLU constraint $y = \max\{0, x\}$ via a big-M MIP reformulation.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, -3 <= x[i in 1:2] <= i);
+
+julia> f = MathOptAI.ReLUBigM(100.0)
+ReLUBigM(100.0)
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_ReLU[1]
+ moai_ReLU[2]
+
+julia> formulation
+ReLUBigM(100.0)
+├ variables [4]
+│ ├ moai_ReLU[1]
+│ ├ moai_ReLU[2]
+│ ├ _[5]
+│ └ _[6]
+└ constraints [8]
+  ├ _[5] binary
+  ├ -x[1] + moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[1] - _[5] ≤ 0
+  ├ -x[1] + moai_ReLU[1] + 3 _[5] ≤ 3
+  ├ _[6] binary
+  ├ -x[2] + moai_ReLU[2] ≥ 0
+  ├ moai_ReLU[2] - 2 _[6] ≤ 0
+  └ -x[2] + moai_ReLU[2] + 3 _[6] ≤ 3
source

ReLUQuadratic

MathOptAI.ReLUQuadratic — Type
ReLUQuadratic() <: AbstractPredictor

An AbstractPredictor that implements the ReLU constraint $y = \max\{0, x\}$ by the reformulation:

\[\begin{aligned} +x = y - z \\ +y \times z = 0 \\ +y, z \ge 0 +\end{aligned}\]

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2] >= -1);
+
+julia> f = MathOptAI.ReLUQuadratic()
+ReLUQuadratic()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_ReLU[1]
+ moai_ReLU[2]
+
+julia> formulation
+ReLUQuadratic()
+├ variables [4]
+│ ├ moai_ReLU[1]
+│ ├ moai_ReLU[2]
+│ ├ moai_z[1]
+│ └ moai_z[2]
+└ constraints [4]
+  ├ x[1] - moai_ReLU[1] + moai_z[1] = 0
+  ├ x[2] - moai_ReLU[2] + moai_z[2] = 0
+  ├ moai_ReLU[1]*moai_z[1] = 0
+  └ moai_ReLU[2]*moai_z[2] = 0
source

ReLUSOS1

MathOptAI.ReLUSOS1 — Type
ReLUSOS1() <: AbstractPredictor

An AbstractPredictor that implements the ReLU constraint $y = \max\{0, x\}$ by the reformulation:

\[\begin{aligned} +x = y - z \\ +[y, z] \in SOS1 \\ +y, z \ge 0 +\end{aligned}\]

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2] >= -1);
+
+julia> f = MathOptAI.ReLUSOS1()
+ReLUSOS1()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_ReLU[1]
+ moai_ReLU[2]
+
+julia> formulation
+ReLUSOS1()
+├ variables [4]
+│ ├ moai_ReLU[1]
+│ ├ moai_ReLU[2]
+│ ├ moai_z[1]
+│ └ moai_z[2]
+└ constraints [4]
+  ├ x[1] - moai_ReLU[1] + moai_z[1] = 0
+  ├ x[2] - moai_ReLU[2] + moai_z[2] = 0
+  ├ [moai_ReLU[1], moai_z[1]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])
+  └ [moai_ReLU[2], moai_z[2]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])
source

Scale

MathOptAI.Scale — Type
Scale(
+    scale::Vector{T},
+    bias::Vector{T},
+) where {T} <: AbstractPredictor

An AbstractPredictor that represents the affine relationship:

\[f(x) = Diag(scale)x + bias\]

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.Scale([2.0, 3.0], [4.0, 5.0])
+Scale(scale, bias)
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_Scale[1]
+ moai_Scale[2]
+
+julia> formulation
+Scale(scale, bias)
+├ variables [2]
+│ ├ moai_Scale[1]
+│ └ moai_Scale[2]
+└ constraints [2]
+  ├ 2 x[1] - moai_Scale[1] = -4
+  └ 3 x[2] - moai_Scale[2] = -5
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{AffExpr}:
+ 2 x[1] + 4
+ 3 x[2] + 5
+
+julia> formulation
+ReducedSpace(Scale(scale, bias))
+├ variables [0]
+└ constraints [0]
source

Sigmoid

MathOptAI.Sigmoid — Type
Sigmoid() <: AbstractPredictor

An AbstractPredictor that implements the Sigmoid constraint $y = \frac{1}{1 + e^{-x}}$ as a smooth nonlinear constraint.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.Sigmoid()
+Sigmoid()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_Sigmoid[1]
+ moai_Sigmoid[2]
+
+julia> formulation
+Sigmoid()
+├ variables [2]
+│ ├ moai_Sigmoid[1]
+│ └ moai_Sigmoid[2]
+└ constraints [6]
+  ├ moai_Sigmoid[1] ≥ 0
+  ├ moai_Sigmoid[2] ≥ 0
+  ├ moai_Sigmoid[1] ≤ 1
+  ├ moai_Sigmoid[2] ≤ 1
+  ├ moai_Sigmoid[1] - (1.0 / (1.0 + exp(-x[1]))) = 0
+  └ moai_Sigmoid[2] - (1.0 / (1.0 + exp(-x[2]))) = 0
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ 1.0 / (1.0 + exp(-x[1]))
+ 1.0 / (1.0 + exp(-x[2]))
+
+julia> formulation
+ReducedSpace(Sigmoid())
+├ variables [0]
+└ constraints [0]
source

SoftMax

MathOptAI.SoftMax — Type
SoftMax() <: AbstractPredictor

An AbstractPredictor that implements the SoftMax constraint $y_i = \frac{e^{x_i}}{\sum_j e^{x_j}}$ as a smooth nonlinear constraint.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.SoftMax()
+SoftMax()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_SoftMax[1]
+ moai_SoftMax[2]
+
+julia> formulation
+SoftMax()
+├ variables [3]
+│ ├ moai_SoftMax_denom
+│ ├ moai_SoftMax[1]
+│ └ moai_SoftMax[2]
+└ constraints [8]
+  ├ moai_SoftMax[1] ≥ 0
+  ├ moai_SoftMax[2] ≥ 0
+  ├ moai_SoftMax[1] ≤ 1
+  ├ moai_SoftMax[2] ≤ 1
+  ├ moai_SoftMax_denom ≥ 0
+  ├ moai_SoftMax_denom - (0.0 + exp(x[2]) + exp(x[1])) = 0
+  ├ moai_SoftMax[1] - (exp(x[1]) / moai_SoftMax_denom) = 0
+  └ moai_SoftMax[2] - (exp(x[2]) / moai_SoftMax_denom) = 0
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ exp(x[1]) / moai_SoftMax_denom
+ exp(x[2]) / moai_SoftMax_denom
+
+julia> formulation
+ReducedSpace(SoftMax())
+├ variables [1]
+│ └ moai_SoftMax_denom
+└ constraints [2]
+  ├ moai_SoftMax_denom ≥ 0
+  └ moai_SoftMax_denom - (0.0 + exp(x[2]) + exp(x[1])) = 0
source

SoftPlus

MathOptAI.SoftPlus — Type
SoftPlus(; beta = 1.0) <: AbstractPredictor

An AbstractPredictor that implements the SoftPlus constraint $y = \frac{1}{\beta} \log(1 + e^{\beta x})$ as a smooth nonlinear constraint.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.SoftPlus(; beta = 2.0)
+SoftPlus(2.0)
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_SoftPlus[1]
+ moai_SoftPlus[2]
+
+julia> formulation
+SoftPlus(2.0)
+├ variables [2]
+│ ├ moai_SoftPlus[1]
+│ └ moai_SoftPlus[2]
+└ constraints [4]
+  ├ moai_SoftPlus[1] ≥ 0
+  ├ moai_SoftPlus[2] ≥ 0
+  ├ moai_SoftPlus[1] - (log(1.0 + exp(2 x[1])) / 2.0) = 0
+  └ moai_SoftPlus[2] - (log(1.0 + exp(2 x[2])) / 2.0) = 0
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ log(1.0 + exp(2 x[1])) / 2.0
+ log(1.0 + exp(2 x[2])) / 2.0
+
+julia> formulation
+ReducedSpace(SoftPlus(2.0))
+├ variables [0]
+└ constraints [0]
source

Tanh

MathOptAI.Tanh — Type
Tanh() <: AbstractPredictor

An AbstractPredictor that implements the Tanh constraint $y = \tanh(x)$ as a smooth nonlinear constraint.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.Tanh()
+Tanh()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_Tanh[1]
+ moai_Tanh[2]
+
+julia> formulation
+Tanh()
+├ variables [2]
+│ ├ moai_Tanh[1]
+│ └ moai_Tanh[2]
+└ constraints [6]
+  ├ moai_Tanh[1] ≥ -1
+  ├ moai_Tanh[2] ≥ -1
+  ├ moai_Tanh[1] ≤ 1
+  ├ moai_Tanh[2] ≤ 1
+  ├ moai_Tanh[1] - tanh(x[1]) = 0
+  └ moai_Tanh[2] - tanh(x[2]) = 0
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ tanh(x[1])
+ tanh(x[2])
+
+julia> formulation
+ReducedSpace(Tanh())
+├ variables [0]
+└ constraints [0]
source

AbstractFormulation

Formulation

MathOptAI.Formulation — Type
struct Formulation{P<:AbstractPredictor} <: AbstractFormulation
+    predictor::P
+    variables::Vector{Any}
+    constraints::Vector{Any}
+end

Fields

  • predictor: the predictor object used to build the formulation
  • variables: a vector of new decision variables added to the model
  • constraints: a vector of new constraints added to the model

Check the docstring of the predictor for an explanation of the formulation and the order of the elements in .variables and .constraints.

source

PipelineFormulation

MathOptAI.PipelineFormulation — Type
struct PipelineFormulation{P<:AbstractPredictor} <: AbstractFormulation
+    predictor::P
+    layers::Vector{Any}
+end

Fields

  • predictor: the predictor object used to build the formulation
  • layers: the formulation associated with each of the layers in the pipeline
source

Extensions

MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::MathOptAI.Quantile{<:AbstractGPs.PosteriorGP},
+    x::Vector,
+)

Add the quantiles of a trained Gaussian Process from AbstractGPs.jl to model.

Example

julia> using JuMP, MathOptAI, AbstractGPs
+
+julia> x_data = 2π .* (0.0:0.1:1.0);
+
+julia> y_data = sin.(x_data);
+
+julia> fx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.1);
+
+julia> p_fx = AbstractGPs.posterior(fx, y_data);
+
+julia> model = Model();
+
+julia> @variable(model, 1 <= x[1:1] <= 6, start = 3);
+
+julia> predictor = MathOptAI.Quantile(p_fx, [0.1, 0.9]);
+
+julia> y, _ = MathOptAI.add_predictor(model, predictor, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_quantile[1]
+ moai_quantile[2]
+
+julia> @objective(model, Max, y[2] - y[1])
+moai_quantile[2] - moai_quantile[1]
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::Union{DecisionTree.Root,DecisionTree.DecisionTreeClassifier},
+    x::Vector,
+)

Add a binary decision tree from DecisionTree.jl to model.

Example

julia> using JuMP, MathOptAI, DecisionTree
+
+julia> truth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)
+truth (generic function with 1 method)
+
+julia> features = abs.(sin.((1:10) .* (3:4)'));
+
+julia> size(features)
+(10, 2)
+
+julia> labels = truth.(Vector.(eachrow(features)));
+
+julia> ml_model = DecisionTree.build_tree(labels, features)
+Decision Tree
+Leaves: 3
+Depth:  2
+
+julia> model = Model();
+
+julia> @variable(model, 0 <= x[1:2] <= 1);
+
+julia> y, _ = MathOptAI.add_predictor(model, ml_model, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_BinaryDecisionTree_value
source
MathOptAI.build_predictor — Method
MathOptAI.build_predictor(predictor::DecisionTree.Root)

Convert a binary decision tree from DecisionTree.jl to a BinaryDecisionTree.

Example

julia> using MathOptAI, DecisionTree
+
+julia> truth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)
+truth (generic function with 1 method)
+
+julia> features = abs.(sin.((1:10) .* (3:4)'));
+
+julia> size(features)
+(10, 2)
+
+julia> labels = truth.(Vector.(eachrow(features)));
+
+julia> ml_model = DecisionTree.build_tree(labels, features)
+Decision Tree
+Leaves: 3
+Depth:  2
+
+julia> MathOptAI.build_predictor(ml_model)
+BinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::Flux.Chain,
+    x::Vector;
+    config::Dict = Dict{Any,Any}(),
+    reduced_space::Bool = false,
+    gray_box::Bool = false,
+)

Add a trained neural network from Flux.jl to model.

Supported layers

  • Flux.Dense
  • Flux.Scale
  • Flux.softmax

Supported activation functions

  • Flux.relu
  • Flux.sigmoid
  • Flux.softplus
  • Flux.tanh

Keyword arguments

  • config: a dictionary that maps supported Flux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Flux.sigmoid => MathOptAI.Sigmoid() or Flux.relu => MathOptAI.QuadraticReLU().
  • gray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by Flux.withjacobian.

Example

julia> using JuMP, Flux, MathOptAI
+
+julia> chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));
+
+julia> model = Model();
+
+julia> @variable(model, x[1:1]);
+
+julia> y, _ = MathOptAI.add_predictor(
+           model,
+           chain,
+           x;
+           config = Dict(Flux.relu => MathOptAI.ReLU()),
+       );
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Affine[1]
source
MathOptAI.build_predictor — Method
MathOptAI.build_predictor(
+    predictor::Flux.Chain;
+    config::Dict = Dict{Any,Any}(),
+    gray_box::Bool = false,
+    gray_box_hessian::Bool = false,
+)

Convert a trained neural network from Flux.jl to a Pipeline.

Supported layers

  • Flux.Dense
  • Flux.Scale
  • Flux.softmax

Supported activation functions

  • Flux.relu
  • Flux.sigmoid
  • Flux.softplus
  • Flux.tanh

Keyword arguments

  • config: a dictionary that maps supported Flux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Flux.sigmoid => MathOptAI.Sigmoid() or Flux.relu => MathOptAI.QuadraticReLU().
  • gray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by Flux.withjacobian.
  • gray_box_hessian: if true, the gray box additionally computes the Hessian of the output using Flux.hessian.

Example

julia> using Flux, MathOptAI
+
+julia> chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));
+
+julia> MathOptAI.build_predictor(
+           chain;
+           config = Dict(Flux.relu => MathOptAI.ReLU()),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 1, output: 16]
+ * ReLU()
+ * Affine(A, b) [input: 16, output: 1]
+
+julia> MathOptAI.build_predictor(
+           chain;
+           config = Dict(Flux.relu => MathOptAI.ReLUQuadratic()),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 1, output: 16]
+ * ReLUQuadratic()
+ * Affine(A, b) [input: 16, output: 1]
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::GLM.GeneralizedLinearModel{
+        GLM.GlmResp{Vector{Float64},GLM.Bernoulli{Float64},GLM.LogitLink},
+    },
+    x::Vector;
+    sigmoid::AbstractPredictor = MathOptAI.Sigmoid(),
+    reduced_space::Bool = false,
+)

Add a trained logistic regression model from GLM.jl to model.

Keyword arguments

  • sigmoid: the predictor to use for the sigmoid layer.

Example

julia> using GLM, JuMP, MathOptAI
+
+julia> X, Y = rand(10, 2), rand(Bool, 10);
+
+julia> model_glm = GLM.glm(X, Y, GLM.Bernoulli());
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> y, _ = MathOptAI.add_predictor(
+           model,
+           model_glm,
+           x;
+           sigmoid = MathOptAI.Sigmoid(),
+       );
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Sigmoid[1]
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::GLM.LinearModel,
+    x::Vector;
+    reduced_space::Bool = false,
+)

Add a trained linear model from GLM.jl to model.

Example

julia> using GLM, JuMP, MathOptAI
+
+julia> X, Y = rand(10, 2), rand(10);
+
+julia> model_glm = GLM.lm(X, Y);
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> y, _ = MathOptAI.add_predictor(model, model_glm, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Affine[1]
source
MathOptAI.build_predictor — Method
MathOptAI.build_predictor(
+    predictor::GLM.GeneralizedLinearModel{
+        GLM.GlmResp{Vector{Float64},GLM.Bernoulli{Float64},GLM.LogitLink},
+    };
+    sigmoid::MathOptAI.AbstractPredictor = MathOptAI.Sigmoid(),
+)

Convert a trained logistic model from GLM.jl to a Pipeline layer.

Keyword arguments

  • sigmoid: the predictor to use for the sigmoid layer.

Example

julia> using GLM, MathOptAI
+
+julia> X, Y = rand(10, 2), rand(Bool, 10);
+
+julia> model_glm = GLM.glm(X, Y, GLM.Bernoulli());
+
+julia> MathOptAI.build_predictor(model_glm)
+Pipeline with layers:
+ * Affine(A, b) [input: 2, output: 1]
+ * Sigmoid()
source
MathOptAI.build_predictor — Method
MathOptAI.build_predictor(predictor::GLM.LinearModel)

Convert a trained linear model from GLM.jl to an Affine layer.

Example

julia> using GLM, MathOptAI
+
+julia> X, Y = rand(10, 2), rand(10);
+
+julia> model_glm = GLM.lm(X, Y);
+
+julia> MathOptAI.build_predictor(model_glm)
+Affine(A, b) [input: 2, output: 1]
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::Tuple{<:Lux.Chain,<:NamedTuple,<:NamedTuple},
+    x::Vector;
+    config::Dict = Dict{Any,Any}(),
+    reduced_space::Bool = false,
+)

Add a trained neural network from Lux.jl to model.

Supported layers

  • Lux.Dense
  • Lux.Scale

Supported activation functions

  • Lux.relu
  • Lux.sigmoid
  • Lux.softplus
  • Lux.softmax
  • Lux.tanh

Keyword arguments

  • config: a dictionary that maps supported Lux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Lux.sigmoid => MathOptAI.Sigmoid() or Lux.relu => MathOptAI.QuadraticReLU().

Example

julia> using JuMP, Lux, MathOptAI, Random
+
+julia> rng = Random.MersenneTwister();
+
+julia> chain = Lux.Chain(Lux.Dense(1 => 16, Lux.relu), Lux.Dense(16 => 1))
+Chain(
+    layer_1 = Dense(1 => 16, relu),     # 32 parameters
+    layer_2 = Dense(16 => 1),           # 17 parameters
+)         # Total: 49 parameters,
+          #        plus 0 states.
+
+julia> parameters, state = Lux.setup(rng, chain);
+
+julia> predictor = (chain, parameters, state);
+
+julia> model = Model();
+
+julia> @variable(model, x[1:1]);
+
+julia> y, _ = MathOptAI.add_predictor(
+           model,
+           predictor,
+           x;
+           config = Dict(Lux.relu => MathOptAI.ReLU()),
+       );
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Affine[1]
source
MathOptAI.build_predictor — Method
MathOptAI.build_predictor(
+    predictor::Tuple{<:Lux.Chain,<:NamedTuple,<:NamedTuple};
+    config::Dict = Dict{Any,Any}(),
+)

Convert a trained neural network from Lux.jl to a Pipeline.

Supported layers

  • Lux.Dense
  • Lux.Scale

Supported activation functions

  • Lux.relu
  • Lux.sigmoid
  • Lux.softplus
  • Lux.softmax
  • Lux.tanh

Keyword arguments

  • config: a dictionary that maps supported Lux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Lux.sigmoid => MathOptAI.Sigmoid() or Lux.relu => MathOptAI.QuadraticReLU().

Example

julia> using Lux, MathOptAI, Random
+
+julia> rng = Random.MersenneTwister();
+
+julia> chain = Lux.Chain(Lux.Dense(1 => 16, Lux.relu), Lux.Dense(16 => 1))
+Chain(
+    layer_1 = Dense(1 => 16, relu),     # 32 parameters
+    layer_2 = Dense(16 => 1),           # 17 parameters
+)         # Total: 49 parameters,
+          #        plus 0 states.
+
+julia> parameters, state = Lux.setup(rng, chain);
+
+julia> predictor = MathOptAI.build_predictor(
+           (chain, parameters, state);
+           config = Dict(Lux.relu => MathOptAI.ReLU()),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 1, output: 16]
+ * ReLU()
+ * Affine(A, b) [input: 16, output: 1]
+
+julia> MathOptAI.build_predictor(
+           (chain, parameters, state);
+           config = Dict(Lux.relu => MathOptAI.ReLUQuadratic()),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 1, output: 16]
+ * ReLUQuadratic()
+ * Affine(A, b) [input: 16, output: 1]
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::MathOptAI.PytorchModel,
+    x::Vector;
+    config::Dict = Dict{Any,Any}(),
+    reduced_space::Bool = false,
+    gray_box::Bool = false,
+)

Add a trained neural network from PyTorch via PythonCall.jl to model.

Supported layers

  • nn.Linear
  • nn.ReLU
  • nn.Sequential
  • nn.Sigmoid
  • nn.Softplus
  • nn.Tanh

Keyword arguments

  • config: a dictionary that maps Symbols to AbstractPredictors that control how the activation functions are reformulated. For example, :Sigmoid => MathOptAI.Sigmoid() or :ReLU => MathOptAI.QuadraticReLU(). The supported Symbols are :ReLU, :Sigmoid, :SoftPlus, and :Tanh.
  • gray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by torch.func.jacrev.
  • gray_box_hessian: if true, the gray box additionally computes the Hessian of the output using torch.func.hessian.
source
MathOptAI.build_predictor — Method
MathOptAI.build_predictor(
+    predictor::MathOptAI.PytorchModel;
+    config::Dict = Dict{Any,Any}(),
+    gray_box::Bool = false,
+    gray_box_hessian::Bool = false,
+)

Convert a trained neural network from PyTorch via PythonCall.jl to a Pipeline.

Supported layers

  • nn.Linear
  • nn.ReLU
  • nn.Sequential
  • nn.Sigmoid
  • nn.Softplus
  • nn.Tanh

Keyword arguments

  • config: a dictionary that maps Symbols to AbstractPredictors that control how the activation functions are reformulated. For example, :Sigmoid => MathOptAI.Sigmoid() or :ReLU => MathOptAI.QuadraticReLU(). The supported Symbols are :ReLU, :Sigmoid, :SoftPlus, and :Tanh.
  • gray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by torch.func.jacrev.
  • gray_box_hessian: if true, the gray box additionally computes the Hessian of the output using torch.func.hessian.
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::StatsModels.TableRegressionModel,
+    x::DataFrames.DataFrame;
+    kwargs...,
+)

Add a trained regression model from StatsModels.jl to model, using the DataFrame x as input.

In most cases, predictor should be a GLM.jl predictor supported by MathOptAI, but trained using @formula and a DataFrame instead of the raw matrix input.

In general, x may have some columns that are constant (Float64) and some columns that are JuMP decision variables.

Keyword arguments

All keyword arguments are passed to the corresponding add_predictor of the GLM extension.

Example

julia> using DataFrames, GLM, JuMP, MathOptAI
+
+julia> train_df = DataFrames.DataFrame(x1 = rand(10), x2 = rand(10));
+
+julia> train_df.y = 1.0 .* train_df.x1 + 2.0 .* train_df.x2 .+ rand(10);
+
+julia> predictor = GLM.lm(GLM.@formula(y ~ x1 + x2), train_df);
+
+julia> model = Model();
+
+julia> test_df = DataFrames.DataFrame(
+           x1 = rand(6),
+           x2 = @variable(model, [1:6]),
+       );
+
+julia> test_df.y, _ = MathOptAI.add_predictor(model, predictor, test_df);
+
+julia> test_df.y
+6-element Vector{VariableRef}:
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
source
diff --git a/v0.1.2/assets/documenter.js b/v0.1.2/assets/documenter.js new file mode 100644 index 00000000..82252a11 --- /dev/null +++ b/v0.1.2/assets/documenter.js @@ -0,0 +1,1064 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on( + "click", + ".docstring .docstring-article-toggle-button", + function () { + let articleToggleTitle = "Expand docstring"; + const parent = $(this).parent(); + + debounce(() => { + if (parent.siblings("section").is(":visible")) { + parent + .find("a.docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + parent + .find("a.docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + parent + .children(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + parent.siblings("section").slideToggle(); + }); + } +); + +$(document).on("click", ".docs-article-toggle-button", function (event) { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + let animationSpeed = event.noToggleAnimation ? 0 : 400; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $("a.docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(animationSpeed); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $("a.docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(animationSpeed); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-xmark"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-xmark"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let meta = $("div[data-docstringscollapsed]").data(); + + if (meta?.docstringscollapsed) { + $("#documenter-article-toggle-button").trigger({ + type: "click", + noToggleAnimation: true, + }); + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +/* +To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +PSEUDOCODE: + +Searching happens automatically as the user types or adjusts the selected filters. +To preserve responsiveness, as much as possible of the slow parts of the search are done +in a web worker. Searching and result generation are done in the worker, and filtering and +DOM updates are done in the main thread. The filters are in the main thread as they should +be very quick to apply. This lets filters be changed without re-searching with minisearch +(which is possible even if filtering is on the worker thread) and also lets filters be +changed _while_ the worker is searching and without message passing (neither of which are +possible if filtering is on the worker thread) + +SEARCH WORKER: + +Import minisearch + +Build index + +On message from main thread + run search + find the first 200 unique results from each category, and compute their divs for display + note that this is necessary and sufficient information for the main thread to find the + first 200 unique results from any given filter set + post results to main thread + +MAIN: + +Launch worker + +Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results) + +On text update + if worker is not running, launch_search() + +launch_search + set worker_is_running to true, set last_search_text to the search text + post the search query to worker + +on message from worker + if last_search_text is not the same as the text in the search field, + the latest search result is not reflective of the latest search query, so update again + launch_search() + otherwise + set worker_is_running to false + + regardless, display the new search results to the user + save the unfiltered_results as a global + update_search() + +on filter click + adjust the filter selection + update_search() + +update_search + apply search filters by looping through the unfiltered_results and finding the first 200 + unique results that match the filters + + Update the DOM +*/ + +/////// SEARCH WORKER /////// + +function worker_function(documenterSearchIndex, documenterBaseURL, filters) { + importScripts( + "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js" + ); + + let data = documenterSearchIndex.map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; + }); + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", + ]); + + let index = new MiniSearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + + word = word.toLowerCase(); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not + // find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + prefix: true, + boost: { title: 100 }, + fuzzy: 2, + }, + }); + + index.addAll(data); + + /** + * Used to map characters to HTML entities. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const htmlEscapes = { + "&": "&", + "<": "<", + ">": ">", + '"': """, + "'": "'", + }; + + /** + * Used to match HTML entities and HTML characters. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const reUnescapedHtml = /[&<>"']/g; + const reHasUnescapedHtml = RegExp(reUnescapedHtml.source); + + /** + * Escape function from lodash + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + function escape(string) { + return string && reHasUnescapedHtml.test(string) + ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr]) + : string || ""; + } + + /** + * RegX escape function from MDN + * Refer: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping + */ + function escapeRegExp(string) { + return string.replace(/[.*+?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string + } + + /** + * Make the result component given a minisearch result data object and the value + * of the search input as queryString. To view the result object structure, refer: + * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ + function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + searchstring = escapeRegExp(querystring); + let textindex = new RegExp(`${searchstring}`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + text = text.length ? escape(text) : ""; + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`${escape(searchstring)}`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${escape(result.title)}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+ + ${search_divider} + `; + + return result_div; + } + + self.onmessage = function (e) { + let query = e.data; + let results = index.search(query, { + filter: (result) => { + // Only return relevant results + return result.score >= 1; + }, + combineWith: "AND", + }); + + // Pre-filter to deduplicate and limit to 200 per category to the extent + // possible without knowing what the filters are. + let filtered_results = []; + let counts = {}; + for (let filter of filters) { + counts[filter] = 0; + } + let present = {}; + + for (let result of results) { + cat = result.category; + cnt = counts[cat]; + if (cnt < 200) { + id = cat + "---" + result.location; + if (present[id]) { + continue; + } + present[id] = true; + filtered_results.push({ + location: result.location, + category: cat, + div: make_search_result(result, query), + }); + } + } + + postMessage(filtered_results); + }; +} + +// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript! +const filters = [ + ...new Set(documenterSearchIndex["docs"].map((x) => x.category)), +]; +const worker_str = + "(" + + worker_function.toString() + + ")(" + + JSON.stringify(documenterSearchIndex["docs"]) + + "," + + JSON.stringify(documenterBaseURL) + + "," + + JSON.stringify(filters) + + ")"; +const worker_blob = new Blob([worker_str], { type: "text/javascript" }); +const worker = new Worker(URL.createObjectURL(worker_blob)); + +/////// SEARCH MAIN /////// + +// Whether the worker is currently handling a search. This is a boolean +// as the worker only ever handles 1 or 0 searches at a time. +var worker_is_running = false; + +// The last search text that was sent to the worker. This is used to determine +// if the worker should be launched again when it reports back results. +var last_search_text = ""; + +// The results of the last search. This, in combination with the state of the filters +// in the DOM, is used compute the results to display on calls to update_search. +var unfiltered_results = []; + +// Which filter is currently selected +var selected_filter = ""; + +$(document).on("input", ".documenter-search-input", function (event) { + if (!worker_is_running) { + launch_search(); + } +}); + +function launch_search() { + worker_is_running = true; + last_search_text = $(".documenter-search-input").val(); + worker.postMessage(last_search_text); +} + +worker.onmessage = function (e) { + if (last_search_text !== $(".documenter-search-input").val()) { + launch_search(); + } else { + worker_is_running = false; + } + + unfiltered_results = e.data; + update_search(); +}; + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + selected_filter = ""; + } else { + selected_filter = $(this).text().toLowerCase(); + } + + // This updates search results and toggles classes for UI: + update_search(); +}); + +/** + * Make/Update the search component + */ +function update_search() { + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + if (selected_filter == "") { + results = unfiltered_results; + } else { + results = unfiltered_results.filter((result) => { + return selected_filter == result.category.toLowerCase(); + }); + } + + let search_result_container = ``; + let modal_filters = make_modal_body_filters(); + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + for (var i = 0, n = results.length; i < n && count < 200; ++i) { + let result = results[i]; + if (result.location && !links.includes(result.location)) { + search_results += result.div; + count++; + links.push(result.location); + } + } + + if (count == 1) { + count_str = "1 result"; + } else if (count == 200) { + count_str = "200+ results"; + } else { + count_str = count + " results"; + } + let result_count = `
${count_str}
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
+
No result found!
+ `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(` +
Type something to get started!
+ `); + } +} + +/** + * Make the modal filter html + * + * @returns string + */ +function make_modal_body_filters() { + let str = filters + .map((val) => { + if (selected_filter == val.toLowerCase()) { + return `${val}`; + } else { + return `${val}`; + } + }) + .join(""); + + return ` +
+ Filters: + ${str} +
`; +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); + }); + // Close the dialog if X is clicked + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); + }); + // Close dialog if ESC is pressed + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let search_modal_header = ` +
+
+

+ + + + +

+
+
+ +
+
+ `; + + let initial_search_body = ` +
Type something to get started!
+ `; + + let search_modal_footer = ` +
+ + Ctrl + + / to search + + esc to close +
+ `; + + $(document.body).append( + ` + + ` + ); + + document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); + }); + + document + .querySelector(".close-search-modal") + .addEventListener("click", () => { + closeModal(); + }); + + $(document).on("click", ".search-result-link", function () { + closeModal(); + }); + + document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; + }); + + // Functions to open and close a modal + function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); + } + + function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
Type something to get started!
+ `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); + } + + document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function () { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { + ev.preventDefault(); + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind("click", function (ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); + } + }); +}); + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function () { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css("max-width"), 10); + var L0 = e.width(); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on("orientationchange", resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function () { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if (typeof active !== "undefined") { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Theme picker setup +$(document).ready(function () { + // onchange callback + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); + } + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function () { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== "undefined") { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $( + "" + ); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}); + +}) diff --git a/v0.1.2/assets/themes/catppuccin-frappe.css b/v0.1.2/assets/themes/catppuccin-frappe.css new file mode 100644 index 00000000..32e3f008 --- /dev/null +++ b/v0.1.2/assets/themes/catppuccin-frappe.css @@ -0,0 +1 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.button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-black.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-light{background-color:#f5f5f5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light:hover,html.theme--catppuccin-frappe .button.is-light.is-hovered{background-color:#eee;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light:focus,html.theme--catppuccin-frappe .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light:focus:not(:active),html.theme--catppuccin-frappe .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(245,245,245,0.25)}html.theme--catppuccin-frappe .button.is-light:active,html.theme--catppuccin-frappe .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-light{background-color:#f5f5f5;border-color:#f5f5f5;box-shadow:none}html.theme--catppuccin-frappe .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-frappe 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.button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-frappe .button.is-light.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-light.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-frappe 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kbd.button.is-inverted{background-color:#fff;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-inverted:hover,html.theme--catppuccin-frappe .content kbd.button.is-inverted:hover,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-hovered,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-frappe .button.is-dark.is-inverted[disabled],html.theme--catppuccin-frappe .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-dark.is-inverted,fieldset[disabled] html.theme--catppuccin-frappe .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-loading::after,html.theme--catppuccin-frappe .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe 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!important}html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-dark.is-outlined[disabled],html.theme--catppuccin-frappe .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-frappe .content kbd.button.is-outlined{background-color:transparent;border-color:#414559;box-shadow:none;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #414559 #414559 !important}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined[disabled],html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-primary,html.theme--catppuccin-frappe .docstring>section>a.button.docs-sourcelink{background-color:#8caaee;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-primary:hover,html.theme--catppuccin-frappe .docstring>section>a.button.docs-sourcelink:hover,html.theme--catppuccin-frappe .button.is-primary.is-hovered,html.theme--catppuccin-frappe .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#81a2ec;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-primary:focus,html.theme--catppuccin-frappe 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.button.is-success{background-color:#a6d189;border-color:#a6d189;box-shadow:none}html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-focused{background-color:#a6d189;border-color:#a6d189;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-light{background-color:#f4f9f0;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:hover,html.theme--catppuccin-frappe .button.is-success.is-light.is-hovered{background-color:#edf6e7;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:active,html.theme--catppuccin-frappe .button.is-success.is-light.is-active{background-color:#e6f2de;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-warning{background-color:#e5c890;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:hover,html.theme--catppuccin-frappe .button.is-warning.is-hovered{background-color:#e3c386;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:focus,html.theme--catppuccin-frappe .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:focus:not(:active),html.theme--catppuccin-frappe .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(229,200,144,0.25)}html.theme--catppuccin-frappe .button.is-warning:active,html.theme--catppuccin-frappe .button.is-warning.is-active{background-color:#e0be7b;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning{background-color:#e5c890;border-color:#e5c890;box-shadow:none}html.theme--catppuccin-frappe .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-outlined:hover,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-warning.is-outlined:focus,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-focused{background-color:#e5c890;border-color:#e5c890;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #e5c890 #e5c890 !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e5c890 #e5c890 !important}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-light{background-color:#fbf7ee;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:hover,html.theme--catppuccin-frappe .button.is-warning.is-light.is-hovered{background-color:#f9f2e4;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:active,html.theme--catppuccin-frappe .button.is-warning.is-light.is-active{background-color:#f6edda;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-danger{background-color:#e78284;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:hover,html.theme--catppuccin-frappe .button.is-danger.is-hovered{background-color:#e57779;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:focus,html.theme--catppuccin-frappe .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:focus:not(:active),html.theme--catppuccin-frappe .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(231,130,132,0.25)}html.theme--catppuccin-frappe .button.is-danger:active,html.theme--catppuccin-frappe .button.is-danger.is-active{background-color:#e36d6f;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger{background-color:#e78284;border-color:#e78284;box-shadow:none}html.theme--catppuccin-frappe .button.is-danger.is-inverted{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-frappe .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-focused{background-color:#e78284;border-color:#e78284;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-light{background-color:#fceeee;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:hover,html.theme--catppuccin-frappe .button.is-danger.is-light.is-hovered{background-color:#fae3e4;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:active,html.theme--catppuccin-frappe .button.is-danger.is-light.is-active{background-color:#f8d8d9;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-frappe .button.is-small:not(.is-rounded),html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .button.is-normal{font-size:1rem}html.theme--catppuccin-frappe .button.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .button.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .button[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button{background-color:#737994;border-color:#626880;box-shadow:none;opacity:.5}html.theme--catppuccin-frappe .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-frappe .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-frappe .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-frappe .button.is-static{background-color:#292c3c;border-color:#626880;color:#838ba7;box-shadow:none;pointer-events:none}html.theme--catppuccin-frappe .button.is-rounded,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-frappe .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-frappe .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-frappe .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-frappe .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-frappe .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-frappe .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-frappe .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-frappe .buttons.has-addons .button:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-frappe .buttons.has-addons .button:focus,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused,html.theme--catppuccin-frappe .buttons.has-addons .button:active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-frappe .buttons.has-addons .button:focus:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-frappe .buttons.has-addons .button:active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-frappe .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .buttons.is-centered{justify-content:center}html.theme--catppuccin-frappe .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-frappe .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-frappe .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-frappe .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-frappe .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-frappe .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-frappe .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-frappe .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-frappe .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-frappe .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-frappe .content li+li{margin-top:0.25em}html.theme--catppuccin-frappe .content p:not(:last-child),html.theme--catppuccin-frappe .content dl:not(:last-child),html.theme--catppuccin-frappe .content ol:not(:last-child),html.theme--catppuccin-frappe .content ul:not(:last-child),html.theme--catppuccin-frappe .content blockquote:not(:last-child),html.theme--catppuccin-frappe .content pre:not(:last-child),html.theme--catppuccin-frappe .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-frappe .content h1,html.theme--catppuccin-frappe .content h2,html.theme--catppuccin-frappe .content h3,html.theme--catppuccin-frappe .content h4,html.theme--catppuccin-frappe .content h5,html.theme--catppuccin-frappe .content h6{color:#c6d0f5;font-weight:600;line-height:1.125}html.theme--catppuccin-frappe .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-frappe .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-frappe .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-frappe .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-frappe .content 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body.has-spaced-navbar-fixed-bottom{padding-bottom:6rem}html.theme--catppuccin-frappe a.navbar-item.is-active,html.theme--catppuccin-frappe .navbar-link.is-active{color:#8caaee}html.theme--catppuccin-frappe a.navbar-item.is-active:not(:focus):not(:hover),html.theme--catppuccin-frappe .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--catppuccin-frappe .navbar-item.has-dropdown:focus .navbar-link,html.theme--catppuccin-frappe .navbar-item.has-dropdown:hover .navbar-link,html.theme--catppuccin-frappe .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--catppuccin-frappe .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--catppuccin-frappe .pagination{font-size:1rem;margin:-.25rem}html.theme--catppuccin-frappe .pagination.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.pagination{font-size:.75rem}html.theme--catppuccin-frappe 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.button.is-white:focus:not(:active),html.theme--catppuccin-latte .button.is-white.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(255,255,255,0.25)}html.theme--catppuccin-latte .button.is-white:active,html.theme--catppuccin-latte .button.is-white.is-active{background-color:#f2f2f2;border-color:transparent;color:#0a0a0a}html.theme--catppuccin-latte .button.is-white[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-white{background-color:#fff;border-color:#fff;box-shadow:none}html.theme--catppuccin-latte .button.is-white.is-inverted{background-color:#0a0a0a;color:#fff}html.theme--catppuccin-latte .button.is-white.is-inverted:hover,html.theme--catppuccin-latte .button.is-white.is-inverted.is-hovered{background-color:#000}html.theme--catppuccin-latte .button.is-white.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-white.is-inverted{background-color:#0a0a0a;border-color:transparent;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-white.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-latte .button.is-white.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-white.is-outlined:hover,html.theme--catppuccin-latte .button.is-white.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-white.is-outlined:focus,html.theme--catppuccin-latte .button.is-white.is-outlined.is-focused{background-color:#fff;border-color:#fff;color:#0a0a0a}html.theme--catppuccin-latte .button.is-white.is-outlined.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-white.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-white.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-white.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-white.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-latte .button.is-white.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-white.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-latte .button.is-white.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-white.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-white.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-white.is-inverted.is-outlined.is-focused{background-color:#0a0a0a;color:#fff}html.theme--catppuccin-latte .button.is-white.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-white.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-white.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black:hover,html.theme--catppuccin-latte .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black:focus,html.theme--catppuccin-latte .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black:focus:not(:active),html.theme--catppuccin-latte .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--catppuccin-latte .button.is-black:active,html.theme--catppuccin-latte .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--catppuccin-latte .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted:hover,html.theme--catppuccin-latte .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-outlined:hover,html.theme--catppuccin-latte .button.is-black.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-black.is-outlined:focus,html.theme--catppuccin-latte .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-light{background-color:#f5f5f5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:hover,html.theme--catppuccin-latte .button.is-light.is-hovered{background-color:#eee;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:focus,html.theme--catppuccin-latte .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:focus:not(:active),html.theme--catppuccin-latte .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(245,245,245,0.25)}html.theme--catppuccin-latte .button.is-light:active,html.theme--catppuccin-latte .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light{background-color:#f5f5f5;border-color:#f5f5f5;box-shadow:none}html.theme--catppuccin-latte .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-inverted:hover,html.theme--catppuccin-latte .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-outlined:hover,html.theme--catppuccin-latte .button.is-light.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-light.is-outlined:focus,html.theme--catppuccin-latte .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark,html.theme--catppuccin-latte .content kbd.button{background-color:#ccd0da;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark:hover,html.theme--catppuccin-latte .content kbd.button:hover,html.theme--catppuccin-latte .button.is-dark.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-hovered{background-color:#c5c9d5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark:focus,html.theme--catppuccin-latte .content kbd.button:focus,html.theme--catppuccin-latte .button.is-dark.is-focused,html.theme--catppuccin-latte .content kbd.button.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark:focus:not(:active),html.theme--catppuccin-latte .content kbd.button:focus:not(:active),html.theme--catppuccin-latte .button.is-dark.is-focused:not(:active),html.theme--catppuccin-latte .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(204,208,218,0.25)}html.theme--catppuccin-latte .button.is-dark:active,html.theme--catppuccin-latte .content kbd.button:active,html.theme--catppuccin-latte .button.is-dark.is-active,html.theme--catppuccin-latte .content kbd.button.is-active{background-color:#bdc2cf;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark[disabled],html.theme--catppuccin-latte .content kbd.button[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button{background-color:#ccd0da;border-color:#ccd0da;box-shadow:none}html.theme--catppuccin-latte .button.is-dark.is-inverted,html.theme--catppuccin-latte .content kbd.button.is-inverted{background-color:rgba(0,0,0,0.7);color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted:hover,html.theme--catppuccin-latte .content kbd.button.is-inverted:hover,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-inverted[disabled],html.theme--catppuccin-latte .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-inverted,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-loading::after,html.theme--catppuccin-latte .content kbd.button.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-dark.is-outlined,html.theme--catppuccin-latte .content kbd.button.is-outlined{background-color:transparent;border-color:#ccd0da;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-outlined:hover,html.theme--catppuccin-latte .content kbd.button.is-outlined:hover,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-dark.is-outlined:focus,html.theme--catppuccin-latte .content kbd.button.is-outlined:focus,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-focused,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-focused{background-color:#ccd0da;border-color:#ccd0da;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #ccd0da #ccd0da !important}html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-dark.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-outlined{background-color:transparent;border-color:#ccd0da;box-shadow:none;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ccd0da #ccd0da !important}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-primary,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink{background-color:#1e66f5;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-primary:hover,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#125ef4;border-color:transparent;color:#fff}html.theme--catppuccin-latte 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.button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #40a02b #40a02b !important}html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-outlined{background-color:transparent;border-color:#40a02b;box-shadow:none;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-focused{background-color:#fff;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #40a02b #40a02b !important}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-success.is-light{background-color:#f1fbef;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:hover,html.theme--catppuccin-latte .button.is-success.is-light.is-hovered{background-color:#e8f8e5;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:active,html.theme--catppuccin-latte .button.is-success.is-light.is-active{background-color:#e0f5db;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:hover,html.theme--catppuccin-latte .button.is-warning.is-hovered{background-color:#d4871c;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus,html.theme--catppuccin-latte .button.is-warning.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus:not(:active),html.theme--catppuccin-latte .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(223,142,29,0.25)}html.theme--catppuccin-latte .button.is-warning:active,html.theme--catppuccin-latte .button.is-warning.is-active{background-color:#c8801a;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:#df8e1d;box-shadow:none}html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-focused{background-color:#df8e1d;border-color:#df8e1d;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-light{background-color:#fdf6ed;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:hover,html.theme--catppuccin-latte .button.is-warning.is-light.is-hovered{background-color:#fbf1e2;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:active,html.theme--catppuccin-latte .button.is-warning.is-light.is-active{background-color:#faebd6;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:hover,html.theme--catppuccin-latte .button.is-danger.is-hovered{background-color:#c60e36;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus,html.theme--catppuccin-latte .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus:not(:active),html.theme--catppuccin-latte .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(210,15,57,0.25)}html.theme--catppuccin-latte .button.is-danger:active,html.theme--catppuccin-latte .button.is-danger.is-active{background-color:#ba0d33;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:#d20f39;box-shadow:none}html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-focused{background-color:#d20f39;border-color:#d20f39;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-light{background-color:#feecf0;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:hover,html.theme--catppuccin-latte .button.is-danger.is-light.is-hovered{background-color:#fde0e6;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:active,html.theme--catppuccin-latte .button.is-danger.is-light.is-active{background-color:#fcd4dd;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-latte .button.is-small:not(.is-rounded),html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .button.is-normal{font-size:1rem}html.theme--catppuccin-latte .button.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .button.is-large{font-size:1.5rem}html.theme--catppuccin-latte .button[disabled],fieldset[disabled] html.theme--catppuccin-latte .button{background-color:#9ca0b0;border-color:#acb0be;box-shadow:none;opacity:.5}html.theme--catppuccin-latte .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-latte .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-latte .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-latte .button.is-static{background-color:#e6e9ef;border-color:#acb0be;color:#8c8fa1;box-shadow:none;pointer-events:none}html.theme--catppuccin-latte .button.is-rounded,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-latte .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-latte .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-latte .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-latte .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-latte .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-latte .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-latte .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-latte .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-latte .buttons.has-addons .button:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-latte .buttons.has-addons .button:focus,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused,html.theme--catppuccin-latte .buttons.has-addons .button:active,html.theme--catppuccin-latte .buttons.has-addons .button.is-active,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-latte .buttons.has-addons .button:focus:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-latte .buttons.has-addons .button:active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-latte .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .buttons.is-centered{justify-content:center}html.theme--catppuccin-latte .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-latte .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-latte .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-latte .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-latte .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-latte .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-latte .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-latte .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-latte .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-latte .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-latte .content li+li{margin-top:0.25em}html.theme--catppuccin-latte .content p:not(:last-child),html.theme--catppuccin-latte .content dl:not(:last-child),html.theme--catppuccin-latte .content ol:not(:last-child),html.theme--catppuccin-latte 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h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-latte .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-latte .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-latte .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-latte .content blockquote{background-color:#e6e9ef;border-left:5px solid #acb0be;padding:1.25em 1.5em}html.theme--catppuccin-latte .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-latte .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-latte .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-latte .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-latte .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-latte .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-latte .content 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.file.is-link.is-active .file-cta{background-color:#0b57ef;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-info .file-cta{background-color:#179299;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-info:hover .file-cta,html.theme--catppuccin-latte .file.is-info.is-hovered .file-cta{background-color:#15878e;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-info:focus .file-cta,html.theme--catppuccin-latte .file.is-info.is-focused .file-cta{border-color:transparent;box-shadow:0 0 0.5em rgba(23,146,153,0.25);color:#fff}html.theme--catppuccin-latte .file.is-info:active .file-cta,html.theme--catppuccin-latte .file.is-info.is-active .file-cta{background-color:#147d83;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-success .file-cta{background-color:#40a02b;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-success:hover .file-cta,html.theme--catppuccin-latte .file.is-success.is-hovered .file-cta{background-color:#3c9628;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-success:focus .file-cta,html.theme--catppuccin-latte .file.is-success.is-focused .file-cta{border-color:transparent;box-shadow:0 0 0.5em rgba(64,160,43,0.25);color:#fff}html.theme--catppuccin-latte .file.is-success:active .file-cta,html.theme--catppuccin-latte .file.is-success.is-active .file-cta{background-color:#388c26;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-warning .file-cta{background-color:#df8e1d;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-warning:hover .file-cta,html.theme--catppuccin-latte .file.is-warning.is-hovered .file-cta{background-color:#d4871c;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-warning:focus .file-cta,html.theme--catppuccin-latte .file.is-warning.is-focused .file-cta{border-color:transparent;box-shadow:0 0 0.5em rgba(223,142,29,0.25);color:#fff}html.theme--catppuccin-latte .file.is-warning:active .file-cta,html.theme--catppuccin-latte .file.is-warning.is-active .file-cta{background-color:#c8801a;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-danger .file-cta{background-color:#d20f39;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-danger:hover .file-cta,html.theme--catppuccin-latte .file.is-danger.is-hovered .file-cta{background-color:#c60e36;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-danger:focus .file-cta,html.theme--catppuccin-latte .file.is-danger.is-focused .file-cta{border-color:transparent;box-shadow:0 0 0.5em rgba(210,15,57,0.25);color:#fff}html.theme--catppuccin-latte .file.is-danger:active .file-cta,html.theme--catppuccin-latte .file.is-danger.is-active .file-cta{background-color:#ba0d33;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.file{font-size:.75rem}html.theme--catppuccin-latte .file.is-normal{font-size:1rem}html.theme--catppuccin-latte .file.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .file.is-medium .file-icon .fa{font-size:21px}html.theme--catppuccin-latte .file.is-large{font-size:1.5rem}html.theme--catppuccin-latte .file.is-large .file-icon .fa{font-size:28px}html.theme--catppuccin-latte .file.has-name .file-cta{border-bottom-right-radius:0;border-top-right-radius:0}html.theme--catppuccin-latte .file.has-name .file-name{border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .file.has-name.is-empty .file-cta{border-radius:.4em}html.theme--catppuccin-latte .file.has-name.is-empty .file-name{display:none}html.theme--catppuccin-latte .file.is-boxed .file-label{flex-direction:column}html.theme--catppuccin-latte .file.is-boxed .file-cta{flex-direction:column;height:auto;padding:1em 3em}html.theme--catppuccin-latte .file.is-boxed .file-name{border-width:0 1px 1px}html.theme--catppuccin-latte .file.is-boxed .file-icon{height:1.5em;width:1.5em}html.theme--catppuccin-latte .file.is-boxed .file-icon .fa{font-size:21px}html.theme--catppuccin-latte .file.is-boxed.is-small .file-icon .fa,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-boxed .file-icon .fa{font-size:14px}html.theme--catppuccin-latte .file.is-boxed.is-medium .file-icon .fa{font-size:28px}html.theme--catppuccin-latte .file.is-boxed.is-large .file-icon .fa{font-size:35px}html.theme--catppuccin-latte .file.is-boxed.has-name .file-cta{border-radius:.4em .4em 0 0}html.theme--catppuccin-latte .file.is-boxed.has-name .file-name{border-radius:0 0 .4em .4em;border-width:0 1px 1px}html.theme--catppuccin-latte .file.is-centered{justify-content:center}html.theme--catppuccin-latte .file.is-fullwidth .file-label{width:100%}html.theme--catppuccin-latte .file.is-fullwidth .file-name{flex-grow:1;max-width:none}html.theme--catppuccin-latte .file.is-right{justify-content:flex-end}html.theme--catppuccin-latte .file.is-right .file-cta{border-radius:0 .4em .4em 0}html.theme--catppuccin-latte .file.is-right .file-name{border-radius:.4em 0 0 .4em;border-width:1px 0 1px 1px;order:-1}html.theme--catppuccin-latte .file-label{align-items:stretch;display:flex;cursor:pointer;justify-content:flex-start;overflow:hidden;position:relative}html.theme--catppuccin-latte .file-label:hover .file-cta{background-color:#c5c9d5;color:#41445a}html.theme--catppuccin-latte .file-label:hover .file-name{border-color:#a5a9b8}html.theme--catppuccin-latte .file-label:active .file-cta{background-color:#bdc2cf;color:#41445a}html.theme--catppuccin-latte .file-label:active .file-name{border-color:#9ea2b3}html.theme--catppuccin-latte .file-input{height:100%;left:0;opacity:0;outline:none;position:absolute;top:0;width:100%}html.theme--catppuccin-latte .file-cta,html.theme--catppuccin-latte .file-name{border-color:#acb0be;border-radius:.4em;font-size:1em;padding-left:1em;padding-right:1em;white-space:nowrap}html.theme--catppuccin-latte .file-cta{background-color:#ccd0da;color:#4c4f69}html.theme--catppuccin-latte .file-name{border-color:#acb0be;border-style:solid;border-width:1px 1px 1px 0;display:block;max-width:16em;overflow:hidden;text-align:inherit;text-overflow:ellipsis}html.theme--catppuccin-latte .file-icon{align-items:center;display:flex;height:1em;justify-content:center;margin-right:.5em;width:1em}html.theme--catppuccin-latte .file-icon .fa{font-size:14px}html.theme--catppuccin-latte .label{color:#41445a;display:block;font-size:1rem;font-weight:700}html.theme--catppuccin-latte .label:not(:last-child){margin-bottom:0.5em}html.theme--catppuccin-latte .label.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.label{font-size:.75rem}html.theme--catppuccin-latte .label.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .label.is-large{font-size:1.5rem}html.theme--catppuccin-latte .help{display:block;font-size:.75rem;margin-top:0.25rem}html.theme--catppuccin-latte .help.is-white{color:#fff}html.theme--catppuccin-latte .help.is-black{color:#0a0a0a}html.theme--catppuccin-latte .help.is-light{color:#f5f5f5}html.theme--catppuccin-latte .help.is-dark,html.theme--catppuccin-latte .content kbd.help{color:#ccd0da}html.theme--catppuccin-latte .help.is-primary,html.theme--catppuccin-latte .docstring>section>a.help.docs-sourcelink{color:#1e66f5}html.theme--catppuccin-latte .help.is-link{color:#1e66f5}html.theme--catppuccin-latte .help.is-info{color:#179299}html.theme--catppuccin-latte .help.is-success{color:#40a02b}html.theme--catppuccin-latte .help.is-warning{color:#df8e1d}html.theme--catppuccin-latte .help.is-danger{color:#d20f39}html.theme--catppuccin-latte .field:not(:last-child){margin-bottom:0.75rem}html.theme--catppuccin-latte .field.has-addons{display:flex;justify-content:flex-start}html.theme--catppuccin-latte .field.has-addons .control:not(:last-child){margin-right:-1px}html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .button,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .input,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:not(:first-child):not(:last-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .select select{border-radius:0}html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .button,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .input,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:first-child:not(:only-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .select select{border-bottom-right-radius:0;border-top-right-radius:0}html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .button,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .input,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:last-child:not(:only-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .select select{border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-hovered:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-hovered:not([disabled]){z-index:2}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .button.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .button.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):focus,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .input.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-focused:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):active,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .input.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-active:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .select select.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .select select.is-active:not([disabled]){z-index:3}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):focus:hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):active:hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-active:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-active:not([disabled]):hover{z-index:4}html.theme--catppuccin-latte .field.has-addons .control.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .field.has-addons.has-addons-centered{justify-content:center}html.theme--catppuccin-latte .field.has-addons.has-addons-right{justify-content:flex-end}html.theme--catppuccin-latte .field.has-addons.has-addons-fullwidth .control{flex-grow:1;flex-shrink:0}html.theme--catppuccin-latte .field.is-grouped{display:flex;justify-content:flex-start}html.theme--catppuccin-latte .field.is-grouped>.control{flex-shrink:0}html.theme--catppuccin-latte .field.is-grouped>.control:not(:last-child){margin-bottom:0;margin-right:.75rem}html.theme--catppuccin-latte .field.is-grouped>.control.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .field.is-grouped.is-grouped-centered{justify-content:center}html.theme--catppuccin-latte .field.is-grouped.is-grouped-right{justify-content:flex-end}html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline{flex-wrap:wrap}html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline>.control:last-child,html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline>.control:not(:last-child){margin-bottom:0.75rem}html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline:last-child{margin-bottom:-0.75rem}html.theme--catppuccin-latte 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.icon:only-child,html.theme--catppuccin-latte .navbar-link .icon:only-child{margin-left:-0.25rem;margin-right:-0.25rem}html.theme--catppuccin-latte a.navbar-item,html.theme--catppuccin-latte .navbar-link{cursor:pointer}html.theme--catppuccin-latte a.navbar-item:focus,html.theme--catppuccin-latte a.navbar-item:focus-within,html.theme--catppuccin-latte a.navbar-item:hover,html.theme--catppuccin-latte a.navbar-item.is-active,html.theme--catppuccin-latte .navbar-link:focus,html.theme--catppuccin-latte .navbar-link:focus-within,html.theme--catppuccin-latte .navbar-link:hover,html.theme--catppuccin-latte .navbar-link.is-active{background-color:rgba(0,0,0,0);color:#1e66f5}html.theme--catppuccin-latte .navbar-item{flex-grow:0;flex-shrink:0}html.theme--catppuccin-latte .navbar-item img{max-height:1.75rem}html.theme--catppuccin-latte .navbar-item.has-dropdown{padding:0}html.theme--catppuccin-latte .navbar-item.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .navbar-item.is-tab{border-bottom:1px solid transparent;min-height:4rem;padding-bottom:calc(0.5rem - 1px)}html.theme--catppuccin-latte .navbar-item.is-tab:focus,html.theme--catppuccin-latte .navbar-item.is-tab:hover{background-color:rgba(0,0,0,0);border-bottom-color:#1e66f5}html.theme--catppuccin-latte .navbar-item.is-tab.is-active{background-color:rgba(0,0,0,0);border-bottom-color:#1e66f5;border-bottom-style:solid;border-bottom-width:3px;color:#1e66f5;padding-bottom:calc(0.5rem - 3px)}html.theme--catppuccin-latte .navbar-content{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .navbar-link:not(.is-arrowless){padding-right:2.5em}html.theme--catppuccin-latte .navbar-link:not(.is-arrowless)::after{border-color:#fff;margin-top:-0.375em;right:1.125em}html.theme--catppuccin-latte .navbar-dropdown{font-size:0.875rem;padding-bottom:0.5rem;padding-top:0.5rem}html.theme--catppuccin-latte .navbar-dropdown .navbar-item{padding-left:1.5rem;padding-right:1.5rem}html.theme--catppuccin-latte .navbar-divider{background-color:rgba(0,0,0,0.2);border:none;display:none;height:2px;margin:0.5rem 0}@media screen and (max-width: 1055px){html.theme--catppuccin-latte .navbar>.container{display:block}html.theme--catppuccin-latte .navbar-brand .navbar-item,html.theme--catppuccin-latte .navbar-tabs .navbar-item{align-items:center;display:flex}html.theme--catppuccin-latte .navbar-link::after{display:none}html.theme--catppuccin-latte .navbar-menu{background-color:#1e66f5;box-shadow:0 8px 16px rgba(10,10,10,0.1);padding:0.5rem 0}html.theme--catppuccin-latte .navbar-menu.is-active{display:block}html.theme--catppuccin-latte .navbar.is-fixed-bottom-touch,html.theme--catppuccin-latte .navbar.is-fixed-top-touch{left:0;position:fixed;right:0;z-index:30}html.theme--catppuccin-latte .navbar.is-fixed-bottom-touch{bottom:0}html.theme--catppuccin-latte .navbar.is-fixed-bottom-touch.has-shadow{box-shadow:0 -2px 3px rgba(10,10,10,0.1)}html.theme--catppuccin-latte .navbar.is-fixed-top-touch{top:0}html.theme--catppuccin-latte .navbar.is-fixed-top .navbar-menu,html.theme--catppuccin-latte .navbar.is-fixed-top-touch .navbar-menu{-webkit-overflow-scrolling:touch;max-height:calc(100vh - 4rem);overflow:auto}html.theme--catppuccin-latte html.has-navbar-fixed-top-touch,html.theme--catppuccin-latte body.has-navbar-fixed-top-touch{padding-top:4rem}html.theme--catppuccin-latte html.has-navbar-fixed-bottom-touch,html.theme--catppuccin-latte body.has-navbar-fixed-bottom-touch{padding-bottom:4rem}}@media screen and (min-width: 1056px){html.theme--catppuccin-latte .navbar,html.theme--catppuccin-latte .navbar-menu,html.theme--catppuccin-latte .navbar-start,html.theme--catppuccin-latte .navbar-end{align-items:stretch;display:flex}html.theme--catppuccin-latte .navbar{min-height:4rem}html.theme--catppuccin-latte .navbar.is-spaced{padding:1rem 2rem}html.theme--catppuccin-latte .navbar.is-spaced .navbar-start,html.theme--catppuccin-latte .navbar.is-spaced .navbar-end{align-items:center}html.theme--catppuccin-latte .navbar.is-spaced a.navbar-item,html.theme--catppuccin-latte .navbar.is-spaced .navbar-link{border-radius:.4em}html.theme--catppuccin-latte .navbar.is-transparent a.navbar-item:focus,html.theme--catppuccin-latte .navbar.is-transparent a.navbar-item:hover,html.theme--catppuccin-latte .navbar.is-transparent a.navbar-item.is-active,html.theme--catppuccin-latte .navbar.is-transparent .navbar-link:focus,html.theme--catppuccin-latte .navbar.is-transparent .navbar-link:hover,html.theme--catppuccin-latte .navbar.is-transparent .navbar-link.is-active{background-color:transparent !important}html.theme--catppuccin-latte .navbar.is-transparent .navbar-item.has-dropdown.is-active .navbar-link,html.theme--catppuccin-latte .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus .navbar-link,html.theme--catppuccin-latte .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus-within 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.navbar-dropdown.is-boxed,.navbar.is-spaced html.theme--catppuccin-latte .navbar-item.is-hoverable:hover .navbar-dropdown,html.theme--catppuccin-latte .navbar-item.is-hoverable:hover .navbar-dropdown.is-boxed{opacity:1;pointer-events:auto;transform:translateY(0)}html.theme--catppuccin-latte .navbar-menu{flex-grow:1;flex-shrink:0}html.theme--catppuccin-latte .navbar-start{justify-content:flex-start;margin-right:auto}html.theme--catppuccin-latte .navbar-end{justify-content:flex-end;margin-left:auto}html.theme--catppuccin-latte .navbar-dropdown{background-color:#1e66f5;border-bottom-left-radius:8px;border-bottom-right-radius:8px;border-top:1px solid rgba(0,0,0,0.2);box-shadow:0 8px 8px rgba(10,10,10,0.1);display:none;font-size:0.875rem;left:0;min-width:100%;position:absolute;top:100%;z-index:20}html.theme--catppuccin-latte .navbar-dropdown .navbar-item{padding:0.375rem 1rem;white-space:nowrap}html.theme--catppuccin-latte .navbar-dropdown a.navbar-item{padding-right:3rem}html.theme--catppuccin-latte .navbar-dropdown a.navbar-item:focus,html.theme--catppuccin-latte .navbar-dropdown a.navbar-item:hover{background-color:rgba(0,0,0,0);color:#8c8fa1}html.theme--catppuccin-latte .navbar-dropdown a.navbar-item.is-active{background-color:rgba(0,0,0,0);color:#1e66f5}.navbar.is-spaced html.theme--catppuccin-latte .navbar-dropdown,html.theme--catppuccin-latte .navbar-dropdown.is-boxed{border-radius:8px;border-top:none;box-shadow:0 8px 8px rgba(10,10,10,0.1), 0 0 0 1px rgba(10,10,10,0.1);display:block;opacity:0;pointer-events:none;top:calc(100% + (-4px));transform:translateY(-5px);transition-duration:86ms;transition-property:opacity, transform}html.theme--catppuccin-latte .navbar-dropdown.is-right{left:auto;right:0}html.theme--catppuccin-latte .navbar-divider{display:block}html.theme--catppuccin-latte .navbar>.container .navbar-brand,html.theme--catppuccin-latte .container>.navbar .navbar-brand{margin-left:-.75rem}html.theme--catppuccin-latte .navbar>.container .navbar-menu,html.theme--catppuccin-latte .container>.navbar .navbar-menu{margin-right:-.75rem}html.theme--catppuccin-latte .navbar.is-fixed-bottom-desktop,html.theme--catppuccin-latte .navbar.is-fixed-top-desktop{left:0;position:fixed;right:0;z-index:30}html.theme--catppuccin-latte .navbar.is-fixed-bottom-desktop{bottom:0}html.theme--catppuccin-latte .navbar.is-fixed-bottom-desktop.has-shadow{box-shadow:0 -2px 3px rgba(10,10,10,0.1)}html.theme--catppuccin-latte .navbar.is-fixed-top-desktop{top:0}html.theme--catppuccin-latte html.has-navbar-fixed-top-desktop,html.theme--catppuccin-latte body.has-navbar-fixed-top-desktop{padding-top:4rem}html.theme--catppuccin-latte html.has-navbar-fixed-bottom-desktop,html.theme--catppuccin-latte body.has-navbar-fixed-bottom-desktop{padding-bottom:4rem}html.theme--catppuccin-latte html.has-spaced-navbar-fixed-top,html.theme--catppuccin-latte body.has-spaced-navbar-fixed-top{padding-top:6rem}html.theme--catppuccin-latte html.has-spaced-navbar-fixed-bottom,html.theme--catppuccin-latte body.has-spaced-navbar-fixed-bottom{padding-bottom:6rem}html.theme--catppuccin-latte a.navbar-item.is-active,html.theme--catppuccin-latte .navbar-link.is-active{color:#1e66f5}html.theme--catppuccin-latte a.navbar-item.is-active:not(:focus):not(:hover),html.theme--catppuccin-latte .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--catppuccin-latte .navbar-item.has-dropdown:focus .navbar-link,html.theme--catppuccin-latte .navbar-item.has-dropdown:hover .navbar-link,html.theme--catppuccin-latte .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--catppuccin-latte .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--catppuccin-latte .pagination{font-size:1rem;margin:-.25rem}html.theme--catppuccin-latte .pagination.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.pagination{font-size:.75rem}html.theme--catppuccin-latte .pagination.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .pagination.is-large{font-size:1.5rem}html.theme--catppuccin-latte .pagination.is-rounded .pagination-previous,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.pagination .pagination-previous,html.theme--catppuccin-latte .pagination.is-rounded .pagination-next,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.pagination .pagination-next{padding-left:1em;padding-right:1em;border-radius:9999px}html.theme--catppuccin-latte .pagination.is-rounded .pagination-link,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.pagination .pagination-link{border-radius:9999px}html.theme--catppuccin-latte .pagination,html.theme--catppuccin-latte .pagination-list{align-items:center;display:flex;justify-content:center;text-align:center}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next,html.theme--catppuccin-latte .pagination-link,html.theme--catppuccin-latte .pagination-ellipsis{font-size:1em;justify-content:center;margin:.25rem;padding-left:.5em;padding-right:.5em;text-align:center}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next,html.theme--catppuccin-latte .pagination-link{border-color:#acb0be;color:#1e66f5;min-width:2.5em}html.theme--catppuccin-latte .pagination-previous:hover,html.theme--catppuccin-latte .pagination-next:hover,html.theme--catppuccin-latte .pagination-link:hover{border-color:#9ca0b0;color:#04a5e5}html.theme--catppuccin-latte .pagination-previous:focus,html.theme--catppuccin-latte .pagination-next:focus,html.theme--catppuccin-latte .pagination-link:focus{border-color:#9ca0b0}html.theme--catppuccin-latte .pagination-previous:active,html.theme--catppuccin-latte .pagination-next:active,html.theme--catppuccin-latte .pagination-link:active{box-shadow:inset 0 1px 2px rgba(10,10,10,0.2)}html.theme--catppuccin-latte .pagination-previous[disabled],html.theme--catppuccin-latte .pagination-previous.is-disabled,html.theme--catppuccin-latte .pagination-next[disabled],html.theme--catppuccin-latte .pagination-next.is-disabled,html.theme--catppuccin-latte .pagination-link[disabled],html.theme--catppuccin-latte .pagination-link.is-disabled{background-color:#acb0be;border-color:#acb0be;box-shadow:none;color:#616587;opacity:0.5}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next{padding-left:.75em;padding-right:.75em;white-space:nowrap}html.theme--catppuccin-latte .pagination-link.is-current{background-color:#1e66f5;border-color:#1e66f5;color:#fff}html.theme--catppuccin-latte .pagination-ellipsis{color:#9ca0b0;pointer-events:none}html.theme--catppuccin-latte .pagination-list{flex-wrap:wrap}html.theme--catppuccin-latte .pagination-list li{list-style:none}@media screen and (max-width: 768px){html.theme--catppuccin-latte .pagination{flex-wrap:wrap}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .pagination-list li{flex-grow:1;flex-shrink:1}}@media screen and (min-width: 769px),print{html.theme--catppuccin-latte .pagination-list{flex-grow:1;flex-shrink:1;justify-content:flex-start;order:1}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next,html.theme--catppuccin-latte .pagination-link,html.theme--catppuccin-latte .pagination-ellipsis{margin-bottom:0;margin-top:0}html.theme--catppuccin-latte .pagination-previous{order:2}html.theme--catppuccin-latte .pagination-next{order:3}html.theme--catppuccin-latte .pagination{justify-content:space-between;margin-bottom:0;margin-top:0}html.theme--catppuccin-latte .pagination.is-centered .pagination-previous{order:1}html.theme--catppuccin-latte .pagination.is-centered .pagination-list{justify-content:center;order:2}html.theme--catppuccin-latte .pagination.is-centered .pagination-next{order:3}html.theme--catppuccin-latte .pagination.is-right .pagination-previous{order:1}html.theme--catppuccin-latte .pagination.is-right .pagination-next{order:2}html.theme--catppuccin-latte .pagination.is-right .pagination-list{justify-content:flex-end;order:3}}html.theme--catppuccin-latte .panel{border-radius:8px;box-shadow:#171717;font-size:1rem}html.theme--catppuccin-latte .panel:not(:last-child){margin-bottom:1.5rem}html.theme--catppuccin-latte .panel.is-white .panel-heading{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-latte .panel.is-white .panel-tabs a.is-active{border-bottom-color:#fff}html.theme--catppuccin-latte .panel.is-white .panel-block.is-active .panel-icon{color:#fff}html.theme--catppuccin-latte .panel.is-black .panel-heading{background-color:#0a0a0a;color:#fff}html.theme--catppuccin-latte .panel.is-black .panel-tabs a.is-active{border-bottom-color:#0a0a0a}html.theme--catppuccin-latte .panel.is-black .panel-block.is-active .panel-icon{color:#0a0a0a}html.theme--catppuccin-latte .panel.is-light .panel-heading{background-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .panel.is-light .panel-tabs a.is-active{border-bottom-color:#f5f5f5}html.theme--catppuccin-latte .panel.is-light .panel-block.is-active .panel-icon{color:#f5f5f5}html.theme--catppuccin-latte .panel.is-dark .panel-heading,html.theme--catppuccin-latte .content kbd.panel .panel-heading{background-color:#ccd0da;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .panel.is-dark .panel-tabs a.is-active,html.theme--catppuccin-latte .content kbd.panel .panel-tabs a.is-active{border-bottom-color:#ccd0da}html.theme--catppuccin-latte .panel.is-dark .panel-block.is-active .panel-icon,html.theme--catppuccin-latte .content kbd.panel .panel-block.is-active .panel-icon{color:#ccd0da}html.theme--catppuccin-latte .panel.is-primary .panel-heading,html.theme--catppuccin-latte .docstring>section>a.panel.docs-sourcelink .panel-heading{background-color:#1e66f5;color:#fff}html.theme--catppuccin-latte .panel.is-primary .panel-tabs a.is-active,html.theme--catppuccin-latte .docstring>section>a.panel.docs-sourcelink .panel-tabs a.is-active{border-bottom-color:#1e66f5}html.theme--catppuccin-latte .panel.is-primary .panel-block.is-active .panel-icon,html.theme--catppuccin-latte .docstring>section>a.panel.docs-sourcelink .panel-block.is-active .panel-icon{color:#1e66f5}html.theme--catppuccin-latte .panel.is-link .panel-heading{background-color:#1e66f5;color:#fff}html.theme--catppuccin-latte .panel.is-link .panel-tabs a.is-active{border-bottom-color:#1e66f5}html.theme--catppuccin-latte .panel.is-link .panel-block.is-active .panel-icon{color:#1e66f5}html.theme--catppuccin-latte .panel.is-info 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kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-dark.is-outlined[disabled],html.theme--catppuccin-macchiato .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-macchiato .content kbd.button.is-outlined{background-color:transparent;border-color:#363a4f;box-shadow:none;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363a4f #363a4f !important}html.theme--catppuccin-macchiato 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.button.is-link.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-link.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-link.is-outlined.is-focused{background-color:#8aadf4;border-color:#8aadf4;color:#fff}html.theme--catppuccin-macchiato .button.is-link.is-outlined.is-loading::after{border-color:transparent transparent #8aadf4 #8aadf4 !important}html.theme--catppuccin-macchiato .button.is-link.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-link.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-link.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-link.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-link.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-link.is-outlined{background-color:transparent;border-color:#8aadf4;box-shadow:none;color:#8aadf4}html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined.is-focused{background-color:#fff;color:#8aadf4}html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #8aadf4 #8aadf4 !important}html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-link.is-light{background-color:#ecf2fd;color:#0e3b95}html.theme--catppuccin-macchiato .button.is-link.is-light:hover,html.theme--catppuccin-macchiato .button.is-link.is-light.is-hovered{background-color:#e1eafc;border-color:transparent;color:#0e3b95}html.theme--catppuccin-macchiato .button.is-link.is-light:active,html.theme--catppuccin-macchiato .button.is-link.is-light.is-active{background-color:#d5e2fb;border-color:transparent;color:#0e3b95}html.theme--catppuccin-macchiato 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.button.is-info{background-color:#8bd5ca;border-color:#8bd5ca;box-shadow:none}html.theme--catppuccin-macchiato .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined{background-color:transparent;border-color:#8bd5ca;color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-info.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-focused{background-color:#8bd5ca;border-color:#8bd5ca;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #8bd5ca #8bd5ca !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-outlined{background-color:transparent;border-color:#8bd5ca;box-shadow:none;color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #8bd5ca #8bd5ca !important}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-light{background-color:#f0faf8;color:#276d62}html.theme--catppuccin-macchiato .button.is-info.is-light:hover,html.theme--catppuccin-macchiato .button.is-info.is-light.is-hovered{background-color:#e7f6f4;border-color:transparent;color:#276d62}html.theme--catppuccin-macchiato .button.is-info.is-light:active,html.theme--catppuccin-macchiato .button.is-info.is-light.is-active{background-color:#ddf3f0;border-color:transparent;color:#276d62}html.theme--catppuccin-macchiato .button.is-success{background-color:#a6da95;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:hover,html.theme--catppuccin-macchiato .button.is-success.is-hovered{background-color:#9ed78c;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:focus,html.theme--catppuccin-macchiato .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:focus:not(:active),html.theme--catppuccin-macchiato .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,218,149,0.25)}html.theme--catppuccin-macchiato .button.is-success:active,html.theme--catppuccin-macchiato .button.is-success.is-active{background-color:#96d382;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success{background-color:#a6da95;border-color:#a6da95;box-shadow:none}html.theme--catppuccin-macchiato .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined{background-color:transparent;border-color:#a6da95;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-success.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-focused{background-color:#a6da95;border-color:#a6da95;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6da95 #a6da95 !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-outlined{background-color:transparent;border-color:#a6da95;box-shadow:none;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6da95 #a6da95 !important}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-light{background-color:#f2faf0;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:hover,html.theme--catppuccin-macchiato .button.is-success.is-light.is-hovered{background-color:#eaf6e6;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:active,html.theme--catppuccin-macchiato .button.is-success.is-light.is-active{background-color:#e2f3dd;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:hover,html.theme--catppuccin-macchiato .button.is-warning.is-hovered{background-color:#eccf94;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus,html.theme--catppuccin-macchiato .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus:not(:active),html.theme--catppuccin-macchiato .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(238,212,159,0.25)}html.theme--catppuccin-macchiato .button.is-warning:active,html.theme--catppuccin-macchiato .button.is-warning.is-active{background-color:#eaca89;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:#eed49f;box-shadow:none}html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-focused{background-color:#eed49f;border-color:#eed49f;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-light{background-color:#fcf7ee;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:hover,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-hovered{background-color:#faf2e3;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:active,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-active{background-color:#f8eed8;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:hover,html.theme--catppuccin-macchiato .button.is-danger.is-hovered{background-color:#eb7c8c;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus,html.theme--catppuccin-macchiato .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus:not(:active),html.theme--catppuccin-macchiato .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(237,135,150,0.25)}html.theme--catppuccin-macchiato .button.is-danger:active,html.theme--catppuccin-macchiato .button.is-danger.is-active{background-color:#ea7183;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:#ed8796;box-shadow:none}html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-macchiato .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-outlined:hover,html.theme--catppuccin-macchiato 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.button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-light{background-color:#fcedef;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:hover,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-hovered{background-color:#fbe2e6;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:active,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-active{background-color:#f9d7dc;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-small:not(.is-rounded),html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-macchiato .button.is-normal{font-size:1rem}html.theme--catppuccin-macchiato .button.is-medium{font-size:1.25rem}html.theme--catppuccin-macchiato .button.is-large{font-size:1.5rem}html.theme--catppuccin-macchiato .button[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button{background-color:#6e738d;border-color:#5b6078;box-shadow:none;opacity:.5}html.theme--catppuccin-macchiato .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-macchiato .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-macchiato .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-macchiato .button.is-static{background-color:#1e2030;border-color:#5b6078;color:#8087a2;box-shadow:none;pointer-events:none}html.theme--catppuccin-macchiato .button.is-rounded,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-macchiato .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-macchiato .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-macchiato .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-macchiato .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-macchiato .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-macchiato .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-macchiato .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-macchiato .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-macchiato .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-macchiato .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-macchiato .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-macchiato .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-macchiato .buttons.has-addons .button:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-macchiato .buttons.has-addons .button:focus,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-focused,html.theme--catppuccin-macchiato .buttons.has-addons .button:active,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-active,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-macchiato .buttons.has-addons .button:focus:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button:active:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-macchiato .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-macchiato .buttons.is-centered{justify-content:center}html.theme--catppuccin-macchiato .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-macchiato .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-macchiato .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-macchiato .button.is-responsive.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-macchiato .button.is-responsive,html.theme--catppuccin-macchiato .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-macchiato .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-macchiato .button.is-responsive.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-macchiato .button.is-responsive,html.theme--catppuccin-macchiato .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-macchiato .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-macchiato .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-macchiato .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-macchiato .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-macchiato .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-macchiato .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-macchiato .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-macchiato .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-macchiato .content li+li{margin-top:0.25em}html.theme--catppuccin-macchiato .content p:not(:last-child),html.theme--catppuccin-macchiato .content dl:not(:last-child),html.theme--catppuccin-macchiato .content ol:not(:last-child),html.theme--catppuccin-macchiato .content ul:not(:last-child),html.theme--catppuccin-macchiato .content blockquote:not(:last-child),html.theme--catppuccin-macchiato .content pre:not(:last-child),html.theme--catppuccin-macchiato .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-macchiato .content h1,html.theme--catppuccin-macchiato .content h2,html.theme--catppuccin-macchiato .content h3,html.theme--catppuccin-macchiato .content h4,html.theme--catppuccin-macchiato .content h5,html.theme--catppuccin-macchiato .content h6{color:#cad3f5;font-weight:600;line-height:1.125}html.theme--catppuccin-macchiato .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-macchiato .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-macchiato .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-macchiato .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-macchiato .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-macchiato .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-macchiato .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-macchiato .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-macchiato .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-macchiato .content blockquote{background-color:#1e2030;border-left:5px solid #5b6078;padding:1.25em 1.5em}html.theme--catppuccin-macchiato .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-macchiato .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-macchiato .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-macchiato .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-macchiato .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-macchiato .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-macchiato .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-macchiato .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-macchiato .content ul ul ul{list-style-type:square}html.theme--catppuccin-macchiato .content dd{margin-left:2em}html.theme--catppuccin-macchiato .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-macchiato .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-macchiato .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-macchiato .content figure img{display:inline-block}html.theme--catppuccin-macchiato .content figure figcaption{font-style:italic}html.theme--catppuccin-macchiato .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-macchiato .content sup,html.theme--catppuccin-macchiato .content sub{font-size:75%}html.theme--catppuccin-macchiato .content table{width:100%}html.theme--catppuccin-macchiato .content table td,html.theme--catppuccin-macchiato .content table th{border:1px solid #5b6078;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-macchiato .content table th{color:#b5c1f1}html.theme--catppuccin-macchiato .content table th:not([align]){text-align:inherit}html.theme--catppuccin-macchiato .content table thead td,html.theme--catppuccin-macchiato .content table thead th{border-width:0 0 2px;color:#b5c1f1}html.theme--catppuccin-macchiato .content table tfoot td,html.theme--catppuccin-macchiato .content table tfoot th{border-width:2px 0 0;color:#b5c1f1}html.theme--catppuccin-macchiato .content table tbody tr:last-child td,html.theme--catppuccin-macchiato .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-macchiato .content .tabs li+li{margin-top:0}html.theme--catppuccin-macchiato .content.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-macchiato .content.is-normal{font-size:1rem}html.theme--catppuccin-macchiato .content.is-medium{font-size:1.25rem}html.theme--catppuccin-macchiato .content.is-large{font-size:1.5rem}html.theme--catppuccin-macchiato .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-macchiato .icon.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-macchiato .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-macchiato .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-macchiato .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-macchiato .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-macchiato .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--catppuccin-macchiato .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--catppuccin-macchiato div.icon-text{display:flex}html.theme--catppuccin-macchiato .image,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--catppuccin-macchiato .image img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--catppuccin-macchiato .image img.is-rounded,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--catppuccin-macchiato .image.is-fullwidth,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--catppuccin-macchiato .image.is-square img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--catppuccin-macchiato .image.is-square .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--catppuccin-macchiato .image.is-1by1 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--catppuccin-macchiato .image.is-1by1 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--catppuccin-macchiato .image.is-5by4 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--catppuccin-macchiato .image.is-5by4 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--catppuccin-macchiato .image.is-4by3 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--catppuccin-macchiato .image.is-4by3 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--catppuccin-macchiato .image.is-3by2 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--catppuccin-macchiato .image.is-3by2 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--catppuccin-macchiato .image.is-5by3 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--catppuccin-macchiato .image.is-5by3 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--catppuccin-macchiato .image.is-16by9 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--catppuccin-macchiato .image.is-16by9 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--catppuccin-macchiato .image.is-2by1 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--catppuccin-macchiato .image.is-2by1 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--catppuccin-macchiato .image.is-3by1 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--catppuccin-macchiato .image.is-3by1 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-3by1 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select[disabled]:-moz-placeholder,html.theme--catppuccin-macchiato .textarea[disabled]:-moz-placeholder,html.theme--catppuccin-macchiato .input[disabled]:-moz-placeholder,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input[disabled]:-moz-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato .select select:-moz-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato .textarea:-moz-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato .input:-moz-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input:-moz-placeholder{color:rgba(245,247,253,0.3)}html.theme--catppuccin-macchiato .select select[disabled]:-ms-input-placeholder,html.theme--catppuccin-macchiato .textarea[disabled]:-ms-input-placeholder,html.theme--catppuccin-macchiato .input[disabled]:-ms-input-placeholder,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input[disabled]:-ms-input-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato .select select:-ms-input-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato .textarea:-ms-input-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato .input:-ms-input-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input:-ms-input-placeholder{color:rgba(245,247,253,0.3)}html.theme--catppuccin-macchiato .textarea,html.theme--catppuccin-macchiato .input,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input{box-shadow:inset 0 0.0625em 0.125em rgba(10,10,10,0.05);max-width:100%;width:100%}html.theme--catppuccin-macchiato .textarea[readonly],html.theme--catppuccin-macchiato .input[readonly],html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input[readonly]{box-shadow:none}html.theme--catppuccin-macchiato 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form.docs-search>input.is-active{box-shadow:0 0 0 0.125em rgba(255,255,255,0.25)}html.theme--catppuccin-macchiato .is-black.textarea,html.theme--catppuccin-macchiato .is-black.input,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black{border-color:#0a0a0a}html.theme--catppuccin-macchiato .is-black.textarea:focus,html.theme--catppuccin-macchiato .is-black.input:focus,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black:focus,html.theme--catppuccin-macchiato .is-black.is-focused.textarea,html.theme--catppuccin-macchiato .is-black.is-focused.input,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-focused,html.theme--catppuccin-macchiato .is-black.textarea:active,html.theme--catppuccin-macchiato .is-black.input:active,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black:active,html.theme--catppuccin-macchiato 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kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#313244}html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .content 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html.theme--catppuccin-mocha .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-link.is-light{background-color:#ebf3fe;color:#063c93}html.theme--catppuccin-mocha .button.is-link.is-light:hover,html.theme--catppuccin-mocha .button.is-link.is-light.is-hovered{background-color:#dfebfe;border-color:transparent;color:#063c93}html.theme--catppuccin-mocha .button.is-link.is-light:active,html.theme--catppuccin-mocha .button.is-link.is-light.is-active{background-color:#d3e3fd;border-color:transparent;color:#063c93}html.theme--catppuccin-mocha .button.is-info{background-color:#94e2d5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:hover,html.theme--catppuccin-mocha .button.is-info.is-hovered{background-color:#8adfd1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:focus,html.theme--catppuccin-mocha .button.is-info.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:focus:not(:active),html.theme--catppuccin-mocha .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(148,226,213,0.25)}html.theme--catppuccin-mocha .button.is-info:active,html.theme--catppuccin-mocha .button.is-info.is-active{background-color:#80ddcd;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info{background-color:#94e2d5;border-color:#94e2d5;box-shadow:none}html.theme--catppuccin-mocha .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted:hover,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-info.is-outlined{background-color:transparent;border-color:#94e2d5;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-outlined:hover,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-info.is-outlined:focus,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-focused{background-color:#94e2d5;border-color:#94e2d5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #94e2d5 #94e2d5 !important}html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-outlined{background-color:transparent;border-color:#94e2d5;box-shadow:none;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #94e2d5 #94e2d5 !important}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-light{background-color:#effbf9;color:#207466}html.theme--catppuccin-mocha .button.is-info.is-light:hover,html.theme--catppuccin-mocha .button.is-info.is-light.is-hovered{background-color:#e5f8f5;border-color:transparent;color:#207466}html.theme--catppuccin-mocha .button.is-info.is-light:active,html.theme--catppuccin-mocha .button.is-info.is-light.is-active{background-color:#dbf5f1;border-color:transparent;color:#207466}html.theme--catppuccin-mocha .button.is-success{background-color:#a6e3a1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:hover,html.theme--catppuccin-mocha .button.is-success.is-hovered{background-color:#9de097;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:focus,html.theme--catppuccin-mocha .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:focus:not(:active),html.theme--catppuccin-mocha .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,227,161,0.25)}html.theme--catppuccin-mocha .button.is-success:active,html.theme--catppuccin-mocha .button.is-success.is-active{background-color:#93dd8d;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success{background-color:#a6e3a1;border-color:#a6e3a1;box-shadow:none}html.theme--catppuccin-mocha .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted:hover,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-success.is-outlined{background-color:transparent;border-color:#a6e3a1;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-outlined:hover,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-success.is-outlined:focus,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-focused{background-color:#a6e3a1;border-color:#a6e3a1;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-outlined{background-color:transparent;border-color:#a6e3a1;box-shadow:none;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-light{background-color:#f0faef;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:hover,html.theme--catppuccin-mocha .button.is-success.is-light.is-hovered{background-color:#e7f7e5;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:active,html.theme--catppuccin-mocha .button.is-success.is-light.is-active{background-color:#def4dc;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:hover,html.theme--catppuccin-mocha .button.is-warning.is-hovered{background-color:#f8dea3;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus,html.theme--catppuccin-mocha .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus:not(:active),html.theme--catppuccin-mocha .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(249,226,175,0.25)}html.theme--catppuccin-mocha .button.is-warning:active,html.theme--catppuccin-mocha .button.is-warning.is-active{background-color:#f7d997;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:#f9e2af;box-shadow:none}html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-focused{background-color:#f9e2af;border-color:#f9e2af;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-light{background-color:#fef8ec;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:hover,html.theme--catppuccin-mocha .button.is-warning.is-light.is-hovered{background-color:#fdf4e0;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:active,html.theme--catppuccin-mocha .button.is-warning.is-light.is-active{background-color:#fcf0d4;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:hover,html.theme--catppuccin-mocha .button.is-danger.is-hovered{background-color:#f27f9f;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus,html.theme--catppuccin-mocha .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus:not(:active),html.theme--catppuccin-mocha .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(243,139,168,0.25)}html.theme--catppuccin-mocha .button.is-danger:active,html.theme--catppuccin-mocha .button.is-danger.is-active{background-color:#f17497;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:#f38ba8;box-shadow:none}html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-mocha .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-focused{background-color:#f38ba8;border-color:#f38ba8;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-light{background-color:#fdedf1;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:hover,html.theme--catppuccin-mocha .button.is-danger.is-light.is-hovered{background-color:#fce1e8;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:active,html.theme--catppuccin-mocha .button.is-danger.is-light.is-active{background-color:#fbd5e0;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-mocha .button.is-small:not(.is-rounded),html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .button.is-normal{font-size:1rem}html.theme--catppuccin-mocha .button.is-medium{font-size:1.25rem}html.theme--catppuccin-mocha .button.is-large{font-size:1.5rem}html.theme--catppuccin-mocha .button[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button{background-color:#6c7086;border-color:#585b70;box-shadow:none;opacity:.5}html.theme--catppuccin-mocha .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-mocha .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-mocha .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-mocha .button.is-static{background-color:#181825;border-color:#585b70;color:#7f849c;box-shadow:none;pointer-events:none}html.theme--catppuccin-mocha .button.is-rounded,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-mocha .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-mocha .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-mocha .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-mocha .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-mocha .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-mocha .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-mocha .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-mocha .buttons.has-addons .button:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-mocha .buttons.has-addons .button:focus,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused,html.theme--catppuccin-mocha .buttons.has-addons .button:active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-mocha .buttons.has-addons .button:focus:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-mocha .buttons.has-addons .button:active:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-mocha .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-mocha .buttons.is-centered{justify-content:center}html.theme--catppuccin-mocha .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-mocha .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-mocha .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-mocha .button.is-responsive.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-mocha .button.is-responsive,html.theme--catppuccin-mocha .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-mocha .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-mocha .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-mocha .button.is-responsive.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-mocha .button.is-responsive,html.theme--catppuccin-mocha .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-mocha .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-mocha .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-mocha .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-mocha .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-mocha .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-mocha .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-mocha .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-mocha .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-mocha .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-mocha .content li+li{margin-top:0.25em}html.theme--catppuccin-mocha .content p:not(:last-child),html.theme--catppuccin-mocha .content dl:not(:last-child),html.theme--catppuccin-mocha .content ol:not(:last-child),html.theme--catppuccin-mocha .content ul:not(:last-child),html.theme--catppuccin-mocha .content blockquote:not(:last-child),html.theme--catppuccin-mocha .content pre:not(:last-child),html.theme--catppuccin-mocha .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-mocha .content h1,html.theme--catppuccin-mocha .content h2,html.theme--catppuccin-mocha .content h3,html.theme--catppuccin-mocha .content h4,html.theme--catppuccin-mocha .content h5,html.theme--catppuccin-mocha .content h6{color:#cdd6f4;font-weight:600;line-height:1.125}html.theme--catppuccin-mocha .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-mocha .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-mocha .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-mocha .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-mocha .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-mocha .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-mocha .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-mocha .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-mocha .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-mocha .content blockquote{background-color:#181825;border-left:5px solid #585b70;padding:1.25em 1.5em}html.theme--catppuccin-mocha .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-mocha .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-mocha .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-mocha .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-mocha .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-mocha .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-mocha .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-mocha .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-mocha .content ul ul ul{list-style-type:square}html.theme--catppuccin-mocha .content dd{margin-left:2em}html.theme--catppuccin-mocha .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-mocha .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-mocha .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-mocha .content figure img{display:inline-block}html.theme--catppuccin-mocha .content figure figcaption{font-style:italic}html.theme--catppuccin-mocha .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-mocha .content sup,html.theme--catppuccin-mocha .content sub{font-size:75%}html.theme--catppuccin-mocha .content table{width:100%}html.theme--catppuccin-mocha .content table 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.content.is-normal{font-size:1rem}html.theme--catppuccin-mocha .content.is-medium{font-size:1.25rem}html.theme--catppuccin-mocha .content.is-large{font-size:1.5rem}html.theme--catppuccin-mocha .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-mocha .icon.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-mocha .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-mocha .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-mocha .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-mocha .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-mocha .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--catppuccin-mocha .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--catppuccin-mocha div.icon-text{display:flex}html.theme--catppuccin-mocha .image,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--catppuccin-mocha .image img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--catppuccin-mocha .image img.is-rounded,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--catppuccin-mocha .image.is-fullwidth,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--catppuccin-mocha .image.is-square img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--catppuccin-mocha .image.is-square .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--catppuccin-mocha .image.is-1by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar 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.has-ratio,html.theme--catppuccin-mocha .image.is-5by3 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--catppuccin-mocha .image.is-5by3 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--catppuccin-mocha .image.is-16by9 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--catppuccin-mocha .image.is-16by9 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--catppuccin-mocha .image.is-2by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--catppuccin-mocha .image.is-2by1 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--catppuccin-mocha .image.is-3by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--catppuccin-mocha 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img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--catppuccin-mocha .image.is-3by5 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--catppuccin-mocha .image.is-9by16 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--catppuccin-mocha .image.is-9by16 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-9by16 .has-ratio,html.theme--catppuccin-mocha .image.is-1by2 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by2 img,html.theme--catppuccin-mocha .image.is-1by2 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by2 .has-ratio,html.theme--catppuccin-mocha .image.is-1by3 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by3 img,html.theme--catppuccin-mocha .image.is-1by3 .has-ratio,html.theme--catppuccin-mocha 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html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fbefef;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#f8e6e5;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#f6dcda;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#5e6d6f;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 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.button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark 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pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark 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img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--documenter-dark .image img.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--documenter-dark .image.is-fullwidth,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--documenter-dark .image.is-5by4 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GitHub

Design principles

This project is inspired by two existing projects:

OMLT is a framework built around Pyomo, and gurobi-machinelearning is a framework build around gurobipy.

These projects served as inspiration, but we also departed from them in some carefully considered ways.

All of our design decisions were guided by two principles:

  1. To be simple
  2. To leverage Julia's Pkg extensions and multiple dispatch.

Terminology

Because the field is relatively new, there is no settled choice of terminology.

MathOptAI chooses to use "predictor" as the synonym for the machine learning model. Hence, we have AbstractPredictor, add_predictor, and build_predictor.

In contrast, gurob-machinelearning tends to use "regression model" and OMLT uses "formulation."

We choose "predictor" because all models we implement are of the form $y = f(x)$.

We do not use "machine learning model" because we have support for the linear and logistic regression models of classical statistical fitting. We could have used "regression model", but we find that models like neural networks and binary decision trees are not commonly thought of as regression models.

Inputs are vectors

MathOptAI assumes that all inputs $x$ and outputs $y$ to $y = predictor(x)$ are Base.Vectors.

We make this choice for simplicity.

In our opinion, Julia libraries often take a laissez-faire approach to the types that they support. In the optimistic case, this can lead to novel behavior by combining two packages that the package author had previously not considered or tested. In the pessimistic case, this can lead to incorrect results or cryptic error messagges.

Exceptions to the Vector rule will be carefully considered and tested.

Currently, there are two exceptions:

  1. If x is a Matrix, then the columns of x are interpreted as independent observations, and the output y will be a Matrix with the same number of columns
  2. The StatsModels extension allows x to be a DataFrames.DataFrame, if the predictor is a StatsModels.TableRegressionModel.

Exceptions 1 and 2 are combined in the StatsModels exception, so that the predictor is mapped over the rows of the DataFrames.DataFrame (which we assume will be a common use-case).

We choose to interpret the rows as input variables and columns as independent observations (rather than the more traditional table-based approach where columns are the input variables and rows are observations) because Julia uses column-major ordering in Matrix. Another justification follows from the Affine predictor, $f(x) = Ax + b$, where passing in a Matrix as x with column observations naturally leads to a Matrix output for y of the appropriate dimensions.

We choose to make y a Vector, even for scalar outputs, to simplify code that works generically for many different predictors. Without this principle, there will inevitably be cases where a scalar and length-1 vector are confused.

If you want to use a predictor that does not take Vector input (for example, it is an image as input to a neural network), the first preprocessing step should be to vec the input into a single Vector.

Inputs are provided, outputs are returned

The main job of MathOptAI is to embed models of the form y = predictor(x) into a JuMP model. A key design decision is how to represent the input x and output y.

gurobi-machinelearning

gurobi-machinelearning implements an API of the following general form:

pred_constr = add_predictor_constr(model, predictor, x, y)

Here, both the input x and the output y must be created and provided by the user, and a new object pred_constr is returned.

The benefit of this design is that pred_constr can contain statistics about the reformulation (for example, the number of variables that were added), and it can be used to delete a predictor from model.

The downside is that the user must ensure that the shape and size of y is correct.

OMLT

OMLT implements an API of the following general form:

model.pred_constr = OmltBlock()
+model.pred_constr.build_formulation(predictor)
+x, y = model.pred_constr.inputs, model.pred_constr.outputs

First, a new OmltBlock() is created. Then the formulation is built inside the block, and both the input and output are provided to the user.

The benefit of this design is that pred_constr can contain statistics about the reformulation (for example, the number of variables that were added), and it can be used to delete a predictor from model.

The downside is that the user must often write additional constraints to connect the input and output of the OmltBlock to their existing decision variables:

#connect pyomo model input and output to the neural network
+@model.Constraint()
+def connect_input(mdl):
+    return mdl.input == mdl.nn.inputs[0]
+
+@model.Constraint()
+def connect_output(mdl):
+    return mdl.output == mdl.nn.outputs[0]

A second downside is that the predictor must describe the input and output dimension; these cannot be inferred automatically. As one example, this means that it cannot do the following:

# Not possible because dimension not given
+model.pred_constr.build_formulation(ReLU())

In the context of MathOptAI, something like ReLU() is useful so that we can map generic layers like Flux.relu => MathOptAI.ReLU(), and so that we do not duplicate required dimension information in input and predictor (see the MathOptAI section below).

MathOptAI

The main entry-point to MathOptAI is add_predictor:

y, formulation = MathOptAI.add_predictor(model, predictor, x)

The user provides the input x, and the output y is returned.

The main benefit of this approach is simplicity.

First, the user probably already has the input x as decision variables or an expression in the model, so we do not need the connect_input constraint, and because we use a full-space formulation by default, the output y will always be a vector of decision variables, which avoids the need for a connect_output constraint.

Second, predictors do not need to store dimension information, so we can have:

y, formulation = MathOptAI.add_predictor(model, MathOptAI.ReLU(), x)

for any size of x.

Activations are predictors

OMLT makes a distinction between layers, like full_space_dense_layer, and elementwise activation functions, like sigmoid_activation_function.

The downside to this approach is that it treats activation functions as special, leading to issues such as OMLT#125.

In constrast, MathOptAI treats activation functions as a vector-valued predictor like any other:

y, formulation = MathOptAI.add_predictor(model, MathOptAI.ReLU(), x)

This means that we can pipeline them to create predictors such as:

function LogisticRegression(A)
+    return MathOptAI.Pipeline(MathOptAI.Affine(A), MathOptAI.Sigmoid())
+end

Controlling transformations

Many predictors have multiple ways that they can be formulated in an optimization model. For example, ReLU implements the non-smooth nonlinear formulation $y = \max\{x, 0\}$, while ReLUQuadratic implements a the complementarity formulation $x = y - slack; y, slack \ge 0; y * slack = 0$.

Choosing the appropriate formulation for the combination of model and solver can have a large impact on the performance.

Because gurobi-machinelearning is specific to the Gurobi solver, they have a limited ability for the user to choose and implement different formulations.

OMLT is more general, in that it has multiple ways of formulating layers such as ReLU. However, these are hard-coded into complete formulations such as omlt.neuralnet.nn_formulation.ReluBigMFormulation or omlt.neuralnet.nn_formulation.ReluComplementarityFormulation.

In contrast, MathOptAI tries to take a maximally modular approach, where the user can control how the layers are formulated at runtime, including using a custom formulation that is not defined in MathOptAI.jl.

Currently, we achive this with a config dictionary, which maps the various neural network layers to an AbstractPredictor. For example:

chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));
+config = Dict(Flux.relu => MathOptAI.ReLU())
+predictor = MathOptAI.build_predictor(chain; config)

Please open a GitHub issue if you have a suggestion for a better API.

Full-space or reduced-space

OMLT has two ways that it can formulate neural networks: full-space and reduced-space.

The full-space formulations add intermediate variables to represent the output of all layers.

For example, in a Flux.Dense(2, 3, Flux.relu) layer, a full-space formulation will add an intermediate y_tmp variable to represent the output of the affine layer prior to the ReLU:

layer = Flux.Dense(2, 3, Flux.relu)
+model_full_space = Model()
+@variable(model_full_space, x[1:2])
+@variable(model_full_space, y_tmp[1:3])
+@variable(model_full_space, y[1:3])
+@constraint(model_full_space, y_tmp == layer.A * x + layer.b)
+@constraint(model_full_space, y .== max.(0, y_tmp))

In contrast, a reduced-space formulation encodes the input-output relationship as a single nonlinear constraint:

layer = Flux.Dense(2, 3, Flux.relu)
+model_reduced_space = Model()
+@variable(model_reduced_space, x[1:2])
+@variable(model_reduced_space, y[1:3])
+@constraint(model_reduced_space, y .== max.(0, layer.A * x + layer.b))

In general, the full-space formulations have more variables and constraints but simpler nonlinear expressions, whereas the reduced-space formulations have fewer variables and constraints but more complicated nonlinear expressions.

MathOptAI.jl implements the full-space formulation by default, but some layers support the reduced-space formulation with the ReducedSpace wrapper.

diff --git a/v0.1.2/index.html b/v0.1.2/index.html new file mode 100644 index 00000000..b61fc0c0 --- /dev/null +++ b/v0.1.2/index.html @@ -0,0 +1,30 @@ + +MathOptAI.jl · MathOptAI.jl
GitHub

MathOptAI.jl

MathOptAI.jl is a JuMP extension for embedding trained AI, machine learning, and statistical learning models into a JuMP optimization model.

License

MathOptAI.jl is provided under a BSD-3 license as part of the Optimization and Machine Learning Toolbox project, O4806.

See LICENSE.md for details.

Despite the name similarity, this project is not affiliated with OMLT, the Optimization and Machine Learning Toolkit.

Installation

Install MathOptAI.jl using the Julia package manager:

import Pkg
+Pkg.add("MathOptAI")

Getting started

Here's an example of using MathOptAI to embed a trained neural network from Flux into a JuMP model. The vector of JuMP variables x is fed as input to the neural network. The output y is a vector of JuMP variables that represents the output layer of the neural network. The formulation object stores the additional variables and constraints that were added to model.

julia> using JuMP, MathOptAI, Flux
+
+julia> predictor = Flux.Chain(
+           Flux.Dense(28^2 => 32, Flux.sigmoid),
+           Flux.Dense(32 => 10),
+           Flux.softmax,
+       );
+
+julia> #= Train the Flux model. Code not shown for simplicity =#
+
+julia> model = JuMP.Model();
+
+julia> JuMP.@variable(model, 0 <= x[1:28^2] <= 1);
+
+julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
+
+julia> y
+10-element Vector{VariableRef}:
+ moai_SoftMax[1]
+ moai_SoftMax[2]
+ moai_SoftMax[3]
+ moai_SoftMax[4]
+ moai_SoftMax[5]
+ moai_SoftMax[6]
+ moai_SoftMax[7]
+ moai_SoftMax[8]
+ moai_SoftMax[9]
+ moai_SoftMax[10]

Getting help

This package is under active development. For help, questions, comments, and suggestions, please open a GitHub issue.

Inspiration

This project is mainly inspired by two existing projects:

Other works, from which we took less inspiration, include:

The 2024 paper of López-Flores et al. is an excellent summary of the state of the field at the time that we started development of MathOptAI.

López-Flores, F.J., Ramírez-Márquez, C., Ponce-Ortega J.M. (2024). Process Systems Engineering Tools for Optimization of Trained Machine Learning Models: Comparative and Perspective. Industrial & Engineering Chemistry Research, 63(32), 13966-13979. DOI: 10.1021/acs.iecr.4c00632

diff --git a/v0.1.2/manual/AbstractGPs/index.html b/v0.1.2/manual/AbstractGPs/index.html new file mode 100644 index 00000000..f4c361f2 --- /dev/null +++ b/v0.1.2/manual/AbstractGPs/index.html @@ -0,0 +1,26 @@ + +AbstractGPs · MathOptAI.jl
GitHub

AbstractGPs

AbstractGPs.jl is a library for fittinng Gaussian Processes in Julia.

Here is an example:

julia> using JuMP, MathOptAI, AbstractGPs
+
+julia> x_data = 2π .* (0.0:0.1:1.0);
+
+julia> y_data = sin.(x_data);
+
+julia> fx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.1);
+
+julia> p_fx = AbstractGPs.posterior(fx, y_data);
+
+julia> model = Model();
+
+julia> @variable(model, 1 <= x[1:1] <= 6, start = 3);
+
+julia> predictor = MathOptAI.Quantile(p_fx, [0.1, 0.9]);
+
+julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_quantile[1]
+ moai_quantile[2]
+
+julia> @objective(model, Max, y[2] - y[1])
+moai_quantile[2] - moai_quantile[1]
diff --git a/v0.1.2/manual/DecisionTree/index.html b/v0.1.2/manual/DecisionTree/index.html new file mode 100644 index 00000000..c6e01685 --- /dev/null +++ b/v0.1.2/manual/DecisionTree/index.html @@ -0,0 +1,27 @@ + +DecisionTree · MathOptAI.jl
GitHub

DecisionTree

DecisionTree.jl is a library for fitting decision trees in Julia.

Here is an example:

julia> using JuMP, MathOptAI, DecisionTree
+
+julia> truth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)
+truth (generic function with 1 method)
+
+julia> features = abs.(sin.((1:10) .* (3:4)'));
+
+julia> size(features)
+(10, 2)
+
+julia> labels = truth.(Vector.(eachrow(features)));
+
+julia> ml_model = DecisionTree.build_tree(labels, features)
+Decision Tree
+Leaves: 3
+Depth:  2
+
+julia> model = Model();
+
+julia> @variable(model, 0 <= x[1:2] <= 1);
+
+julia> y, formulation = MathOptAI.add_predictor(model, ml_model, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_BinaryDecisionTree_value
diff --git a/v0.1.2/manual/Flux/index.html b/v0.1.2/manual/Flux/index.html new file mode 100644 index 00000000..4f024c83 --- /dev/null +++ b/v0.1.2/manual/Flux/index.html @@ -0,0 +1,19 @@ + +Flux · MathOptAI.jl
GitHub

Flux

Flux.jl is a library for machine learning in Julia.

MathOptAI supports embedding Flux models in JuMP if they are a chain composed of:

  • Flux.Dense
  • Flux.softmax
  • Flux.relu
  • Flux.sigmoid
  • Flux.softplus
  • Flux.tanh

Here is an example:

julia> using JuMP, Flux, MathOptAI
+
+julia> chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));
+
+julia> model = Model();
+
+julia> @variable(model, x[1:1]);
+
+julia> y, formulation = MathOptAI.add_predictor(
+           model,
+           chain,
+           x;
+           config = Dict(Flux.relu => MathOptAI.ReLU()),
+       );
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Affine[1]
diff --git a/v0.1.2/manual/GLM/index.html b/v0.1.2/manual/GLM/index.html new file mode 100644 index 00000000..cd317b63 --- /dev/null +++ b/v0.1.2/manual/GLM/index.html @@ -0,0 +1,54 @@ + +GLM · MathOptAI.jl
GitHub

GLM

GLM.jl is a library for fitting generalized linear models in Julia.

MathOptAI.jl supports embedding two types of regression models from GLM:

  • GLM.lm(X, Y)
  • GLM.glm(X, Y, GLM.Bernoulli())

Linear regression

The input x to add_predictor must be a vector with the same number of elements as columns in the training matrix. The return is a vector of JuMP variables with a single element.

julia> using GLM, JuMP, MathOptAI
+
+julia> X, Y = rand(10, 2), rand(10);
+
+julia> model_glm = GLM.lm(X, Y);
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> y, formulation = MathOptAI.add_predictor(model, model_glm, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Affine[1]

Logistic regression

The input x to add_predictor must be a vector with the same number of elements as columns in the training matrix. The return is a vector of JuMP variables with a single element.

julia> using GLM, JuMP, MathOptAI
+
+julia> X, Y = rand(10, 2), rand(Bool, 10);
+
+julia> model_glm = GLM.glm(X, Y, GLM.Bernoulli());
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> y, formulation = MathOptAI.add_predictor(model, model_glm, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Sigmoid[1]

DataFrames

DataFrames.jl can be used with GLM.jl.

The input x to add_predictor must be a DataFrame with the same feature columns as the training DataFrame. The return is a vector of JuMP variables, with one element for each row in the DataFrame.

julia> using DataFrames, GLM, JuMP, MathOptAI
+
+julia> train_df = DataFrames.DataFrame(x1 = rand(10), x2 = rand(10));
+
+julia> train_df.y = 1.0 .* train_df.x1 + 2.0 .* train_df.x2 .+ rand(10);
+
+julia> predictor = GLM.lm(GLM.@formula(y ~ x1 + x2), train_df);
+
+julia> model = Model();
+
+julia> test_df = DataFrames.DataFrame(
+           x1 = rand(6),
+           x2 = @variable(model, [1:6]),
+       );
+
+julia> test_df.y, _ = MathOptAI.add_predictor(model, predictor, test_df);
+
+julia> test_df.y
+6-element Vector{VariableRef}:
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
diff --git a/v0.1.2/manual/Lux/index.html b/v0.1.2/manual/Lux/index.html new file mode 100644 index 00000000..8b4954eb --- /dev/null +++ b/v0.1.2/manual/Lux/index.html @@ -0,0 +1,30 @@ + +Lux · MathOptAI.jl
GitHub

Lux

Lux.jl is a library for machine learning in Julia.

MathOptAI supports embedding Lux models in JuMP if they are a chain composed of:

  • Lux.Dense
  • Lux.relu
  • Lux.sigmoid
  • Lux.softplus
  • Lux.tanh

Here is an example:

julia> using JuMP, Lux, MathOptAI, Random
+
+julia> rng = Random.MersenneTwister();
+
+julia> chain = Lux.Chain(Lux.Dense(1 => 16, Lux.relu), Lux.Dense(16 => 1))
+Chain(
+    layer_1 = Dense(1 => 16, relu),     # 32 parameters
+    layer_2 = Dense(16 => 1),           # 17 parameters
+)         # Total: 49 parameters,
+          #        plus 0 states.
+
+julia> parameters, state = Lux.setup(rng, chain);
+
+julia> predictor = (chain, parameters, state);
+
+julia> model = Model();
+
+julia> @variable(model, x[1:1]);
+
+julia> y, formulation = MathOptAI.add_predictor(
+           model,
+           predictor,
+           x;
+           config = Dict(Lux.relu => MathOptAI.ReLU()),
+       );
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Affine[1]
diff --git a/v0.1.2/manual/PyTorch/index.html b/v0.1.2/manual/PyTorch/index.html new file mode 100644 index 00000000..ab3f24a9 --- /dev/null +++ b/v0.1.2/manual/PyTorch/index.html @@ -0,0 +1,10 @@ + +PyTorch · MathOptAI.jl
GitHub

PyTorch

PyTorch is a library for machine learning in Python.

MathOptAI supports embedding PyTorch models in JuMP if they are composed of:

  • nn.Linear
  • nn.ReLU
  • nn.Sequential
  • nn.Sigmoid
  • nn.Tanh

Here is an example:

julia> using JuMP, MathOptAI
+
+julia> model = Model()
+
+julia> @variable(model, x[1:2]);
+
+julia> predictor = MathOptAI.PytorchModel("saved_pytorch_model.pt");
+
+julia> y, _ = MathOptAI.add_predictor(model, predictor, x);
diff --git a/v0.1.2/manual/predictors/index.html b/v0.1.2/manual/predictors/index.html new file mode 100644 index 00000000..1c6982ea --- /dev/null +++ b/v0.1.2/manual/predictors/index.html @@ -0,0 +1,2 @@ + +Predictors · MathOptAI.jl
GitHub

Predictors

The main entry point for embedding prediction models into JuMP is add_predictor.

All methods use the form y, formulation = MathOptAI.add_predictor(model, predictor, x) to add the relationship y = predictor(x) to model.

Supported predictors

The following predictors are supported. See their docstrings for details:

PredictorRelationshipDimensions
Affine$f(x) = Ax + b$$M \rightarrow N$
BinaryDecisionTreeA binary decision tree$M \rightarrow 1$
GrayBox$f(x)$$M \rightarrow N$
Pipeline$f(x) = (l_1 \circ \ldots \circ l_N)(x)$$M \rightarrow N$
QuantileThe quantiles of a distribution$M \rightarrow N$
ReLU$f(x) = \max.(0, x)$$M \rightarrow M$
ReLUBigM$f(x) = \max.(0, x)$$M \rightarrow M$
ReLUQuadratic$f(x) = \max.(0, x)$$M \rightarrow M$
ReLUSOS1$f(x) = \max.(0, x)$$M \rightarrow M$
Scale$f(x) = scale .* x .+ bias$$M \rightarrow M$
Sigmoid$f(x) = \frac{1}{1 + e^{-x}}$$M \rightarrow M$
SoftMax$f(x) = \frac{e^x}{\sum e^{x_i}}$$M \rightarrow M$
SoftPlus$f(x) = \frac{1}{\beta} \log(1 + e^{\beta x})$$M \rightarrow M$
Tanh$f(x) = \tanh.(x)$$M \rightarrow M$

Note that some predictors, such as the ReLU ones, offer multiple formulations of the same mathematical relationship. The ''right'' choice is solver- and problem-dependent.

ReLU

There are a number of different mathematical formulations for the rectified linear unit (ReLU).

  • ReLU: requires the solver to support the max nonlinear operator.
  • ReLUBigM: requires the solver to support mixed-integer linear programs, and requires the user to have a priori knowledge of a suitable value for the "big-M" parameter.
  • ReLUQuadratic: requires the solver to support quadratic equality constraints
  • ReLUSOS1: requires the solver to support SOS-I constraints.

The correct choice for which ReLU formulation to use is problem- and solver-dependent.

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literal 0 HcmV?d00001 diff --git a/v0.1.2/search_index.js b/v0.1.2/search_index.js new file mode 100644 index 00000000..9d38ead3 --- /dev/null +++ b/v0.1.2/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"manual/Flux/#Flux","page":"Flux","title":"Flux","text":"","category":"section"},{"location":"manual/Flux/","page":"Flux","title":"Flux","text":"Flux.jl is a library for machine learning in Julia.","category":"page"},{"location":"manual/Flux/","page":"Flux","title":"Flux","text":"MathOptAI supports embedding Flux models in JuMP if they are a chain composed of:","category":"page"},{"location":"manual/Flux/","page":"Flux","title":"Flux","text":"Flux.Dense\nFlux.softmax\nFlux.relu\nFlux.sigmoid\nFlux.softplus\nFlux.tanh","category":"page"},{"location":"manual/Flux/","page":"Flux","title":"Flux","text":"Here is an example:","category":"page"},{"location":"manual/Flux/","page":"Flux","title":"Flux","text":"julia> using JuMP, Flux, MathOptAI\n\njulia> chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));\n\njulia> model = Model();\n\njulia> @variable(model, x[1:1]);\n\njulia> y, formulation = MathOptAI.add_predictor(\n model,\n chain,\n x;\n config = Dict(Flux.relu => MathOptAI.ReLU()),\n );\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Affine[1]","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"EditURL = \"mnist.jl\"","category":"page"},{"location":"tutorials/mnist/#Adversarial-machine-learning-with-Flux.jl","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"","category":"section"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"The purpose of this tutorial is to explain how to embed a neural network model from Flux.jl into JuMP.","category":"page"},{"location":"tutorials/mnist/#Required-packages","page":"Adversarial machine learning with Flux.jl","title":"Required packages","text":"","category":"section"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"This tutorial requires the following packages","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"using JuMP\nimport Flux\nimport Ipopt\nimport MathOptAI\nimport MLDatasets\nimport Plots","category":"page"},{"location":"tutorials/mnist/#Data","page":"Adversarial machine learning with Flux.jl","title":"Data","text":"","category":"section"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"This tutorial uses images from the MNIST dataset.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"We load the predefined train and test splits:","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"train_data = MLDatasets.MNIST(; split = :train)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"test_data = MLDatasets.MNIST(; split = :test)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Since the data are images, it is helpful to plot them. (This requires a transpose and reversing the rows to get the orientation correct.)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"function plot_image(x::Matrix; kwargs...)\n return Plots.heatmap(\n x'[size(x, 1):-1:1, :];\n xlims = (1, size(x, 2)),\n ylims = (1, size(x, 1)),\n aspect_ratio = true,\n legend = false,\n xaxis = false,\n yaxis = false,\n kwargs...,\n )\nend\n\nfunction plot_image(instance::NamedTuple)\n return plot_image(instance.features; title = \"Label = $(instance.targets)\")\nend\n\nPlots.plot([plot_image(train_data[i]) for i in 1:6]...; layout = (2, 3))","category":"page"},{"location":"tutorials/mnist/#Training","page":"Adversarial machine learning with Flux.jl","title":"Training","text":"","category":"section"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"We use a simple neural network with one hidden layer and a sigmoid activation function. (There are better performing networks; try experimenting.)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"ml_model = Flux.Chain(\n Flux.Dense(28^2 => 32, Flux.sigmoid),\n Flux.Dense(32 => 10),\n Flux.softmax,\n)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Here is a function to load our data into the format that ml_model expects:","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"function data_loader(data; batchsize, shuffle = false)\n x = reshape(data.features, 28^2, :)\n y = Flux.onehotbatch(data.targets, 0:9)\n return Flux.DataLoader((x, y); batchsize, shuffle)\nend","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"and here is a function to score the percentage of correct labels, where we assign a label by choosing the label of the highest softmax in the final layer.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"function score_model(ml_model, data)\n x, y = only(data_loader(data; batchsize = length(data)))\n y_hat = ml_model(x)\n is_correct = Flux.onecold(y) .== Flux.onecold(y_hat)\n p = round(100 * sum(is_correct) / length(is_correct); digits = 2)\n println(\"Accuracy = $p %\")\n return\nend","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"The accuracy of our model is only around 10% before training:","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"score_model(ml_model, train_data)\nscore_model(ml_model, test_data)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Let's improve that by training our model.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"note: Note\nIt is not the purpose of this tutorial to explain how Flux works; see the documentation at https://fluxml.ai for more details. Changing the number of epochs or the learning rate can improve the loss.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"begin\n train_loader = data_loader(train_data; batchsize = 256, shuffle = true)\n optimizer_state = Flux.setup(Flux.Adam(3e-4), ml_model)\n for epoch in 1:30\n loss = 0.0\n for (x, y) in train_loader\n loss_batch, gradient = Flux.withgradient(ml_model) do model\n return Flux.crossentropy(model(x), y)\n end\n Flux.update!(optimizer_state, ml_model, only(gradient))\n loss += loss_batch\n end\n loss = round(loss / length(train_loader); digits = 4)\n print(\"Epoch $epoch: loss = $loss\\t\")\n score_model(ml_model, test_data)\n end\nend","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Here are the first eight predictions of the test data:","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"function plot_image(ml_model, x::Matrix)\n score, index = findmax(ml_model(vec(x)))\n title = \"Predicted: $(index - 1) ($(round(Int, 100 * score))%)\"\n return plot_image(x; title)\nend\n\nplots = [plot_image(ml_model, test_data[i].features) for i in 1:8]\nPlots.plot(plots...; size = (1200, 600), layout = (2, 4))","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"We can also look at the best and worst four predictions:","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"x, y = only(data_loader(test_data; batchsize = length(test_data)))\nlosses = Flux.crossentropy(ml_model(x), y; agg = identity)\nindices = sortperm(losses; dims = 2)[[1:4; end-3:end]]\nplots = [plot_image(ml_model, test_data[i].features) for i in indices]\nPlots.plot(plots...; size = (1200, 600), layout = (2, 4))","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"There are still some fairly bad mistakes. Can you change the model or training parameters improve to improve things?","category":"page"},{"location":"tutorials/mnist/#JuMP","page":"Adversarial machine learning with Flux.jl","title":"JuMP","text":"","category":"section"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Now that we have a trained machine learning model, we can embed it in a JuMP model.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Here's a function which takes a test case and returns an example that maximizes the probability of the adversarial example.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"function find_adversarial_image(test_case; adversary_label, δ = 0.05)\n model = Model(Ipopt.Optimizer)\n set_silent(model)\n @variable(model, 0 <= x[1:28, 1:28] <= 1)\n @constraint(model, -δ .<= x .- test_case.features .<= δ)\n # Note: we need to use `vec` here because `x` is a 28-by-28 Matrix, but our\n # neural network expects a 28^2 length vector.\n y, _ = MathOptAI.add_predictor(model, ml_model, vec(x))\n @objective(model, Max, y[adversary_label+1] - y[test_case.targets+1])\n optimize!(model)\n @assert is_solved_and_feasible(model)\n return value.(x)\nend","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Let's try finding an adversarial example to the third test image. The image on the left is our input image. The network thinks this is a 1 with probability 99%. The image on the right is the adversarial image. The network thinks this is a 7, although it is less confident.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"x_adversary = find_adversarial_image(test_data[3]; adversary_label = 7);\nPlots.plot(\n plot_image(ml_model, test_data[3].features),\n plot_image(ml_model, Float32.(x_adversary)),\n)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"This page was generated using Literate.jl.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"EditURL = \"student_enrollment.jl\"","category":"page"},{"location":"tutorials/student_enrollment/#Logistic-regression-with-GLM.jl","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"","category":"section"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The purpose of this tutorial is to explain how to embed a logistic regression model from GLM.jl into JuMP.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The data and example in this tutorial comes from the paper: David Bergman, Teng Huang, Philip Brooks, Andrea Lodi, Arvind U. Raghunathan (2021) JANOS: An Integrated Predictive and Prescriptive Modeling Framework. INFORMS Journal on Computing 34(2):807-816. https://doi.org/10.1287/ijoc.2020.1023","category":"page"},{"location":"tutorials/student_enrollment/#Required-packages","page":"Logistic regression with GLM.jl","title":"Required packages","text":"","category":"section"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"This tutorial uses the following packages.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"using JuMP\nimport CSV\nimport DataFrames\nimport Downloads\nimport GLM\nimport Ipopt\nimport MathOptAI\nimport Statistics","category":"page"},{"location":"tutorials/student_enrollment/#Data","page":"Logistic regression with GLM.jl","title":"Data","text":"","category":"section"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Here is a function to load the data directly from the JANOS repository:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"function read_df(filename)\n url = \"https://raw.githubusercontent.com/INFORMSJoC/2020.1023/master/data/\"\n data = Downloads.download(url * filename)\n return CSV.read(data, DataFrames.DataFrame)\nend","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"There are two important files. The first, college_student_enroll-s1-1.csv, contains historial admissions data on anonymized students, their SAT score, their GPA, their merit scholarships, and whether the enrolled in the college.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"train_df = read_df(\"college_student_enroll-s1-1.csv\")","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The second, college_applications6000.csv, contains the SAT and GPA data of students who are currently applying:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"evaluate_df = read_df(\"college_applications6000.csv\")","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"There are 6,000 prospective students:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"n_students = size(evaluate_df, 1)","category":"page"},{"location":"tutorials/student_enrollment/#Prediction-model","page":"Logistic regression with GLM.jl","title":"Prediction model","text":"","category":"section"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The first step is to train a logistic regression model to predict the Boolean enroll column based on the SAT, GPA, and merit columns.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"model_glm = GLM.glm(\n GLM.@formula(enroll ~ 0 + SAT + GPA + merit),\n train_df,\n GLM.Bernoulli(),\n)","category":"page"},{"location":"tutorials/student_enrollment/#Decision-model","page":"Logistic regression with GLM.jl","title":"Decision model","text":"","category":"section"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Now that we have a trained logistic regression model, we want a decision model that chooses the optimal merit scholarship for each student in","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"evaluate_df","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Here's an empty JuMP model to start:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"model = Model()","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"First, we add a new columnn to evaluate_df, with one JuMP decision variable for each row. It is important the the .merit column name in evaluate_df matches the name in train_df.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"evaluate_df.merit = @variable(model, 0 <= x_merit[1:n_students] <= 2.5);\nevaluate_df","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Then, we use MathOptAI.add_predictor to embed model_glm into the JuMP model. MathOptAI.add_predictor returns a vector of variables, one for each row inn evaluate_df, corresponding to the output enroll of our logistic regression.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"evaluate_df.enroll, _ = MathOptAI.add_predictor(model, model_glm, evaluate_df);\nevaluate_df","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The .enroll column name in evaluate_df is just a name. It doesn't have to match the name in train_df.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The objective of our problem is to maximize the expected number of students who enroll:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"@objective(model, Max, sum(evaluate_df.enroll))","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Subject to the constraint that we can spend at most 0.2 * n_students on merit scholarships:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"@constraint(model, sum(evaluate_df.merit) <= 0.2 * n_students)","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Because logistic regression involves a Sigmoid layer, we need to use a smooth nonlinear optimizer. A common choice is Ipopt. Solve and check the optimizer found a feasible solution:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"set_optimizer(model, Ipopt.Optimizer)\nset_silent(model)\noptimize!(model)\n@assert is_solved_and_feasible(model)\nsolution_summary(model)","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Let's store the solution in evaluate_df for analysis:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"evaluate_df.merit_sol = value.(evaluate_df.merit);\nevaluate_df.enroll_sol = value.(evaluate_df.enroll);\nevaluate_df","category":"page"},{"location":"tutorials/student_enrollment/#Solution-analysis","page":"Logistic regression with GLM.jl","title":"Solution analysis","text":"","category":"section"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"We expect that just under 2,500 students will enroll:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"sum(evaluate_df.enroll_sol)","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"We awarded merit scholarships to approximately 1 in 6 students:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"count(evaluate_df.merit_sol .> 1e-5)","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The average merit scholarship was worth just over $1,000:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"1_000 * Statistics.mean(evaluate_df.merit_sol[evaluate_df.merit_sol.>1e-5])","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"This page was generated using Literate.jl.","category":"page"},{"location":"manual/GLM/#GLM","page":"GLM","title":"GLM","text":"","category":"section"},{"location":"manual/GLM/","page":"GLM","title":"GLM","text":"GLM.jl is a library for fitting generalized linear models in Julia.","category":"page"},{"location":"manual/GLM/","page":"GLM","title":"GLM","text":"MathOptAI.jl supports embedding two types of regression models from GLM:","category":"page"},{"location":"manual/GLM/","page":"GLM","title":"GLM","text":"GLM.lm(X, Y)\nGLM.glm(X, Y, GLM.Bernoulli())","category":"page"},{"location":"manual/GLM/#Linear-regression","page":"GLM","title":"Linear regression","text":"","category":"section"},{"location":"manual/GLM/","page":"GLM","title":"GLM","text":"The input x to add_predictor must be a vector with the same number of elements as columns in the training matrix. The return is a vector of JuMP variables with a single element.","category":"page"},{"location":"manual/GLM/","page":"GLM","title":"GLM","text":"julia> using GLM, JuMP, MathOptAI\n\njulia> X, Y = rand(10, 2), rand(10);\n\njulia> model_glm = GLM.lm(X, Y);\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> y, formulation = MathOptAI.add_predictor(model, model_glm, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Affine[1]","category":"page"},{"location":"manual/GLM/#Logistic-regression","page":"GLM","title":"Logistic regression","text":"","category":"section"},{"location":"manual/GLM/","page":"GLM","title":"GLM","text":"The input x to add_predictor must be a vector with the same number of elements as columns in the training matrix. The return is a vector of JuMP variables with a single element.","category":"page"},{"location":"manual/GLM/","page":"GLM","title":"GLM","text":"julia> using GLM, JuMP, MathOptAI\n\njulia> X, Y = rand(10, 2), rand(Bool, 10);\n\njulia> model_glm = GLM.glm(X, Y, GLM.Bernoulli());\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> y, formulation = MathOptAI.add_predictor(model, model_glm, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Sigmoid[1]","category":"page"},{"location":"manual/GLM/#DataFrames","page":"GLM","title":"DataFrames","text":"","category":"section"},{"location":"manual/GLM/","page":"GLM","title":"GLM","text":"DataFrames.jl can be used with GLM.jl.","category":"page"},{"location":"manual/GLM/","page":"GLM","title":"GLM","text":"The input x to add_predictor must be a DataFrame with the same feature columns as the training DataFrame. The return is a vector of JuMP variables, with one element for each row in the DataFrame.","category":"page"},{"location":"manual/GLM/","page":"GLM","title":"GLM","text":"julia> using DataFrames, GLM, JuMP, MathOptAI\n\njulia> train_df = DataFrames.DataFrame(x1 = rand(10), x2 = rand(10));\n\njulia> train_df.y = 1.0 .* train_df.x1 + 2.0 .* train_df.x2 .+ rand(10);\n\njulia> predictor = GLM.lm(GLM.@formula(y ~ x1 + x2), train_df);\n\njulia> model = Model();\n\njulia> test_df = DataFrames.DataFrame(\n x1 = rand(6),\n x2 = @variable(model, [1:6]),\n );\n\njulia> test_df.y, _ = MathOptAI.add_predictor(model, predictor, test_df);\n\njulia> test_df.y\n6-element Vector{VariableRef}:\n moai_Affine[1]\n moai_Affine[1]\n moai_Affine[1]\n moai_Affine[1]\n moai_Affine[1]\n moai_Affine[1]","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"CurrentModule = MathOptAI","category":"page"},{"location":"developers/design_principles/#Design-principles","page":"Design principles","title":"Design principles","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"This project is inspired by two existing projects:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"OMLT\ngurobi-machinelearning","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"OMLT is a framework built around Pyomo, and gurobi-machinelearning is a framework build around gurobipy.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"These projects served as inspiration, but we also departed from them in some carefully considered ways.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"All of our design decisions were guided by two principles:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"To be simple\nTo leverage Julia's Pkg extensions and multiple dispatch.","category":"page"},{"location":"developers/design_principles/#Terminology","page":"Design principles","title":"Terminology","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Because the field is relatively new, there is no settled choice of terminology.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"MathOptAI chooses to use \"predictor\" as the synonym for the machine learning model. Hence, we have AbstractPredictor, add_predictor, and build_predictor.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In contrast, gurob-machinelearning tends to use \"regression model\" and OMLT uses \"formulation.\"","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"We choose \"predictor\" because all models we implement are of the form y = f(x).","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"We do not use \"machine learning model\" because we have support for the linear and logistic regression models of classical statistical fitting. We could have used \"regression model\", but we find that models like neural networks and binary decision trees are not commonly thought of as regression models.","category":"page"},{"location":"developers/design_principles/#Inputs-are-vectors","page":"Design principles","title":"Inputs are vectors","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"MathOptAI assumes that all inputs x and outputs y to y = predictor(x) are Base.Vectors.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"We make this choice for simplicity.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In our opinion, Julia libraries often take a laissez-faire approach to the types that they support. In the optimistic case, this can lead to novel behavior by combining two packages that the package author had previously not considered or tested. In the pessimistic case, this can lead to incorrect results or cryptic error messagges.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Exceptions to the Vector rule will be carefully considered and tested.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Currently, there are two exceptions:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"If x is a Matrix, then the columns of x are interpreted as independent observations, and the output y will be a Matrix with the same number of columns\nThe StatsModels extension allows x to be a DataFrames.DataFrame, if the predictor is a StatsModels.TableRegressionModel.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Exceptions 1 and 2 are combined in the StatsModels exception, so that the predictor is mapped over the rows of the DataFrames.DataFrame (which we assume will be a common use-case).","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"We choose to interpret the rows as input variables and columns as independent observations (rather than the more traditional table-based approach where columns are the input variables and rows are observations) because Julia uses column-major ordering in Matrix. Another justification follows from the Affine predictor, f(x) = Ax + b, where passing in a Matrix as x with column observations naturally leads to a Matrix output for y of the appropriate dimensions.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"We choose to make y a Vector, even for scalar outputs, to simplify code that works generically for many different predictors. Without this principle, there will inevitably be cases where a scalar and length-1 vector are confused.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"If you want to use a predictor that does not take Vector input (for example, it is an image as input to a neural network), the first preprocessing step should be to vec the input into a single Vector.","category":"page"},{"location":"developers/design_principles/#Inputs-are-provided,-outputs-are-returned","page":"Design principles","title":"Inputs are provided, outputs are returned","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The main job of MathOptAI is to embed models of the form y = predictor(x) into a JuMP model. A key design decision is how to represent the input x and output y.","category":"page"},{"location":"developers/design_principles/#gurobi-machinelearning","page":"Design principles","title":"gurobi-machinelearning","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"gurobi-machinelearning implements an API of the following general form:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"pred_constr = add_predictor_constr(model, predictor, x, y)","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Here, both the input x and the output y must be created and provided by the user, and a new object pred_constr is returned.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The benefit of this design is that pred_constr can contain statistics about the reformulation (for example, the number of variables that were added), and it can be used to delete a predictor from model.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The downside is that the user must ensure that the shape and size of y is correct.","category":"page"},{"location":"developers/design_principles/#OMLT","page":"Design principles","title":"OMLT","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"OMLT implements an API of the following general form:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"model.pred_constr = OmltBlock()\nmodel.pred_constr.build_formulation(predictor)\nx, y = model.pred_constr.inputs, model.pred_constr.outputs","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"First, a new OmltBlock() is created. Then the formulation is built inside the block, and both the input and output are provided to the user.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The benefit of this design is that pred_constr can contain statistics about the reformulation (for example, the number of variables that were added), and it can be used to delete a predictor from model.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The downside is that the user must often write additional constraints to connect the input and output of the OmltBlock to their existing decision variables:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"#connect pyomo model input and output to the neural network\n@model.Constraint()\ndef connect_input(mdl):\n return mdl.input == mdl.nn.inputs[0]\n\n@model.Constraint()\ndef connect_output(mdl):\n return mdl.output == mdl.nn.outputs[0]","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"A second downside is that the predictor must describe the input and output dimension; these cannot be inferred automatically. As one example, this means that it cannot do the following:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"# Not possible because dimension not given\nmodel.pred_constr.build_formulation(ReLU())","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In the context of MathOptAI, something like ReLU() is useful so that we can map generic layers like Flux.relu => MathOptAI.ReLU(), and so that we do not duplicate required dimension information in input and predictor (see the MathOptAI section below).","category":"page"},{"location":"developers/design_principles/#MathOptAI","page":"Design principles","title":"MathOptAI","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The main entry-point to MathOptAI is add_predictor:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"y, formulation = MathOptAI.add_predictor(model, predictor, x)","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The user provides the input x, and the output y is returned.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The main benefit of this approach is simplicity.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"First, the user probably already has the input x as decision variables or an expression in the model, so we do not need the connect_input constraint, and because we use a full-space formulation by default, the output y will always be a vector of decision variables, which avoids the need for a connect_output constraint.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Second, predictors do not need to store dimension information, so we can have:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"y, formulation = MathOptAI.add_predictor(model, MathOptAI.ReLU(), x)","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"for any size of x.","category":"page"},{"location":"developers/design_principles/#Activations-are-predictors","page":"Design principles","title":"Activations are predictors","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"OMLT makes a distinction between layers, like full_space_dense_layer, and elementwise activation functions, like sigmoid_activation_function.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The downside to this approach is that it treats activation functions as special, leading to issues such as OMLT#125.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In constrast, MathOptAI treats activation functions as a vector-valued predictor like any other:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"y, formulation = MathOptAI.add_predictor(model, MathOptAI.ReLU(), x)","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"This means that we can pipeline them to create predictors such as:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"function LogisticRegression(A)\n return MathOptAI.Pipeline(MathOptAI.Affine(A), MathOptAI.Sigmoid())\nend","category":"page"},{"location":"developers/design_principles/#Controlling-transformations","page":"Design principles","title":"Controlling transformations","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Many predictors have multiple ways that they can be formulated in an optimization model. For example, ReLU implements the non-smooth nonlinear formulation y = maxx 0, while ReLUQuadratic implements a the complementarity formulation x = y - slack y slack ge 0 y * slack = 0.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Choosing the appropriate formulation for the combination of model and solver can have a large impact on the performance.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Because gurobi-machinelearning is specific to the Gurobi solver, they have a limited ability for the user to choose and implement different formulations.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"OMLT is more general, in that it has multiple ways of formulating layers such as ReLU. However, these are hard-coded into complete formulations such as omlt.neuralnet.nn_formulation.ReluBigMFormulation or omlt.neuralnet.nn_formulation.ReluComplementarityFormulation.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In contrast, MathOptAI tries to take a maximally modular approach, where the user can control how the layers are formulated at runtime, including using a custom formulation that is not defined in MathOptAI.jl.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Currently, we achive this with a config dictionary, which maps the various neural network layers to an AbstractPredictor. For example:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));\nconfig = Dict(Flux.relu => MathOptAI.ReLU())\npredictor = MathOptAI.build_predictor(chain; config)","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Please open a GitHub issue if you have a suggestion for a better API.","category":"page"},{"location":"developers/design_principles/#Full-space-or-reduced-space","page":"Design principles","title":"Full-space or reduced-space","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"OMLT has two ways that it can formulate neural networks: full-space and reduced-space.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The full-space formulations add intermediate variables to represent the output of all layers.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"For example, in a Flux.Dense(2, 3, Flux.relu) layer, a full-space formulation will add an intermediate y_tmp variable to represent the output of the affine layer prior to the ReLU:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"layer = Flux.Dense(2, 3, Flux.relu)\nmodel_full_space = Model()\n@variable(model_full_space, x[1:2])\n@variable(model_full_space, y_tmp[1:3])\n@variable(model_full_space, y[1:3])\n@constraint(model_full_space, y_tmp == layer.A * x + layer.b)\n@constraint(model_full_space, y .== max.(0, y_tmp))","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In contrast, a reduced-space formulation encodes the input-output relationship as a single nonlinear constraint:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"layer = Flux.Dense(2, 3, Flux.relu)\nmodel_reduced_space = Model()\n@variable(model_reduced_space, x[1:2])\n@variable(model_reduced_space, y[1:3])\n@constraint(model_reduced_space, y .== max.(0, layer.A * x + layer.b))","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In general, the full-space formulations have more variables and constraints but simpler nonlinear expressions, whereas the reduced-space formulations have fewer variables and constraints but more complicated nonlinear expressions.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"MathOptAI.jl implements the full-space formulation by default, but some layers support the reduced-space formulation with the ReducedSpace wrapper.","category":"page"},{"location":"manual/DecisionTree/#DecisionTree","page":"DecisionTree","title":"DecisionTree","text":"","category":"section"},{"location":"manual/DecisionTree/","page":"DecisionTree","title":"DecisionTree","text":"DecisionTree.jl is a library for fitting decision trees in Julia.","category":"page"},{"location":"manual/DecisionTree/","page":"DecisionTree","title":"DecisionTree","text":"Here is an example:","category":"page"},{"location":"manual/DecisionTree/","page":"DecisionTree","title":"DecisionTree","text":"julia> using JuMP, MathOptAI, DecisionTree\n\njulia> truth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)\ntruth (generic function with 1 method)\n\njulia> features = abs.(sin.((1:10) .* (3:4)'));\n\njulia> size(features)\n(10, 2)\n\njulia> labels = truth.(Vector.(eachrow(features)));\n\njulia> ml_model = DecisionTree.build_tree(labels, features)\nDecision Tree\nLeaves: 3\nDepth: 2\n\njulia> model = Model();\n\njulia> @variable(model, 0 <= x[1:2] <= 1);\n\njulia> y, formulation = MathOptAI.add_predictor(model, ml_model, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_BinaryDecisionTree_value","category":"page"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"CurrentModule = MathOptAI","category":"page"},{"location":"manual/predictors/#Predictors","page":"Predictors","title":"Predictors","text":"","category":"section"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"The main entry point for embedding prediction models into JuMP is add_predictor.","category":"page"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"All methods use the form y, formulation = MathOptAI.add_predictor(model, predictor, x) to add the relationship y = predictor(x) to model.","category":"page"},{"location":"manual/predictors/#Supported-predictors","page":"Predictors","title":"Supported predictors","text":"","category":"section"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"The following predictors are supported. See their docstrings for details:","category":"page"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"Predictor Relationship Dimensions\nAffine f(x) = Ax + b M rightarrow N\nBinaryDecisionTree A binary decision tree M rightarrow 1\nGrayBox f(x) M rightarrow N\nPipeline f(x) = (l_1 circ ldots circ l_N)(x) M rightarrow N\nQuantile The quantiles of a distribution M rightarrow N\nReLU f(x) = max(0 x) M rightarrow M\nReLUBigM f(x) = max(0 x) M rightarrow M\nReLUQuadratic f(x) = max(0 x) M rightarrow M\nReLUSOS1 f(x) = max(0 x) M rightarrow M\nScale f(x) = scale * x + bias M rightarrow M\nSigmoid f(x) = frac11 + e^-x M rightarrow M\nSoftMax f(x) = frace^xsum e^x_i M rightarrow M\nSoftPlus f(x) = frac1beta log(1 + e^beta x) M rightarrow M\nTanh f(x) = tanh(x) M rightarrow M","category":"page"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"Note that some predictors, such as the ReLU ones, offer multiple formulations of the same mathematical relationship. The ''right'' choice is solver- and problem-dependent.","category":"page"},{"location":"manual/predictors/#ReLU","page":"Predictors","title":"ReLU","text":"","category":"section"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"There are a number of different mathematical formulations for the rectified linear unit (ReLU).","category":"page"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"ReLU: requires the solver to support the max nonlinear operator.\nReLUBigM: requires the solver to support mixed-integer linear programs, and requires the user to have a priori knowledge of a suitable value for the \"big-M\" parameter.\nReLUQuadratic: requires the solver to support quadratic equality constraints\nReLUSOS1: requires the solver to support SOS-I constraints.","category":"page"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"The correct choice for which ReLU formulation to use is problem- and solver-dependent.","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"CurrentModule = MathOptAI","category":"page"},{"location":"api/#API-Reference","page":"API Reference","title":"API Reference","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"This page lists the public API of MathOptAI.","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"info: Info\nThis page is an unstructured list of the MathOptAI API. For a more structured overview, read the Manual or Tutorial parts of this documentation.","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Load all of the public the API into the current scope with:","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"using MathOptAI","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Alternatively, load only the module with:","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"import MathOptAI","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"and then prefix all calls with MathOptAI. to create MathOptAI..","category":"page"},{"location":"api/#AbstractPredictor","page":"API Reference","title":"AbstractPredictor","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"AbstractPredictor","category":"page"},{"location":"api/#MathOptAI.AbstractPredictor","page":"API Reference","title":"MathOptAI.AbstractPredictor","text":"abstract type AbstractPredictor end\n\nAn abstract type representing different types of prediction models.\n\nMethods\n\nAll subtypes must implement:\n\nadd_predictor\n\n\n\n\n\n","category":"type"},{"location":"api/#add_predictor","page":"API Reference","title":"add_predictor","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"add_predictor","category":"page"},{"location":"api/#MathOptAI.add_predictor","page":"API Reference","title":"MathOptAI.add_predictor","text":"add_predictor(\n model::JuMP.AbstractModel,\n predictor::AbstractPredictor,\n x::Vector,\n)::Vector\n\nReturn a Vector representing y such that y = predictor(x).\n\nThe element type of x is deliberately unspecified. The vector x may contain any mix of scalar constants, JuMP decision variables, and scalar JuMP functions like AffExpr, QuadExpr, or NonlinearExpr.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.Affine([2.0, 3.0])\nAffine(A, b) [input: 2, output: 1]\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Affine[1]\n\njulia> formulation\nAffine(A, b) [input: 2, output: 1]\n├ variables [1]\n│ └ moai_Affine[1]\n└ constraints [1]\n └ 2 x[1] + 3 x[2] - moai_Affine[1] = 0\n\n\n\n\n\n","category":"function"},{"location":"api/#build_predictor","page":"API Reference","title":"build_predictor","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"build_predictor","category":"page"},{"location":"api/#MathOptAI.build_predictor","page":"API Reference","title":"MathOptAI.build_predictor","text":"MathOptAI.build_predictor(predictor::DecisionTree.Root)\n\nConvert a binary decision tree from DecisionTree.jl to a BinaryDecisionTree.\n\nExample\n\njulia> using MathOptAI, DecisionTree\n\njulia> truth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)\ntruth (generic function with 1 method)\n\njulia> features = abs.(sin.((1:10) .* (3:4)'));\n\njulia> size(features)\n(10, 2)\n\njulia> labels = truth.(Vector.(eachrow(features)));\n\njulia> ml_model = DecisionTree.build_tree(labels, features)\nDecision Tree\nLeaves: 3\nDepth: 2\n\njulia> MathOptAI.build_predictor(ml_model)\nBinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]\n\n\n\n\n\nbuild_predictor(extension; kwargs...)::AbstractPredictor\n\nA uniform interface to convert various extension types to an AbstractPredictor.\n\nSee the various extension docstrings for details.\n\n\n\n\n\nMathOptAI.build_predictor(\n predictor::Tuple{<:Lux.Chain,<:NamedTuple,<:NamedTuple};\n config::Dict = Dict{Any,Any}(),\n)\n\nConvert a trained neural network from Lux.jl to a Pipeline.\n\nSupported layers\n\nLux.Dense\nLux.Scale\n\nSupported activation functions\n\nLux.relu\nLux.sigmoid\nLux.softplus\nLux.softmax\nLux.tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps supported Lux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Lux.sigmoid => MathOptAI.Sigmoid() or Lux.relu => MathOptAI.QuadraticReLU().\n\nExample\n\njulia> using Lux, MathOptAI, Random\n\njulia> rng = Random.MersenneTwister();\n\njulia> chain = Lux.Chain(Lux.Dense(1 => 16, Lux.relu), Lux.Dense(16 => 1))\nChain(\n layer_1 = Dense(1 => 16, relu), # 32 parameters\n layer_2 = Dense(16 => 1), # 17 parameters\n) # Total: 49 parameters,\n # plus 0 states.\n\njulia> parameters, state = Lux.setup(rng, chain);\n\njulia> predictor = MathOptAI.build_predictor(\n (chain, parameters, state);\n config = Dict(Lux.relu => MathOptAI.ReLU()),\n )\nPipeline with layers:\n * Affine(A, b) [input: 1, output: 16]\n * ReLU()\n * Affine(A, b) [input: 16, output: 1]\n\njulia> MathOptAI.build_predictor(\n (chain, parameters, state);\n config = Dict(Lux.relu => MathOptAI.ReLUQuadratic()),\n )\nPipeline with layers:\n * Affine(A, b) [input: 1, output: 16]\n * ReLUQuadratic()\n * Affine(A, b) [input: 16, output: 1]\n\n\n\n\n\nMathOptAI.build_predictor(predictor::GLM.LinearModel)\n\nConvert a trained linear model from GLM.jl to an Affine layer.\n\nExample\n\njulia> using GLM, MathOptAI\n\njulia> X, Y = rand(10, 2), rand(10);\n\njulia> model_glm = GLM.lm(X, Y);\n\njulia> MathOptAI.build_predictor(model_glm)\nAffine(A, b) [input: 2, output: 1]\n\n\n\n\n\nMathOptAI.build_predictor(\n predictor::GLM.GeneralizedLinearModel{\n GLM.GlmResp{Vector{Float64},GLM.Bernoulli{Float64},GLM.LogitLink},\n };\n sigmoid::MathOptAI.AbstractPredictor = MathOptAI.Sigmoid(),\n)\n\nConvert a trained logistic model from GLM.jl to a Pipeline layer.\n\nKeyword arguments\n\nsigmoid: the predictor to use for the sigmoid layer.\n\nExample\n\njulia> using GLM, MathOptAI\n\njulia> X, Y = rand(10, 2), rand(Bool, 10);\n\njulia> model_glm = GLM.glm(X, Y, GLM.Bernoulli());\n\njulia> MathOptAI.build_predictor(model_glm)\nPipeline with layers:\n * Affine(A, b) [input: 2, output: 1]\n * Sigmoid()\n\n\n\n\n\nMathOptAI.build_predictor(\n predictor::MathOptAI.PytorchModel;\n config::Dict = Dict{Any,Any}(),\n gray_box::Bool = false,\n gray_box_hessian::Bool = false,\n)\n\nConvert a trained neural network from PyTorch via PythonCall.jl to a Pipeline.\n\nSupported layers\n\nnn.Linear\nnn.ReLU\nnn.Sequential\nnn.Sigmoid\nnn.Softplus\nnn.Tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps Symbols to AbstractPredictors that control how the activation functions are reformulated. For example, :Sigmoid => MathOptAI.Sigmoid() or :ReLU => MathOptAI.QuadraticReLU(). The supported Symbols are :ReLU, :Sigmoid, :SoftPlus, and :Tanh.\ngray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by torch.func.jacrev.\ngray_box_hessian: if true, the gray box additionally computes the Hessian of the output using torch.func.hessian.\n\n\n\n\n\nMathOptAI.build_predictor(\n predictor::Flux.Chain;\n config::Dict = Dict{Any,Any}(),\n gray_box::Bool = false,\n gray_box_hessian::Bool = false,\n)\n\nConvert a trained neural network from Flux.jl to a Pipeline.\n\nSupported layers\n\nFlux.Dense\nFlux.Scale\nFlux.softmax\n\nSupported activation functions\n\nFlux.relu\nFlux.sigmoid\nFlux.softplus\nFlux.tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps supported Flux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Flux.sigmoid => MathOptAI.Sigmoid() or Flux.relu => MathOptAI.QuadraticReLU().\ngray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by Flux.withjacobian.\ngray_box_hessian: if true, the gray box additionally computes the Hessian of the output using Flux.hessian.\n\nExample\n\njulia> using Flux, MathOptAI\n\njulia> chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));\n\njulia> MathOptAI.build_predictor(\n chain;\n config = Dict(Flux.relu => MathOptAI.ReLU()),\n )\nPipeline with layers:\n * Affine(A, b) [input: 1, output: 16]\n * ReLU()\n * Affine(A, b) [input: 16, output: 1]\n\njulia> MathOptAI.build_predictor(\n chain;\n config = Dict(Flux.relu => MathOptAI.ReLUQuadratic()),\n )\nPipeline with layers:\n * Affine(A, b) [input: 1, output: 16]\n * ReLUQuadratic()\n * Affine(A, b) [input: 16, output: 1]\n\n\n\n\n\n","category":"function"},{"location":"api/#Affine","page":"API Reference","title":"Affine","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Affine","category":"page"},{"location":"api/#MathOptAI.Affine","page":"API Reference","title":"MathOptAI.Affine","text":"Affine(\n A::Matrix{T},\n b::Vector{T} = zeros(T, size(A, 1)),\n) where {T} <: AbstractPredictor\n\nAn AbstractPredictor that represents the affine relationship:\n\nf(x) = A x + b\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.Affine([2.0 3.0], [4.0])\nAffine(A, b) [input: 2, output: 1]\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Affine[1]\n\njulia> formulation\nAffine(A, b) [input: 2, output: 1]\n├ variables [1]\n│ └ moai_Affine[1]\n└ constraints [1]\n └ 2 x[1] + 3 x[2] - moai_Affine[1] = -4\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n1-element Vector{AffExpr}:\n 2 x[1] + 3 x[2] + 4\n\njulia> formulation\nReducedSpace(Affine(A, b) [input: 2, output: 1])\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#BinaryDecisionTree","page":"API Reference","title":"BinaryDecisionTree","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"BinaryDecisionTree","category":"page"},{"location":"api/#MathOptAI.BinaryDecisionTree","page":"API Reference","title":"MathOptAI.BinaryDecisionTree","text":"BinaryDecisionTree{K,V}(\n feat_id::Int,\n feat_value::K,\n lhs::Union{V,BinaryDecisionTree{K,V}},\n rhs::Union{V,BinaryDecisionTree{K,V}},\n)\n\nAn AbstractPredictor that represents a binary decision tree.\n\nIf x[feat_id] <= feat_value, then return lhs\nIf x[feat_id] > feat_value, then return rhs\n\nExample\n\nTo represent the tree x[1] <= 0.0 ? -1 : (x[1] <= 1.0 ? 0 : 1), do:\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:1]);\n\njulia> f = MathOptAI.BinaryDecisionTree{Float64,Int}(\n 1,\n 0.0,\n -1,\n MathOptAI.BinaryDecisionTree{Float64,Int}(1, 1.0, 0, 1),\n )\nBinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_BinaryDecisionTree_value\n\njulia> formulation\nBinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]\n├ variables [4]\n│ ├ moai_BinaryDecisionTree_value\n│ ├ moai_BinaryDecisionTree_z[1]\n│ ├ moai_BinaryDecisionTree_z[2]\n│ └ moai_BinaryDecisionTree_z[3]\n└ constraints [7]\n ├ moai_BinaryDecisionTree_z[1] + moai_BinaryDecisionTree_z[2] + moai_BinaryDecisionTree_z[3] = 1\n ├ moai_BinaryDecisionTree_z[1] --> {x[1] ≤ 0}\n ├ moai_BinaryDecisionTree_z[2] --> {x[1] ≥ 0}\n ├ moai_BinaryDecisionTree_z[2] --> {x[1] ≤ 1}\n ├ moai_BinaryDecisionTree_z[3] --> {x[1] ≥ 0}\n ├ moai_BinaryDecisionTree_z[3] --> {x[1] ≥ 1}\n └ moai_BinaryDecisionTree_z[1] - moai_BinaryDecisionTree_z[3] + moai_BinaryDecisionTree_value = 0\n\n\n\n\n\n","category":"type"},{"location":"api/#GrayBox","page":"API Reference","title":"GrayBox","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"GrayBox","category":"page"},{"location":"api/#MathOptAI.GrayBox","page":"API Reference","title":"MathOptAI.GrayBox","text":"GrayBox(\n output_size::Function,\n callback::Function;\n has_hessian::Bool = false,\n) <: AbstractPredictor\n\nAn AbstractPredictor that represents the function f(x) as a user-defined nonlinear operator.\n\nArguments\n\noutput_size(x::Vector):Int: given an input vector x, return the dimension of the output vector\ncallback(x::Vector)::NamedTuple -> (;value, jacobian[, hessian]): given an input vector x, return a NamedTuple that computes the primal value and Jacobian of the output value with respect to the input. jacobian[j, i] is the partial derivative of value[j] with respect to x[i].\nhas_hessian: if true, the callback additionally contains a field hessian, which is an N × N × M matrix, where hessian[i, j, k] is the partial derivative of value[k] with respect to x[i] and x[j].\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.GrayBox(\n x -> 2,\n x -> (value = x.^2, jacobian = [2 * x[1] 0.0; 0.0 2 * x[2]]),\n );\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_GrayBox[1]\n moai_GrayBox[2]\n\njulia> formulation\nGrayBox\n├ variables [2]\n│ ├ moai_GrayBox[1]\n│ └ moai_GrayBox[2]\n└ constraints [2]\n ├ op_##330(x[1], x[2]) - moai_GrayBox[1] = 0\n └ op_##331(x[1], x[2]) - moai_GrayBox[2] = 0\n\njulia> y, formulation = MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n op_##332(x[1], x[2])\n op_##333(x[1], x[2])\n\njulia> formulation\nReducedSpace(GrayBox)\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#Pipeline","page":"API Reference","title":"Pipeline","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Pipeline","category":"page"},{"location":"api/#MathOptAI.Pipeline","page":"API Reference","title":"MathOptAI.Pipeline","text":"Pipeline(layers::Vector{AbstractPredictor}) <: AbstractPredictor\n\nAn AbstractPredictor that represents a pipeline (composition) of nested layers:\n\nf(x) = (l_1 cdots (l_N(x))\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.Pipeline(\n MathOptAI.Affine([1.0 2.0], [0.0]),\n MathOptAI.ReLUQuadratic(),\n )\nPipeline with layers:\n * Affine(A, b) [input: 2, output: 1]\n * ReLUQuadratic()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_ReLU[1]\n\njulia> formulation\nAffine(A, b) [input: 2, output: 1]\n├ variables [1]\n│ └ moai_Affine[1]\n└ constraints [1]\n └ x[1] + 2 x[2] - moai_Affine[1] = 0\nReLUQuadratic()\n├ variables [2]\n│ ├ moai_ReLU[1]\n│ └ moai_z[1]\n└ constraints [2]\n ├ moai_Affine[1] - moai_ReLU[1] + moai_z[1] = 0\n └ moai_ReLU[1]*moai_z[1] = 0\n\n\n\n\n\n","category":"type"},{"location":"api/#PytorchModel","page":"API Reference","title":"PytorchModel","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"PytorchModel","category":"page"},{"location":"api/#MathOptAI.PytorchModel","page":"API Reference","title":"MathOptAI.PytorchModel","text":"PytorchModel(filename::String)\n\nA wrapper struct for loading a PyTorch model.\n\nThe only supported file extension is .pt, where the .pt file has been created using torch.save(model, filename).\n\nExample\n\njulia> using PythonCall, MathOptAI\n\njulia> ml_model = PytorchModel(\"model.pt\");\n\n\n\n\n\n","category":"type"},{"location":"api/#Quantile","page":"API Reference","title":"Quantile","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Quantile","category":"page"},{"location":"api/#MathOptAI.Quantile","page":"API Reference","title":"MathOptAI.Quantile","text":"Quantile(distribution, quantiles::Vector{Float64})\n\nAn AbstractPredictor that represents the quantiles of distribution.\n\nExample\n\njulia> using JuMP, Distributions, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, 1 <= x <= 2);\n\njulia> predictor = MathOptAI.Quantile([0.1, 0.9]) do x\n return Distributions.Normal(x, 3 - x)\n end\nQuantile(_, [0.1, 0.9])\n\njulia> y, formulation = MathOptAI.add_predictor(model, predictor, [x]);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_quantile[1]\n moai_quantile[2]\n\n\n\n\n\n","category":"type"},{"location":"api/#ReducedSpace","page":"API Reference","title":"ReducedSpace","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"ReducedSpace","category":"page"},{"location":"api/#MathOptAI.ReducedSpace","page":"API Reference","title":"MathOptAI.ReducedSpace","text":"ReducedSpace(predictor::AbstractPredictor)\n\nA wrapper type for other predictors that implement a reduced-space formulation.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> predictor = MathOptAI.ReducedSpace(MathOptAI.ReLU());\n\njulia> y, formulation = MathOptAI.add_predictor(model, predictor, x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n max(0.0, x[1])\n max(0.0, x[2])\n\n\n\n\n\n","category":"type"},{"location":"api/#ReLU","page":"API Reference","title":"ReLU","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"ReLU","category":"page"},{"location":"api/#MathOptAI.ReLU","page":"API Reference","title":"MathOptAI.ReLU","text":"ReLU() <: AbstractPredictor\n\nAn AbstractPredictor that implements the ReLU constraint y = max0 x as a non-smooth nonlinear constraint.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.ReLU()\nReLU()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_ReLU[1]\n moai_ReLU[2]\n\njulia> formulation\nReLU()\n├ variables [2]\n│ ├ moai_ReLU[1]\n│ └ moai_ReLU[2]\n└ constraints [4]\n ├ moai_ReLU[1] ≥ 0\n ├ moai_ReLU[2] ≥ 0\n ├ moai_ReLU[1] - max(0.0, x[1]) = 0\n └ moai_ReLU[2] - max(0.0, x[2]) = 0\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n max(0.0, x[1])\n max(0.0, x[2])\n\njulia> formulation\nReducedSpace(ReLU())\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#ReLUBigM","page":"API Reference","title":"ReLUBigM","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"ReLUBigM","category":"page"},{"location":"api/#MathOptAI.ReLUBigM","page":"API Reference","title":"MathOptAI.ReLUBigM","text":"ReLUBigM(M::Float64) <: AbstractPredictor\n\nAn AbstractPredictor that implements the ReLU constraint y = max0 x via a big-M MIP reformulation.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, -3 <= x[i in 1:2] <= i);\n\njulia> f = MathOptAI.ReLUBigM(100.0)\nReLUBigM(100.0)\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_ReLU[1]\n moai_ReLU[2]\n\njulia> formulation\nReLUBigM(100.0)\n├ variables [4]\n│ ├ moai_ReLU[1]\n│ ├ moai_ReLU[2]\n│ ├ _[5]\n│ └ _[6]\n└ constraints [8]\n ├ _[5] binary\n ├ -x[1] + moai_ReLU[1] ≥ 0\n ├ moai_ReLU[1] - _[5] ≤ 0\n ├ -x[1] + moai_ReLU[1] + 3 _[5] ≤ 3\n ├ _[6] binary\n ├ -x[2] + moai_ReLU[2] ≥ 0\n ├ moai_ReLU[2] - 2 _[6] ≤ 0\n └ -x[2] + moai_ReLU[2] + 3 _[6] ≤ 3\n\n\n\n\n\n","category":"type"},{"location":"api/#ReLUQuadratic","page":"API Reference","title":"ReLUQuadratic","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"ReLUQuadratic","category":"page"},{"location":"api/#MathOptAI.ReLUQuadratic","page":"API Reference","title":"MathOptAI.ReLUQuadratic","text":"ReLUQuadratic() <: AbstractPredictor\n\nAn AbstractPredictor that implements the ReLU constraint y = max0 x by the reformulation:\n\nbeginaligned\nx = y - z \ny times z = 0 \ny z ge 0\nendaligned\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2] >= -1);\n\njulia> f = MathOptAI.ReLUQuadratic()\nReLUQuadratic()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_ReLU[1]\n moai_ReLU[2]\n\njulia> formulation\nReLUQuadratic()\n├ variables [4]\n│ ├ moai_ReLU[1]\n│ ├ moai_ReLU[2]\n│ ├ moai_z[1]\n│ └ moai_z[2]\n└ constraints [4]\n ├ x[1] - moai_ReLU[1] + moai_z[1] = 0\n ├ x[2] - moai_ReLU[2] + moai_z[2] = 0\n ├ moai_ReLU[1]*moai_z[1] = 0\n └ moai_ReLU[2]*moai_z[2] = 0\n\n\n\n\n\n","category":"type"},{"location":"api/#ReLUSOS1","page":"API Reference","title":"ReLUSOS1","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"ReLUSOS1","category":"page"},{"location":"api/#MathOptAI.ReLUSOS1","page":"API Reference","title":"MathOptAI.ReLUSOS1","text":"ReLUSOS1() <: AbstractPredictor\n\nAn AbstractPredictor that implements the ReLU constraint y = max0 x by the reformulation:\n\nbeginaligned\nx = y - z \ny z in SOS1 \ny z ge 0\nendaligned\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2] >= -1);\n\njulia> f = MathOptAI.ReLUSOS1()\nReLUSOS1()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_ReLU[1]\n moai_ReLU[2]\n\njulia> formulation\nReLUSOS1()\n├ variables [4]\n│ ├ moai_ReLU[1]\n│ ├ moai_ReLU[2]\n│ ├ moai_z[1]\n│ └ moai_z[2]\n└ constraints [4]\n ├ x[1] - moai_ReLU[1] + moai_z[1] = 0\n ├ x[2] - moai_ReLU[2] + moai_z[2] = 0\n ├ [moai_ReLU[1], moai_z[1]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])\n └ [moai_ReLU[2], moai_z[2]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])\n\n\n\n\n\n","category":"type"},{"location":"api/#Scale","page":"API Reference","title":"Scale","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Scale","category":"page"},{"location":"api/#MathOptAI.Scale","page":"API Reference","title":"MathOptAI.Scale","text":"Scale(\n scale::Vector{T},\n bias::Vector{T},\n) where {T} <: AbstractPredictor\n\nAn AbstractPredictor that represents the affine relationship:\n\nf(x) = Diag(scale)x + bias\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.Scale([2.0, 3.0], [4.0, 5.0])\nScale(scale, bias)\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_Scale[1]\n moai_Scale[2]\n\njulia> formulation\nScale(scale, bias)\n├ variables [2]\n│ ├ moai_Scale[1]\n│ └ moai_Scale[2]\n└ constraints [2]\n ├ 2 x[1] - moai_Scale[1] = -4\n └ 3 x[2] - moai_Scale[2] = -5\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{AffExpr}:\n 2 x[1] + 4\n 3 x[2] + 5\n\njulia> formulation\nReducedSpace(Scale(scale, bias))\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#Sigmoid","page":"API Reference","title":"Sigmoid","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Sigmoid","category":"page"},{"location":"api/#MathOptAI.Sigmoid","page":"API Reference","title":"MathOptAI.Sigmoid","text":"Sigmoid() <: AbstractPredictor\n\nAn AbstractPredictor that implements the Sigmoid constraint y = frac11 + e^-x as a smooth nonlinear constraint.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.Sigmoid()\nSigmoid()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_Sigmoid[1]\n moai_Sigmoid[2]\n\njulia> formulation\nSigmoid()\n├ variables [2]\n│ ├ moai_Sigmoid[1]\n│ └ moai_Sigmoid[2]\n└ constraints [6]\n ├ moai_Sigmoid[1] ≥ 0\n ├ moai_Sigmoid[2] ≥ 0\n ├ moai_Sigmoid[1] ≤ 1\n ├ moai_Sigmoid[2] ≤ 1\n ├ moai_Sigmoid[1] - (1.0 / (1.0 + exp(-x[1]))) = 0\n └ moai_Sigmoid[2] - (1.0 / (1.0 + exp(-x[2]))) = 0\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n 1.0 / (1.0 + exp(-x[1]))\n 1.0 / (1.0 + exp(-x[2]))\n\njulia> formulation\nReducedSpace(Sigmoid())\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#SoftMax","page":"API Reference","title":"SoftMax","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"SoftMax","category":"page"},{"location":"api/#MathOptAI.SoftMax","page":"API Reference","title":"MathOptAI.SoftMax","text":"SoftMax() <: AbstractPredictor\n\nAn AbstractPredictor that implements the SoftMax constraint y_i = frace^x_isum_j e^x_j as a smooth nonlinear constraint.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.SoftMax()\nSoftMax()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_SoftMax[1]\n moai_SoftMax[2]\n\njulia> formulation\nSoftMax()\n├ variables [3]\n│ ├ moai_SoftMax_denom\n│ ├ moai_SoftMax[1]\n│ └ moai_SoftMax[2]\n└ constraints [8]\n ├ moai_SoftMax[1] ≥ 0\n ├ moai_SoftMax[2] ≥ 0\n ├ moai_SoftMax[1] ≤ 1\n ├ moai_SoftMax[2] ≤ 1\n ├ moai_SoftMax_denom ≥ 0\n ├ moai_SoftMax_denom - (0.0 + exp(x[2]) + exp(x[1])) = 0\n ├ moai_SoftMax[1] - (exp(x[1]) / moai_SoftMax_denom) = 0\n └ moai_SoftMax[2] - (exp(x[2]) / moai_SoftMax_denom) = 0\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n exp(x[1]) / moai_SoftMax_denom\n exp(x[2]) / moai_SoftMax_denom\n\njulia> formulation\nReducedSpace(SoftMax())\n├ variables [1]\n│ └ moai_SoftMax_denom\n└ constraints [2]\n ├ moai_SoftMax_denom ≥ 0\n └ moai_SoftMax_denom - (0.0 + exp(x[2]) + exp(x[1])) = 0\n\n\n\n\n\n","category":"type"},{"location":"api/#SoftPlus","page":"API Reference","title":"SoftPlus","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"SoftPlus","category":"page"},{"location":"api/#MathOptAI.SoftPlus","page":"API Reference","title":"MathOptAI.SoftPlus","text":"SoftPlus(; beta = 1.0) <: AbstractPredictor\n\nAn AbstractPredictor that implements the SoftPlus constraint y = frac1beta log(1 + e^beta x) as a smooth nonlinear constraint.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.SoftPlus(; beta = 2.0)\nSoftPlus(2.0)\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_SoftPlus[1]\n moai_SoftPlus[2]\n\njulia> formulation\nSoftPlus(2.0)\n├ variables [2]\n│ ├ moai_SoftPlus[1]\n│ └ moai_SoftPlus[2]\n└ constraints [4]\n ├ moai_SoftPlus[1] ≥ 0\n ├ moai_SoftPlus[2] ≥ 0\n ├ moai_SoftPlus[1] - (log(1.0 + exp(2 x[1])) / 2.0) = 0\n └ moai_SoftPlus[2] - (log(1.0 + exp(2 x[2])) / 2.0) = 0\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n log(1.0 + exp(2 x[1])) / 2.0\n log(1.0 + exp(2 x[2])) / 2.0\n\njulia> formulation\nReducedSpace(SoftPlus(2.0))\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#Tanh","page":"API Reference","title":"Tanh","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Tanh","category":"page"},{"location":"api/#MathOptAI.Tanh","page":"API Reference","title":"MathOptAI.Tanh","text":"Tanh() <: AbstractPredictor\n\nAn AbstractPredictor that implements the Tanh constraint y = tanh(x) as a smooth nonlinear constraint.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.Tanh()\nTanh()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_Tanh[1]\n moai_Tanh[2]\n\njulia> formulation\nTanh()\n├ variables [2]\n│ ├ moai_Tanh[1]\n│ └ moai_Tanh[2]\n└ constraints [6]\n ├ moai_Tanh[1] ≥ -1\n ├ moai_Tanh[2] ≥ -1\n ├ moai_Tanh[1] ≤ 1\n ├ moai_Tanh[2] ≤ 1\n ├ moai_Tanh[1] - tanh(x[1]) = 0\n └ moai_Tanh[2] - tanh(x[2]) = 0\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n tanh(x[1])\n tanh(x[2])\n\njulia> formulation\nReducedSpace(Tanh())\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#AbstractFormulation","page":"API Reference","title":"AbstractFormulation","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"AbstractFormulation","category":"page"},{"location":"api/#MathOptAI.AbstractFormulation","page":"API Reference","title":"MathOptAI.AbstractFormulation","text":"abstract type AbstractFormulation end\n\nAn abstract type representing different formulations.\n\n\n\n\n\n","category":"type"},{"location":"api/#Formulation","page":"API Reference","title":"Formulation","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Formulation","category":"page"},{"location":"api/#MathOptAI.Formulation","page":"API Reference","title":"MathOptAI.Formulation","text":"struct Formulation{P<:AbstractPredictor} <: AbstractFormulation\n predictor::P\n variables::Vector{Any}\n constraints::Vector{Any}\nend\n\nFields\n\npredictor: the predictor object used to build the formulation\nvariables: a vector of new decision variables added to the model\nconstraints: a vector of new constraints added to the model\n\nCheck the docstring of the predictor for an explanation of the formulation and the order of the elements in .variables and .constraints.\n\n\n\n\n\n","category":"type"},{"location":"api/#PipelineFormulation","page":"API Reference","title":"PipelineFormulation","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"PipelineFormulation","category":"page"},{"location":"api/#MathOptAI.PipelineFormulation","page":"API Reference","title":"MathOptAI.PipelineFormulation","text":"struct PipelineFormulation{P<:AbstractPredictor} <: AbstractFormulation\n predictor::P\n layers::Vector{Any}\nend\n\nFields\n\npredictor: the predictor object used to build the formulation\nlayers: the formulation associated with each of the layers in the pipeline\n\n\n\n\n\n","category":"type"},{"location":"api/#Extensions","page":"API Reference","title":"Extensions","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Modules = [\n Base.get_extension(MathOptAI, :MathOptAIAbstractGPsExt),\n Base.get_extension(MathOptAI, :MathOptAIDecisionTreeExt),\n Base.get_extension(MathOptAI, :MathOptAIFluxExt),\n Base.get_extension(MathOptAI, :MathOptAIGLMExt),\n Base.get_extension(MathOptAI, :MathOptAILuxExt),\n Base.get_extension(MathOptAI, :MathOptAIPythonCallExt),\n Base.get_extension(MathOptAI, :MathOptAIStatsModelsExt),\n]","category":"page"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, MathOptAI.Quantile{<:AbstractGPs.PosteriorGP}, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::MathOptAI.Quantile{<:AbstractGPs.PosteriorGP},\n x::Vector,\n)\n\nAdd the quantiles of a trained Gaussian Process from AbstractGPs.jl to model.\n\nExample\n\njulia> using JuMP, MathOptAI, AbstractGPs\n\njulia> x_data = 2π .* (0.0:0.1:1.0);\n\njulia> y_data = sin.(x_data);\n\njulia> fx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.1);\n\njulia> p_fx = AbstractGPs.posterior(fx, y_data);\n\njulia> model = Model();\n\njulia> @variable(model, 1 <= x[1:1] <= 6, start = 3);\n\njulia> predictor = MathOptAI.Quantile(p_fx, [0.1, 0.9]);\n\njulia> y, _ = MathOptAI.add_predictor(model, predictor, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_quantile[1]\n moai_quantile[2]\n\njulia> @objective(model, Max, y[2] - y[1])\nmoai_quantile[2] - moai_quantile[1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, Union{DecisionTree.DecisionTreeClassifier, DecisionTree.Root}, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::Union{DecisionTree.Root,DecisionTree.DecisionTreeClassifier},\n x::Vector,\n)\n\nAdd a binary decision tree from DecisionTree.jl to model.\n\nExample\n\njulia> using JuMP, MathOptAI, DecisionTree\n\njulia> truth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)\ntruth (generic function with 1 method)\n\njulia> features = abs.(sin.((1:10) .* (3:4)'));\n\njulia> size(features)\n(10, 2)\n\njulia> labels = truth.(Vector.(eachrow(features)));\n\njulia> ml_model = DecisionTree.build_tree(labels, features)\nDecision Tree\nLeaves: 3\nDepth: 2\n\njulia> model = Model();\n\njulia> @variable(model, 0 <= x[1:2] <= 1);\n\njulia> y, _ = MathOptAI.add_predictor(model, ml_model, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_BinaryDecisionTree_value\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.build_predictor-Tuple{DecisionTree.Root}","page":"API Reference","title":"MathOptAI.build_predictor","text":"MathOptAI.build_predictor(predictor::DecisionTree.Root)\n\nConvert a binary decision tree from DecisionTree.jl to a BinaryDecisionTree.\n\nExample\n\njulia> using MathOptAI, DecisionTree\n\njulia> truth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)\ntruth (generic function with 1 method)\n\njulia> features = abs.(sin.((1:10) .* (3:4)'));\n\njulia> size(features)\n(10, 2)\n\njulia> labels = truth.(Vector.(eachrow(features)));\n\njulia> ml_model = DecisionTree.build_tree(labels, features)\nDecision Tree\nLeaves: 3\nDepth: 2\n\njulia> MathOptAI.build_predictor(ml_model)\nBinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, Flux.Chain, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::Flux.Chain,\n x::Vector;\n config::Dict = Dict{Any,Any}(),\n reduced_space::Bool = false,\n gray_box::Bool = false,\n)\n\nAdd a trained neural network from Flux.jl to model.\n\nSupported layers\n\nFlux.Dense\nFlux.Scale\nFlux.softmax\n\nSupported activation functions\n\nFlux.relu\nFlux.sigmoid\nFlux.softplus\nFlux.tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps supported Flux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Flux.sigmoid => MathOptAI.Sigmoid() or Flux.relu => MathOptAI.QuadraticReLU().\ngray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by Flux.withjacobian.\n\nExample\n\njulia> using JuMP, Flux, MathOptAI\n\njulia> chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));\n\njulia> model = Model();\n\njulia> @variable(model, x[1:1]);\n\njulia> y, _ = MathOptAI.add_predictor(\n model,\n chain,\n x;\n config = Dict(Flux.relu => MathOptAI.ReLU()),\n );\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Affine[1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.build_predictor-Tuple{Flux.Chain}","page":"API Reference","title":"MathOptAI.build_predictor","text":"MathOptAI.build_predictor(\n predictor::Flux.Chain;\n config::Dict = Dict{Any,Any}(),\n gray_box::Bool = false,\n gray_box_hessian::Bool = false,\n)\n\nConvert a trained neural network from Flux.jl to a Pipeline.\n\nSupported layers\n\nFlux.Dense\nFlux.Scale\nFlux.softmax\n\nSupported activation functions\n\nFlux.relu\nFlux.sigmoid\nFlux.softplus\nFlux.tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps supported Flux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Flux.sigmoid => MathOptAI.Sigmoid() or Flux.relu => MathOptAI.QuadraticReLU().\ngray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by Flux.withjacobian.\ngray_box_hessian: if true, the gray box additionally computes the Hessian of the output using Flux.hessian.\n\nExample\n\njulia> using Flux, MathOptAI\n\njulia> chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));\n\njulia> MathOptAI.build_predictor(\n chain;\n config = Dict(Flux.relu => MathOptAI.ReLU()),\n )\nPipeline with layers:\n * Affine(A, b) [input: 1, output: 16]\n * ReLU()\n * Affine(A, b) [input: 16, output: 1]\n\njulia> MathOptAI.build_predictor(\n chain;\n config = Dict(Flux.relu => MathOptAI.ReLUQuadratic()),\n )\nPipeline with layers:\n * Affine(A, b) [input: 1, output: 16]\n * ReLUQuadratic()\n * Affine(A, b) [input: 16, output: 1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, GLM.GeneralizedLinearModel{GLM.GlmResp{Vector{Float64}, Distributions.Bernoulli{Float64}, GLM.LogitLink}}, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::GLM.GeneralizedLinearModel{\n GLM.GlmResp{Vector{Float64},GLM.Bernoulli{Float64},GLM.LogitLink},\n },\n x::Vector;\n sigmoid::AbstractPredictor = MathOptAI.Sigmoid(),\n reduced_space::Bool = false,\n)\n\nAdd a trained logistic regression model from GLM.jl to model.\n\nKeyword arguments\n\nsigmoid: the predictor to use for the sigmoid layer.\n\nExample\n\njulia> using GLM, JuMP, MathOptAI\n\njulia> X, Y = rand(10, 2), rand(Bool, 10);\n\njulia> model_glm = GLM.glm(X, Y, GLM.Bernoulli());\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> y, _ = MathOptAI.add_predictor(\n model,\n model_glm,\n x;\n sigmoid = MathOptAI.Sigmoid(),\n );\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Sigmoid[1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, GLM.LinearModel, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::GLM.LinearModel,\n x::Vector;\n reduced_space::Bool = false,\n)\n\nAdd a trained linear model from GLM.jl to model.\n\nExample\n\njulia> using GLM, JuMP, MathOptAI\n\njulia> X, Y = rand(10, 2), rand(10);\n\njulia> model_glm = GLM.lm(X, Y);\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> y, _ = MathOptAI.add_predictor(model, model_glm, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Affine[1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.build_predictor-Tuple{GLM.GeneralizedLinearModel{GLM.GlmResp{Vector{Float64}, Distributions.Bernoulli{Float64}, GLM.LogitLink}}}","page":"API Reference","title":"MathOptAI.build_predictor","text":"MathOptAI.build_predictor(\n predictor::GLM.GeneralizedLinearModel{\n GLM.GlmResp{Vector{Float64},GLM.Bernoulli{Float64},GLM.LogitLink},\n };\n sigmoid::MathOptAI.AbstractPredictor = MathOptAI.Sigmoid(),\n)\n\nConvert a trained logistic model from GLM.jl to a Pipeline layer.\n\nKeyword arguments\n\nsigmoid: the predictor to use for the sigmoid layer.\n\nExample\n\njulia> using GLM, MathOptAI\n\njulia> X, Y = rand(10, 2), rand(Bool, 10);\n\njulia> model_glm = GLM.glm(X, Y, GLM.Bernoulli());\n\njulia> MathOptAI.build_predictor(model_glm)\nPipeline with layers:\n * Affine(A, b) [input: 2, output: 1]\n * Sigmoid()\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.build_predictor-Tuple{GLM.LinearModel}","page":"API Reference","title":"MathOptAI.build_predictor","text":"MathOptAI.build_predictor(predictor::GLM.LinearModel)\n\nConvert a trained linear model from GLM.jl to an Affine layer.\n\nExample\n\njulia> using GLM, MathOptAI\n\njulia> X, Y = rand(10, 2), rand(10);\n\njulia> model_glm = GLM.lm(X, Y);\n\njulia> MathOptAI.build_predictor(model_glm)\nAffine(A, b) [input: 2, output: 1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, Tuple{Lux.Chain, NamedTuple, NamedTuple}, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::Tuple{<:Lux.Chain,<:NamedTuple,<:NamedTuple},\n x::Vector;\n config::Dict = Dict{Any,Any}(),\n reduced_space::Bool = false,\n)\n\nAdd a trained neural network from Lux.jl to model.\n\nSupported layers\n\nLux.Dense\nLux.Scale\n\nSupported activation functions\n\nLux.relu\nLux.sigmoid\nLux.softplus\nLux.softmax\nLux.tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps supported Lux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Lux.sigmoid => MathOptAI.Sigmoid() or Lux.relu => MathOptAI.QuadraticReLU().\n\nExample\n\njulia> using JuMP, Lux, MathOptAI, Random\n\njulia> rng = Random.MersenneTwister();\n\njulia> chain = Lux.Chain(Lux.Dense(1 => 16, Lux.relu), Lux.Dense(16 => 1))\nChain(\n layer_1 = Dense(1 => 16, relu), # 32 parameters\n layer_2 = Dense(16 => 1), # 17 parameters\n) # Total: 49 parameters,\n # plus 0 states.\n\njulia> parameters, state = Lux.setup(rng, chain);\n\njulia> predictor = (chain, parameters, state);\n\njulia> model = Model();\n\njulia> @variable(model, x[1:1]);\n\njulia> y, _ = MathOptAI.add_predictor(\n model,\n predictor,\n x;\n config = Dict(Lux.relu => MathOptAI.ReLU()),\n );\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Affine[1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.build_predictor-Tuple{Tuple{Lux.Chain, NamedTuple, NamedTuple}}","page":"API Reference","title":"MathOptAI.build_predictor","text":"MathOptAI.build_predictor(\n predictor::Tuple{<:Lux.Chain,<:NamedTuple,<:NamedTuple};\n config::Dict = Dict{Any,Any}(),\n)\n\nConvert a trained neural network from Lux.jl to a Pipeline.\n\nSupported layers\n\nLux.Dense\nLux.Scale\n\nSupported activation functions\n\nLux.relu\nLux.sigmoid\nLux.softplus\nLux.softmax\nLux.tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps supported Lux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Lux.sigmoid => MathOptAI.Sigmoid() or Lux.relu => MathOptAI.QuadraticReLU().\n\nExample\n\njulia> using Lux, MathOptAI, Random\n\njulia> rng = Random.MersenneTwister();\n\njulia> chain = Lux.Chain(Lux.Dense(1 => 16, Lux.relu), Lux.Dense(16 => 1))\nChain(\n layer_1 = Dense(1 => 16, relu), # 32 parameters\n layer_2 = Dense(16 => 1), # 17 parameters\n) # Total: 49 parameters,\n # plus 0 states.\n\njulia> parameters, state = Lux.setup(rng, chain);\n\njulia> predictor = MathOptAI.build_predictor(\n (chain, parameters, state);\n config = Dict(Lux.relu => MathOptAI.ReLU()),\n )\nPipeline with layers:\n * Affine(A, b) [input: 1, output: 16]\n * ReLU()\n * Affine(A, b) [input: 16, output: 1]\n\njulia> MathOptAI.build_predictor(\n (chain, parameters, state);\n config = Dict(Lux.relu => MathOptAI.ReLUQuadratic()),\n )\nPipeline with layers:\n * Affine(A, b) [input: 1, output: 16]\n * ReLUQuadratic()\n * Affine(A, b) [input: 16, output: 1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, MathOptAI.PytorchModel, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::MathOptAI.PytorchModel,\n x::Vector;\n config::Dict = Dict{Any,Any}(),\n reduced_space::Bool = false,\n gray_box::Bool = false,\n)\n\nAdd a trained neural network from PyTorch via PythonCall.jl to model.\n\nSupported layers\n\nnn.Linear\nnn.ReLU\nnn.Sequential\nnn.Sigmoid\nnn.Softplus\nnn.Tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps Symbols to AbstractPredictors that control how the activation functions are reformulated. For example, :Sigmoid => MathOptAI.Sigmoid() or :ReLU => MathOptAI.QuadraticReLU(). The supported Symbols are :ReLU, :Sigmoid, :SoftPlus, and :Tanh.\ngray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by torch.func.jacrev.\ngray_box_hessian: if true, the gray box additionally computes the Hessian of the output using torch.func.hessian.\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.build_predictor-Tuple{MathOptAI.PytorchModel}","page":"API Reference","title":"MathOptAI.build_predictor","text":"MathOptAI.build_predictor(\n predictor::MathOptAI.PytorchModel;\n config::Dict = Dict{Any,Any}(),\n gray_box::Bool = false,\n gray_box_hessian::Bool = false,\n)\n\nConvert a trained neural network from PyTorch via PythonCall.jl to a Pipeline.\n\nSupported layers\n\nnn.Linear\nnn.ReLU\nnn.Sequential\nnn.Sigmoid\nnn.Softplus\nnn.Tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps Symbols to AbstractPredictors that control how the activation functions are reformulated. For example, :Sigmoid => MathOptAI.Sigmoid() or :ReLU => MathOptAI.QuadraticReLU(). The supported Symbols are :ReLU, :Sigmoid, :SoftPlus, and :Tanh.\ngray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by torch.func.jacrev.\ngray_box_hessian: if true, the gray box additionally computes the Hessian of the output using torch.func.hessian.\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, StatsModels.TableRegressionModel, DataFrames.DataFrame}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::StatsModels.TableRegressionModel,\n x::DataFrames.DataFrame;\n kwargs...,\n)\n\nAdd a trained regression model from StatsModels.jl to model, using the DataFrame x as input.\n\nIn most cases, predictor should be a GLM.jl predictor supported by MathOptAI, but trained using @formula and a DataFrame instead of the raw matrix input.\n\nIn general, x may have some columns that are constant (Float64) and some columns that are JuMP decision variables.\n\nKeyword arguments\n\nAll keyword arguments are passed to the corresponding add_predictor of the GLM extension.\n\nExample\n\njulia> using DataFrames, GLM, JuMP, MathOptAI\n\njulia> train_df = DataFrames.DataFrame(x1 = rand(10), x2 = rand(10));\n\njulia> train_df.y = 1.0 .* train_df.x1 + 2.0 .* train_df.x2 .+ rand(10);\n\njulia> predictor = GLM.lm(GLM.@formula(y ~ x1 + x2), train_df);\n\njulia> model = Model();\n\njulia> test_df = DataFrames.DataFrame(\n x1 = rand(6),\n x2 = @variable(model, [1:6]),\n );\n\njulia> test_df.y, _ = MathOptAI.add_predictor(model, predictor, test_df);\n\njulia> test_df.y\n6-element Vector{VariableRef}:\n moai_Affine[1]\n moai_Affine[1]\n moai_Affine[1]\n moai_Affine[1]\n moai_Affine[1]\n moai_Affine[1]\n\n\n\n\n\n","category":"method"},{"location":"manual/AbstractGPs/#AbstractGPs","page":"AbstractGPs","title":"AbstractGPs","text":"","category":"section"},{"location":"manual/AbstractGPs/","page":"AbstractGPs","title":"AbstractGPs","text":"AbstractGPs.jl is a library for fittinng Gaussian Processes in Julia.","category":"page"},{"location":"manual/AbstractGPs/","page":"AbstractGPs","title":"AbstractGPs","text":"Here is an example:","category":"page"},{"location":"manual/AbstractGPs/","page":"AbstractGPs","title":"AbstractGPs","text":"julia> using JuMP, MathOptAI, AbstractGPs\n\njulia> x_data = 2π .* (0.0:0.1:1.0);\n\njulia> y_data = sin.(x_data);\n\njulia> fx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.1);\n\njulia> p_fx = AbstractGPs.posterior(fx, y_data);\n\njulia> model = Model();\n\njulia> @variable(model, 1 <= x[1:1] <= 6, start = 3);\n\njulia> predictor = MathOptAI.Quantile(p_fx, [0.1, 0.9]);\n\njulia> y, formulation = MathOptAI.add_predictor(model, predictor, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_quantile[1]\n moai_quantile[2]\n\njulia> @objective(model, Max, y[2] - y[1])\nmoai_quantile[2] - moai_quantile[1]","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"EditURL = \"pytorch.jl\"","category":"page"},{"location":"tutorials/pytorch/#Function-fitting-with-PyTorch","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"","category":"section"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"The purpose of this tutorial is to explain how to embed a neural network model from PyTorch into JuMP.","category":"page"},{"location":"tutorials/pytorch/#Python-integration","page":"Function fitting with PyTorch","title":"Python integration","text":"","category":"section"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"MathOptAI uses PythonCall.jl to call from Julia into Python.","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"See CondaPkg.jl for more control over how to link Julia to an existing Python environment. For example, if you have an existing Python installation (with PyTorch installed), and it is available in the current conda environment, set:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"ENV[\"JULIA_CONDAPKG_BACKEND\"] = \"Current\"","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"before importing PythonCall.jl. If the Python installation can be found on the path and it is not in a conda environment, set:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"ENV[\"JULIA_CONDAPKG_BACKEND\"] = \"Null\"","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"If python is not on your path, you may additionally need to set JULIA_PYTHONCALL_EXE, for example, to:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"ENV[\"JULIA_PYTHONCALL_EXE\"] = \"python3\"","category":"page"},{"location":"tutorials/pytorch/#Required-packages","page":"Function fitting with PyTorch","title":"Required packages","text":"","category":"section"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"This tutorial requires the following packages","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"using JuMP\nusing Test\nimport Ipopt\nimport MathOptAI\nimport Plots","category":"page"},{"location":"tutorials/pytorch/#Training-a-model","page":"Function fitting with PyTorch","title":"Training a model","text":"","category":"section"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"The following script builds and trains a simple neural network in PyTorch. For simplicity, we do not evaluate out-of-sample test performance, or use a batched data loader. In general, you should train your model in Python, and then use torch.save(model, filename) to save it to a .pt file for later use in Julia.","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"The model is unimportant, but for this example, we are trying to fit noisy observations of the function f(x) = x^2 - 2x.","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"In Python, I ran:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"#!/usr/bin/python3\nimport torch\nmodel = torch.nn.Sequential(\n torch.nn.Linear(1, 16),\n torch.nn.ReLU(),\n torch.nn.Linear(16, 1),\n)\n\nn = 1024\nx = torch.arange(-2, 2 + 4 / (n - 1), 4 / (n - 1)).reshape(n, 1)\nloss_fn = torch.nn.MSELoss()\noptimizer = torch.optim.Adam(model.parameters(), lr=0.01)\nfor epoch in range(100):\n optimizer.zero_grad()\n N = torch.normal(torch.zeros(n, 1), torch.ones(n, 1))\n y = x ** 2 -2 * x + 0.1 * N\n loss = loss_fn(model(x), y)\n loss.backward()\n optimizer.step()\n\ntorch.save(model, \"model.pt\")","category":"page"},{"location":"tutorials/pytorch/#JuMP-model","page":"Function fitting with PyTorch","title":"JuMP model","text":"","category":"section"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"Our goal for this JuMP model is to load the Neural Network from PyTorch into the objective function, and then minimize the objective for different fixed values of x to recreate the function that the Neural Network has learned to approximate.","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"First, create a JuMP model:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"model = Model(Ipopt.Optimizer)\nset_silent(model)\n@variable(model, x)","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"Then, load the model from PyTorch using MathOptAI.PytorchModel:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"ml_model = MathOptAI.PytorchModel(joinpath(@__DIR__, \"model.pt\"))\ny, _ = MathOptAI.add_predictor(model, ml_model, [x])\n@objective(model, Min, only(y))","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"Now, visualize the fitted function y = ml_model(x) by repeatedly solving the optimization problem for different fixed values of x:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"X, Y = -2:0.1:2, Float64[]\n@constraint(model, c, x == 0.0)\nfor xi in X\n set_normalized_rhs(c, xi)\n optimize!(model)\n @test is_solved_and_feasible(model)\n push!(Y, objective_value(model))\nend\nPlots.plot(x -> x^2 - 2x, X; label = \"Truth\", linestype = :dot)\nPlots.plot!(X, Y; label = \"Fitted\")","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"This page was generated using Literate.jl.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"EditURL = \"decision_trees.jl\"","category":"page"},{"location":"tutorials/decision_trees/#Classification-problems-with-DecisionTree.jl","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"","category":"section"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The purpose of this tutorial is to explain how to embed a decision tree model from DecisionTree.jl into JuMP.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The data and example in this tutorial comes from the paper: David Bergman, Teng Huang, Philip Brooks, Andrea Lodi, Arvind U. Raghunathan (2021) JANOS: An Integrated Predictive and Prescriptive Modeling Framework. INFORMS Journal on Computing 34(2):807-816. https://doi.org/10.1287/ijoc.2020.1023","category":"page"},{"location":"tutorials/decision_trees/#Required-packages","page":"Classification problems with DecisionTree.jl","title":"Required packages","text":"","category":"section"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"This tutorial uses the following packages.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"using JuMP\nimport CSV\nimport DataFrames\nimport Downloads\nimport DecisionTree\nimport HiGHS\nimport MathOptAI\nimport Statistics","category":"page"},{"location":"tutorials/decision_trees/#Data","page":"Classification problems with DecisionTree.jl","title":"Data","text":"","category":"section"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Here is a function to load the data directly from the JANOS repository:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"function read_df(filename)\n url = \"https://raw.githubusercontent.com/INFORMSJoC/2020.1023/master/data/\"\n data = Downloads.download(url * filename)\n return CSV.read(data, DataFrames.DataFrame)\nend","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"There are two important files. The first, college_student_enroll-s1-1.csv, contains historial admissions data on anonymized students, their SAT score, their GPA, their merit scholarships, and whether the enrolled in the college.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"train_df = read_df(\"college_student_enroll-s1-1.csv\")","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The second, college_applications6000.csv, contains the SAT and GPA data of students who are currently applying:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"evaluate_df = read_df(\"college_applications6000.csv\")","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"There are 6,000 prospective students:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"n_students = size(evaluate_df, 1)","category":"page"},{"location":"tutorials/decision_trees/#Prediction-model","page":"Classification problems with DecisionTree.jl","title":"Prediction model","text":"","category":"section"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The first step is to train a logistic regression model to predict the Boolean enroll column based on the SAT, GPA, and merit columns.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"train_features = Matrix(train_df[:, [:SAT, :GPA, :merit]])\ntrain_labels = train_df[:, :enroll]\nml_model = DecisionTree.DecisionTreeClassifier(; max_depth = 3)\nDecisionTree.fit!(ml_model, train_features, train_labels)\nDecisionTree.print_tree(ml_model)","category":"page"},{"location":"tutorials/decision_trees/#Decision-model","page":"Classification problems with DecisionTree.jl","title":"Decision model","text":"","category":"section"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Now that we have a trained decision tree, we want a decision model that chooses the optimal merit scholarship for each student in:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"evaluate_df","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Here's an empty JuMP model to start:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"model = Model()","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"First, we add a new columnn to evaluate_df, with one JuMP decision variable for each row. It is important the the .merit column name in evaluate_df matches the name in train_df.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"evaluate_df.merit = @variable(model, 0 <= x_merit[1:n_students] <= 2.5);\nevaluate_df","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Then, we use MathOptAI.add_predictor to embed model_ml into the JuMP model. MathOptAI.add_predictor returns a vector of variables, one for each row in evaluate_df, corresponding to the output enroll of our logistic regression.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"evaluate_features = Matrix(evaluate_df[:, [:SAT, :GPA, :merit]])\nevaluate_df.enroll = mapreduce(vcat, 1:size(evaluate_features, 1)) do i\n y, _ = MathOptAI.add_predictor(model, ml_model, evaluate_features[i, :])\n return y\nend\nevaluate_df","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The .enroll column name in evaluate_df is just a name. It doesn't have to match the name in train_df.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The objective of our problem is to maximize the expected number of students who enroll:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"@objective(model, Max, sum(evaluate_df.enroll))","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Subject to the constraint that we can spend at most 0.2 * n_students on merit scholarships:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"@constraint(model, sum(evaluate_df.merit) <= 0.2 * n_students)","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Because logistic regression involves a Sigmoid layer, we need to use a smooth nonlinear optimizer. A common choice is Ipopt. Solve and check the optimizer found a feasible solution:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"set_optimizer(model, HiGHS.Optimizer)\nset_silent(model)\noptimize!(model)\n@assert is_solved_and_feasible(model)","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Let's store the solution in evaluate_df for analysis:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"evaluate_df.merit_sol = value.(evaluate_df.merit);\nevaluate_df.enroll_sol = value.(evaluate_df.enroll);\nevaluate_df","category":"page"},{"location":"tutorials/decision_trees/#Solution-analysis","page":"Classification problems with DecisionTree.jl","title":"Solution analysis","text":"","category":"section"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"We expect that just under 2,500 students will enroll:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"sum(evaluate_df.enroll_sol)","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"We awarded merit scholarships to approximately 1 in 6 students:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"count(evaluate_df.merit_sol .> 1e-5)","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The average merit scholarship was worth just under $1,000:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"1_000 * Statistics.mean(evaluate_df.merit_sol[evaluate_df.merit_sol.>1e-5])","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"This page was generated using Literate.jl.","category":"page"},{"location":"manual/Lux/#Lux","page":"Lux","title":"Lux","text":"","category":"section"},{"location":"manual/Lux/","page":"Lux","title":"Lux","text":"Lux.jl is a library for machine learning in Julia.","category":"page"},{"location":"manual/Lux/","page":"Lux","title":"Lux","text":"MathOptAI supports embedding Lux models in JuMP if they are a chain composed of:","category":"page"},{"location":"manual/Lux/","page":"Lux","title":"Lux","text":"Lux.Dense\nLux.relu\nLux.sigmoid\nLux.softplus\nLux.tanh","category":"page"},{"location":"manual/Lux/","page":"Lux","title":"Lux","text":"Here is an example:","category":"page"},{"location":"manual/Lux/","page":"Lux","title":"Lux","text":"julia> using JuMP, Lux, MathOptAI, Random\n\njulia> rng = Random.MersenneTwister();\n\njulia> chain = Lux.Chain(Lux.Dense(1 => 16, Lux.relu), Lux.Dense(16 => 1))\nChain(\n layer_1 = Dense(1 => 16, relu), # 32 parameters\n layer_2 = Dense(16 => 1), # 17 parameters\n) # Total: 49 parameters,\n # plus 0 states.\n\njulia> parameters, state = Lux.setup(rng, chain);\n\njulia> predictor = (chain, parameters, state);\n\njulia> model = Model();\n\njulia> @variable(model, x[1:1]);\n\njulia> y, formulation = MathOptAI.add_predictor(\n model,\n predictor,\n x;\n config = Dict(Lux.relu => MathOptAI.ReLU()),\n );\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Affine[1]","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"EditURL = \"mnist_lux.jl\"","category":"page"},{"location":"tutorials/mnist_lux/#Adversarial-machine-learning-with-Lux.jl","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"","category":"section"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"The purpose of this tutorial is to explain how to embed a neural network model from Lux.jl into JuMP.","category":"page"},{"location":"tutorials/mnist_lux/#Required-packages","page":"Adversarial machine learning with Lux.jl","title":"Required packages","text":"","category":"section"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"This tutorial requires the following packages","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"using JuMP\nimport Lux\nimport Ipopt\nimport MathOptAI\nimport MLDatasets\nimport MLUtils\nimport OneHotArrays\nimport Optimisers\nimport Plots\nimport Random\nimport Zygote","category":"page"},{"location":"tutorials/mnist_lux/#Data","page":"Adversarial machine learning with Lux.jl","title":"Data","text":"","category":"section"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"This tutorial uses images from the MNIST dataset.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"We load the predefined train and test splits:","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"train_data = MLDatasets.MNIST(; split = :train)","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"test_data = MLDatasets.MNIST(; split = :test)","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Since the data are images, it is helpful to plot them. (This requires a transpose and reversing the rows to get the orientation correct.)","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"function plot_image(x::Matrix; kwargs...)\n return Plots.heatmap(\n x'[size(x, 1):-1:1, :];\n xlims = (1, size(x, 2)),\n ylims = (1, size(x, 1)),\n aspect_ratio = true,\n legend = false,\n xaxis = false,\n yaxis = false,\n kwargs...,\n )\nend\n\nfunction plot_image(instance::NamedTuple)\n return plot_image(instance.features; title = \"Label = $(instance.targets)\")\nend\n\nPlots.plot([plot_image(train_data[i]) for i in 1:6]...; layout = (2, 3))","category":"page"},{"location":"tutorials/mnist_lux/#Training","page":"Adversarial machine learning with Lux.jl","title":"Training","text":"","category":"section"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"We use a simple neural network with one hidden layer and a sigmoid activation function. (There are better performing networks; try experimenting.)","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"chain = Lux.Chain(\n Lux.Dense(28^2 => 32, Lux.sigmoid),\n Lux.Dense(32 => 10),\n Lux.softmax,\n)\nrng = Random.MersenneTwister();\nparameters, state = Lux.setup(rng, chain)\nml_model = (chain, parameters, state);\nnothing #hide","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Here is a function to load our data into the format that ml_model expects:","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"function data_loader(data; batchsize, shuffle = false)\n x = reshape(data.features, 28^2, :)\n y = OneHotArrays.onehotbatch(data.targets, 0:9)\n return MLUtils.DataLoader((x, y); batchsize, shuffle)\nend","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"and here is a function to score the percentage of correct labels, where we assign a label by choosing the label of the highest softmax in the final layer.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"function score_model(ml_model, data)\n chain, parameters, state = ml_model\n x, y = only(data_loader(data; batchsize = length(data)))\n y_hat, _ = chain(x, parameters, state)\n is_correct = OneHotArrays.onecold(y) .== OneHotArrays.onecold(y_hat)\n p = round(100 * sum(is_correct) / length(is_correct); digits = 2)\n println(\"Accuracy = $p %\")\n return\nend","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"The accuracy of our model is only around 10% before training:","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"score_model(ml_model, train_data)\nscore_model(ml_model, test_data)","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Let's improve that by training our model.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"note: Note\nIt is not the purpose of this tutorial to explain how Lux works; see the documentation at https://lux.csail.mit.edu for more details. Changing the number of epochs or the learning rate can improve the loss.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"begin\n train_loader = data_loader(train_data; batchsize = 256, shuffle = true)\n optimizer_state = Optimisers.setup(Optimisers.Adam(0.0003f0), parameters)\n for epoch in 1:30\n loss = 0.0\n for (x, y) in train_loader\n global state\n (loss_batch, state), pullback = Zygote.pullback(parameters) do p\n y_model, new_state = chain(x, p, state)\n return Lux.CrossEntropyLoss()(y_model, y), new_state\n end\n gradients = only(pullback((one(loss), nothing)))\n Optimisers.update!(optimizer_state, parameters, gradients)\n loss += loss_batch\n end\n loss = round(loss / length(train_loader); digits = 4)\n print(\"Epoch $epoch: loss = $loss\\t\")\n score_model(ml_model, test_data)\n end\nend","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Here are the first eight predictions of the test data:","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"function plot_image(ml_model, x::Matrix)\n y, _ = chain(vec(x), parameters, state)\n score, index = findmax(y)\n title = \"Predicted: $(index - 1) ($(round(Int, 100 * score))%)\"\n return plot_image(x; title)\nend\n\nplots = [plot_image(ml_model, test_data[i].features) for i in 1:8]\nPlots.plot(plots...; size = (1200, 600), layout = (2, 4))","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"We can also look at the best and worst four predictions:","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"x, y = only(data_loader(test_data; batchsize = length(test_data)))\ny_model, _ = chain(x, parameters, state)\nlosses = Lux.CrossEntropyLoss(; agg = identity)(y_model, y)\nindices = sortperm(losses; dims = 2)[[1:4; end-3:end]]\nplots = [plot_image(ml_model, test_data[i].features) for i in indices]\nPlots.plot(plots...; size = (1200, 600), layout = (2, 4))","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"There are still some fairly bad mistakes. Can you change the model or training parameters improve to improve things?","category":"page"},{"location":"tutorials/mnist_lux/#JuMP","page":"Adversarial machine learning with Lux.jl","title":"JuMP","text":"","category":"section"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Now that we have a trained machine learning model, we can embed it in a JuMP model.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Here's a function which takes a test case and returns an example that maximizes the probability of the adversarial example.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"function find_adversarial_image(test_case; adversary_label, δ = 0.05)\n model = Model(Ipopt.Optimizer)\n set_silent(model)\n @variable(model, 0 <= x[1:28, 1:28] <= 1)\n @constraint(model, -δ .<= x .- test_case.features .<= δ)\n # Note: we need to use `vec` here because `x` is a 28-by-28 Matrix, but our\n # neural network expects a 28^2 length vector.\n y, _ = MathOptAI.add_predictor(model, ml_model, vec(x))\n @objective(model, Max, y[adversary_label+1] - y[test_case.targets+1])\n optimize!(model)\n @assert is_solved_and_feasible(model)\n return value.(x)\nend","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Let's try finding an adversarial example to the third test image. The image on the left is our input image. The network thinks this is a 1 with probability 99%. The image on the right is the adversarial image. The network thinks this is a 7, although it is less confident.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"x_adversary = find_adversarial_image(test_data[3]; adversary_label = 7);\nPlots.plot(\n plot_image(ml_model, test_data[3].features),\n plot_image(ml_model, Float32.(x_adversary)),\n)","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"This page was generated using Literate.jl.","category":"page"},{"location":"manual/PyTorch/#PyTorch","page":"PyTorch","title":"PyTorch","text":"","category":"section"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"PyTorch is a library for machine learning in Python.","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"MathOptAI supports embedding PyTorch models in JuMP if they are composed of:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"nn.Linear\nnn.ReLU\nnn.Sequential\nnn.Sigmoid\nnn.Tanh","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"Here is an example:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"julia> using JuMP, MathOptAI\n\njulia> model = Model()\n\njulia> @variable(model, x[1:2]);\n\njulia> predictor = MathOptAI.PytorchModel(\"saved_pytorch_model.pt\");\n\njulia> y, _ = MathOptAI.add_predictor(model, predictor, x);","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"(Image: )","category":"page"},{"location":"#MathOptAI.jl","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"","category":"section"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"MathOptAI.jl is a JuMP extension for embedding trained AI, machine learning, and statistical learning models into a JuMP optimization model.","category":"page"},{"location":"#License","page":"MathOptAI.jl","title":"License","text":"","category":"section"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"MathOptAI.jl is provided under a BSD-3 license as part of the Optimization and Machine Learning Toolbox project, O4806.","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"See LICENSE.md for details.","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"Despite the name similarity, this project is not affiliated with OMLT, the Optimization and Machine Learning Toolkit.","category":"page"},{"location":"#Installation","page":"MathOptAI.jl","title":"Installation","text":"","category":"section"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"Install MathOptAI.jl using the Julia package manager:","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"import Pkg\nPkg.add(\"MathOptAI\")","category":"page"},{"location":"#Getting-started","page":"MathOptAI.jl","title":"Getting started","text":"","category":"section"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"Here's an example of using MathOptAI to embed a trained neural network from Flux into a JuMP model. The vector of JuMP variables x is fed as input to the neural network. The output y is a vector of JuMP variables that represents the output layer of the neural network. The formulation object stores the additional variables and constraints that were added to model.","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"julia> using JuMP, MathOptAI, Flux\n\njulia> predictor = Flux.Chain(\n Flux.Dense(28^2 => 32, Flux.sigmoid),\n Flux.Dense(32 => 10),\n Flux.softmax,\n );\n\njulia> #= Train the Flux model. Code not shown for simplicity =#\n\njulia> model = JuMP.Model();\n\njulia> JuMP.@variable(model, 0 <= x[1:28^2] <= 1);\n\njulia> y, formulation = MathOptAI.add_predictor(model, predictor, x);\n\njulia> y\n10-element Vector{VariableRef}:\n moai_SoftMax[1]\n moai_SoftMax[2]\n moai_SoftMax[3]\n moai_SoftMax[4]\n moai_SoftMax[5]\n moai_SoftMax[6]\n moai_SoftMax[7]\n moai_SoftMax[8]\n moai_SoftMax[9]\n moai_SoftMax[10]","category":"page"},{"location":"#Getting-help","page":"MathOptAI.jl","title":"Getting help","text":"","category":"section"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"This package is under active development. For help, questions, comments, and suggestions, please open a GitHub issue.","category":"page"},{"location":"#Inspiration","page":"MathOptAI.jl","title":"Inspiration","text":"","category":"section"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"This project is mainly inspired by two existing projects:","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"OMLT\ngurobi-machinelearning","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"Other works, from which we took less inspiration, include:","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"JANOS\nMeLOn\nENTMOOT\nreluMIP\nOptiCL\nPySCIPOpt-ML","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"The 2024 paper of López-Flores et al. is an excellent summary of the state of the field at the time that we started development of MathOptAI.","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"López-Flores, F.J., Ramírez-Márquez, C., Ponce-Ortega J.M. (2024). Process Systems Engineering Tools for Optimization of Trained Machine Learning Models: Comparative and Perspective. Industrial & Engineering Chemistry Research, 63(32), 13966-13979. DOI: 10.1021/acs.iecr.4c00632","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"EditURL = \"gaussian.jl\"","category":"page"},{"location":"tutorials/gaussian/#Function-fitting-with-AbstractGPs","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"","category":"section"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"The purpose of this tutorial is to explain how to embed a Gaussian Process from AbstractGPs into JuMP.","category":"page"},{"location":"tutorials/gaussian/#Required-packages","page":"Function fitting with AbstractGPs","title":"Required packages","text":"","category":"section"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"This tutorial requires the following packages","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"using JuMP\nusing Test\nimport AbstractGPs\nimport Ipopt\nimport MathOptAI\nimport Plots","category":"page"},{"location":"tutorials/gaussian/#Prediction-model","page":"Function fitting with AbstractGPs","title":"Prediction model","text":"","category":"section"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"Assume that we have some true underlying univariate function:","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"x_domain = 0:0.01:2π\ntrue_function(x) = sin(x)\nPlots.plot(x_domain, true_function.(x_domain); label = \"truth\")","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"We don't know the function, but we have access to a limited set of noisy sample points:","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"N = 20\nx_data = rand(x_domain, N)\nnoisy_sampler(x) = true_function(x) + 0.25 * (2rand() - 1)\ny_data = noisy_sampler.(x_data)\nPlots.scatter!(x_data, y_data; label = \"data\")","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"Using the data, we want to build a predictor y = predictor(x). One choice is a Gaussian Process:","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"fx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.4)\np_fx = AbstractGPs.posterior(fx, y_data)\nPlots.plot!(x_domain, p_fx; label = \"GP\", fillalpha = 0.1)","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"Gaussian Processes fit a mean and variance function:","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"AbstractGPs.mean_and_var(p_fx, [π / 2])","category":"page"},{"location":"tutorials/gaussian/#Decision-model","page":"Function fitting with AbstractGPs","title":"Decision model","text":"","category":"section"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"Our goal for this JuMP model is to embed the Gaussian Process from AbstractGPs into the model and then solve for different fixed values of x to recreate the function that the Gaussian Process has learned to approximate.","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"First, create a JuMP model:","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"model = Model(Ipopt.Optimizer)\nset_silent(model)\n@variable(model, x)","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"Since a Gaussian Process is a infinite dimensional object (its prediction is a distribution), we need some way of converting the Gaussian Process into a finite set of scalar values. For this, we use the Quantile predictor:","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"predictor = MathOptAI.Quantile(p_fx, [0.25, 0.75]);\ny, _ = MathOptAI.add_predictor(model, predictor, [x])","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"Now, visualize the fitted function y = predictor(x) by repeatedly solving the optimization problem for different fixed values of x. Each value of y has two elements: one for the 25th percentile and one for the 75th.","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"X, Y = range(0, 2π; length = 20), Any[]\n@constraint(model, c, x == 0.0)\nfor xi in X\n set_normalized_rhs(c, xi)\n optimize!(model)\n if is_solved_and_feasible(model)\n push!(Y, value.(y))\n else\n push!(Y, [NaN, NaN])\n end\nend\nPlots.plot!(X, reduce(hcat, Y)'; label = [\"P25\" \"P75\"], linewidth = 3)","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"This page was generated using Literate.jl.","category":"page"}] +} diff --git a/v0.1.2/siteinfo.js b/v0.1.2/siteinfo.js new file mode 100644 index 00000000..9cdef155 --- /dev/null +++ b/v0.1.2/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "v0.1.2"; diff --git a/v0.1.2/tutorials/decision_trees.jl b/v0.1.2/tutorials/decision_trees.jl new file mode 100644 index 00000000..d132d588 --- /dev/null +++ b/v0.1.2/tutorials/decision_trees.jl @@ -0,0 +1,138 @@ +# Copyright (c) 2024: Oscar Dowson and contributors #src +# Copyright (c) 2024: Triad National Security, LLC #src +# #src +# Use of this source code is governed by a BSD-style license that can be #src +# found in the LICENSE.md file. #src + +# # Classification problems with DecisionTree.jl + +# The purpose of this tutorial is to explain how to embed a decision tree +# model from [DecisionTree.jl](https://github.com/JuliaAI/DecisionTree.jl) into +# JuMP. + +# The data and example in this tutorial comes from the paper: David Bergman, +# Teng Huang, Philip Brooks, Andrea Lodi, Arvind U. Raghunathan (2021) JANOS: An +# Integrated Predictive and Prescriptive Modeling Framework. INFORMS Journal on +# Computing 34(2):807-816. +# [https://doi.org/10.1287/ijoc.2020.1023](https://doi.org/10.1287/ijoc.2020.1023) + +# ## Required packages + +# This tutorial uses the following packages. + +using JuMP +import CSV +import DataFrames +import Downloads +import DecisionTree +import HiGHS +import MathOptAI +import Statistics + +# ## Data + +# Here is a function to load the data directly from the JANOS repository: + +function read_df(filename) + url = "https://raw.githubusercontent.com/INFORMSJoC/2020.1023/master/data/" + data = Downloads.download(url * filename) + return CSV.read(data, DataFrames.DataFrame) +end + +# There are two important files. The first, `college_student_enroll-s1-1.csv`, +# contains historial admissions data on anonymized students, their SAT score, +# their GPA, their merit scholarships, and whether the enrolled in the college. + +train_df = read_df("college_student_enroll-s1-1.csv") + +# The second, `college_applications6000.csv`, contains the SAT and GPA data of +# students who are currently applying: + +evaluate_df = read_df("college_applications6000.csv") + +# There are 6,000 prospective students: + +n_students = size(evaluate_df, 1) + +# ## Prediction model + +# The first step is to train a logistic regression model to predict the Boolean +# `enroll` column based on the `SAT`, `GPA`, and `merit` columns. + +train_features = Matrix(train_df[:, [:SAT, :GPA, :merit]]) +train_labels = train_df[:, :enroll] +ml_model = DecisionTree.DecisionTreeClassifier(; max_depth = 3) +DecisionTree.fit!(ml_model, train_features, train_labels) +DecisionTree.print_tree(ml_model) + +# ## Decision model + +# Now that we have a trained decision tree, we want a decision model that +# chooses the optimal merit scholarship for each student in: + +evaluate_df + +# Here's an empty JuMP model to start: + +model = Model() + +# First, we add a new columnn to `evaluate_df`, with one JuMP decision variable +# for each row. It is important the the `.merit` column name in `evaluate_df` +# matches the name in `train_df`. + +evaluate_df.merit = @variable(model, 0 <= x_merit[1:n_students] <= 2.5); +evaluate_df + +# Then, we use [`MathOptAI.add_predictor`](@ref) to embed `model_ml` into the +# JuMP `model`. [`MathOptAI.add_predictor`](@ref) returns a vector of variables, +# one for each row in `evaluate_df`, corresponding to the output `enroll` of +# our logistic regression. + +evaluate_features = Matrix(evaluate_df[:, [:SAT, :GPA, :merit]]) +evaluate_df.enroll = mapreduce(vcat, 1:size(evaluate_features, 1)) do i + y, _ = MathOptAI.add_predictor(model, ml_model, evaluate_features[i, :]) + return y +end +evaluate_df + +# The `.enroll` column name in `evaluate_df` is just a name. It doesn't have to +# match the name in `train_df`. + +# The objective of our problem is to maximize the expected number of students +# who enroll: + +@objective(model, Max, sum(evaluate_df.enroll)) + +# Subject to the constraint that we can spend at most `0.2 * n_students` on +# merit scholarships: + +@constraint(model, sum(evaluate_df.merit) <= 0.2 * n_students) + +# Because logistic regression involves a [`Sigmoid`](@ref) layer, we need to use +# a smooth nonlinear optimizer. A common choice is Ipopt. Solve and check the +# optimizer found a feasible solution: + +set_optimizer(model, HiGHS.Optimizer) +set_silent(model) +optimize!(model) +@assert is_solved_and_feasible(model) + +# Let's store the solution in `evaluate_df` for analysis: + +evaluate_df.merit_sol = value.(evaluate_df.merit); +evaluate_df.enroll_sol = value.(evaluate_df.enroll); +evaluate_df + +# ## Solution analysis + +# We expect that just under 2,500 students will enroll: + +sum(evaluate_df.enroll_sol) + +# We awarded merit scholarships to approximately 1 in 6 students: + +count(evaluate_df.merit_sol .> 1e-5) + +# The average merit scholarship was worth just under \$1,000: + +1_000 * Statistics.mean(evaluate_df.merit_sol[evaluate_df.merit_sol.>1e-5]) diff --git a/v0.1.2/tutorials/decision_trees/index.html b/v0.1.2/tutorials/decision_trees/index.html new file mode 100644 index 00000000..daf4899d --- /dev/null +++ b/v0.1.2/tutorials/decision_trees/index.html @@ -0,0 +1,246 @@ + +Classification problems with DecisionTree.jl · MathOptAI.jl
GitHub

Classification problems with DecisionTree.jl

The purpose of this tutorial is to explain how to embed a decision tree model from DecisionTree.jl into JuMP.

The data and example in this tutorial comes from the paper: David Bergman, Teng Huang, Philip Brooks, Andrea Lodi, Arvind U. Raghunathan (2021) JANOS: An Integrated Predictive and Prescriptive Modeling Framework. INFORMS Journal on Computing 34(2):807-816. https://doi.org/10.1287/ijoc.2020.1023

Required packages

This tutorial uses the following packages.

julia> using JuMP
julia> import CSV
julia> import DataFrames
julia> import Downloads
julia> import DecisionTree
julia> import HiGHS
julia> import MathOptAI
julia> import Statistics

Data

Here is a function to load the data directly from the JANOS repository:

julia> function read_df(filename)
+           url = "https://raw.githubusercontent.com/INFORMSJoC/2020.1023/master/data/"
+           data = Downloads.download(url * filename)
+           return CSV.read(data, DataFrames.DataFrame)
+       endread_df (generic function with 1 method)

There are two important files. The first, college_student_enroll-s1-1.csv, contains historial admissions data on anonymized students, their SAT score, their GPA, their merit scholarships, and whether the enrolled in the college.

julia> train_df = read_df("college_student_enroll-s1-1.csv")20000×6 DataFrame
+   Row │ Column1  StudentID  SAT    GPA      merit    enroll 
+       │ Int64    Int64      Int64  Float64  Float64  Int64  
+───────┼─────────────────────────────────────────────────────
+     1 │       1          1   1507     3.72     1.64       0
+     2 │       2          2   1532     3.93     0.52       0
+     3 │       3          3   1487     3.77     1.67       0
+     4 │       4          4   1259     3.05     1.21       1
+     5 │       5          5   1354     3.39     1.65       1
+     6 │       6          6   1334     3.22     0.0        0
+     7 │       7          7   1125     2.73     1.68       1
+     8 │       8          8   1180     2.82     0.0        1
+   ⋮   │    ⋮         ⋮        ⋮       ⋮        ⋮       ⋮
+ 19994 │   19994      19994   1185     3.09     1.16       1
+ 19995 │   19995      19995   1471     3.7      1.05       0
+ 19996 │   19996      19996   1139     3.03     1.21       1
+ 19997 │   19997      19997   1371     3.39     1.26       0
+ 19998 │   19998      19998   1424     3.72     0.85       0
+ 19999 │   19999      19999   1170     3.01     0.73       1
+ 20000 │   20000      20000   1389     3.57     0.55       0
+                                           19985 rows omitted

The second, college_applications6000.csv, contains the SAT and GPA data of students who are currently applying:

julia> evaluate_df = read_df("college_applications6000.csv")6000×3 DataFrame
+  Row │ StudentID  SAT    GPA     
+      │ Int64      Int64  Float64 
+──────┼───────────────────────────
+    1 │         1   1240     3.22
+    2 │         2   1206     2.87
+    3 │         3   1520     3.74
+    4 │         4   1238     3.11
+    5 │         5   1142     2.74
+    6 │         6   1086     2.77
+    7 │         7   1367     3.28
+    8 │         8   1034     2.41
+  ⋮   │     ⋮        ⋮       ⋮
+ 5994 │      5994   1121     2.96
+ 5995 │      5995   1564     4.1
+ 5996 │      5996   1332     3.14
+ 5997 │      5997   1228     2.95
+ 5998 │      5998   1165     2.81
+ 5999 │      5999   1400     3.43
+ 6000 │      6000   1097     2.65
+                 5985 rows omitted

There are 6,000 prospective students:

julia> n_students = size(evaluate_df, 1)6000

Prediction model

The first step is to train a logistic regression model to predict the Boolean enroll column based on the SAT, GPA, and merit columns.

julia> train_features = Matrix(train_df[:, [:SAT, :GPA, :merit]])20000×3 Matrix{Float64}:
+ 1507.0  3.72  1.64
+ 1532.0  3.93  0.52
+ 1487.0  3.77  1.67
+ 1259.0  3.05  1.21
+ 1354.0  3.39  1.65
+ 1334.0  3.22  0.0
+ 1125.0  2.73  1.68
+ 1180.0  2.82  0.0
+ 1098.0  2.91  0.0
+ 1116.0  2.95  0.0
+    ⋮
+ 1048.0  2.51  0.73
+ 1157.0  2.79  2.11
+ 1185.0  3.09  1.16
+ 1471.0  3.7   1.05
+ 1139.0  3.03  1.21
+ 1371.0  3.39  1.26
+ 1424.0  3.72  0.85
+ 1170.0  3.01  0.73
+ 1389.0  3.57  0.55
julia> train_labels = train_df[:, :enroll]20000-element Vector{Int64}:
+ 0
+ 0
+ 0
+ 1
+ 1
+ 0
+ 1
+ 1
+ 1
+ 1
+ ⋮
+ 1
+ 1
+ 1
+ 0
+ 1
+ 0
+ 0
+ 1
+ 0
julia> ml_model = DecisionTree.DecisionTreeClassifier(; max_depth = 3)DecisionTreeClassifier
+max_depth:                3
+min_samples_leaf:         1
+min_samples_split:        2
+min_purity_increase:      0.0
+pruning_purity_threshold: 1.0
+n_subfeatures:            0
+classes:                  nothing
+root:                     nothing
julia> DecisionTree.fit!(ml_model, train_features, train_labels)DecisionTreeClassifier
+max_depth:                3
+min_samples_leaf:         1
+min_samples_split:        2
+min_purity_increase:      0.0
+pruning_purity_threshold: 1.0
+n_subfeatures:            0
+classes:                  [0, 1]
+root:                     Decision Tree
+Leaves: 8
+Depth:  3
julia> DecisionTree.print_tree(ml_model)Feature 1 < 1228.0 ?
+├─ Feature 2 < 3.125 ?
+    ├─ Feature 1 < 1214.0 ?
+        ├─ 1 : 7336/7336
+        └─ 1 : 334/361
+    └─ Feature 3 < 0.255 ?
+        ├─ 0 : 161/220
+        └─ 1 : 121/121
+└─ Feature 1 < 1412.0 ?
+    ├─ Feature 3 < 1.005 ?
+        ├─ 0 : 3600/4046
+        └─ 1 : 1603/2338
+    └─ Feature 3 < 1.865 ?
+        ├─ 0 : 4530/4530
+        └─ 0 : 947/1048

Decision model

Now that we have a trained decision tree, we want a decision model that chooses the optimal merit scholarship for each student in:

julia> evaluate_df6000×3 DataFrame
+  Row │ StudentID  SAT    GPA     
+      │ Int64      Int64  Float64 
+──────┼───────────────────────────
+    1 │         1   1240     3.22
+    2 │         2   1206     2.87
+    3 │         3   1520     3.74
+    4 │         4   1238     3.11
+    5 │         5   1142     2.74
+    6 │         6   1086     2.77
+    7 │         7   1367     3.28
+    8 │         8   1034     2.41
+  ⋮   │     ⋮        ⋮       ⋮
+ 5994 │      5994   1121     2.96
+ 5995 │      5995   1564     4.1
+ 5996 │      5996   1332     3.14
+ 5997 │      5997   1228     2.95
+ 5998 │      5998   1165     2.81
+ 5999 │      5999   1400     3.43
+ 6000 │      6000   1097     2.65
+                 5985 rows omitted

Here's an empty JuMP model to start:

julia> model = Model()A JuMP Model
+├ solver: none
+├ objective_sense: FEASIBILITY_SENSE
+├ num_variables: 0
+├ num_constraints: 0
+└ Names registered in the model: none

First, we add a new columnn to evaluate_df, with one JuMP decision variable for each row. It is important the the .merit column name in evaluate_df matches the name in train_df.

julia> evaluate_df.merit = @variable(model, 0 <= x_merit[1:n_students] <= 2.5);
julia> evaluate_df6000×4 DataFrame
+  Row │ StudentID  SAT    GPA      merit         
+      │ Int64      Int64  Float64  GenericV…     
+──────┼──────────────────────────────────────────
+    1 │         1   1240     3.22  x_merit[1]
+    2 │         2   1206     2.87  x_merit[2]
+    3 │         3   1520     3.74  x_merit[3]
+    4 │         4   1238     3.11  x_merit[4]
+    5 │         5   1142     2.74  x_merit[5]
+    6 │         6   1086     2.77  x_merit[6]
+    7 │         7   1367     3.28  x_merit[7]
+    8 │         8   1034     2.41  x_merit[8]
+  ⋮   │     ⋮        ⋮       ⋮           ⋮
+ 5994 │      5994   1121     2.96  x_merit[5994]
+ 5995 │      5995   1564     4.1   x_merit[5995]
+ 5996 │      5996   1332     3.14  x_merit[5996]
+ 5997 │      5997   1228     2.95  x_merit[5997]
+ 5998 │      5998   1165     2.81  x_merit[5998]
+ 5999 │      5999   1400     3.43  x_merit[5999]
+ 6000 │      6000   1097     2.65  x_merit[6000]
+                                5985 rows omitted

Then, we use MathOptAI.add_predictor to embed model_ml into the JuMP model. MathOptAI.add_predictor returns a vector of variables, one for each row in evaluate_df, corresponding to the output enroll of our logistic regression.

julia> evaluate_features = Matrix(evaluate_df[:, [:SAT, :GPA, :merit]])6000×3 Matrix{JuMP.AffExpr}:
+ 1240  3.22  x_merit[1]
+ 1206  2.87  x_merit[2]
+ 1520  3.74  x_merit[3]
+ 1238  3.11  x_merit[4]
+ 1142  2.74  x_merit[5]
+ 1086  2.77  x_merit[6]
+ 1367  3.28  x_merit[7]
+ 1034  2.41  x_merit[8]
+ 1547  3.82  x_merit[9]
+ 1453  3.65  x_merit[10]
+ ⋮
+ 1299  3.16  x_merit[5992]
+ 1400  3.59  x_merit[5993]
+ 1121  2.96  x_merit[5994]
+ 1564  4.1   x_merit[5995]
+ 1332  3.14  x_merit[5996]
+ 1228  2.95  x_merit[5997]
+ 1165  2.81  x_merit[5998]
+ 1400  3.43  x_merit[5999]
+ 1097  2.65  x_merit[6000]
julia> evaluate_df.enroll = mapreduce(vcat, 1:size(evaluate_features, 1)) do i
+           y, _ = MathOptAI.add_predictor(model, ml_model, evaluate_features[i, :])
+           return y
+       end6000-element Vector{JuMP.VariableRef}:
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ ⋮
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
julia> evaluate_df6000×5 DataFrame
+  Row │ StudentID  SAT    GPA      merit          enroll                       ⋯
+      │ Int64      Int64  Float64  GenericV…      GenericV…                    ⋯
+──────┼─────────────────────────────────────────────────────────────────────────
+    1 │         1   1240     3.22  x_merit[1]     moai_BinaryDecisionTree_valu ⋯
+    2 │         2   1206     2.87  x_merit[2]     moai_BinaryDecisionTree_valu
+    3 │         3   1520     3.74  x_merit[3]     moai_BinaryDecisionTree_valu
+    4 │         4   1238     3.11  x_merit[4]     moai_BinaryDecisionTree_valu
+    5 │         5   1142     2.74  x_merit[5]     moai_BinaryDecisionTree_valu ⋯
+    6 │         6   1086     2.77  x_merit[6]     moai_BinaryDecisionTree_valu
+    7 │         7   1367     3.28  x_merit[7]     moai_BinaryDecisionTree_valu
+    8 │         8   1034     2.41  x_merit[8]     moai_BinaryDecisionTree_valu
+  ⋮   │     ⋮        ⋮       ⋮           ⋮                      ⋮              ⋱
+ 5994 │      5994   1121     2.96  x_merit[5994]  moai_BinaryDecisionTree_valu ⋯
+ 5995 │      5995   1564     4.1   x_merit[5995]  moai_BinaryDecisionTree_valu
+ 5996 │      5996   1332     3.14  x_merit[5996]  moai_BinaryDecisionTree_valu
+ 5997 │      5997   1228     2.95  x_merit[5997]  moai_BinaryDecisionTree_valu
+ 5998 │      5998   1165     2.81  x_merit[5998]  moai_BinaryDecisionTree_valu ⋯
+ 5999 │      5999   1400     3.43  x_merit[5999]  moai_BinaryDecisionTree_valu
+ 6000 │      6000   1097     2.65  x_merit[6000]  moai_BinaryDecisionTree_valu
+                                                  1 column and 5985 rows omitted

The .enroll column name in evaluate_df is just a name. It doesn't have to match the name in train_df.

The objective of our problem is to maximize the expected number of students who enroll:

julia> @objective(model, Max, sum(evaluate_df.enroll))moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + [[...5940 terms omitted...]] + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value

Subject to the constraint that we can spend at most 0.2 * n_students on merit scholarships:

julia> @constraint(model, sum(evaluate_df.merit) <= 0.2 * n_students)x_merit[1] + x_merit[2] + x_merit[3] + x_merit[4] + x_merit[5] + x_merit[6] + x_merit[7] + x_merit[8] + x_merit[9] + x_merit[10] + x_merit[11] + x_merit[12] + x_merit[13] + x_merit[14] + x_merit[15] + x_merit[16] + x_merit[17] + x_merit[18] + x_merit[19] + x_merit[20] + x_merit[21] + x_merit[22] + x_merit[23] + x_merit[24] + x_merit[25] + x_merit[26] + x_merit[27] + x_merit[28] + x_merit[29] + x_merit[30] + [[...5940 terms omitted...]] + x_merit[5971] + x_merit[5972] + x_merit[5973] + x_merit[5974] + x_merit[5975] + x_merit[5976] + x_merit[5977] + x_merit[5978] + x_merit[5979] + x_merit[5980] + x_merit[5981] + x_merit[5982] + x_merit[5983] + x_merit[5984] + x_merit[5985] + x_merit[5986] + x_merit[5987] + x_merit[5988] + x_merit[5989] + x_merit[5990] + x_merit[5991] + x_merit[5992] + x_merit[5993] + x_merit[5994] + x_merit[5995] + x_merit[5996] + x_merit[5997] + x_merit[5998] + x_merit[5999] + x_merit[6000] ≤ 1200

Because logistic regression involves a Sigmoid layer, we need to use a smooth nonlinear optimizer. A common choice is Ipopt. Solve and check the optimizer found a feasible solution:

julia> set_optimizer(model, HiGHS.Optimizer)
julia> set_silent(model)
julia> optimize!(model)
julia> @assert is_solved_and_feasible(model)

Let's store the solution in evaluate_df for analysis:

julia> evaluate_df.merit_sol = value.(evaluate_df.merit);
julia> evaluate_df.enroll_sol = value.(evaluate_df.enroll);
julia> evaluate_df6000×7 DataFrame
+  Row │ StudentID  SAT    GPA      merit          enroll                       ⋯
+      │ Int64      Int64  Float64  GenericV…      GenericV…                    ⋯
+──────┼─────────────────────────────────────────────────────────────────────────
+    1 │         1   1240     3.22  x_merit[1]     moai_BinaryDecisionTree_valu ⋯
+    2 │         2   1206     2.87  x_merit[2]     moai_BinaryDecisionTree_valu
+    3 │         3   1520     3.74  x_merit[3]     moai_BinaryDecisionTree_valu
+    4 │         4   1238     3.11  x_merit[4]     moai_BinaryDecisionTree_valu
+    5 │         5   1142     2.74  x_merit[5]     moai_BinaryDecisionTree_valu ⋯
+    6 │         6   1086     2.77  x_merit[6]     moai_BinaryDecisionTree_valu
+    7 │         7   1367     3.28  x_merit[7]     moai_BinaryDecisionTree_valu
+    8 │         8   1034     2.41  x_merit[8]     moai_BinaryDecisionTree_valu
+  ⋮   │     ⋮        ⋮       ⋮           ⋮                      ⋮              ⋱
+ 5994 │      5994   1121     2.96  x_merit[5994]  moai_BinaryDecisionTree_valu ⋯
+ 5995 │      5995   1564     4.1   x_merit[5995]  moai_BinaryDecisionTree_valu
+ 5996 │      5996   1332     3.14  x_merit[5996]  moai_BinaryDecisionTree_valu
+ 5997 │      5997   1228     2.95  x_merit[5997]  moai_BinaryDecisionTree_valu
+ 5998 │      5998   1165     2.81  x_merit[5998]  moai_BinaryDecisionTree_valu ⋯
+ 5999 │      5999   1400     3.43  x_merit[5999]  moai_BinaryDecisionTree_valu
+ 6000 │      6000   1097     2.65  x_merit[6000]  moai_BinaryDecisionTree_valu
+                                                 3 columns and 5985 rows omitted

Solution analysis

We expect that just under 2,500 students will enroll:

julia> sum(evaluate_df.enroll_sol)3530.0

We awarded merit scholarships to approximately 1 in 6 students:

julia> count(evaluate_df.merit_sol .> 1e-5)1278

The average merit scholarship was worth just under $1,000:

julia> 1_000 * Statistics.mean(evaluate_df.merit_sol[evaluate_df.merit_sol.>1e-5])938.6854460093895

This page was generated using Literate.jl.

diff --git a/v0.1.2/tutorials/gaussian.jl b/v0.1.2/tutorials/gaussian.jl new file mode 100644 index 00000000..3bf78e90 --- /dev/null +++ b/v0.1.2/tutorials/gaussian.jl @@ -0,0 +1,87 @@ +# Copyright (c) 2024: Oscar Dowson and contributors #src +# Copyright (c) 2024: Triad National Security, LLC #src +# #src +# Use of this source code is governed by a BSD-style license that can be #src +# found in the LICENSE.md file. #src + +# # Function fitting with AbstractGPs + +# The purpose of this tutorial is to explain how to embed a Gaussian Process +# from [AbstractGPs](https://github.com/JuliaGaussianProcesses/AbstractGPs.jl) +# into JuMP. + +# ## Required packages + +# This tutorial requires the following packages + +using JuMP +using Test +import AbstractGPs +import Ipopt +import MathOptAI +import Plots + +# ## Prediction model + +# Assume that we have some true underlying univariate function: + +x_domain = 0:0.01:2π +true_function(x) = sin(x) +Plots.plot(x_domain, true_function.(x_domain); label = "truth") + +# We don't know the function, but we have access to a limited set of noisy +# sample points: + +N = 20 +x_data = rand(x_domain, N) +noisy_sampler(x) = true_function(x) + 0.25 * (2rand() - 1) +y_data = noisy_sampler.(x_data) +Plots.scatter!(x_data, y_data; label = "data") + +# Using the data, we want to build a predictor `y = predictor(x)`. One choice is +# a Gaussian Process: + +fx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.4) +p_fx = AbstractGPs.posterior(fx, y_data) +Plots.plot!(x_domain, p_fx; label = "GP", fillalpha = 0.1) + +# Gaussian Processes fit a mean and variance function: + +AbstractGPs.mean_and_var(p_fx, [π / 2]) + +# ## Decision model + +# Our goal for this JuMP model is to embed the Gaussian Process from AbstractGPs +# into the model and then solve for different fixed values of `x` to recreate +# the function that the Gaussian Process has learned to approximate. + +# First, create a JuMP model: + +model = Model(Ipopt.Optimizer) +set_silent(model) +@variable(model, x) + +# Since a Gaussian Process is a infinite dimensional object (its prediction is a +# distribution), we need some way of converting the Gaussian Process into a +# finite set of scalar values. For this, we use the [`Quantile`](@ref) +# predictor: + +predictor = MathOptAI.Quantile(p_fx, [0.25, 0.75]); +y, _ = MathOptAI.add_predictor(model, predictor, [x]) + +# Now, visualize the fitted function `y = predictor(x)` by repeatedly solving +# the optimization problem for different fixed values of `x`. Each value of `y` +# has two elements: one for the 25th percentile and one for the 75th. + +X, Y = range(0, 2π; length = 20), Any[] +@constraint(model, c, x == 0.0) +for xi in X + set_normalized_rhs(c, xi) + optimize!(model) + if is_solved_and_feasible(model) + push!(Y, value.(y)) + else + push!(Y, [NaN, NaN]) + end +end +Plots.plot!(X, reduce(hcat, Y)'; label = ["P25" "P75"], linewidth = 3) diff --git a/v0.1.2/tutorials/gaussian/133ea4ce.svg b/v0.1.2/tutorials/gaussian/133ea4ce.svg new file mode 100644 index 00000000..d8c32506 --- /dev/null +++ b/v0.1.2/tutorials/gaussian/133ea4ce.svg @@ -0,0 +1,71 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.2/tutorials/gaussian/3cf4958e.svg b/v0.1.2/tutorials/gaussian/3cf4958e.svg new file mode 100644 index 00000000..67c1d810 --- /dev/null +++ b/v0.1.2/tutorials/gaussian/3cf4958e.svg @@ -0,0 +1,82 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.2/tutorials/gaussian/4ec3291e.svg b/v0.1.2/tutorials/gaussian/4ec3291e.svg new file mode 100644 index 00000000..61cf2fa9 --- /dev/null +++ b/v0.1.2/tutorials/gaussian/4ec3291e.svg @@ -0,0 +1,76 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.2/tutorials/gaussian/661896d3.svg b/v0.1.2/tutorials/gaussian/661896d3.svg new file mode 100644 index 00000000..59382b9b --- /dev/null +++ b/v0.1.2/tutorials/gaussian/661896d3.svg @@ -0,0 +1,50 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.2/tutorials/gaussian/index.html b/v0.1.2/tutorials/gaussian/index.html new file mode 100644 index 00000000..f02cc7e5 --- /dev/null +++ b/v0.1.2/tutorials/gaussian/index.html @@ -0,0 +1,31 @@ + +Function fitting with AbstractGPs · MathOptAI.jl
GitHub

Function fitting with AbstractGPs

The purpose of this tutorial is to explain how to embed a Gaussian Process from AbstractGPs into JuMP.

Required packages

This tutorial requires the following packages

using JuMP
+using Test
+import AbstractGPs
+import Ipopt
+import MathOptAI
+import Plots

Prediction model

Assume that we have some true underlying univariate function:

x_domain = 0:0.01:2π
+true_function(x) = sin(x)
+Plots.plot(x_domain, true_function.(x_domain); label = "truth")
Example block output

We don't know the function, but we have access to a limited set of noisy sample points:

N = 20
+x_data = rand(x_domain, N)
+noisy_sampler(x) = true_function(x) + 0.25 * (2rand() - 1)
+y_data = noisy_sampler.(x_data)
+Plots.scatter!(x_data, y_data; label = "data")
Example block output

Using the data, we want to build a predictor y = predictor(x). One choice is a Gaussian Process:

fx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.4)
+p_fx = AbstractGPs.posterior(fx, y_data)
+Plots.plot!(x_domain, p_fx; label = "GP", fillalpha = 0.1)
Example block output

Gaussian Processes fit a mean and variance function:

AbstractGPs.mean_and_var(p_fx, [π / 2])
([1.0140389306269286], [0.13858632888403088])

Decision model

Our goal for this JuMP model is to embed the Gaussian Process from AbstractGPs into the model and then solve for different fixed values of x to recreate the function that the Gaussian Process has learned to approximate.

First, create a JuMP model:

model = Model(Ipopt.Optimizer)
+set_silent(model)
+@variable(model, x)

\[ x \]

Since a Gaussian Process is a infinite dimensional object (its prediction is a distribution), we need some way of converting the Gaussian Process into a finite set of scalar values. For this, we use the Quantile predictor:

predictor = MathOptAI.Quantile(p_fx, [0.25, 0.75]);
+y, _ = MathOptAI.add_predictor(model, predictor, [x])
(JuMP.VariableRef[moai_quantile[1], moai_quantile[2]], Quantile(_, [0.25, 0.75])
+├ variables [0]
+└ constraints [0])

Now, visualize the fitted function y = predictor(x) by repeatedly solving the optimization problem for different fixed values of x. Each value of y has two elements: one for the 25th percentile and one for the 75th.

X, Y = range(0, 2π; length = 20), Any[]
+@constraint(model, c, x == 0.0)
+for xi in X
+    set_normalized_rhs(c, xi)
+    optimize!(model)
+    if is_solved_and_feasible(model)
+        push!(Y, value.(y))
+    else
+        push!(Y, [NaN, NaN])
+    end
+end
+Plots.plot!(X, reduce(hcat, Y)'; label = ["P25" "P75"], linewidth = 3)
Example block output

This page was generated using Literate.jl.

diff --git a/v0.1.2/tutorials/mnist.jl b/v0.1.2/tutorials/mnist.jl new file mode 100644 index 00000000..afb34aab --- /dev/null +++ b/v0.1.2/tutorials/mnist.jl @@ -0,0 +1,171 @@ +# Copyright (c) 2024: Oscar Dowson and contributors #src +# Copyright (c) 2024: Triad National Security, LLC #src +# #src +# Use of this source code is governed by a BSD-style license that can be #src +# found in the LICENSE.md file. #src + +# # Adversarial machine learning with Flux.jl + +# The purpose of this tutorial is to explain how to embed a neural network model +# from [Flux.jl](https://github.com/FluxML/Flux.jl) into JuMP. + +# ## Required packages + +# This tutorial requires the following packages + +using JuMP +import Flux +import Ipopt +import MathOptAI +import MLDatasets +import Plots + +# ## Data + +# This tutorial uses images from the MNIST dataset. + +# We load the predefined train and test splits: + +train_data = MLDatasets.MNIST(; split = :train) + +#- + +test_data = MLDatasets.MNIST(; split = :test) + +# Since the data are images, it is helpful to plot them. (This requires a +# transpose and reversing the rows to get the orientation correct.) + +function plot_image(x::Matrix; kwargs...) + return Plots.heatmap( + x'[size(x, 1):-1:1, :]; + xlims = (1, size(x, 2)), + ylims = (1, size(x, 1)), + aspect_ratio = true, + legend = false, + xaxis = false, + yaxis = false, + kwargs..., + ) +end + +function plot_image(instance::NamedTuple) + return plot_image(instance.features; title = "Label = $(instance.targets)") +end + +Plots.plot([plot_image(train_data[i]) for i in 1:6]...; layout = (2, 3)) + +# ## Training + +# We use a simple neural network with one hidden layer and a sigmoid activation +# function. (There are better performing networks; try experimenting.) + +ml_model = Flux.Chain( + Flux.Dense(28^2 => 32, Flux.sigmoid), + Flux.Dense(32 => 10), + Flux.softmax, +) + +# Here is a function to load our data into the format that `ml_model` expects: +function data_loader(data; batchsize, shuffle = false) + x = reshape(data.features, 28^2, :) + y = Flux.onehotbatch(data.targets, 0:9) + return Flux.DataLoader((x, y); batchsize, shuffle) +end + +# and here is a function to score the percentage of correct labels, where we +# assign a label by choosing the label of the highest softmax in the final +# layer. + +function score_model(ml_model, data) + x, y = only(data_loader(data; batchsize = length(data))) + y_hat = ml_model(x) + is_correct = Flux.onecold(y) .== Flux.onecold(y_hat) + p = round(100 * sum(is_correct) / length(is_correct); digits = 2) + println("Accuracy = $p %") + return +end + +# The accuracy of our model is only around 10% before training: + +score_model(ml_model, train_data) +score_model(ml_model, test_data) + +# Let's improve that by training our model. + +# !!! note +# It is not the purpose of this tutorial to explain how Flux works; see the +# documentation at [https://fluxml.ai](https://fluxml.ai) for more details. +# Changing the number of epochs or the learning rate can improve the loss. + +begin + train_loader = data_loader(train_data; batchsize = 256, shuffle = true) + optimizer_state = Flux.setup(Flux.Adam(3e-4), ml_model) + for epoch in 1:30 + loss = 0.0 + for (x, y) in train_loader + loss_batch, gradient = Flux.withgradient(ml_model) do model + return Flux.crossentropy(model(x), y) + end + Flux.update!(optimizer_state, ml_model, only(gradient)) + loss += loss_batch + end + loss = round(loss / length(train_loader); digits = 4) + print("Epoch $epoch: loss = $loss\t") + score_model(ml_model, test_data) + end +end + +# Here are the first eight predictions of the test data: + +function plot_image(ml_model, x::Matrix) + score, index = findmax(ml_model(vec(x))) + title = "Predicted: $(index - 1) ($(round(Int, 100 * score))%)" + return plot_image(x; title) +end + +plots = [plot_image(ml_model, test_data[i].features) for i in 1:8] +Plots.plot(plots...; size = (1200, 600), layout = (2, 4)) + +# We can also look at the best and worst four predictions: + +x, y = only(data_loader(test_data; batchsize = length(test_data))) +losses = Flux.crossentropy(ml_model(x), y; agg = identity) +indices = sortperm(losses; dims = 2)[[1:4; end-3:end]] +plots = [plot_image(ml_model, test_data[i].features) for i in indices] +Plots.plot(plots...; size = (1200, 600), layout = (2, 4)) + +# There are still some fairly bad mistakes. Can you change the model or training +# parameters improve to improve things? + +# ## JuMP + +# Now that we have a trained machine learning model, we can embed it in a JuMP +# model. + +# Here's a function which takes a test case and returns an example that +# maximizes the probability of the adversarial example. + +function find_adversarial_image(test_case; adversary_label, δ = 0.05) + model = Model(Ipopt.Optimizer) + set_silent(model) + @variable(model, 0 <= x[1:28, 1:28] <= 1) + @constraint(model, -δ .<= x .- test_case.features .<= δ) + ## Note: we need to use `vec` here because `x` is a 28-by-28 Matrix, but our + ## neural network expects a 28^2 length vector. + y, _ = MathOptAI.add_predictor(model, ml_model, vec(x)) + @objective(model, Max, y[adversary_label+1] - y[test_case.targets+1]) + optimize!(model) + @assert is_solved_and_feasible(model) + return value.(x) +end + +# Let's try finding an adversarial example to the third test image. The image on +# the left is our input image. The network thinks this is a `1` with probability +# 99%. The image on the right is the adversarial image. The network thinks this +# is a `7`, although it is less confident. + +x_adversary = find_adversarial_image(test_data[3]; adversary_label = 7); +Plots.plot( + plot_image(ml_model, test_data[3].features), + plot_image(ml_model, Float32.(x_adversary)), +) diff --git a/v0.1.2/tutorials/mnist/88b719b6.svg b/v0.1.2/tutorials/mnist/88b719b6.svg new file mode 100644 index 00000000..0a336635 --- /dev/null +++ b/v0.1.2/tutorials/mnist/88b719b6.svg @@ -0,0 +1,1199 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.2/tutorials/mnist/d3ad6436.svg b/v0.1.2/tutorials/mnist/d3ad6436.svg new file mode 100644 index 00000000..90d7c654 --- /dev/null +++ b/v0.1.2/tutorials/mnist/d3ad6436.svg @@ -0,0 +1,328 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.2/tutorials/mnist/dac86b7c.svg b/v0.1.2/tutorials/mnist/dac86b7c.svg new file mode 100644 index 00000000..32ac07f0 --- /dev/null +++ b/v0.1.2/tutorials/mnist/dac86b7c.svg @@ -0,0 +1,511 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.2/tutorials/mnist/f5d64a4f.svg b/v0.1.2/tutorials/mnist/f5d64a4f.svg new file mode 100644 index 00000000..5ebd9581 --- /dev/null +++ b/v0.1.2/tutorials/mnist/f5d64a4f.svg @@ -0,0 +1,1212 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.2/tutorials/mnist/index.html b/v0.1.2/tutorials/mnist/index.html new file mode 100644 index 00000000..8f2cd812 --- /dev/null +++ b/v0.1.2/tutorials/mnist/index.html @@ -0,0 +1,125 @@ + +Adversarial machine learning with Flux.jl · MathOptAI.jl
GitHub

Adversarial machine learning with Flux.jl

The purpose of this tutorial is to explain how to embed a neural network model from Flux.jl into JuMP.

Required packages

This tutorial requires the following packages

using JuMP
+import Flux
+import Ipopt
+import MathOptAI
+import MLDatasets
+import Plots

Data

This tutorial uses images from the MNIST dataset.

We load the predefined train and test splits:

train_data = MLDatasets.MNIST(; split = :train)
dataset MNIST:
+  metadata  =>    Dict{String, Any} with 3 entries
+  split     =>    :train
+  features  =>    28×28×60000 Array{Float32, 3}
+  targets   =>    60000-element Vector{Int64}
test_data = MLDatasets.MNIST(; split = :test)
dataset MNIST:
+  metadata  =>    Dict{String, Any} with 3 entries
+  split     =>    :test
+  features  =>    28×28×10000 Array{Float32, 3}
+  targets   =>    10000-element Vector{Int64}

Since the data are images, it is helpful to plot them. (This requires a transpose and reversing the rows to get the orientation correct.)

function plot_image(x::Matrix; kwargs...)
+    return Plots.heatmap(
+        x'[size(x, 1):-1:1, :];
+        xlims = (1, size(x, 2)),
+        ylims = (1, size(x, 1)),
+        aspect_ratio = true,
+        legend = false,
+        xaxis = false,
+        yaxis = false,
+        kwargs...,
+    )
+end
+
+function plot_image(instance::NamedTuple)
+    return plot_image(instance.features; title = "Label = $(instance.targets)")
+end
+
+Plots.plot([plot_image(train_data[i]) for i in 1:6]...; layout = (2, 3))
Example block output

Training

We use a simple neural network with one hidden layer and a sigmoid activation function. (There are better performing networks; try experimenting.)

ml_model = Flux.Chain(
+    Flux.Dense(28^2 => 32, Flux.sigmoid),
+    Flux.Dense(32 => 10),
+    Flux.softmax,
+)
Chain(
+  Dense(784 => 32, σ),                  # 25_120 parameters
+  Dense(32 => 10),                      # 330 parameters
+  NNlib.softmax,
+)                   # Total: 4 arrays, 25_450 parameters, 99.617 KiB.

Here is a function to load our data into the format that ml_model expects:

function data_loader(data; batchsize, shuffle = false)
+    x = reshape(data.features, 28^2, :)
+    y = Flux.onehotbatch(data.targets, 0:9)
+    return Flux.DataLoader((x, y); batchsize, shuffle)
+end
data_loader (generic function with 1 method)

and here is a function to score the percentage of correct labels, where we assign a label by choosing the label of the highest softmax in the final layer.

function score_model(ml_model, data)
+    x, y = only(data_loader(data; batchsize = length(data)))
+    y_hat = ml_model(x)
+    is_correct = Flux.onecold(y) .== Flux.onecold(y_hat)
+    p = round(100 * sum(is_correct) / length(is_correct); digits = 2)
+    println("Accuracy = $p %")
+    return
+end
score_model (generic function with 1 method)

The accuracy of our model is only around 10% before training:

score_model(ml_model, train_data)
+score_model(ml_model, test_data)
Accuracy = 6.95 %
+Accuracy = 6.87 %

Let's improve that by training our model.

Note

It is not the purpose of this tutorial to explain how Flux works; see the documentation at https://fluxml.ai for more details. Changing the number of epochs or the learning rate can improve the loss.

begin
+    train_loader = data_loader(train_data; batchsize = 256, shuffle = true)
+    optimizer_state = Flux.setup(Flux.Adam(3e-4), ml_model)
+    for epoch in 1:30
+        loss = 0.0
+        for (x, y) in train_loader
+            loss_batch, gradient = Flux.withgradient(ml_model) do model
+                return Flux.crossentropy(model(x), y)
+            end
+            Flux.update!(optimizer_state, ml_model, only(gradient))
+            loss += loss_batch
+        end
+        loss = round(loss / length(train_loader); digits = 4)
+        print("Epoch $epoch: loss = $loss\t")
+        score_model(ml_model, test_data)
+    end
+end
Epoch 1: loss = 1.8024	Accuracy = 78.24 %
+Epoch 2: loss = 1.1538	Accuracy = 84.95 %
+Epoch 3: loss = 0.8443	Accuracy = 87.27 %
+Epoch 4: loss = 0.6684	Accuracy = 88.84 %
+Epoch 5: loss = 0.5594	Accuracy = 89.81 %
+Epoch 6: loss = 0.4871	Accuracy = 90.4 %
+Epoch 7: loss = 0.4364	Accuracy = 90.84 %
+Epoch 8: loss = 0.3989	Accuracy = 91.13 %
+Epoch 9: loss = 0.3699	Accuracy = 91.3 %
+Epoch 10: loss = 0.3469	Accuracy = 91.59 %
+Epoch 11: loss = 0.3281	Accuracy = 91.75 %
+Epoch 12: loss = 0.3126	Accuracy = 91.89 %
+Epoch 13: loss = 0.2996	Accuracy = 92.19 %
+Epoch 14: loss = 0.2878	Accuracy = 92.3 %
+Epoch 15: loss = 0.2776	Accuracy = 92.53 %
+Epoch 16: loss = 0.2687	Accuracy = 92.72 %
+Epoch 17: loss = 0.2605	Accuracy = 92.81 %
+Epoch 18: loss = 0.2527	Accuracy = 93.0 %
+Epoch 19: loss = 0.246	Accuracy = 93.09 %
+Epoch 20: loss = 0.2393	Accuracy = 93.24 %
+Epoch 21: loss = 0.2334	Accuracy = 93.27 %
+Epoch 22: loss = 0.2281	Accuracy = 93.47 %
+Epoch 23: loss = 0.2228	Accuracy = 93.52 %
+Epoch 24: loss = 0.2178	Accuracy = 93.69 %
+Epoch 25: loss = 0.2131	Accuracy = 93.79 %
+Epoch 26: loss = 0.2088	Accuracy = 93.92 %
+Epoch 27: loss = 0.2047	Accuracy = 93.96 %
+Epoch 28: loss = 0.2012	Accuracy = 94.07 %
+Epoch 29: loss = 0.1969	Accuracy = 94.17 %
+Epoch 30: loss = 0.1937	Accuracy = 94.24 %

Here are the first eight predictions of the test data:

function plot_image(ml_model, x::Matrix)
+    score, index = findmax(ml_model(vec(x)))
+    title = "Predicted: $(index - 1) ($(round(Int, 100 * score))%)"
+    return plot_image(x; title)
+end
+
+plots = [plot_image(ml_model, test_data[i].features) for i in 1:8]
+Plots.plot(plots...; size = (1200, 600), layout = (2, 4))
Example block output

We can also look at the best and worst four predictions:

x, y = only(data_loader(test_data; batchsize = length(test_data)))
+losses = Flux.crossentropy(ml_model(x), y; agg = identity)
+indices = sortperm(losses; dims = 2)[[1:4; end-3:end]]
+plots = [plot_image(ml_model, test_data[i].features) for i in indices]
+Plots.plot(plots...; size = (1200, 600), layout = (2, 4))
Example block output

There are still some fairly bad mistakes. Can you change the model or training parameters improve to improve things?

JuMP

Now that we have a trained machine learning model, we can embed it in a JuMP model.

Here's a function which takes a test case and returns an example that maximizes the probability of the adversarial example.

function find_adversarial_image(test_case; adversary_label, δ = 0.05)
+    model = Model(Ipopt.Optimizer)
+    set_silent(model)
+    @variable(model, 0 <= x[1:28, 1:28] <= 1)
+    @constraint(model, -δ .<= x .- test_case.features .<= δ)
+    # Note: we need to use `vec` here because `x` is a 28-by-28 Matrix, but our
+    # neural network expects a 28^2 length vector.
+    y, _ = MathOptAI.add_predictor(model, ml_model, vec(x))
+    @objective(model, Max, y[adversary_label+1] - y[test_case.targets+1])
+    optimize!(model)
+    @assert is_solved_and_feasible(model)
+    return value.(x)
+end
find_adversarial_image (generic function with 1 method)

Let's try finding an adversarial example to the third test image. The image on the left is our input image. The network thinks this is a 1 with probability 99%. The image on the right is the adversarial image. The network thinks this is a 7, although it is less confident.

x_adversary = find_adversarial_image(test_data[3]; adversary_label = 7);
+Plots.plot(
+    plot_image(ml_model, test_data[3].features),
+    plot_image(ml_model, Float32.(x_adversary)),
+)
Example block output

This page was generated using Literate.jl.

diff --git a/v0.1.2/tutorials/mnist_lux.jl b/v0.1.2/tutorials/mnist_lux.jl new file mode 100644 index 00000000..8135da68 --- /dev/null +++ b/v0.1.2/tutorials/mnist_lux.jl @@ -0,0 +1,186 @@ +# Copyright (c) 2024: Oscar Dowson and contributors #src +# Copyright (c) 2024: Triad National Security, LLC #src +# #src +# Use of this source code is governed by a BSD-style license that can be #src +# found in the LICENSE.md file. #src + +# # Adversarial machine learning with Lux.jl + +# The purpose of this tutorial is to explain how to embed a neural network model +# from [Lux.jl](https://github.com/SciML/Lux.jl) into JuMP. + +# ## Required packages + +# This tutorial requires the following packages + +using JuMP +import Lux +import Ipopt +import MathOptAI +import MLDatasets +import MLUtils +import OneHotArrays +import Optimisers +import Plots +import Random +import Zygote + +# ## Data + +# This tutorial uses images from the MNIST dataset. + +# We load the predefined train and test splits: + +train_data = MLDatasets.MNIST(; split = :train) + +#- + +test_data = MLDatasets.MNIST(; split = :test) + +# Since the data are images, it is helpful to plot them. (This requires a +# transpose and reversing the rows to get the orientation correct.) + +function plot_image(x::Matrix; kwargs...) + return Plots.heatmap( + x'[size(x, 1):-1:1, :]; + xlims = (1, size(x, 2)), + ylims = (1, size(x, 1)), + aspect_ratio = true, + legend = false, + xaxis = false, + yaxis = false, + kwargs..., + ) +end + +function plot_image(instance::NamedTuple) + return plot_image(instance.features; title = "Label = $(instance.targets)") +end + +Plots.plot([plot_image(train_data[i]) for i in 1:6]...; layout = (2, 3)) + +# ## Training + +# We use a simple neural network with one hidden layer and a sigmoid activation +# function. (There are better performing networks; try experimenting.) + +chain = Lux.Chain( + Lux.Dense(28^2 => 32, Lux.sigmoid), + Lux.Dense(32 => 10), + Lux.softmax, +) +rng = Random.MersenneTwister(); +parameters, state = Lux.setup(rng, chain) +ml_model = (chain, parameters, state); + +# Here is a function to load our data into the format that `ml_model` expects: +function data_loader(data; batchsize, shuffle = false) + x = reshape(data.features, 28^2, :) + y = OneHotArrays.onehotbatch(data.targets, 0:9) + return MLUtils.DataLoader((x, y); batchsize, shuffle) +end + +# and here is a function to score the percentage of correct labels, where we +# assign a label by choosing the label of the highest softmax in the final +# layer. + +function score_model(ml_model, data) + chain, parameters, state = ml_model + x, y = only(data_loader(data; batchsize = length(data))) + y_hat, _ = chain(x, parameters, state) + is_correct = OneHotArrays.onecold(y) .== OneHotArrays.onecold(y_hat) + p = round(100 * sum(is_correct) / length(is_correct); digits = 2) + println("Accuracy = $p %") + return +end + +# The accuracy of our model is only around 10% before training: + +score_model(ml_model, train_data) +score_model(ml_model, test_data) + +# Let's improve that by training our model. + +# !!! note +# It is not the purpose of this tutorial to explain how Lux works; see the +# documentation at [https://lux.csail.mit.edu](https://lux.csail.mit.edu/stable/) +# for more details. Changing the number of epochs or the learning rate can +# improve the loss. + +begin + train_loader = data_loader(train_data; batchsize = 256, shuffle = true) + optimizer_state = Optimisers.setup(Optimisers.Adam(0.0003f0), parameters) + for epoch in 1:30 + loss = 0.0 + for (x, y) in train_loader + global state + (loss_batch, state), pullback = Zygote.pullback(parameters) do p + y_model, new_state = chain(x, p, state) + return Lux.CrossEntropyLoss()(y_model, y), new_state + end + gradients = only(pullback((one(loss), nothing))) + Optimisers.update!(optimizer_state, parameters, gradients) + loss += loss_batch + end + loss = round(loss / length(train_loader); digits = 4) + print("Epoch $epoch: loss = $loss\t") + score_model(ml_model, test_data) + end +end + +# Here are the first eight predictions of the test data: + +function plot_image(ml_model, x::Matrix) + y, _ = chain(vec(x), parameters, state) + score, index = findmax(y) + title = "Predicted: $(index - 1) ($(round(Int, 100 * score))%)" + return plot_image(x; title) +end + +plots = [plot_image(ml_model, test_data[i].features) for i in 1:8] +Plots.plot(plots...; size = (1200, 600), layout = (2, 4)) + +# We can also look at the best and worst four predictions: + +x, y = only(data_loader(test_data; batchsize = length(test_data))) +y_model, _ = chain(x, parameters, state) +losses = Lux.CrossEntropyLoss(; agg = identity)(y_model, y) +indices = sortperm(losses; dims = 2)[[1:4; end-3:end]] +plots = [plot_image(ml_model, test_data[i].features) for i in indices] +Plots.plot(plots...; size = (1200, 600), layout = (2, 4)) + +# There are still some fairly bad mistakes. Can you change the model or training +# parameters improve to improve things? + +# ## JuMP + +# Now that we have a trained machine learning model, we can embed it in a JuMP +# model. + +# Here's a function which takes a test case and returns an example that +# maximizes the probability of the adversarial example. + +function find_adversarial_image(test_case; adversary_label, δ = 0.05) + model = Model(Ipopt.Optimizer) + set_silent(model) + @variable(model, 0 <= x[1:28, 1:28] <= 1) + @constraint(model, -δ .<= x .- test_case.features .<= δ) + ## Note: we need to use `vec` here because `x` is a 28-by-28 Matrix, but our + ## neural network expects a 28^2 length vector. + y, _ = MathOptAI.add_predictor(model, ml_model, vec(x)) + @objective(model, Max, y[adversary_label+1] - y[test_case.targets+1]) + optimize!(model) + @assert is_solved_and_feasible(model) + return value.(x) +end + +# Let's try finding an adversarial example to the third test image. The image on +# the left is our input image. The network thinks this is a `1` with probability +# 99%. The image on the right is the adversarial image. The network thinks this +# is a `7`, although it is less confident. + +x_adversary = find_adversarial_image(test_data[3]; adversary_label = 7); +Plots.plot( + plot_image(ml_model, test_data[3].features), + plot_image(ml_model, Float32.(x_adversary)), +) diff --git a/v0.1.2/tutorials/mnist_lux/06a1f82d.svg b/v0.1.2/tutorials/mnist_lux/06a1f82d.svg new file mode 100644 index 00000000..abc4df8b --- /dev/null +++ b/v0.1.2/tutorials/mnist_lux/06a1f82d.svg @@ -0,0 +1,1199 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.2/tutorials/mnist_lux/44d82a2c.svg b/v0.1.2/tutorials/mnist_lux/44d82a2c.svg new file mode 100644 index 00000000..9e1c17c2 --- /dev/null +++ b/v0.1.2/tutorials/mnist_lux/44d82a2c.svg @@ -0,0 +1,325 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.2/tutorials/mnist_lux/65ac60bc.svg b/v0.1.2/tutorials/mnist_lux/65ac60bc.svg new file mode 100644 index 00000000..991488f9 --- /dev/null +++ b/v0.1.2/tutorials/mnist_lux/65ac60bc.svg @@ -0,0 +1,511 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.2/tutorials/mnist_lux/e3376dad.svg b/v0.1.2/tutorials/mnist_lux/e3376dad.svg new file mode 100644 index 00000000..ee842f65 --- /dev/null +++ b/v0.1.2/tutorials/mnist_lux/e3376dad.svg @@ -0,0 +1,1223 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.2/tutorials/mnist_lux/index.html b/v0.1.2/tutorials/mnist_lux/index.html new file mode 100644 index 00000000..8d7f5a66 --- /dev/null +++ b/v0.1.2/tutorials/mnist_lux/index.html @@ -0,0 +1,135 @@ + +Adversarial machine learning with Lux.jl · MathOptAI.jl
GitHub

Adversarial machine learning with Lux.jl

The purpose of this tutorial is to explain how to embed a neural network model from Lux.jl into JuMP.

Required packages

This tutorial requires the following packages

using JuMP
+import Lux
+import Ipopt
+import MathOptAI
+import MLDatasets
+import MLUtils
+import OneHotArrays
+import Optimisers
+import Plots
+import Random
+import Zygote

Data

This tutorial uses images from the MNIST dataset.

We load the predefined train and test splits:

train_data = MLDatasets.MNIST(; split = :train)
dataset MNIST:
+  metadata  =>    Dict{String, Any} with 3 entries
+  split     =>    :train
+  features  =>    28×28×60000 Array{Float32, 3}
+  targets   =>    60000-element Vector{Int64}
test_data = MLDatasets.MNIST(; split = :test)
dataset MNIST:
+  metadata  =>    Dict{String, Any} with 3 entries
+  split     =>    :test
+  features  =>    28×28×10000 Array{Float32, 3}
+  targets   =>    10000-element Vector{Int64}

Since the data are images, it is helpful to plot them. (This requires a transpose and reversing the rows to get the orientation correct.)

function plot_image(x::Matrix; kwargs...)
+    return Plots.heatmap(
+        x'[size(x, 1):-1:1, :];
+        xlims = (1, size(x, 2)),
+        ylims = (1, size(x, 1)),
+        aspect_ratio = true,
+        legend = false,
+        xaxis = false,
+        yaxis = false,
+        kwargs...,
+    )
+end
+
+function plot_image(instance::NamedTuple)
+    return plot_image(instance.features; title = "Label = $(instance.targets)")
+end
+
+Plots.plot([plot_image(train_data[i]) for i in 1:6]...; layout = (2, 3))
Example block output

Training

We use a simple neural network with one hidden layer and a sigmoid activation function. (There are better performing networks; try experimenting.)

chain = Lux.Chain(
+    Lux.Dense(28^2 => 32, Lux.sigmoid),
+    Lux.Dense(32 => 10),
+    Lux.softmax,
+)
+rng = Random.MersenneTwister();
+parameters, state = Lux.setup(rng, chain)
+ml_model = (chain, parameters, state);

Here is a function to load our data into the format that ml_model expects:

function data_loader(data; batchsize, shuffle = false)
+    x = reshape(data.features, 28^2, :)
+    y = OneHotArrays.onehotbatch(data.targets, 0:9)
+    return MLUtils.DataLoader((x, y); batchsize, shuffle)
+end
data_loader (generic function with 1 method)

and here is a function to score the percentage of correct labels, where we assign a label by choosing the label of the highest softmax in the final layer.

function score_model(ml_model, data)
+    chain, parameters, state = ml_model
+    x, y = only(data_loader(data; batchsize = length(data)))
+    y_hat, _ = chain(x, parameters, state)
+    is_correct = OneHotArrays.onecold(y) .== OneHotArrays.onecold(y_hat)
+    p = round(100 * sum(is_correct) / length(is_correct); digits = 2)
+    println("Accuracy = $p %")
+    return
+end
score_model (generic function with 1 method)

The accuracy of our model is only around 10% before training:

score_model(ml_model, train_data)
+score_model(ml_model, test_data)
Accuracy = 16.73 %
+Accuracy = 17.14 %

Let's improve that by training our model.

Note

It is not the purpose of this tutorial to explain how Lux works; see the documentation at https://lux.csail.mit.edu for more details. Changing the number of epochs or the learning rate can improve the loss.

begin
+    train_loader = data_loader(train_data; batchsize = 256, shuffle = true)
+    optimizer_state = Optimisers.setup(Optimisers.Adam(0.0003f0), parameters)
+    for epoch in 1:30
+        loss = 0.0
+        for (x, y) in train_loader
+            global state
+            (loss_batch, state), pullback = Zygote.pullback(parameters) do p
+                y_model, new_state = chain(x, p, state)
+                return Lux.CrossEntropyLoss()(y_model, y), new_state
+            end
+            gradients = only(pullback((one(loss), nothing)))
+            Optimisers.update!(optimizer_state, parameters, gradients)
+            loss += loss_batch
+        end
+        loss = round(loss / length(train_loader); digits = 4)
+        print("Epoch $epoch: loss = $loss\t")
+        score_model(ml_model, test_data)
+    end
+end
Epoch 1: loss = 1.7649	Accuracy = 78.28 %
+Epoch 2: loss = 1.1331	Accuracy = 84.29 %
+Epoch 3: loss = 0.8295	Accuracy = 87.4 %
+Epoch 4: loss = 0.6577	Accuracy = 88.52 %
+Epoch 5: loss = 0.5523	Accuracy = 89.24 %
+Epoch 6: loss = 0.4836	Accuracy = 89.82 %
+Epoch 7: loss = 0.4348	Accuracy = 90.37 %
+Epoch 8: loss = 0.3992	Accuracy = 90.67 %
+Epoch 9: loss = 0.3718	Accuracy = 90.98 %
+Epoch 10: loss = 0.3497	Accuracy = 91.25 %
+Epoch 11: loss = 0.3316	Accuracy = 91.51 %
+Epoch 12: loss = 0.3161	Accuracy = 91.92 %
+Epoch 13: loss = 0.3028	Accuracy = 92.18 %
+Epoch 14: loss = 0.2914	Accuracy = 92.38 %
+Epoch 15: loss = 0.281	Accuracy = 92.62 %
+Epoch 16: loss = 0.272	Accuracy = 92.69 %
+Epoch 17: loss = 0.2639	Accuracy = 92.92 %
+Epoch 18: loss = 0.256	Accuracy = 92.95 %
+Epoch 19: loss = 0.2489	Accuracy = 93.07 %
+Epoch 20: loss = 0.2422	Accuracy = 93.24 %
+Epoch 21: loss = 0.2363	Accuracy = 93.28 %
+Epoch 22: loss = 0.2309	Accuracy = 93.43 %
+Epoch 23: loss = 0.2253	Accuracy = 93.46 %
+Epoch 24: loss = 0.2204	Accuracy = 93.61 %
+Epoch 25: loss = 0.2159	Accuracy = 93.66 %
+Epoch 26: loss = 0.2112	Accuracy = 93.75 %
+Epoch 27: loss = 0.2068	Accuracy = 93.8 %
+Epoch 28: loss = 0.2028	Accuracy = 93.94 %
+Epoch 29: loss = 0.1991	Accuracy = 94.0 %
+Epoch 30: loss = 0.1955	Accuracy = 94.05 %

Here are the first eight predictions of the test data:

function plot_image(ml_model, x::Matrix)
+    y, _ = chain(vec(x), parameters, state)
+    score, index = findmax(y)
+    title = "Predicted: $(index - 1) ($(round(Int, 100 * score))%)"
+    return plot_image(x; title)
+end
+
+plots = [plot_image(ml_model, test_data[i].features) for i in 1:8]
+Plots.plot(plots...; size = (1200, 600), layout = (2, 4))
Example block output

We can also look at the best and worst four predictions:

x, y = only(data_loader(test_data; batchsize = length(test_data)))
+y_model, _ = chain(x, parameters, state)
+losses = Lux.CrossEntropyLoss(; agg = identity)(y_model, y)
+indices = sortperm(losses; dims = 2)[[1:4; end-3:end]]
+plots = [plot_image(ml_model, test_data[i].features) for i in indices]
+Plots.plot(plots...; size = (1200, 600), layout = (2, 4))
Example block output

There are still some fairly bad mistakes. Can you change the model or training parameters improve to improve things?

JuMP

Now that we have a trained machine learning model, we can embed it in a JuMP model.

Here's a function which takes a test case and returns an example that maximizes the probability of the adversarial example.

function find_adversarial_image(test_case; adversary_label, δ = 0.05)
+    model = Model(Ipopt.Optimizer)
+    set_silent(model)
+    @variable(model, 0 <= x[1:28, 1:28] <= 1)
+    @constraint(model, -δ .<= x .- test_case.features .<= δ)
+    # Note: we need to use `vec` here because `x` is a 28-by-28 Matrix, but our
+    # neural network expects a 28^2 length vector.
+    y, _ = MathOptAI.add_predictor(model, ml_model, vec(x))
+    @objective(model, Max, y[adversary_label+1] - y[test_case.targets+1])
+    optimize!(model)
+    @assert is_solved_and_feasible(model)
+    return value.(x)
+end
find_adversarial_image (generic function with 1 method)

Let's try finding an adversarial example to the third test image. The image on the left is our input image. The network thinks this is a 1 with probability 99%. The image on the right is the adversarial image. The network thinks this is a 7, although it is less confident.

x_adversary = find_adversarial_image(test_data[3]; adversary_label = 7);
+Plots.plot(
+    plot_image(ml_model, test_data[3].features),
+    plot_image(ml_model, Float32.(x_adversary)),
+)
Example block output

This page was generated using Literate.jl.

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For example, if you +# have an existing Python installation (with PyTorch installed), and it is +# available in the current conda environment, set: +# +# ```julia +# ENV["JULIA_CONDAPKG_BACKEND"] = "Current" +# ``` +# +# before importing PythonCall.jl. If the Python installation can be found on +# the path and it is not in a conda environment, set: +# +# ```julia +# ENV["JULIA_CONDAPKG_BACKEND"] = "Null" +# ``` +# +# If `python` is not on your path, you may additionally need to set +# `JULIA_PYTHONCALL_EXE`, for example, to: +# +# ```julia +# ENV["JULIA_PYTHONCALL_EXE"] = "python3" +# ``` + +# ## Required packages + +# This tutorial requires the following packages + +using JuMP +using Test +import Ipopt +import MathOptAI +import Plots + +# ## Training a model + +# The following script builds and trains a simple neural network in PyTorch. +# For simplicity, we do not evaluate out-of-sample test performance, or use +# a batched data loader. In general, you should train your model in Python, +# and then use `torch.save(model, filename)` to save it to a `.pt` file for +# later use in Julia. + +# The model is unimportant, but for this example, we are trying to fit noisy +# observations of the function ``f(x) = x^2 - 2x``. + +# In Python, I ran: +# ```python +# #!/usr/bin/python3 +# import torch +# model = torch.nn.Sequential( +# torch.nn.Linear(1, 16), +# torch.nn.ReLU(), +# torch.nn.Linear(16, 1), +# ) +# +# n = 1024 +# x = torch.arange(-2, 2 + 4 / (n - 1), 4 / (n - 1)).reshape(n, 1) +# loss_fn = torch.nn.MSELoss() +# optimizer = torch.optim.Adam(model.parameters(), lr=0.01) +# for epoch in range(100): +# optimizer.zero_grad() +# N = torch.normal(torch.zeros(n, 1), torch.ones(n, 1)) +# y = x ** 2 -2 * x + 0.1 * N +# loss = loss_fn(model(x), y) +# loss.backward() +# optimizer.step() +# +# torch.save(model, "model.pt") +# ``` + +# ## JuMP model + +# Our goal for this JuMP model is to load the Neural Network from PyTorch into +# the objective function, and then minimize the objective for different fixed +# values of `x` to recreate the function that the Neural Network has learned to +# approximate. + +# First, create a JuMP model: + +model = Model(Ipopt.Optimizer) +set_silent(model) +@variable(model, x) + +# Then, load the model from PyTorch using [`MathOptAI.PytorchModel`](@ref): + +ml_model = MathOptAI.PytorchModel(joinpath(@__DIR__, "model.pt")) +y, _ = MathOptAI.add_predictor(model, ml_model, [x]) +@objective(model, Min, only(y)) + +# Now, visualize the fitted function `y = ml_model(x)` by repeatedly solving the +# optimization problem for different fixed values of `x`: + +X, Y = -2:0.1:2, Float64[] +@constraint(model, c, x == 0.0) +for xi in X + set_normalized_rhs(c, xi) + optimize!(model) + @test is_solved_and_feasible(model) + push!(Y, objective_value(model)) +end +Plots.plot(x -> x^2 - 2x, X; label = "Truth", linestype = :dot) +Plots.plot!(X, Y; label = "Fitted") diff --git a/v0.1.2/tutorials/pytorch/009d3b6f.svg b/v0.1.2/tutorials/pytorch/009d3b6f.svg new file mode 100644 index 00000000..9f13933a --- /dev/null +++ b/v0.1.2/tutorials/pytorch/009d3b6f.svg @@ -0,0 +1,48 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.2/tutorials/pytorch/index.html b/v0.1.2/tutorials/pytorch/index.html new file mode 100644 index 00000000..bc2d4990 --- /dev/null +++ b/v0.1.2/tutorials/pytorch/index.html @@ -0,0 +1,39 @@ + +Function fitting with PyTorch · MathOptAI.jl
GitHub

Function fitting with PyTorch

The purpose of this tutorial is to explain how to embed a neural network model from PyTorch into JuMP.

Python integration

MathOptAI uses PythonCall.jl to call from Julia into Python.

See CondaPkg.jl for more control over how to link Julia to an existing Python environment. For example, if you have an existing Python installation (with PyTorch installed), and it is available in the current conda environment, set:

ENV["JULIA_CONDAPKG_BACKEND"] = "Current"

before importing PythonCall.jl. If the Python installation can be found on the path and it is not in a conda environment, set:

ENV["JULIA_CONDAPKG_BACKEND"] = "Null"

If python is not on your path, you may additionally need to set JULIA_PYTHONCALL_EXE, for example, to:

ENV["JULIA_PYTHONCALL_EXE"] = "python3"

Required packages

This tutorial requires the following packages

using JuMP
+using Test
+import Ipopt
+import MathOptAI
+import Plots

Training a model

The following script builds and trains a simple neural network in PyTorch. For simplicity, we do not evaluate out-of-sample test performance, or use a batched data loader. In general, you should train your model in Python, and then use torch.save(model, filename) to save it to a .pt file for later use in Julia.

The model is unimportant, but for this example, we are trying to fit noisy observations of the function $f(x) = x^2 - 2x$.

In Python, I ran:

#!/usr/bin/python3
+import torch
+model = torch.nn.Sequential(
+    torch.nn.Linear(1, 16),
+    torch.nn.ReLU(),
+    torch.nn.Linear(16, 1),
+)
+
+n = 1024
+x = torch.arange(-2, 2 + 4 / (n - 1), 4 / (n - 1)).reshape(n, 1)
+loss_fn = torch.nn.MSELoss()
+optimizer = torch.optim.Adam(model.parameters(), lr=0.01)
+for epoch in range(100):
+    optimizer.zero_grad()
+    N = torch.normal(torch.zeros(n, 1), torch.ones(n, 1))
+    y = x ** 2 -2 * x + 0.1 * N
+    loss = loss_fn(model(x), y)
+    loss.backward()
+    optimizer.step()
+
+torch.save(model, "model.pt")

JuMP model

Our goal for this JuMP model is to load the Neural Network from PyTorch into the objective function, and then minimize the objective for different fixed values of x to recreate the function that the Neural Network has learned to approximate.

First, create a JuMP model:

model = Model(Ipopt.Optimizer)
+set_silent(model)
+@variable(model, x)

\[ x \]

Then, load the model from PyTorch using MathOptAI.PytorchModel:

ml_model = MathOptAI.PytorchModel(joinpath(@__DIR__, "model.pt"))
+y, _ = MathOptAI.add_predictor(model, ml_model, [x])
+@objective(model, Min, only(y))

\[ moai\_Affine_{1} \]

Now, visualize the fitted function y = ml_model(x) by repeatedly solving the optimization problem for different fixed values of x:

X, Y = -2:0.1:2, Float64[]
+@constraint(model, c, x == 0.0)
+for xi in X
+    set_normalized_rhs(c, xi)
+    optimize!(model)
+    @test is_solved_and_feasible(model)
+    push!(Y, objective_value(model))
+end
+Plots.plot(x -> x^2 - 2x, X; label = "Truth", linestype = :dot)
+Plots.plot!(X, Y; label = "Fitted")
Example block output

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diff --git a/v0.1.2/tutorials/student_enrollment.jl b/v0.1.2/tutorials/student_enrollment.jl new file mode 100644 index 00000000..fc1497ca --- /dev/null +++ b/v0.1.2/tutorials/student_enrollment.jl @@ -0,0 +1,134 @@ +# Copyright (c) 2024: Oscar Dowson and contributors #src +# Copyright (c) 2024: Triad National Security, LLC #src +# #src +# Use of this source code is governed by a BSD-style license that can be #src +# found in the LICENSE.md file. #src + +# # Logistic regression with GLM.jl + +# The purpose of this tutorial is to explain how to embed a logistic regression +# model from [GLM.jl](https://github.com/JuliaStats/GLM.jl) into JuMP. + +# The data and example in this tutorial comes from the paper: David Bergman, +# Teng Huang, Philip Brooks, Andrea Lodi, Arvind U. Raghunathan (2021) JANOS: An +# Integrated Predictive and Prescriptive Modeling Framework. INFORMS Journal on +# Computing 34(2):807-816. +# [https://doi.org/10.1287/ijoc.2020.1023](https://doi.org/10.1287/ijoc.2020.1023) + +# ## Required packages + +# This tutorial uses the following packages. + +using JuMP +import CSV +import DataFrames +import Downloads +import GLM +import Ipopt +import MathOptAI +import Statistics + +# ## Data + +# Here is a function to load the data directly from the JANOS repository: + +function read_df(filename) + url = "https://raw.githubusercontent.com/INFORMSJoC/2020.1023/master/data/" + data = Downloads.download(url * filename) + return CSV.read(data, DataFrames.DataFrame) +end + +# There are two important files. The first, `college_student_enroll-s1-1.csv`, +# contains historial admissions data on anonymized students, their SAT score, +# their GPA, their merit scholarships, and whether the enrolled in the college. + +train_df = read_df("college_student_enroll-s1-1.csv") + +# The second, `college_applications6000.csv`, contains the SAT and GPA data of +# students who are currently applying: + +evaluate_df = read_df("college_applications6000.csv") + +# There are 6,000 prospective students: + +n_students = size(evaluate_df, 1) + +# ## Prediction model + +# The first step is to train a logistic regression model to predict the Boolean +# `enroll` column based on the `SAT`, `GPA`, and `merit` columns. + +model_glm = GLM.glm( + GLM.@formula(enroll ~ 0 + SAT + GPA + merit), + train_df, + GLM.Bernoulli(), +) + +# ## Decision model + +# Now that we have a trained logistic regression model, we want a decision model +# that chooses the optimal merit scholarship for each student in + +evaluate_df + +# Here's an empty JuMP model to start: + +model = Model() + +# First, we add a new columnn to `evaluate_df`, with one JuMP decision variable +# for each row. It is important the the `.merit` column name in `evaluate_df` +# matches the name in `train_df`. + +evaluate_df.merit = @variable(model, 0 <= x_merit[1:n_students] <= 2.5); +evaluate_df + +# Then, we use [`MathOptAI.add_predictor`](@ref) to embed `model_glm` into the +# JuMP `model`. [`MathOptAI.add_predictor`](@ref) returns a vector of variables, +# one for each row inn `evaluate_df`, corresponding to the output `enroll` of +# our logistic regression. + +evaluate_df.enroll, _ = MathOptAI.add_predictor(model, model_glm, evaluate_df); +evaluate_df + +# The `.enroll` column name in `evaluate_df` is just a name. It doesn't have to +# match the name in `train_df`. + +# The objective of our problem is to maximize the expected number of students +# who enroll: + +@objective(model, Max, sum(evaluate_df.enroll)) + +# Subject to the constraint that we can spend at most `0.2 * n_students` on +# merit scholarships: + +@constraint(model, sum(evaluate_df.merit) <= 0.2 * n_students) + +# Because logistic regression involves a [`Sigmoid`](@ref) layer, we need to use +# a smooth nonlinear optimizer. A common choice is Ipopt. Solve and check the +# optimizer found a feasible solution: + +set_optimizer(model, Ipopt.Optimizer) +set_silent(model) +optimize!(model) +@assert is_solved_and_feasible(model) +solution_summary(model) + +# Let's store the solution in `evaluate_df` for analysis: + +evaluate_df.merit_sol = value.(evaluate_df.merit); +evaluate_df.enroll_sol = value.(evaluate_df.enroll); +evaluate_df + +# ## Solution analysis + +# We expect that just under 2,500 students will enroll: + +sum(evaluate_df.enroll_sol) + +# We awarded merit scholarships to approximately 1 in 6 students: + +count(evaluate_df.merit_sol .> 1e-5) + +# The average merit scholarship was worth just over \$1,000: + +1_000 * Statistics.mean(evaluate_df.merit_sol[evaluate_df.merit_sol.>1e-5]) diff --git a/v0.1.2/tutorials/student_enrollment/index.html b/v0.1.2/tutorials/student_enrollment/index.html new file mode 100644 index 00000000..5523b315 --- /dev/null +++ b/v0.1.2/tutorials/student_enrollment/index.html @@ -0,0 +1,162 @@ + +Logistic regression with GLM.jl · MathOptAI.jl
GitHub

Logistic regression with GLM.jl

The purpose of this tutorial is to explain how to embed a logistic regression model from GLM.jl into JuMP.

The data and example in this tutorial comes from the paper: David Bergman, Teng Huang, Philip Brooks, Andrea Lodi, Arvind U. Raghunathan (2021) JANOS: An Integrated Predictive and Prescriptive Modeling Framework. INFORMS Journal on Computing 34(2):807-816. https://doi.org/10.1287/ijoc.2020.1023

Required packages

This tutorial uses the following packages.

julia> using JuMP
julia> import CSV
julia> import DataFrames
julia> import Downloads
julia> import GLM
julia> import Ipopt
julia> import MathOptAI
julia> import Statistics

Data

Here is a function to load the data directly from the JANOS repository:

julia> function read_df(filename)
+           url = "https://raw.githubusercontent.com/INFORMSJoC/2020.1023/master/data/"
+           data = Downloads.download(url * filename)
+           return CSV.read(data, DataFrames.DataFrame)
+       endread_df (generic function with 1 method)

There are two important files. The first, college_student_enroll-s1-1.csv, contains historial admissions data on anonymized students, their SAT score, their GPA, their merit scholarships, and whether the enrolled in the college.

julia> train_df = read_df("college_student_enroll-s1-1.csv")20000×6 DataFrame
+   Row │ Column1  StudentID  SAT    GPA      merit    enroll 
+       │ Int64    Int64      Int64  Float64  Float64  Int64  
+───────┼─────────────────────────────────────────────────────
+     1 │       1          1   1507     3.72     1.64       0
+     2 │       2          2   1532     3.93     0.52       0
+     3 │       3          3   1487     3.77     1.67       0
+     4 │       4          4   1259     3.05     1.21       1
+     5 │       5          5   1354     3.39     1.65       1
+     6 │       6          6   1334     3.22     0.0        0
+     7 │       7          7   1125     2.73     1.68       1
+     8 │       8          8   1180     2.82     0.0        1
+   ⋮   │    ⋮         ⋮        ⋮       ⋮        ⋮       ⋮
+ 19994 │   19994      19994   1185     3.09     1.16       1
+ 19995 │   19995      19995   1471     3.7      1.05       0
+ 19996 │   19996      19996   1139     3.03     1.21       1
+ 19997 │   19997      19997   1371     3.39     1.26       0
+ 19998 │   19998      19998   1424     3.72     0.85       0
+ 19999 │   19999      19999   1170     3.01     0.73       1
+ 20000 │   20000      20000   1389     3.57     0.55       0
+                                           19985 rows omitted

The second, college_applications6000.csv, contains the SAT and GPA data of students who are currently applying:

julia> evaluate_df = read_df("college_applications6000.csv")6000×3 DataFrame
+  Row │ StudentID  SAT    GPA     
+      │ Int64      Int64  Float64 
+──────┼───────────────────────────
+    1 │         1   1240     3.22
+    2 │         2   1206     2.87
+    3 │         3   1520     3.74
+    4 │         4   1238     3.11
+    5 │         5   1142     2.74
+    6 │         6   1086     2.77
+    7 │         7   1367     3.28
+    8 │         8   1034     2.41
+  ⋮   │     ⋮        ⋮       ⋮
+ 5994 │      5994   1121     2.96
+ 5995 │      5995   1564     4.1
+ 5996 │      5996   1332     3.14
+ 5997 │      5997   1228     2.95
+ 5998 │      5998   1165     2.81
+ 5999 │      5999   1400     3.43
+ 6000 │      6000   1097     2.65
+                 5985 rows omitted

There are 6,000 prospective students:

julia> n_students = size(evaluate_df, 1)6000

Prediction model

The first step is to train a logistic regression model to predict the Boolean enroll column based on the SAT, GPA, and merit columns.

julia> model_glm = GLM.glm(
+           GLM.@formula(enroll ~ 0 + SAT + GPA + merit),
+           train_df,
+           GLM.Bernoulli(),
+       )StatsModels.TableRegressionModel{GLM.GeneralizedLinearModel{GLM.GlmResp{Vector{Float64}, Distributions.Bernoulli{Float64}, GLM.LogitLink}, GLM.DensePredChol{Float64, LinearAlgebra.CholeskyPivoted{Float64, Matrix{Float64}, Vector{Int64}}}}, Matrix{Float64}}
+
+enroll ~ 0 + SAT + GPA + merit
+
+Coefficients:
+──────────────────────────────────────────────────────────────────────────
+             Coef.   Std. Error      z  Pr(>|z|)    Lower 95%    Upper 95%
+──────────────────────────────────────────────────────────────────────────
+SAT     0.00243882  0.000309312   7.88    <1e-14   0.00183258   0.00304506
+GPA    -1.09868     0.123796     -8.87    <1e-18  -1.34132     -0.856045
+merit   0.248294    0.0191086    12.99    <1e-37   0.210842     0.285747
+──────────────────────────────────────────────────────────────────────────

Decision model

Now that we have a trained logistic regression model, we want a decision model that chooses the optimal merit scholarship for each student in

julia> evaluate_df6000×3 DataFrame
+  Row │ StudentID  SAT    GPA     
+      │ Int64      Int64  Float64 
+──────┼───────────────────────────
+    1 │         1   1240     3.22
+    2 │         2   1206     2.87
+    3 │         3   1520     3.74
+    4 │         4   1238     3.11
+    5 │         5   1142     2.74
+    6 │         6   1086     2.77
+    7 │         7   1367     3.28
+    8 │         8   1034     2.41
+  ⋮   │     ⋮        ⋮       ⋮
+ 5994 │      5994   1121     2.96
+ 5995 │      5995   1564     4.1
+ 5996 │      5996   1332     3.14
+ 5997 │      5997   1228     2.95
+ 5998 │      5998   1165     2.81
+ 5999 │      5999   1400     3.43
+ 6000 │      6000   1097     2.65
+                 5985 rows omitted

Here's an empty JuMP model to start:

julia> model = Model()A JuMP Model
+├ solver: none
+├ objective_sense: FEASIBILITY_SENSE
+├ num_variables: 0
+├ num_constraints: 0
+└ Names registered in the model: none

First, we add a new columnn to evaluate_df, with one JuMP decision variable for each row. It is important the the .merit column name in evaluate_df matches the name in train_df.

julia> evaluate_df.merit = @variable(model, 0 <= x_merit[1:n_students] <= 2.5);
julia> evaluate_df6000×4 DataFrame
+  Row │ StudentID  SAT    GPA      merit         
+      │ Int64      Int64  Float64  GenericV…     
+──────┼──────────────────────────────────────────
+    1 │         1   1240     3.22  x_merit[1]
+    2 │         2   1206     2.87  x_merit[2]
+    3 │         3   1520     3.74  x_merit[3]
+    4 │         4   1238     3.11  x_merit[4]
+    5 │         5   1142     2.74  x_merit[5]
+    6 │         6   1086     2.77  x_merit[6]
+    7 │         7   1367     3.28  x_merit[7]
+    8 │         8   1034     2.41  x_merit[8]
+  ⋮   │     ⋮        ⋮       ⋮           ⋮
+ 5994 │      5994   1121     2.96  x_merit[5994]
+ 5995 │      5995   1564     4.1   x_merit[5995]
+ 5996 │      5996   1332     3.14  x_merit[5996]
+ 5997 │      5997   1228     2.95  x_merit[5997]
+ 5998 │      5998   1165     2.81  x_merit[5998]
+ 5999 │      5999   1400     3.43  x_merit[5999]
+ 6000 │      6000   1097     2.65  x_merit[6000]
+                                5985 rows omitted

Then, we use MathOptAI.add_predictor to embed model_glm into the JuMP model. MathOptAI.add_predictor returns a vector of variables, one for each row inn evaluate_df, corresponding to the output enroll of our logistic regression.

julia> evaluate_df.enroll, _ = MathOptAI.add_predictor(model, model_glm, evaluate_df);
julia> evaluate_df6000×5 DataFrame
+  Row │ StudentID  SAT    GPA      merit          enroll          
+      │ Int64      Int64  Float64  GenericV…      GenericV…       
+──────┼───────────────────────────────────────────────────────────
+    1 │         1   1240     3.22  x_merit[1]     moai_Sigmoid[1]
+    2 │         2   1206     2.87  x_merit[2]     moai_Sigmoid[1]
+    3 │         3   1520     3.74  x_merit[3]     moai_Sigmoid[1]
+    4 │         4   1238     3.11  x_merit[4]     moai_Sigmoid[1]
+    5 │         5   1142     2.74  x_merit[5]     moai_Sigmoid[1]
+    6 │         6   1086     2.77  x_merit[6]     moai_Sigmoid[1]
+    7 │         7   1367     3.28  x_merit[7]     moai_Sigmoid[1]
+    8 │         8   1034     2.41  x_merit[8]     moai_Sigmoid[1]
+  ⋮   │     ⋮        ⋮       ⋮           ⋮               ⋮
+ 5994 │      5994   1121     2.96  x_merit[5994]  moai_Sigmoid[1]
+ 5995 │      5995   1564     4.1   x_merit[5995]  moai_Sigmoid[1]
+ 5996 │      5996   1332     3.14  x_merit[5996]  moai_Sigmoid[1]
+ 5997 │      5997   1228     2.95  x_merit[5997]  moai_Sigmoid[1]
+ 5998 │      5998   1165     2.81  x_merit[5998]  moai_Sigmoid[1]
+ 5999 │      5999   1400     3.43  x_merit[5999]  moai_Sigmoid[1]
+ 6000 │      6000   1097     2.65  x_merit[6000]  moai_Sigmoid[1]
+                                                 5985 rows omitted

The .enroll column name in evaluate_df is just a name. It doesn't have to match the name in train_df.

The objective of our problem is to maximize the expected number of students who enroll:

julia> @objective(model, Max, sum(evaluate_df.enroll))moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + [[...5940 terms omitted...]] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1]

Subject to the constraint that we can spend at most 0.2 * n_students on merit scholarships:

julia> @constraint(model, sum(evaluate_df.merit) <= 0.2 * n_students)x_merit[1] + x_merit[2] + x_merit[3] + x_merit[4] + x_merit[5] + x_merit[6] + x_merit[7] + x_merit[8] + x_merit[9] + x_merit[10] + x_merit[11] + x_merit[12] + x_merit[13] + x_merit[14] + x_merit[15] + x_merit[16] + x_merit[17] + x_merit[18] + x_merit[19] + x_merit[20] + x_merit[21] + x_merit[22] + x_merit[23] + x_merit[24] + x_merit[25] + x_merit[26] + x_merit[27] + x_merit[28] + x_merit[29] + x_merit[30] + [[...5940 terms omitted...]] + x_merit[5971] + x_merit[5972] + x_merit[5973] + x_merit[5974] + x_merit[5975] + x_merit[5976] + x_merit[5977] + x_merit[5978] + x_merit[5979] + x_merit[5980] + x_merit[5981] + x_merit[5982] + x_merit[5983] + x_merit[5984] + x_merit[5985] + x_merit[5986] + x_merit[5987] + x_merit[5988] + x_merit[5989] + x_merit[5990] + x_merit[5991] + x_merit[5992] + x_merit[5993] + x_merit[5994] + x_merit[5995] + x_merit[5996] + x_merit[5997] + x_merit[5998] + x_merit[5999] + x_merit[6000] ≤ 1200

Because logistic regression involves a Sigmoid layer, we need to use a smooth nonlinear optimizer. A common choice is Ipopt. Solve and check the optimizer found a feasible solution:

julia> set_optimizer(model, Ipopt.Optimizer)
julia> set_silent(model)
julia> optimize!(model)
julia> @assert is_solved_and_feasible(model)
julia> solution_summary(model)* Solver : Ipopt
+
+* Status
+  Result count       : 1
+  Termination status : LOCALLY_SOLVED
+  Message from the solver:
+  "Solve_Succeeded"
+
+* Candidate solution (result #1)
+  Primal status      : FEASIBLE_POINT
+  Dual status        : FEASIBLE_POINT
+  Objective value    : 2.48820e+03
+  Dual objective value : -4.91918e+02
+
+* Work counters
+  Solve time (sec)   : 5.77478e+00
+  Barrier iterations : 142

Let's store the solution in evaluate_df for analysis:

julia> evaluate_df.merit_sol = value.(evaluate_df.merit);
julia> evaluate_df.enroll_sol = value.(evaluate_df.enroll);
julia> evaluate_df6000×7 DataFrame
+  Row │ StudentID  SAT    GPA      merit          enroll           merit_sol   ⋯
+      │ Int64      Int64  Float64  GenericV…      GenericV…        Float64     ⋯
+──────┼─────────────────────────────────────────────────────────────────────────
+    1 │         1   1240     3.22  x_merit[1]     moai_Sigmoid[1]  6.37389e-7  ⋯
+    2 │         2   1206     2.87  x_merit[2]     moai_Sigmoid[1]  1.08151
+    3 │         3   1520     3.74  x_merit[3]     moai_Sigmoid[1]  1.03717e-6
+    4 │         4   1238     3.11  x_merit[4]     moai_Sigmoid[1]  1.06046e-6
+    5 │         5   1142     2.74  x_merit[5]     moai_Sigmoid[1]  1.13489     ⋯
+    6 │         6   1086     2.77  x_merit[6]     moai_Sigmoid[1]  1.0759e-6
+    7 │         7   1367     3.28  x_merit[7]     moai_Sigmoid[1]  2.33948e-6
+    8 │         8   1034     2.41  x_merit[8]     moai_Sigmoid[1]  0.735482
+  ⋮   │     ⋮        ⋮       ⋮           ⋮               ⋮             ⋮       ⋱
+ 5994 │      5994   1121     2.96  x_merit[5994]  moai_Sigmoid[1]  6.26387e-7  ⋯
+ 5995 │      5995   1564     4.1   x_merit[5995]  moai_Sigmoid[1]  3.58792e-7
+ 5996 │      5996   1332     3.14  x_merit[5996]  moai_Sigmoid[1]  1.03863
+ 5997 │      5997   1228     2.95  x_merit[5997]  moai_Sigmoid[1]  1.21941
+ 5998 │      5998   1165     2.81  x_merit[5998]  moai_Sigmoid[1]  1.21872     ⋯
+ 5999 │      5999   1400     3.43  x_merit[5999]  moai_Sigmoid[1]  1.33971e-6
+ 6000 │      6000   1097     2.65  x_merit[6000]  moai_Sigmoid[1]  1.17865
+                                                  1 column and 5985 rows omitted

Solution analysis

We expect that just under 2,500 students will enroll:

julia> sum(evaluate_df.enroll_sol)2488.1951671444017

We awarded merit scholarships to approximately 1 in 6 students:

julia> count(evaluate_df.merit_sol .> 1e-5)1152

The average merit scholarship was worth just over $1,000:

julia> 1_000 * Statistics.mean(evaluate_df.merit_sol[evaluate_df.merit_sol.>1e-5])1041.6622990671967

This page was generated using Literate.jl.

diff --git a/v0.1.3/.documenter-siteinfo.json b/v0.1.3/.documenter-siteinfo.json new file mode 100644 index 00000000..396373f6 --- /dev/null +++ b/v0.1.3/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-10-24T03:43:22","documenter_version":"1.7.0"}} \ No newline at end of file diff --git a/v0.1.3/api/index.html b/v0.1.3/api/index.html new file mode 100644 index 00000000..2d5a2576 --- /dev/null +++ b/v0.1.3/api/index.html @@ -0,0 +1,944 @@ + +API Reference · MathOptAI.jl
GitHub

API Reference

This page lists the public API of MathOptAI.

Info

This page is an unstructured list of the MathOptAI API. For a more structured overview, read the Manual or Tutorial parts of this documentation.

Load all of the public the API into the current scope with:

using MathOptAI

Alternatively, load only the module with:

import MathOptAI

and then prefix all calls with MathOptAI. to create MathOptAI.<NAME>.

AbstractPredictor

add_predictor

MathOptAI.add_predictor — Function
add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::AbstractPredictor,
+    x::Vector,
+)::Vector

Return a Vector representing y such that y = predictor(x).

The element type of x is deliberately unspecified. The vector x may contain any mix of scalar constants, JuMP decision variables, and scalar JuMP functions like AffExpr, QuadExpr, or NonlinearExpr.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.Affine([2.0, 3.0])
+Affine(A, b) [input: 2, output: 1]
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Affine[1]
+
+julia> formulation
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ 2 x[1] + 3 x[2] - moai_Affine[1] = 0
source

build_predictor

MathOptAI.build_predictor — Function
MathOptAI.build_predictor(predictor::DecisionTree.Root)

Convert a binary decision tree from DecisionTree.jl to a BinaryDecisionTree.

Example

julia> using MathOptAI, DecisionTree
+
+julia> truth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)
+truth (generic function with 1 method)
+
+julia> features = abs.(sin.((1:10) .* (3:4)'));
+
+julia> size(features)
+(10, 2)
+
+julia> labels = truth.(Vector.(eachrow(features)));
+
+julia> ml_model = DecisionTree.build_tree(labels, features)
+Decision Tree
+Leaves: 3
+Depth:  2
+
+julia> MathOptAI.build_predictor(ml_model)
+BinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]
source
build_predictor(extension; kwargs...)::AbstractPredictor

A uniform interface to convert various extension types to an AbstractPredictor.

See the various extension docstrings for details.

source
MathOptAI.build_predictor(
+    predictor::Tuple{<:Lux.Chain,<:NamedTuple,<:NamedTuple};
+    config::Dict = Dict{Any,Any}(),
+)

Convert a trained neural network from Lux.jl to a Pipeline.

Supported layers

  • Lux.Dense
  • Lux.Scale

Supported activation functions

  • Lux.relu
  • Lux.sigmoid
  • Lux.softplus
  • Lux.softmax
  • Lux.tanh

Keyword arguments

  • config: a dictionary that maps supported Lux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Lux.sigmoid => MathOptAI.Sigmoid() or Lux.relu => MathOptAI.QuadraticReLU().

Example

julia> using Lux, MathOptAI, Random
+
+julia> rng = Random.MersenneTwister();
+
+julia> chain = Lux.Chain(Lux.Dense(1 => 16, Lux.relu), Lux.Dense(16 => 1))
+Chain(
+    layer_1 = Dense(1 => 16, relu),     # 32 parameters
+    layer_2 = Dense(16 => 1),           # 17 parameters
+)         # Total: 49 parameters,
+          #        plus 0 states.
+
+julia> parameters, state = Lux.setup(rng, chain);
+
+julia> predictor = MathOptAI.build_predictor(
+           (chain, parameters, state);
+           config = Dict(Lux.relu => MathOptAI.ReLU()),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 1, output: 16]
+ * ReLU()
+ * Affine(A, b) [input: 16, output: 1]
+
+julia> MathOptAI.build_predictor(
+           (chain, parameters, state);
+           config = Dict(Lux.relu => MathOptAI.ReLUQuadratic()),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 1, output: 16]
+ * ReLUQuadratic()
+ * Affine(A, b) [input: 16, output: 1]
source
MathOptAI.build_predictor(predictor::GLM.LinearModel)

Convert a trained linear model from GLM.jl to an Affine layer.

Example

julia> using GLM, MathOptAI
+
+julia> X, Y = rand(10, 2), rand(10);
+
+julia> model_glm = GLM.lm(X, Y);
+
+julia> MathOptAI.build_predictor(model_glm)
+Affine(A, b) [input: 2, output: 1]
source
MathOptAI.build_predictor(
+    predictor::GLM.GeneralizedLinearModel{
+        GLM.GlmResp{Vector{Float64},GLM.Bernoulli{Float64},GLM.LogitLink},
+    };
+    sigmoid::MathOptAI.AbstractPredictor = MathOptAI.Sigmoid(),
+)

Convert a trained logistic model from GLM.jl to a Pipeline layer.

Keyword arguments

  • sigmoid: the predictor to use for the sigmoid layer.

Example

julia> using GLM, MathOptAI
+
+julia> X, Y = rand(10, 2), rand(Bool, 10);
+
+julia> model_glm = GLM.glm(X, Y, GLM.Bernoulli());
+
+julia> MathOptAI.build_predictor(model_glm)
+Pipeline with layers:
+ * Affine(A, b) [input: 2, output: 1]
+ * Sigmoid()
source
MathOptAI.build_predictor(
+    predictor::MathOptAI.PytorchModel;
+    config::Dict = Dict{Any,Any}(),
+    gray_box::Bool = false,
+    gray_box_hessian::Bool = false,
+)

Convert a trained neural network from PyTorch via PythonCall.jl to a Pipeline.

Supported layers

  • nn.Linear
  • nn.ReLU
  • nn.Sequential
  • nn.Sigmoid
  • nn.Softplus
  • nn.Tanh

Keyword arguments

  • config: a dictionary that maps Symbols to AbstractPredictors that control how the activation functions are reformulated. For example, :Sigmoid => MathOptAI.Sigmoid() or :ReLU => MathOptAI.QuadraticReLU(). The supported Symbols are :ReLU, :Sigmoid, :SoftPlus, and :Tanh.
  • gray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by torch.func.jacrev.
  • gray_box_hessian: if true, the gray box additionally computes the Hessian of the output using torch.func.hessian.
source
MathOptAI.build_predictor(
+    predictor::Flux.Chain;
+    config::Dict = Dict{Any,Any}(),
+    gray_box::Bool = false,
+    gray_box_hessian::Bool = false,
+)

Convert a trained neural network from Flux.jl to a Pipeline.

Supported layers

  • Flux.Dense
  • Flux.Scale
  • Flux.softmax

Supported activation functions

  • Flux.relu
  • Flux.sigmoid
  • Flux.softplus
  • Flux.tanh

Keyword arguments

  • config: a dictionary that maps supported Flux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Flux.sigmoid => MathOptAI.Sigmoid() or Flux.relu => MathOptAI.QuadraticReLU().
  • gray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by Flux.withjacobian.
  • gray_box_hessian: if true, the gray box additionally computes the Hessian of the output using Flux.hessian.

Example

julia> using Flux, MathOptAI
+
+julia> chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));
+
+julia> MathOptAI.build_predictor(
+           chain;
+           config = Dict(Flux.relu => MathOptAI.ReLU()),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 1, output: 16]
+ * ReLU()
+ * Affine(A, b) [input: 16, output: 1]
+
+julia> MathOptAI.build_predictor(
+           chain;
+           config = Dict(Flux.relu => MathOptAI.ReLUQuadratic()),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 1, output: 16]
+ * ReLUQuadratic()
+ * Affine(A, b) [input: 16, output: 1]
source

Affine

MathOptAI.Affine — Type
Affine(
+    A::Matrix{T},
+    b::Vector{T} = zeros(T, size(A, 1)),
+) where {T} <: AbstractPredictor

An AbstractPredictor that represents the affine relationship:

\[f(x) = A x + b\]

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.Affine([2.0 3.0], [4.0])
+Affine(A, b) [input: 2, output: 1]
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Affine[1]
+
+julia> formulation
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ 2 x[1] + 3 x[2] - moai_Affine[1] = -4
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+1-element Vector{AffExpr}:
+ 2 x[1] + 3 x[2] + 4
+
+julia> formulation
+ReducedSpace(Affine(A, b) [input: 2, output: 1])
+├ variables [0]
+└ constraints [0]
source

BinaryDecisionTree

MathOptAI.BinaryDecisionTree — Type
BinaryDecisionTree{K,V}(
+    feat_id::Int,
+    feat_value::K,
+    lhs::Union{V,BinaryDecisionTree{K,V}},
+    rhs::Union{V,BinaryDecisionTree{K,V}},
+)

An AbstractPredictor that represents a binary decision tree.

  • If x[feat_id] <= feat_value, then return lhs
  • If x[feat_id] > feat_value, then return rhs

Example

To represent the tree x[1] <= 0.0 ? -1 : (x[1] <= 1.0 ? 0 : 1), do:

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:1]);
+
+julia> f = MathOptAI.BinaryDecisionTree{Float64,Int}(
+           1,
+           0.0,
+           -1,
+           MathOptAI.BinaryDecisionTree{Float64,Int}(1, 1.0, 0, 1),
+       )
+BinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_BinaryDecisionTree_value
+
+julia> formulation
+BinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]
+├ variables [4]
+│ ├ moai_BinaryDecisionTree_value
+│ ├ moai_BinaryDecisionTree_z[1]
+│ ├ moai_BinaryDecisionTree_z[2]
+│ └ moai_BinaryDecisionTree_z[3]
+└ constraints [7]
+  ├ moai_BinaryDecisionTree_z[1] + moai_BinaryDecisionTree_z[2] + moai_BinaryDecisionTree_z[3] = 1
+  ├ moai_BinaryDecisionTree_z[1] --> {x[1] ≤ 0}
+  ├ moai_BinaryDecisionTree_z[2] --> {x[1] ≥ 0}
+  ├ moai_BinaryDecisionTree_z[2] --> {x[1] ≤ 1}
+  ├ moai_BinaryDecisionTree_z[3] --> {x[1] ≥ 0}
+  ├ moai_BinaryDecisionTree_z[3] --> {x[1] ≥ 1}
+  └ moai_BinaryDecisionTree_z[1] - moai_BinaryDecisionTree_z[3] + moai_BinaryDecisionTree_value = 0
source

GrayBox

MathOptAI.GrayBox — Type
GrayBox(
+    output_size::Function,
+    callback::Function;
+    has_hessian::Bool = false,
+) <: AbstractPredictor

An AbstractPredictor that represents the function $f(x)$ as a user-defined nonlinear operator.

Arguments

  • output_size(x::Vector):Int: given an input vector x, return the dimension of the output vector
  • callback(x::Vector)::NamedTuple -> (;value, jacobian[, hessian]): given an input vector x, return a NamedTuple that computes the primal value and Jacobian of the output value with respect to the input. jacobian[j, i] is the partial derivative of value[j] with respect to x[i].
  • has_hessian: if true, the callback additionally contains a field hessian, which is an N × N × M matrix, where hessian[i, j, k] is the partial derivative of value[k] with respect to x[i] and x[j].

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.GrayBox(
+           x -> 2,
+           x -> (value = x.^2, jacobian = [2 * x[1] 0.0; 0.0 2 * x[2]]),
+       );
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_GrayBox[1]
+ moai_GrayBox[2]
+
+julia> formulation
+GrayBox
+├ variables [2]
+│ ├ moai_GrayBox[1]
+│ └ moai_GrayBox[2]
+└ constraints [2]
+  ├ op_##330(x[1], x[2]) - moai_GrayBox[1] = 0
+  └ op_##331(x[1], x[2]) - moai_GrayBox[2] = 0
+
+julia> y, formulation = MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ op_##332(x[1], x[2])
+ op_##333(x[1], x[2])
+
+julia> formulation
+ReducedSpace(GrayBox)
+├ variables [0]
+└ constraints [0]
source

Pipeline

MathOptAI.Pipeline — Type
Pipeline(layers::Vector{AbstractPredictor}) <: AbstractPredictor

An AbstractPredictor that represents a pipeline (composition) of nested layers:

\[f(x) = (l_1 \cdots (l_N(x))\]

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.Pipeline(
+           MathOptAI.Affine([1.0 2.0], [0.0]),
+           MathOptAI.ReLUQuadratic(),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 2, output: 1]
+ * ReLUQuadratic()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_ReLU[1]
+
+julia> formulation
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ x[1] + 2 x[2] - moai_Affine[1] = 0
+ReLUQuadratic()
+├ variables [2]
+│ ├ moai_ReLU[1]
+│ └ moai_z[1]
+└ constraints [2]
+  ├ moai_Affine[1] - moai_ReLU[1] + moai_z[1] = 0
+  └ moai_ReLU[1]*moai_z[1] = 0
source

PytorchModel

MathOptAI.PytorchModel — Type
PytorchModel(filename::String)

A wrapper struct for loading a PyTorch model.

The only supported file extension is .pt, where the .pt file has been created using torch.save(model, filename).

Example

julia> using PythonCall, MathOptAI
+
+julia> predictor = PytorchModel("model.pt");
source

Quantile

MathOptAI.Quantile — Type
Quantile(distribution, quantiles::Vector{Float64})

An AbstractPredictor that represents the quantiles of distribution.

Example

julia> using JuMP, Distributions, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, 1 <= x <= 2);
+
+julia> predictor = MathOptAI.Quantile([0.1, 0.9]) do x
+           return Distributions.Normal(x, 3 - x)
+       end
+Quantile(_, [0.1, 0.9])
+
+julia> y, formulation = MathOptAI.add_predictor(model, predictor, [x]);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_quantile[1]
+ moai_quantile[2]
source

ReducedSpace

MathOptAI.ReducedSpace — Type
ReducedSpace(predictor::AbstractPredictor)

A wrapper type for other predictors that implement a reduced-space formulation.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> predictor = MathOptAI.ReducedSpace(MathOptAI.ReLU());
+
+julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ max(0.0, x[1])
+ max(0.0, x[2])
source

ReLU

MathOptAI.ReLU — Type
ReLU() <: AbstractPredictor

An AbstractPredictor that implements the ReLU constraint $y = \max\{0, x\}$ as a non-smooth nonlinear constraint.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.ReLU()
+ReLU()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_ReLU[1]
+ moai_ReLU[2]
+
+julia> formulation
+ReLU()
+├ variables [2]
+│ ├ moai_ReLU[1]
+│ └ moai_ReLU[2]
+└ constraints [4]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[2] ≥ 0
+  ├ moai_ReLU[1] - max(0.0, x[1]) = 0
+  └ moai_ReLU[2] - max(0.0, x[2]) = 0
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ max(0.0, x[1])
+ max(0.0, x[2])
+
+julia> formulation
+ReducedSpace(ReLU())
+├ variables [0]
+└ constraints [0]
source

ReLUBigM

MathOptAI.ReLUBigM — Type
ReLUBigM(M::Float64) <: AbstractPredictor

An AbstractPredictor that implements the ReLU constraint $y = \max\{0, x\}$ via a big-M MIP reformulation.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, -3 <= x[i in 1:2] <= i);
+
+julia> f = MathOptAI.ReLUBigM(100.0)
+ReLUBigM(100.0)
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_ReLU[1]
+ moai_ReLU[2]
+
+julia> formulation
+ReLUBigM(100.0)
+├ variables [4]
+│ ├ moai_ReLU[1]
+│ ├ moai_ReLU[2]
+│ ├ _[5]
+│ └ _[6]
+└ constraints [8]
+  ├ _[5] binary
+  ├ -x[1] + moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[1] - _[5] ≤ 0
+  ├ -x[1] + moai_ReLU[1] + 3 _[5] ≤ 3
+  ├ _[6] binary
+  ├ -x[2] + moai_ReLU[2] ≥ 0
+  ├ moai_ReLU[2] - 2 _[6] ≤ 0
+  └ -x[2] + moai_ReLU[2] + 3 _[6] ≤ 3
source

ReLUQuadratic

MathOptAI.ReLUQuadratic — Type
ReLUQuadratic() <: AbstractPredictor

An AbstractPredictor that implements the ReLU constraint $y = \max\{0, x\}$ by the reformulation:

\[\begin{aligned} +x = y - z \\ +y \times z = 0 \\ +y, z \ge 0 +\end{aligned}\]

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2] >= -1);
+
+julia> f = MathOptAI.ReLUQuadratic()
+ReLUQuadratic()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_ReLU[1]
+ moai_ReLU[2]
+
+julia> formulation
+ReLUQuadratic()
+├ variables [4]
+│ ├ moai_ReLU[1]
+│ ├ moai_ReLU[2]
+│ ├ moai_z[1]
+│ └ moai_z[2]
+└ constraints [4]
+  ├ x[1] - moai_ReLU[1] + moai_z[1] = 0
+  ├ x[2] - moai_ReLU[2] + moai_z[2] = 0
+  ├ moai_ReLU[1]*moai_z[1] = 0
+  └ moai_ReLU[2]*moai_z[2] = 0
source

ReLUSOS1

MathOptAI.ReLUSOS1 — Type
ReLUSOS1() <: AbstractPredictor

An AbstractPredictor that implements the ReLU constraint $y = \max\{0, x\}$ by the reformulation:

\[\begin{aligned} +x = y - z \\ +[y, z] \in SOS1 \\ +y, z \ge 0 +\end{aligned}\]

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2] >= -1);
+
+julia> f = MathOptAI.ReLUSOS1()
+ReLUSOS1()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_ReLU[1]
+ moai_ReLU[2]
+
+julia> formulation
+ReLUSOS1()
+├ variables [4]
+│ ├ moai_ReLU[1]
+│ ├ moai_ReLU[2]
+│ ├ moai_z[1]
+│ └ moai_z[2]
+└ constraints [4]
+  ├ x[1] - moai_ReLU[1] + moai_z[1] = 0
+  ├ x[2] - moai_ReLU[2] + moai_z[2] = 0
+  ├ [moai_ReLU[1], moai_z[1]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])
+  └ [moai_ReLU[2], moai_z[2]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])
source

Scale

MathOptAI.Scale — Type
Scale(
+    scale::Vector{T},
+    bias::Vector{T},
+) where {T} <: AbstractPredictor

An AbstractPredictor that represents the affine relationship:

\[f(x) = Diag(scale)x + bias\]

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.Scale([2.0, 3.0], [4.0, 5.0])
+Scale(scale, bias)
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_Scale[1]
+ moai_Scale[2]
+
+julia> formulation
+Scale(scale, bias)
+├ variables [2]
+│ ├ moai_Scale[1]
+│ └ moai_Scale[2]
+└ constraints [2]
+  ├ 2 x[1] - moai_Scale[1] = -4
+  └ 3 x[2] - moai_Scale[2] = -5
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{AffExpr}:
+ 2 x[1] + 4
+ 3 x[2] + 5
+
+julia> formulation
+ReducedSpace(Scale(scale, bias))
+├ variables [0]
+└ constraints [0]
source

Sigmoid

MathOptAI.Sigmoid — Type
Sigmoid() <: AbstractPredictor

An AbstractPredictor that implements the Sigmoid constraint $y = \frac{1}{1 + e^{-x}}$ as a smooth nonlinear constraint.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.Sigmoid()
+Sigmoid()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_Sigmoid[1]
+ moai_Sigmoid[2]
+
+julia> formulation
+Sigmoid()
+├ variables [2]
+│ ├ moai_Sigmoid[1]
+│ └ moai_Sigmoid[2]
+└ constraints [6]
+  ├ moai_Sigmoid[1] ≥ 0
+  ├ moai_Sigmoid[2] ≥ 0
+  ├ moai_Sigmoid[1] ≤ 1
+  ├ moai_Sigmoid[2] ≤ 1
+  ├ moai_Sigmoid[1] - (1.0 / (1.0 + exp(-x[1]))) = 0
+  └ moai_Sigmoid[2] - (1.0 / (1.0 + exp(-x[2]))) = 0
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ 1.0 / (1.0 + exp(-x[1]))
+ 1.0 / (1.0 + exp(-x[2]))
+
+julia> formulation
+ReducedSpace(Sigmoid())
+├ variables [0]
+└ constraints [0]
source

SoftMax

MathOptAI.SoftMax — Type
SoftMax() <: AbstractPredictor

An AbstractPredictor that implements the SoftMax constraint $y_i = \frac{e^{x_i}}{\sum_j e^{x_j}}$ as a smooth nonlinear constraint.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.SoftMax()
+SoftMax()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_SoftMax[1]
+ moai_SoftMax[2]
+
+julia> formulation
+SoftMax()
+├ variables [3]
+│ ├ moai_SoftMax_denom
+│ ├ moai_SoftMax[1]
+│ └ moai_SoftMax[2]
+└ constraints [8]
+  ├ moai_SoftMax[1] ≥ 0
+  ├ moai_SoftMax[2] ≥ 0
+  ├ moai_SoftMax[1] ≤ 1
+  ├ moai_SoftMax[2] ≤ 1
+  ├ moai_SoftMax_denom ≥ 0
+  ├ moai_SoftMax_denom - (0.0 + exp(x[2]) + exp(x[1])) = 0
+  ├ moai_SoftMax[1] - (exp(x[1]) / moai_SoftMax_denom) = 0
+  └ moai_SoftMax[2] - (exp(x[2]) / moai_SoftMax_denom) = 0
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ exp(x[1]) / moai_SoftMax_denom
+ exp(x[2]) / moai_SoftMax_denom
+
+julia> formulation
+ReducedSpace(SoftMax())
+├ variables [1]
+│ └ moai_SoftMax_denom
+└ constraints [2]
+  ├ moai_SoftMax_denom ≥ 0
+  └ moai_SoftMax_denom - (0.0 + exp(x[2]) + exp(x[1])) = 0
source

SoftPlus

MathOptAI.SoftPlus — Type
SoftPlus(; beta = 1.0) <: AbstractPredictor

An AbstractPredictor that implements the SoftPlus constraint $y = \frac{1}{\beta} \log(1 + e^{\beta x})$ as a smooth nonlinear constraint.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.SoftPlus(; beta = 2.0)
+SoftPlus(2.0)
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_SoftPlus[1]
+ moai_SoftPlus[2]
+
+julia> formulation
+SoftPlus(2.0)
+├ variables [2]
+│ ├ moai_SoftPlus[1]
+│ └ moai_SoftPlus[2]
+└ constraints [4]
+  ├ moai_SoftPlus[1] ≥ 0
+  ├ moai_SoftPlus[2] ≥ 0
+  ├ moai_SoftPlus[1] - (log(1.0 + exp(2 x[1])) / 2.0) = 0
+  └ moai_SoftPlus[2] - (log(1.0 + exp(2 x[2])) / 2.0) = 0
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ log(1.0 + exp(2 x[1])) / 2.0
+ log(1.0 + exp(2 x[2])) / 2.0
+
+julia> formulation
+ReducedSpace(SoftPlus(2.0))
+├ variables [0]
+└ constraints [0]
source

Tanh

MathOptAI.Tanh — Type
Tanh() <: AbstractPredictor

An AbstractPredictor that implements the Tanh constraint $y = \tanh(x)$ as a smooth nonlinear constraint.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.Tanh()
+Tanh()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_Tanh[1]
+ moai_Tanh[2]
+
+julia> formulation
+Tanh()
+├ variables [2]
+│ ├ moai_Tanh[1]
+│ └ moai_Tanh[2]
+└ constraints [6]
+  ├ moai_Tanh[1] ≥ -1
+  ├ moai_Tanh[2] ≥ -1
+  ├ moai_Tanh[1] ≤ 1
+  ├ moai_Tanh[2] ≤ 1
+  ├ moai_Tanh[1] - tanh(x[1]) = 0
+  └ moai_Tanh[2] - tanh(x[2]) = 0
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ tanh(x[1])
+ tanh(x[2])
+
+julia> formulation
+ReducedSpace(Tanh())
+├ variables [0]
+└ constraints [0]
source

AbstractFormulation

Formulation

MathOptAI.Formulation — Type
struct Formulation{P<:AbstractPredictor} <: AbstractFormulation
+    predictor::P
+    variables::Vector{Any}
+    constraints::Vector{Any}
+end

Fields

  • predictor: the predictor object used to build the formulation
  • variables: a vector of new decision variables added to the model
  • constraints: a vector of new constraints added to the model

Check the docstring of the predictor for an explanation of the formulation and the order of the elements in .variables and .constraints.

source

PipelineFormulation

MathOptAI.PipelineFormulation — Type
struct PipelineFormulation{P<:AbstractPredictor} <: AbstractFormulation
+    predictor::P
+    layers::Vector{Any}
+end

Fields

  • predictor: the predictor object used to build the formulation
  • layers: the formulation associated with each of the layers in the pipeline
source

Extensions

MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::MathOptAI.Quantile{<:AbstractGPs.PosteriorGP},
+    x::Vector,
+)

Add the quantiles of a trained Gaussian Process from AbstractGPs.jl to model.

Example

julia> using JuMP, MathOptAI, AbstractGPs
+
+julia> x_data = 2π .* (0.0:0.1:1.0);
+
+julia> y_data = sin.(x_data);
+
+julia> fx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.1);
+
+julia> p_fx = AbstractGPs.posterior(fx, y_data);
+
+julia> model = Model();
+
+julia> @variable(model, 1 <= x[1:1] <= 6, start = 3);
+
+julia> predictor = MathOptAI.Quantile(p_fx, [0.1, 0.9]);
+
+julia> y, _ = MathOptAI.add_predictor(model, predictor, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_quantile[1]
+ moai_quantile[2]
+
+julia> @objective(model, Max, y[2] - y[1])
+moai_quantile[2] - moai_quantile[1]
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::Union{DecisionTree.Root,DecisionTree.DecisionTreeClassifier},
+    x::Vector,
+)

Add a binary decision tree from DecisionTree.jl to model.

Example

julia> using JuMP, MathOptAI, DecisionTree
+
+julia> truth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)
+truth (generic function with 1 method)
+
+julia> features = abs.(sin.((1:10) .* (3:4)'));
+
+julia> size(features)
+(10, 2)
+
+julia> labels = truth.(Vector.(eachrow(features)));
+
+julia> ml_model = DecisionTree.build_tree(labels, features)
+Decision Tree
+Leaves: 3
+Depth:  2
+
+julia> model = Model();
+
+julia> @variable(model, 0 <= x[1:2] <= 1);
+
+julia> y, _ = MathOptAI.add_predictor(model, ml_model, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_BinaryDecisionTree_value
source
MathOptAI.build_predictor — Method
MathOptAI.build_predictor(predictor::DecisionTree.Root)

Convert a binary decision tree from DecisionTree.jl to a BinaryDecisionTree.

Example

julia> using MathOptAI, DecisionTree
+
+julia> truth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)
+truth (generic function with 1 method)
+
+julia> features = abs.(sin.((1:10) .* (3:4)'));
+
+julia> size(features)
+(10, 2)
+
+julia> labels = truth.(Vector.(eachrow(features)));
+
+julia> ml_model = DecisionTree.build_tree(labels, features)
+Decision Tree
+Leaves: 3
+Depth:  2
+
+julia> MathOptAI.build_predictor(ml_model)
+BinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::Flux.Chain,
+    x::Vector;
+    config::Dict = Dict{Any,Any}(),
+    reduced_space::Bool = false,
+    gray_box::Bool = false,
+)

Add a trained neural network from Flux.jl to model.

Supported layers

  • Flux.Dense
  • Flux.Scale
  • Flux.softmax

Supported activation functions

  • Flux.relu
  • Flux.sigmoid
  • Flux.softplus
  • Flux.tanh

Keyword arguments

  • config: a dictionary that maps supported Flux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Flux.sigmoid => MathOptAI.Sigmoid() or Flux.relu => MathOptAI.QuadraticReLU().
  • gray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by Flux.withjacobian.

Example

julia> using JuMP, Flux, MathOptAI
+
+julia> chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));
+
+julia> model = Model();
+
+julia> @variable(model, x[1:1]);
+
+julia> y, _ = MathOptAI.add_predictor(
+           model,
+           chain,
+           x;
+           config = Dict(Flux.relu => MathOptAI.ReLU()),
+       );
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Affine[1]
source
MathOptAI.build_predictor — Method
MathOptAI.build_predictor(
+    predictor::Flux.Chain;
+    config::Dict = Dict{Any,Any}(),
+    gray_box::Bool = false,
+    gray_box_hessian::Bool = false,
+)

Convert a trained neural network from Flux.jl to a Pipeline.

Supported layers

  • Flux.Dense
  • Flux.Scale
  • Flux.softmax

Supported activation functions

  • Flux.relu
  • Flux.sigmoid
  • Flux.softplus
  • Flux.tanh

Keyword arguments

  • config: a dictionary that maps supported Flux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Flux.sigmoid => MathOptAI.Sigmoid() or Flux.relu => MathOptAI.QuadraticReLU().
  • gray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by Flux.withjacobian.
  • gray_box_hessian: if true, the gray box additionally computes the Hessian of the output using Flux.hessian.

Example

julia> using Flux, MathOptAI
+
+julia> chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));
+
+julia> MathOptAI.build_predictor(
+           chain;
+           config = Dict(Flux.relu => MathOptAI.ReLU()),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 1, output: 16]
+ * ReLU()
+ * Affine(A, b) [input: 16, output: 1]
+
+julia> MathOptAI.build_predictor(
+           chain;
+           config = Dict(Flux.relu => MathOptAI.ReLUQuadratic()),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 1, output: 16]
+ * ReLUQuadratic()
+ * Affine(A, b) [input: 16, output: 1]
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::GLM.GeneralizedLinearModel{
+        GLM.GlmResp{Vector{Float64},GLM.Bernoulli{Float64},GLM.LogitLink},
+    },
+    x::Vector;
+    sigmoid::AbstractPredictor = MathOptAI.Sigmoid(),
+    reduced_space::Bool = false,
+)

Add a trained logistic regression model from GLM.jl to model.

Keyword arguments

  • sigmoid: the predictor to use for the sigmoid layer.

Example

julia> using GLM, JuMP, MathOptAI
+
+julia> X, Y = rand(10, 2), rand(Bool, 10);
+
+julia> model_glm = GLM.glm(X, Y, GLM.Bernoulli());
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> y, _ = MathOptAI.add_predictor(
+           model,
+           model_glm,
+           x;
+           sigmoid = MathOptAI.Sigmoid(),
+       );
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Sigmoid[1]
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::GLM.LinearModel,
+    x::Vector;
+    reduced_space::Bool = false,
+)

Add a trained linear model from GLM.jl to model.

Example

julia> using GLM, JuMP, MathOptAI
+
+julia> X, Y = rand(10, 2), rand(10);
+
+julia> model_glm = GLM.lm(X, Y);
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> y, _ = MathOptAI.add_predictor(model, model_glm, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Affine[1]
source
MathOptAI.build_predictor — Method
MathOptAI.build_predictor(
+    predictor::GLM.GeneralizedLinearModel{
+        GLM.GlmResp{Vector{Float64},GLM.Bernoulli{Float64},GLM.LogitLink},
+    };
+    sigmoid::MathOptAI.AbstractPredictor = MathOptAI.Sigmoid(),
+)

Convert a trained logistic model from GLM.jl to a Pipeline layer.

Keyword arguments

  • sigmoid: the predictor to use for the sigmoid layer.

Example

julia> using GLM, MathOptAI
+
+julia> X, Y = rand(10, 2), rand(Bool, 10);
+
+julia> model_glm = GLM.glm(X, Y, GLM.Bernoulli());
+
+julia> MathOptAI.build_predictor(model_glm)
+Pipeline with layers:
+ * Affine(A, b) [input: 2, output: 1]
+ * Sigmoid()
source
MathOptAI.build_predictor — Method
MathOptAI.build_predictor(predictor::GLM.LinearModel)

Convert a trained linear model from GLM.jl to an Affine layer.

Example

julia> using GLM, MathOptAI
+
+julia> X, Y = rand(10, 2), rand(10);
+
+julia> model_glm = GLM.lm(X, Y);
+
+julia> MathOptAI.build_predictor(model_glm)
+Affine(A, b) [input: 2, output: 1]
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::Tuple{<:Lux.Chain,<:NamedTuple,<:NamedTuple},
+    x::Vector;
+    config::Dict = Dict{Any,Any}(),
+    reduced_space::Bool = false,
+)

Add a trained neural network from Lux.jl to model.

Supported layers

  • Lux.Dense
  • Lux.Scale

Supported activation functions

  • Lux.relu
  • Lux.sigmoid
  • Lux.softplus
  • Lux.softmax
  • Lux.tanh

Keyword arguments

  • config: a dictionary that maps supported Lux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Lux.sigmoid => MathOptAI.Sigmoid() or Lux.relu => MathOptAI.QuadraticReLU().

Example

julia> using JuMP, Lux, MathOptAI, Random
+
+julia> rng = Random.MersenneTwister();
+
+julia> chain = Lux.Chain(Lux.Dense(1 => 16, Lux.relu), Lux.Dense(16 => 1))
+Chain(
+    layer_1 = Dense(1 => 16, relu),     # 32 parameters
+    layer_2 = Dense(16 => 1),           # 17 parameters
+)         # Total: 49 parameters,
+          #        plus 0 states.
+
+julia> parameters, state = Lux.setup(rng, chain);
+
+julia> predictor = (chain, parameters, state);
+
+julia> model = Model();
+
+julia> @variable(model, x[1:1]);
+
+julia> y, _ = MathOptAI.add_predictor(
+           model,
+           predictor,
+           x;
+           config = Dict(Lux.relu => MathOptAI.ReLU()),
+       );
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Affine[1]
source
MathOptAI.build_predictor — Method
MathOptAI.build_predictor(
+    predictor::Tuple{<:Lux.Chain,<:NamedTuple,<:NamedTuple};
+    config::Dict = Dict{Any,Any}(),
+)

Convert a trained neural network from Lux.jl to a Pipeline.

Supported layers

  • Lux.Dense
  • Lux.Scale

Supported activation functions

  • Lux.relu
  • Lux.sigmoid
  • Lux.softplus
  • Lux.softmax
  • Lux.tanh

Keyword arguments

  • config: a dictionary that maps supported Lux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Lux.sigmoid => MathOptAI.Sigmoid() or Lux.relu => MathOptAI.QuadraticReLU().

Example

julia> using Lux, MathOptAI, Random
+
+julia> rng = Random.MersenneTwister();
+
+julia> chain = Lux.Chain(Lux.Dense(1 => 16, Lux.relu), Lux.Dense(16 => 1))
+Chain(
+    layer_1 = Dense(1 => 16, relu),     # 32 parameters
+    layer_2 = Dense(16 => 1),           # 17 parameters
+)         # Total: 49 parameters,
+          #        plus 0 states.
+
+julia> parameters, state = Lux.setup(rng, chain);
+
+julia> predictor = MathOptAI.build_predictor(
+           (chain, parameters, state);
+           config = Dict(Lux.relu => MathOptAI.ReLU()),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 1, output: 16]
+ * ReLU()
+ * Affine(A, b) [input: 16, output: 1]
+
+julia> MathOptAI.build_predictor(
+           (chain, parameters, state);
+           config = Dict(Lux.relu => MathOptAI.ReLUQuadratic()),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 1, output: 16]
+ * ReLUQuadratic()
+ * Affine(A, b) [input: 16, output: 1]
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::MathOptAI.PytorchModel,
+    x::Vector;
+    config::Dict = Dict{Any,Any}(),
+    reduced_space::Bool = false,
+    gray_box::Bool = false,
+)

Add a trained neural network from PyTorch via PythonCall.jl to model.

Supported layers

  • nn.Linear
  • nn.ReLU
  • nn.Sequential
  • nn.Sigmoid
  • nn.Softplus
  • nn.Tanh

Keyword arguments

  • config: a dictionary that maps Symbols to AbstractPredictors that control how the activation functions are reformulated. For example, :Sigmoid => MathOptAI.Sigmoid() or :ReLU => MathOptAI.QuadraticReLU(). The supported Symbols are :ReLU, :Sigmoid, :SoftPlus, and :Tanh.
  • gray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by torch.func.jacrev.
  • gray_box_hessian: if true, the gray box additionally computes the Hessian of the output using torch.func.hessian.
source
MathOptAI.build_predictor — Method
MathOptAI.build_predictor(
+    predictor::MathOptAI.PytorchModel;
+    config::Dict = Dict{Any,Any}(),
+    gray_box::Bool = false,
+    gray_box_hessian::Bool = false,
+)

Convert a trained neural network from PyTorch via PythonCall.jl to a Pipeline.

Supported layers

  • nn.Linear
  • nn.ReLU
  • nn.Sequential
  • nn.Sigmoid
  • nn.Softplus
  • nn.Tanh

Keyword arguments

  • config: a dictionary that maps Symbols to AbstractPredictors that control how the activation functions are reformulated. For example, :Sigmoid => MathOptAI.Sigmoid() or :ReLU => MathOptAI.QuadraticReLU(). The supported Symbols are :ReLU, :Sigmoid, :SoftPlus, and :Tanh.
  • gray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by torch.func.jacrev.
  • gray_box_hessian: if true, the gray box additionally computes the Hessian of the output using torch.func.hessian.
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::StatsModels.TableRegressionModel,
+    x::DataFrames.DataFrame;
+    kwargs...,
+)

Add a trained regression model from StatsModels.jl to model, using the DataFrame x as input.

In most cases, predictor should be a GLM.jl predictor supported by MathOptAI, but trained using @formula and a DataFrame instead of the raw matrix input.

In general, x may have some columns that are constant (Float64) and some columns that are JuMP decision variables.

Keyword arguments

All keyword arguments are passed to the corresponding add_predictor of the GLM extension.

Example

julia> using DataFrames, GLM, JuMP, MathOptAI
+
+julia> train_df = DataFrames.DataFrame(x1 = rand(10), x2 = rand(10));
+
+julia> train_df.y = 1.0 .* train_df.x1 + 2.0 .* train_df.x2 .+ rand(10);
+
+julia> predictor = GLM.lm(GLM.@formula(y ~ x1 + x2), train_df);
+
+julia> model = Model();
+
+julia> test_df = DataFrames.DataFrame(
+           x1 = rand(6),
+           x2 = @variable(model, [1:6]),
+       );
+
+julia> test_df.y, _ = MathOptAI.add_predictor(model, predictor, test_df);
+
+julia> test_df.y
+6-element Vector{VariableRef}:
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
source
diff --git a/v0.1.3/assets/documenter.js b/v0.1.3/assets/documenter.js new file mode 100644 index 00000000..82252a11 --- /dev/null +++ b/v0.1.3/assets/documenter.js @@ -0,0 +1,1064 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on( + "click", + ".docstring .docstring-article-toggle-button", + function () { + let articleToggleTitle = "Expand docstring"; + const parent = $(this).parent(); + + debounce(() => { + if (parent.siblings("section").is(":visible")) { + parent + .find("a.docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + parent + .find("a.docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + parent + .children(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + parent.siblings("section").slideToggle(); + }); + } +); + +$(document).on("click", ".docs-article-toggle-button", function (event) { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + let animationSpeed = event.noToggleAnimation ? 0 : 400; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $("a.docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(animationSpeed); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $("a.docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(animationSpeed); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-xmark"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-xmark"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let meta = $("div[data-docstringscollapsed]").data(); + + if (meta?.docstringscollapsed) { + $("#documenter-article-toggle-button").trigger({ + type: "click", + noToggleAnimation: true, + }); + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +/* +To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +PSEUDOCODE: + +Searching happens automatically as the user types or adjusts the selected filters. +To preserve responsiveness, as much as possible of the slow parts of the search are done +in a web worker. Searching and result generation are done in the worker, and filtering and +DOM updates are done in the main thread. The filters are in the main thread as they should +be very quick to apply. This lets filters be changed without re-searching with minisearch +(which is possible even if filtering is on the worker thread) and also lets filters be +changed _while_ the worker is searching and without message passing (neither of which are +possible if filtering is on the worker thread) + +SEARCH WORKER: + +Import minisearch + +Build index + +On message from main thread + run search + find the first 200 unique results from each category, and compute their divs for display + note that this is necessary and sufficient information for the main thread to find the + first 200 unique results from any given filter set + post results to main thread + +MAIN: + +Launch worker + +Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results) + +On text update + if worker is not running, launch_search() + +launch_search + set worker_is_running to true, set last_search_text to the search text + post the search query to worker + +on message from worker + if last_search_text is not the same as the text in the search field, + the latest search result is not reflective of the latest search query, so update again + launch_search() + otherwise + set worker_is_running to false + + regardless, display the new search results to the user + save the unfiltered_results as a global + update_search() + +on filter click + adjust the filter selection + update_search() + +update_search + apply search filters by looping through the unfiltered_results and finding the first 200 + unique results that match the filters + + Update the DOM +*/ + +/////// SEARCH WORKER /////// + +function worker_function(documenterSearchIndex, documenterBaseURL, filters) { + importScripts( + "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js" + ); + + let data = documenterSearchIndex.map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; + }); + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", + ]); + + let index = new MiniSearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + + word = word.toLowerCase(); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not + // find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + prefix: true, + boost: { title: 100 }, + fuzzy: 2, + }, + }); + + index.addAll(data); + + /** + * Used to map characters to HTML entities. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const htmlEscapes = { + "&": "&", + "<": "<", + ">": ">", + '"': """, + "'": "'", + }; + + /** + * Used to match HTML entities and HTML characters. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const reUnescapedHtml = /[&<>"']/g; + const reHasUnescapedHtml = RegExp(reUnescapedHtml.source); + + /** + * Escape function from lodash + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + function escape(string) { + return string && reHasUnescapedHtml.test(string) + ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr]) + : string || ""; + } + + /** + * RegX escape function from MDN + * Refer: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping + */ + function escapeRegExp(string) { + return string.replace(/[.*+?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string + } + + /** + * Make the result component given a minisearch result data object and the value + * of the search input as queryString. To view the result object structure, refer: + * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ + function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + searchstring = escapeRegExp(querystring); + let textindex = new RegExp(`${searchstring}`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + text = text.length ? escape(text) : ""; + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`${escape(searchstring)}`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${escape(result.title)}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+ + ${search_divider} + `; + + return result_div; + } + + self.onmessage = function (e) { + let query = e.data; + let results = index.search(query, { + filter: (result) => { + // Only return relevant results + return result.score >= 1; + }, + combineWith: "AND", + }); + + // Pre-filter to deduplicate and limit to 200 per category to the extent + // possible without knowing what the filters are. + let filtered_results = []; + let counts = {}; + for (let filter of filters) { + counts[filter] = 0; + } + let present = {}; + + for (let result of results) { + cat = result.category; + cnt = counts[cat]; + if (cnt < 200) { + id = cat + "---" + result.location; + if (present[id]) { + continue; + } + present[id] = true; + filtered_results.push({ + location: result.location, + category: cat, + div: make_search_result(result, query), + }); + } + } + + postMessage(filtered_results); + }; +} + +// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript! +const filters = [ + ...new Set(documenterSearchIndex["docs"].map((x) => x.category)), +]; +const worker_str = + "(" + + worker_function.toString() + + ")(" + + JSON.stringify(documenterSearchIndex["docs"]) + + "," + + JSON.stringify(documenterBaseURL) + + "," + + JSON.stringify(filters) + + ")"; +const worker_blob = new Blob([worker_str], { type: "text/javascript" }); +const worker = new Worker(URL.createObjectURL(worker_blob)); + +/////// SEARCH MAIN /////// + +// Whether the worker is currently handling a search. This is a boolean +// as the worker only ever handles 1 or 0 searches at a time. +var worker_is_running = false; + +// The last search text that was sent to the worker. This is used to determine +// if the worker should be launched again when it reports back results. +var last_search_text = ""; + +// The results of the last search. This, in combination with the state of the filters +// in the DOM, is used compute the results to display on calls to update_search. +var unfiltered_results = []; + +// Which filter is currently selected +var selected_filter = ""; + +$(document).on("input", ".documenter-search-input", function (event) { + if (!worker_is_running) { + launch_search(); + } +}); + +function launch_search() { + worker_is_running = true; + last_search_text = $(".documenter-search-input").val(); + worker.postMessage(last_search_text); +} + +worker.onmessage = function (e) { + if (last_search_text !== $(".documenter-search-input").val()) { + launch_search(); + } else { + worker_is_running = false; + } + + unfiltered_results = e.data; + update_search(); +}; + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + selected_filter = ""; + } else { + selected_filter = $(this).text().toLowerCase(); + } + + // This updates search results and toggles classes for UI: + update_search(); +}); + +/** + * Make/Update the search component + */ +function update_search() { + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + if (selected_filter == "") { + results = unfiltered_results; + } else { + results = unfiltered_results.filter((result) => { + return selected_filter == result.category.toLowerCase(); + }); + } + + let search_result_container = ``; + let modal_filters = make_modal_body_filters(); + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + for (var i = 0, n = results.length; i < n && count < 200; ++i) { + let result = results[i]; + if (result.location && !links.includes(result.location)) { + search_results += result.div; + count++; + links.push(result.location); + } + } + + if (count == 1) { + count_str = "1 result"; + } else if (count == 200) { + count_str = "200+ results"; + } else { + count_str = count + " results"; + } + let result_count = `
${count_str}
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
+
No result found!
+ `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(` +
Type something to get started!
+ `); + } +} + +/** + * Make the modal filter html + * + * @returns string + */ +function make_modal_body_filters() { + let str = filters + .map((val) => { + if (selected_filter == val.toLowerCase()) { + return `${val}`; + } else { + return `${val}`; + } + }) + .join(""); + + return ` +
+ Filters: + ${str} +
`; +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); + }); + // Close the dialog if X is clicked + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); + }); + // Close dialog if ESC is pressed + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let search_modal_header = ` +
+
+

+ + + + +

+
+
+ +
+
+ `; + + let initial_search_body = ` +
Type something to get started!
+ `; + + let search_modal_footer = ` +
+ + Ctrl + + / to search + + esc to close +
+ `; + + $(document.body).append( + ` + + ` + ); + + document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); + }); + + document + .querySelector(".close-search-modal") + .addEventListener("click", () => { + closeModal(); + }); + + $(document).on("click", ".search-result-link", function () { + closeModal(); + }); + + document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; + }); + + // Functions to open and close a modal + function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); + } + + function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
Type something to get started!
+ `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); + } + + document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function () { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { + ev.preventDefault(); + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind("click", function (ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); + } + }); +}); + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function () { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css("max-width"), 10); + var L0 = e.width(); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on("orientationchange", resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function () { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if (typeof active !== "undefined") { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Theme picker setup +$(document).ready(function () { + // onchange callback + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); + } + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function () { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== "undefined") { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $( + "" + ); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}); + +}) diff --git a/v0.1.3/assets/themes/catppuccin-frappe.css b/v0.1.3/assets/themes/catppuccin-frappe.css new file mode 100644 index 00000000..32e3f008 --- /dev/null +++ b/v0.1.3/assets/themes/catppuccin-frappe.css @@ -0,0 +1 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html.theme--catppuccin-frappe .content kbd.button.is-outlined{background-color:transparent;border-color:#414559;box-shadow:none;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-frappe .content 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.button.is-link.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#8caaee}html.theme--catppuccin-frappe .button.is-link.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-link.is-outlined{background-color:transparent;border-color:#8caaee;color:#8caaee}html.theme--catppuccin-frappe .button.is-link.is-outlined:hover,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-link.is-outlined:focus,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-focused{background-color:#8caaee;border-color:#8caaee;color:#fff}html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading::after{border-color:transparent transparent #8caaee #8caaee !important}html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe 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.button.is-link.is-inverted.is-outlined.is-focused{background-color:#fff;color:#8caaee}html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #8caaee #8caaee !important}html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-link.is-light{background-color:#edf2fc;color:#153a8e}html.theme--catppuccin-frappe .button.is-link.is-light:hover,html.theme--catppuccin-frappe .button.is-link.is-light.is-hovered{background-color:#e2eafb;border-color:transparent;color:#153a8e}html.theme--catppuccin-frappe .button.is-link.is-light:active,html.theme--catppuccin-frappe .button.is-link.is-light.is-active{background-color:#d7e1f9;border-color:transparent;color:#153a8e}html.theme--catppuccin-frappe .button.is-info{background-color:#81c8be;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info:hover,html.theme--catppuccin-frappe .button.is-info.is-hovered{background-color:#78c4b9;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info:focus,html.theme--catppuccin-frappe .button.is-info.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info:focus:not(:active),html.theme--catppuccin-frappe .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(129,200,190,0.25)}html.theme--catppuccin-frappe .button.is-info:active,html.theme--catppuccin-frappe .button.is-info.is-active{background-color:#6fc0b5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info{background-color:#81c8be;border-color:#81c8be;box-shadow:none}html.theme--catppuccin-frappe .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted:hover,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-info.is-outlined{background-color:transparent;border-color:#81c8be;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-outlined:hover,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-info.is-outlined:focus,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-focused{background-color:#81c8be;border-color:#81c8be;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #81c8be #81c8be !important}html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-outlined{background-color:transparent;border-color:#81c8be;box-shadow:none;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #81c8be #81c8be !important}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-light{background-color:#f1f9f8;color:#2d675f}html.theme--catppuccin-frappe .button.is-info.is-light:hover,html.theme--catppuccin-frappe .button.is-info.is-light.is-hovered{background-color:#e8f5f3;border-color:transparent;color:#2d675f}html.theme--catppuccin-frappe .button.is-info.is-light:active,html.theme--catppuccin-frappe .button.is-info.is-light.is-active{background-color:#dff1ef;border-color:transparent;color:#2d675f}html.theme--catppuccin-frappe 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.button.is-success{background-color:#a6d189;border-color:#a6d189;box-shadow:none}html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-focused{background-color:#a6d189;border-color:#a6d189;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-light{background-color:#f4f9f0;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:hover,html.theme--catppuccin-frappe .button.is-success.is-light.is-hovered{background-color:#edf6e7;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:active,html.theme--catppuccin-frappe .button.is-success.is-light.is-active{background-color:#e6f2de;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-warning{background-color:#e5c890;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:hover,html.theme--catppuccin-frappe .button.is-warning.is-hovered{background-color:#e3c386;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:focus,html.theme--catppuccin-frappe .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:focus:not(:active),html.theme--catppuccin-frappe .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(229,200,144,0.25)}html.theme--catppuccin-frappe .button.is-warning:active,html.theme--catppuccin-frappe .button.is-warning.is-active{background-color:#e0be7b;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning{background-color:#e5c890;border-color:#e5c890;box-shadow:none}html.theme--catppuccin-frappe .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-outlined:hover,html.theme--catppuccin-frappe 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.button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e5c890 #e5c890 !important}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-light{background-color:#fbf7ee;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:hover,html.theme--catppuccin-frappe .button.is-warning.is-light.is-hovered{background-color:#f9f2e4;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:active,html.theme--catppuccin-frappe .button.is-warning.is-light.is-active{background-color:#f6edda;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-danger{background-color:#e78284;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:hover,html.theme--catppuccin-frappe .button.is-danger.is-hovered{background-color:#e57779;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:focus,html.theme--catppuccin-frappe .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:focus:not(:active),html.theme--catppuccin-frappe .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(231,130,132,0.25)}html.theme--catppuccin-frappe .button.is-danger:active,html.theme--catppuccin-frappe .button.is-danger.is-active{background-color:#e36d6f;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger{background-color:#e78284;border-color:#e78284;box-shadow:none}html.theme--catppuccin-frappe .button.is-danger.is-inverted{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-frappe .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-focused{background-color:#e78284;border-color:#e78284;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-light{background-color:#fceeee;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:hover,html.theme--catppuccin-frappe .button.is-danger.is-light.is-hovered{background-color:#fae3e4;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:active,html.theme--catppuccin-frappe .button.is-danger.is-light.is-active{background-color:#f8d8d9;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-frappe .button.is-small:not(.is-rounded),html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .button.is-normal{font-size:1rem}html.theme--catppuccin-frappe .button.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .button.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .button[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button{background-color:#737994;border-color:#626880;box-shadow:none;opacity:.5}html.theme--catppuccin-frappe .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-frappe .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-frappe .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-frappe .button.is-static{background-color:#292c3c;border-color:#626880;color:#838ba7;box-shadow:none;pointer-events:none}html.theme--catppuccin-frappe .button.is-rounded,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-frappe .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-frappe .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-frappe .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-frappe .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-frappe .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-frappe .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-frappe .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-frappe .buttons.has-addons .button:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-frappe .buttons.has-addons .button:focus,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused,html.theme--catppuccin-frappe .buttons.has-addons .button:active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-frappe .buttons.has-addons .button:focus:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-frappe .buttons.has-addons .button:active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-frappe .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .buttons.is-centered{justify-content:center}html.theme--catppuccin-frappe .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-frappe .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-frappe .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-frappe .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-frappe .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-frappe .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-frappe .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-frappe .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-frappe .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-frappe .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-frappe .content li+li{margin-top:0.25em}html.theme--catppuccin-frappe .content p:not(:last-child),html.theme--catppuccin-frappe .content dl:not(:last-child),html.theme--catppuccin-frappe .content ol:not(:last-child),html.theme--catppuccin-frappe .content ul:not(:last-child),html.theme--catppuccin-frappe .content blockquote:not(:last-child),html.theme--catppuccin-frappe .content pre:not(:last-child),html.theme--catppuccin-frappe .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-frappe .content h1,html.theme--catppuccin-frappe .content h2,html.theme--catppuccin-frappe .content h3,html.theme--catppuccin-frappe .content h4,html.theme--catppuccin-frappe .content h5,html.theme--catppuccin-frappe .content h6{color:#c6d0f5;font-weight:600;line-height:1.125}html.theme--catppuccin-frappe .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-frappe .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-frappe .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-frappe .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-frappe .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-frappe .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-frappe .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-frappe .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-frappe .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-frappe .content blockquote{background-color:#292c3c;border-left:5px solid #626880;padding:1.25em 1.5em}html.theme--catppuccin-frappe .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-frappe .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-frappe .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-frappe .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-frappe .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-frappe .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-frappe .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-frappe .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-frappe .content ul ul ul{list-style-type:square}html.theme--catppuccin-frappe .content dd{margin-left:2em}html.theme--catppuccin-frappe .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-frappe .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-frappe .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-frappe .content figure img{display:inline-block}html.theme--catppuccin-frappe .content figure figcaption{font-style:italic}html.theme--catppuccin-frappe .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-frappe .content sup,html.theme--catppuccin-frappe .content sub{font-size:75%}html.theme--catppuccin-frappe .content table{width:100%}html.theme--catppuccin-frappe .content table td,html.theme--catppuccin-frappe .content table th{border:1px solid #626880;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-frappe .content table th{color:#b0bef1}html.theme--catppuccin-frappe .content table th:not([align]){text-align:inherit}html.theme--catppuccin-frappe .content table thead td,html.theme--catppuccin-frappe .content table thead th{border-width:0 0 2px;color:#b0bef1}html.theme--catppuccin-frappe .content table tfoot td,html.theme--catppuccin-frappe .content table tfoot th{border-width:2px 0 0;color:#b0bef1}html.theme--catppuccin-frappe .content table tbody tr:last-child td,html.theme--catppuccin-frappe .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-frappe .content .tabs li+li{margin-top:0}html.theme--catppuccin-frappe .content.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-frappe .content.is-normal{font-size:1rem}html.theme--catppuccin-frappe .content.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .content.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-frappe .icon.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-frappe .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-frappe .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-frappe .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-frappe .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-frappe .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--catppuccin-frappe .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--catppuccin-frappe div.icon-text{display:flex}html.theme--catppuccin-frappe .image,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--catppuccin-frappe .image img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--catppuccin-frappe .image img.is-rounded,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--catppuccin-frappe .image.is-fullwidth,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--catppuccin-frappe .image.is-square img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--catppuccin-frappe .image.is-square .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--catppuccin-frappe .image.is-1by1 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--catppuccin-frappe .image.is-1by1 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--catppuccin-frappe .image.is-5by4 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--catppuccin-frappe .image.is-5by4 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--catppuccin-frappe .image.is-4by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--catppuccin-frappe .image.is-4by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--catppuccin-frappe .image.is-3by2 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--catppuccin-frappe .image.is-3by2 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--catppuccin-frappe .image.is-5by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--catppuccin-frappe .image.is-5by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--catppuccin-frappe .image.is-16by9 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--catppuccin-frappe .image.is-16by9 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--catppuccin-frappe .image.is-2by1 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--catppuccin-frappe .image.is-2by1 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--catppuccin-frappe .image.is-3by1 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--catppuccin-frappe .image.is-3by1 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by1 .has-ratio,html.theme--catppuccin-frappe .image.is-4by5 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by5 img,html.theme--catppuccin-frappe .image.is-4by5 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by5 .has-ratio,html.theme--catppuccin-frappe .image.is-3by4 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by4 img,html.theme--catppuccin-frappe .image.is-3by4 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by4 .has-ratio,html.theme--catppuccin-frappe .image.is-2by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by3 img,html.theme--catppuccin-frappe .image.is-2by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by3 .has-ratio,html.theme--catppuccin-frappe .image.is-3by5 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--catppuccin-frappe .image.is-3by5 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--catppuccin-frappe .image.is-9by16 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--catppuccin-frappe .image.is-9by16 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-9by16 .has-ratio,html.theme--catppuccin-frappe .image.is-1by2 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by2 img,html.theme--catppuccin-frappe .image.is-1by2 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by2 .has-ratio,html.theme--catppuccin-frappe .image.is-1by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by3 img,html.theme--catppuccin-frappe .image.is-1by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by3 .has-ratio{height:100%;width:100%}html.theme--catppuccin-frappe .image.is-square,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-square,html.theme--catppuccin-frappe .image.is-1by1,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by1{padding-top:100%}html.theme--catppuccin-frappe .image.is-5by4,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by4{padding-top:80%}html.theme--catppuccin-frappe .image.is-4by3,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by3{padding-top:75%}html.theme--catppuccin-frappe 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.modal-card{display:flex;flex-direction:column;max-height:calc(100vh - 40px);overflow:hidden;-ms-overflow-y:visible}html.theme--catppuccin-frappe .modal-card-head,html.theme--catppuccin-frappe .modal-card-foot{align-items:center;background-color:#292c3c;display:flex;flex-shrink:0;justify-content:flex-start;padding:20px;position:relative}html.theme--catppuccin-frappe .modal-card-head{border-bottom:1px solid #626880;border-top-left-radius:8px;border-top-right-radius:8px}html.theme--catppuccin-frappe .modal-card-title{color:#c6d0f5;flex-grow:1;flex-shrink:0;font-size:1.5rem;line-height:1}html.theme--catppuccin-frappe .modal-card-foot{border-bottom-left-radius:8px;border-bottom-right-radius:8px;border-top:1px solid #626880}html.theme--catppuccin-frappe .modal-card-foot .button:not(:last-child){margin-right:.5em}html.theme--catppuccin-frappe 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kbd.button.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ccd0da #ccd0da !important}html.theme--catppuccin-latte 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.docstring>section>a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #1e66f5 #1e66f5 !important}html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined[disabled],html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-primary.is-light,html.theme--catppuccin-latte .docstring>section>a.button.is-light.docs-sourcelink{background-color:#ebf2fe;color:#0a52e1}html.theme--catppuccin-latte .button.is-primary.is-light:hover,html.theme--catppuccin-latte .docstring>section>a.button.is-light.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-light.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-light.is-hovered.docs-sourcelink{background-color:#dfe9fe;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-primary.is-light:active,html.theme--catppuccin-latte .docstring>section>a.button.is-light.docs-sourcelink:active,html.theme--catppuccin-latte .button.is-primary.is-light.is-active,html.theme--catppuccin-latte .docstring>section>a.button.is-light.is-active.docs-sourcelink{background-color:#d3e1fd;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-link{background-color:#1e66f5;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-link:hover,html.theme--catppuccin-latte .button.is-link.is-hovered{background-color:#125ef4;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-link:focus,html.theme--catppuccin-latte .button.is-link.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-link:focus:not(:active),html.theme--catppuccin-latte .button.is-link.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(30,102,245,0.25)}html.theme--catppuccin-latte .button.is-link:active,html.theme--catppuccin-latte .button.is-link.is-active{background-color:#0b57ef;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-link[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-link{background-color:#1e66f5;border-color:#1e66f5;box-shadow:none}html.theme--catppuccin-latte .button.is-link.is-inverted{background-color:#fff;color:#1e66f5}html.theme--catppuccin-latte .button.is-link.is-inverted:hover,html.theme--catppuccin-latte .button.is-link.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-link.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-link.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#1e66f5}html.theme--catppuccin-latte .button.is-link.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-link.is-outlined{background-color:transparent;border-color:#1e66f5;color:#1e66f5}html.theme--catppuccin-latte .button.is-link.is-outlined:hover,html.theme--catppuccin-latte .button.is-link.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-link.is-outlined:focus,html.theme--catppuccin-latte .button.is-link.is-outlined.is-focused{background-color:#1e66f5;border-color:#1e66f5;color:#fff}html.theme--catppuccin-latte .button.is-link.is-outlined.is-loading::after{border-color:transparent transparent #1e66f5 #1e66f5 !important}html.theme--catppuccin-latte .button.is-link.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-link.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-link.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-link.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-link.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-link.is-outlined{background-color:transparent;border-color:#1e66f5;box-shadow:none;color:#1e66f5}html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-focused{background-color:#fff;color:#1e66f5}html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #1e66f5 #1e66f5 !important}html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-link.is-light{background-color:#ebf2fe;color:#0a52e1}html.theme--catppuccin-latte .button.is-link.is-light:hover,html.theme--catppuccin-latte .button.is-link.is-light.is-hovered{background-color:#dfe9fe;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-link.is-light:active,html.theme--catppuccin-latte .button.is-link.is-light.is-active{background-color:#d3e1fd;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-info{background-color:#179299;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-info:hover,html.theme--catppuccin-latte .button.is-info.is-hovered{background-color:#15878e;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-info:focus,html.theme--catppuccin-latte .button.is-info.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-info:focus:not(:active),html.theme--catppuccin-latte .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(23,146,153,0.25)}html.theme--catppuccin-latte .button.is-info:active,html.theme--catppuccin-latte .button.is-info.is-active{background-color:#147d83;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-info[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info{background-color:#179299;border-color:#179299;box-shadow:none}html.theme--catppuccin-latte .button.is-info.is-inverted{background-color:#fff;color:#179299}html.theme--catppuccin-latte .button.is-info.is-inverted:hover,html.theme--catppuccin-latte .button.is-info.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#179299}html.theme--catppuccin-latte .button.is-info.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-info.is-outlined{background-color:transparent;border-color:#179299;color:#179299}html.theme--catppuccin-latte .button.is-info.is-outlined:hover,html.theme--catppuccin-latte .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-info.is-outlined:focus,html.theme--catppuccin-latte .button.is-info.is-outlined.is-focused{background-color:#179299;border-color:#179299;color:#fff}html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #179299 #179299 !important}html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info.is-outlined{background-color:transparent;border-color:#179299;box-shadow:none;color:#179299}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-focused{background-color:#fff;color:#179299}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #179299 #179299 !important}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-info.is-light{background-color:#edfcfc;color:#1cb2ba}html.theme--catppuccin-latte .button.is-info.is-light:hover,html.theme--catppuccin-latte .button.is-info.is-light.is-hovered{background-color:#e2f9fb;border-color:transparent;color:#1cb2ba}html.theme--catppuccin-latte .button.is-info.is-light:active,html.theme--catppuccin-latte .button.is-info.is-light.is-active{background-color:#d7f7f9;border-color:transparent;color:#1cb2ba}html.theme--catppuccin-latte .button.is-success{background-color:#40a02b;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:hover,html.theme--catppuccin-latte .button.is-success.is-hovered{background-color:#3c9628;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:focus,html.theme--catppuccin-latte .button.is-success.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:focus:not(:active),html.theme--catppuccin-latte .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(64,160,43,0.25)}html.theme--catppuccin-latte .button.is-success:active,html.theme--catppuccin-latte .button.is-success.is-active{background-color:#388c26;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success{background-color:#40a02b;border-color:#40a02b;box-shadow:none}html.theme--catppuccin-latte .button.is-success.is-inverted{background-color:#fff;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted:hover,html.theme--catppuccin-latte .button.is-success.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-success.is-outlined{background-color:transparent;border-color:#40a02b;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-outlined:hover,html.theme--catppuccin-latte .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-success.is-outlined:focus,html.theme--catppuccin-latte .button.is-success.is-outlined.is-focused{background-color:#40a02b;border-color:#40a02b;color:#fff}html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #40a02b #40a02b !important}html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-outlined{background-color:transparent;border-color:#40a02b;box-shadow:none;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-focused{background-color:#fff;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #40a02b #40a02b !important}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-success.is-light{background-color:#f1fbef;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:hover,html.theme--catppuccin-latte .button.is-success.is-light.is-hovered{background-color:#e8f8e5;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:active,html.theme--catppuccin-latte .button.is-success.is-light.is-active{background-color:#e0f5db;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:hover,html.theme--catppuccin-latte .button.is-warning.is-hovered{background-color:#d4871c;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus,html.theme--catppuccin-latte .button.is-warning.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus:not(:active),html.theme--catppuccin-latte .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(223,142,29,0.25)}html.theme--catppuccin-latte .button.is-warning:active,html.theme--catppuccin-latte .button.is-warning.is-active{background-color:#c8801a;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:#df8e1d;box-shadow:none}html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-focused{background-color:#df8e1d;border-color:#df8e1d;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-light{background-color:#fdf6ed;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:hover,html.theme--catppuccin-latte .button.is-warning.is-light.is-hovered{background-color:#fbf1e2;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:active,html.theme--catppuccin-latte .button.is-warning.is-light.is-active{background-color:#faebd6;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:hover,html.theme--catppuccin-latte .button.is-danger.is-hovered{background-color:#c60e36;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus,html.theme--catppuccin-latte .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus:not(:active),html.theme--catppuccin-latte .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(210,15,57,0.25)}html.theme--catppuccin-latte .button.is-danger:active,html.theme--catppuccin-latte .button.is-danger.is-active{background-color:#ba0d33;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:#d20f39;box-shadow:none}html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-focused{background-color:#d20f39;border-color:#d20f39;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-light{background-color:#feecf0;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:hover,html.theme--catppuccin-latte .button.is-danger.is-light.is-hovered{background-color:#fde0e6;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:active,html.theme--catppuccin-latte .button.is-danger.is-light.is-active{background-color:#fcd4dd;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-latte .button.is-small:not(.is-rounded),html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .button.is-normal{font-size:1rem}html.theme--catppuccin-latte .button.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .button.is-large{font-size:1.5rem}html.theme--catppuccin-latte .button[disabled],fieldset[disabled] html.theme--catppuccin-latte .button{background-color:#9ca0b0;border-color:#acb0be;box-shadow:none;opacity:.5}html.theme--catppuccin-latte .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-latte .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-latte .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-latte .button.is-static{background-color:#e6e9ef;border-color:#acb0be;color:#8c8fa1;box-shadow:none;pointer-events:none}html.theme--catppuccin-latte .button.is-rounded,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-latte .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-latte .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-latte .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-latte .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-latte .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-latte .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-latte .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-latte .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-latte .buttons.has-addons .button:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-latte .buttons.has-addons .button:focus,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused,html.theme--catppuccin-latte .buttons.has-addons .button:active,html.theme--catppuccin-latte .buttons.has-addons .button.is-active,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-latte .buttons.has-addons .button:focus:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-latte .buttons.has-addons .button:active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-latte .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .buttons.is-centered{justify-content:center}html.theme--catppuccin-latte .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-latte .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-latte .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-latte .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-latte .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-latte .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-latte .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-latte .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-latte .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-latte .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-latte .content li+li{margin-top:0.25em}html.theme--catppuccin-latte .content p:not(:last-child),html.theme--catppuccin-latte .content dl:not(:last-child),html.theme--catppuccin-latte .content ol:not(:last-child),html.theme--catppuccin-latte .content ul:not(:last-child),html.theme--catppuccin-latte .content blockquote:not(:last-child),html.theme--catppuccin-latte .content pre:not(:last-child),html.theme--catppuccin-latte .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-latte .content h1,html.theme--catppuccin-latte .content h2,html.theme--catppuccin-latte .content h3,html.theme--catppuccin-latte .content h4,html.theme--catppuccin-latte .content h5,html.theme--catppuccin-latte .content h6{color:#4c4f69;font-weight:600;line-height:1.125}html.theme--catppuccin-latte .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-latte .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-latte .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-latte .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-latte .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-latte .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-latte .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-latte .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-latte .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-latte .content blockquote{background-color:#e6e9ef;border-left:5px solid #acb0be;padding:1.25em 1.5em}html.theme--catppuccin-latte .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-latte .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-latte .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-latte .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-latte .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-latte .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-latte .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-latte .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-latte .content ul ul ul{list-style-type:square}html.theme--catppuccin-latte .content dd{margin-left:2em}html.theme--catppuccin-latte .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-latte .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-latte .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-latte .content figure img{display:inline-block}html.theme--catppuccin-latte .content figure figcaption{font-style:italic}html.theme--catppuccin-latte .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-latte .content sup,html.theme--catppuccin-latte .content sub{font-size:75%}html.theme--catppuccin-latte .content table{width:100%}html.theme--catppuccin-latte .content table td,html.theme--catppuccin-latte .content table th{border:1px solid #acb0be;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-latte .content table th{color:#41445a}html.theme--catppuccin-latte .content table th:not([align]){text-align:inherit}html.theme--catppuccin-latte .content table thead td,html.theme--catppuccin-latte .content table thead th{border-width:0 0 2px;color:#41445a}html.theme--catppuccin-latte .content table tfoot td,html.theme--catppuccin-latte .content table tfoot th{border-width:2px 0 0;color:#41445a}html.theme--catppuccin-latte .content table tbody tr:last-child td,html.theme--catppuccin-latte .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-latte .content .tabs li+li{margin-top:0}html.theme--catppuccin-latte .content.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-latte .content.is-normal{font-size:1rem}html.theme--catppuccin-latte .content.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .content.is-large{font-size:1.5rem}html.theme--catppuccin-latte .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-latte .icon.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-latte .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-latte .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-latte .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-latte .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-latte .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--catppuccin-latte .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--catppuccin-latte div.icon-text{display:flex}html.theme--catppuccin-latte .image,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--catppuccin-latte .image img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--catppuccin-latte .image img.is-rounded,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--catppuccin-latte .image.is-fullwidth,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--catppuccin-latte .image.is-square img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--catppuccin-latte .image.is-square .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--catppuccin-latte .image.is-1by1 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--catppuccin-latte .image.is-1by1 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--catppuccin-latte .image.is-5by4 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--catppuccin-latte .image.is-5by4 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--catppuccin-latte .image.is-4by3 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--catppuccin-latte .image.is-4by3 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--catppuccin-latte .image.is-3by2 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--catppuccin-latte .image.is-3by2 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--catppuccin-latte .image.is-5by3 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--catppuccin-latte .image.is-5by3 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--catppuccin-latte .image.is-16by9 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--catppuccin-latte .image.is-16by9 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--catppuccin-latte .image.is-2by1 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--catppuccin-latte .image.is-2by1 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--catppuccin-latte .image.is-3by1 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--catppuccin-latte 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img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--catppuccin-latte .image.is-3by5 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--catppuccin-latte .image.is-9by16 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--catppuccin-latte .image.is-9by16 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-9by16 .has-ratio,html.theme--catppuccin-latte .image.is-1by2 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by2 img,html.theme--catppuccin-latte .image.is-1by2 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by2 .has-ratio,html.theme--catppuccin-latte .image.is-1by3 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by3 img,html.theme--catppuccin-latte .image.is-1by3 .has-ratio,html.theme--catppuccin-latte 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.button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-black:hover,html.theme--catppuccin-macchiato .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-black:focus,html.theme--catppuccin-macchiato .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-black:focus:not(:active),html.theme--catppuccin-macchiato .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--catppuccin-macchiato .button.is-black:active,html.theme--catppuccin-macchiato .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-black[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--catppuccin-macchiato .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-macchiato .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-black.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-light{background-color:#f5f5f5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light:hover,html.theme--catppuccin-macchiato .button.is-light.is-hovered{background-color:#eee;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light:focus,html.theme--catppuccin-macchiato .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light:focus:not(:active),html.theme--catppuccin-macchiato .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(245,245,245,0.25)}html.theme--catppuccin-macchiato .button.is-light:active,html.theme--catppuccin-macchiato .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-light{background-color:#f5f5f5;border-color:#f5f5f5;box-shadow:none}html.theme--catppuccin-macchiato .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-macchiato .button.is-light.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-macchiato .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--catppuccin-macchiato .button.is-light.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-light.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-macchiato 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.content kbd.button{background-color:#363a4f;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-dark:hover,html.theme--catppuccin-macchiato .content kbd.button:hover,html.theme--catppuccin-macchiato .button.is-dark.is-hovered,html.theme--catppuccin-macchiato .content kbd.button.is-hovered{background-color:#313447;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-dark:focus,html.theme--catppuccin-macchiato .content kbd.button:focus,html.theme--catppuccin-macchiato .button.is-dark.is-focused,html.theme--catppuccin-macchiato .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-dark:focus:not(:active),html.theme--catppuccin-macchiato .content kbd.button:focus:not(:active),html.theme--catppuccin-macchiato .button.is-dark.is-focused:not(:active),html.theme--catppuccin-macchiato .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(54,58,79,0.25)}html.theme--catppuccin-macchiato .button.is-dark:active,html.theme--catppuccin-macchiato .content kbd.button:active,html.theme--catppuccin-macchiato .button.is-dark.is-active,html.theme--catppuccin-macchiato .content kbd.button.is-active{background-color:#2c2f40;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-dark[disabled],html.theme--catppuccin-macchiato .content kbd.button[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-dark,fieldset[disabled] html.theme--catppuccin-macchiato .content kbd.button{background-color:#363a4f;border-color:#363a4f;box-shadow:none}html.theme--catppuccin-macchiato .button.is-dark.is-inverted,html.theme--catppuccin-macchiato .content kbd.button.is-inverted{background-color:#fff;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted:hover,html.theme--catppuccin-macchiato .content kbd.button.is-inverted:hover,html.theme--catppuccin-macchiato 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.button.is-dark.is-outlined:hover,html.theme--catppuccin-macchiato .content kbd.button.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-hovered,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-dark.is-outlined:focus,html.theme--catppuccin-macchiato .content kbd.button.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-focused,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-focused{background-color:#363a4f;border-color:#363a4f;color:#fff}html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #363a4f #363a4f !important}html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-dark.is-outlined[disabled],html.theme--catppuccin-macchiato .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-macchiato .content kbd.button.is-outlined{background-color:transparent;border-color:#363a4f;box-shadow:none;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-macchiato .content 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.button.is-info.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-info.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-focused{background-color:#8bd5ca;border-color:#8bd5ca;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #8bd5ca #8bd5ca !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-outlined{background-color:transparent;border-color:#8bd5ca;box-shadow:none;color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #8bd5ca #8bd5ca !important}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-light{background-color:#f0faf8;color:#276d62}html.theme--catppuccin-macchiato .button.is-info.is-light:hover,html.theme--catppuccin-macchiato .button.is-info.is-light.is-hovered{background-color:#e7f6f4;border-color:transparent;color:#276d62}html.theme--catppuccin-macchiato .button.is-info.is-light:active,html.theme--catppuccin-macchiato .button.is-info.is-light.is-active{background-color:#ddf3f0;border-color:transparent;color:#276d62}html.theme--catppuccin-macchiato .button.is-success{background-color:#a6da95;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:hover,html.theme--catppuccin-macchiato .button.is-success.is-hovered{background-color:#9ed78c;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:focus,html.theme--catppuccin-macchiato .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:focus:not(:active),html.theme--catppuccin-macchiato .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,218,149,0.25)}html.theme--catppuccin-macchiato .button.is-success:active,html.theme--catppuccin-macchiato .button.is-success.is-active{background-color:#96d382;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success{background-color:#a6da95;border-color:#a6da95;box-shadow:none}html.theme--catppuccin-macchiato .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined{background-color:transparent;border-color:#a6da95;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-success.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-focused{background-color:#a6da95;border-color:#a6da95;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6da95 #a6da95 !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-outlined{background-color:transparent;border-color:#a6da95;box-shadow:none;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6da95 #a6da95 !important}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-light{background-color:#f2faf0;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:hover,html.theme--catppuccin-macchiato .button.is-success.is-light.is-hovered{background-color:#eaf6e6;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:active,html.theme--catppuccin-macchiato .button.is-success.is-light.is-active{background-color:#e2f3dd;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:hover,html.theme--catppuccin-macchiato .button.is-warning.is-hovered{background-color:#eccf94;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus,html.theme--catppuccin-macchiato .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus:not(:active),html.theme--catppuccin-macchiato .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(238,212,159,0.25)}html.theme--catppuccin-macchiato .button.is-warning:active,html.theme--catppuccin-macchiato .button.is-warning.is-active{background-color:#eaca89;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:#eed49f;box-shadow:none}html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-focused{background-color:#eed49f;border-color:#eed49f;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-light{background-color:#fcf7ee;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:hover,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-hovered{background-color:#faf2e3;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:active,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-active{background-color:#f8eed8;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:hover,html.theme--catppuccin-macchiato .button.is-danger.is-hovered{background-color:#eb7c8c;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus,html.theme--catppuccin-macchiato .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus:not(:active),html.theme--catppuccin-macchiato .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(237,135,150,0.25)}html.theme--catppuccin-macchiato .button.is-danger:active,html.theme--catppuccin-macchiato .button.is-danger.is-active{background-color:#ea7183;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:#ed8796;box-shadow:none}html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-macchiato .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-focused{background-color:#ed8796;border-color:#ed8796;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-light{background-color:#fcedef;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:hover,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-hovered{background-color:#fbe2e6;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:active,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-active{background-color:#f9d7dc;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-small:not(.is-rounded),html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-macchiato .button.is-normal{font-size:1rem}html.theme--catppuccin-macchiato .button.is-medium{font-size:1.25rem}html.theme--catppuccin-macchiato .button.is-large{font-size:1.5rem}html.theme--catppuccin-macchiato .button[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button{background-color:#6e738d;border-color:#5b6078;box-shadow:none;opacity:.5}html.theme--catppuccin-macchiato .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-macchiato .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-macchiato .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-macchiato .button.is-static{background-color:#1e2030;border-color:#5b6078;color:#8087a2;box-shadow:none;pointer-events:none}html.theme--catppuccin-macchiato .button.is-rounded,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-macchiato .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-macchiato .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-macchiato .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-macchiato .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-macchiato .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-macchiato .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-macchiato .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-macchiato .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-macchiato .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-macchiato .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-macchiato .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-macchiato .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-macchiato .buttons.has-addons .button:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-macchiato .buttons.has-addons .button:focus,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-focused,html.theme--catppuccin-macchiato .buttons.has-addons .button:active,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-active,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-macchiato .buttons.has-addons .button:focus:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button:active:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-macchiato .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-macchiato .buttons.is-centered{justify-content:center}html.theme--catppuccin-macchiato .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-macchiato 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kbd.button.is-hovered{background-color:#2c2d3d;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-dark:focus,html.theme--catppuccin-mocha .content kbd.button:focus,html.theme--catppuccin-mocha .button.is-dark.is-focused,html.theme--catppuccin-mocha .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-dark:focus:not(:active),html.theme--catppuccin-mocha .content kbd.button:focus:not(:active),html.theme--catppuccin-mocha .button.is-dark.is-focused:not(:active),html.theme--catppuccin-mocha .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(49,50,68,0.25)}html.theme--catppuccin-mocha .button.is-dark:active,html.theme--catppuccin-mocha .content kbd.button:active,html.theme--catppuccin-mocha .button.is-dark.is-active,html.theme--catppuccin-mocha .content kbd.button.is-active{background-color:#262735;border-color:transparent;color:#fff}html.theme--catppuccin-mocha 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kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#313244}html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #313244 #313244 !important}html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined[disabled],html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-primary,html.theme--catppuccin-mocha .docstring>section>a.button.docs-sourcelink{background-color:#89b4fa;border-color:transparent;color:#fff}html.theme--catppuccin-mocha 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html.theme--catppuccin-mocha .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-link.is-light{background-color:#ebf3fe;color:#063c93}html.theme--catppuccin-mocha .button.is-link.is-light:hover,html.theme--catppuccin-mocha .button.is-link.is-light.is-hovered{background-color:#dfebfe;border-color:transparent;color:#063c93}html.theme--catppuccin-mocha .button.is-link.is-light:active,html.theme--catppuccin-mocha .button.is-link.is-light.is-active{background-color:#d3e3fd;border-color:transparent;color:#063c93}html.theme--catppuccin-mocha .button.is-info{background-color:#94e2d5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:hover,html.theme--catppuccin-mocha .button.is-info.is-hovered{background-color:#8adfd1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:focus,html.theme--catppuccin-mocha 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.button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-info.is-outlined{background-color:transparent;border-color:#94e2d5;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-outlined:hover,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-info.is-outlined:focus,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-focused{background-color:#94e2d5;border-color:#94e2d5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #94e2d5 #94e2d5 !important}html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-outlined{background-color:transparent;border-color:#94e2d5;box-shadow:none;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #94e2d5 #94e2d5 !important}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-light{background-color:#effbf9;color:#207466}html.theme--catppuccin-mocha .button.is-info.is-light:hover,html.theme--catppuccin-mocha .button.is-info.is-light.is-hovered{background-color:#e5f8f5;border-color:transparent;color:#207466}html.theme--catppuccin-mocha .button.is-info.is-light:active,html.theme--catppuccin-mocha .button.is-info.is-light.is-active{background-color:#dbf5f1;border-color:transparent;color:#207466}html.theme--catppuccin-mocha .button.is-success{background-color:#a6e3a1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:hover,html.theme--catppuccin-mocha .button.is-success.is-hovered{background-color:#9de097;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:focus,html.theme--catppuccin-mocha .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:focus:not(:active),html.theme--catppuccin-mocha .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,227,161,0.25)}html.theme--catppuccin-mocha .button.is-success:active,html.theme--catppuccin-mocha .button.is-success.is-active{background-color:#93dd8d;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success{background-color:#a6e3a1;border-color:#a6e3a1;box-shadow:none}html.theme--catppuccin-mocha .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted:hover,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-success.is-outlined{background-color:transparent;border-color:#a6e3a1;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-outlined:hover,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-success.is-outlined:focus,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-focused{background-color:#a6e3a1;border-color:#a6e3a1;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-outlined{background-color:transparent;border-color:#a6e3a1;box-shadow:none;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-light{background-color:#f0faef;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:hover,html.theme--catppuccin-mocha .button.is-success.is-light.is-hovered{background-color:#e7f7e5;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:active,html.theme--catppuccin-mocha .button.is-success.is-light.is-active{background-color:#def4dc;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:hover,html.theme--catppuccin-mocha .button.is-warning.is-hovered{background-color:#f8dea3;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus,html.theme--catppuccin-mocha .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus:not(:active),html.theme--catppuccin-mocha .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(249,226,175,0.25)}html.theme--catppuccin-mocha .button.is-warning:active,html.theme--catppuccin-mocha .button.is-warning.is-active{background-color:#f7d997;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:#f9e2af;box-shadow:none}html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-focused{background-color:#f9e2af;border-color:#f9e2af;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-light{background-color:#fef8ec;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:hover,html.theme--catppuccin-mocha .button.is-warning.is-light.is-hovered{background-color:#fdf4e0;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:active,html.theme--catppuccin-mocha .button.is-warning.is-light.is-active{background-color:#fcf0d4;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:hover,html.theme--catppuccin-mocha .button.is-danger.is-hovered{background-color:#f27f9f;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus,html.theme--catppuccin-mocha .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus:not(:active),html.theme--catppuccin-mocha .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(243,139,168,0.25)}html.theme--catppuccin-mocha .button.is-danger:active,html.theme--catppuccin-mocha .button.is-danger.is-active{background-color:#f17497;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:#f38ba8;box-shadow:none}html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-mocha .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-focused{background-color:#f38ba8;border-color:#f38ba8;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-light{background-color:#fdedf1;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:hover,html.theme--catppuccin-mocha .button.is-danger.is-light.is-hovered{background-color:#fce1e8;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:active,html.theme--catppuccin-mocha .button.is-danger.is-light.is-active{background-color:#fbd5e0;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-mocha .button.is-small:not(.is-rounded),html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .button.is-normal{font-size:1rem}html.theme--catppuccin-mocha .button.is-medium{font-size:1.25rem}html.theme--catppuccin-mocha .button.is-large{font-size:1.5rem}html.theme--catppuccin-mocha .button[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button{background-color:#6c7086;border-color:#585b70;box-shadow:none;opacity:.5}html.theme--catppuccin-mocha .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-mocha .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-mocha .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-mocha .button.is-static{background-color:#181825;border-color:#585b70;color:#7f849c;box-shadow:none;pointer-events:none}html.theme--catppuccin-mocha .button.is-rounded,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-mocha .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-mocha .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-mocha .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-mocha .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-mocha .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-mocha .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-mocha .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-mocha .buttons.has-addons .button:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-mocha .buttons.has-addons .button:focus,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused,html.theme--catppuccin-mocha .buttons.has-addons .button:active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-mocha .buttons.has-addons 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.button.is-link.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-link.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-link.is-outlined{background-color:transparent;border-color:#1abc9c;box-shadow:none;color:#1abc9c}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-focused{background-color:#fff;color:#1abc9c}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #1abc9c #1abc9c !important}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-link.is-light{background-color:#edfdf9;color:#15987e}html.theme--documenter-dark .button.is-link.is-light:hover,html.theme--documenter-dark .button.is-link.is-light.is-hovered{background-color:#e2fbf6;border-color:transparent;color:#15987e}html.theme--documenter-dark .button.is-link.is-light:active,html.theme--documenter-dark 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.button.is-info.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-focused{background-color:#fff;color:#3c5dcd}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #3c5dcd #3c5dcd !important}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark 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.button.is-success.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#259a12}html.theme--documenter-dark .button.is-success.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-success.is-outlined{background-color:transparent;border-color:#259a12;color:#259a12}html.theme--documenter-dark .button.is-success.is-outlined:hover,html.theme--documenter-dark .button.is-success.is-outlined.is-hovered,html.theme--documenter-dark .button.is-success.is-outlined:focus,html.theme--documenter-dark .button.is-success.is-outlined.is-focused{background-color:#259a12;border-color:#259a12;color:#fff}html.theme--documenter-dark .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #259a12 #259a12 !important}html.theme--documenter-dark .button.is-success.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-outlined{background-color:transparent;border-color:#259a12;box-shadow:none;color:#259a12}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-focused{background-color:#fff;color:#259a12}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #259a12 #259a12 !important}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-success.is-light{background-color:#effded;color:#2ec016}html.theme--documenter-dark .button.is-success.is-light:hover,html.theme--documenter-dark 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rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#f4c72f;box-shadow:none;color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f4c72f #f4c72f !important}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning.is-light{background-color:#fefaec;color:#8c6e07}html.theme--documenter-dark .button.is-warning.is-light:hover,html.theme--documenter-dark .button.is-warning.is-light.is-hovered{background-color:#fdf7e0;border-color:transparent;color:#8c6e07}html.theme--documenter-dark .button.is-warning.is-light:active,html.theme--documenter-dark .button.is-warning.is-light.is-active{background-color:#fdf3d3;border-color:transparent;color:#8c6e07}html.theme--documenter-dark .button.is-danger{background-color:#cb3c33;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:hover,html.theme--documenter-dark .button.is-danger.is-hovered{background-color:#c13930;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:focus,html.theme--documenter-dark .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:focus:not(:active),html.theme--documenter-dark .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(203,60,51,0.25)}html.theme--documenter-dark .button.is-danger:active,html.theme--documenter-dark .button.is-danger.is-active{background-color:#b7362e;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger{background-color:#cb3c33;border-color:#cb3c33;box-shadow:none}html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-inverted:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#cb3c33;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-outlined.is-hovered,html.theme--documenter-dark 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html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fbefef;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#f8e6e5;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#f6dcda;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#5e6d6f;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 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.buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark 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img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--documenter-dark .image img.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--documenter-dark .image.is-fullwidth,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--documenter-dark .image.is-5by4 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.docs-logo>img.is-3by1{padding-top:33.3333%}html.theme--documenter-dark .image.is-4by5,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by5{padding-top:125%}html.theme--documenter-dark .image.is-3by4,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by4{padding-top:133.3333%}html.theme--documenter-dark .image.is-2by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by3{padding-top:150%}html.theme--documenter-dark .image.is-3by5,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by5{padding-top:166.6666%}html.theme--documenter-dark .image.is-9by16,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-9by16{padding-top:177.7777%}html.theme--documenter-dark .image.is-1by2,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by2{padding-top:200%}html.theme--documenter-dark .image.is-1by3,html.theme--documenter-dark #documenter .docs-sidebar 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GitHub

Design principles

This project is inspired by two existing projects:

OMLT is a framework built around Pyomo, and gurobi-machinelearning is a framework build around gurobipy.

These projects served as inspiration, but we also departed from them in some carefully considered ways.

All of our design decisions were guided by two principles:

  1. To be simple
  2. To leverage Julia's Pkg extensions and multiple dispatch.

Terminology

Because the field is relatively new, there is no settled choice of terminology.

MathOptAI chooses to use "predictor" as the synonym for the machine learning model. Hence, we have AbstractPredictor, add_predictor, and build_predictor.

In contrast, gurob-machinelearning tends to use "regression model" and OMLT uses "formulation."

We choose "predictor" because all models we implement are of the form $y = f(x)$.

We do not use "machine learning model" because we have support for the linear and logistic regression models of classical statistical fitting. We could have used "regression model", but we find that models like neural networks and binary decision trees are not commonly thought of as regression models.

Inputs are vectors

MathOptAI assumes that all inputs $x$ and outputs $y$ to $y = predictor(x)$ are Base.Vectors.

We make this choice for simplicity.

In our opinion, Julia libraries often take a laissez-faire approach to the types that they support. In the optimistic case, this can lead to novel behavior by combining two packages that the package author had previously not considered or tested. In the pessimistic case, this can lead to incorrect results or cryptic error messagges.

Exceptions to the Vector rule will be carefully considered and tested.

Currently, there are two exceptions:

  1. If x is a Matrix, then the columns of x are interpreted as independent observations, and the output y will be a Matrix with the same number of columns
  2. The StatsModels extension allows x to be a DataFrames.DataFrame, if the predictor is a StatsModels.TableRegressionModel.

Exceptions 1 and 2 are combined in the StatsModels exception, so that the predictor is mapped over the rows of the DataFrames.DataFrame (which we assume will be a common use-case).

We choose to interpret the rows as input variables and columns as independent observations (rather than the more traditional table-based approach where columns are the input variables and rows are observations) because Julia uses column-major ordering in Matrix. Another justification follows from the Affine predictor, $f(x) = Ax + b$, where passing in a Matrix as x with column observations naturally leads to a Matrix output for y of the appropriate dimensions.

We choose to make y a Vector, even for scalar outputs, to simplify code that works generically for many different predictors. Without this principle, there will inevitably be cases where a scalar and length-1 vector are confused.

If you want to use a predictor that does not take Vector input (for example, it is an image as input to a neural network), the first preprocessing step should be to vec the input into a single Vector.

Inputs are provided, outputs are returned

The main job of MathOptAI is to embed models of the form y = predictor(x) into a JuMP model. A key design decision is how to represent the input x and output y.

gurobi-machinelearning

gurobi-machinelearning implements an API of the following general form:

pred_constr = add_predictor_constr(model, predictor, x, y)

Here, both the input x and the output y must be created and provided by the user, and a new object pred_constr is returned.

The benefit of this design is that pred_constr can contain statistics about the reformulation (for example, the number of variables that were added), and it can be used to delete a predictor from model.

The downside is that the user must ensure that the shape and size of y is correct.

OMLT

OMLT implements an API of the following general form:

model.pred_constr = OmltBlock()
+model.pred_constr.build_formulation(predictor)
+x, y = model.pred_constr.inputs, model.pred_constr.outputs

First, a new OmltBlock() is created. Then the formulation is built inside the block, and both the input and output are provided to the user.

The benefit of this design is that pred_constr can contain statistics about the reformulation (for example, the number of variables that were added), and it can be used to delete a predictor from model.

The downside is that the user must often write additional constraints to connect the input and output of the OmltBlock to their existing decision variables:

#connect pyomo model input and output to the neural network
+@model.Constraint()
+def connect_input(mdl):
+    return mdl.input == mdl.nn.inputs[0]
+
+@model.Constraint()
+def connect_output(mdl):
+    return mdl.output == mdl.nn.outputs[0]

A second downside is that the predictor must describe the input and output dimension; these cannot be inferred automatically. As one example, this means that it cannot do the following:

# Not possible because dimension not given
+model.pred_constr.build_formulation(ReLU())

In the context of MathOptAI, something like ReLU() is useful so that we can map generic layers like Flux.relu => MathOptAI.ReLU(), and so that we do not duplicate required dimension information in input and predictor (see the MathOptAI section below).

MathOptAI

The main entry-point to MathOptAI is add_predictor:

y, formulation = MathOptAI.add_predictor(model, predictor, x)

The user provides the input x, and the output y is returned.

The main benefit of this approach is simplicity.

First, the user probably already has the input x as decision variables or an expression in the model, so we do not need the connect_input constraint, and because we use a full-space formulation by default, the output y will always be a vector of decision variables, which avoids the need for a connect_output constraint.

Second, predictors do not need to store dimension information, so we can have:

y, formulation = MathOptAI.add_predictor(model, MathOptAI.ReLU(), x)

for any size of x.

Activations are predictors

OMLT makes a distinction between layers, like full_space_dense_layer, and elementwise activation functions, like sigmoid_activation_function.

The downside to this approach is that it treats activation functions as special, leading to issues such as OMLT#125.

In constrast, MathOptAI treats activation functions as a vector-valued predictor like any other:

y, formulation = MathOptAI.add_predictor(model, MathOptAI.ReLU(), x)

This means that we can pipeline them to create predictors such as:

function LogisticRegression(A)
+    return MathOptAI.Pipeline(MathOptAI.Affine(A), MathOptAI.Sigmoid())
+end

Controlling transformations

Many predictors have multiple ways that they can be formulated in an optimization model. For example, ReLU implements the non-smooth nonlinear formulation $y = \max\{x, 0\}$, while ReLUQuadratic implements a the complementarity formulation $x = y - slack; y, slack \ge 0; y * slack = 0$.

Choosing the appropriate formulation for the combination of model and solver can have a large impact on the performance.

Because gurobi-machinelearning is specific to the Gurobi solver, they have a limited ability for the user to choose and implement different formulations.

OMLT is more general, in that it has multiple ways of formulating layers such as ReLU. However, these are hard-coded into complete formulations such as omlt.neuralnet.nn_formulation.ReluBigMFormulation or omlt.neuralnet.nn_formulation.ReluComplementarityFormulation.

In contrast, MathOptAI tries to take a maximally modular approach, where the user can control how the layers are formulated at runtime, including using a custom formulation that is not defined in MathOptAI.jl.

Currently, we achive this with a config dictionary, which maps the various neural network layers to an AbstractPredictor. For example:

chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));
+config = Dict(Flux.relu => MathOptAI.ReLU())
+predictor = MathOptAI.build_predictor(chain; config)

Please open a GitHub issue if you have a suggestion for a better API.

Full-space or reduced-space

OMLT has two ways that it can formulate neural networks: full-space and reduced-space.

The full-space formulations add intermediate variables to represent the output of all layers.

For example, in a Flux.Dense(2, 3, Flux.relu) layer, a full-space formulation will add an intermediate y_tmp variable to represent the output of the affine layer prior to the ReLU:

layer = Flux.Dense(2, 3, Flux.relu)
+model_full_space = Model()
+@variable(model_full_space, x[1:2])
+@variable(model_full_space, y_tmp[1:3])
+@variable(model_full_space, y[1:3])
+@constraint(model_full_space, y_tmp == layer.A * x + layer.b)
+@constraint(model_full_space, y .== max.(0, y_tmp))

In contrast, a reduced-space formulation encodes the input-output relationship as a single nonlinear constraint:

layer = Flux.Dense(2, 3, Flux.relu)
+model_reduced_space = Model()
+@variable(model_reduced_space, x[1:2])
+@variable(model_reduced_space, y[1:3])
+@constraint(model_reduced_space, y .== max.(0, layer.A * x + layer.b))

In general, the full-space formulations have more variables and constraints but simpler nonlinear expressions, whereas the reduced-space formulations have fewer variables and constraints but more complicated nonlinear expressions.

MathOptAI.jl implements the full-space formulation by default, but some layers support the reduced-space formulation with the ReducedSpace wrapper.

diff --git a/v0.1.3/index.html b/v0.1.3/index.html new file mode 100644 index 00000000..c3190123 --- /dev/null +++ b/v0.1.3/index.html @@ -0,0 +1,30 @@ + +MathOptAI.jl · MathOptAI.jl
GitHub

MathOptAI.jl

MathOptAI.jl is a JuMP extension for embedding trained AI, machine learning, and statistical learning models into a JuMP optimization model.

License

MathOptAI.jl is provided under a BSD-3 license as part of the Optimization and Machine Learning Toolbox project, O4806.

See LICENSE.md for details.

Despite the name similarity, this project is not affiliated with OMLT, the Optimization and Machine Learning Toolkit.

Installation

Install MathOptAI.jl using the Julia package manager:

import Pkg
+Pkg.add("MathOptAI")

Getting started

Here's an example of using MathOptAI to embed a trained neural network from Flux into a JuMP model. The vector of JuMP variables x is fed as input to the neural network. The output y is a vector of JuMP variables that represents the output layer of the neural network. The formulation object stores the additional variables and constraints that were added to model.

julia> using JuMP, MathOptAI, Flux
+
+julia> predictor = Flux.Chain(
+           Flux.Dense(28^2 => 32, Flux.sigmoid),
+           Flux.Dense(32 => 10),
+           Flux.softmax,
+       );
+
+julia> #= Train the Flux model. Code not shown for simplicity =#
+
+julia> model = JuMP.Model();
+
+julia> JuMP.@variable(model, 0 <= x[1:28^2] <= 1);
+
+julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
+
+julia> y
+10-element Vector{VariableRef}:
+ moai_SoftMax[1]
+ moai_SoftMax[2]
+ moai_SoftMax[3]
+ moai_SoftMax[4]
+ moai_SoftMax[5]
+ moai_SoftMax[6]
+ moai_SoftMax[7]
+ moai_SoftMax[8]
+ moai_SoftMax[9]
+ moai_SoftMax[10]

Getting help

This package is under active development. For help, questions, comments, and suggestions, please open a GitHub issue.

Inspiration

This project is mainly inspired by two existing projects:

Other works, from which we took less inspiration, include:

The 2024 paper of López-Flores et al. is an excellent summary of the state of the field at the time that we started development of MathOptAI.

López-Flores, F.J., Ramírez-Márquez, C., Ponce-Ortega J.M. (2024). Process Systems Engineering Tools for Optimization of Trained Machine Learning Models: Comparative and Perspective. Industrial & Engineering Chemistry Research, 63(32), 13966-13979. DOI: 10.1021/acs.iecr.4c00632

diff --git a/v0.1.3/manual/AbstractGPs/index.html b/v0.1.3/manual/AbstractGPs/index.html new file mode 100644 index 00000000..fa1885c2 --- /dev/null +++ b/v0.1.3/manual/AbstractGPs/index.html @@ -0,0 +1,6 @@ + +AbstractGPs.jl · MathOptAI.jl
GitHub

AbstractGPs.jl

AbstractGPs.jl is a library for fittinng Gaussian Processes in Julia.

Basic example

Here is an example:

julia> using JuMP, MathOptAI, AbstractGPs
julia> x_data = 2π .* (0.0:0.1:1.0);
julia> y_data = sin.(x_data);
julia> fx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.1);
julia> p_fx = AbstractGPs.posterior(fx, y_data);
julia> model = Model();
julia> @variable(model, 1 <= x[1:1] <= 6, start = 3);
julia> predictor = MathOptAI.Quantile(p_fx, [0.1, 0.9]);
julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
julia> y2-element Vector{JuMP.VariableRef}:
+ moai_quantile[1]
+ moai_quantile[2]
julia> formulationQuantile(_, [0.1, 0.9])
+├ variables [0]
+└ constraints [0]
julia> @objective(model, Max, y[2] - y[1])moai_quantile[2] - moai_quantile[1]
diff --git a/v0.1.3/manual/DecisionTree/index.html b/v0.1.3/manual/DecisionTree/index.html new file mode 100644 index 00000000..ca45abbb --- /dev/null +++ b/v0.1.3/manual/DecisionTree/index.html @@ -0,0 +1,18 @@ + +DecisionTree.jl · MathOptAI.jl
GitHub

DecisionTree.jl

DecisionTree.jl is a library for fitting decision trees in Julia.

Basic example

Here is an example:

julia> using JuMP, MathOptAI, DecisionTree
julia> truth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)truth (generic function with 1 method)
julia> features = abs.(sin.((1:10) .* (3:4)'));
julia> size(features)(10, 2)
julia> labels = truth.(Vector.(eachrow(features)));
julia> predictor = DecisionTree.build_tree(labels, features)Decision Tree
+Leaves: 3
+Depth:  2
julia> model = Model();
julia> @variable(model, 0 <= x[1:2] <= 1);
julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_BinaryDecisionTree_value
julia> formulationBinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]
+├ variables [4]
+│ ├ moai_BinaryDecisionTree_value
+│ ├ moai_BinaryDecisionTree_z[1]
+│ ├ moai_BinaryDecisionTree_z[2]
+│ └ moai_BinaryDecisionTree_z[3]
+└ constraints [7]
+  ├ moai_BinaryDecisionTree_z[1] + moai_BinaryDecisionTree_z[2] + moai_BinaryDecisionTree_z[3] = 1
+  ├ moai_BinaryDecisionTree_z[1] --> {x[1] ≤ 0.4743457016210958}
+  ├ moai_BinaryDecisionTree_z[2] --> {x[1] ≥ 0.4743457016210958}
+  ├ moai_BinaryDecisionTree_z[2] --> {x[2] ≤ 0.41966499895337794}
+  ├ moai_BinaryDecisionTree_z[3] --> {x[1] ≥ 0.4743457016210958}
+  ├ moai_BinaryDecisionTree_z[3] --> {x[2] ≥ 0.41966499895337794}
+  └ 2 moai_BinaryDecisionTree_z[1] - 3 moai_BinaryDecisionTree_z[2] - 4 moai_BinaryDecisionTree_z[3] + moai_BinaryDecisionTree_value = 0
diff --git a/v0.1.3/manual/Flux/index.html b/v0.1.3/manual/Flux/index.html new file mode 100644 index 00000000..8dcd4add --- /dev/null +++ b/v0.1.3/manual/Flux/index.html @@ -0,0 +1,67 @@ + +Flux.jl · MathOptAI.jl
GitHub

Flux.jl

Flux.jl is a library for machine learning in Julia.

The upstream documentation is available at https://fluxml.ai/Flux.jl/stable/.

Supported layers

MathOptAI supports embedding a Flux model into JuMP if it is a Flux.Chain composed of:

Basic example

Use MathOptAI.add_predictor to embed a Flux.Chain into a JuMP model:

julia> using JuMP, Flux, MathOptAI
julia> predictor = Flux.Chain(Flux.Dense(1 => 2, Flux.relu), Flux.Dense(2 => 1));
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_Affine[1]
julia> formulationAffine(A, b) [input: 1, output: 2]
+├ variables [2]
+│ ├ moai_Affine[1]
+│ └ moai_Affine[2]
+└ constraints [2]
+  ├ 0.601884663105011 x[1] - moai_Affine[1] = 0
+  └ -0.9251309037208557 x[1] - moai_Affine[2] = 0
+MathOptAI.ReLU()
+├ variables [2]
+│ ├ moai_ReLU[1]
+│ └ moai_ReLU[2]
+└ constraints [4]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[2] ≥ 0
+  ├ moai_ReLU[1] - max(0.0, moai_Affine[1]) = 0
+  └ moai_ReLU[2] - max(0.0, moai_Affine[2]) = 0
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ 0.12332741171121597 moai_ReLU[1] + 0.9805504679679871 moai_ReLU[2] - moai_Affine[1] = 0

Reduced-space

Use the reduced_space = true keyword to formulate a reduced-space model:

julia> using JuMP, Flux, MathOptAI
julia> predictor = Flux.Chain(Flux.Dense(1 => 2, Flux.relu), Flux.Dense(2 => 1));
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> y, formulation =
+           MathOptAI.add_predictor(model, predictor, x; reduced_space = true);
julia> y1-element Vector{JuMP.NonlinearExpr}:
+ ((+(0.0) + (-0.06484545767307281 * max(0.0, -0.510906457901001 x[1]))) + (0.4941628575325012 * max(0.0, 1.106669545173645 x[1]))) + 0.0
julia> formulationReducedSpace(Affine(A, b) [input: 1, output: 2])
+├ variables [0]
+└ constraints [0]
+ReducedSpace(MathOptAI.ReLU())
+├ variables [0]
+└ constraints [0]
+ReducedSpace(Affine(A, b) [input: 2, output: 1])
+├ variables [0]
+└ constraints [0]

Gray-box

Use the gray_box = true keyword to embed the network as a nonlinear operator:

julia> using JuMP, Flux, MathOptAI
julia> predictor = Flux.Chain(Flux.Dense(1 => 2, Flux.relu), Flux.Dense(2 => 1));
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> y, formulation =
+           MathOptAI.add_predictor(model, predictor, x; gray_box = true);
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_GrayBox[1]
julia> formulationGrayBox
+├ variables [1]
+│ └ moai_GrayBox[1]
+└ constraints [1]
+  └ op_##1220(x[1]) - moai_GrayBox[1] = 0

Change how layers are formulated

Pass a dictionary to the config keyword that maps Flux activation functions to a MathOptAI predictor:

julia> using JuMP, Flux, MathOptAI
julia> predictor = Flux.Chain(Flux.Dense(1 => 2, Flux.relu), Flux.Dense(2 => 1));
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> y, formulation = MathOptAI.add_predictor(
+           model,
+           predictor,
+           x;
+           config = Dict(Flux.relu => MathOptAI.ReLUSOS1()),
+       );
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_Affine[1]
julia> formulationAffine(A, b) [input: 1, output: 2]
+├ variables [2]
+│ ├ moai_Affine[1]
+│ └ moai_Affine[2]
+└ constraints [2]
+  ├ 0.3965674340724945 x[1] - moai_Affine[1] = 0
+  └ -1.2659741640090942 x[1] - moai_Affine[2] = 0
+MathOptAI.ReLUSOS1()
+├ variables [4]
+│ ├ moai_ReLU[1]
+│ ├ moai_ReLU[2]
+│ ├ moai_z[1]
+│ └ moai_z[2]
+└ constraints [4]
+  ├ moai_Affine[1] - moai_ReLU[1] + moai_z[1] = 0
+  ├ moai_Affine[2] - moai_ReLU[2] + moai_z[2] = 0
+  ├ [moai_ReLU[1], moai_z[1]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])
+  └ [moai_ReLU[2], moai_z[2]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ -0.025825228542089462 moai_ReLU[1] - 0.847888708114624 moai_ReLU[2] - moai_Affine[1] = 0
diff --git a/v0.1.3/manual/GLM/index.html b/v0.1.3/manual/GLM/index.html new file mode 100644 index 00000000..53d5087f --- /dev/null +++ b/v0.1.3/manual/GLM/index.html @@ -0,0 +1,28 @@ + +GLM.jl · MathOptAI.jl
GitHub

GLM.jl

GLM.jl is a library for fitting generalized linear models in Julia.

MathOptAI.jl supports embedding two types of regression models from GLM:

  • GLM.lm(X, Y)
  • GLM.glm(X, Y, GLM.Bernoulli())

Linear regression

The input x to add_predictor must be a vector with the same number of elements as columns in the training matrix. The return is a vector of JuMP variables with a single element.

julia> using GLM, JuMP, MathOptAI
julia> X, Y = rand(10, 2), rand(10);
julia> predictor = GLM.lm(X, Y);
julia> model = Model();
julia> @variable(model, x[1:2]);
julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_Affine[1]
julia> formulationAffine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ 0.44118491396329523 x[1] + 0.3847750599449174 x[2] - moai_Affine[1] = 0

Logistic regression

The input x to add_predictor must be a vector with the same number of elements as columns in the training matrix. The return is a vector of JuMP variables with a single element.

julia> using GLM, JuMP, MathOptAI
julia> X, Y = rand(10, 2), rand(Bool, 10);
julia> predictor = GLM.glm(X, Y, GLM.Bernoulli());
julia> model = Model();
julia> @variable(model, x[1:2]);
julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_Sigmoid[1]
julia> formulationAffine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ -2.112522765612591 x[1] + 2.3170444820939706 x[2] - moai_Affine[1] = 0
+MathOptAI.Sigmoid()
+├ variables [1]
+│ └ moai_Sigmoid[1]
+└ constraints [3]
+  ├ moai_Sigmoid[1] ≥ 0
+  ├ moai_Sigmoid[1] ≤ 1
+  └ moai_Sigmoid[1] - (1.0 / (1.0 + exp(-moai_Affine[1]))) = 0

DataFrames

DataFrames.jl can be used with GLM.jl.

The input x to add_predictor must be a DataFrame with the same feature columns as the training DataFrame. The return is a vector of JuMP variables, with one element for each row in the DataFrame.

julia> using DataFrames, GLM, JuMP, MathOptAI
julia> train_df = DataFrames.DataFrame(x1 = rand(10), x2 = rand(10));
julia> train_df.y = 1.0 .* train_df.x1 + 2.0 .* train_df.x2 .+ rand(10);
julia> predictor = GLM.lm(GLM.@formula(y ~ x1 + x2), train_df);
julia> model = Model();
julia> test_df = DataFrames.DataFrame(
+           x1 = rand(6),
+           x2 = @variable(model, [1:6]),
+       );
julia> test_df.y, _ = MathOptAI.add_predictor(model, predictor, test_df);
julia> test_df.y6-element Vector{JuMP.VariableRef}:
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
diff --git a/v0.1.3/manual/Lux/index.html b/v0.1.3/manual/Lux/index.html new file mode 100644 index 00000000..fa5d8188 --- /dev/null +++ b/v0.1.3/manual/Lux/index.html @@ -0,0 +1,73 @@ + +Lux.jl · MathOptAI.jl
GitHub

Lux.jl

Lux.jl is a library for machine learning in Julia.

The upstream documentation is available at https://lux.csail.mit.edu/stable/.

Supported layers

MathOptAI supports embedding a Lux model into JuMP if it is a Lux.Chain composed of:

Basic example

Use MathOptAI.add_predictor to embed a tuple (containing the Lux.Chain, the parameters, and the state) into a JuMP model:

julia> using JuMP, Lux, MathOptAI, Random
julia> rng = Random.MersenneTwister();
julia> chain = Lux.Chain(Lux.Dense(1 => 2, Lux.relu), Lux.Dense(2 => 1))Chain(
+    layer_1 = Dense(1 => 2, relu),      # 4 parameters
+    layer_2 = Dense(2 => 1),            # 3 parameters
+)         # Total: 7 parameters,
+          #        plus 0 states.
julia> parameters, state = Lux.setup(rng, chain);
julia> predictor = (chain, parameters, state);
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_Affine[1]
julia> formulationAffine(A, b) [input: 1, output: 2]
+├ variables [2]
+│ ├ moai_Affine[1]
+│ └ moai_Affine[2]
+└ constraints [2]
+  ├ 0.38484522700309753 x[1] - moai_Affine[1] = 0
+  └ -0.5855771899223328 x[1] - moai_Affine[2] = 0
+MathOptAI.ReLU()
+├ variables [2]
+│ ├ moai_ReLU[1]
+│ └ moai_ReLU[2]
+└ constraints [4]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[2] ≥ 0
+  ├ moai_ReLU[1] - max(0.0, moai_Affine[1]) = 0
+  └ moai_ReLU[2] - max(0.0, moai_Affine[2]) = 0
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ 0.12567515671253204 moai_ReLU[1] + 0.7904617786407471 moai_ReLU[2] - moai_Affine[1] = 0

Reduced-space

Use the reduced_space = true keyword to formulate a reduced-space model:

julia> using JuMP, Lux, MathOptAI, Random
julia> rng = Random.MersenneTwister();
julia> chain = Lux.Chain(Lux.Dense(1 => 2, Lux.relu), Lux.Dense(2 => 1))Chain(
+    layer_1 = Dense(1 => 2, relu),      # 4 parameters
+    layer_2 = Dense(2 => 1),            # 3 parameters
+)         # Total: 7 parameters,
+          #        plus 0 states.
julia> parameters, state = Lux.setup(rng, chain);
julia> predictor = (chain, parameters, state);
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> y, formulation =
+           MathOptAI.add_predictor(model, predictor, x; reduced_space = true);
julia> y1-element Vector{JuMP.NonlinearExpr}:
+ ((+(0.0) + (1.1934810876846313 * max(0.0, 0.005973725579679012 x[1]))) + (0.11072010546922684 * max(0.0, -0.7038850784301758 x[1]))) + 0.0
julia> formulationReducedSpace(Affine(A, b) [input: 1, output: 2])
+├ variables [0]
+└ constraints [0]
+ReducedSpace(MathOptAI.ReLU())
+├ variables [0]
+└ constraints [0]
+ReducedSpace(Affine(A, b) [input: 2, output: 1])
+├ variables [0]
+└ constraints [0]

Gray-box

The Lux extension does not yet support the gray_box keyword argument.

Change how layers are formulated

Pass a dictionary to the config keyword that maps Lux activation functions to a MathOptAI predictor:

julia> using JuMP, Lux, MathOptAI, Random
julia> rng = Random.MersenneTwister();
julia> chain = Lux.Chain(Lux.Dense(1 => 2, Lux.relu), Lux.Dense(2 => 1))Chain(
+    layer_1 = Dense(1 => 2, relu),      # 4 parameters
+    layer_2 = Dense(2 => 1),            # 3 parameters
+)         # Total: 7 parameters,
+          #        plus 0 states.
julia> parameters, state = Lux.setup(rng, chain);
julia> predictor = (chain, parameters, state);
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> y, formulation = MathOptAI.add_predictor(
+           model,
+           predictor,
+           x;
+           config = Dict(Lux.relu => MathOptAI.ReLUSOS1()),
+       );
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_Affine[1]
julia> formulationAffine(A, b) [input: 1, output: 2]
+├ variables [2]
+│ ├ moai_Affine[1]
+│ └ moai_Affine[2]
+└ constraints [2]
+  ├ 0.41449838876724243 x[1] - moai_Affine[1] = 0
+  └ 0.26504331827163696 x[1] - moai_Affine[2] = 0
+MathOptAI.ReLUSOS1()
+├ variables [4]
+│ ├ moai_ReLU[1]
+│ ├ moai_ReLU[2]
+│ ├ moai_z[1]
+│ └ moai_z[2]
+└ constraints [4]
+  ├ moai_Affine[1] - moai_ReLU[1] + moai_z[1] = 0
+  ├ moai_Affine[2] - moai_ReLU[2] + moai_z[2] = 0
+  ├ [moai_ReLU[1], moai_z[1]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])
+  └ [moai_ReLU[2], moai_z[2]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ -0.766775906085968 moai_ReLU[1] - 0.7288127541542053 moai_ReLU[2] - moai_Affine[1] = 0
diff --git a/v0.1.3/manual/PyTorch/index.html b/v0.1.3/manual/PyTorch/index.html new file mode 100644 index 00000000..d2d26f05 --- /dev/null +++ b/v0.1.3/manual/PyTorch/index.html @@ -0,0 +1,74 @@ + +PyTorch · MathOptAI.jl
GitHub

PyTorch

PyTorch is a library for machine learning in Python.

The upstream documentation is available at https://pytorch.org/docs/stable/.

Supported layers

MathOptAI supports embedding a PyTorch models into JuMP if it is a nn.Sequential composed of:

File format

Use torch.save to save a trained PyTorch model to a .pt file:

#!/usr/bin/python3
+import torch
+model = torch.nn.Sequential(
+    torch.nn.Linear(1, 2),
+    torch.nn.ReLU(),
+    torch.nn.Linear(2, 1),
+)
+torch.save(model, "saved_pytorch_model.pt")

Python integration

MathOptAI uses PythonCall.jl to call from Julia into Python.

See CondaPkg.jl for more control over how to link Julia to an existing Python environment. For example, if you have an existing Python installation (with PyTorch installed), and it is available in the current Conda environment, set:

ENV["JULIA_CONDAPKG_BACKEND"] = "Current"

before importing PythonCall.jl. If the Python installation can be found on the path and it is not in a Conda environment, set:

ENV["JULIA_CONDAPKG_BACKEND"] = "Null"

If python is not on your path, you may additionally need to set JULIA_PYTHONCALL_EXE, for example, to:

ENV["JULIA_PYTHONCALL_EXE"] = "python3"

Basic example

Use MathOptAI.add_predictor to embed a PyTorch model into a JuMP model:

julia> using JuMP, MathOptAI
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> predictor = MathOptAI.PytorchModel("saved_pytorch_model.pt");
julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_Affine[1]
julia> formulationAffine(A, b) [input: 1, output: 2]
+├ variables [2]
+│ ├ moai_Affine[1]
+│ └ moai_Affine[2]
+└ constraints [2]
+  ├ 0.7473132610321045 x[1] - moai_Affine[1] = 0.27370238304138184
+  └ -0.8237636089324951 x[1] - moai_Affine[2] = 0.08490216732025146
+MathOptAI.ReLU()
+├ variables [2]
+│ ├ moai_ReLU[1]
+│ └ moai_ReLU[2]
+└ constraints [4]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[2] ≥ 0
+  ├ moai_ReLU[1] - max(0.0, moai_Affine[1]) = 0
+  └ moai_ReLU[2] - max(0.0, moai_Affine[2]) = 0
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ -0.4644489884376526 moai_ReLU[1] + 0.5382549166679382 moai_ReLU[2] - moai_Affine[1] = 0.5698285102844238

Reduced-space

Use the reduced_space = true keyword to formulate a reduced-space model:

julia> using JuMP, MathOptAI
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> predictor = MathOptAI.PytorchModel("saved_pytorch_model.pt");
julia> y, formulation =
+           MathOptAI.add_predictor(model, predictor, x; reduced_space = true);
julia> y1-element Vector{JuMP.NonlinearExpr}:
+ ((+(0.0) + (-0.4644489884376526 * max(0.0, 0.7473132610321045 x[1] - 0.27370238304138184))) + (0.5382549166679382 * max(0.0, -0.8237636089324951 x[1] - 0.08490216732025146))) + -0.5698285102844238
julia> formulationReducedSpace(Affine(A, b) [input: 1, output: 2])
+├ variables [0]
+└ constraints [0]
+ReducedSpace(MathOptAI.ReLU())
+├ variables [0]
+└ constraints [0]
+ReducedSpace(Affine(A, b) [input: 2, output: 1])
+├ variables [0]
+└ constraints [0]

Gray-box

Use the gray_box = true keyword to embed the network as a nonlinear operator:

julia> using JuMP, MathOptAI
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> predictor = MathOptAI.PytorchModel("saved_pytorch_model.pt");
julia> y, formulation =
+           MathOptAI.add_predictor(model, predictor, x; gray_box = true);
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_GrayBox[1]
julia> formulationGrayBox
+├ variables [1]
+│ └ moai_GrayBox[1]
+└ constraints [1]
+  └ op_##1241(x[1]) - moai_GrayBox[1] = 0

Change how layers are formulated

Pass a dictionary to the config keyword that maps the Symbol name of each PyTorch layer to a MathOptAI predictor:

julia> using JuMP, MathOptAI
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> predictor = MathOptAI.PytorchModel("saved_pytorch_model.pt");
julia> y, formulation = MathOptAI.add_predictor(
+           model,
+           predictor,
+           x;
+           config = Dict(:ReLU => MathOptAI.ReLUSOS1()),
+       );
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_Affine[1]
julia> formulationAffine(A, b) [input: 1, output: 2]
+├ variables [2]
+│ ├ moai_Affine[1]
+│ └ moai_Affine[2]
+└ constraints [2]
+  ├ 0.7473132610321045 x[1] - moai_Affine[1] = 0.27370238304138184
+  └ -0.8237636089324951 x[1] - moai_Affine[2] = 0.08490216732025146
+MathOptAI.ReLUSOS1()
+├ variables [4]
+│ ├ moai_ReLU[1]
+│ ├ moai_ReLU[2]
+│ ├ moai_z[1]
+│ └ moai_z[2]
+└ constraints [4]
+  ├ moai_Affine[1] - moai_ReLU[1] + moai_z[1] = 0
+  ├ moai_Affine[2] - moai_ReLU[2] + moai_z[2] = 0
+  ├ [moai_ReLU[1], moai_z[1]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])
+  └ [moai_ReLU[2], moai_z[2]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ -0.4644489884376526 moai_ReLU[1] + 0.5382549166679382 moai_ReLU[2] - moai_Affine[1] = 0.5698285102844238
diff --git a/v0.1.3/manual/predictors/index.html b/v0.1.3/manual/predictors/index.html new file mode 100644 index 00000000..167182f3 --- /dev/null +++ b/v0.1.3/manual/predictors/index.html @@ -0,0 +1,2 @@ + +Predictors · MathOptAI.jl
GitHub

Predictors

The main entry point for embedding prediction models into JuMP is add_predictor.

All methods use the form y, formulation = MathOptAI.add_predictor(model, predictor, x) to add the relationship y = predictor(x) to model.

Supported predictors

The following predictors are supported. See their docstrings for details:

PredictorRelationshipDimensions
Affine$f(x) = Ax + b$$M \rightarrow N$
BinaryDecisionTreeA binary decision tree$M \rightarrow 1$
GrayBox$f(x)$$M \rightarrow N$
Pipeline$f(x) = (l_1 \circ \ldots \circ l_N)(x)$$M \rightarrow N$
QuantileThe quantiles of a distribution$M \rightarrow N$
ReLU$f(x) = \max.(0, x)$$M \rightarrow M$
ReLUBigM$f(x) = \max.(0, x)$$M \rightarrow M$
ReLUQuadratic$f(x) = \max.(0, x)$$M \rightarrow M$
ReLUSOS1$f(x) = \max.(0, x)$$M \rightarrow M$
Scale$f(x) = scale .* x .+ bias$$M \rightarrow M$
Sigmoid$f(x) = \frac{1}{1 + e^{-x}}$$M \rightarrow M$
SoftMax$f(x) = \frac{e^x}{\sum e^{x_i}}$$M \rightarrow M$
SoftPlus$f(x) = \frac{1}{\beta} \log(1 + e^{\beta x})$$M \rightarrow M$
Tanh$f(x) = \tanh.(x)$$M \rightarrow M$

Note that some predictors, such as the ReLU ones, offer multiple formulations of the same mathematical relationship. The ''right'' choice is solver- and problem-dependent.

ReLU

There are a number of different mathematical formulations for the rectified linear unit (ReLU).

  • ReLU: requires the solver to support the max nonlinear operator.
  • ReLUBigM: requires the solver to support mixed-integer linear programs, and requires the user to have a priori knowledge of a suitable value for the "big-M" parameter.
  • ReLUQuadratic: requires the solver to support quadratic equality constraints
  • ReLUSOS1: requires the solver to support SOS-I constraints.

The correct choice for which ReLU formulation to use is problem- and solver-dependent.

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reduced_space = true);\ny\nformulation","category":"page"},{"location":"manual/Flux/#Gray-box","page":"Flux.jl","title":"Gray-box","text":"","category":"section"},{"location":"manual/Flux/","page":"Flux.jl","title":"Flux.jl","text":"Use the gray_box = true keyword to embed the network as a nonlinear operator:","category":"page"},{"location":"manual/Flux/","page":"Flux.jl","title":"Flux.jl","text":"using JuMP, Flux, MathOptAI\npredictor = Flux.Chain(Flux.Dense(1 => 2, Flux.relu), Flux.Dense(2 => 1));\nmodel = Model();\n@variable(model, x[1:1]);\ny, formulation =\n MathOptAI.add_predictor(model, predictor, x; gray_box = true);\ny\nformulation","category":"page"},{"location":"manual/Flux/#Change-how-layers-are-formulated","page":"Flux.jl","title":"Change how layers are formulated","text":"","category":"section"},{"location":"manual/Flux/","page":"Flux.jl","title":"Flux.jl","text":"Pass a dictionary to the config keyword that maps Flux activation functions to a MathOptAI predictor:","category":"page"},{"location":"manual/Flux/","page":"Flux.jl","title":"Flux.jl","text":"using JuMP, Flux, MathOptAI\npredictor = Flux.Chain(Flux.Dense(1 => 2, Flux.relu), Flux.Dense(2 => 1));\nmodel = Model();\n@variable(model, x[1:1]);\ny, formulation = MathOptAI.add_predictor(\n model,\n predictor,\n x;\n config = Dict(Flux.relu => MathOptAI.ReLUSOS1()),\n);\ny\nformulation","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"EditURL = \"mnist.jl\"","category":"page"},{"location":"tutorials/mnist/#Adversarial-machine-learning-with-Flux.jl","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"","category":"section"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"The purpose of this tutorial is to explain how to embed a neural network model from Flux.jl into JuMP.","category":"page"},{"location":"tutorials/mnist/#Required-packages","page":"Adversarial machine learning with Flux.jl","title":"Required packages","text":"","category":"section"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"This tutorial requires the following packages","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"using JuMP\nimport Flux\nimport Ipopt\nimport MathOptAI\nimport MLDatasets\nimport Plots","category":"page"},{"location":"tutorials/mnist/#Data","page":"Adversarial machine learning with Flux.jl","title":"Data","text":"","category":"section"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"This tutorial uses images from the MNIST dataset.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"We load the predefined train and test splits:","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"train_data = MLDatasets.MNIST(; split = :train)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"test_data = MLDatasets.MNIST(; split = :test)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Since the data are images, it is helpful to plot them. (This requires a transpose and reversing the rows to get the orientation correct.)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"function plot_image(x::Matrix; kwargs...)\n return Plots.heatmap(\n x'[size(x, 1):-1:1, :];\n xlims = (1, size(x, 2)),\n ylims = (1, size(x, 1)),\n aspect_ratio = true,\n legend = false,\n xaxis = false,\n yaxis = false,\n kwargs...,\n )\nend\n\nfunction plot_image(instance::NamedTuple)\n return plot_image(instance.features; title = \"Label = $(instance.targets)\")\nend\n\nPlots.plot([plot_image(train_data[i]) for i in 1:6]...; layout = (2, 3))","category":"page"},{"location":"tutorials/mnist/#Training","page":"Adversarial machine learning with Flux.jl","title":"Training","text":"","category":"section"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"We use a simple neural network with one hidden layer and a sigmoid activation function. (There are better performing networks; try experimenting.)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"predictor = Flux.Chain(\n Flux.Dense(28^2 => 32, Flux.sigmoid),\n Flux.Dense(32 => 10),\n Flux.softmax,\n)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Here is a function to load our data into the format that predictor expects:","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"function data_loader(data; batchsize, shuffle = false)\n x = reshape(data.features, 28^2, :)\n y = Flux.onehotbatch(data.targets, 0:9)\n return Flux.DataLoader((x, y); batchsize, shuffle)\nend","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"and here is a function to score the percentage of correct labels, where we assign a label by choosing the label of the highest softmax in the final layer.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"function score_model(predictor, data)\n x, y = only(data_loader(data; batchsize = length(data)))\n y_hat = predictor(x)\n is_correct = Flux.onecold(y) .== Flux.onecold(y_hat)\n p = round(100 * sum(is_correct) / length(is_correct); digits = 2)\n println(\"Accuracy = $p %\")\n return\nend","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"The accuracy of our model is only around 10% before training:","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"score_model(predictor, train_data)\nscore_model(predictor, test_data)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Let's improve that by training our model.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"note: Note\nIt is not the purpose of this tutorial to explain how Flux works; see the documentation at https://fluxml.ai for more details. Changing the number of epochs or the learning rate can improve the loss.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"begin\n train_loader = data_loader(train_data; batchsize = 256, shuffle = true)\n optimizer_state = Flux.setup(Flux.Adam(3e-4), predictor)\n for epoch in 1:30\n loss = 0.0\n for (x, y) in train_loader\n loss_batch, gradient = Flux.withgradient(predictor) do model\n return Flux.crossentropy(model(x), y)\n end\n Flux.update!(optimizer_state, predictor, only(gradient))\n loss += loss_batch\n end\n loss = round(loss / length(train_loader); digits = 4)\n print(\"Epoch $epoch: loss = $loss\\t\")\n score_model(predictor, test_data)\n end\nend","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Here are the first eight predictions of the test data:","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"function plot_image(predictor, x::Matrix)\n score, index = findmax(predictor(vec(x)))\n title = \"Predicted: $(index - 1) ($(round(Int, 100 * score))%)\"\n return plot_image(x; title)\nend\n\nplots = [plot_image(predictor, test_data[i].features) for i in 1:8]\nPlots.plot(plots...; size = (1200, 600), layout = (2, 4))","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"We can also look at the best and worst four predictions:","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"x, y = only(data_loader(test_data; batchsize = length(test_data)))\nlosses = Flux.crossentropy(predictor(x), y; agg = identity)\nindices = sortperm(losses; dims = 2)[[1:4; end-3:end]]\nplots = [plot_image(predictor, test_data[i].features) for i in indices]\nPlots.plot(plots...; size = (1200, 600), layout = (2, 4))","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"There are still some fairly bad mistakes. Can you change the model or training parameters improve to improve things?","category":"page"},{"location":"tutorials/mnist/#JuMP","page":"Adversarial machine learning with Flux.jl","title":"JuMP","text":"","category":"section"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Now that we have a trained machine learning model, we can embed it in a JuMP model.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Here's a function which takes a test case and returns an example that maximizes the probability of the adversarial example.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"function find_adversarial_image(test_case; adversary_label, δ = 0.05)\n model = Model(Ipopt.Optimizer)\n set_silent(model)\n @variable(model, 0 <= x[1:28, 1:28] <= 1)\n @constraint(model, -δ .<= x .- test_case.features .<= δ)\n # Note: we need to use `vec` here because `x` is a 28-by-28 Matrix, but our\n # neural network expects a 28^2 length vector.\n y, _ = MathOptAI.add_predictor(model, predictor, vec(x))\n @objective(model, Max, y[adversary_label+1] - y[test_case.targets+1])\n optimize!(model)\n @assert is_solved_and_feasible(model)\n return value.(x)\nend","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Let's try finding an adversarial example to the third test image. The image on the left is our input image. The network thinks this is a 1 with probability 99%. The image on the right is the adversarial image. The network thinks this is a 7, although it is less confident.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"x_adversary = find_adversarial_image(test_data[3]; adversary_label = 7);\nPlots.plot(\n plot_image(predictor, test_data[3].features),\n plot_image(predictor, Float32.(x_adversary)),\n)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"This page was generated using Literate.jl.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"EditURL = \"student_enrollment.jl\"","category":"page"},{"location":"tutorials/student_enrollment/#Logistic-regression-with-GLM.jl","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"","category":"section"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The purpose of this tutorial is to explain how to embed a logistic regression model from GLM.jl into JuMP.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The data and example in this tutorial comes from the paper: David Bergman, Teng Huang, Philip Brooks, Andrea Lodi, Arvind U. Raghunathan (2021) JANOS: An Integrated Predictive and Prescriptive Modeling Framework. INFORMS Journal on Computing 34(2):807-816. https://doi.org/10.1287/ijoc.2020.1023","category":"page"},{"location":"tutorials/student_enrollment/#Required-packages","page":"Logistic regression with GLM.jl","title":"Required packages","text":"","category":"section"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"This tutorial uses the following packages.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"using JuMP\nimport CSV\nimport DataFrames\nimport Downloads\nimport GLM\nimport Ipopt\nimport MathOptAI\nimport Statistics","category":"page"},{"location":"tutorials/student_enrollment/#Data","page":"Logistic regression with GLM.jl","title":"Data","text":"","category":"section"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Here is a function to load the data directly from the JANOS repository:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"function read_df(filename)\n url = \"https://raw.githubusercontent.com/INFORMSJoC/2020.1023/master/data/\"\n data = Downloads.download(url * filename)\n return CSV.read(data, DataFrames.DataFrame)\nend","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"There are two important files. The first, college_student_enroll-s1-1.csv, contains historial admissions data on anonymized students, their SAT score, their GPA, their merit scholarships, and whether the enrolled in the college.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"train_df = read_df(\"college_student_enroll-s1-1.csv\")","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The second, college_applications6000.csv, contains the SAT and GPA data of students who are currently applying:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"evaluate_df = read_df(\"college_applications6000.csv\")","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"There are 6,000 prospective students:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"n_students = size(evaluate_df, 1)","category":"page"},{"location":"tutorials/student_enrollment/#Prediction-model","page":"Logistic regression with GLM.jl","title":"Prediction model","text":"","category":"section"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The first step is to train a logistic regression model to predict the Boolean enroll column based on the SAT, GPA, and merit columns.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"model_glm = GLM.glm(\n GLM.@formula(enroll ~ 0 + SAT + GPA + merit),\n train_df,\n GLM.Bernoulli(),\n)","category":"page"},{"location":"tutorials/student_enrollment/#Decision-model","page":"Logistic regression with GLM.jl","title":"Decision model","text":"","category":"section"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Now that we have a trained logistic regression model, we want a decision model that chooses the optimal merit scholarship for each student in","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"evaluate_df","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Here's an empty JuMP model to start:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"model = Model()","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"First, we add a new columnn to evaluate_df, with one JuMP decision variable for each row. It is important the the .merit column name in evaluate_df matches the name in train_df.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"evaluate_df.merit = @variable(model, 0 <= x_merit[1:n_students] <= 2.5);\nevaluate_df","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Then, we use MathOptAI.add_predictor to embed model_glm into the JuMP model. MathOptAI.add_predictor returns a vector of variables, one for each row inn evaluate_df, corresponding to the output enroll of our logistic regression.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"evaluate_df.enroll, _ = MathOptAI.add_predictor(model, model_glm, evaluate_df);\nevaluate_df","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The .enroll column name in evaluate_df is just a name. It doesn't have to match the name in train_df.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The objective of our problem is to maximize the expected number of students who enroll:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"@objective(model, Max, sum(evaluate_df.enroll))","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Subject to the constraint that we can spend at most 0.2 * n_students on merit scholarships:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"@constraint(model, sum(evaluate_df.merit) <= 0.2 * n_students)","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Because logistic regression involves a Sigmoid layer, we need to use a smooth nonlinear optimizer. A common choice is Ipopt. Solve and check the optimizer found a feasible solution:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"set_optimizer(model, Ipopt.Optimizer)\nset_silent(model)\noptimize!(model)\n@assert is_solved_and_feasible(model)\nsolution_summary(model)","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Let's store the solution in evaluate_df for analysis:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"evaluate_df.merit_sol = value.(evaluate_df.merit);\nevaluate_df.enroll_sol = value.(evaluate_df.enroll);\nevaluate_df","category":"page"},{"location":"tutorials/student_enrollment/#Solution-analysis","page":"Logistic regression with GLM.jl","title":"Solution analysis","text":"","category":"section"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"We expect that just under 2,500 students will enroll:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"sum(evaluate_df.enroll_sol)","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"We awarded merit scholarships to approximately 1 in 6 students:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"count(evaluate_df.merit_sol .> 1e-5)","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The average merit scholarship was worth just over $1,000:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"1_000 * Statistics.mean(evaluate_df.merit_sol[evaluate_df.merit_sol.>1e-5])","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"This page was generated using Literate.jl.","category":"page"},{"location":"manual/GLM/#GLM.jl","page":"GLM.jl","title":"GLM.jl","text":"","category":"section"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"GLM.jl is a library for fitting generalized linear models in Julia.","category":"page"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"MathOptAI.jl supports embedding two types of regression models from GLM:","category":"page"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"GLM.lm(X, Y)\nGLM.glm(X, Y, GLM.Bernoulli())","category":"page"},{"location":"manual/GLM/#Linear-regression","page":"GLM.jl","title":"Linear regression","text":"","category":"section"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"The input x to add_predictor must be a vector with the same number of elements as columns in the training matrix. The return is a vector of JuMP variables with a single element.","category":"page"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"using GLM, JuMP, MathOptAI\nX, Y = rand(10, 2), rand(10);\npredictor = GLM.lm(X, Y);\nmodel = Model();\n@variable(model, x[1:2]);\ny, formulation = MathOptAI.add_predictor(model, predictor, x);\ny\nformulation","category":"page"},{"location":"manual/GLM/#Logistic-regression","page":"GLM.jl","title":"Logistic regression","text":"","category":"section"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"The input x to add_predictor must be a vector with the same number of elements as columns in the training matrix. The return is a vector of JuMP variables with a single element.","category":"page"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"using GLM, JuMP, MathOptAI\nX, Y = rand(10, 2), rand(Bool, 10);\npredictor = GLM.glm(X, Y, GLM.Bernoulli());\nmodel = Model();\n@variable(model, x[1:2]);\ny, formulation = MathOptAI.add_predictor(model, predictor, x);\ny\nformulation","category":"page"},{"location":"manual/GLM/#DataFrames","page":"GLM.jl","title":"DataFrames","text":"","category":"section"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"DataFrames.jl can be used with GLM.jl.","category":"page"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"The input x to add_predictor must be a DataFrame with the same feature columns as the training DataFrame. The return is a vector of JuMP variables, with one element for each row in the DataFrame.","category":"page"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"using DataFrames, GLM, JuMP, MathOptAI\ntrain_df = DataFrames.DataFrame(x1 = rand(10), x2 = rand(10));\ntrain_df.y = 1.0 .* train_df.x1 + 2.0 .* train_df.x2 .+ rand(10);\npredictor = GLM.lm(GLM.@formula(y ~ x1 + x2), train_df);\nmodel = Model();\ntest_df = DataFrames.DataFrame(\n x1 = rand(6),\n x2 = @variable(model, [1:6]),\n);\ntest_df.y, _ = MathOptAI.add_predictor(model, predictor, test_df);\ntest_df.y","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"CurrentModule = MathOptAI","category":"page"},{"location":"developers/design_principles/#Design-principles","page":"Design principles","title":"Design principles","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"This project is inspired by two existing projects:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"OMLT\ngurobi-machinelearning","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"OMLT is a framework built around Pyomo, and gurobi-machinelearning is a framework build around gurobipy.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"These projects served as inspiration, but we also departed from them in some carefully considered ways.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"All of our design decisions were guided by two principles:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"To be simple\nTo leverage Julia's Pkg extensions and multiple dispatch.","category":"page"},{"location":"developers/design_principles/#Terminology","page":"Design principles","title":"Terminology","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Because the field is relatively new, there is no settled choice of terminology.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"MathOptAI chooses to use \"predictor\" as the synonym for the machine learning model. Hence, we have AbstractPredictor, add_predictor, and build_predictor.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In contrast, gurob-machinelearning tends to use \"regression model\" and OMLT uses \"formulation.\"","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"We choose \"predictor\" because all models we implement are of the form y = f(x).","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"We do not use \"machine learning model\" because we have support for the linear and logistic regression models of classical statistical fitting. We could have used \"regression model\", but we find that models like neural networks and binary decision trees are not commonly thought of as regression models.","category":"page"},{"location":"developers/design_principles/#Inputs-are-vectors","page":"Design principles","title":"Inputs are vectors","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"MathOptAI assumes that all inputs x and outputs y to y = predictor(x) are Base.Vectors.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"We make this choice for simplicity.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In our opinion, Julia libraries often take a laissez-faire approach to the types that they support. In the optimistic case, this can lead to novel behavior by combining two packages that the package author had previously not considered or tested. In the pessimistic case, this can lead to incorrect results or cryptic error messagges.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Exceptions to the Vector rule will be carefully considered and tested.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Currently, there are two exceptions:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"If x is a Matrix, then the columns of x are interpreted as independent observations, and the output y will be a Matrix with the same number of columns\nThe StatsModels extension allows x to be a DataFrames.DataFrame, if the predictor is a StatsModels.TableRegressionModel.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Exceptions 1 and 2 are combined in the StatsModels exception, so that the predictor is mapped over the rows of the DataFrames.DataFrame (which we assume will be a common use-case).","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"We choose to interpret the rows as input variables and columns as independent observations (rather than the more traditional table-based approach where columns are the input variables and rows are observations) because Julia uses column-major ordering in Matrix. Another justification follows from the Affine predictor, f(x) = Ax + b, where passing in a Matrix as x with column observations naturally leads to a Matrix output for y of the appropriate dimensions.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"We choose to make y a Vector, even for scalar outputs, to simplify code that works generically for many different predictors. Without this principle, there will inevitably be cases where a scalar and length-1 vector are confused.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"If you want to use a predictor that does not take Vector input (for example, it is an image as input to a neural network), the first preprocessing step should be to vec the input into a single Vector.","category":"page"},{"location":"developers/design_principles/#Inputs-are-provided,-outputs-are-returned","page":"Design principles","title":"Inputs are provided, outputs are returned","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The main job of MathOptAI is to embed models of the form y = predictor(x) into a JuMP model. A key design decision is how to represent the input x and output y.","category":"page"},{"location":"developers/design_principles/#gurobi-machinelearning","page":"Design principles","title":"gurobi-machinelearning","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"gurobi-machinelearning implements an API of the following general form:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"pred_constr = add_predictor_constr(model, predictor, x, y)","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Here, both the input x and the output y must be created and provided by the user, and a new object pred_constr is returned.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The benefit of this design is that pred_constr can contain statistics about the reformulation (for example, the number of variables that were added), and it can be used to delete a predictor from model.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The downside is that the user must ensure that the shape and size of y is correct.","category":"page"},{"location":"developers/design_principles/#OMLT","page":"Design principles","title":"OMLT","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"OMLT implements an API of the following general form:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"model.pred_constr = OmltBlock()\nmodel.pred_constr.build_formulation(predictor)\nx, y = model.pred_constr.inputs, model.pred_constr.outputs","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"First, a new OmltBlock() is created. Then the formulation is built inside the block, and both the input and output are provided to the user.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The benefit of this design is that pred_constr can contain statistics about the reformulation (for example, the number of variables that were added), and it can be used to delete a predictor from model.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The downside is that the user must often write additional constraints to connect the input and output of the OmltBlock to their existing decision variables:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"#connect pyomo model input and output to the neural network\n@model.Constraint()\ndef connect_input(mdl):\n return mdl.input == mdl.nn.inputs[0]\n\n@model.Constraint()\ndef connect_output(mdl):\n return mdl.output == mdl.nn.outputs[0]","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"A second downside is that the predictor must describe the input and output dimension; these cannot be inferred automatically. As one example, this means that it cannot do the following:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"# Not possible because dimension not given\nmodel.pred_constr.build_formulation(ReLU())","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In the context of MathOptAI, something like ReLU() is useful so that we can map generic layers like Flux.relu => MathOptAI.ReLU(), and so that we do not duplicate required dimension information in input and predictor (see the MathOptAI section below).","category":"page"},{"location":"developers/design_principles/#MathOptAI","page":"Design principles","title":"MathOptAI","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The main entry-point to MathOptAI is add_predictor:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"y, formulation = MathOptAI.add_predictor(model, predictor, x)","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The user provides the input x, and the output y is returned.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The main benefit of this approach is simplicity.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"First, the user probably already has the input x as decision variables or an expression in the model, so we do not need the connect_input constraint, and because we use a full-space formulation by default, the output y will always be a vector of decision variables, which avoids the need for a connect_output constraint.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Second, predictors do not need to store dimension information, so we can have:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"y, formulation = MathOptAI.add_predictor(model, MathOptAI.ReLU(), x)","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"for any size of x.","category":"page"},{"location":"developers/design_principles/#Activations-are-predictors","page":"Design principles","title":"Activations are predictors","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"OMLT makes a distinction between layers, like full_space_dense_layer, and elementwise activation functions, like sigmoid_activation_function.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The downside to this approach is that it treats activation functions as special, leading to issues such as OMLT#125.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In constrast, MathOptAI treats activation functions as a vector-valued predictor like any other:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"y, formulation = MathOptAI.add_predictor(model, MathOptAI.ReLU(), x)","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"This means that we can pipeline them to create predictors such as:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"function LogisticRegression(A)\n return MathOptAI.Pipeline(MathOptAI.Affine(A), MathOptAI.Sigmoid())\nend","category":"page"},{"location":"developers/design_principles/#Controlling-transformations","page":"Design principles","title":"Controlling transformations","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Many predictors have multiple ways that they can be formulated in an optimization model. For example, ReLU implements the non-smooth nonlinear formulation y = maxx 0, while ReLUQuadratic implements a the complementarity formulation x = y - slack y slack ge 0 y * slack = 0.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Choosing the appropriate formulation for the combination of model and solver can have a large impact on the performance.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Because gurobi-machinelearning is specific to the Gurobi solver, they have a limited ability for the user to choose and implement different formulations.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"OMLT is more general, in that it has multiple ways of formulating layers such as ReLU. However, these are hard-coded into complete formulations such as omlt.neuralnet.nn_formulation.ReluBigMFormulation or omlt.neuralnet.nn_formulation.ReluComplementarityFormulation.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In contrast, MathOptAI tries to take a maximally modular approach, where the user can control how the layers are formulated at runtime, including using a custom formulation that is not defined in MathOptAI.jl.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Currently, we achive this with a config dictionary, which maps the various neural network layers to an AbstractPredictor. For example:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));\nconfig = Dict(Flux.relu => MathOptAI.ReLU())\npredictor = MathOptAI.build_predictor(chain; config)","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Please open a GitHub issue if you have a suggestion for a better API.","category":"page"},{"location":"developers/design_principles/#Full-space-or-reduced-space","page":"Design principles","title":"Full-space or reduced-space","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"OMLT has two ways that it can formulate neural networks: full-space and reduced-space.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The full-space formulations add intermediate variables to represent the output of all layers.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"For example, in a Flux.Dense(2, 3, Flux.relu) layer, a full-space formulation will add an intermediate y_tmp variable to represent the output of the affine layer prior to the ReLU:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"layer = Flux.Dense(2, 3, Flux.relu)\nmodel_full_space = Model()\n@variable(model_full_space, x[1:2])\n@variable(model_full_space, y_tmp[1:3])\n@variable(model_full_space, y[1:3])\n@constraint(model_full_space, y_tmp == layer.A * x + layer.b)\n@constraint(model_full_space, y .== max.(0, y_tmp))","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In contrast, a reduced-space formulation encodes the input-output relationship as a single nonlinear constraint:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"layer = Flux.Dense(2, 3, Flux.relu)\nmodel_reduced_space = Model()\n@variable(model_reduced_space, x[1:2])\n@variable(model_reduced_space, y[1:3])\n@constraint(model_reduced_space, y .== max.(0, layer.A * x + layer.b))","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In general, the full-space formulations have more variables and constraints but simpler nonlinear expressions, whereas the reduced-space formulations have fewer variables and constraints but more complicated nonlinear expressions.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"MathOptAI.jl implements the full-space formulation by default, but some layers support the reduced-space formulation with the ReducedSpace wrapper.","category":"page"},{"location":"manual/DecisionTree/#DecisionTree.jl","page":"DecisionTree.jl","title":"DecisionTree.jl","text":"","category":"section"},{"location":"manual/DecisionTree/","page":"DecisionTree.jl","title":"DecisionTree.jl","text":"DecisionTree.jl is a library for fitting decision trees in Julia.","category":"page"},{"location":"manual/DecisionTree/#Basic-example","page":"DecisionTree.jl","title":"Basic example","text":"","category":"section"},{"location":"manual/DecisionTree/","page":"DecisionTree.jl","title":"DecisionTree.jl","text":"Here is an example:","category":"page"},{"location":"manual/DecisionTree/","page":"DecisionTree.jl","title":"DecisionTree.jl","text":"using JuMP, MathOptAI, DecisionTree\ntruth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)\nfeatures = abs.(sin.((1:10) .* (3:4)'));\nsize(features)\nlabels = truth.(Vector.(eachrow(features)));\npredictor = DecisionTree.build_tree(labels, features)\nmodel = Model();\n@variable(model, 0 <= x[1:2] <= 1);\ny, formulation = MathOptAI.add_predictor(model, predictor, x);\ny\nformulation","category":"page"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"CurrentModule = MathOptAI","category":"page"},{"location":"manual/predictors/#Predictors","page":"Predictors","title":"Predictors","text":"","category":"section"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"The main entry point for embedding prediction models into JuMP is add_predictor.","category":"page"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"All methods use the form y, formulation = MathOptAI.add_predictor(model, predictor, x) to add the relationship y = predictor(x) to model.","category":"page"},{"location":"manual/predictors/#Supported-predictors","page":"Predictors","title":"Supported predictors","text":"","category":"section"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"The following predictors are supported. See their docstrings for details:","category":"page"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"Predictor Relationship Dimensions\nAffine f(x) = Ax + b M rightarrow N\nBinaryDecisionTree A binary decision tree M rightarrow 1\nGrayBox f(x) M rightarrow N\nPipeline f(x) = (l_1 circ ldots circ l_N)(x) M rightarrow N\nQuantile The quantiles of a distribution M rightarrow N\nReLU f(x) = max(0 x) M rightarrow M\nReLUBigM f(x) = max(0 x) M rightarrow M\nReLUQuadratic f(x) = max(0 x) M rightarrow M\nReLUSOS1 f(x) = max(0 x) M rightarrow M\nScale f(x) = scale * x + bias M rightarrow M\nSigmoid f(x) = frac11 + e^-x M rightarrow M\nSoftMax f(x) = frace^xsum e^x_i M rightarrow M\nSoftPlus f(x) = frac1beta log(1 + e^beta x) M rightarrow M\nTanh f(x) = tanh(x) M rightarrow M","category":"page"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"Note that some predictors, such as the ReLU ones, offer multiple formulations of the same mathematical relationship. The ''right'' choice is solver- and problem-dependent.","category":"page"},{"location":"manual/predictors/#ReLU","page":"Predictors","title":"ReLU","text":"","category":"section"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"There are a number of different mathematical formulations for the rectified linear unit (ReLU).","category":"page"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"ReLU: requires the solver to support the max nonlinear operator.\nReLUBigM: requires the solver to support mixed-integer linear programs, and requires the user to have a priori knowledge of a suitable value for the \"big-M\" parameter.\nReLUQuadratic: requires the solver to support quadratic equality constraints\nReLUSOS1: requires the solver to support SOS-I constraints.","category":"page"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"The correct choice for which ReLU formulation to use is problem- and solver-dependent.","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"CurrentModule = MathOptAI","category":"page"},{"location":"api/#API-Reference","page":"API Reference","title":"API Reference","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"This page lists the public API of MathOptAI.","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"info: Info\nThis page is an unstructured list of the MathOptAI API. For a more structured overview, read the Manual or Tutorial parts of this documentation.","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Load all of the public the API into the current scope with:","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"using MathOptAI","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Alternatively, load only the module with:","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"import MathOptAI","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"and then prefix all calls with MathOptAI. to create MathOptAI..","category":"page"},{"location":"api/#AbstractPredictor","page":"API Reference","title":"AbstractPredictor","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"AbstractPredictor","category":"page"},{"location":"api/#MathOptAI.AbstractPredictor","page":"API Reference","title":"MathOptAI.AbstractPredictor","text":"abstract type AbstractPredictor end\n\nAn abstract type representing different types of prediction models.\n\nMethods\n\nAll subtypes must implement:\n\nadd_predictor\n\n\n\n\n\n","category":"type"},{"location":"api/#add_predictor","page":"API Reference","title":"add_predictor","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"add_predictor","category":"page"},{"location":"api/#MathOptAI.add_predictor","page":"API Reference","title":"MathOptAI.add_predictor","text":"add_predictor(\n model::JuMP.AbstractModel,\n predictor::AbstractPredictor,\n x::Vector,\n)::Vector\n\nReturn a Vector representing y such that y = predictor(x).\n\nThe element type of x is deliberately unspecified. The vector x may contain any mix of scalar constants, JuMP decision variables, and scalar JuMP functions like AffExpr, QuadExpr, or NonlinearExpr.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.Affine([2.0, 3.0])\nAffine(A, b) [input: 2, output: 1]\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Affine[1]\n\njulia> formulation\nAffine(A, b) [input: 2, output: 1]\n├ variables [1]\n│ └ moai_Affine[1]\n└ constraints [1]\n └ 2 x[1] + 3 x[2] - moai_Affine[1] = 0\n\n\n\n\n\n","category":"function"},{"location":"api/#build_predictor","page":"API Reference","title":"build_predictor","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"build_predictor","category":"page"},{"location":"api/#MathOptAI.build_predictor","page":"API Reference","title":"MathOptAI.build_predictor","text":"MathOptAI.build_predictor(predictor::DecisionTree.Root)\n\nConvert a binary decision tree from DecisionTree.jl to a BinaryDecisionTree.\n\nExample\n\njulia> using MathOptAI, DecisionTree\n\njulia> truth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)\ntruth (generic function with 1 method)\n\njulia> features = abs.(sin.((1:10) .* (3:4)'));\n\njulia> size(features)\n(10, 2)\n\njulia> labels = truth.(Vector.(eachrow(features)));\n\njulia> ml_model = DecisionTree.build_tree(labels, features)\nDecision Tree\nLeaves: 3\nDepth: 2\n\njulia> MathOptAI.build_predictor(ml_model)\nBinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]\n\n\n\n\n\nbuild_predictor(extension; kwargs...)::AbstractPredictor\n\nA uniform interface to convert various extension types to an AbstractPredictor.\n\nSee the various extension docstrings for details.\n\n\n\n\n\nMathOptAI.build_predictor(\n predictor::Tuple{<:Lux.Chain,<:NamedTuple,<:NamedTuple};\n config::Dict = Dict{Any,Any}(),\n)\n\nConvert a trained neural network from Lux.jl to a Pipeline.\n\nSupported layers\n\nLux.Dense\nLux.Scale\n\nSupported activation functions\n\nLux.relu\nLux.sigmoid\nLux.softplus\nLux.softmax\nLux.tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps supported Lux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Lux.sigmoid => MathOptAI.Sigmoid() or Lux.relu => MathOptAI.QuadraticReLU().\n\nExample\n\njulia> using Lux, MathOptAI, Random\n\njulia> rng = Random.MersenneTwister();\n\njulia> chain = Lux.Chain(Lux.Dense(1 => 16, Lux.relu), Lux.Dense(16 => 1))\nChain(\n layer_1 = Dense(1 => 16, relu), # 32 parameters\n layer_2 = Dense(16 => 1), # 17 parameters\n) # Total: 49 parameters,\n # plus 0 states.\n\njulia> parameters, state = Lux.setup(rng, chain);\n\njulia> predictor = MathOptAI.build_predictor(\n (chain, parameters, state);\n config = Dict(Lux.relu => MathOptAI.ReLU()),\n )\nPipeline with layers:\n * Affine(A, b) [input: 1, output: 16]\n * ReLU()\n * Affine(A, b) [input: 16, output: 1]\n\njulia> MathOptAI.build_predictor(\n (chain, parameters, state);\n config = Dict(Lux.relu => MathOptAI.ReLUQuadratic()),\n )\nPipeline with layers:\n * Affine(A, b) [input: 1, output: 16]\n * ReLUQuadratic()\n * Affine(A, b) [input: 16, output: 1]\n\n\n\n\n\nMathOptAI.build_predictor(predictor::GLM.LinearModel)\n\nConvert a trained linear model from GLM.jl to an Affine layer.\n\nExample\n\njulia> using GLM, MathOptAI\n\njulia> X, Y = rand(10, 2), rand(10);\n\njulia> model_glm = GLM.lm(X, Y);\n\njulia> MathOptAI.build_predictor(model_glm)\nAffine(A, b) [input: 2, output: 1]\n\n\n\n\n\nMathOptAI.build_predictor(\n predictor::GLM.GeneralizedLinearModel{\n GLM.GlmResp{Vector{Float64},GLM.Bernoulli{Float64},GLM.LogitLink},\n };\n sigmoid::MathOptAI.AbstractPredictor = MathOptAI.Sigmoid(),\n)\n\nConvert a trained logistic model from GLM.jl to a Pipeline layer.\n\nKeyword arguments\n\nsigmoid: the predictor to use for the sigmoid layer.\n\nExample\n\njulia> using GLM, MathOptAI\n\njulia> X, Y = rand(10, 2), rand(Bool, 10);\n\njulia> model_glm = GLM.glm(X, Y, GLM.Bernoulli());\n\njulia> MathOptAI.build_predictor(model_glm)\nPipeline with layers:\n * Affine(A, b) [input: 2, output: 1]\n * Sigmoid()\n\n\n\n\n\nMathOptAI.build_predictor(\n predictor::MathOptAI.PytorchModel;\n config::Dict = Dict{Any,Any}(),\n gray_box::Bool = false,\n gray_box_hessian::Bool = false,\n)\n\nConvert a trained neural network from PyTorch via PythonCall.jl to a Pipeline.\n\nSupported layers\n\nnn.Linear\nnn.ReLU\nnn.Sequential\nnn.Sigmoid\nnn.Softplus\nnn.Tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps Symbols to AbstractPredictors that control how the activation functions are reformulated. For example, :Sigmoid => MathOptAI.Sigmoid() or :ReLU => MathOptAI.QuadraticReLU(). The supported Symbols are :ReLU, :Sigmoid, :SoftPlus, and :Tanh.\ngray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by torch.func.jacrev.\ngray_box_hessian: if true, the gray box additionally computes the Hessian of the output using torch.func.hessian.\n\n\n\n\n\nMathOptAI.build_predictor(\n predictor::Flux.Chain;\n config::Dict = Dict{Any,Any}(),\n gray_box::Bool = false,\n gray_box_hessian::Bool = false,\n)\n\nConvert a trained neural network from Flux.jl to a Pipeline.\n\nSupported layers\n\nFlux.Dense\nFlux.Scale\nFlux.softmax\n\nSupported activation functions\n\nFlux.relu\nFlux.sigmoid\nFlux.softplus\nFlux.tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps supported Flux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Flux.sigmoid => MathOptAI.Sigmoid() or Flux.relu => MathOptAI.QuadraticReLU().\ngray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by Flux.withjacobian.\ngray_box_hessian: if true, the gray box additionally computes the Hessian of the output using Flux.hessian.\n\nExample\n\njulia> using Flux, MathOptAI\n\njulia> chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));\n\njulia> MathOptAI.build_predictor(\n chain;\n config = Dict(Flux.relu => MathOptAI.ReLU()),\n )\nPipeline with layers:\n * Affine(A, b) [input: 1, output: 16]\n * ReLU()\n * Affine(A, b) [input: 16, output: 1]\n\njulia> MathOptAI.build_predictor(\n chain;\n config = Dict(Flux.relu => MathOptAI.ReLUQuadratic()),\n )\nPipeline with layers:\n * Affine(A, b) [input: 1, output: 16]\n * ReLUQuadratic()\n * Affine(A, b) [input: 16, output: 1]\n\n\n\n\n\n","category":"function"},{"location":"api/#Affine","page":"API Reference","title":"Affine","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Affine","category":"page"},{"location":"api/#MathOptAI.Affine","page":"API Reference","title":"MathOptAI.Affine","text":"Affine(\n A::Matrix{T},\n b::Vector{T} = zeros(T, size(A, 1)),\n) where {T} <: AbstractPredictor\n\nAn AbstractPredictor that represents the affine relationship:\n\nf(x) = A x + b\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.Affine([2.0 3.0], [4.0])\nAffine(A, b) [input: 2, output: 1]\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Affine[1]\n\njulia> formulation\nAffine(A, b) [input: 2, output: 1]\n├ variables [1]\n│ └ moai_Affine[1]\n└ constraints [1]\n └ 2 x[1] + 3 x[2] - moai_Affine[1] = -4\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n1-element Vector{AffExpr}:\n 2 x[1] + 3 x[2] + 4\n\njulia> formulation\nReducedSpace(Affine(A, b) [input: 2, output: 1])\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#BinaryDecisionTree","page":"API Reference","title":"BinaryDecisionTree","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"BinaryDecisionTree","category":"page"},{"location":"api/#MathOptAI.BinaryDecisionTree","page":"API Reference","title":"MathOptAI.BinaryDecisionTree","text":"BinaryDecisionTree{K,V}(\n feat_id::Int,\n feat_value::K,\n lhs::Union{V,BinaryDecisionTree{K,V}},\n rhs::Union{V,BinaryDecisionTree{K,V}},\n)\n\nAn AbstractPredictor that represents a binary decision tree.\n\nIf x[feat_id] <= feat_value, then return lhs\nIf x[feat_id] > feat_value, then return rhs\n\nExample\n\nTo represent the tree x[1] <= 0.0 ? -1 : (x[1] <= 1.0 ? 0 : 1), do:\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:1]);\n\njulia> f = MathOptAI.BinaryDecisionTree{Float64,Int}(\n 1,\n 0.0,\n -1,\n MathOptAI.BinaryDecisionTree{Float64,Int}(1, 1.0, 0, 1),\n )\nBinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_BinaryDecisionTree_value\n\njulia> formulation\nBinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]\n├ variables [4]\n│ ├ moai_BinaryDecisionTree_value\n│ ├ moai_BinaryDecisionTree_z[1]\n│ ├ moai_BinaryDecisionTree_z[2]\n│ └ moai_BinaryDecisionTree_z[3]\n└ constraints [7]\n ├ moai_BinaryDecisionTree_z[1] + moai_BinaryDecisionTree_z[2] + moai_BinaryDecisionTree_z[3] = 1\n ├ moai_BinaryDecisionTree_z[1] --> {x[1] ≤ 0}\n ├ moai_BinaryDecisionTree_z[2] --> {x[1] ≥ 0}\n ├ moai_BinaryDecisionTree_z[2] --> {x[1] ≤ 1}\n ├ moai_BinaryDecisionTree_z[3] --> {x[1] ≥ 0}\n ├ moai_BinaryDecisionTree_z[3] --> {x[1] ≥ 1}\n └ moai_BinaryDecisionTree_z[1] - moai_BinaryDecisionTree_z[3] + moai_BinaryDecisionTree_value = 0\n\n\n\n\n\n","category":"type"},{"location":"api/#GrayBox","page":"API Reference","title":"GrayBox","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"GrayBox","category":"page"},{"location":"api/#MathOptAI.GrayBox","page":"API Reference","title":"MathOptAI.GrayBox","text":"GrayBox(\n output_size::Function,\n callback::Function;\n has_hessian::Bool = false,\n) <: AbstractPredictor\n\nAn AbstractPredictor that represents the function f(x) as a user-defined nonlinear operator.\n\nArguments\n\noutput_size(x::Vector):Int: given an input vector x, return the dimension of the output vector\ncallback(x::Vector)::NamedTuple -> (;value, jacobian[, hessian]): given an input vector x, return a NamedTuple that computes the primal value and Jacobian of the output value with respect to the input. jacobian[j, i] is the partial derivative of value[j] with respect to x[i].\nhas_hessian: if true, the callback additionally contains a field hessian, which is an N × N × M matrix, where hessian[i, j, k] is the partial derivative of value[k] with respect to x[i] and x[j].\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.GrayBox(\n x -> 2,\n x -> (value = x.^2, jacobian = [2 * x[1] 0.0; 0.0 2 * x[2]]),\n );\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_GrayBox[1]\n moai_GrayBox[2]\n\njulia> formulation\nGrayBox\n├ variables [2]\n│ ├ moai_GrayBox[1]\n│ └ moai_GrayBox[2]\n└ constraints [2]\n ├ op_##330(x[1], x[2]) - moai_GrayBox[1] = 0\n └ op_##331(x[1], x[2]) - moai_GrayBox[2] = 0\n\njulia> y, formulation = MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n op_##332(x[1], x[2])\n op_##333(x[1], x[2])\n\njulia> formulation\nReducedSpace(GrayBox)\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#Pipeline","page":"API Reference","title":"Pipeline","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Pipeline","category":"page"},{"location":"api/#MathOptAI.Pipeline","page":"API Reference","title":"MathOptAI.Pipeline","text":"Pipeline(layers::Vector{AbstractPredictor}) <: AbstractPredictor\n\nAn AbstractPredictor that represents a pipeline (composition) of nested layers:\n\nf(x) = (l_1 cdots (l_N(x))\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.Pipeline(\n MathOptAI.Affine([1.0 2.0], [0.0]),\n MathOptAI.ReLUQuadratic(),\n )\nPipeline with layers:\n * Affine(A, b) [input: 2, output: 1]\n * ReLUQuadratic()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_ReLU[1]\n\njulia> formulation\nAffine(A, b) [input: 2, output: 1]\n├ variables [1]\n│ └ moai_Affine[1]\n└ constraints [1]\n └ x[1] + 2 x[2] - moai_Affine[1] = 0\nReLUQuadratic()\n├ variables [2]\n│ ├ moai_ReLU[1]\n│ └ moai_z[1]\n└ constraints [2]\n ├ moai_Affine[1] - moai_ReLU[1] + moai_z[1] = 0\n └ moai_ReLU[1]*moai_z[1] = 0\n\n\n\n\n\n","category":"type"},{"location":"api/#PytorchModel","page":"API Reference","title":"PytorchModel","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"PytorchModel","category":"page"},{"location":"api/#MathOptAI.PytorchModel","page":"API Reference","title":"MathOptAI.PytorchModel","text":"PytorchModel(filename::String)\n\nA wrapper struct for loading a PyTorch model.\n\nThe only supported file extension is .pt, where the .pt file has been created using torch.save(model, filename).\n\nExample\n\njulia> using PythonCall, MathOptAI\n\njulia> predictor = PytorchModel(\"model.pt\");\n\n\n\n\n\n","category":"type"},{"location":"api/#Quantile","page":"API Reference","title":"Quantile","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Quantile","category":"page"},{"location":"api/#MathOptAI.Quantile","page":"API Reference","title":"MathOptAI.Quantile","text":"Quantile(distribution, quantiles::Vector{Float64})\n\nAn AbstractPredictor that represents the quantiles of distribution.\n\nExample\n\njulia> using JuMP, Distributions, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, 1 <= x <= 2);\n\njulia> predictor = MathOptAI.Quantile([0.1, 0.9]) do x\n return Distributions.Normal(x, 3 - x)\n end\nQuantile(_, [0.1, 0.9])\n\njulia> y, formulation = MathOptAI.add_predictor(model, predictor, [x]);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_quantile[1]\n moai_quantile[2]\n\n\n\n\n\n","category":"type"},{"location":"api/#ReducedSpace","page":"API Reference","title":"ReducedSpace","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"ReducedSpace","category":"page"},{"location":"api/#MathOptAI.ReducedSpace","page":"API Reference","title":"MathOptAI.ReducedSpace","text":"ReducedSpace(predictor::AbstractPredictor)\n\nA wrapper type for other predictors that implement a reduced-space formulation.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> predictor = MathOptAI.ReducedSpace(MathOptAI.ReLU());\n\njulia> y, formulation = MathOptAI.add_predictor(model, predictor, x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n max(0.0, x[1])\n max(0.0, x[2])\n\n\n\n\n\n","category":"type"},{"location":"api/#ReLU","page":"API Reference","title":"ReLU","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"ReLU","category":"page"},{"location":"api/#MathOptAI.ReLU","page":"API Reference","title":"MathOptAI.ReLU","text":"ReLU() <: AbstractPredictor\n\nAn AbstractPredictor that implements the ReLU constraint y = max0 x as a non-smooth nonlinear constraint.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.ReLU()\nReLU()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_ReLU[1]\n moai_ReLU[2]\n\njulia> formulation\nReLU()\n├ variables [2]\n│ ├ moai_ReLU[1]\n│ └ moai_ReLU[2]\n└ constraints [4]\n ├ moai_ReLU[1] ≥ 0\n ├ moai_ReLU[2] ≥ 0\n ├ moai_ReLU[1] - max(0.0, x[1]) = 0\n └ moai_ReLU[2] - max(0.0, x[2]) = 0\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n max(0.0, x[1])\n max(0.0, x[2])\n\njulia> formulation\nReducedSpace(ReLU())\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#ReLUBigM","page":"API Reference","title":"ReLUBigM","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"ReLUBigM","category":"page"},{"location":"api/#MathOptAI.ReLUBigM","page":"API Reference","title":"MathOptAI.ReLUBigM","text":"ReLUBigM(M::Float64) <: AbstractPredictor\n\nAn AbstractPredictor that implements the ReLU constraint y = max0 x via a big-M MIP reformulation.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, -3 <= x[i in 1:2] <= i);\n\njulia> f = MathOptAI.ReLUBigM(100.0)\nReLUBigM(100.0)\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_ReLU[1]\n moai_ReLU[2]\n\njulia> formulation\nReLUBigM(100.0)\n├ variables [4]\n│ ├ moai_ReLU[1]\n│ ├ moai_ReLU[2]\n│ ├ _[5]\n│ └ _[6]\n└ constraints [8]\n ├ _[5] binary\n ├ -x[1] + moai_ReLU[1] ≥ 0\n ├ moai_ReLU[1] - _[5] ≤ 0\n ├ -x[1] + moai_ReLU[1] + 3 _[5] ≤ 3\n ├ _[6] binary\n ├ -x[2] + moai_ReLU[2] ≥ 0\n ├ moai_ReLU[2] - 2 _[6] ≤ 0\n └ -x[2] + moai_ReLU[2] + 3 _[6] ≤ 3\n\n\n\n\n\n","category":"type"},{"location":"api/#ReLUQuadratic","page":"API Reference","title":"ReLUQuadratic","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"ReLUQuadratic","category":"page"},{"location":"api/#MathOptAI.ReLUQuadratic","page":"API Reference","title":"MathOptAI.ReLUQuadratic","text":"ReLUQuadratic() <: AbstractPredictor\n\nAn AbstractPredictor that implements the ReLU constraint y = max0 x by the reformulation:\n\nbeginaligned\nx = y - z \ny times z = 0 \ny z ge 0\nendaligned\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2] >= -1);\n\njulia> f = MathOptAI.ReLUQuadratic()\nReLUQuadratic()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_ReLU[1]\n moai_ReLU[2]\n\njulia> formulation\nReLUQuadratic()\n├ variables [4]\n│ ├ moai_ReLU[1]\n│ ├ moai_ReLU[2]\n│ ├ moai_z[1]\n│ └ moai_z[2]\n└ constraints [4]\n ├ x[1] - moai_ReLU[1] + moai_z[1] = 0\n ├ x[2] - moai_ReLU[2] + moai_z[2] = 0\n ├ moai_ReLU[1]*moai_z[1] = 0\n └ moai_ReLU[2]*moai_z[2] = 0\n\n\n\n\n\n","category":"type"},{"location":"api/#ReLUSOS1","page":"API Reference","title":"ReLUSOS1","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"ReLUSOS1","category":"page"},{"location":"api/#MathOptAI.ReLUSOS1","page":"API Reference","title":"MathOptAI.ReLUSOS1","text":"ReLUSOS1() <: AbstractPredictor\n\nAn AbstractPredictor that implements the ReLU constraint y = max0 x by the reformulation:\n\nbeginaligned\nx = y - z \ny z in SOS1 \ny z ge 0\nendaligned\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2] >= -1);\n\njulia> f = MathOptAI.ReLUSOS1()\nReLUSOS1()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_ReLU[1]\n moai_ReLU[2]\n\njulia> formulation\nReLUSOS1()\n├ variables [4]\n│ ├ moai_ReLU[1]\n│ ├ moai_ReLU[2]\n│ ├ moai_z[1]\n│ └ moai_z[2]\n└ constraints [4]\n ├ x[1] - moai_ReLU[1] + moai_z[1] = 0\n ├ x[2] - moai_ReLU[2] + moai_z[2] = 0\n ├ [moai_ReLU[1], moai_z[1]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])\n └ [moai_ReLU[2], moai_z[2]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])\n\n\n\n\n\n","category":"type"},{"location":"api/#Scale","page":"API Reference","title":"Scale","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Scale","category":"page"},{"location":"api/#MathOptAI.Scale","page":"API Reference","title":"MathOptAI.Scale","text":"Scale(\n scale::Vector{T},\n bias::Vector{T},\n) where {T} <: AbstractPredictor\n\nAn AbstractPredictor that represents the affine relationship:\n\nf(x) = Diag(scale)x + bias\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.Scale([2.0, 3.0], [4.0, 5.0])\nScale(scale, bias)\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_Scale[1]\n moai_Scale[2]\n\njulia> formulation\nScale(scale, bias)\n├ variables [2]\n│ ├ moai_Scale[1]\n│ └ moai_Scale[2]\n└ constraints [2]\n ├ 2 x[1] - moai_Scale[1] = -4\n └ 3 x[2] - moai_Scale[2] = -5\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{AffExpr}:\n 2 x[1] + 4\n 3 x[2] + 5\n\njulia> formulation\nReducedSpace(Scale(scale, bias))\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#Sigmoid","page":"API Reference","title":"Sigmoid","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Sigmoid","category":"page"},{"location":"api/#MathOptAI.Sigmoid","page":"API Reference","title":"MathOptAI.Sigmoid","text":"Sigmoid() <: AbstractPredictor\n\nAn AbstractPredictor that implements the Sigmoid constraint y = frac11 + e^-x as a smooth nonlinear constraint.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.Sigmoid()\nSigmoid()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_Sigmoid[1]\n moai_Sigmoid[2]\n\njulia> formulation\nSigmoid()\n├ variables [2]\n│ ├ moai_Sigmoid[1]\n│ └ moai_Sigmoid[2]\n└ constraints [6]\n ├ moai_Sigmoid[1] ≥ 0\n ├ moai_Sigmoid[2] ≥ 0\n ├ moai_Sigmoid[1] ≤ 1\n ├ moai_Sigmoid[2] ≤ 1\n ├ moai_Sigmoid[1] - (1.0 / (1.0 + exp(-x[1]))) = 0\n └ moai_Sigmoid[2] - (1.0 / (1.0 + exp(-x[2]))) = 0\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n 1.0 / (1.0 + exp(-x[1]))\n 1.0 / (1.0 + exp(-x[2]))\n\njulia> formulation\nReducedSpace(Sigmoid())\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#SoftMax","page":"API Reference","title":"SoftMax","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"SoftMax","category":"page"},{"location":"api/#MathOptAI.SoftMax","page":"API Reference","title":"MathOptAI.SoftMax","text":"SoftMax() <: AbstractPredictor\n\nAn AbstractPredictor that implements the SoftMax constraint y_i = frace^x_isum_j e^x_j as a smooth nonlinear constraint.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.SoftMax()\nSoftMax()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_SoftMax[1]\n moai_SoftMax[2]\n\njulia> formulation\nSoftMax()\n├ variables [3]\n│ ├ moai_SoftMax_denom\n│ ├ moai_SoftMax[1]\n│ └ moai_SoftMax[2]\n└ constraints [8]\n ├ moai_SoftMax[1] ≥ 0\n ├ moai_SoftMax[2] ≥ 0\n ├ moai_SoftMax[1] ≤ 1\n ├ moai_SoftMax[2] ≤ 1\n ├ moai_SoftMax_denom ≥ 0\n ├ moai_SoftMax_denom - (0.0 + exp(x[2]) + exp(x[1])) = 0\n ├ moai_SoftMax[1] - (exp(x[1]) / moai_SoftMax_denom) = 0\n └ moai_SoftMax[2] - (exp(x[2]) / moai_SoftMax_denom) = 0\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n exp(x[1]) / moai_SoftMax_denom\n exp(x[2]) / moai_SoftMax_denom\n\njulia> formulation\nReducedSpace(SoftMax())\n├ variables [1]\n│ └ moai_SoftMax_denom\n└ constraints [2]\n ├ moai_SoftMax_denom ≥ 0\n └ moai_SoftMax_denom - (0.0 + exp(x[2]) + exp(x[1])) = 0\n\n\n\n\n\n","category":"type"},{"location":"api/#SoftPlus","page":"API Reference","title":"SoftPlus","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"SoftPlus","category":"page"},{"location":"api/#MathOptAI.SoftPlus","page":"API Reference","title":"MathOptAI.SoftPlus","text":"SoftPlus(; beta = 1.0) <: AbstractPredictor\n\nAn AbstractPredictor that implements the SoftPlus constraint y = frac1beta log(1 + e^beta x) as a smooth nonlinear constraint.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.SoftPlus(; beta = 2.0)\nSoftPlus(2.0)\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_SoftPlus[1]\n moai_SoftPlus[2]\n\njulia> formulation\nSoftPlus(2.0)\n├ variables [2]\n│ ├ moai_SoftPlus[1]\n│ └ moai_SoftPlus[2]\n└ constraints [4]\n ├ moai_SoftPlus[1] ≥ 0\n ├ moai_SoftPlus[2] ≥ 0\n ├ moai_SoftPlus[1] - (log(1.0 + exp(2 x[1])) / 2.0) = 0\n └ moai_SoftPlus[2] - (log(1.0 + exp(2 x[2])) / 2.0) = 0\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n log(1.0 + exp(2 x[1])) / 2.0\n log(1.0 + exp(2 x[2])) / 2.0\n\njulia> formulation\nReducedSpace(SoftPlus(2.0))\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#Tanh","page":"API Reference","title":"Tanh","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Tanh","category":"page"},{"location":"api/#MathOptAI.Tanh","page":"API Reference","title":"MathOptAI.Tanh","text":"Tanh() <: AbstractPredictor\n\nAn AbstractPredictor that implements the Tanh constraint y = tanh(x) as a smooth nonlinear constraint.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.Tanh()\nTanh()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_Tanh[1]\n moai_Tanh[2]\n\njulia> formulation\nTanh()\n├ variables [2]\n│ ├ moai_Tanh[1]\n│ └ moai_Tanh[2]\n└ constraints [6]\n ├ moai_Tanh[1] ≥ -1\n ├ moai_Tanh[2] ≥ -1\n ├ moai_Tanh[1] ≤ 1\n ├ moai_Tanh[2] ≤ 1\n ├ moai_Tanh[1] - tanh(x[1]) = 0\n └ moai_Tanh[2] - tanh(x[2]) = 0\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n tanh(x[1])\n tanh(x[2])\n\njulia> formulation\nReducedSpace(Tanh())\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#AbstractFormulation","page":"API Reference","title":"AbstractFormulation","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"AbstractFormulation","category":"page"},{"location":"api/#MathOptAI.AbstractFormulation","page":"API Reference","title":"MathOptAI.AbstractFormulation","text":"abstract type AbstractFormulation end\n\nAn abstract type representing different formulations.\n\n\n\n\n\n","category":"type"},{"location":"api/#Formulation","page":"API Reference","title":"Formulation","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Formulation","category":"page"},{"location":"api/#MathOptAI.Formulation","page":"API Reference","title":"MathOptAI.Formulation","text":"struct Formulation{P<:AbstractPredictor} <: AbstractFormulation\n predictor::P\n variables::Vector{Any}\n constraints::Vector{Any}\nend\n\nFields\n\npredictor: the predictor object used to build the formulation\nvariables: a vector of new decision variables added to the model\nconstraints: a vector of new constraints added to the model\n\nCheck the docstring of the predictor for an explanation of the formulation and the order of the elements in .variables and .constraints.\n\n\n\n\n\n","category":"type"},{"location":"api/#PipelineFormulation","page":"API Reference","title":"PipelineFormulation","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"PipelineFormulation","category":"page"},{"location":"api/#MathOptAI.PipelineFormulation","page":"API Reference","title":"MathOptAI.PipelineFormulation","text":"struct PipelineFormulation{P<:AbstractPredictor} <: AbstractFormulation\n predictor::P\n layers::Vector{Any}\nend\n\nFields\n\npredictor: the predictor object used to build the formulation\nlayers: the formulation associated with each of the layers in the pipeline\n\n\n\n\n\n","category":"type"},{"location":"api/#Extensions","page":"API Reference","title":"Extensions","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Modules = [\n Base.get_extension(MathOptAI, :MathOptAIAbstractGPsExt),\n Base.get_extension(MathOptAI, :MathOptAIDecisionTreeExt),\n Base.get_extension(MathOptAI, :MathOptAIFluxExt),\n Base.get_extension(MathOptAI, :MathOptAIGLMExt),\n Base.get_extension(MathOptAI, :MathOptAILuxExt),\n Base.get_extension(MathOptAI, :MathOptAIPythonCallExt),\n Base.get_extension(MathOptAI, :MathOptAIStatsModelsExt),\n]","category":"page"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, MathOptAI.Quantile{<:AbstractGPs.PosteriorGP}, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::MathOptAI.Quantile{<:AbstractGPs.PosteriorGP},\n x::Vector,\n)\n\nAdd the quantiles of a trained Gaussian Process from AbstractGPs.jl to model.\n\nExample\n\njulia> using JuMP, MathOptAI, AbstractGPs\n\njulia> x_data = 2π .* (0.0:0.1:1.0);\n\njulia> y_data = sin.(x_data);\n\njulia> fx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.1);\n\njulia> p_fx = AbstractGPs.posterior(fx, y_data);\n\njulia> model = Model();\n\njulia> @variable(model, 1 <= x[1:1] <= 6, start = 3);\n\njulia> predictor = MathOptAI.Quantile(p_fx, [0.1, 0.9]);\n\njulia> y, _ = MathOptAI.add_predictor(model, predictor, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_quantile[1]\n moai_quantile[2]\n\njulia> @objective(model, Max, y[2] - y[1])\nmoai_quantile[2] - moai_quantile[1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, Union{DecisionTree.DecisionTreeClassifier, DecisionTree.Root}, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::Union{DecisionTree.Root,DecisionTree.DecisionTreeClassifier},\n x::Vector,\n)\n\nAdd a binary decision tree from DecisionTree.jl to model.\n\nExample\n\njulia> using JuMP, MathOptAI, DecisionTree\n\njulia> truth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)\ntruth (generic function with 1 method)\n\njulia> features = abs.(sin.((1:10) .* (3:4)'));\n\njulia> size(features)\n(10, 2)\n\njulia> labels = truth.(Vector.(eachrow(features)));\n\njulia> ml_model = DecisionTree.build_tree(labels, features)\nDecision Tree\nLeaves: 3\nDepth: 2\n\njulia> model = Model();\n\njulia> @variable(model, 0 <= x[1:2] <= 1);\n\njulia> y, _ = MathOptAI.add_predictor(model, ml_model, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_BinaryDecisionTree_value\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.build_predictor-Tuple{DecisionTree.Root}","page":"API Reference","title":"MathOptAI.build_predictor","text":"MathOptAI.build_predictor(predictor::DecisionTree.Root)\n\nConvert a binary decision tree from DecisionTree.jl to a BinaryDecisionTree.\n\nExample\n\njulia> using MathOptAI, DecisionTree\n\njulia> truth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)\ntruth (generic function with 1 method)\n\njulia> features = abs.(sin.((1:10) .* (3:4)'));\n\njulia> size(features)\n(10, 2)\n\njulia> labels = truth.(Vector.(eachrow(features)));\n\njulia> ml_model = DecisionTree.build_tree(labels, features)\nDecision Tree\nLeaves: 3\nDepth: 2\n\njulia> MathOptAI.build_predictor(ml_model)\nBinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, Flux.Chain, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::Flux.Chain,\n x::Vector;\n config::Dict = Dict{Any,Any}(),\n reduced_space::Bool = false,\n gray_box::Bool = false,\n)\n\nAdd a trained neural network from Flux.jl to model.\n\nSupported layers\n\nFlux.Dense\nFlux.Scale\nFlux.softmax\n\nSupported activation functions\n\nFlux.relu\nFlux.sigmoid\nFlux.softplus\nFlux.tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps supported Flux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Flux.sigmoid => MathOptAI.Sigmoid() or Flux.relu => MathOptAI.QuadraticReLU().\ngray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by Flux.withjacobian.\n\nExample\n\njulia> using JuMP, Flux, MathOptAI\n\njulia> chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));\n\njulia> model = Model();\n\njulia> @variable(model, x[1:1]);\n\njulia> y, _ = MathOptAI.add_predictor(\n model,\n chain,\n x;\n config = Dict(Flux.relu => MathOptAI.ReLU()),\n );\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Affine[1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.build_predictor-Tuple{Flux.Chain}","page":"API Reference","title":"MathOptAI.build_predictor","text":"MathOptAI.build_predictor(\n predictor::Flux.Chain;\n config::Dict = Dict{Any,Any}(),\n gray_box::Bool = false,\n gray_box_hessian::Bool = false,\n)\n\nConvert a trained neural network from Flux.jl to a Pipeline.\n\nSupported layers\n\nFlux.Dense\nFlux.Scale\nFlux.softmax\n\nSupported activation functions\n\nFlux.relu\nFlux.sigmoid\nFlux.softplus\nFlux.tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps supported Flux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Flux.sigmoid => MathOptAI.Sigmoid() or Flux.relu => MathOptAI.QuadraticReLU().\ngray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by Flux.withjacobian.\ngray_box_hessian: if true, the gray box additionally computes the Hessian of the output using Flux.hessian.\n\nExample\n\njulia> using Flux, MathOptAI\n\njulia> chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));\n\njulia> MathOptAI.build_predictor(\n chain;\n config = Dict(Flux.relu => MathOptAI.ReLU()),\n )\nPipeline with layers:\n * Affine(A, b) [input: 1, output: 16]\n * ReLU()\n * Affine(A, b) [input: 16, output: 1]\n\njulia> MathOptAI.build_predictor(\n chain;\n config = Dict(Flux.relu => MathOptAI.ReLUQuadratic()),\n )\nPipeline with layers:\n * Affine(A, b) [input: 1, output: 16]\n * ReLUQuadratic()\n * Affine(A, b) [input: 16, output: 1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, GLM.GeneralizedLinearModel{GLM.GlmResp{Vector{Float64}, Distributions.Bernoulli{Float64}, GLM.LogitLink}}, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::GLM.GeneralizedLinearModel{\n GLM.GlmResp{Vector{Float64},GLM.Bernoulli{Float64},GLM.LogitLink},\n },\n x::Vector;\n sigmoid::AbstractPredictor = MathOptAI.Sigmoid(),\n reduced_space::Bool = false,\n)\n\nAdd a trained logistic regression model from GLM.jl to model.\n\nKeyword arguments\n\nsigmoid: the predictor to use for the sigmoid layer.\n\nExample\n\njulia> using GLM, JuMP, MathOptAI\n\njulia> X, Y = rand(10, 2), rand(Bool, 10);\n\njulia> model_glm = GLM.glm(X, Y, GLM.Bernoulli());\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> y, _ = MathOptAI.add_predictor(\n model,\n model_glm,\n x;\n sigmoid = MathOptAI.Sigmoid(),\n );\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Sigmoid[1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, GLM.LinearModel, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::GLM.LinearModel,\n x::Vector;\n reduced_space::Bool = false,\n)\n\nAdd a trained linear model from GLM.jl to model.\n\nExample\n\njulia> using GLM, JuMP, MathOptAI\n\njulia> X, Y = rand(10, 2), rand(10);\n\njulia> model_glm = GLM.lm(X, Y);\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> y, _ = MathOptAI.add_predictor(model, model_glm, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Affine[1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.build_predictor-Tuple{GLM.GeneralizedLinearModel{GLM.GlmResp{Vector{Float64}, Distributions.Bernoulli{Float64}, GLM.LogitLink}}}","page":"API Reference","title":"MathOptAI.build_predictor","text":"MathOptAI.build_predictor(\n predictor::GLM.GeneralizedLinearModel{\n GLM.GlmResp{Vector{Float64},GLM.Bernoulli{Float64},GLM.LogitLink},\n };\n sigmoid::MathOptAI.AbstractPredictor = MathOptAI.Sigmoid(),\n)\n\nConvert a trained logistic model from GLM.jl to a Pipeline layer.\n\nKeyword arguments\n\nsigmoid: the predictor to use for the sigmoid layer.\n\nExample\n\njulia> using GLM, MathOptAI\n\njulia> X, Y = rand(10, 2), rand(Bool, 10);\n\njulia> model_glm = GLM.glm(X, Y, GLM.Bernoulli());\n\njulia> MathOptAI.build_predictor(model_glm)\nPipeline with layers:\n * Affine(A, b) [input: 2, output: 1]\n * Sigmoid()\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.build_predictor-Tuple{GLM.LinearModel}","page":"API Reference","title":"MathOptAI.build_predictor","text":"MathOptAI.build_predictor(predictor::GLM.LinearModel)\n\nConvert a trained linear model from GLM.jl to an Affine layer.\n\nExample\n\njulia> using GLM, MathOptAI\n\njulia> X, Y = rand(10, 2), rand(10);\n\njulia> model_glm = GLM.lm(X, Y);\n\njulia> MathOptAI.build_predictor(model_glm)\nAffine(A, b) [input: 2, output: 1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, Tuple{Lux.Chain, NamedTuple, NamedTuple}, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::Tuple{<:Lux.Chain,<:NamedTuple,<:NamedTuple},\n x::Vector;\n config::Dict = Dict{Any,Any}(),\n reduced_space::Bool = false,\n)\n\nAdd a trained neural network from Lux.jl to model.\n\nSupported layers\n\nLux.Dense\nLux.Scale\n\nSupported activation functions\n\nLux.relu\nLux.sigmoid\nLux.softplus\nLux.softmax\nLux.tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps supported Lux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Lux.sigmoid => MathOptAI.Sigmoid() or Lux.relu => MathOptAI.QuadraticReLU().\n\nExample\n\njulia> using JuMP, Lux, MathOptAI, Random\n\njulia> rng = Random.MersenneTwister();\n\njulia> chain = Lux.Chain(Lux.Dense(1 => 16, Lux.relu), Lux.Dense(16 => 1))\nChain(\n layer_1 = Dense(1 => 16, relu), # 32 parameters\n layer_2 = Dense(16 => 1), # 17 parameters\n) # Total: 49 parameters,\n # plus 0 states.\n\njulia> parameters, state = Lux.setup(rng, chain);\n\njulia> predictor = (chain, parameters, state);\n\njulia> model = Model();\n\njulia> @variable(model, x[1:1]);\n\njulia> y, _ = MathOptAI.add_predictor(\n model,\n predictor,\n x;\n config = Dict(Lux.relu => MathOptAI.ReLU()),\n );\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Affine[1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.build_predictor-Tuple{Tuple{Lux.Chain, NamedTuple, NamedTuple}}","page":"API Reference","title":"MathOptAI.build_predictor","text":"MathOptAI.build_predictor(\n predictor::Tuple{<:Lux.Chain,<:NamedTuple,<:NamedTuple};\n config::Dict = Dict{Any,Any}(),\n)\n\nConvert a trained neural network from Lux.jl to a Pipeline.\n\nSupported layers\n\nLux.Dense\nLux.Scale\n\nSupported activation functions\n\nLux.relu\nLux.sigmoid\nLux.softplus\nLux.softmax\nLux.tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps supported Lux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Lux.sigmoid => MathOptAI.Sigmoid() or Lux.relu => MathOptAI.QuadraticReLU().\n\nExample\n\njulia> using Lux, MathOptAI, Random\n\njulia> rng = Random.MersenneTwister();\n\njulia> chain = Lux.Chain(Lux.Dense(1 => 16, Lux.relu), Lux.Dense(16 => 1))\nChain(\n layer_1 = Dense(1 => 16, relu), # 32 parameters\n layer_2 = Dense(16 => 1), # 17 parameters\n) # Total: 49 parameters,\n # plus 0 states.\n\njulia> parameters, state = Lux.setup(rng, chain);\n\njulia> predictor = MathOptAI.build_predictor(\n (chain, parameters, state);\n config = Dict(Lux.relu => MathOptAI.ReLU()),\n )\nPipeline with layers:\n * Affine(A, b) [input: 1, output: 16]\n * ReLU()\n * Affine(A, b) [input: 16, output: 1]\n\njulia> MathOptAI.build_predictor(\n (chain, parameters, state);\n config = Dict(Lux.relu => MathOptAI.ReLUQuadratic()),\n )\nPipeline with layers:\n * Affine(A, b) [input: 1, output: 16]\n * ReLUQuadratic()\n * Affine(A, b) [input: 16, output: 1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, MathOptAI.PytorchModel, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::MathOptAI.PytorchModel,\n x::Vector;\n config::Dict = Dict{Any,Any}(),\n reduced_space::Bool = false,\n gray_box::Bool = false,\n)\n\nAdd a trained neural network from PyTorch via PythonCall.jl to model.\n\nSupported layers\n\nnn.Linear\nnn.ReLU\nnn.Sequential\nnn.Sigmoid\nnn.Softplus\nnn.Tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps Symbols to AbstractPredictors that control how the activation functions are reformulated. For example, :Sigmoid => MathOptAI.Sigmoid() or :ReLU => MathOptAI.QuadraticReLU(). The supported Symbols are :ReLU, :Sigmoid, :SoftPlus, and :Tanh.\ngray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by torch.func.jacrev.\ngray_box_hessian: if true, the gray box additionally computes the Hessian of the output using torch.func.hessian.\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.build_predictor-Tuple{MathOptAI.PytorchModel}","page":"API Reference","title":"MathOptAI.build_predictor","text":"MathOptAI.build_predictor(\n predictor::MathOptAI.PytorchModel;\n config::Dict = Dict{Any,Any}(),\n gray_box::Bool = false,\n gray_box_hessian::Bool = false,\n)\n\nConvert a trained neural network from PyTorch via PythonCall.jl to a Pipeline.\n\nSupported layers\n\nnn.Linear\nnn.ReLU\nnn.Sequential\nnn.Sigmoid\nnn.Softplus\nnn.Tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps Symbols to AbstractPredictors that control how the activation functions are reformulated. For example, :Sigmoid => MathOptAI.Sigmoid() or :ReLU => MathOptAI.QuadraticReLU(). The supported Symbols are :ReLU, :Sigmoid, :SoftPlus, and :Tanh.\ngray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by torch.func.jacrev.\ngray_box_hessian: if true, the gray box additionally computes the Hessian of the output using torch.func.hessian.\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, StatsModels.TableRegressionModel, DataFrames.DataFrame}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::StatsModels.TableRegressionModel,\n x::DataFrames.DataFrame;\n kwargs...,\n)\n\nAdd a trained regression model from StatsModels.jl to model, using the DataFrame x as input.\n\nIn most cases, predictor should be a GLM.jl predictor supported by MathOptAI, but trained using @formula and a DataFrame instead of the raw matrix input.\n\nIn general, x may have some columns that are constant (Float64) and some columns that are JuMP decision variables.\n\nKeyword arguments\n\nAll keyword arguments are passed to the corresponding add_predictor of the GLM extension.\n\nExample\n\njulia> using DataFrames, GLM, JuMP, MathOptAI\n\njulia> train_df = DataFrames.DataFrame(x1 = rand(10), x2 = rand(10));\n\njulia> train_df.y = 1.0 .* train_df.x1 + 2.0 .* train_df.x2 .+ rand(10);\n\njulia> predictor = GLM.lm(GLM.@formula(y ~ x1 + x2), train_df);\n\njulia> model = Model();\n\njulia> test_df = DataFrames.DataFrame(\n x1 = rand(6),\n x2 = @variable(model, [1:6]),\n );\n\njulia> test_df.y, _ = MathOptAI.add_predictor(model, predictor, test_df);\n\njulia> test_df.y\n6-element Vector{VariableRef}:\n moai_Affine[1]\n moai_Affine[1]\n moai_Affine[1]\n moai_Affine[1]\n moai_Affine[1]\n moai_Affine[1]\n\n\n\n\n\n","category":"method"},{"location":"manual/AbstractGPs/#AbstractGPs.jl","page":"AbstractGPs.jl","title":"AbstractGPs.jl","text":"","category":"section"},{"location":"manual/AbstractGPs/","page":"AbstractGPs.jl","title":"AbstractGPs.jl","text":"AbstractGPs.jl is a library for fittinng Gaussian Processes in Julia.","category":"page"},{"location":"manual/AbstractGPs/#Basic-example","page":"AbstractGPs.jl","title":"Basic example","text":"","category":"section"},{"location":"manual/AbstractGPs/","page":"AbstractGPs.jl","title":"AbstractGPs.jl","text":"Here is an example:","category":"page"},{"location":"manual/AbstractGPs/","page":"AbstractGPs.jl","title":"AbstractGPs.jl","text":"using JuMP, MathOptAI, AbstractGPs\nx_data = 2π .* (0.0:0.1:1.0);\ny_data = sin.(x_data);\nfx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.1);\np_fx = AbstractGPs.posterior(fx, y_data);\nmodel = Model();\n@variable(model, 1 <= x[1:1] <= 6, start = 3);\npredictor = MathOptAI.Quantile(p_fx, [0.1, 0.9]);\ny, formulation = MathOptAI.add_predictor(model, predictor, x);\ny\nformulation\n@objective(model, Max, y[2] - y[1])","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"EditURL = \"pytorch.jl\"","category":"page"},{"location":"tutorials/pytorch/#Function-fitting-with-PyTorch","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"","category":"section"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"The purpose of this tutorial is to explain how to embed a neural network model from PyTorch into JuMP.","category":"page"},{"location":"tutorials/pytorch/#Python-integration","page":"Function fitting with PyTorch","title":"Python integration","text":"","category":"section"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"MathOptAI uses PythonCall.jl to call from Julia into Python.","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"See CondaPkg.jl for more control over how to link Julia to an existing Python environment. For example, if you have an existing Python installation (with PyTorch installed), and it is available in the current conda environment, set:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"ENV[\"JULIA_CONDAPKG_BACKEND\"] = \"Current\"","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"before importing PythonCall.jl. If the Python installation can be found on the path and it is not in a conda environment, set:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"ENV[\"JULIA_CONDAPKG_BACKEND\"] = \"Null\"","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"If python is not on your path, you may additionally need to set JULIA_PYTHONCALL_EXE, for example, to:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"ENV[\"JULIA_PYTHONCALL_EXE\"] = \"python3\"","category":"page"},{"location":"tutorials/pytorch/#Required-packages","page":"Function fitting with PyTorch","title":"Required packages","text":"","category":"section"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"This tutorial requires the following packages","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"using JuMP\nusing Test\nimport Ipopt\nimport MathOptAI\nimport Plots","category":"page"},{"location":"tutorials/pytorch/#Training-a-model","page":"Function fitting with PyTorch","title":"Training a model","text":"","category":"section"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"The following script builds and trains a simple neural network in PyTorch. For simplicity, we do not evaluate out-of-sample test performance, or use a batched data loader. In general, you should train your model in Python, and then use torch.save(model, filename) to save it to a .pt file for later use in Julia.","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"The model is unimportant, but for this example, we are trying to fit noisy observations of the function f(x) = x^2 - 2x.","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"In Python, I ran:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"#!/usr/bin/python3\nimport torch\nmodel = torch.nn.Sequential(\n torch.nn.Linear(1, 16),\n torch.nn.ReLU(),\n torch.nn.Linear(16, 1),\n)\n\nn = 1024\nx = torch.arange(-2, 2 + 4 / (n - 1), 4 / (n - 1)).reshape(n, 1)\nloss_fn = torch.nn.MSELoss()\noptimizer = torch.optim.Adam(model.parameters(), lr=0.01)\nfor epoch in range(100):\n optimizer.zero_grad()\n N = torch.normal(torch.zeros(n, 1), torch.ones(n, 1))\n y = x ** 2 -2 * x + 0.1 * N\n loss = loss_fn(model(x), y)\n loss.backward()\n optimizer.step()\n\ntorch.save(model, \"model.pt\")","category":"page"},{"location":"tutorials/pytorch/#JuMP-model","page":"Function fitting with PyTorch","title":"JuMP model","text":"","category":"section"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"Our goal for this JuMP model is to load the Neural Network from PyTorch into the objective function, and then minimize the objective for different fixed values of x to recreate the function that the Neural Network has learned to approximate.","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"First, create a JuMP model:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"model = Model(Ipopt.Optimizer)\nset_silent(model)\n@variable(model, x)","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"Then, load the model from PyTorch using MathOptAI.PytorchModel:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"predictor = MathOptAI.PytorchModel(joinpath(@__DIR__, \"model.pt\"))\ny, _ = MathOptAI.add_predictor(model, predictor, [x])\n@objective(model, Min, only(y))","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"Now, visualize the fitted function y = predictor(x) by repeatedly solving the optimization problem for different fixed values of x:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"X, Y = -2:0.1:2, Float64[]\n@constraint(model, c, x == 0.0)\nfor xi in X\n set_normalized_rhs(c, xi)\n optimize!(model)\n @test is_solved_and_feasible(model)\n push!(Y, objective_value(model))\nend\nPlots.plot(x -> x^2 - 2x, X; label = \"Truth\", linestype = :dot)\nPlots.plot!(X, Y; label = \"Fitted\")","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"This page was generated using Literate.jl.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"EditURL = \"decision_trees.jl\"","category":"page"},{"location":"tutorials/decision_trees/#Classification-problems-with-DecisionTree.jl","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"","category":"section"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The purpose of this tutorial is to explain how to embed a decision tree model from DecisionTree.jl into JuMP.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The data and example in this tutorial comes from the paper: David Bergman, Teng Huang, Philip Brooks, Andrea Lodi, Arvind U. Raghunathan (2021) JANOS: An Integrated Predictive and Prescriptive Modeling Framework. INFORMS Journal on Computing 34(2):807-816. https://doi.org/10.1287/ijoc.2020.1023","category":"page"},{"location":"tutorials/decision_trees/#Required-packages","page":"Classification problems with DecisionTree.jl","title":"Required packages","text":"","category":"section"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"This tutorial uses the following packages.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"using JuMP\nimport CSV\nimport DataFrames\nimport Downloads\nimport DecisionTree\nimport HiGHS\nimport MathOptAI\nimport Statistics","category":"page"},{"location":"tutorials/decision_trees/#Data","page":"Classification problems with DecisionTree.jl","title":"Data","text":"","category":"section"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Here is a function to load the data directly from the JANOS repository:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"function read_df(filename)\n url = \"https://raw.githubusercontent.com/INFORMSJoC/2020.1023/master/data/\"\n data = Downloads.download(url * filename)\n return CSV.read(data, DataFrames.DataFrame)\nend","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"There are two important files. The first, college_student_enroll-s1-1.csv, contains historial admissions data on anonymized students, their SAT score, their GPA, their merit scholarships, and whether the enrolled in the college.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"train_df = read_df(\"college_student_enroll-s1-1.csv\")","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The second, college_applications6000.csv, contains the SAT and GPA data of students who are currently applying:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"evaluate_df = read_df(\"college_applications6000.csv\")","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"There are 6,000 prospective students:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"n_students = size(evaluate_df, 1)","category":"page"},{"location":"tutorials/decision_trees/#Prediction-model","page":"Classification problems with DecisionTree.jl","title":"Prediction model","text":"","category":"section"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The first step is to train a logistic regression model to predict the Boolean enroll column based on the SAT, GPA, and merit columns.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"train_features = Matrix(train_df[:, [:SAT, :GPA, :merit]])\ntrain_labels = train_df[:, :enroll]\npredictor = DecisionTree.DecisionTreeClassifier(; max_depth = 3)\nDecisionTree.fit!(predictor, train_features, train_labels)\nDecisionTree.print_tree(predictor)","category":"page"},{"location":"tutorials/decision_trees/#Decision-model","page":"Classification problems with DecisionTree.jl","title":"Decision model","text":"","category":"section"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Now that we have a trained decision tree, we want a decision model that chooses the optimal merit scholarship for each student in:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"evaluate_df","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Here's an empty JuMP model to start:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"model = Model()","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"First, we add a new columnn to evaluate_df, with one JuMP decision variable for each row. It is important the the .merit column name in evaluate_df matches the name in train_df.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"evaluate_df.merit = @variable(model, 0 <= x_merit[1:n_students] <= 2.5);\nevaluate_df","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Then, we use MathOptAI.add_predictor to embed model_ml into the JuMP model. MathOptAI.add_predictor returns a vector of variables, one for each row in evaluate_df, corresponding to the output enroll of our logistic regression.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"evaluate_features = Matrix(evaluate_df[:, [:SAT, :GPA, :merit]])\nevaluate_df.enroll = mapreduce(vcat, 1:size(evaluate_features, 1)) do i\n y, _ = MathOptAI.add_predictor(model, predictor, evaluate_features[i, :])\n return y\nend\nevaluate_df","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The .enroll column name in evaluate_df is just a name. It doesn't have to match the name in train_df.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The objective of our problem is to maximize the expected number of students who enroll:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"@objective(model, Max, sum(evaluate_df.enroll))","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Subject to the constraint that we can spend at most 0.2 * n_students on merit scholarships:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"@constraint(model, sum(evaluate_df.merit) <= 0.2 * n_students)","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Because logistic regression involves a Sigmoid layer, we need to use a smooth nonlinear optimizer. A common choice is Ipopt. Solve and check the optimizer found a feasible solution:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"set_optimizer(model, HiGHS.Optimizer)\nset_silent(model)\noptimize!(model)\n@assert is_solved_and_feasible(model)","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Let's store the solution in evaluate_df for analysis:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"evaluate_df.merit_sol = value.(evaluate_df.merit);\nevaluate_df.enroll_sol = value.(evaluate_df.enroll);\nevaluate_df","category":"page"},{"location":"tutorials/decision_trees/#Solution-analysis","page":"Classification problems with DecisionTree.jl","title":"Solution analysis","text":"","category":"section"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"We expect that just under 2,500 students will enroll:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"sum(evaluate_df.enroll_sol)","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"We awarded merit scholarships to approximately 1 in 6 students:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"count(evaluate_df.merit_sol .> 1e-5)","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The average merit scholarship was worth just under $1,000:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"1_000 * Statistics.mean(evaluate_df.merit_sol[evaluate_df.merit_sol.>1e-5])","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"This page was generated using Literate.jl.","category":"page"},{"location":"manual/Lux/#Lux.jl","page":"Lux.jl","title":"Lux.jl","text":"","category":"section"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"Lux.jl is a library for machine learning in Julia.","category":"page"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"The upstream documentation is available at https://lux.csail.mit.edu/stable/.","category":"page"},{"location":"manual/Lux/#Supported-layers","page":"Lux.jl","title":"Supported layers","text":"","category":"section"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"MathOptAI supports embedding a Lux model into JuMP if it is a Lux.Chain composed of:","category":"page"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"Lux.Dense\nLux.Scale\nLux.relu\nLux.sigmoid\nLux.softmax\nLux.softplus\nLux.tanh","category":"page"},{"location":"manual/Lux/#Basic-example","page":"Lux.jl","title":"Basic example","text":"","category":"section"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"Use MathOptAI.add_predictor to embed a tuple (containing the Lux.Chain, the parameters, and the state) into a JuMP model:","category":"page"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"using JuMP, Lux, MathOptAI, Random\nrng = Random.MersenneTwister();\nchain = Lux.Chain(Lux.Dense(1 => 2, Lux.relu), Lux.Dense(2 => 1))\nparameters, state = Lux.setup(rng, chain);\npredictor = (chain, parameters, state);\nmodel = Model();\n@variable(model, x[1:1]);\ny, formulation = MathOptAI.add_predictor(model, predictor, x);\ny\nformulation","category":"page"},{"location":"manual/Lux/#Reduced-space","page":"Lux.jl","title":"Reduced-space","text":"","category":"section"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"Use the reduced_space = true keyword to formulate a reduced-space model:","category":"page"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"using JuMP, Lux, MathOptAI, Random\nrng = Random.MersenneTwister();\nchain = Lux.Chain(Lux.Dense(1 => 2, Lux.relu), Lux.Dense(2 => 1))\nparameters, state = Lux.setup(rng, chain);\npredictor = (chain, parameters, state);\nmodel = Model();\n@variable(model, x[1:1]);\ny, formulation =\n MathOptAI.add_predictor(model, predictor, x; reduced_space = true);\ny\nformulation","category":"page"},{"location":"manual/Lux/#Gray-box","page":"Lux.jl","title":"Gray-box","text":"","category":"section"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"The Lux extension does not yet support the gray_box keyword argument.","category":"page"},{"location":"manual/Lux/#Change-how-layers-are-formulated","page":"Lux.jl","title":"Change how layers are formulated","text":"","category":"section"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"Pass a dictionary to the config keyword that maps Lux activation functions to a MathOptAI predictor:","category":"page"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"using JuMP, Lux, MathOptAI, Random\nrng = Random.MersenneTwister();\nchain = Lux.Chain(Lux.Dense(1 => 2, Lux.relu), Lux.Dense(2 => 1))\nparameters, state = Lux.setup(rng, chain);\npredictor = (chain, parameters, state);\nmodel = Model();\n@variable(model, x[1:1]);\ny, formulation = MathOptAI.add_predictor(\n model,\n predictor,\n x;\n config = Dict(Lux.relu => MathOptAI.ReLUSOS1()),\n);\ny\nformulation","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"EditURL = \"mnist_lux.jl\"","category":"page"},{"location":"tutorials/mnist_lux/#Adversarial-machine-learning-with-Lux.jl","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"","category":"section"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"The purpose of this tutorial is to explain how to embed a neural network model from Lux.jl into JuMP.","category":"page"},{"location":"tutorials/mnist_lux/#Required-packages","page":"Adversarial machine learning with Lux.jl","title":"Required packages","text":"","category":"section"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"This tutorial requires the following packages","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"using JuMP\nimport Lux\nimport Ipopt\nimport MathOptAI\nimport MLDatasets\nimport MLUtils\nimport OneHotArrays\nimport Optimisers\nimport Plots\nimport Random\nimport Zygote","category":"page"},{"location":"tutorials/mnist_lux/#Data","page":"Adversarial machine learning with Lux.jl","title":"Data","text":"","category":"section"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"This tutorial uses images from the MNIST dataset.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"We load the predefined train and test splits:","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"train_data = MLDatasets.MNIST(; split = :train)","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"test_data = MLDatasets.MNIST(; split = :test)","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Since the data are images, it is helpful to plot them. (This requires a transpose and reversing the rows to get the orientation correct.)","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"function plot_image(x::Matrix; kwargs...)\n return Plots.heatmap(\n x'[size(x, 1):-1:1, :];\n xlims = (1, size(x, 2)),\n ylims = (1, size(x, 1)),\n aspect_ratio = true,\n legend = false,\n xaxis = false,\n yaxis = false,\n kwargs...,\n )\nend\n\nfunction plot_image(instance::NamedTuple)\n return plot_image(instance.features; title = \"Label = $(instance.targets)\")\nend\n\nPlots.plot([plot_image(train_data[i]) for i in 1:6]...; layout = (2, 3))","category":"page"},{"location":"tutorials/mnist_lux/#Training","page":"Adversarial machine learning with Lux.jl","title":"Training","text":"","category":"section"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"We use a simple neural network with one hidden layer and a sigmoid activation function. (There are better performing networks; try experimenting.)","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"chain = Lux.Chain(\n Lux.Dense(28^2 => 32, Lux.sigmoid),\n Lux.Dense(32 => 10),\n Lux.softmax,\n)\nrng = Random.MersenneTwister();\nparameters, state = Lux.setup(rng, chain)\npredictor = (chain, parameters, state);\nnothing #hide","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Here is a function to load our data into the format that predictor expects:","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"function data_loader(data; batchsize, shuffle = false)\n x = reshape(data.features, 28^2, :)\n y = OneHotArrays.onehotbatch(data.targets, 0:9)\n return MLUtils.DataLoader((x, y); batchsize, shuffle)\nend","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"and here is a function to score the percentage of correct labels, where we assign a label by choosing the label of the highest softmax in the final layer.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"function score_model(predictor, data)\n chain, parameters, state = predictor\n x, y = only(data_loader(data; batchsize = length(data)))\n y_hat, _ = chain(x, parameters, state)\n is_correct = OneHotArrays.onecold(y) .== OneHotArrays.onecold(y_hat)\n p = round(100 * sum(is_correct) / length(is_correct); digits = 2)\n println(\"Accuracy = $p %\")\n return\nend","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"The accuracy of our model is only around 10% before training:","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"score_model(predictor, train_data)\nscore_model(predictor, test_data)","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Let's improve that by training our model.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"note: Note\nIt is not the purpose of this tutorial to explain how Lux works; see the documentation at https://lux.csail.mit.edu for more details. Changing the number of epochs or the learning rate can improve the loss.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"begin\n train_loader = data_loader(train_data; batchsize = 256, shuffle = true)\n optimizer_state = Optimisers.setup(Optimisers.Adam(0.0003f0), parameters)\n for epoch in 1:30\n loss = 0.0\n for (x, y) in train_loader\n global state\n (loss_batch, state), pullback = Zygote.pullback(parameters) do p\n y_model, new_state = chain(x, p, state)\n return Lux.CrossEntropyLoss()(y_model, y), new_state\n end\n gradients = only(pullback((one(loss), nothing)))\n Optimisers.update!(optimizer_state, parameters, gradients)\n loss += loss_batch\n end\n loss = round(loss / length(train_loader); digits = 4)\n print(\"Epoch $epoch: loss = $loss\\t\")\n score_model(predictor, test_data)\n end\nend","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Here are the first eight predictions of the test data:","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"function plot_image(predictor, x::Matrix)\n y, _ = chain(vec(x), parameters, state)\n score, index = findmax(y)\n title = \"Predicted: $(index - 1) ($(round(Int, 100 * score))%)\"\n return plot_image(x; title)\nend\n\nplots = [plot_image(predictor, test_data[i].features) for i in 1:8]\nPlots.plot(plots...; size = (1200, 600), layout = (2, 4))","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"We can also look at the best and worst four predictions:","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"x, y = only(data_loader(test_data; batchsize = length(test_data)))\ny_model, _ = chain(x, parameters, state)\nlosses = Lux.CrossEntropyLoss(; agg = identity)(y_model, y)\nindices = sortperm(losses; dims = 2)[[1:4; end-3:end]]\nplots = [plot_image(predictor, test_data[i].features) for i in indices]\nPlots.plot(plots...; size = (1200, 600), layout = (2, 4))","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"There are still some fairly bad mistakes. Can you change the model or training parameters improve to improve things?","category":"page"},{"location":"tutorials/mnist_lux/#JuMP","page":"Adversarial machine learning with Lux.jl","title":"JuMP","text":"","category":"section"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Now that we have a trained machine learning model, we can embed it in a JuMP model.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Here's a function which takes a test case and returns an example that maximizes the probability of the adversarial example.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"function find_adversarial_image(test_case; adversary_label, δ = 0.05)\n model = Model(Ipopt.Optimizer)\n set_silent(model)\n @variable(model, 0 <= x[1:28, 1:28] <= 1)\n @constraint(model, -δ .<= x .- test_case.features .<= δ)\n # Note: we need to use `vec` here because `x` is a 28-by-28 Matrix, but our\n # neural network expects a 28^2 length vector.\n y, _ = MathOptAI.add_predictor(model, predictor, vec(x))\n @objective(model, Max, y[adversary_label+1] - y[test_case.targets+1])\n optimize!(model)\n @assert is_solved_and_feasible(model)\n return value.(x)\nend","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Let's try finding an adversarial example to the third test image. The image on the left is our input image. The network thinks this is a 1 with probability 99%. The image on the right is the adversarial image. The network thinks this is a 7, although it is less confident.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"x_adversary = find_adversarial_image(test_data[3]; adversary_label = 7);\nPlots.plot(\n plot_image(predictor, test_data[3].features),\n plot_image(predictor, Float32.(x_adversary)),\n)","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"This page was generated using Literate.jl.","category":"page"},{"location":"manual/PyTorch/#PyTorch","page":"PyTorch","title":"PyTorch","text":"","category":"section"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"PyTorch is a library for machine learning in Python.","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"The upstream documentation is available at https://pytorch.org/docs/stable/.","category":"page"},{"location":"manual/PyTorch/#Supported-layers","page":"PyTorch","title":"Supported layers","text":"","category":"section"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"MathOptAI supports embedding a PyTorch models into JuMP if it is a nn.Sequential composed of:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"nn.Linear\nnn.ReLU\nnn.Sigmoid\nnn.Softplus\nnn.Tanh","category":"page"},{"location":"manual/PyTorch/#File-format","page":"PyTorch","title":"File format","text":"","category":"section"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"Use torch.save to save a trained PyTorch model to a .pt file:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"#!/usr/bin/python3\nimport torch\nmodel = torch.nn.Sequential(\n torch.nn.Linear(1, 2),\n torch.nn.ReLU(),\n torch.nn.Linear(2, 1),\n)\ntorch.save(model, \"saved_pytorch_model.pt\")","category":"page"},{"location":"manual/PyTorch/#Python-integration","page":"PyTorch","title":"Python integration","text":"","category":"section"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"MathOptAI uses PythonCall.jl to call from Julia into Python.","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"See CondaPkg.jl for more control over how to link Julia to an existing Python environment. For example, if you have an existing Python installation (with PyTorch installed), and it is available in the current Conda environment, set:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"ENV[\"JULIA_CONDAPKG_BACKEND\"] = \"Current\"","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"before importing PythonCall.jl. If the Python installation can be found on the path and it is not in a Conda environment, set:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"ENV[\"JULIA_CONDAPKG_BACKEND\"] = \"Null\"","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"If python is not on your path, you may additionally need to set JULIA_PYTHONCALL_EXE, for example, to:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"ENV[\"JULIA_PYTHONCALL_EXE\"] = \"python3\"","category":"page"},{"location":"manual/PyTorch/#Basic-example","page":"PyTorch","title":"Basic example","text":"","category":"section"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"Use MathOptAI.add_predictor to embed a PyTorch model into a JuMP model:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"using JuMP, MathOptAI\nmodel = Model();\n@variable(model, x[1:1]);\npredictor = MathOptAI.PytorchModel(\"saved_pytorch_model.pt\");\ny, formulation = MathOptAI.add_predictor(model, predictor, x);\ny\nformulation","category":"page"},{"location":"manual/PyTorch/#Reduced-space","page":"PyTorch","title":"Reduced-space","text":"","category":"section"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"Use the reduced_space = true keyword to formulate a reduced-space model:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"using JuMP, MathOptAI\nmodel = Model();\n@variable(model, x[1:1]);\npredictor = MathOptAI.PytorchModel(\"saved_pytorch_model.pt\");\ny, formulation =\n MathOptAI.add_predictor(model, predictor, x; reduced_space = true);\ny\nformulation","category":"page"},{"location":"manual/PyTorch/#Gray-box","page":"PyTorch","title":"Gray-box","text":"","category":"section"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"Use the gray_box = true keyword to embed the network as a nonlinear operator:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"using JuMP, MathOptAI\nmodel = Model();\n@variable(model, x[1:1]);\npredictor = MathOptAI.PytorchModel(\"saved_pytorch_model.pt\");\ny, formulation =\n MathOptAI.add_predictor(model, predictor, x; gray_box = true);\ny\nformulation","category":"page"},{"location":"manual/PyTorch/#Change-how-layers-are-formulated","page":"PyTorch","title":"Change how layers are formulated","text":"","category":"section"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"Pass a dictionary to the config keyword that maps the Symbol name of each PyTorch layer to a MathOptAI predictor:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"using JuMP, MathOptAI\nmodel = Model();\n@variable(model, x[1:1]);\npredictor = MathOptAI.PytorchModel(\"saved_pytorch_model.pt\");\ny, formulation = MathOptAI.add_predictor(\n model,\n predictor,\n x;\n config = Dict(:ReLU => MathOptAI.ReLUSOS1()),\n);\ny\nformulation","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"(Image: )","category":"page"},{"location":"#MathOptAI.jl","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"","category":"section"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"MathOptAI.jl is a JuMP extension for embedding trained AI, machine learning, and statistical learning models into a JuMP optimization model.","category":"page"},{"location":"#License","page":"MathOptAI.jl","title":"License","text":"","category":"section"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"MathOptAI.jl is provided under a BSD-3 license as part of the Optimization and Machine Learning Toolbox project, O4806.","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"See LICENSE.md for details.","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"Despite the name similarity, this project is not affiliated with OMLT, the Optimization and Machine Learning Toolkit.","category":"page"},{"location":"#Installation","page":"MathOptAI.jl","title":"Installation","text":"","category":"section"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"Install MathOptAI.jl using the Julia package manager:","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"import Pkg\nPkg.add(\"MathOptAI\")","category":"page"},{"location":"#Getting-started","page":"MathOptAI.jl","title":"Getting started","text":"","category":"section"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"Here's an example of using MathOptAI to embed a trained neural network from Flux into a JuMP model. The vector of JuMP variables x is fed as input to the neural network. The output y is a vector of JuMP variables that represents the output layer of the neural network. The formulation object stores the additional variables and constraints that were added to model.","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"julia> using JuMP, MathOptAI, Flux\n\njulia> predictor = Flux.Chain(\n Flux.Dense(28^2 => 32, Flux.sigmoid),\n Flux.Dense(32 => 10),\n Flux.softmax,\n );\n\njulia> #= Train the Flux model. Code not shown for simplicity =#\n\njulia> model = JuMP.Model();\n\njulia> JuMP.@variable(model, 0 <= x[1:28^2] <= 1);\n\njulia> y, formulation = MathOptAI.add_predictor(model, predictor, x);\n\njulia> y\n10-element Vector{VariableRef}:\n moai_SoftMax[1]\n moai_SoftMax[2]\n moai_SoftMax[3]\n moai_SoftMax[4]\n moai_SoftMax[5]\n moai_SoftMax[6]\n moai_SoftMax[7]\n moai_SoftMax[8]\n moai_SoftMax[9]\n moai_SoftMax[10]","category":"page"},{"location":"#Getting-help","page":"MathOptAI.jl","title":"Getting help","text":"","category":"section"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"This package is under active development. For help, questions, comments, and suggestions, please open a GitHub issue.","category":"page"},{"location":"#Inspiration","page":"MathOptAI.jl","title":"Inspiration","text":"","category":"section"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"This project is mainly inspired by two existing projects:","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"OMLT\ngurobi-machinelearning","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"Other works, from which we took less inspiration, include:","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"JANOS\nMeLOn\nENTMOOT\nreluMIP\nOptiCL\nPySCIPOpt-ML","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"The 2024 paper of López-Flores et al. is an excellent summary of the state of the field at the time that we started development of MathOptAI.","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"López-Flores, F.J., Ramírez-Márquez, C., Ponce-Ortega J.M. (2024). Process Systems Engineering Tools for Optimization of Trained Machine Learning Models: Comparative and Perspective. Industrial & Engineering Chemistry Research, 63(32), 13966-13979. DOI: 10.1021/acs.iecr.4c00632","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"EditURL = \"gaussian.jl\"","category":"page"},{"location":"tutorials/gaussian/#Function-fitting-with-AbstractGPs","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"","category":"section"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"The purpose of this tutorial is to explain how to embed a Gaussian Process from AbstractGPs into JuMP.","category":"page"},{"location":"tutorials/gaussian/#Required-packages","page":"Function fitting with AbstractGPs","title":"Required packages","text":"","category":"section"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"This tutorial requires the following packages","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"using JuMP\nusing Test\nimport AbstractGPs\nimport Ipopt\nimport MathOptAI\nimport Plots","category":"page"},{"location":"tutorials/gaussian/#Prediction-model","page":"Function fitting with AbstractGPs","title":"Prediction model","text":"","category":"section"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"Assume that we have some true underlying univariate function:","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"x_domain = 0:0.01:2π\ntrue_function(x) = sin(x)\nPlots.plot(x_domain, true_function.(x_domain); label = \"truth\")","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"We don't know the function, but we have access to a limited set of noisy sample points:","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"N = 20\nx_data = rand(x_domain, N)\nnoisy_sampler(x) = true_function(x) + 0.25 * (2rand() - 1)\ny_data = noisy_sampler.(x_data)\nPlots.scatter!(x_data, y_data; label = \"data\")","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"Using the data, we want to build a predictor y = predictor(x). One choice is a Gaussian Process:","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"fx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.4)\np_fx = AbstractGPs.posterior(fx, y_data)\nPlots.plot!(x_domain, p_fx; label = \"GP\", fillalpha = 0.1)","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"Gaussian Processes fit a mean and variance function:","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"AbstractGPs.mean_and_var(p_fx, [π / 2])","category":"page"},{"location":"tutorials/gaussian/#Decision-model","page":"Function fitting with AbstractGPs","title":"Decision model","text":"","category":"section"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"Our goal for this JuMP model is to embed the Gaussian Process from AbstractGPs into the model and then solve for different fixed values of x to recreate the function that the Gaussian Process has learned to approximate.","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"First, create a JuMP model:","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"model = Model(Ipopt.Optimizer)\nset_silent(model)\n@variable(model, x)","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"Since a Gaussian Process is a infinite dimensional object (its prediction is a distribution), we need some way of converting the Gaussian Process into a finite set of scalar values. For this, we use the Quantile predictor:","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"predictor = MathOptAI.Quantile(p_fx, [0.25, 0.75]);\ny, _ = MathOptAI.add_predictor(model, predictor, [x])","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"Now, visualize the fitted function y = predictor(x) by repeatedly solving the optimization problem for different fixed values of x. Each value of y has two elements: one for the 25th percentile and one for the 75th.","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"X, Y = range(0, 2π; length = 20), Any[]\n@constraint(model, c, x == 0.0)\nfor xi in X\n set_normalized_rhs(c, xi)\n optimize!(model)\n if is_solved_and_feasible(model)\n push!(Y, value.(y))\n else\n push!(Y, [NaN, NaN])\n end\nend\nPlots.plot!(X, reduce(hcat, Y)'; label = [\"P25\" \"P75\"], linewidth = 3)","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"This page was generated using Literate.jl.","category":"page"}] +} diff --git a/v0.1.3/siteinfo.js b/v0.1.3/siteinfo.js new file mode 100644 index 00000000..25003938 --- /dev/null +++ b/v0.1.3/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "v0.1.3"; diff --git a/v0.1.3/tutorials/decision_trees.jl b/v0.1.3/tutorials/decision_trees.jl new file mode 100644 index 00000000..bacacff7 --- /dev/null +++ b/v0.1.3/tutorials/decision_trees.jl @@ -0,0 +1,138 @@ +# Copyright (c) 2024: Oscar Dowson and contributors #src +# Copyright (c) 2024: Triad National Security, LLC #src +# #src +# Use of this source code is governed by a BSD-style license that can be #src +# found in the LICENSE.md file. #src + +# # Classification problems with DecisionTree.jl + +# The purpose of this tutorial is to explain how to embed a decision tree +# model from [DecisionTree.jl](https://github.com/JuliaAI/DecisionTree.jl) into +# JuMP. + +# The data and example in this tutorial comes from the paper: David Bergman, +# Teng Huang, Philip Brooks, Andrea Lodi, Arvind U. Raghunathan (2021) JANOS: An +# Integrated Predictive and Prescriptive Modeling Framework. INFORMS Journal on +# Computing 34(2):807-816. +# [https://doi.org/10.1287/ijoc.2020.1023](https://doi.org/10.1287/ijoc.2020.1023) + +# ## Required packages + +# This tutorial uses the following packages. + +using JuMP +import CSV +import DataFrames +import Downloads +import DecisionTree +import HiGHS +import MathOptAI +import Statistics + +# ## Data + +# Here is a function to load the data directly from the JANOS repository: + +function read_df(filename) + url = "https://raw.githubusercontent.com/INFORMSJoC/2020.1023/master/data/" + data = Downloads.download(url * filename) + return CSV.read(data, DataFrames.DataFrame) +end + +# There are two important files. The first, `college_student_enroll-s1-1.csv`, +# contains historial admissions data on anonymized students, their SAT score, +# their GPA, their merit scholarships, and whether the enrolled in the college. + +train_df = read_df("college_student_enroll-s1-1.csv") + +# The second, `college_applications6000.csv`, contains the SAT and GPA data of +# students who are currently applying: + +evaluate_df = read_df("college_applications6000.csv") + +# There are 6,000 prospective students: + +n_students = size(evaluate_df, 1) + +# ## Prediction model + +# The first step is to train a logistic regression model to predict the Boolean +# `enroll` column based on the `SAT`, `GPA`, and `merit` columns. + +train_features = Matrix(train_df[:, [:SAT, :GPA, :merit]]) +train_labels = train_df[:, :enroll] +predictor = DecisionTree.DecisionTreeClassifier(; max_depth = 3) +DecisionTree.fit!(predictor, train_features, train_labels) +DecisionTree.print_tree(predictor) + +# ## Decision model + +# Now that we have a trained decision tree, we want a decision model that +# chooses the optimal merit scholarship for each student in: + +evaluate_df + +# Here's an empty JuMP model to start: + +model = Model() + +# First, we add a new columnn to `evaluate_df`, with one JuMP decision variable +# for each row. It is important the the `.merit` column name in `evaluate_df` +# matches the name in `train_df`. + +evaluate_df.merit = @variable(model, 0 <= x_merit[1:n_students] <= 2.5); +evaluate_df + +# Then, we use [`MathOptAI.add_predictor`](@ref) to embed `model_ml` into the +# JuMP `model`. [`MathOptAI.add_predictor`](@ref) returns a vector of variables, +# one for each row in `evaluate_df`, corresponding to the output `enroll` of +# our logistic regression. + +evaluate_features = Matrix(evaluate_df[:, [:SAT, :GPA, :merit]]) +evaluate_df.enroll = mapreduce(vcat, 1:size(evaluate_features, 1)) do i + y, _ = MathOptAI.add_predictor(model, predictor, evaluate_features[i, :]) + return y +end +evaluate_df + +# The `.enroll` column name in `evaluate_df` is just a name. It doesn't have to +# match the name in `train_df`. + +# The objective of our problem is to maximize the expected number of students +# who enroll: + +@objective(model, Max, sum(evaluate_df.enroll)) + +# Subject to the constraint that we can spend at most `0.2 * n_students` on +# merit scholarships: + +@constraint(model, sum(evaluate_df.merit) <= 0.2 * n_students) + +# Because logistic regression involves a [`Sigmoid`](@ref) layer, we need to use +# a smooth nonlinear optimizer. A common choice is Ipopt. Solve and check the +# optimizer found a feasible solution: + +set_optimizer(model, HiGHS.Optimizer) +set_silent(model) +optimize!(model) +@assert is_solved_and_feasible(model) + +# Let's store the solution in `evaluate_df` for analysis: + +evaluate_df.merit_sol = value.(evaluate_df.merit); +evaluate_df.enroll_sol = value.(evaluate_df.enroll); +evaluate_df + +# ## Solution analysis + +# We expect that just under 2,500 students will enroll: + +sum(evaluate_df.enroll_sol) + +# We awarded merit scholarships to approximately 1 in 6 students: + +count(evaluate_df.merit_sol .> 1e-5) + +# The average merit scholarship was worth just under \$1,000: + +1_000 * Statistics.mean(evaluate_df.merit_sol[evaluate_df.merit_sol.>1e-5]) diff --git a/v0.1.3/tutorials/decision_trees/index.html b/v0.1.3/tutorials/decision_trees/index.html new file mode 100644 index 00000000..ea7dc90f --- /dev/null +++ b/v0.1.3/tutorials/decision_trees/index.html @@ -0,0 +1,246 @@ + +Classification problems with DecisionTree.jl · MathOptAI.jl
GitHub

Classification problems with DecisionTree.jl

The purpose of this tutorial is to explain how to embed a decision tree model from DecisionTree.jl into JuMP.

The data and example in this tutorial comes from the paper: David Bergman, Teng Huang, Philip Brooks, Andrea Lodi, Arvind U. Raghunathan (2021) JANOS: An Integrated Predictive and Prescriptive Modeling Framework. INFORMS Journal on Computing 34(2):807-816. https://doi.org/10.1287/ijoc.2020.1023

Required packages

This tutorial uses the following packages.

julia> using JuMP
julia> import CSV
julia> import DataFrames
julia> import Downloads
julia> import DecisionTree
julia> import HiGHS
julia> import MathOptAI
julia> import Statistics

Data

Here is a function to load the data directly from the JANOS repository:

julia> function read_df(filename)
+           url = "https://raw.githubusercontent.com/INFORMSJoC/2020.1023/master/data/"
+           data = Downloads.download(url * filename)
+           return CSV.read(data, DataFrames.DataFrame)
+       endread_df (generic function with 1 method)

There are two important files. The first, college_student_enroll-s1-1.csv, contains historial admissions data on anonymized students, their SAT score, their GPA, their merit scholarships, and whether the enrolled in the college.

julia> train_df = read_df("college_student_enroll-s1-1.csv")20000×6 DataFrame
+   Row │ Column1  StudentID  SAT    GPA      merit    enroll 
+       │ Int64    Int64      Int64  Float64  Float64  Int64  
+───────┼─────────────────────────────────────────────────────
+     1 │       1          1   1507     3.72     1.64       0
+     2 │       2          2   1532     3.93     0.52       0
+     3 │       3          3   1487     3.77     1.67       0
+     4 │       4          4   1259     3.05     1.21       1
+     5 │       5          5   1354     3.39     1.65       1
+     6 │       6          6   1334     3.22     0.0        0
+     7 │       7          7   1125     2.73     1.68       1
+     8 │       8          8   1180     2.82     0.0        1
+   ⋮   │    ⋮         ⋮        ⋮       ⋮        ⋮       ⋮
+ 19994 │   19994      19994   1185     3.09     1.16       1
+ 19995 │   19995      19995   1471     3.7      1.05       0
+ 19996 │   19996      19996   1139     3.03     1.21       1
+ 19997 │   19997      19997   1371     3.39     1.26       0
+ 19998 │   19998      19998   1424     3.72     0.85       0
+ 19999 │   19999      19999   1170     3.01     0.73       1
+ 20000 │   20000      20000   1389     3.57     0.55       0
+                                           19985 rows omitted

The second, college_applications6000.csv, contains the SAT and GPA data of students who are currently applying:

julia> evaluate_df = read_df("college_applications6000.csv")6000×3 DataFrame
+  Row │ StudentID  SAT    GPA     
+      │ Int64      Int64  Float64 
+──────┼───────────────────────────
+    1 │         1   1240     3.22
+    2 │         2   1206     2.87
+    3 │         3   1520     3.74
+    4 │         4   1238     3.11
+    5 │         5   1142     2.74
+    6 │         6   1086     2.77
+    7 │         7   1367     3.28
+    8 │         8   1034     2.41
+  ⋮   │     ⋮        ⋮       ⋮
+ 5994 │      5994   1121     2.96
+ 5995 │      5995   1564     4.1
+ 5996 │      5996   1332     3.14
+ 5997 │      5997   1228     2.95
+ 5998 │      5998   1165     2.81
+ 5999 │      5999   1400     3.43
+ 6000 │      6000   1097     2.65
+                 5985 rows omitted

There are 6,000 prospective students:

julia> n_students = size(evaluate_df, 1)6000

Prediction model

The first step is to train a logistic regression model to predict the Boolean enroll column based on the SAT, GPA, and merit columns.

julia> train_features = Matrix(train_df[:, [:SAT, :GPA, :merit]])20000×3 Matrix{Float64}:
+ 1507.0  3.72  1.64
+ 1532.0  3.93  0.52
+ 1487.0  3.77  1.67
+ 1259.0  3.05  1.21
+ 1354.0  3.39  1.65
+ 1334.0  3.22  0.0
+ 1125.0  2.73  1.68
+ 1180.0  2.82  0.0
+ 1098.0  2.91  0.0
+ 1116.0  2.95  0.0
+    ⋮
+ 1048.0  2.51  0.73
+ 1157.0  2.79  2.11
+ 1185.0  3.09  1.16
+ 1471.0  3.7   1.05
+ 1139.0  3.03  1.21
+ 1371.0  3.39  1.26
+ 1424.0  3.72  0.85
+ 1170.0  3.01  0.73
+ 1389.0  3.57  0.55
julia> train_labels = train_df[:, :enroll]20000-element Vector{Int64}:
+ 0
+ 0
+ 0
+ 1
+ 1
+ 0
+ 1
+ 1
+ 1
+ 1
+ ⋮
+ 1
+ 1
+ 1
+ 0
+ 1
+ 0
+ 0
+ 1
+ 0
julia> predictor = DecisionTree.DecisionTreeClassifier(; max_depth = 3)DecisionTreeClassifier
+max_depth:                3
+min_samples_leaf:         1
+min_samples_split:        2
+min_purity_increase:      0.0
+pruning_purity_threshold: 1.0
+n_subfeatures:            0
+classes:                  nothing
+root:                     nothing
julia> DecisionTree.fit!(predictor, train_features, train_labels)DecisionTreeClassifier
+max_depth:                3
+min_samples_leaf:         1
+min_samples_split:        2
+min_purity_increase:      0.0
+pruning_purity_threshold: 1.0
+n_subfeatures:            0
+classes:                  [0, 1]
+root:                     Decision Tree
+Leaves: 8
+Depth:  3
julia> DecisionTree.print_tree(predictor)Feature 1 < 1228.0 ?
+├─ Feature 2 < 3.125 ?
+    ├─ Feature 1 < 1214.0 ?
+        ├─ 1 : 7336/7336
+        └─ 1 : 334/361
+    └─ Feature 3 < 0.255 ?
+        ├─ 0 : 161/220
+        └─ 1 : 121/121
+└─ Feature 1 < 1412.0 ?
+    ├─ Feature 3 < 1.005 ?
+        ├─ 0 : 3600/4046
+        └─ 1 : 1603/2338
+    └─ Feature 3 < 1.865 ?
+        ├─ 0 : 4530/4530
+        └─ 0 : 947/1048

Decision model

Now that we have a trained decision tree, we want a decision model that chooses the optimal merit scholarship for each student in:

julia> evaluate_df6000×3 DataFrame
+  Row │ StudentID  SAT    GPA     
+      │ Int64      Int64  Float64 
+──────┼───────────────────────────
+    1 │         1   1240     3.22
+    2 │         2   1206     2.87
+    3 │         3   1520     3.74
+    4 │         4   1238     3.11
+    5 │         5   1142     2.74
+    6 │         6   1086     2.77
+    7 │         7   1367     3.28
+    8 │         8   1034     2.41
+  ⋮   │     ⋮        ⋮       ⋮
+ 5994 │      5994   1121     2.96
+ 5995 │      5995   1564     4.1
+ 5996 │      5996   1332     3.14
+ 5997 │      5997   1228     2.95
+ 5998 │      5998   1165     2.81
+ 5999 │      5999   1400     3.43
+ 6000 │      6000   1097     2.65
+                 5985 rows omitted

Here's an empty JuMP model to start:

julia> model = Model()A JuMP Model
+├ solver: none
+├ objective_sense: FEASIBILITY_SENSE
+├ num_variables: 0
+├ num_constraints: 0
+└ Names registered in the model: none

First, we add a new columnn to evaluate_df, with one JuMP decision variable for each row. It is important the the .merit column name in evaluate_df matches the name in train_df.

julia> evaluate_df.merit = @variable(model, 0 <= x_merit[1:n_students] <= 2.5);
julia> evaluate_df6000×4 DataFrame
+  Row │ StudentID  SAT    GPA      merit         
+      │ Int64      Int64  Float64  GenericV…     
+──────┼──────────────────────────────────────────
+    1 │         1   1240     3.22  x_merit[1]
+    2 │         2   1206     2.87  x_merit[2]
+    3 │         3   1520     3.74  x_merit[3]
+    4 │         4   1238     3.11  x_merit[4]
+    5 │         5   1142     2.74  x_merit[5]
+    6 │         6   1086     2.77  x_merit[6]
+    7 │         7   1367     3.28  x_merit[7]
+    8 │         8   1034     2.41  x_merit[8]
+  ⋮   │     ⋮        ⋮       ⋮           ⋮
+ 5994 │      5994   1121     2.96  x_merit[5994]
+ 5995 │      5995   1564     4.1   x_merit[5995]
+ 5996 │      5996   1332     3.14  x_merit[5996]
+ 5997 │      5997   1228     2.95  x_merit[5997]
+ 5998 │      5998   1165     2.81  x_merit[5998]
+ 5999 │      5999   1400     3.43  x_merit[5999]
+ 6000 │      6000   1097     2.65  x_merit[6000]
+                                5985 rows omitted

Then, we use MathOptAI.add_predictor to embed model_ml into the JuMP model. MathOptAI.add_predictor returns a vector of variables, one for each row in evaluate_df, corresponding to the output enroll of our logistic regression.

julia> evaluate_features = Matrix(evaluate_df[:, [:SAT, :GPA, :merit]])6000×3 Matrix{JuMP.AffExpr}:
+ 1240  3.22  x_merit[1]
+ 1206  2.87  x_merit[2]
+ 1520  3.74  x_merit[3]
+ 1238  3.11  x_merit[4]
+ 1142  2.74  x_merit[5]
+ 1086  2.77  x_merit[6]
+ 1367  3.28  x_merit[7]
+ 1034  2.41  x_merit[8]
+ 1547  3.82  x_merit[9]
+ 1453  3.65  x_merit[10]
+ ⋮
+ 1299  3.16  x_merit[5992]
+ 1400  3.59  x_merit[5993]
+ 1121  2.96  x_merit[5994]
+ 1564  4.1   x_merit[5995]
+ 1332  3.14  x_merit[5996]
+ 1228  2.95  x_merit[5997]
+ 1165  2.81  x_merit[5998]
+ 1400  3.43  x_merit[5999]
+ 1097  2.65  x_merit[6000]
julia> evaluate_df.enroll = mapreduce(vcat, 1:size(evaluate_features, 1)) do i
+           y, _ = MathOptAI.add_predictor(model, predictor, evaluate_features[i, :])
+           return y
+       end6000-element Vector{JuMP.VariableRef}:
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ ⋮
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
julia> evaluate_df6000×5 DataFrame
+  Row │ StudentID  SAT    GPA      merit          enroll                       ⋯
+      │ Int64      Int64  Float64  GenericV…      GenericV…                    ⋯
+──────┼─────────────────────────────────────────────────────────────────────────
+    1 │         1   1240     3.22  x_merit[1]     moai_BinaryDecisionTree_valu ⋯
+    2 │         2   1206     2.87  x_merit[2]     moai_BinaryDecisionTree_valu
+    3 │         3   1520     3.74  x_merit[3]     moai_BinaryDecisionTree_valu
+    4 │         4   1238     3.11  x_merit[4]     moai_BinaryDecisionTree_valu
+    5 │         5   1142     2.74  x_merit[5]     moai_BinaryDecisionTree_valu ⋯
+    6 │         6   1086     2.77  x_merit[6]     moai_BinaryDecisionTree_valu
+    7 │         7   1367     3.28  x_merit[7]     moai_BinaryDecisionTree_valu
+    8 │         8   1034     2.41  x_merit[8]     moai_BinaryDecisionTree_valu
+  ⋮   │     ⋮        ⋮       ⋮           ⋮                      ⋮              ⋱
+ 5994 │      5994   1121     2.96  x_merit[5994]  moai_BinaryDecisionTree_valu ⋯
+ 5995 │      5995   1564     4.1   x_merit[5995]  moai_BinaryDecisionTree_valu
+ 5996 │      5996   1332     3.14  x_merit[5996]  moai_BinaryDecisionTree_valu
+ 5997 │      5997   1228     2.95  x_merit[5997]  moai_BinaryDecisionTree_valu
+ 5998 │      5998   1165     2.81  x_merit[5998]  moai_BinaryDecisionTree_valu ⋯
+ 5999 │      5999   1400     3.43  x_merit[5999]  moai_BinaryDecisionTree_valu
+ 6000 │      6000   1097     2.65  x_merit[6000]  moai_BinaryDecisionTree_valu
+                                                  1 column and 5985 rows omitted

The .enroll column name in evaluate_df is just a name. It doesn't have to match the name in train_df.

The objective of our problem is to maximize the expected number of students who enroll:

julia> @objective(model, Max, sum(evaluate_df.enroll))moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + [[...5940 terms omitted...]] + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value

Subject to the constraint that we can spend at most 0.2 * n_students on merit scholarships:

julia> @constraint(model, sum(evaluate_df.merit) <= 0.2 * n_students)x_merit[1] + x_merit[2] + x_merit[3] + x_merit[4] + x_merit[5] + x_merit[6] + x_merit[7] + x_merit[8] + x_merit[9] + x_merit[10] + x_merit[11] + x_merit[12] + x_merit[13] + x_merit[14] + x_merit[15] + x_merit[16] + x_merit[17] + x_merit[18] + x_merit[19] + x_merit[20] + x_merit[21] + x_merit[22] + x_merit[23] + x_merit[24] + x_merit[25] + x_merit[26] + x_merit[27] + x_merit[28] + x_merit[29] + x_merit[30] + [[...5940 terms omitted...]] + x_merit[5971] + x_merit[5972] + x_merit[5973] + x_merit[5974] + x_merit[5975] + x_merit[5976] + x_merit[5977] + x_merit[5978] + x_merit[5979] + x_merit[5980] + x_merit[5981] + x_merit[5982] + x_merit[5983] + x_merit[5984] + x_merit[5985] + x_merit[5986] + x_merit[5987] + x_merit[5988] + x_merit[5989] + x_merit[5990] + x_merit[5991] + x_merit[5992] + x_merit[5993] + x_merit[5994] + x_merit[5995] + x_merit[5996] + x_merit[5997] + x_merit[5998] + x_merit[5999] + x_merit[6000] ≤ 1200

Because logistic regression involves a Sigmoid layer, we need to use a smooth nonlinear optimizer. A common choice is Ipopt. Solve and check the optimizer found a feasible solution:

julia> set_optimizer(model, HiGHS.Optimizer)
julia> set_silent(model)
julia> optimize!(model)
julia> @assert is_solved_and_feasible(model)

Let's store the solution in evaluate_df for analysis:

julia> evaluate_df.merit_sol = value.(evaluate_df.merit);
julia> evaluate_df.enroll_sol = value.(evaluate_df.enroll);
julia> evaluate_df6000×7 DataFrame
+  Row │ StudentID  SAT    GPA      merit          enroll                       ⋯
+      │ Int64      Int64  Float64  GenericV…      GenericV…                    ⋯
+──────┼─────────────────────────────────────────────────────────────────────────
+    1 │         1   1240     3.22  x_merit[1]     moai_BinaryDecisionTree_valu ⋯
+    2 │         2   1206     2.87  x_merit[2]     moai_BinaryDecisionTree_valu
+    3 │         3   1520     3.74  x_merit[3]     moai_BinaryDecisionTree_valu
+    4 │         4   1238     3.11  x_merit[4]     moai_BinaryDecisionTree_valu
+    5 │         5   1142     2.74  x_merit[5]     moai_BinaryDecisionTree_valu ⋯
+    6 │         6   1086     2.77  x_merit[6]     moai_BinaryDecisionTree_valu
+    7 │         7   1367     3.28  x_merit[7]     moai_BinaryDecisionTree_valu
+    8 │         8   1034     2.41  x_merit[8]     moai_BinaryDecisionTree_valu
+  ⋮   │     ⋮        ⋮       ⋮           ⋮                      ⋮              ⋱
+ 5994 │      5994   1121     2.96  x_merit[5994]  moai_BinaryDecisionTree_valu ⋯
+ 5995 │      5995   1564     4.1   x_merit[5995]  moai_BinaryDecisionTree_valu
+ 5996 │      5996   1332     3.14  x_merit[5996]  moai_BinaryDecisionTree_valu
+ 5997 │      5997   1228     2.95  x_merit[5997]  moai_BinaryDecisionTree_valu
+ 5998 │      5998   1165     2.81  x_merit[5998]  moai_BinaryDecisionTree_valu ⋯
+ 5999 │      5999   1400     3.43  x_merit[5999]  moai_BinaryDecisionTree_valu
+ 6000 │      6000   1097     2.65  x_merit[6000]  moai_BinaryDecisionTree_valu
+                                                 3 columns and 5985 rows omitted

Solution analysis

We expect that just under 2,500 students will enroll:

julia> sum(evaluate_df.enroll_sol)3530.0

We awarded merit scholarships to approximately 1 in 6 students:

julia> count(evaluate_df.merit_sol .> 1e-5)1278

The average merit scholarship was worth just under $1,000:

julia> 1_000 * Statistics.mean(evaluate_df.merit_sol[evaluate_df.merit_sol.>1e-5])938.6854460093895

This page was generated using Literate.jl.

diff --git a/v0.1.3/tutorials/gaussian.jl b/v0.1.3/tutorials/gaussian.jl new file mode 100644 index 00000000..3bf78e90 --- /dev/null +++ b/v0.1.3/tutorials/gaussian.jl @@ -0,0 +1,87 @@ +# Copyright (c) 2024: Oscar Dowson and contributors #src +# Copyright (c) 2024: Triad National Security, LLC #src +# #src +# Use of this source code is governed by a BSD-style license that can be #src +# found in the LICENSE.md file. #src + +# # Function fitting with AbstractGPs + +# The purpose of this tutorial is to explain how to embed a Gaussian Process +# from [AbstractGPs](https://github.com/JuliaGaussianProcesses/AbstractGPs.jl) +# into JuMP. + +# ## Required packages + +# This tutorial requires the following packages + +using JuMP +using Test +import AbstractGPs +import Ipopt +import MathOptAI +import Plots + +# ## Prediction model + +# Assume that we have some true underlying univariate function: + +x_domain = 0:0.01:2π +true_function(x) = sin(x) +Plots.plot(x_domain, true_function.(x_domain); label = "truth") + +# We don't know the function, but we have access to a limited set of noisy +# sample points: + +N = 20 +x_data = rand(x_domain, N) +noisy_sampler(x) = true_function(x) + 0.25 * (2rand() - 1) +y_data = noisy_sampler.(x_data) +Plots.scatter!(x_data, y_data; label = "data") + +# Using the data, we want to build a predictor `y = predictor(x)`. One choice is +# a Gaussian Process: + +fx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.4) +p_fx = AbstractGPs.posterior(fx, y_data) +Plots.plot!(x_domain, p_fx; label = "GP", fillalpha = 0.1) + +# Gaussian Processes fit a mean and variance function: + +AbstractGPs.mean_and_var(p_fx, [π / 2]) + +# ## Decision model + +# Our goal for this JuMP model is to embed the Gaussian Process from AbstractGPs +# into the model and then solve for different fixed values of `x` to recreate +# the function that the Gaussian Process has learned to approximate. + +# First, create a JuMP model: + +model = Model(Ipopt.Optimizer) +set_silent(model) +@variable(model, x) + +# Since a Gaussian Process is a infinite dimensional object (its prediction is a +# distribution), we need some way of converting the Gaussian Process into a +# finite set of scalar values. For this, we use the [`Quantile`](@ref) +# predictor: + +predictor = MathOptAI.Quantile(p_fx, [0.25, 0.75]); +y, _ = MathOptAI.add_predictor(model, predictor, [x]) + +# Now, visualize the fitted function `y = predictor(x)` by repeatedly solving +# the optimization problem for different fixed values of `x`. Each value of `y` +# has two elements: one for the 25th percentile and one for the 75th. + +X, Y = range(0, 2π; length = 20), Any[] +@constraint(model, c, x == 0.0) +for xi in X + set_normalized_rhs(c, xi) + optimize!(model) + if is_solved_and_feasible(model) + push!(Y, value.(y)) + else + push!(Y, [NaN, NaN]) + end +end +Plots.plot!(X, reduce(hcat, Y)'; label = ["P25" "P75"], linewidth = 3) diff --git a/v0.1.3/tutorials/gaussian/22543b35.svg b/v0.1.3/tutorials/gaussian/22543b35.svg new file mode 100644 index 00000000..0754ca85 --- /dev/null +++ b/v0.1.3/tutorials/gaussian/22543b35.svg @@ -0,0 +1,74 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.3/tutorials/gaussian/9d06420e.svg b/v0.1.3/tutorials/gaussian/9d06420e.svg new file mode 100644 index 00000000..fc0f55ed --- /dev/null +++ b/v0.1.3/tutorials/gaussian/9d06420e.svg @@ -0,0 +1,78 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.3/tutorials/gaussian/add42623.svg b/v0.1.3/tutorials/gaussian/add42623.svg new file mode 100644 index 00000000..006cddaa --- /dev/null +++ b/v0.1.3/tutorials/gaussian/add42623.svg @@ -0,0 +1,50 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.3/tutorials/gaussian/db996092.svg b/v0.1.3/tutorials/gaussian/db996092.svg new file mode 100644 index 00000000..9bcf58e6 --- /dev/null +++ b/v0.1.3/tutorials/gaussian/db996092.svg @@ -0,0 +1,71 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.3/tutorials/gaussian/index.html b/v0.1.3/tutorials/gaussian/index.html new file mode 100644 index 00000000..412a1b70 --- /dev/null +++ b/v0.1.3/tutorials/gaussian/index.html @@ -0,0 +1,31 @@ + +Function fitting with AbstractGPs · MathOptAI.jl
GitHub

Function fitting with AbstractGPs

The purpose of this tutorial is to explain how to embed a Gaussian Process from AbstractGPs into JuMP.

Required packages

This tutorial requires the following packages

using JuMP
+using Test
+import AbstractGPs
+import Ipopt
+import MathOptAI
+import Plots

Prediction model

Assume that we have some true underlying univariate function:

x_domain = 0:0.01:2π
+true_function(x) = sin(x)
+Plots.plot(x_domain, true_function.(x_domain); label = "truth")
Example block output

We don't know the function, but we have access to a limited set of noisy sample points:

N = 20
+x_data = rand(x_domain, N)
+noisy_sampler(x) = true_function(x) + 0.25 * (2rand() - 1)
+y_data = noisy_sampler.(x_data)
+Plots.scatter!(x_data, y_data; label = "data")
Example block output

Using the data, we want to build a predictor y = predictor(x). One choice is a Gaussian Process:

fx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.4)
+p_fx = AbstractGPs.posterior(fx, y_data)
+Plots.plot!(x_domain, p_fx; label = "GP", fillalpha = 0.1)
Example block output

Gaussian Processes fit a mean and variance function:

AbstractGPs.mean_and_var(p_fx, [π / 2])
([0.9685035214574635], [0.13172656154981965])

Decision model

Our goal for this JuMP model is to embed the Gaussian Process from AbstractGPs into the model and then solve for different fixed values of x to recreate the function that the Gaussian Process has learned to approximate.

First, create a JuMP model:

model = Model(Ipopt.Optimizer)
+set_silent(model)
+@variable(model, x)

\[ x \]

Since a Gaussian Process is a infinite dimensional object (its prediction is a distribution), we need some way of converting the Gaussian Process into a finite set of scalar values. For this, we use the Quantile predictor:

predictor = MathOptAI.Quantile(p_fx, [0.25, 0.75]);
+y, _ = MathOptAI.add_predictor(model, predictor, [x])
(JuMP.VariableRef[moai_quantile[1], moai_quantile[2]], Quantile(_, [0.25, 0.75])
+├ variables [0]
+└ constraints [0])

Now, visualize the fitted function y = predictor(x) by repeatedly solving the optimization problem for different fixed values of x. Each value of y has two elements: one for the 25th percentile and one for the 75th.

X, Y = range(0, 2π; length = 20), Any[]
+@constraint(model, c, x == 0.0)
+for xi in X
+    set_normalized_rhs(c, xi)
+    optimize!(model)
+    if is_solved_and_feasible(model)
+        push!(Y, value.(y))
+    else
+        push!(Y, [NaN, NaN])
+    end
+end
+Plots.plot!(X, reduce(hcat, Y)'; label = ["P25" "P75"], linewidth = 3)
Example block output

This page was generated using Literate.jl.

diff --git a/v0.1.3/tutorials/mnist.jl b/v0.1.3/tutorials/mnist.jl new file mode 100644 index 00000000..6b3ed436 --- /dev/null +++ b/v0.1.3/tutorials/mnist.jl @@ -0,0 +1,171 @@ +# Copyright (c) 2024: Oscar Dowson and contributors #src +# Copyright (c) 2024: Triad National Security, LLC #src +# #src +# Use of this source code is governed by a BSD-style license that can be #src +# found in the LICENSE.md file. #src + +# # Adversarial machine learning with Flux.jl + +# The purpose of this tutorial is to explain how to embed a neural network model +# from [Flux.jl](https://github.com/FluxML/Flux.jl) into JuMP. + +# ## Required packages + +# This tutorial requires the following packages + +using JuMP +import Flux +import Ipopt +import MathOptAI +import MLDatasets +import Plots + +# ## Data + +# This tutorial uses images from the MNIST dataset. + +# We load the predefined train and test splits: + +train_data = MLDatasets.MNIST(; split = :train) + +#- + +test_data = MLDatasets.MNIST(; split = :test) + +# Since the data are images, it is helpful to plot them. (This requires a +# transpose and reversing the rows to get the orientation correct.) + +function plot_image(x::Matrix; kwargs...) + return Plots.heatmap( + x'[size(x, 1):-1:1, :]; + xlims = (1, size(x, 2)), + ylims = (1, size(x, 1)), + aspect_ratio = true, + legend = false, + xaxis = false, + yaxis = false, + kwargs..., + ) +end + +function plot_image(instance::NamedTuple) + return plot_image(instance.features; title = "Label = $(instance.targets)") +end + +Plots.plot([plot_image(train_data[i]) for i in 1:6]...; layout = (2, 3)) + +# ## Training + +# We use a simple neural network with one hidden layer and a sigmoid activation +# function. (There are better performing networks; try experimenting.) + +predictor = Flux.Chain( + Flux.Dense(28^2 => 32, Flux.sigmoid), + Flux.Dense(32 => 10), + Flux.softmax, +) + +# Here is a function to load our data into the format that `predictor` expects: +function data_loader(data; batchsize, shuffle = false) + x = reshape(data.features, 28^2, :) + y = Flux.onehotbatch(data.targets, 0:9) + return Flux.DataLoader((x, y); batchsize, shuffle) +end + +# and here is a function to score the percentage of correct labels, where we +# assign a label by choosing the label of the highest softmax in the final +# layer. + +function score_model(predictor, data) + x, y = only(data_loader(data; batchsize = length(data))) + y_hat = predictor(x) + is_correct = Flux.onecold(y) .== Flux.onecold(y_hat) + p = round(100 * sum(is_correct) / length(is_correct); digits = 2) + println("Accuracy = $p %") + return +end + +# The accuracy of our model is only around 10% before training: + +score_model(predictor, train_data) +score_model(predictor, test_data) + +# Let's improve that by training our model. + +# !!! note +# It is not the purpose of this tutorial to explain how Flux works; see the +# documentation at [https://fluxml.ai](https://fluxml.ai) for more details. +# Changing the number of epochs or the learning rate can improve the loss. + +begin + train_loader = data_loader(train_data; batchsize = 256, shuffle = true) + optimizer_state = Flux.setup(Flux.Adam(3e-4), predictor) + for epoch in 1:30 + loss = 0.0 + for (x, y) in train_loader + loss_batch, gradient = Flux.withgradient(predictor) do model + return Flux.crossentropy(model(x), y) + end + Flux.update!(optimizer_state, predictor, only(gradient)) + loss += loss_batch + end + loss = round(loss / length(train_loader); digits = 4) + print("Epoch $epoch: loss = $loss\t") + score_model(predictor, test_data) + end +end + +# Here are the first eight predictions of the test data: + +function plot_image(predictor, x::Matrix) + score, index = findmax(predictor(vec(x))) + title = "Predicted: $(index - 1) ($(round(Int, 100 * score))%)" + return plot_image(x; title) +end + +plots = [plot_image(predictor, test_data[i].features) for i in 1:8] +Plots.plot(plots...; size = (1200, 600), layout = (2, 4)) + +# We can also look at the best and worst four predictions: + +x, y = only(data_loader(test_data; batchsize = length(test_data))) +losses = Flux.crossentropy(predictor(x), y; agg = identity) +indices = sortperm(losses; dims = 2)[[1:4; end-3:end]] +plots = [plot_image(predictor, test_data[i].features) for i in indices] +Plots.plot(plots...; size = (1200, 600), layout = (2, 4)) + +# There are still some fairly bad mistakes. Can you change the model or training +# parameters improve to improve things? + +# ## JuMP + +# Now that we have a trained machine learning model, we can embed it in a JuMP +# model. + +# Here's a function which takes a test case and returns an example that +# maximizes the probability of the adversarial example. + +function find_adversarial_image(test_case; adversary_label, δ = 0.05) + model = Model(Ipopt.Optimizer) + set_silent(model) + @variable(model, 0 <= x[1:28, 1:28] <= 1) + @constraint(model, -δ .<= x .- test_case.features .<= δ) + ## Note: we need to use `vec` here because `x` is a 28-by-28 Matrix, but our + ## neural network expects a 28^2 length vector. + y, _ = MathOptAI.add_predictor(model, predictor, vec(x)) + @objective(model, Max, y[adversary_label+1] - y[test_case.targets+1]) + optimize!(model) + @assert is_solved_and_feasible(model) + return value.(x) +end + +# Let's try finding an adversarial example to the third test image. The image on +# the left is our input image. The network thinks this is a `1` with probability +# 99%. The image on the right is the adversarial image. The network thinks this +# is a `7`, although it is less confident. + +x_adversary = find_adversarial_image(test_data[3]; adversary_label = 7); +Plots.plot( + plot_image(predictor, test_data[3].features), + plot_image(predictor, Float32.(x_adversary)), +) diff --git a/v0.1.3/tutorials/mnist/03ea51eb.svg b/v0.1.3/tutorials/mnist/03ea51eb.svg new file mode 100644 index 00000000..3a04f998 --- /dev/null +++ b/v0.1.3/tutorials/mnist/03ea51eb.svg @@ -0,0 +1,1234 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.3/tutorials/mnist/1d0d5c7b.svg b/v0.1.3/tutorials/mnist/1d0d5c7b.svg new file mode 100644 index 00000000..a5519bcf --- /dev/null +++ b/v0.1.3/tutorials/mnist/1d0d5c7b.svg @@ -0,0 +1,1199 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.3/tutorials/mnist/8b1e498f.svg b/v0.1.3/tutorials/mnist/8b1e498f.svg new file mode 100644 index 00000000..233accd8 --- /dev/null +++ b/v0.1.3/tutorials/mnist/8b1e498f.svg @@ -0,0 +1,326 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.3/tutorials/mnist/b477c1d4.svg b/v0.1.3/tutorials/mnist/b477c1d4.svg new file mode 100644 index 00000000..1838c575 --- /dev/null +++ b/v0.1.3/tutorials/mnist/b477c1d4.svg @@ -0,0 +1,511 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.3/tutorials/mnist/index.html b/v0.1.3/tutorials/mnist/index.html new file mode 100644 index 00000000..13a338a5 --- /dev/null +++ b/v0.1.3/tutorials/mnist/index.html @@ -0,0 +1,125 @@ + +Adversarial machine learning with Flux.jl · MathOptAI.jl
GitHub

Adversarial machine learning with Flux.jl

The purpose of this tutorial is to explain how to embed a neural network model from Flux.jl into JuMP.

Required packages

This tutorial requires the following packages

using JuMP
+import Flux
+import Ipopt
+import MathOptAI
+import MLDatasets
+import Plots

Data

This tutorial uses images from the MNIST dataset.

We load the predefined train and test splits:

train_data = MLDatasets.MNIST(; split = :train)
dataset MNIST:
+  metadata  =>    Dict{String, Any} with 3 entries
+  split     =>    :train
+  features  =>    28×28×60000 Array{Float32, 3}
+  targets   =>    60000-element Vector{Int64}
test_data = MLDatasets.MNIST(; split = :test)
dataset MNIST:
+  metadata  =>    Dict{String, Any} with 3 entries
+  split     =>    :test
+  features  =>    28×28×10000 Array{Float32, 3}
+  targets   =>    10000-element Vector{Int64}

Since the data are images, it is helpful to plot them. (This requires a transpose and reversing the rows to get the orientation correct.)

function plot_image(x::Matrix; kwargs...)
+    return Plots.heatmap(
+        x'[size(x, 1):-1:1, :];
+        xlims = (1, size(x, 2)),
+        ylims = (1, size(x, 1)),
+        aspect_ratio = true,
+        legend = false,
+        xaxis = false,
+        yaxis = false,
+        kwargs...,
+    )
+end
+
+function plot_image(instance::NamedTuple)
+    return plot_image(instance.features; title = "Label = $(instance.targets)")
+end
+
+Plots.plot([plot_image(train_data[i]) for i in 1:6]...; layout = (2, 3))
Example block output

Training

We use a simple neural network with one hidden layer and a sigmoid activation function. (There are better performing networks; try experimenting.)

predictor = Flux.Chain(
+    Flux.Dense(28^2 => 32, Flux.sigmoid),
+    Flux.Dense(32 => 10),
+    Flux.softmax,
+)
Chain(
+  Dense(784 => 32, σ),                  # 25_120 parameters
+  Dense(32 => 10),                      # 330 parameters
+  NNlib.softmax,
+)                   # Total: 4 arrays, 25_450 parameters, 99.617 KiB.

Here is a function to load our data into the format that predictor expects:

function data_loader(data; batchsize, shuffle = false)
+    x = reshape(data.features, 28^2, :)
+    y = Flux.onehotbatch(data.targets, 0:9)
+    return Flux.DataLoader((x, y); batchsize, shuffle)
+end
data_loader (generic function with 1 method)

and here is a function to score the percentage of correct labels, where we assign a label by choosing the label of the highest softmax in the final layer.

function score_model(predictor, data)
+    x, y = only(data_loader(data; batchsize = length(data)))
+    y_hat = predictor(x)
+    is_correct = Flux.onecold(y) .== Flux.onecold(y_hat)
+    p = round(100 * sum(is_correct) / length(is_correct); digits = 2)
+    println("Accuracy = $p %")
+    return
+end
score_model (generic function with 1 method)

The accuracy of our model is only around 10% before training:

score_model(predictor, train_data)
+score_model(predictor, test_data)
Accuracy = 14.09 %
+Accuracy = 13.58 %

Let's improve that by training our model.

Note

It is not the purpose of this tutorial to explain how Flux works; see the documentation at https://fluxml.ai for more details. Changing the number of epochs or the learning rate can improve the loss.

begin
+    train_loader = data_loader(train_data; batchsize = 256, shuffle = true)
+    optimizer_state = Flux.setup(Flux.Adam(3e-4), predictor)
+    for epoch in 1:30
+        loss = 0.0
+        for (x, y) in train_loader
+            loss_batch, gradient = Flux.withgradient(predictor) do model
+                return Flux.crossentropy(model(x), y)
+            end
+            Flux.update!(optimizer_state, predictor, only(gradient))
+            loss += loss_batch
+        end
+        loss = round(loss / length(train_loader); digits = 4)
+        print("Epoch $epoch: loss = $loss\t")
+        score_model(predictor, test_data)
+    end
+end
Epoch 1: loss = 1.766	Accuracy = 76.48 %
+Epoch 2: loss = 1.132	Accuracy = 84.49 %
+Epoch 3: loss = 0.8363	Accuracy = 87.16 %
+Epoch 4: loss = 0.6677	Accuracy = 88.53 %
+Epoch 5: loss = 0.5623	Accuracy = 89.36 %
+Epoch 6: loss = 0.4912	Accuracy = 90.01 %
+Epoch 7: loss = 0.4406	Accuracy = 90.42 %
+Epoch 8: loss = 0.4026	Accuracy = 90.92 %
+Epoch 9: loss = 0.3729	Accuracy = 91.19 %
+Epoch 10: loss = 0.3493	Accuracy = 91.38 %
+Epoch 11: loss = 0.3296	Accuracy = 91.75 %
+Epoch 12: loss = 0.3132	Accuracy = 91.9 %
+Epoch 13: loss = 0.2992	Accuracy = 92.08 %
+Epoch 14: loss = 0.2871	Accuracy = 92.33 %
+Epoch 15: loss = 0.2763	Accuracy = 92.49 %
+Epoch 16: loss = 0.2663	Accuracy = 92.64 %
+Epoch 17: loss = 0.2578	Accuracy = 92.87 %
+Epoch 18: loss = 0.2497	Accuracy = 93.04 %
+Epoch 19: loss = 0.2429	Accuracy = 93.21 %
+Epoch 20: loss = 0.2357	Accuracy = 93.33 %
+Epoch 21: loss = 0.2295	Accuracy = 93.53 %
+Epoch 22: loss = 0.2239	Accuracy = 93.64 %
+Epoch 23: loss = 0.2185	Accuracy = 93.95 %
+Epoch 24: loss = 0.2136	Accuracy = 93.96 %
+Epoch 25: loss = 0.2088	Accuracy = 94.05 %
+Epoch 26: loss = 0.2041	Accuracy = 94.16 %
+Epoch 27: loss = 0.2	Accuracy = 94.31 %
+Epoch 28: loss = 0.1962	Accuracy = 94.42 %
+Epoch 29: loss = 0.1924	Accuracy = 94.47 %
+Epoch 30: loss = 0.189	Accuracy = 94.52 %

Here are the first eight predictions of the test data:

function plot_image(predictor, x::Matrix)
+    score, index = findmax(predictor(vec(x)))
+    title = "Predicted: $(index - 1) ($(round(Int, 100 * score))%)"
+    return plot_image(x; title)
+end
+
+plots = [plot_image(predictor, test_data[i].features) for i in 1:8]
+Plots.plot(plots...; size = (1200, 600), layout = (2, 4))
Example block output

We can also look at the best and worst four predictions:

x, y = only(data_loader(test_data; batchsize = length(test_data)))
+losses = Flux.crossentropy(predictor(x), y; agg = identity)
+indices = sortperm(losses; dims = 2)[[1:4; end-3:end]]
+plots = [plot_image(predictor, test_data[i].features) for i in indices]
+Plots.plot(plots...; size = (1200, 600), layout = (2, 4))
Example block output

There are still some fairly bad mistakes. Can you change the model or training parameters improve to improve things?

JuMP

Now that we have a trained machine learning model, we can embed it in a JuMP model.

Here's a function which takes a test case and returns an example that maximizes the probability of the adversarial example.

function find_adversarial_image(test_case; adversary_label, δ = 0.05)
+    model = Model(Ipopt.Optimizer)
+    set_silent(model)
+    @variable(model, 0 <= x[1:28, 1:28] <= 1)
+    @constraint(model, -δ .<= x .- test_case.features .<= δ)
+    # Note: we need to use `vec` here because `x` is a 28-by-28 Matrix, but our
+    # neural network expects a 28^2 length vector.
+    y, _ = MathOptAI.add_predictor(model, predictor, vec(x))
+    @objective(model, Max, y[adversary_label+1] - y[test_case.targets+1])
+    optimize!(model)
+    @assert is_solved_and_feasible(model)
+    return value.(x)
+end
find_adversarial_image (generic function with 1 method)

Let's try finding an adversarial example to the third test image. The image on the left is our input image. The network thinks this is a 1 with probability 99%. The image on the right is the adversarial image. The network thinks this is a 7, although it is less confident.

x_adversary = find_adversarial_image(test_data[3]; adversary_label = 7);
+Plots.plot(
+    plot_image(predictor, test_data[3].features),
+    plot_image(predictor, Float32.(x_adversary)),
+)
Example block output

This page was generated using Literate.jl.

diff --git a/v0.1.3/tutorials/mnist_lux.jl b/v0.1.3/tutorials/mnist_lux.jl new file mode 100644 index 00000000..296c0158 --- /dev/null +++ b/v0.1.3/tutorials/mnist_lux.jl @@ -0,0 +1,186 @@ +# Copyright (c) 2024: Oscar Dowson and contributors #src +# Copyright (c) 2024: Triad National Security, LLC #src +# #src +# Use of this source code is governed by a BSD-style license that can be #src +# found in the LICENSE.md file. #src + +# # Adversarial machine learning with Lux.jl + +# The purpose of this tutorial is to explain how to embed a neural network model +# from [Lux.jl](https://github.com/SciML/Lux.jl) into JuMP. + +# ## Required packages + +# This tutorial requires the following packages + +using JuMP +import Lux +import Ipopt +import MathOptAI +import MLDatasets +import MLUtils +import OneHotArrays +import Optimisers +import Plots +import Random +import Zygote + +# ## Data + +# This tutorial uses images from the MNIST dataset. + +# We load the predefined train and test splits: + +train_data = MLDatasets.MNIST(; split = :train) + +#- + +test_data = MLDatasets.MNIST(; split = :test) + +# Since the data are images, it is helpful to plot them. (This requires a +# transpose and reversing the rows to get the orientation correct.) + +function plot_image(x::Matrix; kwargs...) + return Plots.heatmap( + x'[size(x, 1):-1:1, :]; + xlims = (1, size(x, 2)), + ylims = (1, size(x, 1)), + aspect_ratio = true, + legend = false, + xaxis = false, + yaxis = false, + kwargs..., + ) +end + +function plot_image(instance::NamedTuple) + return plot_image(instance.features; title = "Label = $(instance.targets)") +end + +Plots.plot([plot_image(train_data[i]) for i in 1:6]...; layout = (2, 3)) + +# ## Training + +# We use a simple neural network with one hidden layer and a sigmoid activation +# function. (There are better performing networks; try experimenting.) + +chain = Lux.Chain( + Lux.Dense(28^2 => 32, Lux.sigmoid), + Lux.Dense(32 => 10), + Lux.softmax, +) +rng = Random.MersenneTwister(); +parameters, state = Lux.setup(rng, chain) +predictor = (chain, parameters, state); + +# Here is a function to load our data into the format that `predictor` expects: +function data_loader(data; batchsize, shuffle = false) + x = reshape(data.features, 28^2, :) + y = OneHotArrays.onehotbatch(data.targets, 0:9) + return MLUtils.DataLoader((x, y); batchsize, shuffle) +end + +# and here is a function to score the percentage of correct labels, where we +# assign a label by choosing the label of the highest softmax in the final +# layer. + +function score_model(predictor, data) + chain, parameters, state = predictor + x, y = only(data_loader(data; batchsize = length(data))) + y_hat, _ = chain(x, parameters, state) + is_correct = OneHotArrays.onecold(y) .== OneHotArrays.onecold(y_hat) + p = round(100 * sum(is_correct) / length(is_correct); digits = 2) + println("Accuracy = $p %") + return +end + +# The accuracy of our model is only around 10% before training: + +score_model(predictor, train_data) +score_model(predictor, test_data) + +# Let's improve that by training our model. + +# !!! note +# It is not the purpose of this tutorial to explain how Lux works; see the +# documentation at [https://lux.csail.mit.edu](https://lux.csail.mit.edu/stable/) +# for more details. Changing the number of epochs or the learning rate can +# improve the loss. + +begin + train_loader = data_loader(train_data; batchsize = 256, shuffle = true) + optimizer_state = Optimisers.setup(Optimisers.Adam(0.0003f0), parameters) + for epoch in 1:30 + loss = 0.0 + for (x, y) in train_loader + global state + (loss_batch, state), pullback = Zygote.pullback(parameters) do p + y_model, new_state = chain(x, p, state) + return Lux.CrossEntropyLoss()(y_model, y), new_state + end + gradients = only(pullback((one(loss), nothing))) + Optimisers.update!(optimizer_state, parameters, gradients) + loss += loss_batch + end + loss = round(loss / length(train_loader); digits = 4) + print("Epoch $epoch: loss = $loss\t") + score_model(predictor, test_data) + end +end + +# Here are the first eight predictions of the test data: + +function plot_image(predictor, x::Matrix) + y, _ = chain(vec(x), parameters, state) + score, index = findmax(y) + title = "Predicted: $(index - 1) ($(round(Int, 100 * score))%)" + return plot_image(x; title) +end + +plots = [plot_image(predictor, test_data[i].features) for i in 1:8] +Plots.plot(plots...; size = (1200, 600), layout = (2, 4)) + +# We can also look at the best and worst four predictions: + +x, y = only(data_loader(test_data; batchsize = length(test_data))) +y_model, _ = chain(x, parameters, state) +losses = Lux.CrossEntropyLoss(; agg = identity)(y_model, y) +indices = sortperm(losses; dims = 2)[[1:4; end-3:end]] +plots = [plot_image(predictor, test_data[i].features) for i in indices] +Plots.plot(plots...; size = (1200, 600), layout = (2, 4)) + +# There are still some fairly bad mistakes. Can you change the model or training +# parameters improve to improve things? + +# ## JuMP + +# Now that we have a trained machine learning model, we can embed it in a JuMP +# model. + +# Here's a function which takes a test case and returns an example that +# maximizes the probability of the adversarial example. + +function find_adversarial_image(test_case; adversary_label, δ = 0.05) + model = Model(Ipopt.Optimizer) + set_silent(model) + @variable(model, 0 <= x[1:28, 1:28] <= 1) + @constraint(model, -δ .<= x .- test_case.features .<= δ) + ## Note: we need to use `vec` here because `x` is a 28-by-28 Matrix, but our + ## neural network expects a 28^2 length vector. + y, _ = MathOptAI.add_predictor(model, predictor, vec(x)) + @objective(model, Max, y[adversary_label+1] - y[test_case.targets+1]) + optimize!(model) + @assert is_solved_and_feasible(model) + return value.(x) +end + +# Let's try finding an adversarial example to the third test image. The image on +# the left is our input image. The network thinks this is a `1` with probability +# 99%. The image on the right is the adversarial image. The network thinks this +# is a `7`, although it is less confident. + +x_adversary = find_adversarial_image(test_data[3]; adversary_label = 7); +Plots.plot( + plot_image(predictor, test_data[3].features), + plot_image(predictor, Float32.(x_adversary)), +) diff --git a/v0.1.3/tutorials/mnist_lux/5c5b9133.svg b/v0.1.3/tutorials/mnist_lux/5c5b9133.svg new file mode 100644 index 00000000..556f2c40 --- /dev/null +++ b/v0.1.3/tutorials/mnist_lux/5c5b9133.svg @@ -0,0 +1,1199 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.3/tutorials/mnist_lux/72047cd7.svg b/v0.1.3/tutorials/mnist_lux/72047cd7.svg new file mode 100644 index 00000000..0a33261d --- /dev/null +++ b/v0.1.3/tutorials/mnist_lux/72047cd7.svg @@ -0,0 +1,1235 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.3/tutorials/mnist_lux/b3c0ead3.svg b/v0.1.3/tutorials/mnist_lux/b3c0ead3.svg new file mode 100644 index 00000000..40d1f782 --- /dev/null +++ b/v0.1.3/tutorials/mnist_lux/b3c0ead3.svg @@ -0,0 +1,511 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.3/tutorials/mnist_lux/d1f02db7.svg b/v0.1.3/tutorials/mnist_lux/d1f02db7.svg new file mode 100644 index 00000000..3ace0ea4 --- /dev/null +++ b/v0.1.3/tutorials/mnist_lux/d1f02db7.svg @@ -0,0 +1,326 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.3/tutorials/mnist_lux/index.html b/v0.1.3/tutorials/mnist_lux/index.html new file mode 100644 index 00000000..5fff92a4 --- /dev/null +++ b/v0.1.3/tutorials/mnist_lux/index.html @@ -0,0 +1,135 @@ + +Adversarial machine learning with Lux.jl · MathOptAI.jl
GitHub

Adversarial machine learning with Lux.jl

The purpose of this tutorial is to explain how to embed a neural network model from Lux.jl into JuMP.

Required packages

This tutorial requires the following packages

using JuMP
+import Lux
+import Ipopt
+import MathOptAI
+import MLDatasets
+import MLUtils
+import OneHotArrays
+import Optimisers
+import Plots
+import Random
+import Zygote

Data

This tutorial uses images from the MNIST dataset.

We load the predefined train and test splits:

train_data = MLDatasets.MNIST(; split = :train)
dataset MNIST:
+  metadata  =>    Dict{String, Any} with 3 entries
+  split     =>    :train
+  features  =>    28×28×60000 Array{Float32, 3}
+  targets   =>    60000-element Vector{Int64}
test_data = MLDatasets.MNIST(; split = :test)
dataset MNIST:
+  metadata  =>    Dict{String, Any} with 3 entries
+  split     =>    :test
+  features  =>    28×28×10000 Array{Float32, 3}
+  targets   =>    10000-element Vector{Int64}

Since the data are images, it is helpful to plot them. (This requires a transpose and reversing the rows to get the orientation correct.)

function plot_image(x::Matrix; kwargs...)
+    return Plots.heatmap(
+        x'[size(x, 1):-1:1, :];
+        xlims = (1, size(x, 2)),
+        ylims = (1, size(x, 1)),
+        aspect_ratio = true,
+        legend = false,
+        xaxis = false,
+        yaxis = false,
+        kwargs...,
+    )
+end
+
+function plot_image(instance::NamedTuple)
+    return plot_image(instance.features; title = "Label = $(instance.targets)")
+end
+
+Plots.plot([plot_image(train_data[i]) for i in 1:6]...; layout = (2, 3))
Example block output

Training

We use a simple neural network with one hidden layer and a sigmoid activation function. (There are better performing networks; try experimenting.)

chain = Lux.Chain(
+    Lux.Dense(28^2 => 32, Lux.sigmoid),
+    Lux.Dense(32 => 10),
+    Lux.softmax,
+)
+rng = Random.MersenneTwister();
+parameters, state = Lux.setup(rng, chain)
+predictor = (chain, parameters, state);

Here is a function to load our data into the format that predictor expects:

function data_loader(data; batchsize, shuffle = false)
+    x = reshape(data.features, 28^2, :)
+    y = OneHotArrays.onehotbatch(data.targets, 0:9)
+    return MLUtils.DataLoader((x, y); batchsize, shuffle)
+end
data_loader (generic function with 1 method)

and here is a function to score the percentage of correct labels, where we assign a label by choosing the label of the highest softmax in the final layer.

function score_model(predictor, data)
+    chain, parameters, state = predictor
+    x, y = only(data_loader(data; batchsize = length(data)))
+    y_hat, _ = chain(x, parameters, state)
+    is_correct = OneHotArrays.onecold(y) .== OneHotArrays.onecold(y_hat)
+    p = round(100 * sum(is_correct) / length(is_correct); digits = 2)
+    println("Accuracy = $p %")
+    return
+end
score_model (generic function with 1 method)

The accuracy of our model is only around 10% before training:

score_model(predictor, train_data)
+score_model(predictor, test_data)
Accuracy = 9.05 %
+Accuracy = 9.19 %

Let's improve that by training our model.

Note

It is not the purpose of this tutorial to explain how Lux works; see the documentation at https://lux.csail.mit.edu for more details. Changing the number of epochs or the learning rate can improve the loss.

begin
+    train_loader = data_loader(train_data; batchsize = 256, shuffle = true)
+    optimizer_state = Optimisers.setup(Optimisers.Adam(0.0003f0), parameters)
+    for epoch in 1:30
+        loss = 0.0
+        for (x, y) in train_loader
+            global state
+            (loss_batch, state), pullback = Zygote.pullback(parameters) do p
+                y_model, new_state = chain(x, p, state)
+                return Lux.CrossEntropyLoss()(y_model, y), new_state
+            end
+            gradients = only(pullback((one(loss), nothing)))
+            Optimisers.update!(optimizer_state, parameters, gradients)
+            loss += loss_batch
+        end
+        loss = round(loss / length(train_loader); digits = 4)
+        print("Epoch $epoch: loss = $loss\t")
+        score_model(predictor, test_data)
+    end
+end
Epoch 1: loss = 1.8152	Accuracy = 78.45 %
+Epoch 2: loss = 1.1676	Accuracy = 84.48 %
+Epoch 3: loss = 0.8573	Accuracy = 86.81 %
+Epoch 4: loss = 0.678	Accuracy = 88.49 %
+Epoch 5: loss = 0.566	Accuracy = 89.46 %
+Epoch 6: loss = 0.4925	Accuracy = 90.05 %
+Epoch 7: loss = 0.4408	Accuracy = 90.53 %
+Epoch 8: loss = 0.4027	Accuracy = 90.93 %
+Epoch 9: loss = 0.3734	Accuracy = 91.34 %
+Epoch 10: loss = 0.3506	Accuracy = 91.65 %
+Epoch 11: loss = 0.3313	Accuracy = 91.77 %
+Epoch 12: loss = 0.3158	Accuracy = 92.1 %
+Epoch 13: loss = 0.3023	Accuracy = 92.2 %
+Epoch 14: loss = 0.2904	Accuracy = 92.5 %
+Epoch 15: loss = 0.2804	Accuracy = 92.64 %
+Epoch 16: loss = 0.2711	Accuracy = 92.77 %
+Epoch 17: loss = 0.2629	Accuracy = 92.95 %
+Epoch 18: loss = 0.2559	Accuracy = 93.13 %
+Epoch 19: loss = 0.2488	Accuracy = 93.22 %
+Epoch 20: loss = 0.2428	Accuracy = 93.38 %
+Epoch 21: loss = 0.2367	Accuracy = 93.41 %
+Epoch 22: loss = 0.2312	Accuracy = 93.61 %
+Epoch 23: loss = 0.2262	Accuracy = 93.56 %
+Epoch 24: loss = 0.2211	Accuracy = 93.72 %
+Epoch 25: loss = 0.2169	Accuracy = 93.75 %
+Epoch 26: loss = 0.2128	Accuracy = 93.81 %
+Epoch 27: loss = 0.2089	Accuracy = 93.96 %
+Epoch 28: loss = 0.2048	Accuracy = 94.08 %
+Epoch 29: loss = 0.2011	Accuracy = 94.17 %
+Epoch 30: loss = 0.1977	Accuracy = 94.21 %

Here are the first eight predictions of the test data:

function plot_image(predictor, x::Matrix)
+    y, _ = chain(vec(x), parameters, state)
+    score, index = findmax(y)
+    title = "Predicted: $(index - 1) ($(round(Int, 100 * score))%)"
+    return plot_image(x; title)
+end
+
+plots = [plot_image(predictor, test_data[i].features) for i in 1:8]
+Plots.plot(plots...; size = (1200, 600), layout = (2, 4))
Example block output

We can also look at the best and worst four predictions:

x, y = only(data_loader(test_data; batchsize = length(test_data)))
+y_model, _ = chain(x, parameters, state)
+losses = Lux.CrossEntropyLoss(; agg = identity)(y_model, y)
+indices = sortperm(losses; dims = 2)[[1:4; end-3:end]]
+plots = [plot_image(predictor, test_data[i].features) for i in indices]
+Plots.plot(plots...; size = (1200, 600), layout = (2, 4))
Example block output

There are still some fairly bad mistakes. Can you change the model or training parameters improve to improve things?

JuMP

Now that we have a trained machine learning model, we can embed it in a JuMP model.

Here's a function which takes a test case and returns an example that maximizes the probability of the adversarial example.

function find_adversarial_image(test_case; adversary_label, δ = 0.05)
+    model = Model(Ipopt.Optimizer)
+    set_silent(model)
+    @variable(model, 0 <= x[1:28, 1:28] <= 1)
+    @constraint(model, -δ .<= x .- test_case.features .<= δ)
+    # Note: we need to use `vec` here because `x` is a 28-by-28 Matrix, but our
+    # neural network expects a 28^2 length vector.
+    y, _ = MathOptAI.add_predictor(model, predictor, vec(x))
+    @objective(model, Max, y[adversary_label+1] - y[test_case.targets+1])
+    optimize!(model)
+    @assert is_solved_and_feasible(model)
+    return value.(x)
+end
find_adversarial_image (generic function with 1 method)

Let's try finding an adversarial example to the third test image. The image on the left is our input image. The network thinks this is a 1 with probability 99%. The image on the right is the adversarial image. The network thinks this is a 7, although it is less confident.

x_adversary = find_adversarial_image(test_data[3]; adversary_label = 7);
+Plots.plot(
+    plot_image(predictor, test_data[3].features),
+    plot_image(predictor, Float32.(x_adversary)),
+)
Example block output

This page was generated using Literate.jl.

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For example, if you +# have an existing Python installation (with PyTorch installed), and it is +# available in the current conda environment, set: +# +# ```julia +# ENV["JULIA_CONDAPKG_BACKEND"] = "Current" +# ``` +# +# before importing PythonCall.jl. If the Python installation can be found on +# the path and it is not in a conda environment, set: +# +# ```julia +# ENV["JULIA_CONDAPKG_BACKEND"] = "Null" +# ``` +# +# If `python` is not on your path, you may additionally need to set +# `JULIA_PYTHONCALL_EXE`, for example, to: +# +# ```julia +# ENV["JULIA_PYTHONCALL_EXE"] = "python3" +# ``` + +# ## Required packages + +# This tutorial requires the following packages + +using JuMP +using Test +import Ipopt +import MathOptAI +import Plots + +# ## Training a model + +# The following script builds and trains a simple neural network in PyTorch. +# For simplicity, we do not evaluate out-of-sample test performance, or use +# a batched data loader. In general, you should train your model in Python, +# and then use `torch.save(model, filename)` to save it to a `.pt` file for +# later use in Julia. + +# The model is unimportant, but for this example, we are trying to fit noisy +# observations of the function ``f(x) = x^2 - 2x``. + +# In Python, I ran: +# ```python +# #!/usr/bin/python3 +# import torch +# model = torch.nn.Sequential( +# torch.nn.Linear(1, 16), +# torch.nn.ReLU(), +# torch.nn.Linear(16, 1), +# ) +# +# n = 1024 +# x = torch.arange(-2, 2 + 4 / (n - 1), 4 / (n - 1)).reshape(n, 1) +# loss_fn = torch.nn.MSELoss() +# optimizer = torch.optim.Adam(model.parameters(), lr=0.01) +# for epoch in range(100): +# optimizer.zero_grad() +# N = torch.normal(torch.zeros(n, 1), torch.ones(n, 1)) +# y = x ** 2 -2 * x + 0.1 * N +# loss = loss_fn(model(x), y) +# loss.backward() +# optimizer.step() +# +# torch.save(model, "model.pt") +# ``` + +# ## JuMP model + +# Our goal for this JuMP model is to load the Neural Network from PyTorch into +# the objective function, and then minimize the objective for different fixed +# values of `x` to recreate the function that the Neural Network has learned to +# approximate. + +# First, create a JuMP model: + +model = Model(Ipopt.Optimizer) +set_silent(model) +@variable(model, x) + +# Then, load the model from PyTorch using [`MathOptAI.PytorchModel`](@ref): + +predictor = MathOptAI.PytorchModel(joinpath(@__DIR__, "model.pt")) +y, _ = MathOptAI.add_predictor(model, predictor, [x]) +@objective(model, Min, only(y)) + +# Now, visualize the fitted function `y = predictor(x)` by repeatedly solving +# the optimization problem for different fixed values of `x`: + +X, Y = -2:0.1:2, Float64[] +@constraint(model, c, x == 0.0) +for xi in X + set_normalized_rhs(c, xi) + optimize!(model) + @test is_solved_and_feasible(model) + push!(Y, objective_value(model)) +end +Plots.plot(x -> x^2 - 2x, X; label = "Truth", linestype = :dot) +Plots.plot!(X, Y; label = "Fitted") diff --git a/v0.1.3/tutorials/pytorch/4dda6807.svg b/v0.1.3/tutorials/pytorch/4dda6807.svg new file mode 100644 index 00000000..8b97fec0 --- /dev/null +++ b/v0.1.3/tutorials/pytorch/4dda6807.svg @@ -0,0 +1,48 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.3/tutorials/pytorch/index.html b/v0.1.3/tutorials/pytorch/index.html new file mode 100644 index 00000000..aa69d647 --- /dev/null +++ b/v0.1.3/tutorials/pytorch/index.html @@ -0,0 +1,39 @@ + +Function fitting with PyTorch · MathOptAI.jl
GitHub

Function fitting with PyTorch

The purpose of this tutorial is to explain how to embed a neural network model from PyTorch into JuMP.

Python integration

MathOptAI uses PythonCall.jl to call from Julia into Python.

See CondaPkg.jl for more control over how to link Julia to an existing Python environment. For example, if you have an existing Python installation (with PyTorch installed), and it is available in the current conda environment, set:

ENV["JULIA_CONDAPKG_BACKEND"] = "Current"

before importing PythonCall.jl. If the Python installation can be found on the path and it is not in a conda environment, set:

ENV["JULIA_CONDAPKG_BACKEND"] = "Null"

If python is not on your path, you may additionally need to set JULIA_PYTHONCALL_EXE, for example, to:

ENV["JULIA_PYTHONCALL_EXE"] = "python3"

Required packages

This tutorial requires the following packages

using JuMP
+using Test
+import Ipopt
+import MathOptAI
+import Plots

Training a model

The following script builds and trains a simple neural network in PyTorch. For simplicity, we do not evaluate out-of-sample test performance, or use a batched data loader. In general, you should train your model in Python, and then use torch.save(model, filename) to save it to a .pt file for later use in Julia.

The model is unimportant, but for this example, we are trying to fit noisy observations of the function $f(x) = x^2 - 2x$.

In Python, I ran:

#!/usr/bin/python3
+import torch
+model = torch.nn.Sequential(
+    torch.nn.Linear(1, 16),
+    torch.nn.ReLU(),
+    torch.nn.Linear(16, 1),
+)
+
+n = 1024
+x = torch.arange(-2, 2 + 4 / (n - 1), 4 / (n - 1)).reshape(n, 1)
+loss_fn = torch.nn.MSELoss()
+optimizer = torch.optim.Adam(model.parameters(), lr=0.01)
+for epoch in range(100):
+    optimizer.zero_grad()
+    N = torch.normal(torch.zeros(n, 1), torch.ones(n, 1))
+    y = x ** 2 -2 * x + 0.1 * N
+    loss = loss_fn(model(x), y)
+    loss.backward()
+    optimizer.step()
+
+torch.save(model, "model.pt")

JuMP model

Our goal for this JuMP model is to load the Neural Network from PyTorch into the objective function, and then minimize the objective for different fixed values of x to recreate the function that the Neural Network has learned to approximate.

First, create a JuMP model:

model = Model(Ipopt.Optimizer)
+set_silent(model)
+@variable(model, x)

\[ x \]

Then, load the model from PyTorch using MathOptAI.PytorchModel:

predictor = MathOptAI.PytorchModel(joinpath(@__DIR__, "model.pt"))
+y, _ = MathOptAI.add_predictor(model, predictor, [x])
+@objective(model, Min, only(y))

\[ moai\_Affine_{1} \]

Now, visualize the fitted function y = predictor(x) by repeatedly solving the optimization problem for different fixed values of x:

X, Y = -2:0.1:2, Float64[]
+@constraint(model, c, x == 0.0)
+for xi in X
+    set_normalized_rhs(c, xi)
+    optimize!(model)
+    @test is_solved_and_feasible(model)
+    push!(Y, objective_value(model))
+end
+Plots.plot(x -> x^2 - 2x, X; label = "Truth", linestype = :dot)
+Plots.plot!(X, Y; label = "Fitted")
Example block output

This page was generated using Literate.jl.

diff --git a/v0.1.3/tutorials/student_enrollment.jl b/v0.1.3/tutorials/student_enrollment.jl new file mode 100644 index 00000000..fc1497ca --- /dev/null +++ b/v0.1.3/tutorials/student_enrollment.jl @@ -0,0 +1,134 @@ +# Copyright (c) 2024: Oscar Dowson and contributors #src +# Copyright (c) 2024: Triad National Security, LLC #src +# #src +# Use of this source code is governed by a BSD-style license that can be #src +# found in the LICENSE.md file. #src + +# # Logistic regression with GLM.jl + +# The purpose of this tutorial is to explain how to embed a logistic regression +# model from [GLM.jl](https://github.com/JuliaStats/GLM.jl) into JuMP. + +# The data and example in this tutorial comes from the paper: David Bergman, +# Teng Huang, Philip Brooks, Andrea Lodi, Arvind U. Raghunathan (2021) JANOS: An +# Integrated Predictive and Prescriptive Modeling Framework. INFORMS Journal on +# Computing 34(2):807-816. +# [https://doi.org/10.1287/ijoc.2020.1023](https://doi.org/10.1287/ijoc.2020.1023) + +# ## Required packages + +# This tutorial uses the following packages. + +using JuMP +import CSV +import DataFrames +import Downloads +import GLM +import Ipopt +import MathOptAI +import Statistics + +# ## Data + +# Here is a function to load the data directly from the JANOS repository: + +function read_df(filename) + url = "https://raw.githubusercontent.com/INFORMSJoC/2020.1023/master/data/" + data = Downloads.download(url * filename) + return CSV.read(data, DataFrames.DataFrame) +end + +# There are two important files. The first, `college_student_enroll-s1-1.csv`, +# contains historial admissions data on anonymized students, their SAT score, +# their GPA, their merit scholarships, and whether the enrolled in the college. + +train_df = read_df("college_student_enroll-s1-1.csv") + +# The second, `college_applications6000.csv`, contains the SAT and GPA data of +# students who are currently applying: + +evaluate_df = read_df("college_applications6000.csv") + +# There are 6,000 prospective students: + +n_students = size(evaluate_df, 1) + +# ## Prediction model + +# The first step is to train a logistic regression model to predict the Boolean +# `enroll` column based on the `SAT`, `GPA`, and `merit` columns. + +model_glm = GLM.glm( + GLM.@formula(enroll ~ 0 + SAT + GPA + merit), + train_df, + GLM.Bernoulli(), +) + +# ## Decision model + +# Now that we have a trained logistic regression model, we want a decision model +# that chooses the optimal merit scholarship for each student in + +evaluate_df + +# Here's an empty JuMP model to start: + +model = Model() + +# First, we add a new columnn to `evaluate_df`, with one JuMP decision variable +# for each row. It is important the the `.merit` column name in `evaluate_df` +# matches the name in `train_df`. + +evaluate_df.merit = @variable(model, 0 <= x_merit[1:n_students] <= 2.5); +evaluate_df + +# Then, we use [`MathOptAI.add_predictor`](@ref) to embed `model_glm` into the +# JuMP `model`. [`MathOptAI.add_predictor`](@ref) returns a vector of variables, +# one for each row inn `evaluate_df`, corresponding to the output `enroll` of +# our logistic regression. + +evaluate_df.enroll, _ = MathOptAI.add_predictor(model, model_glm, evaluate_df); +evaluate_df + +# The `.enroll` column name in `evaluate_df` is just a name. It doesn't have to +# match the name in `train_df`. + +# The objective of our problem is to maximize the expected number of students +# who enroll: + +@objective(model, Max, sum(evaluate_df.enroll)) + +# Subject to the constraint that we can spend at most `0.2 * n_students` on +# merit scholarships: + +@constraint(model, sum(evaluate_df.merit) <= 0.2 * n_students) + +# Because logistic regression involves a [`Sigmoid`](@ref) layer, we need to use +# a smooth nonlinear optimizer. A common choice is Ipopt. Solve and check the +# optimizer found a feasible solution: + +set_optimizer(model, Ipopt.Optimizer) +set_silent(model) +optimize!(model) +@assert is_solved_and_feasible(model) +solution_summary(model) + +# Let's store the solution in `evaluate_df` for analysis: + +evaluate_df.merit_sol = value.(evaluate_df.merit); +evaluate_df.enroll_sol = value.(evaluate_df.enroll); +evaluate_df + +# ## Solution analysis + +# We expect that just under 2,500 students will enroll: + +sum(evaluate_df.enroll_sol) + +# We awarded merit scholarships to approximately 1 in 6 students: + +count(evaluate_df.merit_sol .> 1e-5) + +# The average merit scholarship was worth just over \$1,000: + +1_000 * Statistics.mean(evaluate_df.merit_sol[evaluate_df.merit_sol.>1e-5]) diff --git a/v0.1.3/tutorials/student_enrollment/index.html b/v0.1.3/tutorials/student_enrollment/index.html new file mode 100644 index 00000000..5d4ef51f --- /dev/null +++ b/v0.1.3/tutorials/student_enrollment/index.html @@ -0,0 +1,162 @@ + +Logistic regression with GLM.jl · MathOptAI.jl
GitHub

Logistic regression with GLM.jl

The purpose of this tutorial is to explain how to embed a logistic regression model from GLM.jl into JuMP.

The data and example in this tutorial comes from the paper: David Bergman, Teng Huang, Philip Brooks, Andrea Lodi, Arvind U. Raghunathan (2021) JANOS: An Integrated Predictive and Prescriptive Modeling Framework. INFORMS Journal on Computing 34(2):807-816. https://doi.org/10.1287/ijoc.2020.1023

Required packages

This tutorial uses the following packages.

julia> using JuMP
julia> import CSV
julia> import DataFrames
julia> import Downloads
julia> import GLM
julia> import Ipopt
julia> import MathOptAI
julia> import Statistics

Data

Here is a function to load the data directly from the JANOS repository:

julia> function read_df(filename)
+           url = "https://raw.githubusercontent.com/INFORMSJoC/2020.1023/master/data/"
+           data = Downloads.download(url * filename)
+           return CSV.read(data, DataFrames.DataFrame)
+       endread_df (generic function with 1 method)

There are two important files. The first, college_student_enroll-s1-1.csv, contains historial admissions data on anonymized students, their SAT score, their GPA, their merit scholarships, and whether the enrolled in the college.

julia> train_df = read_df("college_student_enroll-s1-1.csv")20000×6 DataFrame
+   Row │ Column1  StudentID  SAT    GPA      merit    enroll 
+       │ Int64    Int64      Int64  Float64  Float64  Int64  
+───────┼─────────────────────────────────────────────────────
+     1 │       1          1   1507     3.72     1.64       0
+     2 │       2          2   1532     3.93     0.52       0
+     3 │       3          3   1487     3.77     1.67       0
+     4 │       4          4   1259     3.05     1.21       1
+     5 │       5          5   1354     3.39     1.65       1
+     6 │       6          6   1334     3.22     0.0        0
+     7 │       7          7   1125     2.73     1.68       1
+     8 │       8          8   1180     2.82     0.0        1
+   ⋮   │    ⋮         ⋮        ⋮       ⋮        ⋮       ⋮
+ 19994 │   19994      19994   1185     3.09     1.16       1
+ 19995 │   19995      19995   1471     3.7      1.05       0
+ 19996 │   19996      19996   1139     3.03     1.21       1
+ 19997 │   19997      19997   1371     3.39     1.26       0
+ 19998 │   19998      19998   1424     3.72     0.85       0
+ 19999 │   19999      19999   1170     3.01     0.73       1
+ 20000 │   20000      20000   1389     3.57     0.55       0
+                                           19985 rows omitted

The second, college_applications6000.csv, contains the SAT and GPA data of students who are currently applying:

julia> evaluate_df = read_df("college_applications6000.csv")6000×3 DataFrame
+  Row │ StudentID  SAT    GPA     
+      │ Int64      Int64  Float64 
+──────┼───────────────────────────
+    1 │         1   1240     3.22
+    2 │         2   1206     2.87
+    3 │         3   1520     3.74
+    4 │         4   1238     3.11
+    5 │         5   1142     2.74
+    6 │         6   1086     2.77
+    7 │         7   1367     3.28
+    8 │         8   1034     2.41
+  ⋮   │     ⋮        ⋮       ⋮
+ 5994 │      5994   1121     2.96
+ 5995 │      5995   1564     4.1
+ 5996 │      5996   1332     3.14
+ 5997 │      5997   1228     2.95
+ 5998 │      5998   1165     2.81
+ 5999 │      5999   1400     3.43
+ 6000 │      6000   1097     2.65
+                 5985 rows omitted

There are 6,000 prospective students:

julia> n_students = size(evaluate_df, 1)6000

Prediction model

The first step is to train a logistic regression model to predict the Boolean enroll column based on the SAT, GPA, and merit columns.

julia> model_glm = GLM.glm(
+           GLM.@formula(enroll ~ 0 + SAT + GPA + merit),
+           train_df,
+           GLM.Bernoulli(),
+       )StatsModels.TableRegressionModel{GLM.GeneralizedLinearModel{GLM.GlmResp{Vector{Float64}, Distributions.Bernoulli{Float64}, GLM.LogitLink}, GLM.DensePredChol{Float64, LinearAlgebra.CholeskyPivoted{Float64, Matrix{Float64}, Vector{Int64}}}}, Matrix{Float64}}
+
+enroll ~ 0 + SAT + GPA + merit
+
+Coefficients:
+──────────────────────────────────────────────────────────────────────────
+             Coef.   Std. Error      z  Pr(>|z|)    Lower 95%    Upper 95%
+──────────────────────────────────────────────────────────────────────────
+SAT     0.00243882  0.000309312   7.88    <1e-14   0.00183258   0.00304506
+GPA    -1.09868     0.123796     -8.87    <1e-18  -1.34132     -0.856045
+merit   0.248294    0.0191086    12.99    <1e-37   0.210842     0.285747
+──────────────────────────────────────────────────────────────────────────

Decision model

Now that we have a trained logistic regression model, we want a decision model that chooses the optimal merit scholarship for each student in

julia> evaluate_df6000×3 DataFrame
+  Row │ StudentID  SAT    GPA     
+      │ Int64      Int64  Float64 
+──────┼───────────────────────────
+    1 │         1   1240     3.22
+    2 │         2   1206     2.87
+    3 │         3   1520     3.74
+    4 │         4   1238     3.11
+    5 │         5   1142     2.74
+    6 │         6   1086     2.77
+    7 │         7   1367     3.28
+    8 │         8   1034     2.41
+  ⋮   │     ⋮        ⋮       ⋮
+ 5994 │      5994   1121     2.96
+ 5995 │      5995   1564     4.1
+ 5996 │      5996   1332     3.14
+ 5997 │      5997   1228     2.95
+ 5998 │      5998   1165     2.81
+ 5999 │      5999   1400     3.43
+ 6000 │      6000   1097     2.65
+                 5985 rows omitted

Here's an empty JuMP model to start:

julia> model = Model()A JuMP Model
+├ solver: none
+├ objective_sense: FEASIBILITY_SENSE
+├ num_variables: 0
+├ num_constraints: 0
+└ Names registered in the model: none

First, we add a new columnn to evaluate_df, with one JuMP decision variable for each row. It is important the the .merit column name in evaluate_df matches the name in train_df.

julia> evaluate_df.merit = @variable(model, 0 <= x_merit[1:n_students] <= 2.5);
julia> evaluate_df6000×4 DataFrame
+  Row │ StudentID  SAT    GPA      merit         
+      │ Int64      Int64  Float64  GenericV…     
+──────┼──────────────────────────────────────────
+    1 │         1   1240     3.22  x_merit[1]
+    2 │         2   1206     2.87  x_merit[2]
+    3 │         3   1520     3.74  x_merit[3]
+    4 │         4   1238     3.11  x_merit[4]
+    5 │         5   1142     2.74  x_merit[5]
+    6 │         6   1086     2.77  x_merit[6]
+    7 │         7   1367     3.28  x_merit[7]
+    8 │         8   1034     2.41  x_merit[8]
+  ⋮   │     ⋮        ⋮       ⋮           ⋮
+ 5994 │      5994   1121     2.96  x_merit[5994]
+ 5995 │      5995   1564     4.1   x_merit[5995]
+ 5996 │      5996   1332     3.14  x_merit[5996]
+ 5997 │      5997   1228     2.95  x_merit[5997]
+ 5998 │      5998   1165     2.81  x_merit[5998]
+ 5999 │      5999   1400     3.43  x_merit[5999]
+ 6000 │      6000   1097     2.65  x_merit[6000]
+                                5985 rows omitted

Then, we use MathOptAI.add_predictor to embed model_glm into the JuMP model. MathOptAI.add_predictor returns a vector of variables, one for each row inn evaluate_df, corresponding to the output enroll of our logistic regression.

julia> evaluate_df.enroll, _ = MathOptAI.add_predictor(model, model_glm, evaluate_df);
julia> evaluate_df6000×5 DataFrame
+  Row │ StudentID  SAT    GPA      merit          enroll          
+      │ Int64      Int64  Float64  GenericV…      GenericV…       
+──────┼───────────────────────────────────────────────────────────
+    1 │         1   1240     3.22  x_merit[1]     moai_Sigmoid[1]
+    2 │         2   1206     2.87  x_merit[2]     moai_Sigmoid[1]
+    3 │         3   1520     3.74  x_merit[3]     moai_Sigmoid[1]
+    4 │         4   1238     3.11  x_merit[4]     moai_Sigmoid[1]
+    5 │         5   1142     2.74  x_merit[5]     moai_Sigmoid[1]
+    6 │         6   1086     2.77  x_merit[6]     moai_Sigmoid[1]
+    7 │         7   1367     3.28  x_merit[7]     moai_Sigmoid[1]
+    8 │         8   1034     2.41  x_merit[8]     moai_Sigmoid[1]
+  ⋮   │     ⋮        ⋮       ⋮           ⋮               ⋮
+ 5994 │      5994   1121     2.96  x_merit[5994]  moai_Sigmoid[1]
+ 5995 │      5995   1564     4.1   x_merit[5995]  moai_Sigmoid[1]
+ 5996 │      5996   1332     3.14  x_merit[5996]  moai_Sigmoid[1]
+ 5997 │      5997   1228     2.95  x_merit[5997]  moai_Sigmoid[1]
+ 5998 │      5998   1165     2.81  x_merit[5998]  moai_Sigmoid[1]
+ 5999 │      5999   1400     3.43  x_merit[5999]  moai_Sigmoid[1]
+ 6000 │      6000   1097     2.65  x_merit[6000]  moai_Sigmoid[1]
+                                                 5985 rows omitted

The .enroll column name in evaluate_df is just a name. It doesn't have to match the name in train_df.

The objective of our problem is to maximize the expected number of students who enroll:

julia> @objective(model, Max, sum(evaluate_df.enroll))moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + [[...5940 terms omitted...]] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1]

Subject to the constraint that we can spend at most 0.2 * n_students on merit scholarships:

julia> @constraint(model, sum(evaluate_df.merit) <= 0.2 * n_students)x_merit[1] + x_merit[2] + x_merit[3] + x_merit[4] + x_merit[5] + x_merit[6] + x_merit[7] + x_merit[8] + x_merit[9] + x_merit[10] + x_merit[11] + x_merit[12] + x_merit[13] + x_merit[14] + x_merit[15] + x_merit[16] + x_merit[17] + x_merit[18] + x_merit[19] + x_merit[20] + x_merit[21] + x_merit[22] + x_merit[23] + x_merit[24] + x_merit[25] + x_merit[26] + x_merit[27] + x_merit[28] + x_merit[29] + x_merit[30] + [[...5940 terms omitted...]] + x_merit[5971] + x_merit[5972] + x_merit[5973] + x_merit[5974] + x_merit[5975] + x_merit[5976] + x_merit[5977] + x_merit[5978] + x_merit[5979] + x_merit[5980] + x_merit[5981] + x_merit[5982] + x_merit[5983] + x_merit[5984] + x_merit[5985] + x_merit[5986] + x_merit[5987] + x_merit[5988] + x_merit[5989] + x_merit[5990] + x_merit[5991] + x_merit[5992] + x_merit[5993] + x_merit[5994] + x_merit[5995] + x_merit[5996] + x_merit[5997] + x_merit[5998] + x_merit[5999] + x_merit[6000] ≤ 1200

Because logistic regression involves a Sigmoid layer, we need to use a smooth nonlinear optimizer. A common choice is Ipopt. Solve and check the optimizer found a feasible solution:

julia> set_optimizer(model, Ipopt.Optimizer)
julia> set_silent(model)
julia> optimize!(model)
julia> @assert is_solved_and_feasible(model)
julia> solution_summary(model)* Solver : Ipopt
+
+* Status
+  Result count       : 1
+  Termination status : LOCALLY_SOLVED
+  Message from the solver:
+  "Solve_Succeeded"
+
+* Candidate solution (result #1)
+  Primal status      : FEASIBLE_POINT
+  Dual status        : FEASIBLE_POINT
+  Objective value    : 2.48820e+03
+  Dual objective value : -4.91918e+02
+
+* Work counters
+  Solve time (sec)   : 5.71676e+00
+  Barrier iterations : 142

Let's store the solution in evaluate_df for analysis:

julia> evaluate_df.merit_sol = value.(evaluate_df.merit);
julia> evaluate_df.enroll_sol = value.(evaluate_df.enroll);
julia> evaluate_df6000×7 DataFrame
+  Row │ StudentID  SAT    GPA      merit          enroll           merit_sol   ⋯
+      │ Int64      Int64  Float64  GenericV…      GenericV…        Float64     ⋯
+──────┼─────────────────────────────────────────────────────────────────────────
+    1 │         1   1240     3.22  x_merit[1]     moai_Sigmoid[1]  6.37389e-7  ⋯
+    2 │         2   1206     2.87  x_merit[2]     moai_Sigmoid[1]  1.08151
+    3 │         3   1520     3.74  x_merit[3]     moai_Sigmoid[1]  1.03717e-6
+    4 │         4   1238     3.11  x_merit[4]     moai_Sigmoid[1]  1.06046e-6
+    5 │         5   1142     2.74  x_merit[5]     moai_Sigmoid[1]  1.13489     ⋯
+    6 │         6   1086     2.77  x_merit[6]     moai_Sigmoid[1]  1.0759e-6
+    7 │         7   1367     3.28  x_merit[7]     moai_Sigmoid[1]  2.33948e-6
+    8 │         8   1034     2.41  x_merit[8]     moai_Sigmoid[1]  0.735482
+  ⋮   │     ⋮        ⋮       ⋮           ⋮               ⋮             ⋮       ⋱
+ 5994 │      5994   1121     2.96  x_merit[5994]  moai_Sigmoid[1]  6.26387e-7  ⋯
+ 5995 │      5995   1564     4.1   x_merit[5995]  moai_Sigmoid[1]  3.58792e-7
+ 5996 │      5996   1332     3.14  x_merit[5996]  moai_Sigmoid[1]  1.03863
+ 5997 │      5997   1228     2.95  x_merit[5997]  moai_Sigmoid[1]  1.21941
+ 5998 │      5998   1165     2.81  x_merit[5998]  moai_Sigmoid[1]  1.21872     ⋯
+ 5999 │      5999   1400     3.43  x_merit[5999]  moai_Sigmoid[1]  1.33971e-6
+ 6000 │      6000   1097     2.65  x_merit[6000]  moai_Sigmoid[1]  1.17865
+                                                  1 column and 5985 rows omitted

Solution analysis

We expect that just under 2,500 students will enroll:

julia> sum(evaluate_df.enroll_sol)2488.1951671444017

We awarded merit scholarships to approximately 1 in 6 students:

julia> count(evaluate_df.merit_sol .> 1e-5)1152

The average merit scholarship was worth just over $1,000:

julia> 1_000 * Statistics.mean(evaluate_df.merit_sol[evaluate_df.merit_sol.>1e-5])1041.6622990671967

This page was generated using Literate.jl.

diff --git a/v0.1.4/.documenter-siteinfo.json b/v0.1.4/.documenter-siteinfo.json new file mode 100644 index 00000000..8424ba44 --- /dev/null +++ b/v0.1.4/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-10-25T02:53:58","documenter_version":"1.7.0"}} \ No newline at end of file diff --git a/v0.1.4/api/index.html b/v0.1.4/api/index.html new file mode 100644 index 00000000..66edad81 --- /dev/null +++ b/v0.1.4/api/index.html @@ -0,0 +1,889 @@ + +API Reference · MathOptAI.jl
GitHub

API Reference

This page lists the public API of MathOptAI.

Info

This page is an unstructured list of the MathOptAI API. For a more structured overview, read the Manual or Tutorial parts of this documentation.

Load all of the public the API into the current scope with:

using MathOptAI

Alternatively, load only the module with:

import MathOptAI

and then prefix all calls with MathOptAI. to create MathOptAI.<NAME>.

AbstractPredictor

add_predictor

MathOptAI.add_predictor — Function
add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::AbstractPredictor,
+    x::Vector,
+)::Vector

Return a Vector representing y such that y = predictor(x).

The element type of x is deliberately unspecified. The vector x may contain any mix of scalar constants, JuMP decision variables, and scalar JuMP functions like AffExpr, QuadExpr, or NonlinearExpr.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.Affine([2.0, 3.0])
+Affine(A, b) [input: 2, output: 1]
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Affine[1]
+
+julia> formulation
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ 2 x[1] + 3 x[2] - moai_Affine[1] = 0
source

build_predictor

Affine

MathOptAI.Affine — Type
Affine(
+    A::Matrix{T},
+    b::Vector{T} = zeros(T, size(A, 1)),
+) where {T} <: AbstractPredictor

An AbstractPredictor that represents the relationship:

\[y = A x + b\]

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, 0 <= x[i in 1:2] <= i);
+
+julia> f = MathOptAI.Affine([2.0 3.0], [4.0])
+Affine(A, b) [input: 2, output: 1]
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Affine[1]
+
+julia> formulation
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [3]
+  ├ moai_Affine[1] ≥ 4
+  ├ moai_Affine[1] ≤ 12
+  └ 2 x[1] + 3 x[2] - moai_Affine[1] = -4
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+1-element Vector{AffExpr}:
+ 2 x[1] + 3 x[2] + 4
+
+julia> formulation
+ReducedSpace(Affine(A, b) [input: 2, output: 1])
+├ variables [0]
+└ constraints [0]
source

BinaryDecisionTree

MathOptAI.BinaryDecisionTree — Type
BinaryDecisionTree{K,V}(
+    feat_id::Int,
+    feat_value::K,
+    lhs::Union{V,BinaryDecisionTree{K,V}},
+    rhs::Union{V,BinaryDecisionTree{K,V}},
+)

An AbstractPredictor that represents a binary decision tree.

  • If x[feat_id] <= feat_value, then return lhs
  • If x[feat_id] > feat_value, then return rhs

Example

To represent the tree x[1] <= 0.0 ? -1 : (x[1] <= 1.0 ? 0 : 1), do:

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:1]);
+
+julia> f = MathOptAI.BinaryDecisionTree{Float64,Int}(
+           1,
+           0.0,
+           -1,
+           MathOptAI.BinaryDecisionTree{Float64,Int}(1, 1.0, 0, 1),
+       )
+BinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_BinaryDecisionTree_value
+
+julia> formulation
+BinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]
+├ variables [4]
+│ ├ moai_BinaryDecisionTree_value
+│ ├ moai_BinaryDecisionTree_z[1]
+│ ├ moai_BinaryDecisionTree_z[2]
+│ └ moai_BinaryDecisionTree_z[3]
+└ constraints [7]
+  ├ moai_BinaryDecisionTree_z[1] + moai_BinaryDecisionTree_z[2] + moai_BinaryDecisionTree_z[3] = 1
+  ├ moai_BinaryDecisionTree_z[1] --> {x[1] ≤ 0}
+  ├ moai_BinaryDecisionTree_z[2] --> {x[1] ≥ 0}
+  ├ moai_BinaryDecisionTree_z[2] --> {x[1] ≤ 1}
+  ├ moai_BinaryDecisionTree_z[3] --> {x[1] ≥ 0}
+  ├ moai_BinaryDecisionTree_z[3] --> {x[1] ≥ 1}
+  └ moai_BinaryDecisionTree_z[1] - moai_BinaryDecisionTree_z[3] + moai_BinaryDecisionTree_value = 0
source

GrayBox

MathOptAI.GrayBox — Type
GrayBox(
+    output_size::Function,
+    callback::Function;
+    has_hessian::Bool = false,
+) <: AbstractPredictor

An AbstractPredictor that represents the relationship:

\[y = f(x)\]

as a user-defined nonlinear operator.

Arguments

  • output_size(x::Vector):Int: given an input vector x, return the dimension of the output vector
  • callback(x::Vector)::NamedTuple -> (;value, jacobian[, hessian]): given an input vector x, return a NamedTuple that computes the primal value and Jacobian of the output value with respect to the input. jacobian[j, i] is the partial derivative of value[j] with respect to x[i].
  • has_hessian: if true, the callback additionally contains a field hessian, which is an N × N × M matrix, where hessian[i, j, k] is the partial derivative of value[k] with respect to x[i] and x[j].

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.GrayBox(
+           x -> 2,
+           x -> (value = x.^2, jacobian = [2 * x[1] 0.0; 0.0 2 * x[2]]),
+       );
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_GrayBox[1]
+ moai_GrayBox[2]
+
+julia> formulation
+GrayBox
+├ variables [2]
+│ ├ moai_GrayBox[1]
+│ └ moai_GrayBox[2]
+└ constraints [2]
+  ├ op_##330(x[1], x[2]) - moai_GrayBox[1] = 0
+  └ op_##331(x[1], x[2]) - moai_GrayBox[2] = 0
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ op_##332(x[1], x[2])
+ op_##333(x[1], x[2])
+
+julia> formulation
+ReducedSpace(GrayBox)
+├ variables [0]
+└ constraints [0]
source

Pipeline

MathOptAI.Pipeline — Type
Pipeline(layers::Vector{AbstractPredictor}) <: AbstractPredictor

An AbstractPredictor that represents the relationship:

\[y = (l_1 \circ \ldots \circ l_N)(x)\]

where $l_i$ are a list of other AbstractPredictors.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.Pipeline(
+           MathOptAI.Affine([1.0 2.0], [0.0]),
+           MathOptAI.ReLUQuadratic(),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 2, output: 1]
+ * ReLUQuadratic()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_ReLU[1]
+
+julia> formulation
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ x[1] + 2 x[2] - moai_Affine[1] = 0
+ReLUQuadratic()
+├ variables [2]
+│ ├ moai_ReLU[1]
+│ └ moai_z[1]
+└ constraints [4]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_z[1] ≥ 0
+  ├ moai_Affine[1] - moai_ReLU[1] + moai_z[1] = 0
+  └ moai_ReLU[1]*moai_z[1] = 0
source

PytorchModel

MathOptAI.PytorchModel — Type
PytorchModel(filename::String)

A wrapper struct for loading a PyTorch model.

The only supported file extension is .pt, where the .pt file has been created using torch.save(model, filename).

Example

julia> using PythonCall, MathOptAI
+
+julia> predictor = PytorchModel("model.pt");
source

Quantile

MathOptAI.Quantile — Type
Quantile{D}(distribution::D, quantiles::Vector{Float64}) where {D}

An AbstractPredictor that represents the quantiles of distribution.

Example

julia> using JuMP, Distributions, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, 1 <= x <= 2);
+
+julia> predictor = MathOptAI.Quantile([0.1, 0.9]) do x
+           return Distributions.Normal(x, 3 - x)
+       end
+Quantile(_, [0.1, 0.9])
+
+julia> y, formulation = MathOptAI.add_predictor(model, predictor, [x]);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_quantile[1]
+ moai_quantile[2]
+
+julia> formulation
+Quantile(_, [0.1, 0.9])
+├ variables [2]
+│ ├ moai_quantile[1]
+│ └ moai_quantile[2]
+└ constraints [2]
+  ├ moai_quantile[1] - op_quantile_0.1(x) = 0
+  └ moai_quantile[2] - op_quantile_0.9(x) = 0
source

ReducedSpace

MathOptAI.ReducedSpace — Type
ReducedSpace(predictor::AbstractPredictor)

A wrapper type for other predictors that implement a reduced-space formulation.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> predictor = MathOptAI.ReducedSpace(MathOptAI.ReLU());
+
+julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ max(0.0, x[1])
+ max(0.0, x[2])
source

ReLU

MathOptAI.ReLU — Type
ReLU() <: AbstractPredictor

An AbstractPredictor that represents the relationship:

\[y = \max\{0, x\}\]

as a non-smooth nonlinear constraint.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, -1 <= x[i in 1:2] <= i);
+
+julia> f = MathOptAI.ReLU()
+ReLU()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_ReLU[1]
+ moai_ReLU[2]
+
+julia> formulation
+ReLU()
+├ variables [2]
+│ ├ moai_ReLU[1]
+│ └ moai_ReLU[2]
+└ constraints [6]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[1] ≤ 1
+  ├ moai_ReLU[2] ≥ 0
+  ├ moai_ReLU[2] ≤ 2
+  ├ moai_ReLU[1] - max(0.0, x[1]) = 0
+  └ moai_ReLU[2] - max(0.0, x[2]) = 0
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ max(0.0, x[1])
+ max(0.0, x[2])
+
+julia> formulation
+ReducedSpace(ReLU())
+├ variables [0]
+└ constraints [0]
source

ReLUBigM

MathOptAI.ReLUBigM — Type
ReLUBigM(M::Float64) <: AbstractPredictor

An AbstractPredictor that represents the relationship:

\[y = \max\{0, x\}\]

via the big-M MIP reformulation:

\[\begin{aligned} +y \ge 0 \\ +y \ge x \\ +y \le M z \\ +y \le x + M(1 - z) \\ +z \in\{0, 1\} +\end{aligned}\]

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, -3 <= x[i in 1:2] <= i);
+
+julia> f = MathOptAI.ReLUBigM(100.0)
+ReLUBigM(100.0)
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_ReLU[1]
+ moai_ReLU[2]
+
+julia> formulation
+ReLUBigM(100.0)
+├ variables [4]
+│ ├ moai_ReLU[1]
+│ ├ moai_ReLU[2]
+│ ├ moai_z[1]
+│ └ moai_z[2]
+└ constraints [12]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[1] ≤ 1
+  ├ moai_ReLU[2] ≥ 0
+  ├ moai_ReLU[2] ≤ 2
+  ├ moai_z[1] binary
+  ├ -x[1] + moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[1] - moai_z[1] ≤ 0
+  ├ -x[1] + moai_ReLU[1] + 3 moai_z[1] ≤ 3
+  ├ moai_z[2] binary
+  ├ -x[2] + moai_ReLU[2] ≥ 0
+  ├ moai_ReLU[2] - 2 moai_z[2] ≤ 0
+  └ -x[2] + moai_ReLU[2] + 3 moai_z[2] ≤ 3
source

ReLUQuadratic

MathOptAI.ReLUQuadratic — Type
ReLUQuadratic() <: AbstractPredictor

An AbstractPredictor that represents the relationship:

\[y = \max\{0, x\}\]

by the reformulation:

\[\begin{aligned} +x = y - z \\ +y \cdot z = 0 \\ +y, z \ge 0 +\end{aligned}\]

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, -1 <= x[i in 1:2] <= i);
+
+julia> f = MathOptAI.ReLUQuadratic()
+ReLUQuadratic()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_ReLU[1]
+ moai_ReLU[2]
+
+julia> formulation
+ReLUQuadratic()
+├ variables [4]
+│ ├ moai_ReLU[1]
+│ ├ moai_ReLU[2]
+│ ├ moai_z[1]
+│ └ moai_z[2]
+└ constraints [12]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[1] ≤ 1
+  ├ moai_ReLU[2] ≥ 0
+  ├ moai_ReLU[2] ≤ 2
+  ├ moai_z[1] ≥ 0
+  ├ moai_z[1] ≤ 1
+  ├ moai_z[2] ≥ 0
+  ├ moai_z[2] ≤ 1
+  ├ x[1] - moai_ReLU[1] + moai_z[1] = 0
+  ├ x[2] - moai_ReLU[2] + moai_z[2] = 0
+  ├ moai_ReLU[1]*moai_z[1] = 0
+  └ moai_ReLU[2]*moai_z[2] = 0
source

ReLUSOS1

MathOptAI.ReLUSOS1 — Type
ReLUSOS1() <: AbstractPredictor

An AbstractPredictor that represents the relationship:

\[y = \max\{0, x\}\]

by the reformulation:

\[\begin{aligned} +x = y - z \\ +[y, z] \in SOS1 \\ +y, z \ge 0 +\end{aligned}\]

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, -1 <= x[i in 1:2] <= i);
+
+julia> f = MathOptAI.ReLUSOS1()
+ReLUSOS1()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_ReLU[1]
+ moai_ReLU[2]
+
+julia> formulation
+ReLUSOS1()
+├ variables [4]
+│ ├ moai_ReLU[1]
+│ ├ moai_ReLU[2]
+│ ├ moai_z[1]
+│ └ moai_z[2]
+└ constraints [10]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[1] ≤ 1
+  ├ moai_ReLU[2] ≥ 0
+  ├ moai_ReLU[2] ≤ 2
+  ├ moai_z[1] ≤ 1
+  ├ moai_z[2] ≤ 1
+  ├ x[1] - moai_ReLU[1] + moai_z[1] = 0
+  ├ x[2] - moai_ReLU[2] + moai_z[2] = 0
+  ├ [moai_ReLU[1], moai_z[1]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])
+  └ [moai_ReLU[2], moai_z[2]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])
source

Scale

MathOptAI.Scale — Type
Scale(
+    scale::Vector{T},
+    bias::Vector{T},
+) where {T} <: AbstractPredictor

An AbstractPredictor that represents the relationship:

\[y = Diag(scale)x + bias\]

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, 0 <= x[i in 1:2] <= i);
+
+julia> f = MathOptAI.Scale([2.0, 3.0], [4.0, 5.0])
+Scale(scale, bias)
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_Scale[1]
+ moai_Scale[2]
+
+julia> formulation
+Scale(scale, bias)
+├ variables [2]
+│ ├ moai_Scale[1]
+│ └ moai_Scale[2]
+└ constraints [6]
+  ├ moai_Scale[1] ≥ 4
+  ├ moai_Scale[1] ≤ 6
+  ├ moai_Scale[2] ≥ 5
+  ├ moai_Scale[2] ≤ 11
+  ├ 2 x[1] - moai_Scale[1] = -4
+  └ 3 x[2] - moai_Scale[2] = -5
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{AffExpr}:
+ 2 x[1] + 4
+ 3 x[2] + 5
+
+julia> formulation
+ReducedSpace(Scale(scale, bias))
+├ variables [0]
+└ constraints [0]
source

Sigmoid

MathOptAI.Sigmoid — Type
Sigmoid() <: AbstractPredictor

An AbstractPredictor that represents the relationship:

\[y = \frac{1}{1 + e^{-x}}\]

as a smooth nonlinear constraint.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, -1 <= x[i in 1:2] <= i);
+
+julia> f = MathOptAI.Sigmoid()
+Sigmoid()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_Sigmoid[1]
+ moai_Sigmoid[2]
+
+julia> formulation
+Sigmoid()
+├ variables [2]
+│ ├ moai_Sigmoid[1]
+│ └ moai_Sigmoid[2]
+└ constraints [6]
+  ├ moai_Sigmoid[1] ≥ 0.2689414213699951
+  ├ moai_Sigmoid[1] ≤ 0.7310585786300049
+  ├ moai_Sigmoid[2] ≥ 0.2689414213699951
+  ├ moai_Sigmoid[2] ≤ 0.8807970779778823
+  ├ moai_Sigmoid[1] - (1.0 / (1.0 + exp(-x[1]))) = 0
+  └ moai_Sigmoid[2] - (1.0 / (1.0 + exp(-x[2]))) = 0
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ 1.0 / (1.0 + exp(-x[1]))
+ 1.0 / (1.0 + exp(-x[2]))
+
+julia> formulation
+ReducedSpace(Sigmoid())
+├ variables [0]
+└ constraints [0]
source

SoftMax

MathOptAI.SoftMax — Type
SoftMax() <: AbstractPredictor

An AbstractPredictor that represents the relationship:

\[y = \frac{e^{x}}{||e^{x}||_1}\]

as a smooth nonlinear constraint.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> f = MathOptAI.SoftMax()
+SoftMax()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_SoftMax[1]
+ moai_SoftMax[2]
+
+julia> formulation
+SoftMax()
+├ variables [3]
+│ ├ moai_SoftMax_denom
+│ ├ moai_SoftMax[1]
+│ └ moai_SoftMax[2]
+└ constraints [8]
+  ├ moai_SoftMax[1] ≥ 0
+  ├ moai_SoftMax[1] ≤ 1
+  ├ moai_SoftMax[2] ≥ 0
+  ├ moai_SoftMax[2] ≤ 1
+  ├ moai_SoftMax_denom ≥ 0
+  ├ moai_SoftMax_denom - (0.0 + exp(x[2]) + exp(x[1])) = 0
+  ├ moai_SoftMax[1] - (exp(x[1]) / moai_SoftMax_denom) = 0
+  └ moai_SoftMax[2] - (exp(x[2]) / moai_SoftMax_denom) = 0
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ exp(x[1]) / moai_SoftMax_denom
+ exp(x[2]) / moai_SoftMax_denom
+
+julia> formulation
+ReducedSpace(SoftMax())
+├ variables [1]
+│ └ moai_SoftMax_denom
+└ constraints [2]
+  ├ moai_SoftMax_denom ≥ 0
+  └ moai_SoftMax_denom - (0.0 + exp(x[2]) + exp(x[1])) = 0
source

SoftPlus

MathOptAI.SoftPlus — Type
SoftPlus(; beta = 1.0) <: AbstractPredictor

An AbstractPredictor that represents the relationship:

\[y = \frac{1}{\beta} \log(1 + e^{\beta x})\]

as a smooth nonlinear constraint.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, -1 <= x[i in 1:2] <= i);
+
+julia> f = MathOptAI.SoftPlus(; beta = 2.0)
+SoftPlus(2.0)
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_SoftPlus[1]
+ moai_SoftPlus[2]
+
+julia> formulation
+SoftPlus(2.0)
+├ variables [2]
+│ ├ moai_SoftPlus[1]
+│ └ moai_SoftPlus[2]
+└ constraints [6]
+  ├ moai_SoftPlus[1] ≥ 0.0634640055214863
+  ├ moai_SoftPlus[1] ≤ 1.0634640055214863
+  ├ moai_SoftPlus[2] ≥ 0.0634640055214863
+  ├ moai_SoftPlus[2] ≤ 2.0090749639589047
+  ├ moai_SoftPlus[1] - (log(1.0 + exp(2 x[1])) / 2.0) = 0
+  └ moai_SoftPlus[2] - (log(1.0 + exp(2 x[2])) / 2.0) = 0
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ log(1.0 + exp(2 x[1])) / 2.0
+ log(1.0 + exp(2 x[2])) / 2.0
+
+julia> formulation
+ReducedSpace(SoftPlus(2.0))
+├ variables [0]
+└ constraints [0]
source

Tanh

MathOptAI.Tanh — Type
Tanh() <: AbstractPredictor

An AbstractPredictor that represents the relationship:

\[y = \tanh(x)\]

as a smooth nonlinear constraint.

Example

julia> using JuMP, MathOptAI
+
+julia> model = Model();
+
+julia> @variable(model, -1 <= x[i in 1:2] <= i);
+
+julia> f = MathOptAI.Tanh()
+Tanh()
+
+julia> y, formulation = MathOptAI.add_predictor(model, f, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_Tanh[1]
+ moai_Tanh[2]
+
+julia> formulation
+Tanh()
+├ variables [2]
+│ ├ moai_Tanh[1]
+│ └ moai_Tanh[2]
+└ constraints [6]
+  ├ moai_Tanh[1] ≥ -0.7615941559557649
+  ├ moai_Tanh[1] ≤ 0.7615941559557649
+  ├ moai_Tanh[2] ≥ -0.7615941559557649
+  ├ moai_Tanh[2] ≤ 0.9640275800758169
+  ├ moai_Tanh[1] - tanh(x[1]) = 0
+  └ moai_Tanh[2] - tanh(x[2]) = 0
+
+julia> y, formulation =
+           MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);
+
+julia> y
+2-element Vector{NonlinearExpr}:
+ tanh(x[1])
+ tanh(x[2])
+
+julia> formulation
+ReducedSpace(Tanh())
+├ variables [0]
+└ constraints [0]
source

AbstractFormulation

Formulation

MathOptAI.Formulation — Type
struct Formulation{P<:AbstractPredictor} <: AbstractFormulation
+    predictor::P
+    variables::Vector{Any}
+    constraints::Vector{Any}
+end

Fields

  • predictor: the predictor object used to build the formulation
  • variables: a vector of new decision variables added to the model
  • constraints: a vector of new constraints added to the model

Check the docstring of the predictor for an explanation of the formulation and the order of the elements in .variables and .constraints.

source

PipelineFormulation

MathOptAI.PipelineFormulation — Type
struct PipelineFormulation{P<:AbstractPredictor} <: AbstractFormulation
+    predictor::P
+    layers::Vector{Any}
+end

Fields

  • predictor: the predictor object used to build the formulation
  • layers: the formulation associated with each of the layers in the pipeline
source

Extensions

MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::MathOptAI.Quantile{<:AbstractGPs.PosteriorGP},
+    x::Vector,
+)

Add the quantiles of a trained Gaussian Process from AbstractGPs.jl to model.

Example

julia> using JuMP, MathOptAI, AbstractGPs
+
+julia> x_data = 2π .* (0.0:0.1:1.0);
+
+julia> y_data = sin.(x_data);
+
+julia> fx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.1);
+
+julia> p_fx = AbstractGPs.posterior(fx, y_data);
+
+julia> model = Model();
+
+julia> @variable(model, 1 <= x[1:1] <= 6, start = 3);
+
+julia> predictor = MathOptAI.Quantile(p_fx, [0.1, 0.9]);
+
+julia> y, _ = MathOptAI.add_predictor(model, predictor, x);
+
+julia> y
+2-element Vector{VariableRef}:
+ moai_quantile[1]
+ moai_quantile[2]
+
+julia> @objective(model, Max, y[2] - y[1])
+moai_quantile[2] - moai_quantile[1]
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::Union{DecisionTree.Root,DecisionTree.DecisionTreeClassifier},
+    x::Vector,
+)

Add a binary decision tree from DecisionTree.jl to model.

Example

julia> using JuMP, MathOptAI, DecisionTree
+
+julia> truth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)
+truth (generic function with 1 method)
+
+julia> features = abs.(sin.((1:10) .* (3:4)'));
+
+julia> size(features)
+(10, 2)
+
+julia> labels = truth.(Vector.(eachrow(features)));
+
+julia> predictor = DecisionTree.build_tree(labels, features)
+Decision Tree
+Leaves: 3
+Depth:  2
+
+julia> model = Model();
+
+julia> @variable(model, 0 <= x[1:2] <= 1);
+
+julia> y, _ = MathOptAI.add_predictor(model, predictor, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_BinaryDecisionTree_value
source
MathOptAI.build_predictor — Method
MathOptAI.build_predictor(predictor::DecisionTree.Root)

Convert a binary decision tree from DecisionTree.jl to a BinaryDecisionTree.

Example

julia> using MathOptAI, DecisionTree
+
+julia> truth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)
+truth (generic function with 1 method)
+
+julia> features = abs.(sin.((1:10) .* (3:4)'));
+
+julia> size(features)
+(10, 2)
+
+julia> labels = truth.(Vector.(eachrow(features)));
+
+julia> tree = DecisionTree.build_tree(labels, features)
+Decision Tree
+Leaves: 3
+Depth:  2
+
+julia> predictor = MathOptAI.build_predictor(tree)
+BinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::Flux.Chain,
+    x::Vector;
+    config::Dict = Dict{Any,Any}(),
+    reduced_space::Bool = false,
+    gray_box::Bool = false,
+)

Add a trained neural network from Flux.jl to model.

Supported layers

  • Flux.Dense
  • Flux.Scale
  • Flux.softmax

Supported activation functions

  • Flux.relu
  • Flux.sigmoid
  • Flux.softplus
  • Flux.tanh

Keyword arguments

  • config: a dictionary that maps supported Flux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Flux.sigmoid => MathOptAI.Sigmoid() or Flux.relu => MathOptAI.QuadraticReLU().
  • gray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by Flux.withjacobian.

Example

julia> using JuMP, Flux, MathOptAI
+
+julia> chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));
+
+julia> model = Model();
+
+julia> @variable(model, x[1:1]);
+
+julia> y, _ = MathOptAI.add_predictor(
+           model,
+           chain,
+           x;
+           config = Dict(Flux.relu => MathOptAI.ReLU()),
+       );
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Affine[1]
source
MathOptAI.build_predictor — Method
MathOptAI.build_predictor(
+    predictor::Flux.Chain;
+    config::Dict = Dict{Any,Any}(),
+    gray_box::Bool = false,
+    gray_box_hessian::Bool = false,
+)

Convert a trained neural network from Flux.jl to a Pipeline.

Supported layers

  • Flux.Dense
  • Flux.Scale
  • Flux.softmax

Supported activation functions

  • Flux.relu
  • Flux.sigmoid
  • Flux.softplus
  • Flux.tanh

Keyword arguments

  • config: a dictionary that maps supported Flux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Flux.sigmoid => MathOptAI.Sigmoid() or Flux.relu => MathOptAI.QuadraticReLU().
  • gray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by Flux.withjacobian.
  • gray_box_hessian: if true, the gray box additionally computes the Hessian of the output using Flux.hessian.

Example

julia> using Flux, MathOptAI
+
+julia> chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));
+
+julia> MathOptAI.build_predictor(
+           chain;
+           config = Dict(Flux.relu => MathOptAI.ReLU()),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 1, output: 16]
+ * ReLU()
+ * Affine(A, b) [input: 16, output: 1]
+
+julia> MathOptAI.build_predictor(
+           chain;
+           config = Dict(Flux.relu => MathOptAI.ReLUQuadratic()),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 1, output: 16]
+ * ReLUQuadratic()
+ * Affine(A, b) [input: 16, output: 1]
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::GLM.GeneralizedLinearModel{
+        GLM.GlmResp{Vector{Float64},GLM.Bernoulli{Float64},GLM.LogitLink},
+    },
+    x::Vector;
+    sigmoid::AbstractPredictor = MathOptAI.Sigmoid(),
+    reduced_space::Bool = false,
+)

Add a trained logistic regression model from GLM.jl to model.

Keyword arguments

  • sigmoid: the predictor to use for the sigmoid layer.

Example

julia> using GLM, JuMP, MathOptAI
+
+julia> X, Y = rand(10, 2), rand(Bool, 10);
+
+julia> predictor = GLM.glm(X, Y, GLM.Bernoulli());
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> y, _ = MathOptAI.add_predictor(
+           model,
+           predictor,
+           x;
+           sigmoid = MathOptAI.Sigmoid(),
+       );
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Sigmoid[1]
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::GLM.LinearModel,
+    x::Vector;
+    reduced_space::Bool = false,
+)

Add a trained linear model from GLM.jl to model.

Example

julia> using GLM, JuMP, MathOptAI
+
+julia> X, Y = rand(10, 2), rand(10);
+
+julia> predictor = GLM.lm(X, Y);
+
+julia> model = Model();
+
+julia> @variable(model, x[1:2]);
+
+julia> y, _ = MathOptAI.add_predictor(model, predictor, x);
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Affine[1]
source
MathOptAI.build_predictor — Method
MathOptAI.build_predictor(
+    predictor::GLM.GeneralizedLinearModel{
+        GLM.GlmResp{Vector{Float64},GLM.Bernoulli{Float64},GLM.LogitLink},
+    };
+    sigmoid::MathOptAI.AbstractPredictor = MathOptAI.Sigmoid(),
+)

Convert a trained logistic model from GLM.jl to a Pipeline layer.

Keyword arguments

  • sigmoid: the predictor to use for the sigmoid layer.

Example

julia> using GLM, MathOptAI
+
+julia> X, Y = rand(10, 2), rand(Bool, 10);
+
+julia> model = GLM.glm(X, Y, GLM.Bernoulli());
+
+julia> predictor = MathOptAI.build_predictor(model)
+Pipeline with layers:
+ * Affine(A, b) [input: 2, output: 1]
+ * Sigmoid()
source
MathOptAI.build_predictor — Method
MathOptAI.build_predictor(predictor::GLM.LinearModel)

Convert a trained linear model from GLM.jl to an Affine layer.

Example

julia> using GLM, MathOptAI
+
+julia> X, Y = rand(10, 2), rand(10);
+
+julia> model = GLM.lm(X, Y);
+
+julia> predictor = MathOptAI.build_predictor(model)
+Affine(A, b) [input: 2, output: 1]
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::Tuple{<:Lux.Chain,<:NamedTuple,<:NamedTuple},
+    x::Vector;
+    config::Dict = Dict{Any,Any}(),
+    reduced_space::Bool = false,
+)

Add a trained neural network from Lux.jl to model.

Supported layers

  • Lux.Dense
  • Lux.Scale

Supported activation functions

  • Lux.relu
  • Lux.sigmoid
  • Lux.softplus
  • Lux.softmax
  • Lux.tanh

Keyword arguments

  • config: a dictionary that maps supported Lux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Lux.sigmoid => MathOptAI.Sigmoid() or Lux.relu => MathOptAI.QuadraticReLU().

Example

julia> using JuMP, Lux, MathOptAI, Random
+
+julia> rng = Random.MersenneTwister();
+
+julia> chain = Lux.Chain(Lux.Dense(1 => 16, Lux.relu), Lux.Dense(16 => 1))
+Chain(
+    layer_1 = Dense(1 => 16, relu),     # 32 parameters
+    layer_2 = Dense(16 => 1),           # 17 parameters
+)         # Total: 49 parameters,
+          #        plus 0 states.
+
+julia> parameters, state = Lux.setup(rng, chain);
+
+julia> predictor = (chain, parameters, state);
+
+julia> model = Model();
+
+julia> @variable(model, x[1:1]);
+
+julia> y, _ = MathOptAI.add_predictor(
+           model,
+           predictor,
+           x;
+           config = Dict(Lux.relu => MathOptAI.ReLU()),
+       );
+
+julia> y
+1-element Vector{VariableRef}:
+ moai_Affine[1]
source
MathOptAI.build_predictor — Method
MathOptAI.build_predictor(
+    predictor::Tuple{<:Lux.Chain,<:NamedTuple,<:NamedTuple};
+    config::Dict = Dict{Any,Any}(),
+)

Convert a trained neural network from Lux.jl to a Pipeline.

Supported layers

  • Lux.Dense
  • Lux.Scale

Supported activation functions

  • Lux.relu
  • Lux.sigmoid
  • Lux.softplus
  • Lux.softmax
  • Lux.tanh

Keyword arguments

  • config: a dictionary that maps supported Lux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Lux.sigmoid => MathOptAI.Sigmoid() or Lux.relu => MathOptAI.QuadraticReLU().

Example

julia> using Lux, MathOptAI, Random
+
+julia> rng = Random.MersenneTwister();
+
+julia> chain = Lux.Chain(Lux.Dense(1 => 16, Lux.relu), Lux.Dense(16 => 1))
+Chain(
+    layer_1 = Dense(1 => 16, relu),     # 32 parameters
+    layer_2 = Dense(16 => 1),           # 17 parameters
+)         # Total: 49 parameters,
+          #        plus 0 states.
+
+julia> parameters, state = Lux.setup(rng, chain);
+
+julia> predictor = MathOptAI.build_predictor(
+           (chain, parameters, state);
+           config = Dict(Lux.relu => MathOptAI.ReLU()),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 1, output: 16]
+ * ReLU()
+ * Affine(A, b) [input: 16, output: 1]
+
+julia> MathOptAI.build_predictor(
+           (chain, parameters, state);
+           config = Dict(Lux.relu => MathOptAI.ReLUQuadratic()),
+       )
+Pipeline with layers:
+ * Affine(A, b) [input: 1, output: 16]
+ * ReLUQuadratic()
+ * Affine(A, b) [input: 16, output: 1]
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::MathOptAI.PytorchModel,
+    x::Vector;
+    config::Dict = Dict{Any,Any}(),
+    reduced_space::Bool = false,
+    gray_box::Bool = false,
+)

Add a trained neural network from PyTorch via PythonCall.jl to model.

Supported layers

  • nn.Linear
  • nn.ReLU
  • nn.Sequential
  • nn.Sigmoid
  • nn.Softplus
  • nn.Tanh

Keyword arguments

  • config: a dictionary that maps Symbols to AbstractPredictors that control how the activation functions are reformulated. For example, :Sigmoid => MathOptAI.Sigmoid() or :ReLU => MathOptAI.QuadraticReLU(). The supported Symbols are :ReLU, :Sigmoid, :SoftPlus, and :Tanh.
  • gray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by torch.func.jacrev.
  • gray_box_hessian: if true, the gray box additionally computes the Hessian of the output using torch.func.hessian.
source
MathOptAI.build_predictor — Method
MathOptAI.build_predictor(
+    predictor::MathOptAI.PytorchModel;
+    config::Dict = Dict{Any,Any}(),
+    gray_box::Bool = false,
+    gray_box_hessian::Bool = false,
+)

Convert a trained neural network from PyTorch via PythonCall.jl to a Pipeline.

Supported layers

  • nn.Linear
  • nn.ReLU
  • nn.Sequential
  • nn.Sigmoid
  • nn.Softplus
  • nn.Tanh

Keyword arguments

  • config: a dictionary that maps Symbols to AbstractPredictors that control how the activation functions are reformulated. For example, :Sigmoid => MathOptAI.Sigmoid() or :ReLU => MathOptAI.QuadraticReLU(). The supported Symbols are :ReLU, :Sigmoid, :SoftPlus, and :Tanh.
  • gray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by torch.func.jacrev.
  • gray_box_hessian: if true, the gray box additionally computes the Hessian of the output using torch.func.hessian.
source
MathOptAI.add_predictor — Method
MathOptAI.add_predictor(
+    model::JuMP.AbstractModel,
+    predictor::StatsModels.TableRegressionModel,
+    x::DataFrames.DataFrame;
+    kwargs...,
+)

Add a trained regression model from StatsModels.jl to model, using the DataFrame x as input.

In most cases, predictor should be a GLM.jl predictor supported by MathOptAI, but trained using @formula and a DataFrame instead of the raw matrix input.

In general, x may have some columns that are constant (Float64) and some columns that are JuMP decision variables.

Keyword arguments

All keyword arguments are passed to the corresponding add_predictor of the GLM extension.

Example

julia> using DataFrames, GLM, JuMP, MathOptAI
+
+julia> train_df = DataFrames.DataFrame(x1 = rand(10), x2 = rand(10));
+
+julia> train_df.y = 1.0 .* train_df.x1 + 2.0 .* train_df.x2 .+ rand(10);
+
+julia> predictor = GLM.lm(GLM.@formula(y ~ x1 + x2), train_df);
+
+julia> model = Model();
+
+julia> test_df = DataFrames.DataFrame(
+           x1 = rand(6),
+           x2 = @variable(model, [1:6]),
+       );
+
+julia> test_df.y, _ = MathOptAI.add_predictor(model, predictor, test_df);
+
+julia> test_df.y
+6-element Vector{VariableRef}:
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
source
diff --git a/v0.1.4/assets/documenter.js b/v0.1.4/assets/documenter.js new file mode 100644 index 00000000..82252a11 --- /dev/null +++ b/v0.1.4/assets/documenter.js @@ -0,0 +1,1064 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on( + "click", + ".docstring .docstring-article-toggle-button", + function () { + let articleToggleTitle = "Expand docstring"; + const parent = $(this).parent(); + + debounce(() => { + if (parent.siblings("section").is(":visible")) { + parent + .find("a.docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + parent + .find("a.docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + parent + .children(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + parent.siblings("section").slideToggle(); + }); + } +); + +$(document).on("click", ".docs-article-toggle-button", function (event) { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + let animationSpeed = event.noToggleAnimation ? 0 : 400; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $("a.docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(animationSpeed); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $("a.docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(animationSpeed); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-xmark"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-xmark"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let meta = $("div[data-docstringscollapsed]").data(); + + if (meta?.docstringscollapsed) { + $("#documenter-article-toggle-button").trigger({ + type: "click", + noToggleAnimation: true, + }); + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +/* +To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +PSEUDOCODE: + +Searching happens automatically as the user types or adjusts the selected filters. +To preserve responsiveness, as much as possible of the slow parts of the search are done +in a web worker. Searching and result generation are done in the worker, and filtering and +DOM updates are done in the main thread. The filters are in the main thread as they should +be very quick to apply. This lets filters be changed without re-searching with minisearch +(which is possible even if filtering is on the worker thread) and also lets filters be +changed _while_ the worker is searching and without message passing (neither of which are +possible if filtering is on the worker thread) + +SEARCH WORKER: + +Import minisearch + +Build index + +On message from main thread + run search + find the first 200 unique results from each category, and compute their divs for display + note that this is necessary and sufficient information for the main thread to find the + first 200 unique results from any given filter set + post results to main thread + +MAIN: + +Launch worker + +Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results) + +On text update + if worker is not running, launch_search() + +launch_search + set worker_is_running to true, set last_search_text to the search text + post the search query to worker + +on message from worker + if last_search_text is not the same as the text in the search field, + the latest search result is not reflective of the latest search query, so update again + launch_search() + otherwise + set worker_is_running to false + + regardless, display the new search results to the user + save the unfiltered_results as a global + update_search() + +on filter click + adjust the filter selection + update_search() + +update_search + apply search filters by looping through the unfiltered_results and finding the first 200 + unique results that match the filters + + Update the DOM +*/ + +/////// SEARCH WORKER /////// + +function worker_function(documenterSearchIndex, documenterBaseURL, filters) { + importScripts( + "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js" + ); + + let data = documenterSearchIndex.map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; + }); + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", + ]); + + let index = new MiniSearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + + word = word.toLowerCase(); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not + // find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + prefix: true, + boost: { title: 100 }, + fuzzy: 2, + }, + }); + + index.addAll(data); + + /** + * Used to map characters to HTML entities. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const htmlEscapes = { + "&": "&", + "<": "<", + ">": ">", + '"': """, + "'": "'", + }; + + /** + * Used to match HTML entities and HTML characters. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const reUnescapedHtml = /[&<>"']/g; + const reHasUnescapedHtml = RegExp(reUnescapedHtml.source); + + /** + * Escape function from lodash + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + function escape(string) { + return string && reHasUnescapedHtml.test(string) + ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr]) + : string || ""; + } + + /** + * RegX escape function from MDN + * Refer: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping + */ + function escapeRegExp(string) { + return string.replace(/[.*+?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string + } + + /** + * Make the result component given a minisearch result data object and the value + * of the search input as queryString. To view the result object structure, refer: + * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ + function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + searchstring = escapeRegExp(querystring); + let textindex = new RegExp(`${searchstring}`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + text = text.length ? escape(text) : ""; + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`${escape(searchstring)}`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${escape(result.title)}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+ + ${search_divider} + `; + + return result_div; + } + + self.onmessage = function (e) { + let query = e.data; + let results = index.search(query, { + filter: (result) => { + // Only return relevant results + return result.score >= 1; + }, + combineWith: "AND", + }); + + // Pre-filter to deduplicate and limit to 200 per category to the extent + // possible without knowing what the filters are. + let filtered_results = []; + let counts = {}; + for (let filter of filters) { + counts[filter] = 0; + } + let present = {}; + + for (let result of results) { + cat = result.category; + cnt = counts[cat]; + if (cnt < 200) { + id = cat + "---" + result.location; + if (present[id]) { + continue; + } + present[id] = true; + filtered_results.push({ + location: result.location, + category: cat, + div: make_search_result(result, query), + }); + } + } + + postMessage(filtered_results); + }; +} + +// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript! +const filters = [ + ...new Set(documenterSearchIndex["docs"].map((x) => x.category)), +]; +const worker_str = + "(" + + worker_function.toString() + + ")(" + + JSON.stringify(documenterSearchIndex["docs"]) + + "," + + JSON.stringify(documenterBaseURL) + + "," + + JSON.stringify(filters) + + ")"; +const worker_blob = new Blob([worker_str], { type: "text/javascript" }); +const worker = new Worker(URL.createObjectURL(worker_blob)); + +/////// SEARCH MAIN /////// + +// Whether the worker is currently handling a search. This is a boolean +// as the worker only ever handles 1 or 0 searches at a time. +var worker_is_running = false; + +// The last search text that was sent to the worker. This is used to determine +// if the worker should be launched again when it reports back results. +var last_search_text = ""; + +// The results of the last search. This, in combination with the state of the filters +// in the DOM, is used compute the results to display on calls to update_search. +var unfiltered_results = []; + +// Which filter is currently selected +var selected_filter = ""; + +$(document).on("input", ".documenter-search-input", function (event) { + if (!worker_is_running) { + launch_search(); + } +}); + +function launch_search() { + worker_is_running = true; + last_search_text = $(".documenter-search-input").val(); + worker.postMessage(last_search_text); +} + +worker.onmessage = function (e) { + if (last_search_text !== $(".documenter-search-input").val()) { + launch_search(); + } else { + worker_is_running = false; + } + + unfiltered_results = e.data; + update_search(); +}; + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + selected_filter = ""; + } else { + selected_filter = $(this).text().toLowerCase(); + } + + // This updates search results and toggles classes for UI: + update_search(); +}); + +/** + * Make/Update the search component + */ +function update_search() { + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + if (selected_filter == "") { + results = unfiltered_results; + } else { + results = unfiltered_results.filter((result) => { + return selected_filter == result.category.toLowerCase(); + }); + } + + let search_result_container = ``; + let modal_filters = make_modal_body_filters(); + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + for (var i = 0, n = results.length; i < n && count < 200; ++i) { + let result = results[i]; + if (result.location && !links.includes(result.location)) { + search_results += result.div; + count++; + links.push(result.location); + } + } + + if (count == 1) { + count_str = "1 result"; + } else if (count == 200) { + count_str = "200+ results"; + } else { + count_str = count + " results"; + } + let result_count = `
${count_str}
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
+
No result found!
+ `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(` +
Type something to get started!
+ `); + } +} + +/** + * Make the modal filter html + * + * @returns string + */ +function make_modal_body_filters() { + let str = filters + .map((val) => { + if (selected_filter == val.toLowerCase()) { + return `${val}`; + } else { + return `${val}`; + } + }) + .join(""); + + return ` +
+ Filters: + ${str} +
`; +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); + }); + // Close the dialog if X is clicked + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); + }); + // Close dialog if ESC is pressed + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let search_modal_header = ` +
+
+

+ + + + +

+
+
+ +
+
+ `; + + let initial_search_body = ` +
Type something to get started!
+ `; + + let search_modal_footer = ` +
+ + Ctrl + + / to search + + esc to close +
+ `; + + $(document.body).append( + ` + + ` + ); + + document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); + }); + + document + .querySelector(".close-search-modal") + .addEventListener("click", () => { + closeModal(); + }); + + $(document).on("click", ".search-result-link", function () { + closeModal(); + }); + + document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; + }); + + // Functions to open and close a modal + function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); + } + + function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
Type something to get started!
+ `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); + } + + document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function () { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { + ev.preventDefault(); + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind("click", function (ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); + } + }); +}); + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function () { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css("max-width"), 10); + var L0 = e.width(); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on("orientationchange", resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function () { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if (typeof active !== "undefined") { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Theme picker setup +$(document).ready(function () { + // onchange callback + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); + } + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function () { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== "undefined") { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $( + "" + ); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}); + +}) diff --git a/v0.1.4/assets/themes/catppuccin-frappe.css b/v0.1.4/assets/themes/catppuccin-frappe.css new file mode 100644 index 00000000..32e3f008 --- /dev/null +++ b/v0.1.4/assets/themes/catppuccin-frappe.css @@ -0,0 +1 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.button.is-primary.is-light.is-hovered,html.theme--catppuccin-frappe .docstring>section>a.button.is-light.is-hovered.docs-sourcelink{background-color:#e2eafb;border-color:transparent;color:#153a8e}html.theme--catppuccin-frappe .button.is-primary.is-light:active,html.theme--catppuccin-frappe .docstring>section>a.button.is-light.docs-sourcelink:active,html.theme--catppuccin-frappe .button.is-primary.is-light.is-active,html.theme--catppuccin-frappe .docstring>section>a.button.is-light.is-active.docs-sourcelink{background-color:#d7e1f9;border-color:transparent;color:#153a8e}html.theme--catppuccin-frappe .button.is-link{background-color:#8caaee;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-link:hover,html.theme--catppuccin-frappe .button.is-link.is-hovered{background-color:#81a2ec;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-link:focus,html.theme--catppuccin-frappe 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.button.is-link.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#8caaee}html.theme--catppuccin-frappe .button.is-link.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-link.is-outlined{background-color:transparent;border-color:#8caaee;color:#8caaee}html.theme--catppuccin-frappe .button.is-link.is-outlined:hover,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-link.is-outlined:focus,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-focused{background-color:#8caaee;border-color:#8caaee;color:#fff}html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading::after{border-color:transparent transparent #8caaee #8caaee !important}html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-link.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-link.is-outlined{background-color:transparent;border-color:#8caaee;box-shadow:none;color:#8caaee}html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe 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.button.is-link.is-light.is-hovered{background-color:#e2eafb;border-color:transparent;color:#153a8e}html.theme--catppuccin-frappe .button.is-link.is-light:active,html.theme--catppuccin-frappe .button.is-link.is-light.is-active{background-color:#d7e1f9;border-color:transparent;color:#153a8e}html.theme--catppuccin-frappe .button.is-info{background-color:#81c8be;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info:hover,html.theme--catppuccin-frappe .button.is-info.is-hovered{background-color:#78c4b9;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info:focus,html.theme--catppuccin-frappe .button.is-info.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info:focus:not(:active),html.theme--catppuccin-frappe .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(129,200,190,0.25)}html.theme--catppuccin-frappe .button.is-info:active,html.theme--catppuccin-frappe .button.is-info.is-active{background-color:#6fc0b5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info{background-color:#81c8be;border-color:#81c8be;box-shadow:none}html.theme--catppuccin-frappe .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted:hover,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-info.is-outlined{background-color:transparent;border-color:#81c8be;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-outlined:hover,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-info.is-outlined:focus,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-focused{background-color:#81c8be;border-color:#81c8be;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #81c8be #81c8be !important}html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-outlined{background-color:transparent;border-color:#81c8be;box-shadow:none;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #81c8be #81c8be !important}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-light{background-color:#f1f9f8;color:#2d675f}html.theme--catppuccin-frappe .button.is-info.is-light:hover,html.theme--catppuccin-frappe .button.is-info.is-light.is-hovered{background-color:#e8f5f3;border-color:transparent;color:#2d675f}html.theme--catppuccin-frappe .button.is-info.is-light:active,html.theme--catppuccin-frappe .button.is-info.is-light.is-active{background-color:#dff1ef;border-color:transparent;color:#2d675f}html.theme--catppuccin-frappe 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.button.is-success{background-color:#a6d189;border-color:#a6d189;box-shadow:none}html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-focused{background-color:#a6d189;border-color:#a6d189;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-light{background-color:#f4f9f0;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:hover,html.theme--catppuccin-frappe .button.is-success.is-light.is-hovered{background-color:#edf6e7;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:active,html.theme--catppuccin-frappe .button.is-success.is-light.is-active{background-color:#e6f2de;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe 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.button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-warning.is-outlined:focus,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-focused{background-color:#e5c890;border-color:#e5c890;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #e5c890 #e5c890 !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e5c890 #e5c890 !important}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-light{background-color:#fbf7ee;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:hover,html.theme--catppuccin-frappe .button.is-warning.is-light.is-hovered{background-color:#f9f2e4;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:active,html.theme--catppuccin-frappe .button.is-warning.is-light.is-active{background-color:#f6edda;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-danger{background-color:#e78284;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:hover,html.theme--catppuccin-frappe .button.is-danger.is-hovered{background-color:#e57779;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:focus,html.theme--catppuccin-frappe .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:focus:not(:active),html.theme--catppuccin-frappe .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(231,130,132,0.25)}html.theme--catppuccin-frappe .button.is-danger:active,html.theme--catppuccin-frappe .button.is-danger.is-active{background-color:#e36d6f;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger{background-color:#e78284;border-color:#e78284;box-shadow:none}html.theme--catppuccin-frappe .button.is-danger.is-inverted{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-frappe .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-focused{background-color:#e78284;border-color:#e78284;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-light{background-color:#fceeee;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:hover,html.theme--catppuccin-frappe .button.is-danger.is-light.is-hovered{background-color:#fae3e4;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:active,html.theme--catppuccin-frappe .button.is-danger.is-light.is-active{background-color:#f8d8d9;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-frappe .button.is-small:not(.is-rounded),html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .button.is-normal{font-size:1rem}html.theme--catppuccin-frappe .button.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .button.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .button[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button{background-color:#737994;border-color:#626880;box-shadow:none;opacity:.5}html.theme--catppuccin-frappe .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-frappe .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-frappe .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-frappe .button.is-static{background-color:#292c3c;border-color:#626880;color:#838ba7;box-shadow:none;pointer-events:none}html.theme--catppuccin-frappe .button.is-rounded,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-frappe .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-frappe .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-frappe .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-frappe .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-frappe .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-frappe .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-frappe .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-frappe .buttons.has-addons .button:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-frappe .buttons.has-addons .button:focus,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused,html.theme--catppuccin-frappe .buttons.has-addons .button:active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-frappe .buttons.has-addons .button:focus:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-frappe .buttons.has-addons .button:active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-frappe .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .buttons.is-centered{justify-content:center}html.theme--catppuccin-frappe .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-frappe .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-frappe .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-frappe .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-frappe .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-frappe .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-frappe .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-frappe .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-frappe .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-frappe .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-frappe .content li+li{margin-top:0.25em}html.theme--catppuccin-frappe .content p:not(:last-child),html.theme--catppuccin-frappe .content dl:not(:last-child),html.theme--catppuccin-frappe .content ol:not(:last-child),html.theme--catppuccin-frappe .content ul:not(:last-child),html.theme--catppuccin-frappe .content blockquote:not(:last-child),html.theme--catppuccin-frappe .content pre:not(:last-child),html.theme--catppuccin-frappe .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-frappe .content h1,html.theme--catppuccin-frappe .content h2,html.theme--catppuccin-frappe .content h3,html.theme--catppuccin-frappe .content h4,html.theme--catppuccin-frappe .content h5,html.theme--catppuccin-frappe .content h6{color:#c6d0f5;font-weight:600;line-height:1.125}html.theme--catppuccin-frappe .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-frappe .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-frappe .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-frappe .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-frappe .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-frappe .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-frappe .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-frappe .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-frappe .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-frappe .content blockquote{background-color:#292c3c;border-left:5px solid #626880;padding:1.25em 1.5em}html.theme--catppuccin-frappe .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-frappe .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-frappe .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-frappe .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-frappe .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-frappe .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-frappe .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-frappe .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-frappe .content ul ul ul{list-style-type:square}html.theme--catppuccin-frappe .content dd{margin-left:2em}html.theme--catppuccin-frappe .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-frappe .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-frappe .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-frappe .content figure img{display:inline-block}html.theme--catppuccin-frappe .content figure figcaption{font-style:italic}html.theme--catppuccin-frappe .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-frappe .content sup,html.theme--catppuccin-frappe .content sub{font-size:75%}html.theme--catppuccin-frappe .content table{width:100%}html.theme--catppuccin-frappe .content table td,html.theme--catppuccin-frappe .content table th{border:1px solid #626880;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-frappe .content table th{color:#b0bef1}html.theme--catppuccin-frappe .content table th:not([align]){text-align:inherit}html.theme--catppuccin-frappe .content table thead td,html.theme--catppuccin-frappe .content table thead th{border-width:0 0 2px;color:#b0bef1}html.theme--catppuccin-frappe .content table tfoot td,html.theme--catppuccin-frappe .content table tfoot th{border-width:2px 0 0;color:#b0bef1}html.theme--catppuccin-frappe .content table tbody tr:last-child td,html.theme--catppuccin-frappe .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-frappe .content .tabs li+li{margin-top:0}html.theme--catppuccin-frappe .content.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-frappe .content.is-normal{font-size:1rem}html.theme--catppuccin-frappe .content.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .content.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-frappe .icon.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-frappe .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-frappe .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-frappe .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-frappe .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-frappe .icon-text 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a.navbar-item:focus,html.theme--catppuccin-frappe a.navbar-item:focus-within,html.theme--catppuccin-frappe a.navbar-item:hover,html.theme--catppuccin-frappe a.navbar-item.is-active,html.theme--catppuccin-frappe .navbar-link:focus,html.theme--catppuccin-frappe .navbar-link:focus-within,html.theme--catppuccin-frappe .navbar-link:hover,html.theme--catppuccin-frappe .navbar-link.is-active{background-color:rgba(0,0,0,0);color:#8caaee}html.theme--catppuccin-frappe .navbar-item{flex-grow:0;flex-shrink:0}html.theme--catppuccin-frappe .navbar-item img{max-height:1.75rem}html.theme--catppuccin-frappe .navbar-item.has-dropdown{padding:0}html.theme--catppuccin-frappe .navbar-item.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .navbar-item.is-tab{border-bottom:1px solid transparent;min-height:4rem;padding-bottom:calc(0.5rem - 1px)}html.theme--catppuccin-frappe .navbar-item.is-tab:focus,html.theme--catppuccin-frappe .navbar-item.is-tab:hover{background-color:rgba(0,0,0,0);border-bottom-color:#8caaee}html.theme--catppuccin-frappe .navbar-item.is-tab.is-active{background-color:rgba(0,0,0,0);border-bottom-color:#8caaee;border-bottom-style:solid;border-bottom-width:3px;color:#8caaee;padding-bottom:calc(0.5rem - 3px)}html.theme--catppuccin-frappe .navbar-content{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .navbar-link:not(.is-arrowless){padding-right:2.5em}html.theme--catppuccin-frappe .navbar-link:not(.is-arrowless)::after{border-color:#fff;margin-top:-0.375em;right:1.125em}html.theme--catppuccin-frappe .navbar-dropdown{font-size:0.875rem;padding-bottom:0.5rem;padding-top:0.5rem}html.theme--catppuccin-frappe .navbar-dropdown .navbar-item{padding-left:1.5rem;padding-right:1.5rem}html.theme--catppuccin-frappe .navbar-divider{background-color:rgba(0,0,0,0.2);border:none;display:none;height:2px;margin:0.5rem 0}@media screen and (max-width: 1055px){html.theme--catppuccin-frappe 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a.navbar-item:hover{background-color:rgba(0,0,0,0);color:#838ba7}html.theme--catppuccin-frappe .navbar-dropdown a.navbar-item.is-active{background-color:rgba(0,0,0,0);color:#8caaee}.navbar.is-spaced html.theme--catppuccin-frappe .navbar-dropdown,html.theme--catppuccin-frappe .navbar-dropdown.is-boxed{border-radius:8px;border-top:none;box-shadow:0 8px 8px rgba(10,10,10,0.1), 0 0 0 1px rgba(10,10,10,0.1);display:block;opacity:0;pointer-events:none;top:calc(100% + (-4px));transform:translateY(-5px);transition-duration:86ms;transition-property:opacity, transform}html.theme--catppuccin-frappe .navbar-dropdown.is-right{left:auto;right:0}html.theme--catppuccin-frappe .navbar-divider{display:block}html.theme--catppuccin-frappe .navbar>.container .navbar-brand,html.theme--catppuccin-frappe .container>.navbar .navbar-brand{margin-left:-.75rem}html.theme--catppuccin-frappe .navbar>.container .navbar-menu,html.theme--catppuccin-frappe .container>.navbar 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body.has-spaced-navbar-fixed-bottom{padding-bottom:6rem}html.theme--catppuccin-frappe a.navbar-item.is-active,html.theme--catppuccin-frappe .navbar-link.is-active{color:#8caaee}html.theme--catppuccin-frappe a.navbar-item.is-active:not(:focus):not(:hover),html.theme--catppuccin-frappe .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--catppuccin-frappe .navbar-item.has-dropdown:focus .navbar-link,html.theme--catppuccin-frappe .navbar-item.has-dropdown:hover .navbar-link,html.theme--catppuccin-frappe .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--catppuccin-frappe .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--catppuccin-frappe .pagination{font-size:1rem;margin:-.25rem}html.theme--catppuccin-frappe .pagination.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.pagination{font-size:.75rem}html.theme--catppuccin-frappe .pagination.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .pagination.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .pagination.is-rounded .pagination-previous,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.pagination .pagination-previous,html.theme--catppuccin-frappe .pagination.is-rounded .pagination-next,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.pagination .pagination-next{padding-left:1em;padding-right:1em;border-radius:9999px}html.theme--catppuccin-frappe .pagination.is-rounded .pagination-link,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.pagination .pagination-link{border-radius:9999px}html.theme--catppuccin-frappe .pagination,html.theme--catppuccin-frappe .pagination-list{align-items:center;display:flex;justify-content:center;text-align:center}html.theme--catppuccin-frappe .pagination-previous,html.theme--catppuccin-frappe .pagination-next,html.theme--catppuccin-frappe .pagination-link,html.theme--catppuccin-frappe .pagination-ellipsis{font-size:1em;justify-content:center;margin:.25rem;padding-left:.5em;padding-right:.5em;text-align:center}html.theme--catppuccin-frappe .pagination-previous,html.theme--catppuccin-frappe .pagination-next,html.theme--catppuccin-frappe .pagination-link{border-color:#626880;color:#8caaee;min-width:2.5em}html.theme--catppuccin-frappe .pagination-previous:hover,html.theme--catppuccin-frappe .pagination-next:hover,html.theme--catppuccin-frappe .pagination-link:hover{border-color:#737994;color:#99d1db}html.theme--catppuccin-frappe .pagination-previous:focus,html.theme--catppuccin-frappe .pagination-next:focus,html.theme--catppuccin-frappe .pagination-link:focus{border-color:#737994}html.theme--catppuccin-frappe .pagination-previous:active,html.theme--catppuccin-frappe .pagination-next:active,html.theme--catppuccin-frappe .pagination-link:active{box-shadow:inset 0 1px 2px 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768px){html.theme--catppuccin-frappe .pagination{flex-wrap:wrap}html.theme--catppuccin-frappe .pagination-previous,html.theme--catppuccin-frappe .pagination-next{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .pagination-list li{flex-grow:1;flex-shrink:1}}@media screen and (min-width: 769px),print{html.theme--catppuccin-frappe .pagination-list{flex-grow:1;flex-shrink:1;justify-content:flex-start;order:1}html.theme--catppuccin-frappe .pagination-previous,html.theme--catppuccin-frappe .pagination-next,html.theme--catppuccin-frappe .pagination-link,html.theme--catppuccin-frappe .pagination-ellipsis{margin-bottom:0;margin-top:0}html.theme--catppuccin-frappe .pagination-previous{order:2}html.theme--catppuccin-frappe .pagination-next{order:3}html.theme--catppuccin-frappe .pagination{justify-content:space-between;margin-bottom:0;margin-top:0}html.theme--catppuccin-frappe .pagination.is-centered .pagination-previous{order:1}html.theme--catppuccin-frappe .pagination.is-centered 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a.is-active{border-bottom-color:#0a0a0a}html.theme--catppuccin-frappe .panel.is-black .panel-block.is-active .panel-icon{color:#0a0a0a}html.theme--catppuccin-frappe .panel.is-light .panel-heading{background-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .panel.is-light .panel-tabs a.is-active{border-bottom-color:#f5f5f5}html.theme--catppuccin-frappe .panel.is-light .panel-block.is-active .panel-icon{color:#f5f5f5}html.theme--catppuccin-frappe .panel.is-dark .panel-heading,html.theme--catppuccin-frappe .content kbd.panel .panel-heading{background-color:#414559;color:#fff}html.theme--catppuccin-frappe .panel.is-dark .panel-tabs a.is-active,html.theme--catppuccin-frappe .content kbd.panel .panel-tabs a.is-active{border-bottom-color:#414559}html.theme--catppuccin-frappe .panel.is-dark .panel-block.is-active .panel-icon,html.theme--catppuccin-frappe .content kbd.panel .panel-block.is-active .panel-icon{color:#414559}html.theme--catppuccin-frappe .panel.is-primary 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.button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black:focus,html.theme--catppuccin-latte .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black:focus:not(:active),html.theme--catppuccin-latte .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--catppuccin-latte .button.is-black:active,html.theme--catppuccin-latte .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--catppuccin-latte .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted:hover,html.theme--catppuccin-latte .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-outlined:hover,html.theme--catppuccin-latte .button.is-black.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-black.is-outlined:focus,html.theme--catppuccin-latte .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-light{background-color:#f5f5f5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:hover,html.theme--catppuccin-latte .button.is-light.is-hovered{background-color:#eee;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:focus,html.theme--catppuccin-latte .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:focus:not(:active),html.theme--catppuccin-latte .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(245,245,245,0.25)}html.theme--catppuccin-latte .button.is-light:active,html.theme--catppuccin-latte .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light{background-color:#f5f5f5;border-color:#f5f5f5;box-shadow:none}html.theme--catppuccin-latte 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.button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark,html.theme--catppuccin-latte .content kbd.button{background-color:#ccd0da;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark:hover,html.theme--catppuccin-latte .content kbd.button:hover,html.theme--catppuccin-latte .button.is-dark.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-hovered{background-color:#c5c9d5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark:focus,html.theme--catppuccin-latte .content kbd.button:focus,html.theme--catppuccin-latte .button.is-dark.is-focused,html.theme--catppuccin-latte .content kbd.button.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte 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kbd.button.is-inverted{background-color:rgba(0,0,0,0.7);color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted:hover,html.theme--catppuccin-latte .content kbd.button.is-inverted:hover,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-inverted[disabled],html.theme--catppuccin-latte .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-inverted,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-loading::after,html.theme--catppuccin-latte .content kbd.button.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-dark.is-outlined,html.theme--catppuccin-latte .content kbd.button.is-outlined{background-color:transparent;border-color:#ccd0da;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-outlined:hover,html.theme--catppuccin-latte .content kbd.button.is-outlined:hover,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-dark.is-outlined:focus,html.theme--catppuccin-latte .content kbd.button.is-outlined:focus,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-focused,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-focused{background-color:#ccd0da;border-color:#ccd0da;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #ccd0da #ccd0da !important}html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-dark.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-outlined{background-color:transparent;border-color:#ccd0da;box-shadow:none;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ccd0da #ccd0da !important}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-primary,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink{background-color:#1e66f5;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-primary:hover,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#125ef4;border-color:transparent;color:#fff}html.theme--catppuccin-latte 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.docstring>section>a.button.is-active.docs-sourcelink{background-color:#0b57ef;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-primary[disabled],html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-primary,fieldset[disabled] html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink{background-color:#1e66f5;border-color:#1e66f5;box-shadow:none}html.theme--catppuccin-latte .button.is-primary.is-inverted,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.docs-sourcelink{background-color:#fff;color:#1e66f5}html.theme--catppuccin-latte .button.is-primary.is-inverted:hover,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-inverted.is-hovered,html.theme--catppuccin-latte 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.button.is-success.is-light{background-color:#f1fbef;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:hover,html.theme--catppuccin-latte .button.is-success.is-light.is-hovered{background-color:#e8f8e5;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:active,html.theme--catppuccin-latte .button.is-success.is-light.is-active{background-color:#e0f5db;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:hover,html.theme--catppuccin-latte .button.is-warning.is-hovered{background-color:#d4871c;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus,html.theme--catppuccin-latte .button.is-warning.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus:not(:active),html.theme--catppuccin-latte .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(223,142,29,0.25)}html.theme--catppuccin-latte .button.is-warning:active,html.theme--catppuccin-latte .button.is-warning.is-active{background-color:#c8801a;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:#df8e1d;box-shadow:none}html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-focused{background-color:#df8e1d;border-color:#df8e1d;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-light{background-color:#fdf6ed;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:hover,html.theme--catppuccin-latte .button.is-warning.is-light.is-hovered{background-color:#fbf1e2;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:active,html.theme--catppuccin-latte .button.is-warning.is-light.is-active{background-color:#faebd6;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:hover,html.theme--catppuccin-latte .button.is-danger.is-hovered{background-color:#c60e36;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus,html.theme--catppuccin-latte .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus:not(:active),html.theme--catppuccin-latte .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(210,15,57,0.25)}html.theme--catppuccin-latte .button.is-danger:active,html.theme--catppuccin-latte .button.is-danger.is-active{background-color:#ba0d33;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:#d20f39;box-shadow:none}html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-focused{background-color:#d20f39;border-color:#d20f39;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-light{background-color:#feecf0;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:hover,html.theme--catppuccin-latte .button.is-danger.is-light.is-hovered{background-color:#fde0e6;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:active,html.theme--catppuccin-latte .button.is-danger.is-light.is-active{background-color:#fcd4dd;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-latte .button.is-small:not(.is-rounded),html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .button.is-normal{font-size:1rem}html.theme--catppuccin-latte .button.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .button.is-large{font-size:1.5rem}html.theme--catppuccin-latte .button[disabled],fieldset[disabled] html.theme--catppuccin-latte .button{background-color:#9ca0b0;border-color:#acb0be;box-shadow:none;opacity:.5}html.theme--catppuccin-latte .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-latte .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-latte .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-latte .button.is-static{background-color:#e6e9ef;border-color:#acb0be;color:#8c8fa1;box-shadow:none;pointer-events:none}html.theme--catppuccin-latte .button.is-rounded,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-latte .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-latte .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-latte .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-latte .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-latte .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-latte .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-latte .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-latte .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-latte .buttons.has-addons .button:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-latte .buttons.has-addons .button:focus,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused,html.theme--catppuccin-latte .buttons.has-addons .button:active,html.theme--catppuccin-latte .buttons.has-addons .button.is-active,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-latte .buttons.has-addons .button:focus:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-latte .buttons.has-addons .button:active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-latte .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .buttons.is-centered{justify-content:center}html.theme--catppuccin-latte .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-latte .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-latte .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-latte .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-latte .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-latte .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-latte .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-latte .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-latte .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-latte .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-latte .content li+li{margin-top:0.25em}html.theme--catppuccin-latte .content p:not(:last-child),html.theme--catppuccin-latte .content dl:not(:last-child),html.theme--catppuccin-latte .content ol:not(:last-child),html.theme--catppuccin-latte .content ul:not(:last-child),html.theme--catppuccin-latte .content blockquote:not(:last-child),html.theme--catppuccin-latte .content pre:not(:last-child),html.theme--catppuccin-latte .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-latte .content h1,html.theme--catppuccin-latte .content h2,html.theme--catppuccin-latte .content h3,html.theme--catppuccin-latte .content h4,html.theme--catppuccin-latte .content h5,html.theme--catppuccin-latte .content h6{color:#4c4f69;font-weight:600;line-height:1.125}html.theme--catppuccin-latte .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-latte .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-latte .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-latte .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-latte .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-latte .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-latte .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-latte .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-latte .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-latte .content blockquote{background-color:#e6e9ef;border-left:5px solid #acb0be;padding:1.25em 1.5em}html.theme--catppuccin-latte .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-latte .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-latte .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-latte .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-latte .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-latte .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-latte .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-latte .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-latte .content ul ul ul{list-style-type:square}html.theme--catppuccin-latte .content dd{margin-left:2em}html.theme--catppuccin-latte .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-latte .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-latte .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-latte .content figure img{display:inline-block}html.theme--catppuccin-latte .content figure figcaption{font-style:italic}html.theme--catppuccin-latte .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-latte .content sup,html.theme--catppuccin-latte .content sub{font-size:75%}html.theme--catppuccin-latte .content table{width:100%}html.theme--catppuccin-latte .content table td,html.theme--catppuccin-latte .content table th{border:1px solid #acb0be;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-latte .content table th{color:#41445a}html.theme--catppuccin-latte .content table th:not([align]){text-align:inherit}html.theme--catppuccin-latte .content table thead td,html.theme--catppuccin-latte .content table thead th{border-width:0 0 2px;color:#41445a}html.theme--catppuccin-latte .content table tfoot td,html.theme--catppuccin-latte .content table tfoot th{border-width:2px 0 0;color:#41445a}html.theme--catppuccin-latte .content table tbody tr:last-child td,html.theme--catppuccin-latte .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-latte .content .tabs li+li{margin-top:0}html.theme--catppuccin-latte .content.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-latte 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.file.is-boxed .file-name{border-width:0 1px 1px}html.theme--catppuccin-latte .file.is-boxed .file-icon{height:1.5em;width:1.5em}html.theme--catppuccin-latte .file.is-boxed .file-icon .fa{font-size:21px}html.theme--catppuccin-latte .file.is-boxed.is-small .file-icon .fa,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-boxed .file-icon .fa{font-size:14px}html.theme--catppuccin-latte .file.is-boxed.is-medium .file-icon .fa{font-size:28px}html.theme--catppuccin-latte .file.is-boxed.is-large .file-icon .fa{font-size:35px}html.theme--catppuccin-latte .file.is-boxed.has-name .file-cta{border-radius:.4em .4em 0 0}html.theme--catppuccin-latte .file.is-boxed.has-name .file-name{border-radius:0 0 .4em .4em;border-width:0 1px 1px}html.theme--catppuccin-latte .file.is-centered{justify-content:center}html.theme--catppuccin-latte .file.is-fullwidth .file-label{width:100%}html.theme--catppuccin-latte .file.is-fullwidth .file-name{flex-grow:1;max-width:none}html.theme--catppuccin-latte .file.is-right{justify-content:flex-end}html.theme--catppuccin-latte .file.is-right .file-cta{border-radius:0 .4em .4em 0}html.theme--catppuccin-latte .file.is-right .file-name{border-radius:.4em 0 0 .4em;border-width:1px 0 1px 1px;order:-1}html.theme--catppuccin-latte .file-label{align-items:stretch;display:flex;cursor:pointer;justify-content:flex-start;overflow:hidden;position:relative}html.theme--catppuccin-latte .file-label:hover .file-cta{background-color:#c5c9d5;color:#41445a}html.theme--catppuccin-latte .file-label:hover .file-name{border-color:#a5a9b8}html.theme--catppuccin-latte .file-label:active .file-cta{background-color:#bdc2cf;color:#41445a}html.theme--catppuccin-latte .file-label:active .file-name{border-color:#9ea2b3}html.theme--catppuccin-latte .file-input{height:100%;left:0;opacity:0;outline:none;position:absolute;top:0;width:100%}html.theme--catppuccin-latte .file-cta,html.theme--catppuccin-latte .file-name{border-color:#acb0be;border-radius:.4em;font-size:1em;padding-left:1em;padding-right:1em;white-space:nowrap}html.theme--catppuccin-latte .file-cta{background-color:#ccd0da;color:#4c4f69}html.theme--catppuccin-latte .file-name{border-color:#acb0be;border-style:solid;border-width:1px 1px 1px 0;display:block;max-width:16em;overflow:hidden;text-align:inherit;text-overflow:ellipsis}html.theme--catppuccin-latte .file-icon{align-items:center;display:flex;height:1em;justify-content:center;margin-right:.5em;width:1em}html.theme--catppuccin-latte .file-icon .fa{font-size:14px}html.theme--catppuccin-latte .label{color:#41445a;display:block;font-size:1rem;font-weight:700}html.theme--catppuccin-latte .label:not(:last-child){margin-bottom:0.5em}html.theme--catppuccin-latte .label.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.label{font-size:.75rem}html.theme--catppuccin-latte .label.is-medium{font-size:1.25rem}html.theme--catppuccin-latte 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.field.has-addons{display:flex;justify-content:flex-start}html.theme--catppuccin-latte .field.has-addons .control:not(:last-child){margin-right:-1px}html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .button,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .input,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:not(:first-child):not(:last-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .select select{border-radius:0}html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .button,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .input,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:first-child:not(:only-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .select select{border-bottom-right-radius:0;border-top-right-radius:0}html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .button,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .input,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:last-child:not(:only-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .select select{border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-hovered:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-hovered:not([disabled]){z-index:2}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .button.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .button.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):focus,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .input.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-focused:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):active,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .input.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-active:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .select select.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .select select.is-active:not([disabled]){z-index:3}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):focus:hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):active:hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-active:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-active:not([disabled]):hover{z-index:4}html.theme--catppuccin-latte .field.has-addons .control.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .field.has-addons.has-addons-centered{justify-content:center}html.theme--catppuccin-latte .field.has-addons.has-addons-right{justify-content:flex-end}html.theme--catppuccin-latte .field.has-addons.has-addons-fullwidth 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.field.is-grouped.is-grouped-multiline:not(:last-child){margin-bottom:0}@media screen and (min-width: 769px),print{html.theme--catppuccin-latte .field.is-horizontal{display:flex}}html.theme--catppuccin-latte .field-label .label{font-size:inherit}@media screen and (max-width: 768px){html.theme--catppuccin-latte .field-label{margin-bottom:0.5rem}}@media screen and (min-width: 769px),print{html.theme--catppuccin-latte .field-label{flex-basis:0;flex-grow:1;flex-shrink:0;margin-right:1.5rem;text-align:right}html.theme--catppuccin-latte .field-label.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.field-label{font-size:.75rem;padding-top:0.375em}html.theme--catppuccin-latte .field-label.is-normal{padding-top:0.375em}html.theme--catppuccin-latte .field-label.is-medium{font-size:1.25rem;padding-top:0.375em}html.theme--catppuccin-latte .field-label.is-large{font-size:1.5rem;padding-top:0.375em}}html.theme--catppuccin-latte .field-body .field 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form.docs-search>input~.icon,html.theme--catppuccin-latte .control.has-icons-right .select.is-small~.icon{font-size:.75rem}html.theme--catppuccin-latte .control.has-icons-left .input.is-medium~.icon,html.theme--catppuccin-latte .control.has-icons-left #documenter .docs-sidebar form.docs-search>input.is-medium~.icon,html.theme--catppuccin-latte #documenter .docs-sidebar .control.has-icons-left form.docs-search>input.is-medium~.icon,html.theme--catppuccin-latte .control.has-icons-left .select.is-medium~.icon,html.theme--catppuccin-latte .control.has-icons-right .input.is-medium~.icon,html.theme--catppuccin-latte .control.has-icons-right #documenter .docs-sidebar form.docs-search>input.is-medium~.icon,html.theme--catppuccin-latte #documenter .docs-sidebar .control.has-icons-right form.docs-search>input.is-medium~.icon,html.theme--catppuccin-latte .control.has-icons-right .select.is-medium~.icon{font-size:1.25rem}html.theme--catppuccin-latte .control.has-icons-left .input.is-large~.icon,html.theme--catppuccin-latte .control.has-icons-left #documenter .docs-sidebar form.docs-search>input.is-large~.icon,html.theme--catppuccin-latte #documenter .docs-sidebar .control.has-icons-left form.docs-search>input.is-large~.icon,html.theme--catppuccin-latte .control.has-icons-left .select.is-large~.icon,html.theme--catppuccin-latte .control.has-icons-right .input.is-large~.icon,html.theme--catppuccin-latte .control.has-icons-right #documenter .docs-sidebar form.docs-search>input.is-large~.icon,html.theme--catppuccin-latte #documenter .docs-sidebar .control.has-icons-right form.docs-search>input.is-large~.icon,html.theme--catppuccin-latte .control.has-icons-right .select.is-large~.icon{font-size:1.5rem}html.theme--catppuccin-latte .control.has-icons-left .icon,html.theme--catppuccin-latte .control.has-icons-right .icon{color:#acb0be;height:2.5em;pointer-events:none;position:absolute;top:0;width:2.5em;z-index:4}html.theme--catppuccin-latte 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.pagination-list{align-items:center;display:flex;justify-content:center;text-align:center}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next,html.theme--catppuccin-latte .pagination-link,html.theme--catppuccin-latte .pagination-ellipsis{font-size:1em;justify-content:center;margin:.25rem;padding-left:.5em;padding-right:.5em;text-align:center}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next,html.theme--catppuccin-latte .pagination-link{border-color:#acb0be;color:#1e66f5;min-width:2.5em}html.theme--catppuccin-latte .pagination-previous:hover,html.theme--catppuccin-latte .pagination-next:hover,html.theme--catppuccin-latte .pagination-link:hover{border-color:#9ca0b0;color:#04a5e5}html.theme--catppuccin-latte .pagination-previous:focus,html.theme--catppuccin-latte .pagination-next:focus,html.theme--catppuccin-latte .pagination-link:focus{border-color:#9ca0b0}html.theme--catppuccin-latte 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kbd.button.is-outlined{background-color:transparent;border-color:#363a4f;box-shadow:none;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-macchiato .content 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.button.is-info.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-info.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-focused{background-color:#8bd5ca;border-color:#8bd5ca;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #8bd5ca #8bd5ca !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-outlined{background-color:transparent;border-color:#8bd5ca;box-shadow:none;color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #8bd5ca #8bd5ca !important}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-light{background-color:#f0faf8;color:#276d62}html.theme--catppuccin-macchiato .button.is-info.is-light:hover,html.theme--catppuccin-macchiato .button.is-info.is-light.is-hovered{background-color:#e7f6f4;border-color:transparent;color:#276d62}html.theme--catppuccin-macchiato .button.is-info.is-light:active,html.theme--catppuccin-macchiato .button.is-info.is-light.is-active{background-color:#ddf3f0;border-color:transparent;color:#276d62}html.theme--catppuccin-macchiato .button.is-success{background-color:#a6da95;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:hover,html.theme--catppuccin-macchiato .button.is-success.is-hovered{background-color:#9ed78c;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:focus,html.theme--catppuccin-macchiato .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:focus:not(:active),html.theme--catppuccin-macchiato .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,218,149,0.25)}html.theme--catppuccin-macchiato .button.is-success:active,html.theme--catppuccin-macchiato .button.is-success.is-active{background-color:#96d382;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success{background-color:#a6da95;border-color:#a6da95;box-shadow:none}html.theme--catppuccin-macchiato .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined{background-color:transparent;border-color:#a6da95;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-success.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-focused{background-color:#a6da95;border-color:#a6da95;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6da95 #a6da95 !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-outlined{background-color:transparent;border-color:#a6da95;box-shadow:none;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6da95 #a6da95 !important}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-light{background-color:#f2faf0;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:hover,html.theme--catppuccin-macchiato .button.is-success.is-light.is-hovered{background-color:#eaf6e6;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:active,html.theme--catppuccin-macchiato .button.is-success.is-light.is-active{background-color:#e2f3dd;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:hover,html.theme--catppuccin-macchiato .button.is-warning.is-hovered{background-color:#eccf94;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus,html.theme--catppuccin-macchiato .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus:not(:active),html.theme--catppuccin-macchiato .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(238,212,159,0.25)}html.theme--catppuccin-macchiato .button.is-warning:active,html.theme--catppuccin-macchiato .button.is-warning.is-active{background-color:#eaca89;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:#eed49f;box-shadow:none}html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-focused{background-color:#eed49f;border-color:#eed49f;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-light{background-color:#fcf7ee;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:hover,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-hovered{background-color:#faf2e3;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:active,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-active{background-color:#f8eed8;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:hover,html.theme--catppuccin-macchiato .button.is-danger.is-hovered{background-color:#eb7c8c;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus,html.theme--catppuccin-macchiato .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus:not(:active),html.theme--catppuccin-macchiato .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(237,135,150,0.25)}html.theme--catppuccin-macchiato .button.is-danger:active,html.theme--catppuccin-macchiato .button.is-danger.is-active{background-color:#ea7183;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:#ed8796;box-shadow:none}html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-macchiato .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-focused{background-color:#ed8796;border-color:#ed8796;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-light{background-color:#fcedef;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:hover,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-hovered{background-color:#fbe2e6;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:active,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-active{background-color:#f9d7dc;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-small:not(.is-rounded),html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-macchiato .button.is-normal{font-size:1rem}html.theme--catppuccin-macchiato .button.is-medium{font-size:1.25rem}html.theme--catppuccin-macchiato .button.is-large{font-size:1.5rem}html.theme--catppuccin-macchiato .button[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button{background-color:#6e738d;border-color:#5b6078;box-shadow:none;opacity:.5}html.theme--catppuccin-macchiato .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-macchiato .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-macchiato .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-macchiato .button.is-static{background-color:#1e2030;border-color:#5b6078;color:#8087a2;box-shadow:none;pointer-events:none}html.theme--catppuccin-macchiato .button.is-rounded,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-macchiato .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-macchiato .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-macchiato .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-macchiato .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-macchiato .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-macchiato .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-macchiato .buttons.are-small 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.container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-macchiato .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-macchiato .content li+li{margin-top:0.25em}html.theme--catppuccin-macchiato .content p:not(:last-child),html.theme--catppuccin-macchiato .content dl:not(:last-child),html.theme--catppuccin-macchiato .content ol:not(:last-child),html.theme--catppuccin-macchiato .content ul:not(:last-child),html.theme--catppuccin-macchiato .content blockquote:not(:last-child),html.theme--catppuccin-macchiato .content pre:not(:last-child),html.theme--catppuccin-macchiato .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-macchiato .content h1,html.theme--catppuccin-macchiato .content h2,html.theme--catppuccin-macchiato .content h3,html.theme--catppuccin-macchiato .content h4,html.theme--catppuccin-macchiato .content h5,html.theme--catppuccin-macchiato .content 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ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-macchiato .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-macchiato .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-macchiato .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-macchiato .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-macchiato .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-macchiato .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-macchiato .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-macchiato .content ul ul ul{list-style-type:square}html.theme--catppuccin-macchiato .content dd{margin-left:2em}html.theme--catppuccin-macchiato .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-macchiato 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form.docs-search>input.is-active{box-shadow:0 0 0 0.125em rgba(255,255,255,0.25)}html.theme--catppuccin-macchiato .is-black.textarea,html.theme--catppuccin-macchiato .is-black.input,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black{border-color:#0a0a0a}html.theme--catppuccin-macchiato .is-black.textarea:focus,html.theme--catppuccin-macchiato .is-black.input:focus,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black:focus,html.theme--catppuccin-macchiato .is-black.is-focused.textarea,html.theme--catppuccin-macchiato .is-black.is-focused.input,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-focused,html.theme--catppuccin-macchiato .is-black.textarea:active,html.theme--catppuccin-macchiato .is-black.input:active,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black:active,html.theme--catppuccin-macchiato 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html.theme--catppuccin-mocha .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-link.is-light{background-color:#ebf3fe;color:#063c93}html.theme--catppuccin-mocha .button.is-link.is-light:hover,html.theme--catppuccin-mocha .button.is-link.is-light.is-hovered{background-color:#dfebfe;border-color:transparent;color:#063c93}html.theme--catppuccin-mocha .button.is-link.is-light:active,html.theme--catppuccin-mocha .button.is-link.is-light.is-active{background-color:#d3e3fd;border-color:transparent;color:#063c93}html.theme--catppuccin-mocha .button.is-info{background-color:#94e2d5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:hover,html.theme--catppuccin-mocha .button.is-info.is-hovered{background-color:#8adfd1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:focus,html.theme--catppuccin-mocha .button.is-info.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:focus:not(:active),html.theme--catppuccin-mocha .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(148,226,213,0.25)}html.theme--catppuccin-mocha .button.is-info:active,html.theme--catppuccin-mocha .button.is-info.is-active{background-color:#80ddcd;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info{background-color:#94e2d5;border-color:#94e2d5;box-shadow:none}html.theme--catppuccin-mocha .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted:hover,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-info.is-outlined{background-color:transparent;border-color:#94e2d5;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-outlined:hover,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-info.is-outlined:focus,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-focused{background-color:#94e2d5;border-color:#94e2d5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #94e2d5 #94e2d5 !important}html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-outlined{background-color:transparent;border-color:#94e2d5;box-shadow:none;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #94e2d5 #94e2d5 !important}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-light{background-color:#effbf9;color:#207466}html.theme--catppuccin-mocha .button.is-info.is-light:hover,html.theme--catppuccin-mocha .button.is-info.is-light.is-hovered{background-color:#e5f8f5;border-color:transparent;color:#207466}html.theme--catppuccin-mocha .button.is-info.is-light:active,html.theme--catppuccin-mocha .button.is-info.is-light.is-active{background-color:#dbf5f1;border-color:transparent;color:#207466}html.theme--catppuccin-mocha .button.is-success{background-color:#a6e3a1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:hover,html.theme--catppuccin-mocha .button.is-success.is-hovered{background-color:#9de097;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:focus,html.theme--catppuccin-mocha .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:focus:not(:active),html.theme--catppuccin-mocha .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,227,161,0.25)}html.theme--catppuccin-mocha .button.is-success:active,html.theme--catppuccin-mocha .button.is-success.is-active{background-color:#93dd8d;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success{background-color:#a6e3a1;border-color:#a6e3a1;box-shadow:none}html.theme--catppuccin-mocha .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted:hover,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-success.is-outlined{background-color:transparent;border-color:#a6e3a1;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-outlined:hover,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-success.is-outlined:focus,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-focused{background-color:#a6e3a1;border-color:#a6e3a1;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-outlined{background-color:transparent;border-color:#a6e3a1;box-shadow:none;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-light{background-color:#f0faef;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:hover,html.theme--catppuccin-mocha .button.is-success.is-light.is-hovered{background-color:#e7f7e5;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:active,html.theme--catppuccin-mocha .button.is-success.is-light.is-active{background-color:#def4dc;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:hover,html.theme--catppuccin-mocha .button.is-warning.is-hovered{background-color:#f8dea3;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus,html.theme--catppuccin-mocha .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus:not(:active),html.theme--catppuccin-mocha .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(249,226,175,0.25)}html.theme--catppuccin-mocha .button.is-warning:active,html.theme--catppuccin-mocha .button.is-warning.is-active{background-color:#f7d997;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:#f9e2af;box-shadow:none}html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-focused{background-color:#f9e2af;border-color:#f9e2af;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-light{background-color:#fef8ec;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:hover,html.theme--catppuccin-mocha .button.is-warning.is-light.is-hovered{background-color:#fdf4e0;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:active,html.theme--catppuccin-mocha .button.is-warning.is-light.is-active{background-color:#fcf0d4;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:hover,html.theme--catppuccin-mocha .button.is-danger.is-hovered{background-color:#f27f9f;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus,html.theme--catppuccin-mocha .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus:not(:active),html.theme--catppuccin-mocha .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(243,139,168,0.25)}html.theme--catppuccin-mocha .button.is-danger:active,html.theme--catppuccin-mocha .button.is-danger.is-active{background-color:#f17497;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:#f38ba8;box-shadow:none}html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-mocha .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-focused{background-color:#f38ba8;border-color:#f38ba8;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-light{background-color:#fdedf1;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:hover,html.theme--catppuccin-mocha .button.is-danger.is-light.is-hovered{background-color:#fce1e8;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:active,html.theme--catppuccin-mocha .button.is-danger.is-light.is-active{background-color:#fbd5e0;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-mocha .button.is-small:not(.is-rounded),html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .button.is-normal{font-size:1rem}html.theme--catppuccin-mocha .button.is-medium{font-size:1.25rem}html.theme--catppuccin-mocha .button.is-large{font-size:1.5rem}html.theme--catppuccin-mocha .button[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button{background-color:#6c7086;border-color:#585b70;box-shadow:none;opacity:.5}html.theme--catppuccin-mocha .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-mocha .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-mocha .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-mocha .button.is-static{background-color:#181825;border-color:#585b70;color:#7f849c;box-shadow:none;pointer-events:none}html.theme--catppuccin-mocha .button.is-rounded,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-mocha .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-mocha .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-mocha .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-mocha .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-mocha .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-mocha .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-mocha .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-mocha .buttons.has-addons .button:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-mocha .buttons.has-addons .button:focus,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused,html.theme--catppuccin-mocha .buttons.has-addons .button:active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-mocha .buttons.has-addons .button:focus:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-mocha .buttons.has-addons .button:active:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-mocha .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-mocha .buttons.is-centered{justify-content:center}html.theme--catppuccin-mocha .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-mocha .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-mocha .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-mocha .button.is-responsive.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-mocha .button.is-responsive,html.theme--catppuccin-mocha .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-mocha .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-mocha .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-mocha .button.is-responsive.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-mocha .button.is-responsive,html.theme--catppuccin-mocha .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-mocha .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-mocha .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-mocha .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-mocha .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-mocha .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-mocha .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-mocha .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-mocha .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-mocha .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-mocha .content li+li{margin-top:0.25em}html.theme--catppuccin-mocha .content p:not(:last-child),html.theme--catppuccin-mocha .content dl:not(:last-child),html.theme--catppuccin-mocha .content ol:not(:last-child),html.theme--catppuccin-mocha .content ul:not(:last-child),html.theme--catppuccin-mocha .content blockquote:not(:last-child),html.theme--catppuccin-mocha .content pre:not(:last-child),html.theme--catppuccin-mocha .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-mocha .content h1,html.theme--catppuccin-mocha .content h2,html.theme--catppuccin-mocha .content h3,html.theme--catppuccin-mocha .content h4,html.theme--catppuccin-mocha .content h5,html.theme--catppuccin-mocha .content h6{color:#cdd6f4;font-weight:600;line-height:1.125}html.theme--catppuccin-mocha .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-mocha .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-mocha .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-mocha .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-mocha .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-mocha .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-mocha .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-mocha .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-mocha .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-mocha .content blockquote{background-color:#181825;border-left:5px solid #585b70;padding:1.25em 1.5em}html.theme--catppuccin-mocha .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-mocha .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-mocha .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-mocha .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-mocha .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-mocha .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-mocha .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-mocha .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-mocha .content ul ul ul{list-style-type:square}html.theme--catppuccin-mocha .content dd{margin-left:2em}html.theme--catppuccin-mocha .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-mocha .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-mocha .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-mocha .content figure img{display:inline-block}html.theme--catppuccin-mocha .content figure figcaption{font-style:italic}html.theme--catppuccin-mocha .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-mocha .content sup,html.theme--catppuccin-mocha .content sub{font-size:75%}html.theme--catppuccin-mocha .content table{width:100%}html.theme--catppuccin-mocha .content table td,html.theme--catppuccin-mocha .content table th{border:1px solid #585b70;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-mocha .content table th{color:#b8c5ef}html.theme--catppuccin-mocha .content table th:not([align]){text-align:inherit}html.theme--catppuccin-mocha .content table thead td,html.theme--catppuccin-mocha .content table thead th{border-width:0 0 2px;color:#b8c5ef}html.theme--catppuccin-mocha .content table tfoot td,html.theme--catppuccin-mocha .content table tfoot th{border-width:2px 0 0;color:#b8c5ef}html.theme--catppuccin-mocha .content table tbody tr:last-child td,html.theme--catppuccin-mocha .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-mocha .content .tabs li+li{margin-top:0}html.theme--catppuccin-mocha .content.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-mocha .content.is-normal{font-size:1rem}html.theme--catppuccin-mocha .content.is-medium{font-size:1.25rem}html.theme--catppuccin-mocha .content.is-large{font-size:1.5rem}html.theme--catppuccin-mocha .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-mocha .icon.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-mocha .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-mocha .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-mocha .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-mocha .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-mocha .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--catppuccin-mocha .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--catppuccin-mocha div.icon-text{display:flex}html.theme--catppuccin-mocha .image,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--catppuccin-mocha .image img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--catppuccin-mocha .image img.is-rounded,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--catppuccin-mocha .image.is-fullwidth,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--catppuccin-mocha .image.is-square img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--catppuccin-mocha .image.is-square .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--catppuccin-mocha .image.is-1by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar 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.has-ratio,html.theme--catppuccin-mocha .image.is-5by3 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--catppuccin-mocha .image.is-5by3 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--catppuccin-mocha .image.is-16by9 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--catppuccin-mocha .image.is-16by9 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--catppuccin-mocha .image.is-2by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--catppuccin-mocha .image.is-2by1 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--catppuccin-mocha .image.is-3by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--catppuccin-mocha 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img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--catppuccin-mocha .image.is-3by5 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--catppuccin-mocha .image.is-9by16 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--catppuccin-mocha .image.is-9by16 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-9by16 .has-ratio,html.theme--catppuccin-mocha .image.is-1by2 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by2 img,html.theme--catppuccin-mocha .image.is-1by2 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by2 .has-ratio,html.theme--catppuccin-mocha .image.is-1by3 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by3 img,html.theme--catppuccin-mocha .image.is-1by3 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by3 .has-ratio{height:100%;width:100%}html.theme--catppuccin-mocha .image.is-square,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-square,html.theme--catppuccin-mocha .image.is-1by1,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by1{padding-top:100%}html.theme--catppuccin-mocha .image.is-5by4,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by4{padding-top:80%}html.theme--catppuccin-mocha .image.is-4by3,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-4by3{padding-top:75%}html.theme--catppuccin-mocha .image.is-3by2,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by2{padding-top:66.6666%}html.theme--catppuccin-mocha .image.is-5by3,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by3{padding-top:60%}html.theme--catppuccin-mocha .image.is-16by9,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-16by9{padding-top:56.25%}html.theme--catppuccin-mocha .image.is-2by1,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by1{padding-top:50%}html.theme--catppuccin-mocha .image.is-3by1,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by1{padding-top:33.3333%}html.theme--catppuccin-mocha .image.is-4by5,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-4by5{padding-top:125%}html.theme--catppuccin-mocha .image.is-3by4,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by4{padding-top:133.3333%}html.theme--catppuccin-mocha .image.is-2by3,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by3{padding-top:150%}html.theme--catppuccin-mocha .image.is-3by5,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by5{padding-top:166.6666%}html.theme--catppuccin-mocha .image.is-9by16,html.theme--catppuccin-mocha #documenter 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html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fbefef;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#f8e6e5;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#f6dcda;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark 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.button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark 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h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark 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GitHub

Design principles

This project is inspired by two existing projects:

OMLT is a framework built around Pyomo, and gurobi-machinelearning is a framework build around gurobipy.

These projects served as inspiration, but we also departed from them in some carefully considered ways.

All of our design decisions were guided by two principles:

  1. To be simple
  2. To leverage Julia's Pkg extensions and multiple dispatch.

Terminology

Because the field is relatively new, there is no settled choice of terminology.

MathOptAI chooses to use "predictor" as the synonym for the machine learning model. Hence, we have AbstractPredictor, add_predictor, and build_predictor.

In contrast, gurobi-machinelearning tends to use "regression model" and OMLT uses "formulation."

We choose "predictor" because all models we implement are of the form $y = f(x)$.

We do not use "machine learning model" because we have support for the linear and logistic regression models of classical statistical fitting. We could have used "regression model," but we find that models like neural networks and binary decision trees are not commonly thought of as regression models.

Inputs are vectors

MathOptAI assumes that all inputs $x$ and outputs $y$ to $y = predictor(x)$ are Base.Vectors.

We make this choice for simplicity.

In our opinion, Julia libraries often take a laissez-faire approach to the types that they support. In the optimistic case, this can lead to novel behavior by combining two packages that the package author had previously not considered or tested. In the pessimistic case, this can lead to incorrect results or cryptic error messages.

Exceptions to the Vector rule will be carefully considered and tested.

Currently, there are two exceptions:

  1. If x is a Matrix, then the columns of x are interpreted as independent observations, and the output y will be a Matrix with the same number of columns
  2. The StatsModels extension allows x to be a DataFrames.DataFrame, if the predictor is a StatsModels.TableRegressionModel.

Exceptions 1 and 2 are combined in the StatsModels exception, so that the predictor is mapped over the rows of the DataFrames.DataFrame (which we assume will be a common use-case).

We choose to interpret the rows as input variables and columns as independent observations (rather than the more traditional table-based approach where columns are the input variables and rows are observations) because Julia uses column-major ordering in Matrix. Another justification follows from the Affine predictor, $f(x) = Ax + b$, where passing in a Matrix as x with column observations naturally leads to a Matrix output for y of the appropriate dimensions.

We choose to make y a Vector, even for scalar outputs, to simplify code that works generically for many different predictors. Without this principle, there will inevitably be cases where a scalar and length-1 vector are confused.

If you want to use a predictor that does not take Vector input (for example, it is an image as input to a neural network), the first preprocessing step should be to vec the input into a single Vector.

Inputs are provided, outputs are returned

The main job of MathOptAI is to embed models of the form y = predictor(x) into a JuMP model. A key design decision is how to represent the input x and output y.

gurobi-machinelearning

gurobi-machinelearning implements an API of the following general form:

pred_constr = add_predictor_constr(model, predictor, x, y)

Here, both the input x and the output y must be created and provided by the user, and a new object pred_constr is returned.

The benefit of this design is that pred_constr can contain statistics about the reformulation (for example, the number of variables that were added), and it can be used to delete a predictor from model.

The downside is that the user must ensure that the shape and size of y is correct.

OMLT

OMLT implements an API of the following general form:

model.pred_constr = OmltBlock()
+model.pred_constr.build_formulation(predictor)
+x, y = model.pred_constr.inputs, model.pred_constr.outputs

First, a new OmltBlock() is created. Then the formulation is built inside the block, and both the input and output are provided to the user.

The benefit of this design is that pred_constr can contain statistics about the reformulation (for example, the number of variables that were added), and it can be used to delete a predictor from model.

The downside is that the user must often write additional constraints to connect the input and output of the OmltBlock to their existing decision variables:

#connect pyomo model input and output to the neural network
+@model.Constraint()
+def connect_input(mdl):
+    return mdl.input == mdl.nn.inputs[0]
+
+@model.Constraint()
+def connect_output(mdl):
+    return mdl.output == mdl.nn.outputs[0]

A second downside is that the predictor must describe the input and output dimension; these cannot be inferred automatically. As one example, this means that it cannot do the following:

# Not possible because dimension not given
+model.pred_constr.build_formulation(ReLU())

In the context of MathOptAI, something like ReLU() is useful so that we can map generic layers like Flux.relu => MathOptAI.ReLU(), and so that we do not duplicate required dimension information in input and predictor (see the MathOptAI section below).

MathOptAI

The main entry-point to MathOptAI is add_predictor:

y, formulation = MathOptAI.add_predictor(model, predictor, x)

The user provides the input x, and the output y is returned.

The main benefit of this approach is simplicity.

First, the user probably already has the input x as decision variables or an expression in the model, so we do not need the connect_input constraint, and because we use a full-space formulation by default, the output y will always be a vector of decision variables, which avoids the need for a connect_output constraint.

Second, predictors do not need to store dimension information, so we can have:

y, formulation = MathOptAI.add_predictor(model, MathOptAI.ReLU(), x)

for any size of x.

Activations are predictors

OMLT makes a distinction between layers, like full_space_dense_layer, and elementwise activation functions, like sigmoid_activation_function.

The downside to this approach is that it treats activation functions as special, leading to issues such as OMLT#125.

In contrast, MathOptAI treats activation functions as a vector-valued predictor like any other:

y, formulation = MathOptAI.add_predictor(model, MathOptAI.ReLU(), x)

This means that we can pipeline them to create predictors such as:

function LogisticRegression(A)
+    return MathOptAI.Pipeline(MathOptAI.Affine(A), MathOptAI.Sigmoid())
+end

Controlling transformations

Many predictors have multiple ways that they can be formulated in an optimization model. For example, ReLU implements the non-smooth nonlinear formulation $y = \max\{x, 0\}$, while ReLUQuadratic implements a the complementarity formulation $x = y - slack; y, slack \ge 0; y * slack = 0$.

Choosing the appropriate formulation for the combination of model and solver can have a large impact on the performance.

Because gurobi-machinelearning is specific to the Gurobi solver, they have a limited ability for the user to choose and implement different formulations.

OMLT is more general, in that it has multiple ways of formulating layers such as ReLU. However, these are hard-coded into complete formulations such as omlt.neuralnet.nn_formulation.ReluBigMFormulation or omlt.neuralnet.nn_formulation.ReluComplementarityFormulation.

In contrast, MathOptAI tries to take a maximally modular approach, where the user can control how the layers are formulated at runtime, including using a custom formulation that is not defined in MathOptAI.jl.

Currently, we achieve this with a config dictionary, which maps the various neural network layers to an AbstractPredictor. For example:

chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));
+config = Dict(Flux.relu => MathOptAI.ReLU())
+predictor = MathOptAI.build_predictor(chain; config)

Please open a GitHub issue if you have a suggestion for a better API.

Full-space or reduced-space

OMLT has two ways that it can formulate neural networks: full-space and reduced-space.

The full-space formulations add intermediate variables to represent the output of all layers.

For example, in a Flux.Dense(2, 3, Flux.relu) layer, a full-space formulation will add an intermediate y_tmp variable to represent the output of the affine layer prior to the ReLU:

layer = Flux.Dense(2, 3, Flux.relu)
+model_full_space = Model()
+@variable(model_full_space, x[1:2])
+@variable(model_full_space, y_tmp[1:3])
+@variable(model_full_space, y[1:3])
+@constraint(model_full_space, y_tmp == layer.A * x + layer.b)
+@constraint(model_full_space, y .== max.(0, y_tmp))

In contrast, a reduced-space formulation encodes the input-output relationship as a single nonlinear constraint:

layer = Flux.Dense(2, 3, Flux.relu)
+model_reduced_space = Model()
+@variable(model_reduced_space, x[1:2])
+@variable(model_reduced_space, y[1:3])
+@constraint(model_reduced_space, y .== max.(0, layer.A * x + layer.b))

In general, the full-space formulations have more variables and constraints but simpler nonlinear expressions, whereas the reduced-space formulations have fewer variables and constraints but more complicated nonlinear expressions.

MathOptAI.jl implements the full-space formulation by default, but some layers support the reduced-space formulation with the ReducedSpace wrapper.

diff --git a/v0.1.4/index.html b/v0.1.4/index.html new file mode 100644 index 00000000..a69d75be --- /dev/null +++ b/v0.1.4/index.html @@ -0,0 +1,30 @@ + +MathOptAI.jl · MathOptAI.jl
GitHub

MathOptAI.jl

MathOptAI.jl is a JuMP extension for embedding trained AI, machine learning, and statistical learning models into a JuMP optimization model.

License

MathOptAI.jl is provided under a BSD-3 license as part of the Optimization and Machine Learning Toolbox project, O4806.

See LICENSE.md for details.

Despite the name similarity, this project is not affiliated with OMLT, the Optimization and Machine Learning Toolkit.

Installation

Install MathOptAI.jl using the Julia package manager:

import Pkg
+Pkg.add("MathOptAI")

Getting started

Here's an example of using MathOptAI to embed a trained neural network from Flux into a JuMP model. The vector of JuMP variables x is fed as input to the neural network. The output y is a vector of JuMP variables that represents the output layer of the neural network. The formulation object stores the additional variables and constraints that were added to model.

julia> using JuMP, MathOptAI, Flux
+
+julia> predictor = Flux.Chain(
+           Flux.Dense(28^2 => 32, Flux.sigmoid),
+           Flux.Dense(32 => 10),
+           Flux.softmax,
+       );
+
+julia> #= Train the Flux model. Code not shown for simplicity =#
+
+julia> model = JuMP.Model();
+
+julia> JuMP.@variable(model, 0 <= x[1:28^2] <= 1);
+
+julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
+
+julia> y
+10-element Vector{VariableRef}:
+ moai_SoftMax[1]
+ moai_SoftMax[2]
+ moai_SoftMax[3]
+ moai_SoftMax[4]
+ moai_SoftMax[5]
+ moai_SoftMax[6]
+ moai_SoftMax[7]
+ moai_SoftMax[8]
+ moai_SoftMax[9]
+ moai_SoftMax[10]

Getting help

This package is under active development. For help, questions, comments, and suggestions, please open a GitHub issue.

Inspiration

This project is mainly inspired by two existing projects:

Other works, from which we took less inspiration, include:

The 2024 paper of López-Flores et al. is an excellent summary of the state of the field at the time that we started development of MathOptAI.

López-Flores, F.J., Ramírez-Márquez, C., Ponce-Ortega J.M. (2024). Process Systems Engineering Tools for Optimization of Trained Machine Learning Models: Comparative and Perspective. Industrial & Engineering Chemistry Research, 63(32), 13966-13979. DOI: 10.1021/acs.iecr.4c00632

diff --git a/v0.1.4/manual/AbstractGPs/index.html b/v0.1.4/manual/AbstractGPs/index.html new file mode 100644 index 00000000..b6d8b1df --- /dev/null +++ b/v0.1.4/manual/AbstractGPs/index.html @@ -0,0 +1,6 @@ + +AbstractGPs.jl · MathOptAI.jl
GitHub

AbstractGPs.jl

AbstractGPs.jl is a library for fitting Gaussian Processes in Julia.

Basic example

Here is an example:

julia> using JuMP, MathOptAI, AbstractGPs
julia> x_data = 2π .* (0.0:0.1:1.0);
julia> y_data = sin.(x_data);
julia> fx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.1);
julia> p_fx = AbstractGPs.posterior(fx, y_data);
julia> model = Model();
julia> @variable(model, 1 <= x[1:1] <= 6, start = 3);
julia> predictor = MathOptAI.Quantile(p_fx, [0.1, 0.9]);
julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
julia> y2-element Vector{JuMP.VariableRef}:
+ moai_quantile[1]
+ moai_quantile[2]
julia> formulationQuantile(_, [0.1, 0.9])
+├ variables [0]
+└ constraints [0]
julia> @objective(model, Max, y[2] - y[1])moai_quantile[2] - moai_quantile[1]
diff --git a/v0.1.4/manual/DecisionTree/index.html b/v0.1.4/manual/DecisionTree/index.html new file mode 100644 index 00000000..13c35392 --- /dev/null +++ b/v0.1.4/manual/DecisionTree/index.html @@ -0,0 +1,18 @@ + +DecisionTree.jl · MathOptAI.jl
GitHub

DecisionTree.jl

DecisionTree.jl is a library for fitting decision trees in Julia.

Basic example

Here is an example:

julia> using JuMP, MathOptAI, DecisionTree
julia> truth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)truth (generic function with 1 method)
julia> features = abs.(sin.((1:10) .* (3:4)'));
julia> size(features)(10, 2)
julia> labels = truth.(Vector.(eachrow(features)));
julia> predictor = DecisionTree.build_tree(labels, features)Decision Tree
+Leaves: 3
+Depth:  2
julia> model = Model();
julia> @variable(model, 0 <= x[1:2] <= 1);
julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_BinaryDecisionTree_value
julia> formulationBinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]
+├ variables [4]
+│ ├ moai_BinaryDecisionTree_value
+│ ├ moai_BinaryDecisionTree_z[1]
+│ ├ moai_BinaryDecisionTree_z[2]
+│ └ moai_BinaryDecisionTree_z[3]
+└ constraints [7]
+  ├ moai_BinaryDecisionTree_z[1] + moai_BinaryDecisionTree_z[2] + moai_BinaryDecisionTree_z[3] = 1
+  ├ moai_BinaryDecisionTree_z[1] --> {x[1] ≤ 0.4743457016210958}
+  ├ moai_BinaryDecisionTree_z[2] --> {x[1] ≥ 0.4743457016210958}
+  ├ moai_BinaryDecisionTree_z[2] --> {x[2] ≤ 0.41966499895337794}
+  ├ moai_BinaryDecisionTree_z[3] --> {x[1] ≥ 0.4743457016210958}
+  ├ moai_BinaryDecisionTree_z[3] --> {x[2] ≥ 0.41966499895337794}
+  └ 2 moai_BinaryDecisionTree_z[1] - 3 moai_BinaryDecisionTree_z[2] - 4 moai_BinaryDecisionTree_z[3] + moai_BinaryDecisionTree_value = 0
diff --git a/v0.1.4/manual/Flux/index.html b/v0.1.4/manual/Flux/index.html new file mode 100644 index 00000000..bd171709 --- /dev/null +++ b/v0.1.4/manual/Flux/index.html @@ -0,0 +1,69 @@ + +Flux.jl · MathOptAI.jl
GitHub

Flux.jl

Flux.jl is a library for machine learning in Julia.

The upstream documentation is available at https://fluxml.ai/Flux.jl/stable/.

Supported layers

MathOptAI supports embedding a Flux model into JuMP if it is a Flux.Chain composed of:

Basic example

Use MathOptAI.add_predictor to embed a Flux.Chain into a JuMP model:

julia> using JuMP, Flux, MathOptAI
julia> predictor = Flux.Chain(Flux.Dense(1 => 2, Flux.relu), Flux.Dense(2 => 1));
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_Affine[1]
julia> formulationAffine(A, b) [input: 1, output: 2]
+├ variables [2]
+│ ├ moai_Affine[1]
+│ └ moai_Affine[2]
+└ constraints [2]
+  ├ -0.573231041431427 x[1] - moai_Affine[1] = 0
+  └ 1.1635011434555054 x[1] - moai_Affine[2] = 0
+MathOptAI.ReLU()
+├ variables [2]
+│ ├ moai_ReLU[1]
+│ └ moai_ReLU[2]
+└ constraints [4]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[2] ≥ 0
+  ├ moai_ReLU[1] - max(0.0, moai_Affine[1]) = 0
+  └ moai_ReLU[2] - max(0.0, moai_Affine[2]) = 0
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ 0.7560348510742188 moai_ReLU[1] - 0.07202154397964478 moai_ReLU[2] - moai_Affine[1] = 0

Reduced-space

Use the reduced_space = true keyword to formulate a reduced-space model:

julia> using JuMP, Flux, MathOptAI
julia> predictor = Flux.Chain(Flux.Dense(1 => 2, Flux.relu), Flux.Dense(2 => 1));
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> y, formulation =
+           MathOptAI.add_predictor(model, predictor, x; reduced_space = true);
julia> y1-element Vector{JuMP.NonlinearExpr}:
+ ((+(0.0) + (-0.38966700434684753 * max(0.0, 1.1740339994430542 x[1]))) + (0.9962810277938843 * max(0.0, 0.5712875127792358 x[1]))) + 0.0
julia> formulationReducedSpace(Affine(A, b) [input: 1, output: 2])
+├ variables [0]
+└ constraints [0]
+ReducedSpace(MathOptAI.ReLU())
+├ variables [0]
+└ constraints [0]
+ReducedSpace(Affine(A, b) [input: 2, output: 1])
+├ variables [0]
+└ constraints [0]

Gray-box

Use the gray_box = true keyword to embed the network as a nonlinear operator:

julia> using JuMP, Flux, MathOptAI
julia> predictor = Flux.Chain(Flux.Dense(1 => 2, Flux.relu), Flux.Dense(2 => 1));
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> y, formulation =
+           MathOptAI.add_predictor(model, predictor, x; gray_box = true);
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_GrayBox[1]
julia> formulationGrayBox
+├ variables [1]
+│ └ moai_GrayBox[1]
+└ constraints [1]
+  └ op_##1221(x[1]) - moai_GrayBox[1] = 0

Change how layers are formulated

Pass a dictionary to the config keyword that maps Flux activation functions to a MathOptAI predictor:

julia> using JuMP, Flux, MathOptAI
julia> predictor = Flux.Chain(Flux.Dense(1 => 2, Flux.relu), Flux.Dense(2 => 1));
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> y, formulation = MathOptAI.add_predictor(
+           model,
+           predictor,
+           x;
+           config = Dict(Flux.relu => MathOptAI.ReLUSOS1()),
+       );
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_Affine[1]
julia> formulationAffine(A, b) [input: 1, output: 2]
+├ variables [2]
+│ ├ moai_Affine[1]
+│ └ moai_Affine[2]
+└ constraints [2]
+  ├ 0.2855941355228424 x[1] - moai_Affine[1] = 0
+  └ 1.0478523969650269 x[1] - moai_Affine[2] = 0
+MathOptAI.ReLUSOS1()
+├ variables [4]
+│ ├ moai_ReLU[1]
+│ ├ moai_ReLU[2]
+│ ├ moai_z[1]
+│ └ moai_z[2]
+└ constraints [6]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[2] ≥ 0
+  ├ moai_Affine[1] - moai_ReLU[1] + moai_z[1] = 0
+  ├ moai_Affine[2] - moai_ReLU[2] + moai_z[2] = 0
+  ├ [moai_ReLU[1], moai_z[1]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])
+  └ [moai_ReLU[2], moai_z[2]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ -1.305370807647705 moai_ReLU[1] + 0.9694373607635498 moai_ReLU[2] - moai_Affine[1] = 0
diff --git a/v0.1.4/manual/GLM/index.html b/v0.1.4/manual/GLM/index.html new file mode 100644 index 00000000..5f8edf66 --- /dev/null +++ b/v0.1.4/manual/GLM/index.html @@ -0,0 +1,28 @@ + +GLM.jl · MathOptAI.jl
GitHub

GLM.jl

GLM.jl is a library for fitting generalized linear models in Julia.

MathOptAI.jl supports embedding two types of regression models from GLM:

  • GLM.lm(X, Y)
  • GLM.glm(X, Y, GLM.Bernoulli())

Linear regression

The input x to add_predictor must be a vector with the same number of elements as columns in the training matrix. The return is a vector of JuMP variables with a single element.

julia> using GLM, JuMP, MathOptAI
julia> X, Y = rand(10, 2), rand(10);
julia> predictor = GLM.lm(X, Y);
julia> model = Model();
julia> @variable(model, x[1:2]);
julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_Affine[1]
julia> formulationAffine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ -0.10994663667808285 x[1] + 0.7489085265857259 x[2] - moai_Affine[1] = 0

Logistic regression

The input x to add_predictor must be a vector with the same number of elements as columns in the training matrix. The return is a vector of JuMP variables with a single element.

julia> using GLM, JuMP, MathOptAI
julia> X, Y = rand(10, 2), rand(Bool, 10);
julia> predictor = GLM.glm(X, Y, GLM.Bernoulli());
julia> model = Model();
julia> @variable(model, x[1:2]);
julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_Sigmoid[1]
julia> formulationAffine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ 1.0314193167749655 x[1] - 0.3446975645924237 x[2] - moai_Affine[1] = 0
+MathOptAI.Sigmoid()
+├ variables [1]
+│ └ moai_Sigmoid[1]
+└ constraints [3]
+  ├ moai_Sigmoid[1] ≥ 0
+  ├ moai_Sigmoid[1] ≤ 1
+  └ moai_Sigmoid[1] - (1.0 / (1.0 + exp(-moai_Affine[1]))) = 0

DataFrames

DataFrames.jl can be used with GLM.jl.

The input x to add_predictor must be a DataFrame with the same feature columns as the training DataFrame. The return is a vector of JuMP variables, with one element for each row in the DataFrame.

julia> using DataFrames, GLM, JuMP, MathOptAI
julia> train_df = DataFrames.DataFrame(x1 = rand(10), x2 = rand(10));
julia> train_df.y = 1.0 .* train_df.x1 + 2.0 .* train_df.x2 .+ rand(10);
julia> predictor = GLM.lm(GLM.@formula(y ~ x1 + x2), train_df);
julia> model = Model();
julia> test_df = DataFrames.DataFrame(
+           x1 = rand(6),
+           x2 = @variable(model, [1:6]),
+       );
julia> test_df.y, _ = MathOptAI.add_predictor(model, predictor, test_df);
julia> test_df.y6-element Vector{JuMP.VariableRef}:
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
+ moai_Affine[1]
diff --git a/v0.1.4/manual/Lux/index.html b/v0.1.4/manual/Lux/index.html new file mode 100644 index 00000000..de7093eb --- /dev/null +++ b/v0.1.4/manual/Lux/index.html @@ -0,0 +1,76 @@ + +Lux.jl · MathOptAI.jl
GitHub

Lux.jl

Lux.jl is a library for machine learning in Julia.

The upstream documentation is available at https://lux.csail.mit.edu/stable/.

Supported layers

MathOptAI supports embedding a Lux model into JuMP if it is a Lux.Chain composed of:

Basic example

Use MathOptAI.add_predictor to embed a tuple (containing the Lux.Chain, the parameters, and the state) into a JuMP model:

julia> using JuMP, Lux, MathOptAI, Random
julia> rng = Random.MersenneTwister();
julia> chain = Lux.Chain(Lux.Dense(1 => 2, Lux.relu), Lux.Dense(2 => 1))Chain(
+    layer_1 = Dense(1 => 2, relu),      # 4 parameters
+    layer_2 = Dense(2 => 1),            # 3 parameters
+)         # Total: 7 parameters,
+          #        plus 0 states.
julia> parameters, state = Lux.setup(rng, chain);
julia> predictor = (chain, parameters, state);
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_Affine[1]
julia> formulationAffine(A, b) [input: 1, output: 2]
+├ variables [2]
+│ ├ moai_Affine[1]
+│ └ moai_Affine[2]
+└ constraints [2]
+  ├ -1.2874078750610352 x[1] - moai_Affine[1] = 0
+  └ -0.7287682294845581 x[1] - moai_Affine[2] = 0
+MathOptAI.ReLU()
+├ variables [2]
+│ ├ moai_ReLU[1]
+│ └ moai_ReLU[2]
+└ constraints [4]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[2] ≥ 0
+  ├ moai_ReLU[1] - max(0.0, moai_Affine[1]) = 0
+  └ moai_ReLU[2] - max(0.0, moai_Affine[2]) = 0
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ -0.2623749077320099 moai_ReLU[1] + 0.7335729598999023 moai_ReLU[2] - moai_Affine[1] = 0

Reduced-space

Use the reduced_space = true keyword to formulate a reduced-space model:

julia> using JuMP, Lux, MathOptAI, Random
julia> rng = Random.MersenneTwister();
julia> chain = Lux.Chain(Lux.Dense(1 => 2, Lux.relu), Lux.Dense(2 => 1))Chain(
+    layer_1 = Dense(1 => 2, relu),      # 4 parameters
+    layer_2 = Dense(2 => 1),            # 3 parameters
+)         # Total: 7 parameters,
+          #        plus 0 states.
julia> parameters, state = Lux.setup(rng, chain);
julia> predictor = (chain, parameters, state);
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> y, formulation =
+           MathOptAI.add_predictor(model, predictor, x; reduced_space = true);
julia> y1-element Vector{JuMP.NonlinearExpr}:
+ ((+(0.0) + (-0.1666250377893448 * max(0.0, -0.0003489759110379964 x[1]))) + (0.7532268762588501 * max(0.0, -0.6691581010818481 x[1]))) + 0.0
julia> formulationReducedSpace(Affine(A, b) [input: 1, output: 2])
+├ variables [0]
+└ constraints [0]
+ReducedSpace(MathOptAI.ReLU())
+├ variables [0]
+└ constraints [0]
+ReducedSpace(Affine(A, b) [input: 2, output: 1])
+├ variables [0]
+└ constraints [0]

Gray-box

The Lux extension does not yet support the gray_box keyword argument.

Change how layers are formulated

Pass a dictionary to the config keyword that maps Lux activation functions to a MathOptAI predictor:

julia> using JuMP, Lux, MathOptAI, Random
julia> rng = Random.MersenneTwister();
julia> chain = Lux.Chain(Lux.Dense(1 => 2, Lux.relu), Lux.Dense(2 => 1))Chain(
+    layer_1 = Dense(1 => 2, relu),      # 4 parameters
+    layer_2 = Dense(2 => 1),            # 3 parameters
+)         # Total: 7 parameters,
+          #        plus 0 states.
julia> parameters, state = Lux.setup(rng, chain);
julia> predictor = (chain, parameters, state);
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> y, formulation = MathOptAI.add_predictor(
+           model,
+           predictor,
+           x;
+           config = Dict(Lux.relu => MathOptAI.ReLUSOS1()),
+       );
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_Affine[1]
julia> formulationAffine(A, b) [input: 1, output: 2]
+├ variables [2]
+│ ├ moai_Affine[1]
+│ └ moai_Affine[2]
+└ constraints [2]
+  ├ 0.3074423670768738 x[1] - moai_Affine[1] = 0
+  └ -1.2406009435653687 x[1] - moai_Affine[2] = 0
+MathOptAI.ReLUSOS1()
+├ variables [4]
+│ ├ moai_ReLU[1]
+│ ├ moai_ReLU[2]
+│ ├ moai_z[1]
+│ └ moai_z[2]
+└ constraints [6]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[2] ≥ 0
+  ├ moai_Affine[1] - moai_ReLU[1] + moai_z[1] = 0
+  ├ moai_Affine[2] - moai_ReLU[2] + moai_z[2] = 0
+  ├ [moai_ReLU[1], moai_z[1]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])
+  └ [moai_ReLU[2], moai_z[2]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [2]
+  ├ moai_Affine[1] ≥ 0
+  └ 0.6182379722595215 moai_ReLU[1] + 0.007418182212859392 moai_ReLU[2] - moai_Affine[1] = 0
diff --git a/v0.1.4/manual/PyTorch/index.html b/v0.1.4/manual/PyTorch/index.html new file mode 100644 index 00000000..9b7eee63 --- /dev/null +++ b/v0.1.4/manual/PyTorch/index.html @@ -0,0 +1,76 @@ + +PyTorch · MathOptAI.jl
GitHub

PyTorch

PyTorch is a library for machine learning in Python.

The upstream documentation is available at https://pytorch.org/docs/stable/.

Supported layers

MathOptAI supports embedding a PyTorch models into JuMP if it is a nn.Sequential composed of:

File format

Use torch.save to save a trained PyTorch model to a .pt file:

#!/usr/bin/python3
+import torch
+model = torch.nn.Sequential(
+    torch.nn.Linear(1, 2),
+    torch.nn.ReLU(),
+    torch.nn.Linear(2, 1),
+)
+torch.save(model, "saved_pytorch_model.pt")

Python integration

MathOptAI uses PythonCall.jl to call from Julia into Python.

See CondaPkg.jl for more control over how to link Julia to an existing Python environment. For example, if you have an existing Python installation (with PyTorch installed), and it is available in the current Conda environment, set:

ENV["JULIA_CONDAPKG_BACKEND"] = "Current"

before importing PythonCall.jl. If the Python installation can be found on the path and it is not in a Conda environment, set:

ENV["JULIA_CONDAPKG_BACKEND"] = "Null"

If python is not on your path, you may additionally need to set JULIA_PYTHONCALL_EXE, for example, to:

ENV["JULIA_PYTHONCALL_EXE"] = "python3"

Basic example

Use MathOptAI.add_predictor to embed a PyTorch model into a JuMP model:

julia> using JuMP, MathOptAI
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> predictor = MathOptAI.PytorchModel("saved_pytorch_model.pt");
julia> y, formulation = MathOptAI.add_predictor(model, predictor, x);
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_Affine[1]
julia> formulationAffine(A, b) [input: 1, output: 2]
+├ variables [2]
+│ ├ moai_Affine[1]
+│ └ moai_Affine[2]
+└ constraints [2]
+  ├ 0.7473132610321045 x[1] - moai_Affine[1] = 0.27370238304138184
+  └ -0.8237636089324951 x[1] - moai_Affine[2] = 0.08490216732025146
+MathOptAI.ReLU()
+├ variables [2]
+│ ├ moai_ReLU[1]
+│ └ moai_ReLU[2]
+└ constraints [4]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[2] ≥ 0
+  ├ moai_ReLU[1] - max(0.0, moai_Affine[1]) = 0
+  └ moai_ReLU[2] - max(0.0, moai_Affine[2]) = 0
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ -0.4644489884376526 moai_ReLU[1] + 0.5382549166679382 moai_ReLU[2] - moai_Affine[1] = 0.5698285102844238

Reduced-space

Use the reduced_space = true keyword to formulate a reduced-space model:

julia> using JuMP, MathOptAI
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> predictor = MathOptAI.PytorchModel("saved_pytorch_model.pt");
julia> y, formulation =
+           MathOptAI.add_predictor(model, predictor, x; reduced_space = true);
julia> y1-element Vector{JuMP.NonlinearExpr}:
+ ((+(0.0) + (-0.4644489884376526 * max(0.0, 0.7473132610321045 x[1] - 0.27370238304138184))) + (0.5382549166679382 * max(0.0, -0.8237636089324951 x[1] - 0.08490216732025146))) + -0.5698285102844238
julia> formulationReducedSpace(Affine(A, b) [input: 1, output: 2])
+├ variables [0]
+└ constraints [0]
+ReducedSpace(MathOptAI.ReLU())
+├ variables [0]
+└ constraints [0]
+ReducedSpace(Affine(A, b) [input: 2, output: 1])
+├ variables [0]
+└ constraints [0]

Gray-box

Use the gray_box = true keyword to embed the network as a nonlinear operator:

julia> using JuMP, MathOptAI
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> predictor = MathOptAI.PytorchModel("saved_pytorch_model.pt");
julia> y, formulation =
+           MathOptAI.add_predictor(model, predictor, x; gray_box = true);
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_GrayBox[1]
julia> formulationGrayBox
+├ variables [1]
+│ └ moai_GrayBox[1]
+└ constraints [1]
+  └ op_##1242(x[1]) - moai_GrayBox[1] = 0

Change how layers are formulated

Pass a dictionary to the config keyword that maps the Symbol name of each PyTorch layer to a MathOptAI predictor:

julia> using JuMP, MathOptAI
julia> model = Model();
julia> @variable(model, x[1:1]);
julia> predictor = MathOptAI.PytorchModel("saved_pytorch_model.pt");
julia> y, formulation = MathOptAI.add_predictor(
+           model,
+           predictor,
+           x;
+           config = Dict(:ReLU => MathOptAI.ReLUSOS1()),
+       );
julia> y1-element Vector{JuMP.VariableRef}:
+ moai_Affine[1]
julia> formulationAffine(A, b) [input: 1, output: 2]
+├ variables [2]
+│ ├ moai_Affine[1]
+│ └ moai_Affine[2]
+└ constraints [2]
+  ├ 0.7473132610321045 x[1] - moai_Affine[1] = 0.27370238304138184
+  └ -0.8237636089324951 x[1] - moai_Affine[2] = 0.08490216732025146
+MathOptAI.ReLUSOS1()
+├ variables [4]
+│ ├ moai_ReLU[1]
+│ ├ moai_ReLU[2]
+│ ├ moai_z[1]
+│ └ moai_z[2]
+└ constraints [6]
+  ├ moai_ReLU[1] ≥ 0
+  ├ moai_ReLU[2] ≥ 0
+  ├ moai_Affine[1] - moai_ReLU[1] + moai_z[1] = 0
+  ├ moai_Affine[2] - moai_ReLU[2] + moai_z[2] = 0
+  ├ [moai_ReLU[1], moai_z[1]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])
+  └ [moai_ReLU[2], moai_z[2]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])
+Affine(A, b) [input: 2, output: 1]
+├ variables [1]
+│ └ moai_Affine[1]
+└ constraints [1]
+  └ -0.4644489884376526 moai_ReLU[1] + 0.5382549166679382 moai_ReLU[2] - moai_Affine[1] = 0.5698285102844238
diff --git a/v0.1.4/manual/predictors/index.html b/v0.1.4/manual/predictors/index.html new file mode 100644 index 00000000..a36b7601 --- /dev/null +++ b/v0.1.4/manual/predictors/index.html @@ -0,0 +1,2 @@ + +Predictors · MathOptAI.jl
GitHub

Predictors

The main entry point for embedding prediction models into JuMP is add_predictor.

All methods use the form y, formulation = MathOptAI.add_predictor(model, predictor, x) to add the relationship y = predictor(x) to model.

Supported predictors

The following predictors are supported. See their docstrings for details:

PredictorRelationshipDimensions
Affine$f(x) = Ax + b$$M \rightarrow N$
BinaryDecisionTreeA binary decision tree$M \rightarrow 1$
GrayBox$f(x)$$M \rightarrow N$
Pipeline$f(x) = (l_1 \circ \ldots \circ l_N)(x)$$M \rightarrow N$
QuantileThe quantiles of a distribution$M \rightarrow N$
ReLU$f(x) = \max.(0, x)$$M \rightarrow M$
ReLUBigM$f(x) = \max.(0, x)$$M \rightarrow M$
ReLUQuadratic$f(x) = \max.(0, x)$$M \rightarrow M$
ReLUSOS1$f(x) = \max.(0, x)$$M \rightarrow M$
Scale$f(x) = scale .* x .+ bias$$M \rightarrow M$
Sigmoid$f(x) = \frac{1}{1 + e^{-x}}$$M \rightarrow M$
SoftMax$f(x) = \frac{e^x}{\sum e^{x_i}}$$M \rightarrow M$
SoftPlus$f(x) = \frac{1}{\beta} \log(1 + e^{\beta x})$$M \rightarrow M$
Tanh$f(x) = \tanh.(x)$$M \rightarrow M$

Note that some predictors, such as the ReLU ones, offer multiple formulations of the same mathematical relationship. The ''right'' choice is solver- and problem-dependent.

ReLU

There are a number of different mathematical formulations for the rectified linear unit (ReLU).

  • ReLU: requires the solver to support the max nonlinear operator.
  • ReLUBigM: requires the solver to support mixed-integer linear programs, and requires the user to have prior knowledge of a suitable value for the "big-M" parameter.
  • ReLUQuadratic: requires the solver to support quadratic equality constraints
  • ReLUSOS1: requires the solver to support SOS-I constraints.

The correct choice for which ReLU formulation to use is problem- and solver-dependent.

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zz#BKM=3ObS?n+i+a17|Zf9X!Q&kd|+_GomjNqYLfm6=`?$jCr+z8_FsA4a`ieFtq?LEn} zS9_k<8z!*&=|}MOHS|wO9}6=com~>i1&kTgp)lnReO7_YKi}RCI#j=P)uy!%-YSn@ zmKM~Z=&{s8*|1oznqR|-)txw)+4aa1q^ds^4T93{RyjcGjPip*&7B}f)$Phba({jW z#2u6o0eS6Mc}B}Yub7XH2OQJf)C@!%bgCWuxT+nCi3b^T5bCw-q`Z?Jr33tD81+s= z&;N^HN0<$F>G=*Ga&rF&ruwJDcOBGSMWG{<-?GE4!+ez=Up1O^RefJM2$o&z|0N 2, Flux.relu), Flux.Dense(2 => 1));\nmodel = Model();\n@variable(model, x[1:1]);\ny, formulation = MathOptAI.add_predictor(model, predictor, x);\ny\nformulation","category":"page"},{"location":"manual/Flux/#Reduced-space","page":"Flux.jl","title":"Reduced-space","text":"","category":"section"},{"location":"manual/Flux/","page":"Flux.jl","title":"Flux.jl","text":"Use the reduced_space = true keyword to formulate a reduced-space model:","category":"page"},{"location":"manual/Flux/","page":"Flux.jl","title":"Flux.jl","text":"using JuMP, Flux, MathOptAI\npredictor = Flux.Chain(Flux.Dense(1 => 2, Flux.relu), Flux.Dense(2 => 1));\nmodel = Model();\n@variable(model, x[1:1]);\ny, formulation =\n MathOptAI.add_predictor(model, predictor, x; reduced_space = true);\ny\nformulation","category":"page"},{"location":"manual/Flux/#Gray-box","page":"Flux.jl","title":"Gray-box","text":"","category":"section"},{"location":"manual/Flux/","page":"Flux.jl","title":"Flux.jl","text":"Use the gray_box = true keyword to embed the network as a nonlinear operator:","category":"page"},{"location":"manual/Flux/","page":"Flux.jl","title":"Flux.jl","text":"using JuMP, Flux, MathOptAI\npredictor = Flux.Chain(Flux.Dense(1 => 2, Flux.relu), Flux.Dense(2 => 1));\nmodel = Model();\n@variable(model, x[1:1]);\ny, formulation =\n MathOptAI.add_predictor(model, predictor, x; gray_box = true);\ny\nformulation","category":"page"},{"location":"manual/Flux/#Change-how-layers-are-formulated","page":"Flux.jl","title":"Change how layers are formulated","text":"","category":"section"},{"location":"manual/Flux/","page":"Flux.jl","title":"Flux.jl","text":"Pass a dictionary to the config keyword that maps Flux activation functions to a MathOptAI predictor:","category":"page"},{"location":"manual/Flux/","page":"Flux.jl","title":"Flux.jl","text":"using JuMP, Flux, MathOptAI\npredictor = Flux.Chain(Flux.Dense(1 => 2, Flux.relu), Flux.Dense(2 => 1));\nmodel = Model();\n@variable(model, x[1:1]);\ny, formulation = MathOptAI.add_predictor(\n model,\n predictor,\n x;\n config = Dict(Flux.relu => MathOptAI.ReLUSOS1()),\n);\ny\nformulation","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"EditURL = \"mnist.jl\"","category":"page"},{"location":"tutorials/mnist/#Adversarial-machine-learning-with-Flux.jl","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"","category":"section"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"The purpose of this tutorial is to explain how to embed a neural network model from Flux.jl into JuMP.","category":"page"},{"location":"tutorials/mnist/#Required-packages","page":"Adversarial machine learning with Flux.jl","title":"Required packages","text":"","category":"section"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"This tutorial requires the following packages","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"using JuMP\nimport Flux\nimport Ipopt\nimport MathOptAI\nimport MLDatasets\nimport Plots","category":"page"},{"location":"tutorials/mnist/#Data","page":"Adversarial machine learning with Flux.jl","title":"Data","text":"","category":"section"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"This tutorial uses images from the MNIST dataset.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"We load the predefined train and test splits:","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"train_data = MLDatasets.MNIST(; split = :train)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"test_data = MLDatasets.MNIST(; split = :test)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Since the data are images, it is helpful to plot them. (This requires a transpose and reversing the rows to get the orientation correct.)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"function plot_image(x::Matrix; kwargs...)\n return Plots.heatmap(\n x'[size(x, 1):-1:1, :];\n xlims = (1, size(x, 2)),\n ylims = (1, size(x, 1)),\n aspect_ratio = true,\n legend = false,\n xaxis = false,\n yaxis = false,\n kwargs...,\n )\nend\n\nfunction plot_image(instance::NamedTuple)\n return plot_image(instance.features; title = \"Label = $(instance.targets)\")\nend\n\nPlots.plot([plot_image(train_data[i]) for i in 1:6]...; layout = (2, 3))","category":"page"},{"location":"tutorials/mnist/#Training","page":"Adversarial machine learning with Flux.jl","title":"Training","text":"","category":"section"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"We use a simple neural network with one hidden layer and a sigmoid activation function. (There are better performing networks; try experimenting.)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"predictor = Flux.Chain(\n Flux.Dense(28^2 => 32, Flux.sigmoid),\n Flux.Dense(32 => 10),\n Flux.softmax,\n)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Here is a function to load our data into the format that predictor expects:","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"function data_loader(data; batchsize, shuffle = false)\n x = reshape(data.features, 28^2, :)\n y = Flux.onehotbatch(data.targets, 0:9)\n return Flux.DataLoader((x, y); batchsize, shuffle)\nend","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"and here is a function to score the percentage of correct labels, where we assign a label by choosing the label of the highest softmax in the final layer.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"function score_model(predictor, data)\n x, y = only(data_loader(data; batchsize = length(data)))\n y_hat = predictor(x)\n is_correct = Flux.onecold(y) .== Flux.onecold(y_hat)\n p = round(100 * sum(is_correct) / length(is_correct); digits = 2)\n println(\"Accuracy = $p %\")\n return\nend","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"The accuracy of our model is only around 10% before training:","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"score_model(predictor, train_data)\nscore_model(predictor, test_data)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Let's improve that by training our model.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"note: Note\nIt is not the purpose of this tutorial to explain how Flux works; see the documentation at https://fluxml.ai for more details. Changing the number of epochs or the learning rate can improve the loss.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"begin\n train_loader = data_loader(train_data; batchsize = 256, shuffle = true)\n optimizer_state = Flux.setup(Flux.Adam(3e-4), predictor)\n for epoch in 1:30\n loss = 0.0\n for (x, y) in train_loader\n loss_batch, gradient = Flux.withgradient(predictor) do model\n return Flux.crossentropy(model(x), y)\n end\n Flux.update!(optimizer_state, predictor, only(gradient))\n loss += loss_batch\n end\n loss = round(loss / length(train_loader); digits = 4)\n print(\"Epoch $epoch: loss = $loss\\t\")\n score_model(predictor, test_data)\n end\nend","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Here are the first eight predictions of the test data:","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"function plot_image(predictor, x::Matrix)\n score, index = findmax(predictor(vec(x)))\n title = \"Predicted: $(index - 1) ($(round(Int, 100 * score))%)\"\n return plot_image(x; title)\nend\n\nplots = [plot_image(predictor, test_data[i].features) for i in 1:8]\nPlots.plot(plots...; size = (1200, 600), layout = (2, 4))","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"We can also look at the best and worst four predictions:","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"x, y = only(data_loader(test_data; batchsize = length(test_data)))\nlosses = Flux.crossentropy(predictor(x), y; agg = identity)\nindices = sortperm(losses; dims = 2)[[1:4; end-3:end]]\nplots = [plot_image(predictor, test_data[i].features) for i in indices]\nPlots.plot(plots...; size = (1200, 600), layout = (2, 4))","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"There are still some fairly bad mistakes. Can you change the model or training parameters improve to improve things?","category":"page"},{"location":"tutorials/mnist/#JuMP","page":"Adversarial machine learning with Flux.jl","title":"JuMP","text":"","category":"section"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Now that we have a trained machine learning model, we can embed it in a JuMP model.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Here's a function which takes a test case and returns an example that maximizes the probability of the adversarial example.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"function find_adversarial_image(test_case; adversary_label, δ = 0.05)\n model = Model(Ipopt.Optimizer)\n set_silent(model)\n @variable(model, 0 <= x[1:28, 1:28] <= 1)\n @constraint(model, -δ .<= x .- test_case.features .<= δ)\n # Note: we need to use `vec` here because `x` is a 28-by-28 Matrix, but our\n # neural network expects a 28^2 length vector.\n y, _ = MathOptAI.add_predictor(model, predictor, vec(x))\n @objective(model, Max, y[adversary_label+1] - y[test_case.targets+1])\n optimize!(model)\n @assert is_solved_and_feasible(model)\n return value.(x)\nend","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"Let's try finding an adversarial example to the third test image. The image on the left is our input image. The network thinks this is a 1 with probability 99%. The image on the right is the adversarial image. The network thinks this is a 7, although it is less confident.","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"x_adversary = find_adversarial_image(test_data[3]; adversary_label = 7);\nPlots.plot(\n plot_image(predictor, test_data[3].features),\n plot_image(predictor, Float32.(x_adversary)),\n)","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"","category":"page"},{"location":"tutorials/mnist/","page":"Adversarial machine learning with Flux.jl","title":"Adversarial machine learning with Flux.jl","text":"This page was generated using Literate.jl.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"EditURL = \"student_enrollment.jl\"","category":"page"},{"location":"tutorials/student_enrollment/#Logistic-regression-with-GLM.jl","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"","category":"section"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The purpose of this tutorial is to explain how to embed a logistic regression model from GLM.jl into JuMP.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The data and example in this tutorial comes from the paper: David Bergman, Teng Huang, Philip Brooks, Andrea Lodi, Arvind U. Raghunathan (2021) JANOS: An Integrated Predictive and Prescriptive Modeling Framework. INFORMS Journal on Computing 34(2):807-816. https://doi.org/10.1287/ijoc.2020.1023","category":"page"},{"location":"tutorials/student_enrollment/#Required-packages","page":"Logistic regression with GLM.jl","title":"Required packages","text":"","category":"section"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"This tutorial uses the following packages.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"using JuMP\nimport CSV\nimport DataFrames\nimport Downloads\nimport GLM\nimport Ipopt\nimport MathOptAI\nimport Statistics","category":"page"},{"location":"tutorials/student_enrollment/#Data","page":"Logistic regression with GLM.jl","title":"Data","text":"","category":"section"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Here is a function to load the data directly from the JANOS repository:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"function read_df(filename)\n url = \"https://raw.githubusercontent.com/INFORMSJoC/2020.1023/master/data/\"\n data = Downloads.download(url * filename)\n return CSV.read(data, DataFrames.DataFrame)\nend","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"There are two important files. The first, college_student_enroll-s1-1.csv, contains historical admissions data on anonymized students, their SAT score, their GPA, their merit scholarships, and whether the enrolled in the college.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"train_df = read_df(\"college_student_enroll-s1-1.csv\")","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The second, college_applications6000.csv, contains the SAT and GPA data of students who are currently applying:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"evaluate_df = read_df(\"college_applications6000.csv\")","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"There are 6,000 prospective students:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"n_students = size(evaluate_df, 1)","category":"page"},{"location":"tutorials/student_enrollment/#Prediction-model","page":"Logistic regression with GLM.jl","title":"Prediction model","text":"","category":"section"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The first step is to train a logistic regression model to predict the Boolean enroll column based on the SAT, GPA, and merit columns.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"predictor = GLM.glm(\n GLM.@formula(enroll ~ 0 + SAT + GPA + merit),\n train_df,\n GLM.Bernoulli(),\n)","category":"page"},{"location":"tutorials/student_enrollment/#Decision-model","page":"Logistic regression with GLM.jl","title":"Decision model","text":"","category":"section"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Now that we have a trained logistic regression model, we want a decision model that chooses the optimal merit scholarship for each student in","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"evaluate_df","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Here's an empty JuMP model to start:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"model = Model()","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"First, we add a new column to evaluate_df, with one JuMP decision variable for each row. It is important the .merit column name in evaluate_df matches the name in train_df.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"evaluate_df.merit = @variable(model, 0 <= x_merit[1:n_students] <= 2.5);\nevaluate_df","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Then, we use MathOptAI.add_predictor to embed predictor into the JuMP model. MathOptAI.add_predictor returns a vector of variables, one for each row inn evaluate_df, corresponding to the output enroll of our logistic regression.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"evaluate_df.enroll, _ = MathOptAI.add_predictor(model, predictor, evaluate_df);\nevaluate_df","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The .enroll column name in evaluate_df is just a name. It doesn't have to match the name in train_df.","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The objective of our problem is to maximize the expected number of students who enroll:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"@objective(model, Max, sum(evaluate_df.enroll))","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Subject to the constraint that we can spend at most 0.2 * n_students on merit scholarships:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"@constraint(model, sum(evaluate_df.merit) <= 0.2 * n_students)","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Because logistic regression involves a Sigmoid layer, we need to use a smooth nonlinear optimizer. A common choice is Ipopt. Solve and check the optimizer found a feasible solution:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"set_optimizer(model, Ipopt.Optimizer)\nset_silent(model)\noptimize!(model)\n@assert is_solved_and_feasible(model)\nsolution_summary(model)","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"Let's store the solution in evaluate_df for analysis:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"evaluate_df.merit_sol = value.(evaluate_df.merit);\nevaluate_df.enroll_sol = value.(evaluate_df.enroll);\nevaluate_df","category":"page"},{"location":"tutorials/student_enrollment/#Solution-analysis","page":"Logistic regression with GLM.jl","title":"Solution analysis","text":"","category":"section"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"We expect that just under 2,500 students will enroll:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"sum(evaluate_df.enroll_sol)","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"We awarded merit scholarships to approximately 1 in 6 students:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"count(evaluate_df.merit_sol .> 1e-5)","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"The average merit scholarship was worth just over $1,000:","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"1_000 * Statistics.mean(evaluate_df.merit_sol[evaluate_df.merit_sol.>1e-5])","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"","category":"page"},{"location":"tutorials/student_enrollment/","page":"Logistic regression with GLM.jl","title":"Logistic regression with GLM.jl","text":"This page was generated using Literate.jl.","category":"page"},{"location":"manual/GLM/#GLM.jl","page":"GLM.jl","title":"GLM.jl","text":"","category":"section"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"GLM.jl is a library for fitting generalized linear models in Julia.","category":"page"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"MathOptAI.jl supports embedding two types of regression models from GLM:","category":"page"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"GLM.lm(X, Y)\nGLM.glm(X, Y, GLM.Bernoulli())","category":"page"},{"location":"manual/GLM/#Linear-regression","page":"GLM.jl","title":"Linear regression","text":"","category":"section"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"The input x to add_predictor must be a vector with the same number of elements as columns in the training matrix. The return is a vector of JuMP variables with a single element.","category":"page"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"using GLM, JuMP, MathOptAI\nX, Y = rand(10, 2), rand(10);\npredictor = GLM.lm(X, Y);\nmodel = Model();\n@variable(model, x[1:2]);\ny, formulation = MathOptAI.add_predictor(model, predictor, x);\ny\nformulation","category":"page"},{"location":"manual/GLM/#Logistic-regression","page":"GLM.jl","title":"Logistic regression","text":"","category":"section"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"The input x to add_predictor must be a vector with the same number of elements as columns in the training matrix. The return is a vector of JuMP variables with a single element.","category":"page"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"using GLM, JuMP, MathOptAI\nX, Y = rand(10, 2), rand(Bool, 10);\npredictor = GLM.glm(X, Y, GLM.Bernoulli());\nmodel = Model();\n@variable(model, x[1:2]);\ny, formulation = MathOptAI.add_predictor(model, predictor, x);\ny\nformulation","category":"page"},{"location":"manual/GLM/#DataFrames","page":"GLM.jl","title":"DataFrames","text":"","category":"section"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"DataFrames.jl can be used with GLM.jl.","category":"page"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"The input x to add_predictor must be a DataFrame with the same feature columns as the training DataFrame. The return is a vector of JuMP variables, with one element for each row in the DataFrame.","category":"page"},{"location":"manual/GLM/","page":"GLM.jl","title":"GLM.jl","text":"using DataFrames, GLM, JuMP, MathOptAI\ntrain_df = DataFrames.DataFrame(x1 = rand(10), x2 = rand(10));\ntrain_df.y = 1.0 .* train_df.x1 + 2.0 .* train_df.x2 .+ rand(10);\npredictor = GLM.lm(GLM.@formula(y ~ x1 + x2), train_df);\nmodel = Model();\ntest_df = DataFrames.DataFrame(\n x1 = rand(6),\n x2 = @variable(model, [1:6]),\n);\ntest_df.y, _ = MathOptAI.add_predictor(model, predictor, test_df);\ntest_df.y","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"CurrentModule = MathOptAI","category":"page"},{"location":"developers/design_principles/#Design-principles","page":"Design principles","title":"Design principles","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"This project is inspired by two existing projects:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"OMLT\ngurobi-machinelearning","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"OMLT is a framework built around Pyomo, and gurobi-machinelearning is a framework build around gurobipy.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"These projects served as inspiration, but we also departed from them in some carefully considered ways.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"All of our design decisions were guided by two principles:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"To be simple\nTo leverage Julia's Pkg extensions and multiple dispatch.","category":"page"},{"location":"developers/design_principles/#Terminology","page":"Design principles","title":"Terminology","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Because the field is relatively new, there is no settled choice of terminology.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"MathOptAI chooses to use \"predictor\" as the synonym for the machine learning model. Hence, we have AbstractPredictor, add_predictor, and build_predictor.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In contrast, gurobi-machinelearning tends to use \"regression model\" and OMLT uses \"formulation.\"","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"We choose \"predictor\" because all models we implement are of the form y = f(x).","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"We do not use \"machine learning model\" because we have support for the linear and logistic regression models of classical statistical fitting. We could have used \"regression model,\" but we find that models like neural networks and binary decision trees are not commonly thought of as regression models.","category":"page"},{"location":"developers/design_principles/#Inputs-are-vectors","page":"Design principles","title":"Inputs are vectors","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"MathOptAI assumes that all inputs x and outputs y to y = predictor(x) are Base.Vectors.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"We make this choice for simplicity.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In our opinion, Julia libraries often take a laissez-faire approach to the types that they support. In the optimistic case, this can lead to novel behavior by combining two packages that the package author had previously not considered or tested. In the pessimistic case, this can lead to incorrect results or cryptic error messages.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Exceptions to the Vector rule will be carefully considered and tested.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Currently, there are two exceptions:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"If x is a Matrix, then the columns of x are interpreted as independent observations, and the output y will be a Matrix with the same number of columns\nThe StatsModels extension allows x to be a DataFrames.DataFrame, if the predictor is a StatsModels.TableRegressionModel.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Exceptions 1 and 2 are combined in the StatsModels exception, so that the predictor is mapped over the rows of the DataFrames.DataFrame (which we assume will be a common use-case).","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"We choose to interpret the rows as input variables and columns as independent observations (rather than the more traditional table-based approach where columns are the input variables and rows are observations) because Julia uses column-major ordering in Matrix. Another justification follows from the Affine predictor, f(x) = Ax + b, where passing in a Matrix as x with column observations naturally leads to a Matrix output for y of the appropriate dimensions.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"We choose to make y a Vector, even for scalar outputs, to simplify code that works generically for many different predictors. Without this principle, there will inevitably be cases where a scalar and length-1 vector are confused.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"If you want to use a predictor that does not take Vector input (for example, it is an image as input to a neural network), the first preprocessing step should be to vec the input into a single Vector.","category":"page"},{"location":"developers/design_principles/#Inputs-are-provided,-outputs-are-returned","page":"Design principles","title":"Inputs are provided, outputs are returned","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The main job of MathOptAI is to embed models of the form y = predictor(x) into a JuMP model. A key design decision is how to represent the input x and output y.","category":"page"},{"location":"developers/design_principles/#gurobi-machinelearning","page":"Design principles","title":"gurobi-machinelearning","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"gurobi-machinelearning implements an API of the following general form:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"pred_constr = add_predictor_constr(model, predictor, x, y)","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Here, both the input x and the output y must be created and provided by the user, and a new object pred_constr is returned.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The benefit of this design is that pred_constr can contain statistics about the reformulation (for example, the number of variables that were added), and it can be used to delete a predictor from model.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The downside is that the user must ensure that the shape and size of y is correct.","category":"page"},{"location":"developers/design_principles/#OMLT","page":"Design principles","title":"OMLT","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"OMLT implements an API of the following general form:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"model.pred_constr = OmltBlock()\nmodel.pred_constr.build_formulation(predictor)\nx, y = model.pred_constr.inputs, model.pred_constr.outputs","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"First, a new OmltBlock() is created. Then the formulation is built inside the block, and both the input and output are provided to the user.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The benefit of this design is that pred_constr can contain statistics about the reformulation (for example, the number of variables that were added), and it can be used to delete a predictor from model.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The downside is that the user must often write additional constraints to connect the input and output of the OmltBlock to their existing decision variables:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"#connect pyomo model input and output to the neural network\n@model.Constraint()\ndef connect_input(mdl):\n return mdl.input == mdl.nn.inputs[0]\n\n@model.Constraint()\ndef connect_output(mdl):\n return mdl.output == mdl.nn.outputs[0]","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"A second downside is that the predictor must describe the input and output dimension; these cannot be inferred automatically. As one example, this means that it cannot do the following:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"# Not possible because dimension not given\nmodel.pred_constr.build_formulation(ReLU())","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In the context of MathOptAI, something like ReLU() is useful so that we can map generic layers like Flux.relu => MathOptAI.ReLU(), and so that we do not duplicate required dimension information in input and predictor (see the MathOptAI section below).","category":"page"},{"location":"developers/design_principles/#MathOptAI","page":"Design principles","title":"MathOptAI","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The main entry-point to MathOptAI is add_predictor:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"y, formulation = MathOptAI.add_predictor(model, predictor, x)","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The user provides the input x, and the output y is returned.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The main benefit of this approach is simplicity.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"First, the user probably already has the input x as decision variables or an expression in the model, so we do not need the connect_input constraint, and because we use a full-space formulation by default, the output y will always be a vector of decision variables, which avoids the need for a connect_output constraint.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Second, predictors do not need to store dimension information, so we can have:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"y, formulation = MathOptAI.add_predictor(model, MathOptAI.ReLU(), x)","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"for any size of x.","category":"page"},{"location":"developers/design_principles/#Activations-are-predictors","page":"Design principles","title":"Activations are predictors","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"OMLT makes a distinction between layers, like full_space_dense_layer, and elementwise activation functions, like sigmoid_activation_function.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The downside to this approach is that it treats activation functions as special, leading to issues such as OMLT#125.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In contrast, MathOptAI treats activation functions as a vector-valued predictor like any other:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"y, formulation = MathOptAI.add_predictor(model, MathOptAI.ReLU(), x)","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"This means that we can pipeline them to create predictors such as:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"function LogisticRegression(A)\n return MathOptAI.Pipeline(MathOptAI.Affine(A), MathOptAI.Sigmoid())\nend","category":"page"},{"location":"developers/design_principles/#Controlling-transformations","page":"Design principles","title":"Controlling transformations","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Many predictors have multiple ways that they can be formulated in an optimization model. For example, ReLU implements the non-smooth nonlinear formulation y = maxx 0, while ReLUQuadratic implements a the complementarity formulation x = y - slack y slack ge 0 y * slack = 0.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Choosing the appropriate formulation for the combination of model and solver can have a large impact on the performance.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Because gurobi-machinelearning is specific to the Gurobi solver, they have a limited ability for the user to choose and implement different formulations.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"OMLT is more general, in that it has multiple ways of formulating layers such as ReLU. However, these are hard-coded into complete formulations such as omlt.neuralnet.nn_formulation.ReluBigMFormulation or omlt.neuralnet.nn_formulation.ReluComplementarityFormulation.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In contrast, MathOptAI tries to take a maximally modular approach, where the user can control how the layers are formulated at runtime, including using a custom formulation that is not defined in MathOptAI.jl.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Currently, we achieve this with a config dictionary, which maps the various neural network layers to an AbstractPredictor. For example:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));\nconfig = Dict(Flux.relu => MathOptAI.ReLU())\npredictor = MathOptAI.build_predictor(chain; config)","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"Please open a GitHub issue if you have a suggestion for a better API.","category":"page"},{"location":"developers/design_principles/#Full-space-or-reduced-space","page":"Design principles","title":"Full-space or reduced-space","text":"","category":"section"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"OMLT has two ways that it can formulate neural networks: full-space and reduced-space.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"The full-space formulations add intermediate variables to represent the output of all layers.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"For example, in a Flux.Dense(2, 3, Flux.relu) layer, a full-space formulation will add an intermediate y_tmp variable to represent the output of the affine layer prior to the ReLU:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"layer = Flux.Dense(2, 3, Flux.relu)\nmodel_full_space = Model()\n@variable(model_full_space, x[1:2])\n@variable(model_full_space, y_tmp[1:3])\n@variable(model_full_space, y[1:3])\n@constraint(model_full_space, y_tmp == layer.A * x + layer.b)\n@constraint(model_full_space, y .== max.(0, y_tmp))","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In contrast, a reduced-space formulation encodes the input-output relationship as a single nonlinear constraint:","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"layer = Flux.Dense(2, 3, Flux.relu)\nmodel_reduced_space = Model()\n@variable(model_reduced_space, x[1:2])\n@variable(model_reduced_space, y[1:3])\n@constraint(model_reduced_space, y .== max.(0, layer.A * x + layer.b))","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"In general, the full-space formulations have more variables and constraints but simpler nonlinear expressions, whereas the reduced-space formulations have fewer variables and constraints but more complicated nonlinear expressions.","category":"page"},{"location":"developers/design_principles/","page":"Design principles","title":"Design principles","text":"MathOptAI.jl implements the full-space formulation by default, but some layers support the reduced-space formulation with the ReducedSpace wrapper.","category":"page"},{"location":"manual/DecisionTree/#DecisionTree.jl","page":"DecisionTree.jl","title":"DecisionTree.jl","text":"","category":"section"},{"location":"manual/DecisionTree/","page":"DecisionTree.jl","title":"DecisionTree.jl","text":"DecisionTree.jl is a library for fitting decision trees in Julia.","category":"page"},{"location":"manual/DecisionTree/#Basic-example","page":"DecisionTree.jl","title":"Basic example","text":"","category":"section"},{"location":"manual/DecisionTree/","page":"DecisionTree.jl","title":"DecisionTree.jl","text":"Here is an example:","category":"page"},{"location":"manual/DecisionTree/","page":"DecisionTree.jl","title":"DecisionTree.jl","text":"using JuMP, MathOptAI, DecisionTree\ntruth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)\nfeatures = abs.(sin.((1:10) .* (3:4)'));\nsize(features)\nlabels = truth.(Vector.(eachrow(features)));\npredictor = DecisionTree.build_tree(labels, features)\nmodel = Model();\n@variable(model, 0 <= x[1:2] <= 1);\ny, formulation = MathOptAI.add_predictor(model, predictor, x);\ny\nformulation","category":"page"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"CurrentModule = MathOptAI","category":"page"},{"location":"manual/predictors/#Predictors","page":"Predictors","title":"Predictors","text":"","category":"section"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"The main entry point for embedding prediction models into JuMP is add_predictor.","category":"page"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"All methods use the form y, formulation = MathOptAI.add_predictor(model, predictor, x) to add the relationship y = predictor(x) to model.","category":"page"},{"location":"manual/predictors/#Supported-predictors","page":"Predictors","title":"Supported predictors","text":"","category":"section"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"The following predictors are supported. See their docstrings for details:","category":"page"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"Predictor Relationship Dimensions\nAffine f(x) = Ax + b M rightarrow N\nBinaryDecisionTree A binary decision tree M rightarrow 1\nGrayBox f(x) M rightarrow N\nPipeline f(x) = (l_1 circ ldots circ l_N)(x) M rightarrow N\nQuantile The quantiles of a distribution M rightarrow N\nReLU f(x) = max(0 x) M rightarrow M\nReLUBigM f(x) = max(0 x) M rightarrow M\nReLUQuadratic f(x) = max(0 x) M rightarrow M\nReLUSOS1 f(x) = max(0 x) M rightarrow M\nScale f(x) = scale * x + bias M rightarrow M\nSigmoid f(x) = frac11 + e^-x M rightarrow M\nSoftMax f(x) = frace^xsum e^x_i M rightarrow M\nSoftPlus f(x) = frac1beta log(1 + e^beta x) M rightarrow M\nTanh f(x) = tanh(x) M rightarrow M","category":"page"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"Note that some predictors, such as the ReLU ones, offer multiple formulations of the same mathematical relationship. The ''right'' choice is solver- and problem-dependent.","category":"page"},{"location":"manual/predictors/#ReLU","page":"Predictors","title":"ReLU","text":"","category":"section"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"There are a number of different mathematical formulations for the rectified linear unit (ReLU).","category":"page"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"ReLU: requires the solver to support the max nonlinear operator.\nReLUBigM: requires the solver to support mixed-integer linear programs, and requires the user to have prior knowledge of a suitable value for the \"big-M\" parameter.\nReLUQuadratic: requires the solver to support quadratic equality constraints\nReLUSOS1: requires the solver to support SOS-I constraints.","category":"page"},{"location":"manual/predictors/","page":"Predictors","title":"Predictors","text":"The correct choice for which ReLU formulation to use is problem- and solver-dependent.","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"CurrentModule = MathOptAI","category":"page"},{"location":"api/#API-Reference","page":"API Reference","title":"API Reference","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"This page lists the public API of MathOptAI.","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"info: Info\nThis page is an unstructured list of the MathOptAI API. For a more structured overview, read the Manual or Tutorial parts of this documentation.","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Load all of the public the API into the current scope with:","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"using MathOptAI","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Alternatively, load only the module with:","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"import MathOptAI","category":"page"},{"location":"api/","page":"API Reference","title":"API Reference","text":"and then prefix all calls with MathOptAI. to create MathOptAI..","category":"page"},{"location":"api/#AbstractPredictor","page":"API Reference","title":"AbstractPredictor","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"AbstractPredictor","category":"page"},{"location":"api/#MathOptAI.AbstractPredictor","page":"API Reference","title":"MathOptAI.AbstractPredictor","text":"abstract type AbstractPredictor end\n\nAn abstract type representing different types of prediction models.\n\nMethods\n\nAll subtypes must implement:\n\nadd_predictor\nbuild_predictor\n\n\n\n\n\n","category":"type"},{"location":"api/#add_predictor","page":"API Reference","title":"add_predictor","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"add_predictor","category":"page"},{"location":"api/#MathOptAI.add_predictor","page":"API Reference","title":"MathOptAI.add_predictor","text":"add_predictor(\n model::JuMP.AbstractModel,\n predictor::AbstractPredictor,\n x::Vector,\n)::Vector\n\nReturn a Vector representing y such that y = predictor(x).\n\nThe element type of x is deliberately unspecified. The vector x may contain any mix of scalar constants, JuMP decision variables, and scalar JuMP functions like AffExpr, QuadExpr, or NonlinearExpr.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.Affine([2.0, 3.0])\nAffine(A, b) [input: 2, output: 1]\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Affine[1]\n\njulia> formulation\nAffine(A, b) [input: 2, output: 1]\n├ variables [1]\n│ └ moai_Affine[1]\n└ constraints [1]\n └ 2 x[1] + 3 x[2] - moai_Affine[1] = 0\n\n\n\n\n\n","category":"function"},{"location":"api/#build_predictor","page":"API Reference","title":"build_predictor","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"build_predictor(predictor::AbstractPredictor; kwargs...)","category":"page"},{"location":"api/#MathOptAI.build_predictor-Tuple{MathOptAI.AbstractPredictor}","page":"API Reference","title":"MathOptAI.build_predictor","text":"build_predictor(extension; kwargs...)::AbstractPredictor\n\nA uniform interface to convert various extension types to an AbstractPredictor.\n\nSee the various extension docstrings for details.\n\n\n\n\n\n","category":"method"},{"location":"api/#Affine","page":"API Reference","title":"Affine","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Affine","category":"page"},{"location":"api/#MathOptAI.Affine","page":"API Reference","title":"MathOptAI.Affine","text":"Affine(\n A::Matrix{T},\n b::Vector{T} = zeros(T, size(A, 1)),\n) where {T} <: AbstractPredictor\n\nAn AbstractPredictor that represents the relationship:\n\ny = A x + b\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, 0 <= x[i in 1:2] <= i);\n\njulia> f = MathOptAI.Affine([2.0 3.0], [4.0])\nAffine(A, b) [input: 2, output: 1]\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Affine[1]\n\njulia> formulation\nAffine(A, b) [input: 2, output: 1]\n├ variables [1]\n│ └ moai_Affine[1]\n└ constraints [3]\n ├ moai_Affine[1] ≥ 4\n ├ moai_Affine[1] ≤ 12\n └ 2 x[1] + 3 x[2] - moai_Affine[1] = -4\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n1-element Vector{AffExpr}:\n 2 x[1] + 3 x[2] + 4\n\njulia> formulation\nReducedSpace(Affine(A, b) [input: 2, output: 1])\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#BinaryDecisionTree","page":"API Reference","title":"BinaryDecisionTree","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"BinaryDecisionTree","category":"page"},{"location":"api/#MathOptAI.BinaryDecisionTree","page":"API Reference","title":"MathOptAI.BinaryDecisionTree","text":"BinaryDecisionTree{K,V}(\n feat_id::Int,\n feat_value::K,\n lhs::Union{V,BinaryDecisionTree{K,V}},\n rhs::Union{V,BinaryDecisionTree{K,V}},\n)\n\nAn AbstractPredictor that represents a binary decision tree.\n\nIf x[feat_id] <= feat_value, then return lhs\nIf x[feat_id] > feat_value, then return rhs\n\nExample\n\nTo represent the tree x[1] <= 0.0 ? -1 : (x[1] <= 1.0 ? 0 : 1), do:\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:1]);\n\njulia> f = MathOptAI.BinaryDecisionTree{Float64,Int}(\n 1,\n 0.0,\n -1,\n MathOptAI.BinaryDecisionTree{Float64,Int}(1, 1.0, 0, 1),\n )\nBinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_BinaryDecisionTree_value\n\njulia> formulation\nBinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]\n├ variables [4]\n│ ├ moai_BinaryDecisionTree_value\n│ ├ moai_BinaryDecisionTree_z[1]\n│ ├ moai_BinaryDecisionTree_z[2]\n│ └ moai_BinaryDecisionTree_z[3]\n└ constraints [7]\n ├ moai_BinaryDecisionTree_z[1] + moai_BinaryDecisionTree_z[2] + moai_BinaryDecisionTree_z[3] = 1\n ├ moai_BinaryDecisionTree_z[1] --> {x[1] ≤ 0}\n ├ moai_BinaryDecisionTree_z[2] --> {x[1] ≥ 0}\n ├ moai_BinaryDecisionTree_z[2] --> {x[1] ≤ 1}\n ├ moai_BinaryDecisionTree_z[3] --> {x[1] ≥ 0}\n ├ moai_BinaryDecisionTree_z[3] --> {x[1] ≥ 1}\n └ moai_BinaryDecisionTree_z[1] - moai_BinaryDecisionTree_z[3] + moai_BinaryDecisionTree_value = 0\n\n\n\n\n\n","category":"type"},{"location":"api/#GrayBox","page":"API Reference","title":"GrayBox","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"GrayBox","category":"page"},{"location":"api/#MathOptAI.GrayBox","page":"API Reference","title":"MathOptAI.GrayBox","text":"GrayBox(\n output_size::Function,\n callback::Function;\n has_hessian::Bool = false,\n) <: AbstractPredictor\n\nAn AbstractPredictor that represents the relationship:\n\ny = f(x)\n\nas a user-defined nonlinear operator.\n\nArguments\n\noutput_size(x::Vector):Int: given an input vector x, return the dimension of the output vector\ncallback(x::Vector)::NamedTuple -> (;value, jacobian[, hessian]): given an input vector x, return a NamedTuple that computes the primal value and Jacobian of the output value with respect to the input. jacobian[j, i] is the partial derivative of value[j] with respect to x[i].\nhas_hessian: if true, the callback additionally contains a field hessian, which is an N × N × M matrix, where hessian[i, j, k] is the partial derivative of value[k] with respect to x[i] and x[j].\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.GrayBox(\n x -> 2,\n x -> (value = x.^2, jacobian = [2 * x[1] 0.0; 0.0 2 * x[2]]),\n );\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_GrayBox[1]\n moai_GrayBox[2]\n\njulia> formulation\nGrayBox\n├ variables [2]\n│ ├ moai_GrayBox[1]\n│ └ moai_GrayBox[2]\n└ constraints [2]\n ├ op_##330(x[1], x[2]) - moai_GrayBox[1] = 0\n └ op_##331(x[1], x[2]) - moai_GrayBox[2] = 0\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n op_##332(x[1], x[2])\n op_##333(x[1], x[2])\n\njulia> formulation\nReducedSpace(GrayBox)\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#Pipeline","page":"API Reference","title":"Pipeline","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Pipeline","category":"page"},{"location":"api/#MathOptAI.Pipeline","page":"API Reference","title":"MathOptAI.Pipeline","text":"Pipeline(layers::Vector{AbstractPredictor}) <: AbstractPredictor\n\nAn AbstractPredictor that represents the relationship:\n\ny = (l_1 circ ldots circ l_N)(x)\n\nwhere l_i are a list of other AbstractPredictors.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.Pipeline(\n MathOptAI.Affine([1.0 2.0], [0.0]),\n MathOptAI.ReLUQuadratic(),\n )\nPipeline with layers:\n * Affine(A, b) [input: 2, output: 1]\n * ReLUQuadratic()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_ReLU[1]\n\njulia> formulation\nAffine(A, b) [input: 2, output: 1]\n├ variables [1]\n│ └ moai_Affine[1]\n└ constraints [1]\n └ x[1] + 2 x[2] - moai_Affine[1] = 0\nReLUQuadratic()\n├ variables [2]\n│ ├ moai_ReLU[1]\n│ └ moai_z[1]\n└ constraints [4]\n ├ moai_ReLU[1] ≥ 0\n ├ moai_z[1] ≥ 0\n ├ moai_Affine[1] - moai_ReLU[1] + moai_z[1] = 0\n └ moai_ReLU[1]*moai_z[1] = 0\n\n\n\n\n\n","category":"type"},{"location":"api/#PytorchModel","page":"API Reference","title":"PytorchModel","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"PytorchModel","category":"page"},{"location":"api/#MathOptAI.PytorchModel","page":"API Reference","title":"MathOptAI.PytorchModel","text":"PytorchModel(filename::String)\n\nA wrapper struct for loading a PyTorch model.\n\nThe only supported file extension is .pt, where the .pt file has been created using torch.save(model, filename).\n\nExample\n\njulia> using PythonCall, MathOptAI\n\njulia> predictor = PytorchModel(\"model.pt\");\n\n\n\n\n\n","category":"type"},{"location":"api/#Quantile","page":"API Reference","title":"Quantile","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Quantile","category":"page"},{"location":"api/#MathOptAI.Quantile","page":"API Reference","title":"MathOptAI.Quantile","text":"Quantile{D}(distribution::D, quantiles::Vector{Float64}) where {D}\n\nAn AbstractPredictor that represents the quantiles of distribution.\n\nExample\n\njulia> using JuMP, Distributions, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, 1 <= x <= 2);\n\njulia> predictor = MathOptAI.Quantile([0.1, 0.9]) do x\n return Distributions.Normal(x, 3 - x)\n end\nQuantile(_, [0.1, 0.9])\n\njulia> y, formulation = MathOptAI.add_predictor(model, predictor, [x]);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_quantile[1]\n moai_quantile[2]\n\njulia> formulation\nQuantile(_, [0.1, 0.9])\n├ variables [2]\n│ ├ moai_quantile[1]\n│ └ moai_quantile[2]\n└ constraints [2]\n ├ moai_quantile[1] - op_quantile_0.1(x) = 0\n └ moai_quantile[2] - op_quantile_0.9(x) = 0\n\n\n\n\n\n","category":"type"},{"location":"api/#ReducedSpace","page":"API Reference","title":"ReducedSpace","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"ReducedSpace","category":"page"},{"location":"api/#MathOptAI.ReducedSpace","page":"API Reference","title":"MathOptAI.ReducedSpace","text":"ReducedSpace(predictor::AbstractPredictor)\n\nA wrapper type for other predictors that implement a reduced-space formulation.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> predictor = MathOptAI.ReducedSpace(MathOptAI.ReLU());\n\njulia> y, formulation = MathOptAI.add_predictor(model, predictor, x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n max(0.0, x[1])\n max(0.0, x[2])\n\n\n\n\n\n","category":"type"},{"location":"api/#ReLU","page":"API Reference","title":"ReLU","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"ReLU","category":"page"},{"location":"api/#MathOptAI.ReLU","page":"API Reference","title":"MathOptAI.ReLU","text":"ReLU() <: AbstractPredictor\n\nAn AbstractPredictor that represents the relationship:\n\ny = max0 x\n\nas a non-smooth nonlinear constraint.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, -1 <= x[i in 1:2] <= i);\n\njulia> f = MathOptAI.ReLU()\nReLU()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_ReLU[1]\n moai_ReLU[2]\n\njulia> formulation\nReLU()\n├ variables [2]\n│ ├ moai_ReLU[1]\n│ └ moai_ReLU[2]\n└ constraints [6]\n ├ moai_ReLU[1] ≥ 0\n ├ moai_ReLU[1] ≤ 1\n ├ moai_ReLU[2] ≥ 0\n ├ moai_ReLU[2] ≤ 2\n ├ moai_ReLU[1] - max(0.0, x[1]) = 0\n └ moai_ReLU[2] - max(0.0, x[2]) = 0\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n max(0.0, x[1])\n max(0.0, x[2])\n\njulia> formulation\nReducedSpace(ReLU())\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#ReLUBigM","page":"API Reference","title":"ReLUBigM","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"ReLUBigM","category":"page"},{"location":"api/#MathOptAI.ReLUBigM","page":"API Reference","title":"MathOptAI.ReLUBigM","text":"ReLUBigM(M::Float64) <: AbstractPredictor\n\nAn AbstractPredictor that represents the relationship:\n\ny = max0 x\n\nvia the big-M MIP reformulation:\n\nbeginaligned\ny ge 0 \ny ge x \ny le M z \ny le x + M(1 - z) \nz in0 1\nendaligned\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, -3 <= x[i in 1:2] <= i);\n\njulia> f = MathOptAI.ReLUBigM(100.0)\nReLUBigM(100.0)\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_ReLU[1]\n moai_ReLU[2]\n\njulia> formulation\nReLUBigM(100.0)\n├ variables [4]\n│ ├ moai_ReLU[1]\n│ ├ moai_ReLU[2]\n│ ├ moai_z[1]\n│ └ moai_z[2]\n└ constraints [12]\n ├ moai_ReLU[1] ≥ 0\n ├ moai_ReLU[1] ≤ 1\n ├ moai_ReLU[2] ≥ 0\n ├ moai_ReLU[2] ≤ 2\n ├ moai_z[1] binary\n ├ -x[1] + moai_ReLU[1] ≥ 0\n ├ moai_ReLU[1] - moai_z[1] ≤ 0\n ├ -x[1] + moai_ReLU[1] + 3 moai_z[1] ≤ 3\n ├ moai_z[2] binary\n ├ -x[2] + moai_ReLU[2] ≥ 0\n ├ moai_ReLU[2] - 2 moai_z[2] ≤ 0\n └ -x[2] + moai_ReLU[2] + 3 moai_z[2] ≤ 3\n\n\n\n\n\n","category":"type"},{"location":"api/#ReLUQuadratic","page":"API Reference","title":"ReLUQuadratic","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"ReLUQuadratic","category":"page"},{"location":"api/#MathOptAI.ReLUQuadratic","page":"API Reference","title":"MathOptAI.ReLUQuadratic","text":"ReLUQuadratic() <: AbstractPredictor\n\nAn AbstractPredictor that represents the relationship:\n\ny = max0 x\n\nby the reformulation:\n\nbeginaligned\nx = y - z \ny cdot z = 0 \ny z ge 0\nendaligned\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, -1 <= x[i in 1:2] <= i);\n\njulia> f = MathOptAI.ReLUQuadratic()\nReLUQuadratic()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_ReLU[1]\n moai_ReLU[2]\n\njulia> formulation\nReLUQuadratic()\n├ variables [4]\n│ ├ moai_ReLU[1]\n│ ├ moai_ReLU[2]\n│ ├ moai_z[1]\n│ └ moai_z[2]\n└ constraints [12]\n ├ moai_ReLU[1] ≥ 0\n ├ moai_ReLU[1] ≤ 1\n ├ moai_ReLU[2] ≥ 0\n ├ moai_ReLU[2] ≤ 2\n ├ moai_z[1] ≥ 0\n ├ moai_z[1] ≤ 1\n ├ moai_z[2] ≥ 0\n ├ moai_z[2] ≤ 1\n ├ x[1] - moai_ReLU[1] + moai_z[1] = 0\n ├ x[2] - moai_ReLU[2] + moai_z[2] = 0\n ├ moai_ReLU[1]*moai_z[1] = 0\n └ moai_ReLU[2]*moai_z[2] = 0\n\n\n\n\n\n","category":"type"},{"location":"api/#ReLUSOS1","page":"API Reference","title":"ReLUSOS1","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"ReLUSOS1","category":"page"},{"location":"api/#MathOptAI.ReLUSOS1","page":"API Reference","title":"MathOptAI.ReLUSOS1","text":"ReLUSOS1() <: AbstractPredictor\n\nAn AbstractPredictor that represents the relationship:\n\ny = max0 x\n\nby the reformulation:\n\nbeginaligned\nx = y - z \ny z in SOS1 \ny z ge 0\nendaligned\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, -1 <= x[i in 1:2] <= i);\n\njulia> f = MathOptAI.ReLUSOS1()\nReLUSOS1()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_ReLU[1]\n moai_ReLU[2]\n\njulia> formulation\nReLUSOS1()\n├ variables [4]\n│ ├ moai_ReLU[1]\n│ ├ moai_ReLU[2]\n│ ├ moai_z[1]\n│ └ moai_z[2]\n└ constraints [10]\n ├ moai_ReLU[1] ≥ 0\n ├ moai_ReLU[1] ≤ 1\n ├ moai_ReLU[2] ≥ 0\n ├ moai_ReLU[2] ≤ 2\n ├ moai_z[1] ≤ 1\n ├ moai_z[2] ≤ 1\n ├ x[1] - moai_ReLU[1] + moai_z[1] = 0\n ├ x[2] - moai_ReLU[2] + moai_z[2] = 0\n ├ [moai_ReLU[1], moai_z[1]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])\n └ [moai_ReLU[2], moai_z[2]] ∈ MathOptInterface.SOS1{Float64}([1.0, 2.0])\n\n\n\n\n\n","category":"type"},{"location":"api/#Scale","page":"API Reference","title":"Scale","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Scale","category":"page"},{"location":"api/#MathOptAI.Scale","page":"API Reference","title":"MathOptAI.Scale","text":"Scale(\n scale::Vector{T},\n bias::Vector{T},\n) where {T} <: AbstractPredictor\n\nAn AbstractPredictor that represents the relationship:\n\ny = Diag(scale)x + bias\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, 0 <= x[i in 1:2] <= i);\n\njulia> f = MathOptAI.Scale([2.0, 3.0], [4.0, 5.0])\nScale(scale, bias)\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_Scale[1]\n moai_Scale[2]\n\njulia> formulation\nScale(scale, bias)\n├ variables [2]\n│ ├ moai_Scale[1]\n│ └ moai_Scale[2]\n└ constraints [6]\n ├ moai_Scale[1] ≥ 4\n ├ moai_Scale[1] ≤ 6\n ├ moai_Scale[2] ≥ 5\n ├ moai_Scale[2] ≤ 11\n ├ 2 x[1] - moai_Scale[1] = -4\n └ 3 x[2] - moai_Scale[2] = -5\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{AffExpr}:\n 2 x[1] + 4\n 3 x[2] + 5\n\njulia> formulation\nReducedSpace(Scale(scale, bias))\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#Sigmoid","page":"API Reference","title":"Sigmoid","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Sigmoid","category":"page"},{"location":"api/#MathOptAI.Sigmoid","page":"API Reference","title":"MathOptAI.Sigmoid","text":"Sigmoid() <: AbstractPredictor\n\nAn AbstractPredictor that represents the relationship:\n\ny = frac11 + e^-x\n\nas a smooth nonlinear constraint.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, -1 <= x[i in 1:2] <= i);\n\njulia> f = MathOptAI.Sigmoid()\nSigmoid()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_Sigmoid[1]\n moai_Sigmoid[2]\n\njulia> formulation\nSigmoid()\n├ variables [2]\n│ ├ moai_Sigmoid[1]\n│ └ moai_Sigmoid[2]\n└ constraints [6]\n ├ moai_Sigmoid[1] ≥ 0.2689414213699951\n ├ moai_Sigmoid[1] ≤ 0.7310585786300049\n ├ moai_Sigmoid[2] ≥ 0.2689414213699951\n ├ moai_Sigmoid[2] ≤ 0.8807970779778823\n ├ moai_Sigmoid[1] - (1.0 / (1.0 + exp(-x[1]))) = 0\n └ moai_Sigmoid[2] - (1.0 / (1.0 + exp(-x[2]))) = 0\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n 1.0 / (1.0 + exp(-x[1]))\n 1.0 / (1.0 + exp(-x[2]))\n\njulia> formulation\nReducedSpace(Sigmoid())\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#SoftMax","page":"API Reference","title":"SoftMax","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"SoftMax","category":"page"},{"location":"api/#MathOptAI.SoftMax","page":"API Reference","title":"MathOptAI.SoftMax","text":"SoftMax() <: AbstractPredictor\n\nAn AbstractPredictor that represents the relationship:\n\ny = frace^xe^x_1\n\nas a smooth nonlinear constraint.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> f = MathOptAI.SoftMax()\nSoftMax()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_SoftMax[1]\n moai_SoftMax[2]\n\njulia> formulation\nSoftMax()\n├ variables [3]\n│ ├ moai_SoftMax_denom\n│ ├ moai_SoftMax[1]\n│ └ moai_SoftMax[2]\n└ constraints [8]\n ├ moai_SoftMax[1] ≥ 0\n ├ moai_SoftMax[1] ≤ 1\n ├ moai_SoftMax[2] ≥ 0\n ├ moai_SoftMax[2] ≤ 1\n ├ moai_SoftMax_denom ≥ 0\n ├ moai_SoftMax_denom - (0.0 + exp(x[2]) + exp(x[1])) = 0\n ├ moai_SoftMax[1] - (exp(x[1]) / moai_SoftMax_denom) = 0\n └ moai_SoftMax[2] - (exp(x[2]) / moai_SoftMax_denom) = 0\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n exp(x[1]) / moai_SoftMax_denom\n exp(x[2]) / moai_SoftMax_denom\n\njulia> formulation\nReducedSpace(SoftMax())\n├ variables [1]\n│ └ moai_SoftMax_denom\n└ constraints [2]\n ├ moai_SoftMax_denom ≥ 0\n └ moai_SoftMax_denom - (0.0 + exp(x[2]) + exp(x[1])) = 0\n\n\n\n\n\n","category":"type"},{"location":"api/#SoftPlus","page":"API Reference","title":"SoftPlus","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"SoftPlus","category":"page"},{"location":"api/#MathOptAI.SoftPlus","page":"API Reference","title":"MathOptAI.SoftPlus","text":"SoftPlus(; beta = 1.0) <: AbstractPredictor\n\nAn AbstractPredictor that represents the relationship:\n\ny = frac1beta log(1 + e^beta x)\n\nas a smooth nonlinear constraint.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, -1 <= x[i in 1:2] <= i);\n\njulia> f = MathOptAI.SoftPlus(; beta = 2.0)\nSoftPlus(2.0)\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_SoftPlus[1]\n moai_SoftPlus[2]\n\njulia> formulation\nSoftPlus(2.0)\n├ variables [2]\n│ ├ moai_SoftPlus[1]\n│ └ moai_SoftPlus[2]\n└ constraints [6]\n ├ moai_SoftPlus[1] ≥ 0.0634640055214863\n ├ moai_SoftPlus[1] ≤ 1.0634640055214863\n ├ moai_SoftPlus[2] ≥ 0.0634640055214863\n ├ moai_SoftPlus[2] ≤ 2.0090749639589047\n ├ moai_SoftPlus[1] - (log(1.0 + exp(2 x[1])) / 2.0) = 0\n └ moai_SoftPlus[2] - (log(1.0 + exp(2 x[2])) / 2.0) = 0\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n log(1.0 + exp(2 x[1])) / 2.0\n log(1.0 + exp(2 x[2])) / 2.0\n\njulia> formulation\nReducedSpace(SoftPlus(2.0))\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#Tanh","page":"API Reference","title":"Tanh","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Tanh","category":"page"},{"location":"api/#MathOptAI.Tanh","page":"API Reference","title":"MathOptAI.Tanh","text":"Tanh() <: AbstractPredictor\n\nAn AbstractPredictor that represents the relationship:\n\ny = tanh(x)\n\nas a smooth nonlinear constraint.\n\nExample\n\njulia> using JuMP, MathOptAI\n\njulia> model = Model();\n\njulia> @variable(model, -1 <= x[i in 1:2] <= i);\n\njulia> f = MathOptAI.Tanh()\nTanh()\n\njulia> y, formulation = MathOptAI.add_predictor(model, f, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_Tanh[1]\n moai_Tanh[2]\n\njulia> formulation\nTanh()\n├ variables [2]\n│ ├ moai_Tanh[1]\n│ └ moai_Tanh[2]\n└ constraints [6]\n ├ moai_Tanh[1] ≥ -0.7615941559557649\n ├ moai_Tanh[1] ≤ 0.7615941559557649\n ├ moai_Tanh[2] ≥ -0.7615941559557649\n ├ moai_Tanh[2] ≤ 0.9640275800758169\n ├ moai_Tanh[1] - tanh(x[1]) = 0\n └ moai_Tanh[2] - tanh(x[2]) = 0\n\njulia> y, formulation =\n MathOptAI.add_predictor(model, MathOptAI.ReducedSpace(f), x);\n\njulia> y\n2-element Vector{NonlinearExpr}:\n tanh(x[1])\n tanh(x[2])\n\njulia> formulation\nReducedSpace(Tanh())\n├ variables [0]\n└ constraints [0]\n\n\n\n\n\n","category":"type"},{"location":"api/#AbstractFormulation","page":"API Reference","title":"AbstractFormulation","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"AbstractFormulation","category":"page"},{"location":"api/#MathOptAI.AbstractFormulation","page":"API Reference","title":"MathOptAI.AbstractFormulation","text":"abstract type AbstractFormulation end\n\nAn abstract type representing different formulations.\n\n\n\n\n\n","category":"type"},{"location":"api/#Formulation","page":"API Reference","title":"Formulation","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Formulation","category":"page"},{"location":"api/#MathOptAI.Formulation","page":"API Reference","title":"MathOptAI.Formulation","text":"struct Formulation{P<:AbstractPredictor} <: AbstractFormulation\n predictor::P\n variables::Vector{Any}\n constraints::Vector{Any}\nend\n\nFields\n\npredictor: the predictor object used to build the formulation\nvariables: a vector of new decision variables added to the model\nconstraints: a vector of new constraints added to the model\n\nCheck the docstring of the predictor for an explanation of the formulation and the order of the elements in .variables and .constraints.\n\n\n\n\n\n","category":"type"},{"location":"api/#PipelineFormulation","page":"API Reference","title":"PipelineFormulation","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"PipelineFormulation","category":"page"},{"location":"api/#MathOptAI.PipelineFormulation","page":"API Reference","title":"MathOptAI.PipelineFormulation","text":"struct PipelineFormulation{P<:AbstractPredictor} <: AbstractFormulation\n predictor::P\n layers::Vector{Any}\nend\n\nFields\n\npredictor: the predictor object used to build the formulation\nlayers: the formulation associated with each of the layers in the pipeline\n\n\n\n\n\n","category":"type"},{"location":"api/#Extensions","page":"API Reference","title":"Extensions","text":"","category":"section"},{"location":"api/","page":"API Reference","title":"API Reference","text":"Modules = [\n Base.get_extension(MathOptAI, :MathOptAIAbstractGPsExt),\n Base.get_extension(MathOptAI, :MathOptAIDecisionTreeExt),\n Base.get_extension(MathOptAI, :MathOptAIFluxExt),\n Base.get_extension(MathOptAI, :MathOptAIGLMExt),\n Base.get_extension(MathOptAI, :MathOptAILuxExt),\n Base.get_extension(MathOptAI, :MathOptAIPythonCallExt),\n Base.get_extension(MathOptAI, :MathOptAIStatsModelsExt),\n]","category":"page"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, MathOptAI.Quantile{<:AbstractGPs.PosteriorGP}, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::MathOptAI.Quantile{<:AbstractGPs.PosteriorGP},\n x::Vector,\n)\n\nAdd the quantiles of a trained Gaussian Process from AbstractGPs.jl to model.\n\nExample\n\njulia> using JuMP, MathOptAI, AbstractGPs\n\njulia> x_data = 2π .* (0.0:0.1:1.0);\n\njulia> y_data = sin.(x_data);\n\njulia> fx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.1);\n\njulia> p_fx = AbstractGPs.posterior(fx, y_data);\n\njulia> model = Model();\n\njulia> @variable(model, 1 <= x[1:1] <= 6, start = 3);\n\njulia> predictor = MathOptAI.Quantile(p_fx, [0.1, 0.9]);\n\njulia> y, _ = MathOptAI.add_predictor(model, predictor, x);\n\njulia> y\n2-element Vector{VariableRef}:\n moai_quantile[1]\n moai_quantile[2]\n\njulia> @objective(model, Max, y[2] - y[1])\nmoai_quantile[2] - moai_quantile[1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, Union{DecisionTree.DecisionTreeClassifier, DecisionTree.Root}, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::Union{DecisionTree.Root,DecisionTree.DecisionTreeClassifier},\n x::Vector,\n)\n\nAdd a binary decision tree from DecisionTree.jl to model.\n\nExample\n\njulia> using JuMP, MathOptAI, DecisionTree\n\njulia> truth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)\ntruth (generic function with 1 method)\n\njulia> features = abs.(sin.((1:10) .* (3:4)'));\n\njulia> size(features)\n(10, 2)\n\njulia> labels = truth.(Vector.(eachrow(features)));\n\njulia> predictor = DecisionTree.build_tree(labels, features)\nDecision Tree\nLeaves: 3\nDepth: 2\n\njulia> model = Model();\n\njulia> @variable(model, 0 <= x[1:2] <= 1);\n\njulia> y, _ = MathOptAI.add_predictor(model, predictor, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_BinaryDecisionTree_value\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.build_predictor-Tuple{DecisionTree.Root}","page":"API Reference","title":"MathOptAI.build_predictor","text":"MathOptAI.build_predictor(predictor::DecisionTree.Root)\n\nConvert a binary decision tree from DecisionTree.jl to a BinaryDecisionTree.\n\nExample\n\njulia> using MathOptAI, DecisionTree\n\njulia> truth(x::Vector) = x[1] <= 0.5 ? -2 : (x[2] <= 0.3 ? 3 : 4)\ntruth (generic function with 1 method)\n\njulia> features = abs.(sin.((1:10) .* (3:4)'));\n\njulia> size(features)\n(10, 2)\n\njulia> labels = truth.(Vector.(eachrow(features)));\n\njulia> tree = DecisionTree.build_tree(labels, features)\nDecision Tree\nLeaves: 3\nDepth: 2\n\njulia> predictor = MathOptAI.build_predictor(tree)\nBinaryDecisionTree{Float64,Int64} [leaves=3, depth=2]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, Flux.Chain, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::Flux.Chain,\n x::Vector;\n config::Dict = Dict{Any,Any}(),\n reduced_space::Bool = false,\n gray_box::Bool = false,\n)\n\nAdd a trained neural network from Flux.jl to model.\n\nSupported layers\n\nFlux.Dense\nFlux.Scale\nFlux.softmax\n\nSupported activation functions\n\nFlux.relu\nFlux.sigmoid\nFlux.softplus\nFlux.tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps supported Flux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Flux.sigmoid => MathOptAI.Sigmoid() or Flux.relu => MathOptAI.QuadraticReLU().\ngray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by Flux.withjacobian.\n\nExample\n\njulia> using JuMP, Flux, MathOptAI\n\njulia> chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));\n\njulia> model = Model();\n\njulia> @variable(model, x[1:1]);\n\njulia> y, _ = MathOptAI.add_predictor(\n model,\n chain,\n x;\n config = Dict(Flux.relu => MathOptAI.ReLU()),\n );\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Affine[1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.build_predictor-Tuple{Flux.Chain}","page":"API Reference","title":"MathOptAI.build_predictor","text":"MathOptAI.build_predictor(\n predictor::Flux.Chain;\n config::Dict = Dict{Any,Any}(),\n gray_box::Bool = false,\n gray_box_hessian::Bool = false,\n)\n\nConvert a trained neural network from Flux.jl to a Pipeline.\n\nSupported layers\n\nFlux.Dense\nFlux.Scale\nFlux.softmax\n\nSupported activation functions\n\nFlux.relu\nFlux.sigmoid\nFlux.softplus\nFlux.tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps supported Flux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Flux.sigmoid => MathOptAI.Sigmoid() or Flux.relu => MathOptAI.QuadraticReLU().\ngray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by Flux.withjacobian.\ngray_box_hessian: if true, the gray box additionally computes the Hessian of the output using Flux.hessian.\n\nExample\n\njulia> using Flux, MathOptAI\n\njulia> chain = Flux.Chain(Flux.Dense(1 => 16, Flux.relu), Flux.Dense(16 => 1));\n\njulia> MathOptAI.build_predictor(\n chain;\n config = Dict(Flux.relu => MathOptAI.ReLU()),\n )\nPipeline with layers:\n * Affine(A, b) [input: 1, output: 16]\n * ReLU()\n * Affine(A, b) [input: 16, output: 1]\n\njulia> MathOptAI.build_predictor(\n chain;\n config = Dict(Flux.relu => MathOptAI.ReLUQuadratic()),\n )\nPipeline with layers:\n * Affine(A, b) [input: 1, output: 16]\n * ReLUQuadratic()\n * Affine(A, b) [input: 16, output: 1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, GLM.GeneralizedLinearModel{GLM.GlmResp{Vector{Float64}, Distributions.Bernoulli{Float64}, GLM.LogitLink}}, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::GLM.GeneralizedLinearModel{\n GLM.GlmResp{Vector{Float64},GLM.Bernoulli{Float64},GLM.LogitLink},\n },\n x::Vector;\n sigmoid::AbstractPredictor = MathOptAI.Sigmoid(),\n reduced_space::Bool = false,\n)\n\nAdd a trained logistic regression model from GLM.jl to model.\n\nKeyword arguments\n\nsigmoid: the predictor to use for the sigmoid layer.\n\nExample\n\njulia> using GLM, JuMP, MathOptAI\n\njulia> X, Y = rand(10, 2), rand(Bool, 10);\n\njulia> predictor = GLM.glm(X, Y, GLM.Bernoulli());\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> y, _ = MathOptAI.add_predictor(\n model,\n predictor,\n x;\n sigmoid = MathOptAI.Sigmoid(),\n );\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Sigmoid[1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, GLM.LinearModel, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::GLM.LinearModel,\n x::Vector;\n reduced_space::Bool = false,\n)\n\nAdd a trained linear model from GLM.jl to model.\n\nExample\n\njulia> using GLM, JuMP, MathOptAI\n\njulia> X, Y = rand(10, 2), rand(10);\n\njulia> predictor = GLM.lm(X, Y);\n\njulia> model = Model();\n\njulia> @variable(model, x[1:2]);\n\njulia> y, _ = MathOptAI.add_predictor(model, predictor, x);\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Affine[1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.build_predictor-Tuple{GLM.GeneralizedLinearModel{GLM.GlmResp{Vector{Float64}, Distributions.Bernoulli{Float64}, GLM.LogitLink}}}","page":"API Reference","title":"MathOptAI.build_predictor","text":"MathOptAI.build_predictor(\n predictor::GLM.GeneralizedLinearModel{\n GLM.GlmResp{Vector{Float64},GLM.Bernoulli{Float64},GLM.LogitLink},\n };\n sigmoid::MathOptAI.AbstractPredictor = MathOptAI.Sigmoid(),\n)\n\nConvert a trained logistic model from GLM.jl to a Pipeline layer.\n\nKeyword arguments\n\nsigmoid: the predictor to use for the sigmoid layer.\n\nExample\n\njulia> using GLM, MathOptAI\n\njulia> X, Y = rand(10, 2), rand(Bool, 10);\n\njulia> model = GLM.glm(X, Y, GLM.Bernoulli());\n\njulia> predictor = MathOptAI.build_predictor(model)\nPipeline with layers:\n * Affine(A, b) [input: 2, output: 1]\n * Sigmoid()\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.build_predictor-Tuple{GLM.LinearModel}","page":"API Reference","title":"MathOptAI.build_predictor","text":"MathOptAI.build_predictor(predictor::GLM.LinearModel)\n\nConvert a trained linear model from GLM.jl to an Affine layer.\n\nExample\n\njulia> using GLM, MathOptAI\n\njulia> X, Y = rand(10, 2), rand(10);\n\njulia> model = GLM.lm(X, Y);\n\njulia> predictor = MathOptAI.build_predictor(model)\nAffine(A, b) [input: 2, output: 1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, Tuple{Lux.Chain, NamedTuple, NamedTuple}, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::Tuple{<:Lux.Chain,<:NamedTuple,<:NamedTuple},\n x::Vector;\n config::Dict = Dict{Any,Any}(),\n reduced_space::Bool = false,\n)\n\nAdd a trained neural network from Lux.jl to model.\n\nSupported layers\n\nLux.Dense\nLux.Scale\n\nSupported activation functions\n\nLux.relu\nLux.sigmoid\nLux.softplus\nLux.softmax\nLux.tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps supported Lux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Lux.sigmoid => MathOptAI.Sigmoid() or Lux.relu => MathOptAI.QuadraticReLU().\n\nExample\n\njulia> using JuMP, Lux, MathOptAI, Random\n\njulia> rng = Random.MersenneTwister();\n\njulia> chain = Lux.Chain(Lux.Dense(1 => 16, Lux.relu), Lux.Dense(16 => 1))\nChain(\n layer_1 = Dense(1 => 16, relu), # 32 parameters\n layer_2 = Dense(16 => 1), # 17 parameters\n) # Total: 49 parameters,\n # plus 0 states.\n\njulia> parameters, state = Lux.setup(rng, chain);\n\njulia> predictor = (chain, parameters, state);\n\njulia> model = Model();\n\njulia> @variable(model, x[1:1]);\n\njulia> y, _ = MathOptAI.add_predictor(\n model,\n predictor,\n x;\n config = Dict(Lux.relu => MathOptAI.ReLU()),\n );\n\njulia> y\n1-element Vector{VariableRef}:\n moai_Affine[1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.build_predictor-Tuple{Tuple{Lux.Chain, NamedTuple, NamedTuple}}","page":"API Reference","title":"MathOptAI.build_predictor","text":"MathOptAI.build_predictor(\n predictor::Tuple{<:Lux.Chain,<:NamedTuple,<:NamedTuple};\n config::Dict = Dict{Any,Any}(),\n)\n\nConvert a trained neural network from Lux.jl to a Pipeline.\n\nSupported layers\n\nLux.Dense\nLux.Scale\n\nSupported activation functions\n\nLux.relu\nLux.sigmoid\nLux.softplus\nLux.softmax\nLux.tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps supported Lux activation functions to AbstractPredictors that control how the activation functions are reformulated. For example, Lux.sigmoid => MathOptAI.Sigmoid() or Lux.relu => MathOptAI.QuadraticReLU().\n\nExample\n\njulia> using Lux, MathOptAI, Random\n\njulia> rng = Random.MersenneTwister();\n\njulia> chain = Lux.Chain(Lux.Dense(1 => 16, Lux.relu), Lux.Dense(16 => 1))\nChain(\n layer_1 = Dense(1 => 16, relu), # 32 parameters\n layer_2 = Dense(16 => 1), # 17 parameters\n) # Total: 49 parameters,\n # plus 0 states.\n\njulia> parameters, state = Lux.setup(rng, chain);\n\njulia> predictor = MathOptAI.build_predictor(\n (chain, parameters, state);\n config = Dict(Lux.relu => MathOptAI.ReLU()),\n )\nPipeline with layers:\n * Affine(A, b) [input: 1, output: 16]\n * ReLU()\n * Affine(A, b) [input: 16, output: 1]\n\njulia> MathOptAI.build_predictor(\n (chain, parameters, state);\n config = Dict(Lux.relu => MathOptAI.ReLUQuadratic()),\n )\nPipeline with layers:\n * Affine(A, b) [input: 1, output: 16]\n * ReLUQuadratic()\n * Affine(A, b) [input: 16, output: 1]\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, MathOptAI.PytorchModel, Vector}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::MathOptAI.PytorchModel,\n x::Vector;\n config::Dict = Dict{Any,Any}(),\n reduced_space::Bool = false,\n gray_box::Bool = false,\n)\n\nAdd a trained neural network from PyTorch via PythonCall.jl to model.\n\nSupported layers\n\nnn.Linear\nnn.ReLU\nnn.Sequential\nnn.Sigmoid\nnn.Softplus\nnn.Tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps Symbols to AbstractPredictors that control how the activation functions are reformulated. For example, :Sigmoid => MathOptAI.Sigmoid() or :ReLU => MathOptAI.QuadraticReLU(). The supported Symbols are :ReLU, :Sigmoid, :SoftPlus, and :Tanh.\ngray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by torch.func.jacrev.\ngray_box_hessian: if true, the gray box additionally computes the Hessian of the output using torch.func.hessian.\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.build_predictor-Tuple{MathOptAI.PytorchModel}","page":"API Reference","title":"MathOptAI.build_predictor","text":"MathOptAI.build_predictor(\n predictor::MathOptAI.PytorchModel;\n config::Dict = Dict{Any,Any}(),\n gray_box::Bool = false,\n gray_box_hessian::Bool = false,\n)\n\nConvert a trained neural network from PyTorch via PythonCall.jl to a Pipeline.\n\nSupported layers\n\nnn.Linear\nnn.ReLU\nnn.Sequential\nnn.Sigmoid\nnn.Softplus\nnn.Tanh\n\nKeyword arguments\n\nconfig: a dictionary that maps Symbols to AbstractPredictors that control how the activation functions are reformulated. For example, :Sigmoid => MathOptAI.Sigmoid() or :ReLU => MathOptAI.QuadraticReLU(). The supported Symbols are :ReLU, :Sigmoid, :SoftPlus, and :Tanh.\ngray_box: if true, the neural network is added as a user-defined nonlinear operator, with gradients provided by torch.func.jacrev.\ngray_box_hessian: if true, the gray box additionally computes the Hessian of the output using torch.func.hessian.\n\n\n\n\n\n","category":"method"},{"location":"api/#MathOptAI.add_predictor-Tuple{JuMP.AbstractModel, StatsModels.TableRegressionModel, DataFrames.DataFrame}","page":"API Reference","title":"MathOptAI.add_predictor","text":"MathOptAI.add_predictor(\n model::JuMP.AbstractModel,\n predictor::StatsModels.TableRegressionModel,\n x::DataFrames.DataFrame;\n kwargs...,\n)\n\nAdd a trained regression model from StatsModels.jl to model, using the DataFrame x as input.\n\nIn most cases, predictor should be a GLM.jl predictor supported by MathOptAI, but trained using @formula and a DataFrame instead of the raw matrix input.\n\nIn general, x may have some columns that are constant (Float64) and some columns that are JuMP decision variables.\n\nKeyword arguments\n\nAll keyword arguments are passed to the corresponding add_predictor of the GLM extension.\n\nExample\n\njulia> using DataFrames, GLM, JuMP, MathOptAI\n\njulia> train_df = DataFrames.DataFrame(x1 = rand(10), x2 = rand(10));\n\njulia> train_df.y = 1.0 .* train_df.x1 + 2.0 .* train_df.x2 .+ rand(10);\n\njulia> predictor = GLM.lm(GLM.@formula(y ~ x1 + x2), train_df);\n\njulia> model = Model();\n\njulia> test_df = DataFrames.DataFrame(\n x1 = rand(6),\n x2 = @variable(model, [1:6]),\n );\n\njulia> test_df.y, _ = MathOptAI.add_predictor(model, predictor, test_df);\n\njulia> test_df.y\n6-element Vector{VariableRef}:\n moai_Affine[1]\n moai_Affine[1]\n moai_Affine[1]\n moai_Affine[1]\n moai_Affine[1]\n moai_Affine[1]\n\n\n\n\n\n","category":"method"},{"location":"manual/AbstractGPs/#AbstractGPs.jl","page":"AbstractGPs.jl","title":"AbstractGPs.jl","text":"","category":"section"},{"location":"manual/AbstractGPs/","page":"AbstractGPs.jl","title":"AbstractGPs.jl","text":"AbstractGPs.jl is a library for fitting Gaussian Processes in Julia.","category":"page"},{"location":"manual/AbstractGPs/#Basic-example","page":"AbstractGPs.jl","title":"Basic example","text":"","category":"section"},{"location":"manual/AbstractGPs/","page":"AbstractGPs.jl","title":"AbstractGPs.jl","text":"Here is an example:","category":"page"},{"location":"manual/AbstractGPs/","page":"AbstractGPs.jl","title":"AbstractGPs.jl","text":"using JuMP, MathOptAI, AbstractGPs\nx_data = 2π .* (0.0:0.1:1.0);\ny_data = sin.(x_data);\nfx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.1);\np_fx = AbstractGPs.posterior(fx, y_data);\nmodel = Model();\n@variable(model, 1 <= x[1:1] <= 6, start = 3);\npredictor = MathOptAI.Quantile(p_fx, [0.1, 0.9]);\ny, formulation = MathOptAI.add_predictor(model, predictor, x);\ny\nformulation\n@objective(model, Max, y[2] - y[1])","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"EditURL = \"pytorch.jl\"","category":"page"},{"location":"tutorials/pytorch/#Function-fitting-with-PyTorch","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"","category":"section"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"The purpose of this tutorial is to explain how to embed a neural network model from PyTorch into JuMP.","category":"page"},{"location":"tutorials/pytorch/#Python-integration","page":"Function fitting with PyTorch","title":"Python integration","text":"","category":"section"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"MathOptAI uses PythonCall.jl to call from Julia into Python.","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"See CondaPkg.jl for more control over how to link Julia to an existing Python environment. For example, if you have an existing Python installation (with PyTorch installed), and it is available in the current Conda environment, set:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"ENV[\"JULIA_CONDAPKG_BACKEND\"] = \"Current\"","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"before importing PythonCall.jl. If the Python installation can be found on the path and it is not in a Conda environment, set:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"ENV[\"JULIA_CONDAPKG_BACKEND\"] = \"Null\"","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"If python is not on your path, you may additionally need to set JULIA_PYTHONCALL_EXE, for example, to:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"ENV[\"JULIA_PYTHONCALL_EXE\"] = \"python3\"","category":"page"},{"location":"tutorials/pytorch/#Required-packages","page":"Function fitting with PyTorch","title":"Required packages","text":"","category":"section"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"This tutorial requires the following packages","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"using JuMP\nusing Test\nimport Ipopt\nimport MathOptAI\nimport Plots","category":"page"},{"location":"tutorials/pytorch/#Training-a-model","page":"Function fitting with PyTorch","title":"Training a model","text":"","category":"section"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"The following script builds and trains a simple neural network in PyTorch. For simplicity, we do not evaluate out-of-sample test performance, or use a batched data loader. In general, you should train your model in Python, and then use torch.save(model, filename) to save it to a .pt file for later use in Julia.","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"The model is unimportant, but for this example, we are trying to fit noisy observations of the function f(x) = x^2 - 2x.","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"In Python, we ran:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"#!/usr/bin/python3\nimport torch\nmodel = torch.nn.Sequential(\n torch.nn.Linear(1, 16),\n torch.nn.ReLU(),\n torch.nn.Linear(16, 1),\n)\n\nn = 1024\nx = torch.arange(-2, 2 + 4 / (n - 1), 4 / (n - 1)).reshape(n, 1)\nloss_fn = torch.nn.MSELoss()\noptimizer = torch.optim.Adam(model.parameters(), lr=0.01)\nfor epoch in range(100):\n optimizer.zero_grad()\n N = torch.normal(torch.zeros(n, 1), torch.ones(n, 1))\n y = x ** 2 -2 * x + 0.1 * N\n loss = loss_fn(model(x), y)\n loss.backward()\n optimizer.step()\n\ntorch.save(model, \"model.pt\")","category":"page"},{"location":"tutorials/pytorch/#JuMP-model","page":"Function fitting with PyTorch","title":"JuMP model","text":"","category":"section"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"Our goal for this JuMP model is to load the Neural Network from PyTorch into the objective function, and then minimize the objective for different fixed values of x to recreate the function that the Neural Network has learned to approximate.","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"First, create a JuMP model:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"model = Model(Ipopt.Optimizer)\nset_silent(model)\n@variable(model, x)","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"Then, load the model from PyTorch using MathOptAI.PytorchModel:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"predictor = MathOptAI.PytorchModel(joinpath(@__DIR__, \"model.pt\"))\ny, _ = MathOptAI.add_predictor(model, predictor, [x])\n@objective(model, Min, only(y))","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"Now, visualize the fitted function y = predictor(x) by repeatedly solving the optimization problem for different fixed values of x:","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"X, Y = -2:0.1:2, Float64[]\n@constraint(model, c, x == 0.0)\nfor xi in X\n set_normalized_rhs(c, xi)\n optimize!(model)\n @test is_solved_and_feasible(model)\n push!(Y, objective_value(model))\nend\nPlots.plot(x -> x^2 - 2x, X; label = \"Truth\", linestype = :dot)\nPlots.plot!(X, Y; label = \"Fitted\")","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"","category":"page"},{"location":"tutorials/pytorch/","page":"Function fitting with PyTorch","title":"Function fitting with PyTorch","text":"This page was generated using Literate.jl.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"EditURL = \"decision_trees.jl\"","category":"page"},{"location":"tutorials/decision_trees/#Classification-problems-with-DecisionTree.jl","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"","category":"section"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The purpose of this tutorial is to explain how to embed a decision tree model from DecisionTree.jl into JuMP.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The data and example in this tutorial comes from the paper: David Bergman, Teng Huang, Philip Brooks, Andrea Lodi, Arvind U. Raghunathan (2021) JANOS: An Integrated Predictive and Prescriptive Modeling Framework. INFORMS Journal on Computing 34(2):807-816. https://doi.org/10.1287/ijoc.2020.1023","category":"page"},{"location":"tutorials/decision_trees/#Required-packages","page":"Classification problems with DecisionTree.jl","title":"Required packages","text":"","category":"section"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"This tutorial uses the following packages.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"using JuMP\nimport CSV\nimport DataFrames\nimport Downloads\nimport DecisionTree\nimport HiGHS\nimport MathOptAI\nimport Statistics","category":"page"},{"location":"tutorials/decision_trees/#Data","page":"Classification problems with DecisionTree.jl","title":"Data","text":"","category":"section"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Here is a function to load the data directly from the JANOS repository:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"function read_df(filename)\n url = \"https://raw.githubusercontent.com/INFORMSJoC/2020.1023/master/data/\"\n data = Downloads.download(url * filename)\n return CSV.read(data, DataFrames.DataFrame)\nend","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"There are two important files. The first, college_student_enroll-s1-1.csv, contains historical admissions data on anonymized students, their SAT score, their GPA, their merit scholarships, and whether the enrolled in the college.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"train_df = read_df(\"college_student_enroll-s1-1.csv\")","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The second, college_applications6000.csv, contains the SAT and GPA data of students who are currently applying:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"evaluate_df = read_df(\"college_applications6000.csv\")","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"There are 6,000 prospective students:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"n_students = size(evaluate_df, 1)","category":"page"},{"location":"tutorials/decision_trees/#Prediction-model","page":"Classification problems with DecisionTree.jl","title":"Prediction model","text":"","category":"section"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The first step is to train a logistic regression model to predict the Boolean enroll column based on the SAT, GPA, and merit columns.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"train_features = Matrix(train_df[:, [:SAT, :GPA, :merit]])\ntrain_labels = train_df[:, :enroll]\npredictor = DecisionTree.DecisionTreeClassifier(; max_depth = 3)\nDecisionTree.fit!(predictor, train_features, train_labels)\nDecisionTree.print_tree(predictor)","category":"page"},{"location":"tutorials/decision_trees/#Decision-model","page":"Classification problems with DecisionTree.jl","title":"Decision model","text":"","category":"section"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Now that we have a trained decision tree, we want a decision model that chooses the optimal merit scholarship for each student in:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"evaluate_df","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Here's an empty JuMP model to start:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"model = Model()","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"First, we add a new column to evaluate_df, with one JuMP decision variable for each row. It is important the .merit column name in evaluate_df matches the name in train_df.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"evaluate_df.merit = @variable(model, 0 <= x_merit[1:n_students] <= 2.5);\nevaluate_df","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Then, we use MathOptAI.add_predictor to embed model_ml into the JuMP model. MathOptAI.add_predictor returns a vector of variables, one for each row in evaluate_df, corresponding to the output enroll of our logistic regression.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"evaluate_features = Matrix(evaluate_df[:, [:SAT, :GPA, :merit]])\nevaluate_df.enroll = mapreduce(vcat, 1:size(evaluate_features, 1)) do i\n y, _ = MathOptAI.add_predictor(model, predictor, evaluate_features[i, :])\n return y\nend\nevaluate_df","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The .enroll column name in evaluate_df is just a name. It doesn't have to match the name in train_df.","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The objective of our problem is to maximize the expected number of students who enroll:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"@objective(model, Max, sum(evaluate_df.enroll))","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Subject to the constraint that we can spend at most 0.2 * n_students on merit scholarships:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"@constraint(model, sum(evaluate_df.merit) <= 0.2 * n_students)","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Because logistic regression involves a Sigmoid layer, we need to use a smooth nonlinear optimizer. A common choice is Ipopt. Solve and check the optimizer found a feasible solution:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"set_optimizer(model, HiGHS.Optimizer)\nset_silent(model)\noptimize!(model)\n@assert is_solved_and_feasible(model)","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"Let's store the solution in evaluate_df for analysis:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"evaluate_df.merit_sol = value.(evaluate_df.merit);\nevaluate_df.enroll_sol = value.(evaluate_df.enroll);\nevaluate_df","category":"page"},{"location":"tutorials/decision_trees/#Solution-analysis","page":"Classification problems with DecisionTree.jl","title":"Solution analysis","text":"","category":"section"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"We expect that just under 2,500 students will enroll:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"sum(evaluate_df.enroll_sol)","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"We awarded merit scholarships to approximately 1 in 6 students:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"count(evaluate_df.merit_sol .> 1e-5)","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"The average merit scholarship was worth just under $1,000:","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"1_000 * Statistics.mean(evaluate_df.merit_sol[evaluate_df.merit_sol.>1e-5])","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"","category":"page"},{"location":"tutorials/decision_trees/","page":"Classification problems with DecisionTree.jl","title":"Classification problems with DecisionTree.jl","text":"This page was generated using Literate.jl.","category":"page"},{"location":"manual/Lux/#Lux.jl","page":"Lux.jl","title":"Lux.jl","text":"","category":"section"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"Lux.jl is a library for machine learning in Julia.","category":"page"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"The upstream documentation is available at https://lux.csail.mit.edu/stable/.","category":"page"},{"location":"manual/Lux/#Supported-layers","page":"Lux.jl","title":"Supported layers","text":"","category":"section"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"MathOptAI supports embedding a Lux model into JuMP if it is a Lux.Chain composed of:","category":"page"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"Lux.Dense\nLux.Scale\nLux.relu\nLux.sigmoid\nLux.softmax\nLux.softplus\nLux.tanh","category":"page"},{"location":"manual/Lux/#Basic-example","page":"Lux.jl","title":"Basic example","text":"","category":"section"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"Use MathOptAI.add_predictor to embed a tuple (containing the Lux.Chain, the parameters, and the state) into a JuMP model:","category":"page"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"using JuMP, Lux, MathOptAI, Random\nrng = Random.MersenneTwister();\nchain = Lux.Chain(Lux.Dense(1 => 2, Lux.relu), Lux.Dense(2 => 1))\nparameters, state = Lux.setup(rng, chain);\npredictor = (chain, parameters, state);\nmodel = Model();\n@variable(model, x[1:1]);\ny, formulation = MathOptAI.add_predictor(model, predictor, x);\ny\nformulation","category":"page"},{"location":"manual/Lux/#Reduced-space","page":"Lux.jl","title":"Reduced-space","text":"","category":"section"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"Use the reduced_space = true keyword to formulate a reduced-space model:","category":"page"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"using JuMP, Lux, MathOptAI, Random\nrng = Random.MersenneTwister();\nchain = Lux.Chain(Lux.Dense(1 => 2, Lux.relu), Lux.Dense(2 => 1))\nparameters, state = Lux.setup(rng, chain);\npredictor = (chain, parameters, state);\nmodel = Model();\n@variable(model, x[1:1]);\ny, formulation =\n MathOptAI.add_predictor(model, predictor, x; reduced_space = true);\ny\nformulation","category":"page"},{"location":"manual/Lux/#Gray-box","page":"Lux.jl","title":"Gray-box","text":"","category":"section"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"The Lux extension does not yet support the gray_box keyword argument.","category":"page"},{"location":"manual/Lux/#Change-how-layers-are-formulated","page":"Lux.jl","title":"Change how layers are formulated","text":"","category":"section"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"Pass a dictionary to the config keyword that maps Lux activation functions to a MathOptAI predictor:","category":"page"},{"location":"manual/Lux/","page":"Lux.jl","title":"Lux.jl","text":"using JuMP, Lux, MathOptAI, Random\nrng = Random.MersenneTwister();\nchain = Lux.Chain(Lux.Dense(1 => 2, Lux.relu), Lux.Dense(2 => 1))\nparameters, state = Lux.setup(rng, chain);\npredictor = (chain, parameters, state);\nmodel = Model();\n@variable(model, x[1:1]);\ny, formulation = MathOptAI.add_predictor(\n model,\n predictor,\n x;\n config = Dict(Lux.relu => MathOptAI.ReLUSOS1()),\n);\ny\nformulation","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"EditURL = \"mnist_lux.jl\"","category":"page"},{"location":"tutorials/mnist_lux/#Adversarial-machine-learning-with-Lux.jl","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"","category":"section"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"The purpose of this tutorial is to explain how to embed a neural network model from Lux.jl into JuMP.","category":"page"},{"location":"tutorials/mnist_lux/#Required-packages","page":"Adversarial machine learning with Lux.jl","title":"Required packages","text":"","category":"section"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"This tutorial requires the following packages","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"using JuMP\nimport Lux\nimport Ipopt\nimport MathOptAI\nimport MLDatasets\nimport MLUtils\nimport OneHotArrays\nimport Optimisers\nimport Plots\nimport Random\nimport Zygote","category":"page"},{"location":"tutorials/mnist_lux/#Data","page":"Adversarial machine learning with Lux.jl","title":"Data","text":"","category":"section"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"This tutorial uses images from the MNIST dataset.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"We load the predefined train and test splits:","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"train_data = MLDatasets.MNIST(; split = :train)","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"test_data = MLDatasets.MNIST(; split = :test)","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Since the data are images, it is helpful to plot them. (This requires a transpose and reversing the rows to get the orientation correct.)","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"function plot_image(x::Matrix; kwargs...)\n return Plots.heatmap(\n x'[size(x, 1):-1:1, :];\n xlims = (1, size(x, 2)),\n ylims = (1, size(x, 1)),\n aspect_ratio = true,\n legend = false,\n xaxis = false,\n yaxis = false,\n kwargs...,\n )\nend\n\nfunction plot_image(instance::NamedTuple)\n return plot_image(instance.features; title = \"Label = $(instance.targets)\")\nend\n\nPlots.plot([plot_image(train_data[i]) for i in 1:6]...; layout = (2, 3))","category":"page"},{"location":"tutorials/mnist_lux/#Training","page":"Adversarial machine learning with Lux.jl","title":"Training","text":"","category":"section"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"We use a simple neural network with one hidden layer and a sigmoid activation function. (There are better performing networks; try experimenting.)","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"chain = Lux.Chain(\n Lux.Dense(28^2 => 32, Lux.sigmoid),\n Lux.Dense(32 => 10),\n Lux.softmax,\n)\nrng = Random.MersenneTwister();\nparameters, state = Lux.setup(rng, chain)\npredictor = (chain, parameters, state);\nnothing #hide","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Here is a function to load our data into the format that predictor expects:","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"function data_loader(data; batchsize, shuffle = false)\n x = reshape(data.features, 28^2, :)\n y = OneHotArrays.onehotbatch(data.targets, 0:9)\n return MLUtils.DataLoader((x, y); batchsize, shuffle)\nend","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"and here is a function to score the percentage of correct labels, where we assign a label by choosing the label of the highest softmax in the final layer.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"function score_model(predictor, data)\n chain, parameters, state = predictor\n x, y = only(data_loader(data; batchsize = length(data)))\n y_hat, _ = chain(x, parameters, state)\n is_correct = OneHotArrays.onecold(y) .== OneHotArrays.onecold(y_hat)\n p = round(100 * sum(is_correct) / length(is_correct); digits = 2)\n println(\"Accuracy = $p %\")\n return\nend","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"The accuracy of our model is only around 10% before training:","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"score_model(predictor, train_data)\nscore_model(predictor, test_data)","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Let's improve that by training our model.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"note: Note\nIt is not the purpose of this tutorial to explain how Lux works; see the documentation at https://lux.csail.mit.edu for more details. Changing the number of epochs or the learning rate can improve the loss.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"begin\n train_loader = data_loader(train_data; batchsize = 256, shuffle = true)\n optimizer_state = Optimisers.setup(Optimisers.Adam(0.0003f0), parameters)\n for epoch in 1:30\n loss = 0.0\n for (x, y) in train_loader\n global state\n (loss_batch, state), pullback = Zygote.pullback(parameters) do p\n y_model, new_state = chain(x, p, state)\n return Lux.CrossEntropyLoss()(y_model, y), new_state\n end\n gradients = only(pullback((one(loss), nothing)))\n Optimisers.update!(optimizer_state, parameters, gradients)\n loss += loss_batch\n end\n loss = round(loss / length(train_loader); digits = 4)\n print(\"Epoch $epoch: loss = $loss\\t\")\n score_model(predictor, test_data)\n end\nend","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Here are the first eight predictions of the test data:","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"function plot_image(predictor, x::Matrix)\n y, _ = chain(vec(x), parameters, state)\n score, index = findmax(y)\n title = \"Predicted: $(index - 1) ($(round(Int, 100 * score))%)\"\n return plot_image(x; title)\nend\n\nplots = [plot_image(predictor, test_data[i].features) for i in 1:8]\nPlots.plot(plots...; size = (1200, 600), layout = (2, 4))","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"We can also look at the best and worst four predictions:","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"x, y = only(data_loader(test_data; batchsize = length(test_data)))\ny_model, _ = chain(x, parameters, state)\nlosses = Lux.CrossEntropyLoss(; agg = identity)(y_model, y)\nindices = sortperm(losses; dims = 2)[[1:4; end-3:end]]\nplots = [plot_image(predictor, test_data[i].features) for i in indices]\nPlots.plot(plots...; size = (1200, 600), layout = (2, 4))","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"There are still some fairly bad mistakes. Can you change the model or training parameters improve to improve things?","category":"page"},{"location":"tutorials/mnist_lux/#JuMP","page":"Adversarial machine learning with Lux.jl","title":"JuMP","text":"","category":"section"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Now that we have a trained machine learning model, we can embed it in a JuMP model.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Here's a function which takes a test case and returns an example that maximizes the probability of the adversarial example.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"function find_adversarial_image(test_case; adversary_label, δ = 0.05)\n model = Model(Ipopt.Optimizer)\n set_silent(model)\n @variable(model, 0 <= x[1:28, 1:28] <= 1)\n @constraint(model, -δ .<= x .- test_case.features .<= δ)\n # Note: we need to use `vec` here because `x` is a 28-by-28 Matrix, but our\n # neural network expects a 28^2 length vector.\n y, _ = MathOptAI.add_predictor(model, predictor, vec(x))\n @objective(model, Max, y[adversary_label+1] - y[test_case.targets+1])\n optimize!(model)\n @assert is_solved_and_feasible(model)\n return value.(x)\nend","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"Let's try finding an adversarial example to the third test image. The image on the left is our input image. The network thinks this is a 1 with probability 99%. The image on the right is the adversarial image. The network thinks this is a 7, although it is less confident.","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"x_adversary = find_adversarial_image(test_data[3]; adversary_label = 7);\nPlots.plot(\n plot_image(predictor, test_data[3].features),\n plot_image(predictor, Float32.(x_adversary)),\n)","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"","category":"page"},{"location":"tutorials/mnist_lux/","page":"Adversarial machine learning with Lux.jl","title":"Adversarial machine learning with Lux.jl","text":"This page was generated using Literate.jl.","category":"page"},{"location":"manual/PyTorch/#PyTorch","page":"PyTorch","title":"PyTorch","text":"","category":"section"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"PyTorch is a library for machine learning in Python.","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"The upstream documentation is available at https://pytorch.org/docs/stable/.","category":"page"},{"location":"manual/PyTorch/#Supported-layers","page":"PyTorch","title":"Supported layers","text":"","category":"section"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"MathOptAI supports embedding a PyTorch models into JuMP if it is a nn.Sequential composed of:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"nn.Linear\nnn.ReLU\nnn.Sigmoid\nnn.Softplus\nnn.Tanh","category":"page"},{"location":"manual/PyTorch/#File-format","page":"PyTorch","title":"File format","text":"","category":"section"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"Use torch.save to save a trained PyTorch model to a .pt file:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"#!/usr/bin/python3\nimport torch\nmodel = torch.nn.Sequential(\n torch.nn.Linear(1, 2),\n torch.nn.ReLU(),\n torch.nn.Linear(2, 1),\n)\ntorch.save(model, \"saved_pytorch_model.pt\")","category":"page"},{"location":"manual/PyTorch/#Python-integration","page":"PyTorch","title":"Python integration","text":"","category":"section"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"MathOptAI uses PythonCall.jl to call from Julia into Python.","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"See CondaPkg.jl for more control over how to link Julia to an existing Python environment. For example, if you have an existing Python installation (with PyTorch installed), and it is available in the current Conda environment, set:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"ENV[\"JULIA_CONDAPKG_BACKEND\"] = \"Current\"","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"before importing PythonCall.jl. If the Python installation can be found on the path and it is not in a Conda environment, set:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"ENV[\"JULIA_CONDAPKG_BACKEND\"] = \"Null\"","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"If python is not on your path, you may additionally need to set JULIA_PYTHONCALL_EXE, for example, to:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"ENV[\"JULIA_PYTHONCALL_EXE\"] = \"python3\"","category":"page"},{"location":"manual/PyTorch/#Basic-example","page":"PyTorch","title":"Basic example","text":"","category":"section"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"Use MathOptAI.add_predictor to embed a PyTorch model into a JuMP model:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"using JuMP, MathOptAI\nmodel = Model();\n@variable(model, x[1:1]);\npredictor = MathOptAI.PytorchModel(\"saved_pytorch_model.pt\");\ny, formulation = MathOptAI.add_predictor(model, predictor, x);\ny\nformulation","category":"page"},{"location":"manual/PyTorch/#Reduced-space","page":"PyTorch","title":"Reduced-space","text":"","category":"section"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"Use the reduced_space = true keyword to formulate a reduced-space model:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"using JuMP, MathOptAI\nmodel = Model();\n@variable(model, x[1:1]);\npredictor = MathOptAI.PytorchModel(\"saved_pytorch_model.pt\");\ny, formulation =\n MathOptAI.add_predictor(model, predictor, x; reduced_space = true);\ny\nformulation","category":"page"},{"location":"manual/PyTorch/#Gray-box","page":"PyTorch","title":"Gray-box","text":"","category":"section"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"Use the gray_box = true keyword to embed the network as a nonlinear operator:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"using JuMP, MathOptAI\nmodel = Model();\n@variable(model, x[1:1]);\npredictor = MathOptAI.PytorchModel(\"saved_pytorch_model.pt\");\ny, formulation =\n MathOptAI.add_predictor(model, predictor, x; gray_box = true);\ny\nformulation","category":"page"},{"location":"manual/PyTorch/#Change-how-layers-are-formulated","page":"PyTorch","title":"Change how layers are formulated","text":"","category":"section"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"Pass a dictionary to the config keyword that maps the Symbol name of each PyTorch layer to a MathOptAI predictor:","category":"page"},{"location":"manual/PyTorch/","page":"PyTorch","title":"PyTorch","text":"using JuMP, MathOptAI\nmodel = Model();\n@variable(model, x[1:1]);\npredictor = MathOptAI.PytorchModel(\"saved_pytorch_model.pt\");\ny, formulation = MathOptAI.add_predictor(\n model,\n predictor,\n x;\n config = Dict(:ReLU => MathOptAI.ReLUSOS1()),\n);\ny\nformulation","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"(Image: )","category":"page"},{"location":"#MathOptAI.jl","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"","category":"section"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"MathOptAI.jl is a JuMP extension for embedding trained AI, machine learning, and statistical learning models into a JuMP optimization model.","category":"page"},{"location":"#License","page":"MathOptAI.jl","title":"License","text":"","category":"section"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"MathOptAI.jl is provided under a BSD-3 license as part of the Optimization and Machine Learning Toolbox project, O4806.","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"See LICENSE.md for details.","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"Despite the name similarity, this project is not affiliated with OMLT, the Optimization and Machine Learning Toolkit.","category":"page"},{"location":"#Installation","page":"MathOptAI.jl","title":"Installation","text":"","category":"section"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"Install MathOptAI.jl using the Julia package manager:","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"import Pkg\nPkg.add(\"MathOptAI\")","category":"page"},{"location":"#Getting-started","page":"MathOptAI.jl","title":"Getting started","text":"","category":"section"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"Here's an example of using MathOptAI to embed a trained neural network from Flux into a JuMP model. The vector of JuMP variables x is fed as input to the neural network. The output y is a vector of JuMP variables that represents the output layer of the neural network. The formulation object stores the additional variables and constraints that were added to model.","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"julia> using JuMP, MathOptAI, Flux\n\njulia> predictor = Flux.Chain(\n Flux.Dense(28^2 => 32, Flux.sigmoid),\n Flux.Dense(32 => 10),\n Flux.softmax,\n );\n\njulia> #= Train the Flux model. Code not shown for simplicity =#\n\njulia> model = JuMP.Model();\n\njulia> JuMP.@variable(model, 0 <= x[1:28^2] <= 1);\n\njulia> y, formulation = MathOptAI.add_predictor(model, predictor, x);\n\njulia> y\n10-element Vector{VariableRef}:\n moai_SoftMax[1]\n moai_SoftMax[2]\n moai_SoftMax[3]\n moai_SoftMax[4]\n moai_SoftMax[5]\n moai_SoftMax[6]\n moai_SoftMax[7]\n moai_SoftMax[8]\n moai_SoftMax[9]\n moai_SoftMax[10]","category":"page"},{"location":"#Getting-help","page":"MathOptAI.jl","title":"Getting help","text":"","category":"section"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"This package is under active development. For help, questions, comments, and suggestions, please open a GitHub issue.","category":"page"},{"location":"#Inspiration","page":"MathOptAI.jl","title":"Inspiration","text":"","category":"section"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"This project is mainly inspired by two existing projects:","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"OMLT\ngurobi-machinelearning","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"Other works, from which we took less inspiration, include:","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"JANOS\nMeLOn\nENTMOOT\nreluMIP\nOptiCL\nPySCIPOpt-ML","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"The 2024 paper of López-Flores et al. is an excellent summary of the state of the field at the time that we started development of MathOptAI.","category":"page"},{"location":"","page":"MathOptAI.jl","title":"MathOptAI.jl","text":"López-Flores, F.J., Ramírez-Márquez, C., Ponce-Ortega J.M. (2024). Process Systems Engineering Tools for Optimization of Trained Machine Learning Models: Comparative and Perspective. Industrial & Engineering Chemistry Research, 63(32), 13966-13979. DOI: 10.1021/acs.iecr.4c00632","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"EditURL = \"gaussian.jl\"","category":"page"},{"location":"tutorials/gaussian/#Function-fitting-with-AbstractGPs","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"","category":"section"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"The purpose of this tutorial is to explain how to embed a Gaussian Process from AbstractGPs into JuMP.","category":"page"},{"location":"tutorials/gaussian/#Required-packages","page":"Function fitting with AbstractGPs","title":"Required packages","text":"","category":"section"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"This tutorial requires the following packages","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"using JuMP\nusing Test\nimport AbstractGPs\nimport Ipopt\nimport MathOptAI\nimport Plots","category":"page"},{"location":"tutorials/gaussian/#Prediction-model","page":"Function fitting with AbstractGPs","title":"Prediction model","text":"","category":"section"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"Assume that we have some true underlying univariate function:","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"x_domain = 0:0.01:2π\ntrue_function(x) = sin(x)\nPlots.plot(x_domain, true_function.(x_domain); label = \"truth\")","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"We don't know the function, but we have access to a limited set of noisy sample points:","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"N = 20\nx_data = rand(x_domain, N)\nnoisy_sampler(x) = true_function(x) + 0.25 * (2rand() - 1)\ny_data = noisy_sampler.(x_data)\nPlots.scatter!(x_data, y_data; label = \"data\")","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"Using the data, we want to build a predictor y = predictor(x). One choice is a Gaussian Process:","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"fx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.4)\np_fx = AbstractGPs.posterior(fx, y_data)\nPlots.plot!(x_domain, p_fx; label = \"GP\", fillalpha = 0.1)","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"Gaussian Processes fit a mean and variance function:","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"AbstractGPs.mean_and_var(p_fx, [π / 2])","category":"page"},{"location":"tutorials/gaussian/#Decision-model","page":"Function fitting with AbstractGPs","title":"Decision model","text":"","category":"section"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"Our goal for this JuMP model is to embed the Gaussian Process from AbstractGPs into the model and then solve for different fixed values of x to recreate the function that the Gaussian Process has learned to approximate.","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"First, create a JuMP model:","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"model = Model(Ipopt.Optimizer)\nset_silent(model)\n@variable(model, x)","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"Since a Gaussian Process is a infinite dimensional object (its prediction is a distribution), we need some way of converting the Gaussian Process into a finite set of scalar values. For this, we use the Quantile predictor:","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"predictor = MathOptAI.Quantile(p_fx, [0.25, 0.75]);\ny, _ = MathOptAI.add_predictor(model, predictor, [x])","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"Now, visualize the fitted function y = predictor(x) by repeatedly solving the optimization problem for different fixed values of x. Each value of y has two elements: one for the 25th percentile and one for the 75th.","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"X, Y = range(0, 2π; length = 20), Any[]\n@constraint(model, c, x == 0.0)\nfor xi in X\n set_normalized_rhs(c, xi)\n optimize!(model)\n if is_solved_and_feasible(model)\n push!(Y, value.(y))\n else\n push!(Y, [NaN, NaN])\n end\nend\nPlots.plot!(X, reduce(hcat, Y)'; label = [\"P25\" \"P75\"], linewidth = 3)","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"","category":"page"},{"location":"tutorials/gaussian/","page":"Function fitting with AbstractGPs","title":"Function fitting with AbstractGPs","text":"This page was generated using Literate.jl.","category":"page"}] +} diff --git a/v0.1.4/siteinfo.js b/v0.1.4/siteinfo.js new file mode 100644 index 00000000..1a828890 --- /dev/null +++ b/v0.1.4/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "v0.1.4"; diff --git a/v0.1.4/tutorials/decision_trees.jl b/v0.1.4/tutorials/decision_trees.jl new file mode 100644 index 00000000..7eabb4ea --- /dev/null +++ b/v0.1.4/tutorials/decision_trees.jl @@ -0,0 +1,138 @@ +# Copyright (c) 2024: Oscar Dowson and contributors #src +# Copyright (c) 2024: Triad National Security, LLC #src +# #src +# Use of this source code is governed by a BSD-style license that can be #src +# found in the LICENSE.md file. #src + +# # Classification problems with DecisionTree.jl + +# The purpose of this tutorial is to explain how to embed a decision tree +# model from [DecisionTree.jl](https://github.com/JuliaAI/DecisionTree.jl) into +# JuMP. + +# The data and example in this tutorial comes from the paper: David Bergman, +# Teng Huang, Philip Brooks, Andrea Lodi, Arvind U. Raghunathan (2021) JANOS: An +# Integrated Predictive and Prescriptive Modeling Framework. INFORMS Journal on +# Computing 34(2):807-816. +# [https://doi.org/10.1287/ijoc.2020.1023](https://doi.org/10.1287/ijoc.2020.1023) + +# ## Required packages + +# This tutorial uses the following packages. + +using JuMP +import CSV +import DataFrames +import Downloads +import DecisionTree +import HiGHS +import MathOptAI +import Statistics + +# ## Data + +# Here is a function to load the data directly from the JANOS repository: + +function read_df(filename) + url = "https://raw.githubusercontent.com/INFORMSJoC/2020.1023/master/data/" + data = Downloads.download(url * filename) + return CSV.read(data, DataFrames.DataFrame) +end + +# There are two important files. The first, `college_student_enroll-s1-1.csv`, +# contains historical admissions data on anonymized students, their SAT score, +# their GPA, their merit scholarships, and whether the enrolled in the college. + +train_df = read_df("college_student_enroll-s1-1.csv") + +# The second, `college_applications6000.csv`, contains the SAT and GPA data of +# students who are currently applying: + +evaluate_df = read_df("college_applications6000.csv") + +# There are 6,000 prospective students: + +n_students = size(evaluate_df, 1) + +# ## Prediction model + +# The first step is to train a logistic regression model to predict the Boolean +# `enroll` column based on the `SAT`, `GPA`, and `merit` columns. + +train_features = Matrix(train_df[:, [:SAT, :GPA, :merit]]) +train_labels = train_df[:, :enroll] +predictor = DecisionTree.DecisionTreeClassifier(; max_depth = 3) +DecisionTree.fit!(predictor, train_features, train_labels) +DecisionTree.print_tree(predictor) + +# ## Decision model + +# Now that we have a trained decision tree, we want a decision model that +# chooses the optimal merit scholarship for each student in: + +evaluate_df + +# Here's an empty JuMP model to start: + +model = Model() + +# First, we add a new column to `evaluate_df`, with one JuMP decision variable +# for each row. It is important the `.merit` column name in `evaluate_df` +# matches the name in `train_df`. + +evaluate_df.merit = @variable(model, 0 <= x_merit[1:n_students] <= 2.5); +evaluate_df + +# Then, we use [`MathOptAI.add_predictor`](@ref) to embed `model_ml` into the +# JuMP `model`. [`MathOptAI.add_predictor`](@ref) returns a vector of variables, +# one for each row in `evaluate_df`, corresponding to the output `enroll` of +# our logistic regression. + +evaluate_features = Matrix(evaluate_df[:, [:SAT, :GPA, :merit]]) +evaluate_df.enroll = mapreduce(vcat, 1:size(evaluate_features, 1)) do i + y, _ = MathOptAI.add_predictor(model, predictor, evaluate_features[i, :]) + return y +end +evaluate_df + +# The `.enroll` column name in `evaluate_df` is just a name. It doesn't have to +# match the name in `train_df`. + +# The objective of our problem is to maximize the expected number of students +# who enroll: + +@objective(model, Max, sum(evaluate_df.enroll)) + +# Subject to the constraint that we can spend at most `0.2 * n_students` on +# merit scholarships: + +@constraint(model, sum(evaluate_df.merit) <= 0.2 * n_students) + +# Because logistic regression involves a [`Sigmoid`](@ref) layer, we need to use +# a smooth nonlinear optimizer. A common choice is Ipopt. Solve and check the +# optimizer found a feasible solution: + +set_optimizer(model, HiGHS.Optimizer) +set_silent(model) +optimize!(model) +@assert is_solved_and_feasible(model) + +# Let's store the solution in `evaluate_df` for analysis: + +evaluate_df.merit_sol = value.(evaluate_df.merit); +evaluate_df.enroll_sol = value.(evaluate_df.enroll); +evaluate_df + +# ## Solution analysis + +# We expect that just under 2,500 students will enroll: + +sum(evaluate_df.enroll_sol) + +# We awarded merit scholarships to approximately 1 in 6 students: + +count(evaluate_df.merit_sol .> 1e-5) + +# The average merit scholarship was worth just under \$1,000: + +1_000 * Statistics.mean(evaluate_df.merit_sol[evaluate_df.merit_sol.>1e-5]) diff --git a/v0.1.4/tutorials/decision_trees/index.html b/v0.1.4/tutorials/decision_trees/index.html new file mode 100644 index 00000000..7a0334b9 --- /dev/null +++ b/v0.1.4/tutorials/decision_trees/index.html @@ -0,0 +1,246 @@ + +Classification problems with DecisionTree.jl · MathOptAI.jl
GitHub

Classification problems with DecisionTree.jl

The purpose of this tutorial is to explain how to embed a decision tree model from DecisionTree.jl into JuMP.

The data and example in this tutorial comes from the paper: David Bergman, Teng Huang, Philip Brooks, Andrea Lodi, Arvind U. Raghunathan (2021) JANOS: An Integrated Predictive and Prescriptive Modeling Framework. INFORMS Journal on Computing 34(2):807-816. https://doi.org/10.1287/ijoc.2020.1023

Required packages

This tutorial uses the following packages.

julia> using JuMP
julia> import CSV
julia> import DataFrames
julia> import Downloads
julia> import DecisionTree
julia> import HiGHS
julia> import MathOptAI
julia> import Statistics

Data

Here is a function to load the data directly from the JANOS repository:

julia> function read_df(filename)
+           url = "https://raw.githubusercontent.com/INFORMSJoC/2020.1023/master/data/"
+           data = Downloads.download(url * filename)
+           return CSV.read(data, DataFrames.DataFrame)
+       endread_df (generic function with 1 method)

There are two important files. The first, college_student_enroll-s1-1.csv, contains historical admissions data on anonymized students, their SAT score, their GPA, their merit scholarships, and whether the enrolled in the college.

julia> train_df = read_df("college_student_enroll-s1-1.csv")20000×6 DataFrame
+   Row │ Column1  StudentID  SAT    GPA      merit    enroll 
+       │ Int64    Int64      Int64  Float64  Float64  Int64  
+───────┼─────────────────────────────────────────────────────
+     1 │       1          1   1507     3.72     1.64       0
+     2 │       2          2   1532     3.93     0.52       0
+     3 │       3          3   1487     3.77     1.67       0
+     4 │       4          4   1259     3.05     1.21       1
+     5 │       5          5   1354     3.39     1.65       1
+     6 │       6          6   1334     3.22     0.0        0
+     7 │       7          7   1125     2.73     1.68       1
+     8 │       8          8   1180     2.82     0.0        1
+   ⋮   │    ⋮         ⋮        ⋮       ⋮        ⋮       ⋮
+ 19994 │   19994      19994   1185     3.09     1.16       1
+ 19995 │   19995      19995   1471     3.7      1.05       0
+ 19996 │   19996      19996   1139     3.03     1.21       1
+ 19997 │   19997      19997   1371     3.39     1.26       0
+ 19998 │   19998      19998   1424     3.72     0.85       0
+ 19999 │   19999      19999   1170     3.01     0.73       1
+ 20000 │   20000      20000   1389     3.57     0.55       0
+                                           19985 rows omitted

The second, college_applications6000.csv, contains the SAT and GPA data of students who are currently applying:

julia> evaluate_df = read_df("college_applications6000.csv")6000×3 DataFrame
+  Row │ StudentID  SAT    GPA     
+      │ Int64      Int64  Float64 
+──────┼───────────────────────────
+    1 │         1   1240     3.22
+    2 │         2   1206     2.87
+    3 │         3   1520     3.74
+    4 │         4   1238     3.11
+    5 │         5   1142     2.74
+    6 │         6   1086     2.77
+    7 │         7   1367     3.28
+    8 │         8   1034     2.41
+  ⋮   │     ⋮        ⋮       ⋮
+ 5994 │      5994   1121     2.96
+ 5995 │      5995   1564     4.1
+ 5996 │      5996   1332     3.14
+ 5997 │      5997   1228     2.95
+ 5998 │      5998   1165     2.81
+ 5999 │      5999   1400     3.43
+ 6000 │      6000   1097     2.65
+                 5985 rows omitted

There are 6,000 prospective students:

julia> n_students = size(evaluate_df, 1)6000

Prediction model

The first step is to train a logistic regression model to predict the Boolean enroll column based on the SAT, GPA, and merit columns.

julia> train_features = Matrix(train_df[:, [:SAT, :GPA, :merit]])20000×3 Matrix{Float64}:
+ 1507.0  3.72  1.64
+ 1532.0  3.93  0.52
+ 1487.0  3.77  1.67
+ 1259.0  3.05  1.21
+ 1354.0  3.39  1.65
+ 1334.0  3.22  0.0
+ 1125.0  2.73  1.68
+ 1180.0  2.82  0.0
+ 1098.0  2.91  0.0
+ 1116.0  2.95  0.0
+    ⋮
+ 1048.0  2.51  0.73
+ 1157.0  2.79  2.11
+ 1185.0  3.09  1.16
+ 1471.0  3.7   1.05
+ 1139.0  3.03  1.21
+ 1371.0  3.39  1.26
+ 1424.0  3.72  0.85
+ 1170.0  3.01  0.73
+ 1389.0  3.57  0.55
julia> train_labels = train_df[:, :enroll]20000-element Vector{Int64}:
+ 0
+ 0
+ 0
+ 1
+ 1
+ 0
+ 1
+ 1
+ 1
+ 1
+ ⋮
+ 1
+ 1
+ 1
+ 0
+ 1
+ 0
+ 0
+ 1
+ 0
julia> predictor = DecisionTree.DecisionTreeClassifier(; max_depth = 3)DecisionTreeClassifier
+max_depth:                3
+min_samples_leaf:         1
+min_samples_split:        2
+min_purity_increase:      0.0
+pruning_purity_threshold: 1.0
+n_subfeatures:            0
+classes:                  nothing
+root:                     nothing
julia> DecisionTree.fit!(predictor, train_features, train_labels)DecisionTreeClassifier
+max_depth:                3
+min_samples_leaf:         1
+min_samples_split:        2
+min_purity_increase:      0.0
+pruning_purity_threshold: 1.0
+n_subfeatures:            0
+classes:                  [0, 1]
+root:                     Decision Tree
+Leaves: 8
+Depth:  3
julia> DecisionTree.print_tree(predictor)Feature 1 < 1228.0 ?
+├─ Feature 2 < 3.125 ?
+    ├─ Feature 1 < 1214.0 ?
+        ├─ 1 : 7336/7336
+        └─ 1 : 334/361
+    └─ Feature 3 < 0.255 ?
+        ├─ 0 : 161/220
+        └─ 1 : 121/121
+└─ Feature 1 < 1412.0 ?
+    ├─ Feature 3 < 1.005 ?
+        ├─ 0 : 3600/4046
+        └─ 1 : 1603/2338
+    └─ Feature 3 < 1.865 ?
+        ├─ 0 : 4530/4530
+        └─ 0 : 947/1048

Decision model

Now that we have a trained decision tree, we want a decision model that chooses the optimal merit scholarship for each student in:

julia> evaluate_df6000×3 DataFrame
+  Row │ StudentID  SAT    GPA     
+      │ Int64      Int64  Float64 
+──────┼───────────────────────────
+    1 │         1   1240     3.22
+    2 │         2   1206     2.87
+    3 │         3   1520     3.74
+    4 │         4   1238     3.11
+    5 │         5   1142     2.74
+    6 │         6   1086     2.77
+    7 │         7   1367     3.28
+    8 │         8   1034     2.41
+  ⋮   │     ⋮        ⋮       ⋮
+ 5994 │      5994   1121     2.96
+ 5995 │      5995   1564     4.1
+ 5996 │      5996   1332     3.14
+ 5997 │      5997   1228     2.95
+ 5998 │      5998   1165     2.81
+ 5999 │      5999   1400     3.43
+ 6000 │      6000   1097     2.65
+                 5985 rows omitted

Here's an empty JuMP model to start:

julia> model = Model()A JuMP Model
+├ solver: none
+├ objective_sense: FEASIBILITY_SENSE
+├ num_variables: 0
+├ num_constraints: 0
+└ Names registered in the model: none

First, we add a new column to evaluate_df, with one JuMP decision variable for each row. It is important the .merit column name in evaluate_df matches the name in train_df.

julia> evaluate_df.merit = @variable(model, 0 <= x_merit[1:n_students] <= 2.5);
julia> evaluate_df6000×4 DataFrame
+  Row │ StudentID  SAT    GPA      merit         
+      │ Int64      Int64  Float64  GenericV…     
+──────┼──────────────────────────────────────────
+    1 │         1   1240     3.22  x_merit[1]
+    2 │         2   1206     2.87  x_merit[2]
+    3 │         3   1520     3.74  x_merit[3]
+    4 │         4   1238     3.11  x_merit[4]
+    5 │         5   1142     2.74  x_merit[5]
+    6 │         6   1086     2.77  x_merit[6]
+    7 │         7   1367     3.28  x_merit[7]
+    8 │         8   1034     2.41  x_merit[8]
+  ⋮   │     ⋮        ⋮       ⋮           ⋮
+ 5994 │      5994   1121     2.96  x_merit[5994]
+ 5995 │      5995   1564     4.1   x_merit[5995]
+ 5996 │      5996   1332     3.14  x_merit[5996]
+ 5997 │      5997   1228     2.95  x_merit[5997]
+ 5998 │      5998   1165     2.81  x_merit[5998]
+ 5999 │      5999   1400     3.43  x_merit[5999]
+ 6000 │      6000   1097     2.65  x_merit[6000]
+                                5985 rows omitted

Then, we use MathOptAI.add_predictor to embed model_ml into the JuMP model. MathOptAI.add_predictor returns a vector of variables, one for each row in evaluate_df, corresponding to the output enroll of our logistic regression.

julia> evaluate_features = Matrix(evaluate_df[:, [:SAT, :GPA, :merit]])6000×3 Matrix{JuMP.AffExpr}:
+ 1240  3.22  x_merit[1]
+ 1206  2.87  x_merit[2]
+ 1520  3.74  x_merit[3]
+ 1238  3.11  x_merit[4]
+ 1142  2.74  x_merit[5]
+ 1086  2.77  x_merit[6]
+ 1367  3.28  x_merit[7]
+ 1034  2.41  x_merit[8]
+ 1547  3.82  x_merit[9]
+ 1453  3.65  x_merit[10]
+ ⋮
+ 1299  3.16  x_merit[5992]
+ 1400  3.59  x_merit[5993]
+ 1121  2.96  x_merit[5994]
+ 1564  4.1   x_merit[5995]
+ 1332  3.14  x_merit[5996]
+ 1228  2.95  x_merit[5997]
+ 1165  2.81  x_merit[5998]
+ 1400  3.43  x_merit[5999]
+ 1097  2.65  x_merit[6000]
julia> evaluate_df.enroll = mapreduce(vcat, 1:size(evaluate_features, 1)) do i
+           y, _ = MathOptAI.add_predictor(model, predictor, evaluate_features[i, :])
+           return y
+       end6000-element Vector{JuMP.VariableRef}:
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ ⋮
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
+ moai_BinaryDecisionTree_value
julia> evaluate_df6000×5 DataFrame
+  Row │ StudentID  SAT    GPA      merit          enroll                       ⋯
+      │ Int64      Int64  Float64  GenericV…      GenericV…                    ⋯
+──────┼─────────────────────────────────────────────────────────────────────────
+    1 │         1   1240     3.22  x_merit[1]     moai_BinaryDecisionTree_valu ⋯
+    2 │         2   1206     2.87  x_merit[2]     moai_BinaryDecisionTree_valu
+    3 │         3   1520     3.74  x_merit[3]     moai_BinaryDecisionTree_valu
+    4 │         4   1238     3.11  x_merit[4]     moai_BinaryDecisionTree_valu
+    5 │         5   1142     2.74  x_merit[5]     moai_BinaryDecisionTree_valu ⋯
+    6 │         6   1086     2.77  x_merit[6]     moai_BinaryDecisionTree_valu
+    7 │         7   1367     3.28  x_merit[7]     moai_BinaryDecisionTree_valu
+    8 │         8   1034     2.41  x_merit[8]     moai_BinaryDecisionTree_valu
+  ⋮   │     ⋮        ⋮       ⋮           ⋮                      ⋮              ⋱
+ 5994 │      5994   1121     2.96  x_merit[5994]  moai_BinaryDecisionTree_valu ⋯
+ 5995 │      5995   1564     4.1   x_merit[5995]  moai_BinaryDecisionTree_valu
+ 5996 │      5996   1332     3.14  x_merit[5996]  moai_BinaryDecisionTree_valu
+ 5997 │      5997   1228     2.95  x_merit[5997]  moai_BinaryDecisionTree_valu
+ 5998 │      5998   1165     2.81  x_merit[5998]  moai_BinaryDecisionTree_valu ⋯
+ 5999 │      5999   1400     3.43  x_merit[5999]  moai_BinaryDecisionTree_valu
+ 6000 │      6000   1097     2.65  x_merit[6000]  moai_BinaryDecisionTree_valu
+                                                  1 column and 5985 rows omitted

The .enroll column name in evaluate_df is just a name. It doesn't have to match the name in train_df.

The objective of our problem is to maximize the expected number of students who enroll:

julia> @objective(model, Max, sum(evaluate_df.enroll))moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + [[...5940 terms omitted...]] + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value + moai_BinaryDecisionTree_value

Subject to the constraint that we can spend at most 0.2 * n_students on merit scholarships:

julia> @constraint(model, sum(evaluate_df.merit) <= 0.2 * n_students)x_merit[1] + x_merit[2] + x_merit[3] + x_merit[4] + x_merit[5] + x_merit[6] + x_merit[7] + x_merit[8] + x_merit[9] + x_merit[10] + x_merit[11] + x_merit[12] + x_merit[13] + x_merit[14] + x_merit[15] + x_merit[16] + x_merit[17] + x_merit[18] + x_merit[19] + x_merit[20] + x_merit[21] + x_merit[22] + x_merit[23] + x_merit[24] + x_merit[25] + x_merit[26] + x_merit[27] + x_merit[28] + x_merit[29] + x_merit[30] + [[...5940 terms omitted...]] + x_merit[5971] + x_merit[5972] + x_merit[5973] + x_merit[5974] + x_merit[5975] + x_merit[5976] + x_merit[5977] + x_merit[5978] + x_merit[5979] + x_merit[5980] + x_merit[5981] + x_merit[5982] + x_merit[5983] + x_merit[5984] + x_merit[5985] + x_merit[5986] + x_merit[5987] + x_merit[5988] + x_merit[5989] + x_merit[5990] + x_merit[5991] + x_merit[5992] + x_merit[5993] + x_merit[5994] + x_merit[5995] + x_merit[5996] + x_merit[5997] + x_merit[5998] + x_merit[5999] + x_merit[6000] ≤ 1200

Because logistic regression involves a Sigmoid layer, we need to use a smooth nonlinear optimizer. A common choice is Ipopt. Solve and check the optimizer found a feasible solution:

julia> set_optimizer(model, HiGHS.Optimizer)
julia> set_silent(model)
julia> optimize!(model)
julia> @assert is_solved_and_feasible(model)

Let's store the solution in evaluate_df for analysis:

julia> evaluate_df.merit_sol = value.(evaluate_df.merit);
julia> evaluate_df.enroll_sol = value.(evaluate_df.enroll);
julia> evaluate_df6000×7 DataFrame
+  Row │ StudentID  SAT    GPA      merit          enroll                       ⋯
+      │ Int64      Int64  Float64  GenericV…      GenericV…                    ⋯
+──────┼─────────────────────────────────────────────────────────────────────────
+    1 │         1   1240     3.22  x_merit[1]     moai_BinaryDecisionTree_valu ⋯
+    2 │         2   1206     2.87  x_merit[2]     moai_BinaryDecisionTree_valu
+    3 │         3   1520     3.74  x_merit[3]     moai_BinaryDecisionTree_valu
+    4 │         4   1238     3.11  x_merit[4]     moai_BinaryDecisionTree_valu
+    5 │         5   1142     2.74  x_merit[5]     moai_BinaryDecisionTree_valu ⋯
+    6 │         6   1086     2.77  x_merit[6]     moai_BinaryDecisionTree_valu
+    7 │         7   1367     3.28  x_merit[7]     moai_BinaryDecisionTree_valu
+    8 │         8   1034     2.41  x_merit[8]     moai_BinaryDecisionTree_valu
+  ⋮   │     ⋮        ⋮       ⋮           ⋮                      ⋮              ⋱
+ 5994 │      5994   1121     2.96  x_merit[5994]  moai_BinaryDecisionTree_valu ⋯
+ 5995 │      5995   1564     4.1   x_merit[5995]  moai_BinaryDecisionTree_valu
+ 5996 │      5996   1332     3.14  x_merit[5996]  moai_BinaryDecisionTree_valu
+ 5997 │      5997   1228     2.95  x_merit[5997]  moai_BinaryDecisionTree_valu
+ 5998 │      5998   1165     2.81  x_merit[5998]  moai_BinaryDecisionTree_valu ⋯
+ 5999 │      5999   1400     3.43  x_merit[5999]  moai_BinaryDecisionTree_valu
+ 6000 │      6000   1097     2.65  x_merit[6000]  moai_BinaryDecisionTree_valu
+                                                 3 columns and 5985 rows omitted

Solution analysis

We expect that just under 2,500 students will enroll:

julia> sum(evaluate_df.enroll_sol)3530.0

We awarded merit scholarships to approximately 1 in 6 students:

julia> count(evaluate_df.merit_sol .> 1e-5)1278

The average merit scholarship was worth just under $1,000:

julia> 1_000 * Statistics.mean(evaluate_df.merit_sol[evaluate_df.merit_sol.>1e-5])938.6854460093895

This page was generated using Literate.jl.

diff --git a/v0.1.4/tutorials/gaussian.jl b/v0.1.4/tutorials/gaussian.jl new file mode 100644 index 00000000..3bf78e90 --- /dev/null +++ b/v0.1.4/tutorials/gaussian.jl @@ -0,0 +1,87 @@ +# Copyright (c) 2024: Oscar Dowson and contributors #src +# Copyright (c) 2024: Triad National Security, LLC #src +# #src +# Use of this source code is governed by a BSD-style license that can be #src +# found in the LICENSE.md file. #src + +# # Function fitting with AbstractGPs + +# The purpose of this tutorial is to explain how to embed a Gaussian Process +# from [AbstractGPs](https://github.com/JuliaGaussianProcesses/AbstractGPs.jl) +# into JuMP. + +# ## Required packages + +# This tutorial requires the following packages + +using JuMP +using Test +import AbstractGPs +import Ipopt +import MathOptAI +import Plots + +# ## Prediction model + +# Assume that we have some true underlying univariate function: + +x_domain = 0:0.01:2π +true_function(x) = sin(x) +Plots.plot(x_domain, true_function.(x_domain); label = "truth") + +# We don't know the function, but we have access to a limited set of noisy +# sample points: + +N = 20 +x_data = rand(x_domain, N) +noisy_sampler(x) = true_function(x) + 0.25 * (2rand() - 1) +y_data = noisy_sampler.(x_data) +Plots.scatter!(x_data, y_data; label = "data") + +# Using the data, we want to build a predictor `y = predictor(x)`. One choice is +# a Gaussian Process: + +fx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.4) +p_fx = AbstractGPs.posterior(fx, y_data) +Plots.plot!(x_domain, p_fx; label = "GP", fillalpha = 0.1) + +# Gaussian Processes fit a mean and variance function: + +AbstractGPs.mean_and_var(p_fx, [π / 2]) + +# ## Decision model + +# Our goal for this JuMP model is to embed the Gaussian Process from AbstractGPs +# into the model and then solve for different fixed values of `x` to recreate +# the function that the Gaussian Process has learned to approximate. + +# First, create a JuMP model: + +model = Model(Ipopt.Optimizer) +set_silent(model) +@variable(model, x) + +# Since a Gaussian Process is a infinite dimensional object (its prediction is a +# distribution), we need some way of converting the Gaussian Process into a +# finite set of scalar values. For this, we use the [`Quantile`](@ref) +# predictor: + +predictor = MathOptAI.Quantile(p_fx, [0.25, 0.75]); +y, _ = MathOptAI.add_predictor(model, predictor, [x]) + +# Now, visualize the fitted function `y = predictor(x)` by repeatedly solving +# the optimization problem for different fixed values of `x`. Each value of `y` +# has two elements: one for the 25th percentile and one for the 75th. + +X, Y = range(0, 2π; length = 20), Any[] +@constraint(model, c, x == 0.0) +for xi in X + set_normalized_rhs(c, xi) + optimize!(model) + if is_solved_and_feasible(model) + push!(Y, value.(y)) + else + push!(Y, [NaN, NaN]) + end +end +Plots.plot!(X, reduce(hcat, Y)'; label = ["P25" "P75"], linewidth = 3) diff --git a/v0.1.4/tutorials/gaussian/5169c545.svg b/v0.1.4/tutorials/gaussian/5169c545.svg new file mode 100644 index 00000000..d6a7f88b --- /dev/null +++ b/v0.1.4/tutorials/gaussian/5169c545.svg @@ -0,0 +1,50 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.4/tutorials/gaussian/bf116f93.svg b/v0.1.4/tutorials/gaussian/bf116f93.svg new file mode 100644 index 00000000..f80d5d83 --- /dev/null +++ b/v0.1.4/tutorials/gaussian/bf116f93.svg @@ -0,0 +1,71 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.4/tutorials/gaussian/d76af15a.svg b/v0.1.4/tutorials/gaussian/d76af15a.svg new file mode 100644 index 00000000..21affbc2 --- /dev/null +++ b/v0.1.4/tutorials/gaussian/d76af15a.svg @@ -0,0 +1,74 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.4/tutorials/gaussian/e9c2cdb6.svg b/v0.1.4/tutorials/gaussian/e9c2cdb6.svg new file mode 100644 index 00000000..6ab39261 --- /dev/null +++ b/v0.1.4/tutorials/gaussian/e9c2cdb6.svg @@ -0,0 +1,78 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.4/tutorials/gaussian/index.html b/v0.1.4/tutorials/gaussian/index.html new file mode 100644 index 00000000..5edf8a7c --- /dev/null +++ b/v0.1.4/tutorials/gaussian/index.html @@ -0,0 +1,31 @@ + +Function fitting with AbstractGPs · MathOptAI.jl
GitHub

Function fitting with AbstractGPs

The purpose of this tutorial is to explain how to embed a Gaussian Process from AbstractGPs into JuMP.

Required packages

This tutorial requires the following packages

using JuMP
+using Test
+import AbstractGPs
+import Ipopt
+import MathOptAI
+import Plots

Prediction model

Assume that we have some true underlying univariate function:

x_domain = 0:0.01:2π
+true_function(x) = sin(x)
+Plots.plot(x_domain, true_function.(x_domain); label = "truth")
Example block output

We don't know the function, but we have access to a limited set of noisy sample points:

N = 20
+x_data = rand(x_domain, N)
+noisy_sampler(x) = true_function(x) + 0.25 * (2rand() - 1)
+y_data = noisy_sampler.(x_data)
+Plots.scatter!(x_data, y_data; label = "data")
Example block output

Using the data, we want to build a predictor y = predictor(x). One choice is a Gaussian Process:

fx = AbstractGPs.GP(AbstractGPs.Matern32Kernel())(x_data, 0.4)
+p_fx = AbstractGPs.posterior(fx, y_data)
+Plots.plot!(x_domain, p_fx; label = "GP", fillalpha = 0.1)
Example block output

Gaussian Processes fit a mean and variance function:

AbstractGPs.mean_and_var(p_fx, [π / 2])
([0.8202760734867823], [0.1143721379922652])

Decision model

Our goal for this JuMP model is to embed the Gaussian Process from AbstractGPs into the model and then solve for different fixed values of x to recreate the function that the Gaussian Process has learned to approximate.

First, create a JuMP model:

model = Model(Ipopt.Optimizer)
+set_silent(model)
+@variable(model, x)

\[ x \]

Since a Gaussian Process is a infinite dimensional object (its prediction is a distribution), we need some way of converting the Gaussian Process into a finite set of scalar values. For this, we use the Quantile predictor:

predictor = MathOptAI.Quantile(p_fx, [0.25, 0.75]);
+y, _ = MathOptAI.add_predictor(model, predictor, [x])
(JuMP.VariableRef[moai_quantile[1], moai_quantile[2]], Quantile(_, [0.25, 0.75])
+├ variables [0]
+└ constraints [0])

Now, visualize the fitted function y = predictor(x) by repeatedly solving the optimization problem for different fixed values of x. Each value of y has two elements: one for the 25th percentile and one for the 75th.

X, Y = range(0, 2π; length = 20), Any[]
+@constraint(model, c, x == 0.0)
+for xi in X
+    set_normalized_rhs(c, xi)
+    optimize!(model)
+    if is_solved_and_feasible(model)
+        push!(Y, value.(y))
+    else
+        push!(Y, [NaN, NaN])
+    end
+end
+Plots.plot!(X, reduce(hcat, Y)'; label = ["P25" "P75"], linewidth = 3)
Example block output

This page was generated using Literate.jl.

diff --git a/v0.1.4/tutorials/mnist.jl b/v0.1.4/tutorials/mnist.jl new file mode 100644 index 00000000..e1dbab52 --- /dev/null +++ b/v0.1.4/tutorials/mnist.jl @@ -0,0 +1,171 @@ +# Copyright (c) 2024: Oscar Dowson and contributors #src +# Copyright (c) 2024: Triad National Security, LLC #src +# #src +# Use of this source code is governed by a BSD-style license that can be #src +# found in the LICENSE.md file. #src + +# # Adversarial machine learning with Flux.jl + +# The purpose of this tutorial is to explain how to embed a neural network model +# from [Flux.jl](https://github.com/FluxML/Flux.jl) into JuMP. + +# ## Required packages + +# This tutorial requires the following packages + +using JuMP +import Flux +import Ipopt +import MathOptAI +import MLDatasets +import Plots + +# ## Data + +# This tutorial uses images from the MNIST dataset. + +# We load the predefined train and test splits: + +train_data = MLDatasets.MNIST(; split = :train) + +#- + +test_data = MLDatasets.MNIST(; split = :test) + +# Since the data are images, it is helpful to plot them. (This requires a +# transpose and reversing the rows to get the orientation correct.) + +function plot_image(x::Matrix; kwargs...) + return Plots.heatmap( + x'[size(x, 1):-1:1, :]; + xlims = (1, size(x, 2)), + ylims = (1, size(x, 1)), + aspect_ratio = true, + legend = false, + xaxis = false, + yaxis = false, + kwargs..., + ) +end + +function plot_image(instance::NamedTuple) + return plot_image(instance.features; title = "Label = $(instance.targets)") +end + +Plots.plot([plot_image(train_data[i]) for i in 1:6]...; layout = (2, 3)) + +# ## Training + +# We use a simple neural network with one hidden layer and a sigmoid activation +# function. (There are better performing networks; try experimenting.) + +predictor = Flux.Chain( + Flux.Dense(28^2 => 32, Flux.sigmoid), + Flux.Dense(32 => 10), + Flux.softmax, +) + +# Here is a function to load our data into the format that `predictor` expects: +function data_loader(data; batchsize, shuffle = false) + x = reshape(data.features, 28^2, :) + y = Flux.onehotbatch(data.targets, 0:9) + return Flux.DataLoader((x, y); batchsize, shuffle) +end + +# and here is a function to score the percentage of correct labels, where we +# assign a label by choosing the label of the highest `softmax` in the final +# layer. + +function score_model(predictor, data) + x, y = only(data_loader(data; batchsize = length(data))) + y_hat = predictor(x) + is_correct = Flux.onecold(y) .== Flux.onecold(y_hat) + p = round(100 * sum(is_correct) / length(is_correct); digits = 2) + println("Accuracy = $p %") + return +end + +# The accuracy of our model is only around 10% before training: + +score_model(predictor, train_data) +score_model(predictor, test_data) + +# Let's improve that by training our model. + +# !!! note +# It is not the purpose of this tutorial to explain how Flux works; see the +# documentation at [https://fluxml.ai](https://fluxml.ai) for more details. +# Changing the number of epochs or the learning rate can improve the loss. + +begin + train_loader = data_loader(train_data; batchsize = 256, shuffle = true) + optimizer_state = Flux.setup(Flux.Adam(3e-4), predictor) + for epoch in 1:30 + loss = 0.0 + for (x, y) in train_loader + loss_batch, gradient = Flux.withgradient(predictor) do model + return Flux.crossentropy(model(x), y) + end + Flux.update!(optimizer_state, predictor, only(gradient)) + loss += loss_batch + end + loss = round(loss / length(train_loader); digits = 4) + print("Epoch $epoch: loss = $loss\t") + score_model(predictor, test_data) + end +end + +# Here are the first eight predictions of the test data: + +function plot_image(predictor, x::Matrix) + score, index = findmax(predictor(vec(x))) + title = "Predicted: $(index - 1) ($(round(Int, 100 * score))%)" + return plot_image(x; title) +end + +plots = [plot_image(predictor, test_data[i].features) for i in 1:8] +Plots.plot(plots...; size = (1200, 600), layout = (2, 4)) + +# We can also look at the best and worst four predictions: + +x, y = only(data_loader(test_data; batchsize = length(test_data))) +losses = Flux.crossentropy(predictor(x), y; agg = identity) +indices = sortperm(losses; dims = 2)[[1:4; end-3:end]] +plots = [plot_image(predictor, test_data[i].features) for i in indices] +Plots.plot(plots...; size = (1200, 600), layout = (2, 4)) + +# There are still some fairly bad mistakes. Can you change the model or training +# parameters improve to improve things? + +# ## JuMP + +# Now that we have a trained machine learning model, we can embed it in a JuMP +# model. + +# Here's a function which takes a test case and returns an example that +# maximizes the probability of the adversarial example. + +function find_adversarial_image(test_case; adversary_label, δ = 0.05) + model = Model(Ipopt.Optimizer) + set_silent(model) + @variable(model, 0 <= x[1:28, 1:28] <= 1) + @constraint(model, -δ .<= x .- test_case.features .<= δ) + ## Note: we need to use `vec` here because `x` is a 28-by-28 Matrix, but our + ## neural network expects a 28^2 length vector. + y, _ = MathOptAI.add_predictor(model, predictor, vec(x)) + @objective(model, Max, y[adversary_label+1] - y[test_case.targets+1]) + optimize!(model) + @assert is_solved_and_feasible(model) + return value.(x) +end + +# Let's try finding an adversarial example to the third test image. The image on +# the left is our input image. The network thinks this is a `1` with probability +# 99%. The image on the right is the adversarial image. The network thinks this +# is a `7`, although it is less confident. + +x_adversary = find_adversarial_image(test_data[3]; adversary_label = 7); +Plots.plot( + plot_image(predictor, test_data[3].features), + plot_image(predictor, Float32.(x_adversary)), +) diff --git a/v0.1.4/tutorials/mnist/055b47cc.svg b/v0.1.4/tutorials/mnist/055b47cc.svg new file mode 100644 index 00000000..ea11eae6 --- /dev/null +++ b/v0.1.4/tutorials/mnist/055b47cc.svg @@ -0,0 +1,1194 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.4/tutorials/mnist/2a6a962f.svg b/v0.1.4/tutorials/mnist/2a6a962f.svg new file mode 100644 index 00000000..b2c45675 --- /dev/null +++ b/v0.1.4/tutorials/mnist/2a6a962f.svg @@ -0,0 +1,1199 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.4/tutorials/mnist/3a0e4910.svg b/v0.1.4/tutorials/mnist/3a0e4910.svg new file mode 100644 index 00000000..f925906d --- /dev/null +++ b/v0.1.4/tutorials/mnist/3a0e4910.svg @@ -0,0 +1,511 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.4/tutorials/mnist/c214aa8b.svg b/v0.1.4/tutorials/mnist/c214aa8b.svg new file mode 100644 index 00000000..0b19bf4d --- /dev/null +++ b/v0.1.4/tutorials/mnist/c214aa8b.svg @@ -0,0 +1,327 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.4/tutorials/mnist/index.html b/v0.1.4/tutorials/mnist/index.html new file mode 100644 index 00000000..b5cf3c17 --- /dev/null +++ b/v0.1.4/tutorials/mnist/index.html @@ -0,0 +1,125 @@ + +Adversarial machine learning with Flux.jl · MathOptAI.jl
GitHub

Adversarial machine learning with Flux.jl

The purpose of this tutorial is to explain how to embed a neural network model from Flux.jl into JuMP.

Required packages

This tutorial requires the following packages

using JuMP
+import Flux
+import Ipopt
+import MathOptAI
+import MLDatasets
+import Plots

Data

This tutorial uses images from the MNIST dataset.

We load the predefined train and test splits:

train_data = MLDatasets.MNIST(; split = :train)
dataset MNIST:
+  metadata  =>    Dict{String, Any} with 3 entries
+  split     =>    :train
+  features  =>    28×28×60000 Array{Float32, 3}
+  targets   =>    60000-element Vector{Int64}
test_data = MLDatasets.MNIST(; split = :test)
dataset MNIST:
+  metadata  =>    Dict{String, Any} with 3 entries
+  split     =>    :test
+  features  =>    28×28×10000 Array{Float32, 3}
+  targets   =>    10000-element Vector{Int64}

Since the data are images, it is helpful to plot them. (This requires a transpose and reversing the rows to get the orientation correct.)

function plot_image(x::Matrix; kwargs...)
+    return Plots.heatmap(
+        x'[size(x, 1):-1:1, :];
+        xlims = (1, size(x, 2)),
+        ylims = (1, size(x, 1)),
+        aspect_ratio = true,
+        legend = false,
+        xaxis = false,
+        yaxis = false,
+        kwargs...,
+    )
+end
+
+function plot_image(instance::NamedTuple)
+    return plot_image(instance.features; title = "Label = $(instance.targets)")
+end
+
+Plots.plot([plot_image(train_data[i]) for i in 1:6]...; layout = (2, 3))
Example block output

Training

We use a simple neural network with one hidden layer and a sigmoid activation function. (There are better performing networks; try experimenting.)

predictor = Flux.Chain(
+    Flux.Dense(28^2 => 32, Flux.sigmoid),
+    Flux.Dense(32 => 10),
+    Flux.softmax,
+)
Chain(
+  Dense(784 => 32, σ),                  # 25_120 parameters
+  Dense(32 => 10),                      # 330 parameters
+  NNlib.softmax,
+)                   # Total: 4 arrays, 25_450 parameters, 99.617 KiB.

Here is a function to load our data into the format that predictor expects:

function data_loader(data; batchsize, shuffle = false)
+    x = reshape(data.features, 28^2, :)
+    y = Flux.onehotbatch(data.targets, 0:9)
+    return Flux.DataLoader((x, y); batchsize, shuffle)
+end
data_loader (generic function with 1 method)

and here is a function to score the percentage of correct labels, where we assign a label by choosing the label of the highest softmax in the final layer.

function score_model(predictor, data)
+    x, y = only(data_loader(data; batchsize = length(data)))
+    y_hat = predictor(x)
+    is_correct = Flux.onecold(y) .== Flux.onecold(y_hat)
+    p = round(100 * sum(is_correct) / length(is_correct); digits = 2)
+    println("Accuracy = $p %")
+    return
+end
score_model (generic function with 1 method)

The accuracy of our model is only around 10% before training:

score_model(predictor, train_data)
+score_model(predictor, test_data)
Accuracy = 10.43 %
+Accuracy = 10.29 %

Let's improve that by training our model.

Note

It is not the purpose of this tutorial to explain how Flux works; see the documentation at https://fluxml.ai for more details. Changing the number of epochs or the learning rate can improve the loss.

begin
+    train_loader = data_loader(train_data; batchsize = 256, shuffle = true)
+    optimizer_state = Flux.setup(Flux.Adam(3e-4), predictor)
+    for epoch in 1:30
+        loss = 0.0
+        for (x, y) in train_loader
+            loss_batch, gradient = Flux.withgradient(predictor) do model
+                return Flux.crossentropy(model(x), y)
+            end
+            Flux.update!(optimizer_state, predictor, only(gradient))
+            loss += loss_batch
+        end
+        loss = round(loss / length(train_loader); digits = 4)
+        print("Epoch $epoch: loss = $loss\t")
+        score_model(predictor, test_data)
+    end
+end
Epoch 1: loss = 1.7684	Accuracy = 76.15 %
+Epoch 2: loss = 1.1526	Accuracy = 83.29 %
+Epoch 3: loss = 0.858	Accuracy = 86.35 %
+Epoch 4: loss = 0.6863	Accuracy = 88.02 %
+Epoch 5: loss = 0.576	Accuracy = 89.18 %
+Epoch 6: loss = 0.5009	Accuracy = 89.75 %
+Epoch 7: loss = 0.4474	Accuracy = 90.4 %
+Epoch 8: loss = 0.4078	Accuracy = 90.78 %
+Epoch 9: loss = 0.3769	Accuracy = 91.2 %
+Epoch 10: loss = 0.3529	Accuracy = 91.64 %
+Epoch 11: loss = 0.3332	Accuracy = 91.75 %
+Epoch 12: loss = 0.3169	Accuracy = 92.11 %
+Epoch 13: loss = 0.3029	Accuracy = 92.23 %
+Epoch 14: loss = 0.2906	Accuracy = 92.47 %
+Epoch 15: loss = 0.2802	Accuracy = 92.54 %
+Epoch 16: loss = 0.2703	Accuracy = 92.74 %
+Epoch 17: loss = 0.2616	Accuracy = 92.84 %
+Epoch 18: loss = 0.2539	Accuracy = 93.05 %
+Epoch 19: loss = 0.2467	Accuracy = 93.08 %
+Epoch 20: loss = 0.2402	Accuracy = 93.16 %
+Epoch 21: loss = 0.2342	Accuracy = 93.33 %
+Epoch 22: loss = 0.2283	Accuracy = 93.41 %
+Epoch 23: loss = 0.223	Accuracy = 93.57 %
+Epoch 24: loss = 0.2182	Accuracy = 93.74 %
+Epoch 25: loss = 0.2136	Accuracy = 93.82 %
+Epoch 26: loss = 0.2092	Accuracy = 93.95 %
+Epoch 27: loss = 0.2048	Accuracy = 94.06 %
+Epoch 28: loss = 0.2014	Accuracy = 94.02 %
+Epoch 29: loss = 0.197	Accuracy = 94.26 %
+Epoch 30: loss = 0.1931	Accuracy = 94.35 %

Here are the first eight predictions of the test data:

function plot_image(predictor, x::Matrix)
+    score, index = findmax(predictor(vec(x)))
+    title = "Predicted: $(index - 1) ($(round(Int, 100 * score))%)"
+    return plot_image(x; title)
+end
+
+plots = [plot_image(predictor, test_data[i].features) for i in 1:8]
+Plots.plot(plots...; size = (1200, 600), layout = (2, 4))
Example block output

We can also look at the best and worst four predictions:

x, y = only(data_loader(test_data; batchsize = length(test_data)))
+losses = Flux.crossentropy(predictor(x), y; agg = identity)
+indices = sortperm(losses; dims = 2)[[1:4; end-3:end]]
+plots = [plot_image(predictor, test_data[i].features) for i in indices]
+Plots.plot(plots...; size = (1200, 600), layout = (2, 4))
Example block output

There are still some fairly bad mistakes. Can you change the model or training parameters improve to improve things?

JuMP

Now that we have a trained machine learning model, we can embed it in a JuMP model.

Here's a function which takes a test case and returns an example that maximizes the probability of the adversarial example.

function find_adversarial_image(test_case; adversary_label, δ = 0.05)
+    model = Model(Ipopt.Optimizer)
+    set_silent(model)
+    @variable(model, 0 <= x[1:28, 1:28] <= 1)
+    @constraint(model, -δ .<= x .- test_case.features .<= δ)
+    # Note: we need to use `vec` here because `x` is a 28-by-28 Matrix, but our
+    # neural network expects a 28^2 length vector.
+    y, _ = MathOptAI.add_predictor(model, predictor, vec(x))
+    @objective(model, Max, y[adversary_label+1] - y[test_case.targets+1])
+    optimize!(model)
+    @assert is_solved_and_feasible(model)
+    return value.(x)
+end
find_adversarial_image (generic function with 1 method)

Let's try finding an adversarial example to the third test image. The image on the left is our input image. The network thinks this is a 1 with probability 99%. The image on the right is the adversarial image. The network thinks this is a 7, although it is less confident.

x_adversary = find_adversarial_image(test_data[3]; adversary_label = 7);
+Plots.plot(
+    plot_image(predictor, test_data[3].features),
+    plot_image(predictor, Float32.(x_adversary)),
+)
Example block output

This page was generated using Literate.jl.

diff --git a/v0.1.4/tutorials/mnist_lux.jl b/v0.1.4/tutorials/mnist_lux.jl new file mode 100644 index 00000000..cd41799e --- /dev/null +++ b/v0.1.4/tutorials/mnist_lux.jl @@ -0,0 +1,186 @@ +# Copyright (c) 2024: Oscar Dowson and contributors #src +# Copyright (c) 2024: Triad National Security, LLC #src +# #src +# Use of this source code is governed by a BSD-style license that can be #src +# found in the LICENSE.md file. #src + +# # Adversarial machine learning with Lux.jl + +# The purpose of this tutorial is to explain how to embed a neural network model +# from [Lux.jl](https://github.com/SciML/Lux.jl) into JuMP. + +# ## Required packages + +# This tutorial requires the following packages + +using JuMP +import Lux +import Ipopt +import MathOptAI +import MLDatasets +import MLUtils +import OneHotArrays +import Optimisers +import Plots +import Random +import Zygote + +# ## Data + +# This tutorial uses images from the MNIST dataset. + +# We load the predefined train and test splits: + +train_data = MLDatasets.MNIST(; split = :train) + +#- + +test_data = MLDatasets.MNIST(; split = :test) + +# Since the data are images, it is helpful to plot them. (This requires a +# transpose and reversing the rows to get the orientation correct.) + +function plot_image(x::Matrix; kwargs...) + return Plots.heatmap( + x'[size(x, 1):-1:1, :]; + xlims = (1, size(x, 2)), + ylims = (1, size(x, 1)), + aspect_ratio = true, + legend = false, + xaxis = false, + yaxis = false, + kwargs..., + ) +end + +function plot_image(instance::NamedTuple) + return plot_image(instance.features; title = "Label = $(instance.targets)") +end + +Plots.plot([plot_image(train_data[i]) for i in 1:6]...; layout = (2, 3)) + +# ## Training + +# We use a simple neural network with one hidden layer and a sigmoid activation +# function. (There are better performing networks; try experimenting.) + +chain = Lux.Chain( + Lux.Dense(28^2 => 32, Lux.sigmoid), + Lux.Dense(32 => 10), + Lux.softmax, +) +rng = Random.MersenneTwister(); +parameters, state = Lux.setup(rng, chain) +predictor = (chain, parameters, state); + +# Here is a function to load our data into the format that `predictor` expects: +function data_loader(data; batchsize, shuffle = false) + x = reshape(data.features, 28^2, :) + y = OneHotArrays.onehotbatch(data.targets, 0:9) + return MLUtils.DataLoader((x, y); batchsize, shuffle) +end + +# and here is a function to score the percentage of correct labels, where we +# assign a label by choosing the label of the highest `softmax` in the final +# layer. + +function score_model(predictor, data) + chain, parameters, state = predictor + x, y = only(data_loader(data; batchsize = length(data))) + y_hat, _ = chain(x, parameters, state) + is_correct = OneHotArrays.onecold(y) .== OneHotArrays.onecold(y_hat) + p = round(100 * sum(is_correct) / length(is_correct); digits = 2) + println("Accuracy = $p %") + return +end + +# The accuracy of our model is only around 10% before training: + +score_model(predictor, train_data) +score_model(predictor, test_data) + +# Let's improve that by training our model. + +# !!! note +# It is not the purpose of this tutorial to explain how Lux works; see the +# documentation at [https://lux.csail.mit.edu](https://lux.csail.mit.edu/stable/) +# for more details. Changing the number of epochs or the learning rate can +# improve the loss. + +begin + train_loader = data_loader(train_data; batchsize = 256, shuffle = true) + optimizer_state = Optimisers.setup(Optimisers.Adam(0.0003f0), parameters) + for epoch in 1:30 + loss = 0.0 + for (x, y) in train_loader + global state + (loss_batch, state), pullback = Zygote.pullback(parameters) do p + y_model, new_state = chain(x, p, state) + return Lux.CrossEntropyLoss()(y_model, y), new_state + end + gradients = only(pullback((one(loss), nothing))) + Optimisers.update!(optimizer_state, parameters, gradients) + loss += loss_batch + end + loss = round(loss / length(train_loader); digits = 4) + print("Epoch $epoch: loss = $loss\t") + score_model(predictor, test_data) + end +end + +# Here are the first eight predictions of the test data: + +function plot_image(predictor, x::Matrix) + y, _ = chain(vec(x), parameters, state) + score, index = findmax(y) + title = "Predicted: $(index - 1) ($(round(Int, 100 * score))%)" + return plot_image(x; title) +end + +plots = [plot_image(predictor, test_data[i].features) for i in 1:8] +Plots.plot(plots...; size = (1200, 600), layout = (2, 4)) + +# We can also look at the best and worst four predictions: + +x, y = only(data_loader(test_data; batchsize = length(test_data))) +y_model, _ = chain(x, parameters, state) +losses = Lux.CrossEntropyLoss(; agg = identity)(y_model, y) +indices = sortperm(losses; dims = 2)[[1:4; end-3:end]] +plots = [plot_image(predictor, test_data[i].features) for i in indices] +Plots.plot(plots...; size = (1200, 600), layout = (2, 4)) + +# There are still some fairly bad mistakes. Can you change the model or training +# parameters improve to improve things? + +# ## JuMP + +# Now that we have a trained machine learning model, we can embed it in a JuMP +# model. + +# Here's a function which takes a test case and returns an example that +# maximizes the probability of the adversarial example. + +function find_adversarial_image(test_case; adversary_label, δ = 0.05) + model = Model(Ipopt.Optimizer) + set_silent(model) + @variable(model, 0 <= x[1:28, 1:28] <= 1) + @constraint(model, -δ .<= x .- test_case.features .<= δ) + ## Note: we need to use `vec` here because `x` is a 28-by-28 Matrix, but our + ## neural network expects a 28^2 length vector. + y, _ = MathOptAI.add_predictor(model, predictor, vec(x)) + @objective(model, Max, y[adversary_label+1] - y[test_case.targets+1]) + optimize!(model) + @assert is_solved_and_feasible(model) + return value.(x) +end + +# Let's try finding an adversarial example to the third test image. The image on +# the left is our input image. The network thinks this is a `1` with probability +# 99%. The image on the right is the adversarial image. The network thinks this +# is a `7`, although it is less confident. + +x_adversary = find_adversarial_image(test_data[3]; adversary_label = 7); +Plots.plot( + plot_image(predictor, test_data[3].features), + plot_image(predictor, Float32.(x_adversary)), +) diff --git a/v0.1.4/tutorials/mnist_lux/0a6b536d.svg b/v0.1.4/tutorials/mnist_lux/0a6b536d.svg new file mode 100644 index 00000000..27a73b04 --- /dev/null +++ b/v0.1.4/tutorials/mnist_lux/0a6b536d.svg @@ -0,0 +1,326 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.4/tutorials/mnist_lux/2f21f55f.svg b/v0.1.4/tutorials/mnist_lux/2f21f55f.svg new file mode 100644 index 00000000..1dbc48f3 --- /dev/null +++ b/v0.1.4/tutorials/mnist_lux/2f21f55f.svg @@ -0,0 +1,1199 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.4/tutorials/mnist_lux/7d8afe07.svg b/v0.1.4/tutorials/mnist_lux/7d8afe07.svg new file mode 100644 index 00000000..cfd3205f --- /dev/null +++ b/v0.1.4/tutorials/mnist_lux/7d8afe07.svg @@ -0,0 +1,511 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.4/tutorials/mnist_lux/d39850e4.svg b/v0.1.4/tutorials/mnist_lux/d39850e4.svg new file mode 100644 index 00000000..c2900d4d --- /dev/null +++ b/v0.1.4/tutorials/mnist_lux/d39850e4.svg @@ -0,0 +1,1192 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.4/tutorials/mnist_lux/index.html b/v0.1.4/tutorials/mnist_lux/index.html new file mode 100644 index 00000000..814fb703 --- /dev/null +++ b/v0.1.4/tutorials/mnist_lux/index.html @@ -0,0 +1,135 @@ + +Adversarial machine learning with Lux.jl · MathOptAI.jl
GitHub

Adversarial machine learning with Lux.jl

The purpose of this tutorial is to explain how to embed a neural network model from Lux.jl into JuMP.

Required packages

This tutorial requires the following packages

using JuMP
+import Lux
+import Ipopt
+import MathOptAI
+import MLDatasets
+import MLUtils
+import OneHotArrays
+import Optimisers
+import Plots
+import Random
+import Zygote

Data

This tutorial uses images from the MNIST dataset.

We load the predefined train and test splits:

train_data = MLDatasets.MNIST(; split = :train)
dataset MNIST:
+  metadata  =>    Dict{String, Any} with 3 entries
+  split     =>    :train
+  features  =>    28×28×60000 Array{Float32, 3}
+  targets   =>    60000-element Vector{Int64}
test_data = MLDatasets.MNIST(; split = :test)
dataset MNIST:
+  metadata  =>    Dict{String, Any} with 3 entries
+  split     =>    :test
+  features  =>    28×28×10000 Array{Float32, 3}
+  targets   =>    10000-element Vector{Int64}

Since the data are images, it is helpful to plot them. (This requires a transpose and reversing the rows to get the orientation correct.)

function plot_image(x::Matrix; kwargs...)
+    return Plots.heatmap(
+        x'[size(x, 1):-1:1, :];
+        xlims = (1, size(x, 2)),
+        ylims = (1, size(x, 1)),
+        aspect_ratio = true,
+        legend = false,
+        xaxis = false,
+        yaxis = false,
+        kwargs...,
+    )
+end
+
+function plot_image(instance::NamedTuple)
+    return plot_image(instance.features; title = "Label = $(instance.targets)")
+end
+
+Plots.plot([plot_image(train_data[i]) for i in 1:6]...; layout = (2, 3))
Example block output

Training

We use a simple neural network with one hidden layer and a sigmoid activation function. (There are better performing networks; try experimenting.)

chain = Lux.Chain(
+    Lux.Dense(28^2 => 32, Lux.sigmoid),
+    Lux.Dense(32 => 10),
+    Lux.softmax,
+)
+rng = Random.MersenneTwister();
+parameters, state = Lux.setup(rng, chain)
+predictor = (chain, parameters, state);

Here is a function to load our data into the format that predictor expects:

function data_loader(data; batchsize, shuffle = false)
+    x = reshape(data.features, 28^2, :)
+    y = OneHotArrays.onehotbatch(data.targets, 0:9)
+    return MLUtils.DataLoader((x, y); batchsize, shuffle)
+end
data_loader (generic function with 1 method)

and here is a function to score the percentage of correct labels, where we assign a label by choosing the label of the highest softmax in the final layer.

function score_model(predictor, data)
+    chain, parameters, state = predictor
+    x, y = only(data_loader(data; batchsize = length(data)))
+    y_hat, _ = chain(x, parameters, state)
+    is_correct = OneHotArrays.onecold(y) .== OneHotArrays.onecold(y_hat)
+    p = round(100 * sum(is_correct) / length(is_correct); digits = 2)
+    println("Accuracy = $p %")
+    return
+end
score_model (generic function with 1 method)

The accuracy of our model is only around 10% before training:

score_model(predictor, train_data)
+score_model(predictor, test_data)
Accuracy = 8.65 %
+Accuracy = 8.52 %

Let's improve that by training our model.

Note

It is not the purpose of this tutorial to explain how Lux works; see the documentation at https://lux.csail.mit.edu for more details. Changing the number of epochs or the learning rate can improve the loss.

begin
+    train_loader = data_loader(train_data; batchsize = 256, shuffle = true)
+    optimizer_state = Optimisers.setup(Optimisers.Adam(0.0003f0), parameters)
+    for epoch in 1:30
+        loss = 0.0
+        for (x, y) in train_loader
+            global state
+            (loss_batch, state), pullback = Zygote.pullback(parameters) do p
+                y_model, new_state = chain(x, p, state)
+                return Lux.CrossEntropyLoss()(y_model, y), new_state
+            end
+            gradients = only(pullback((one(loss), nothing)))
+            Optimisers.update!(optimizer_state, parameters, gradients)
+            loss += loss_batch
+        end
+        loss = round(loss / length(train_loader); digits = 4)
+        print("Epoch $epoch: loss = $loss\t")
+        score_model(predictor, test_data)
+    end
+end
Epoch 1: loss = 1.8665	Accuracy = 69.54 %
+Epoch 2: loss = 1.2153	Accuracy = 81.36 %
+Epoch 3: loss = 0.8921	Accuracy = 85.71 %
+Epoch 4: loss = 0.7023	Accuracy = 87.94 %
+Epoch 5: loss = 0.5822	Accuracy = 89.19 %
+Epoch 6: loss = 0.5026	Accuracy = 90.04 %
+Epoch 7: loss = 0.447	Accuracy = 90.5 %
+Epoch 8: loss = 0.406	Accuracy = 91.08 %
+Epoch 9: loss = 0.3747	Accuracy = 91.51 %
+Epoch 10: loss = 0.3501	Accuracy = 91.65 %
+Epoch 11: loss = 0.3304	Accuracy = 92.02 %
+Epoch 12: loss = 0.3138	Accuracy = 92.43 %
+Epoch 13: loss = 0.2998	Accuracy = 92.6 %
+Epoch 14: loss = 0.2876	Accuracy = 92.81 %
+Epoch 15: loss = 0.2768	Accuracy = 92.87 %
+Epoch 16: loss = 0.2674	Accuracy = 93.08 %
+Epoch 17: loss = 0.2593	Accuracy = 93.19 %
+Epoch 18: loss = 0.2514	Accuracy = 93.31 %
+Epoch 19: loss = 0.2443	Accuracy = 93.4 %
+Epoch 20: loss = 0.2377	Accuracy = 93.46 %
+Epoch 21: loss = 0.232	Accuracy = 93.58 %
+Epoch 22: loss = 0.2264	Accuracy = 93.69 %
+Epoch 23: loss = 0.2215	Accuracy = 93.77 %
+Epoch 24: loss = 0.2168	Accuracy = 93.82 %
+Epoch 25: loss = 0.2117	Accuracy = 93.93 %
+Epoch 26: loss = 0.2075	Accuracy = 93.94 %
+Epoch 27: loss = 0.2035	Accuracy = 93.96 %
+Epoch 28: loss = 0.2002	Accuracy = 94.17 %
+Epoch 29: loss = 0.1958	Accuracy = 94.26 %
+Epoch 30: loss = 0.1927	Accuracy = 94.33 %

Here are the first eight predictions of the test data:

function plot_image(predictor, x::Matrix)
+    y, _ = chain(vec(x), parameters, state)
+    score, index = findmax(y)
+    title = "Predicted: $(index - 1) ($(round(Int, 100 * score))%)"
+    return plot_image(x; title)
+end
+
+plots = [plot_image(predictor, test_data[i].features) for i in 1:8]
+Plots.plot(plots...; size = (1200, 600), layout = (2, 4))
Example block output

We can also look at the best and worst four predictions:

x, y = only(data_loader(test_data; batchsize = length(test_data)))
+y_model, _ = chain(x, parameters, state)
+losses = Lux.CrossEntropyLoss(; agg = identity)(y_model, y)
+indices = sortperm(losses; dims = 2)[[1:4; end-3:end]]
+plots = [plot_image(predictor, test_data[i].features) for i in indices]
+Plots.plot(plots...; size = (1200, 600), layout = (2, 4))
Example block output

There are still some fairly bad mistakes. Can you change the model or training parameters improve to improve things?

JuMP

Now that we have a trained machine learning model, we can embed it in a JuMP model.

Here's a function which takes a test case and returns an example that maximizes the probability of the adversarial example.

function find_adversarial_image(test_case; adversary_label, δ = 0.05)
+    model = Model(Ipopt.Optimizer)
+    set_silent(model)
+    @variable(model, 0 <= x[1:28, 1:28] <= 1)
+    @constraint(model, -δ .<= x .- test_case.features .<= δ)
+    # Note: we need to use `vec` here because `x` is a 28-by-28 Matrix, but our
+    # neural network expects a 28^2 length vector.
+    y, _ = MathOptAI.add_predictor(model, predictor, vec(x))
+    @objective(model, Max, y[adversary_label+1] - y[test_case.targets+1])
+    optimize!(model)
+    @assert is_solved_and_feasible(model)
+    return value.(x)
+end
find_adversarial_image (generic function with 1 method)

Let's try finding an adversarial example to the third test image. The image on the left is our input image. The network thinks this is a 1 with probability 99%. The image on the right is the adversarial image. The network thinks this is a 7, although it is less confident.

x_adversary = find_adversarial_image(test_data[3]; adversary_label = 7);
+Plots.plot(
+    plot_image(predictor, test_data[3].features),
+    plot_image(predictor, Float32.(x_adversary)),
+)
Example block output

This page was generated using Literate.jl.

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For example, if you +# have an existing Python installation (with PyTorch installed), and it is +# available in the current Conda environment, set: +# +# ```julia +# ENV["JULIA_CONDAPKG_BACKEND"] = "Current" +# ``` +# +# before importing PythonCall.jl. If the Python installation can be found on +# the path and it is not in a Conda environment, set: +# +# ```julia +# ENV["JULIA_CONDAPKG_BACKEND"] = "Null" +# ``` +# +# If `python` is not on your path, you may additionally need to set +# `JULIA_PYTHONCALL_EXE`, for example, to: +# +# ```julia +# ENV["JULIA_PYTHONCALL_EXE"] = "python3" +# ``` + +# ## Required packages + +# This tutorial requires the following packages + +using JuMP +using Test +import Ipopt +import MathOptAI +import Plots + +# ## Training a model + +# The following script builds and trains a simple neural network in PyTorch. +# For simplicity, we do not evaluate out-of-sample test performance, or use +# a batched data loader. In general, you should train your model in Python, +# and then use `torch.save(model, filename)` to save it to a `.pt` file for +# later use in Julia. + +# The model is unimportant, but for this example, we are trying to fit noisy +# observations of the function ``f(x) = x^2 - 2x``. + +# In Python, we ran: +# ```python +# #!/usr/bin/python3 +# import torch +# model = torch.nn.Sequential( +# torch.nn.Linear(1, 16), +# torch.nn.ReLU(), +# torch.nn.Linear(16, 1), +# ) +# +# n = 1024 +# x = torch.arange(-2, 2 + 4 / (n - 1), 4 / (n - 1)).reshape(n, 1) +# loss_fn = torch.nn.MSELoss() +# optimizer = torch.optim.Adam(model.parameters(), lr=0.01) +# for epoch in range(100): +# optimizer.zero_grad() +# N = torch.normal(torch.zeros(n, 1), torch.ones(n, 1)) +# y = x ** 2 -2 * x + 0.1 * N +# loss = loss_fn(model(x), y) +# loss.backward() +# optimizer.step() +# +# torch.save(model, "model.pt") +# ``` + +# ## JuMP model + +# Our goal for this JuMP model is to load the Neural Network from PyTorch into +# the objective function, and then minimize the objective for different fixed +# values of `x` to recreate the function that the Neural Network has learned to +# approximate. + +# First, create a JuMP model: + +model = Model(Ipopt.Optimizer) +set_silent(model) +@variable(model, x) + +# Then, load the model from PyTorch using [`MathOptAI.PytorchModel`](@ref): + +predictor = MathOptAI.PytorchModel(joinpath(@__DIR__, "model.pt")) +y, _ = MathOptAI.add_predictor(model, predictor, [x]) +@objective(model, Min, only(y)) + +# Now, visualize the fitted function `y = predictor(x)` by repeatedly solving +# the optimization problem for different fixed values of `x`: + +X, Y = -2:0.1:2, Float64[] +@constraint(model, c, x == 0.0) +for xi in X + set_normalized_rhs(c, xi) + optimize!(model) + @test is_solved_and_feasible(model) + push!(Y, objective_value(model)) +end +Plots.plot(x -> x^2 - 2x, X; label = "Truth", linestype = :dot) +Plots.plot!(X, Y; label = "Fitted") diff --git a/v0.1.4/tutorials/pytorch/cc73df64.svg b/v0.1.4/tutorials/pytorch/cc73df64.svg new file mode 100644 index 00000000..92d8d5df --- /dev/null +++ b/v0.1.4/tutorials/pytorch/cc73df64.svg @@ -0,0 +1,48 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.1.4/tutorials/pytorch/index.html b/v0.1.4/tutorials/pytorch/index.html new file mode 100644 index 00000000..3a12edd0 --- /dev/null +++ b/v0.1.4/tutorials/pytorch/index.html @@ -0,0 +1,39 @@ + +Function fitting with PyTorch · MathOptAI.jl
GitHub

Function fitting with PyTorch

The purpose of this tutorial is to explain how to embed a neural network model from PyTorch into JuMP.

Python integration

MathOptAI uses PythonCall.jl to call from Julia into Python.

See CondaPkg.jl for more control over how to link Julia to an existing Python environment. For example, if you have an existing Python installation (with PyTorch installed), and it is available in the current Conda environment, set:

ENV["JULIA_CONDAPKG_BACKEND"] = "Current"

before importing PythonCall.jl. If the Python installation can be found on the path and it is not in a Conda environment, set:

ENV["JULIA_CONDAPKG_BACKEND"] = "Null"

If python is not on your path, you may additionally need to set JULIA_PYTHONCALL_EXE, for example, to:

ENV["JULIA_PYTHONCALL_EXE"] = "python3"

Required packages

This tutorial requires the following packages

using JuMP
+using Test
+import Ipopt
+import MathOptAI
+import Plots

Training a model

The following script builds and trains a simple neural network in PyTorch. For simplicity, we do not evaluate out-of-sample test performance, or use a batched data loader. In general, you should train your model in Python, and then use torch.save(model, filename) to save it to a .pt file for later use in Julia.

The model is unimportant, but for this example, we are trying to fit noisy observations of the function $f(x) = x^2 - 2x$.

In Python, we ran:

#!/usr/bin/python3
+import torch
+model = torch.nn.Sequential(
+    torch.nn.Linear(1, 16),
+    torch.nn.ReLU(),
+    torch.nn.Linear(16, 1),
+)
+
+n = 1024
+x = torch.arange(-2, 2 + 4 / (n - 1), 4 / (n - 1)).reshape(n, 1)
+loss_fn = torch.nn.MSELoss()
+optimizer = torch.optim.Adam(model.parameters(), lr=0.01)
+for epoch in range(100):
+    optimizer.zero_grad()
+    N = torch.normal(torch.zeros(n, 1), torch.ones(n, 1))
+    y = x ** 2 -2 * x + 0.1 * N
+    loss = loss_fn(model(x), y)
+    loss.backward()
+    optimizer.step()
+
+torch.save(model, "model.pt")

JuMP model

Our goal for this JuMP model is to load the Neural Network from PyTorch into the objective function, and then minimize the objective for different fixed values of x to recreate the function that the Neural Network has learned to approximate.

First, create a JuMP model:

model = Model(Ipopt.Optimizer)
+set_silent(model)
+@variable(model, x)

\[ x \]

Then, load the model from PyTorch using MathOptAI.PytorchModel:

predictor = MathOptAI.PytorchModel(joinpath(@__DIR__, "model.pt"))
+y, _ = MathOptAI.add_predictor(model, predictor, [x])
+@objective(model, Min, only(y))

\[ moai\_Affine_{1} \]

Now, visualize the fitted function y = predictor(x) by repeatedly solving the optimization problem for different fixed values of x:

X, Y = -2:0.1:2, Float64[]
+@constraint(model, c, x == 0.0)
+for xi in X
+    set_normalized_rhs(c, xi)
+    optimize!(model)
+    @test is_solved_and_feasible(model)
+    push!(Y, objective_value(model))
+end
+Plots.plot(x -> x^2 - 2x, X; label = "Truth", linestype = :dot)
+Plots.plot!(X, Y; label = "Fitted")
Example block output

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diff --git a/v0.1.4/tutorials/student_enrollment.jl b/v0.1.4/tutorials/student_enrollment.jl new file mode 100644 index 00000000..af0574d7 --- /dev/null +++ b/v0.1.4/tutorials/student_enrollment.jl @@ -0,0 +1,134 @@ +# Copyright (c) 2024: Oscar Dowson and contributors #src +# Copyright (c) 2024: Triad National Security, LLC #src +# #src +# Use of this source code is governed by a BSD-style license that can be #src +# found in the LICENSE.md file. #src + +# # Logistic regression with GLM.jl + +# The purpose of this tutorial is to explain how to embed a logistic regression +# model from [GLM.jl](https://github.com/JuliaStats/GLM.jl) into JuMP. + +# The data and example in this tutorial comes from the paper: David Bergman, +# Teng Huang, Philip Brooks, Andrea Lodi, Arvind U. Raghunathan (2021) JANOS: An +# Integrated Predictive and Prescriptive Modeling Framework. INFORMS Journal on +# Computing 34(2):807-816. +# [https://doi.org/10.1287/ijoc.2020.1023](https://doi.org/10.1287/ijoc.2020.1023) + +# ## Required packages + +# This tutorial uses the following packages. + +using JuMP +import CSV +import DataFrames +import Downloads +import GLM +import Ipopt +import MathOptAI +import Statistics + +# ## Data + +# Here is a function to load the data directly from the JANOS repository: + +function read_df(filename) + url = "https://raw.githubusercontent.com/INFORMSJoC/2020.1023/master/data/" + data = Downloads.download(url * filename) + return CSV.read(data, DataFrames.DataFrame) +end + +# There are two important files. The first, `college_student_enroll-s1-1.csv`, +# contains historical admissions data on anonymized students, their SAT score, +# their GPA, their merit scholarships, and whether the enrolled in the college. + +train_df = read_df("college_student_enroll-s1-1.csv") + +# The second, `college_applications6000.csv`, contains the SAT and GPA data of +# students who are currently applying: + +evaluate_df = read_df("college_applications6000.csv") + +# There are 6,000 prospective students: + +n_students = size(evaluate_df, 1) + +# ## Prediction model + +# The first step is to train a logistic regression model to predict the Boolean +# `enroll` column based on the `SAT`, `GPA`, and `merit` columns. + +predictor = GLM.glm( + GLM.@formula(enroll ~ 0 + SAT + GPA + merit), + train_df, + GLM.Bernoulli(), +) + +# ## Decision model + +# Now that we have a trained logistic regression model, we want a decision model +# that chooses the optimal merit scholarship for each student in + +evaluate_df + +# Here's an empty JuMP model to start: + +model = Model() + +# First, we add a new column to `evaluate_df`, with one JuMP decision variable +# for each row. It is important the `.merit` column name in `evaluate_df` +# matches the name in `train_df`. + +evaluate_df.merit = @variable(model, 0 <= x_merit[1:n_students] <= 2.5); +evaluate_df + +# Then, we use [`MathOptAI.add_predictor`](@ref) to embed `predictor` into the +# JuMP `model`. [`MathOptAI.add_predictor`](@ref) returns a vector of variables, +# one for each row inn `evaluate_df`, corresponding to the output `enroll` of +# our logistic regression. + +evaluate_df.enroll, _ = MathOptAI.add_predictor(model, predictor, evaluate_df); +evaluate_df + +# The `.enroll` column name in `evaluate_df` is just a name. It doesn't have to +# match the name in `train_df`. + +# The objective of our problem is to maximize the expected number of students +# who enroll: + +@objective(model, Max, sum(evaluate_df.enroll)) + +# Subject to the constraint that we can spend at most `0.2 * n_students` on +# merit scholarships: + +@constraint(model, sum(evaluate_df.merit) <= 0.2 * n_students) + +# Because logistic regression involves a [`Sigmoid`](@ref) layer, we need to use +# a smooth nonlinear optimizer. A common choice is Ipopt. Solve and check the +# optimizer found a feasible solution: + +set_optimizer(model, Ipopt.Optimizer) +set_silent(model) +optimize!(model) +@assert is_solved_and_feasible(model) +solution_summary(model) + +# Let's store the solution in `evaluate_df` for analysis: + +evaluate_df.merit_sol = value.(evaluate_df.merit); +evaluate_df.enroll_sol = value.(evaluate_df.enroll); +evaluate_df + +# ## Solution analysis + +# We expect that just under 2,500 students will enroll: + +sum(evaluate_df.enroll_sol) + +# We awarded merit scholarships to approximately 1 in 6 students: + +count(evaluate_df.merit_sol .> 1e-5) + +# The average merit scholarship was worth just over \$1,000: + +1_000 * Statistics.mean(evaluate_df.merit_sol[evaluate_df.merit_sol.>1e-5]) diff --git a/v0.1.4/tutorials/student_enrollment/index.html b/v0.1.4/tutorials/student_enrollment/index.html new file mode 100644 index 00000000..2921e8b4 --- /dev/null +++ b/v0.1.4/tutorials/student_enrollment/index.html @@ -0,0 +1,162 @@ + +Logistic regression with GLM.jl · MathOptAI.jl
GitHub

Logistic regression with GLM.jl

The purpose of this tutorial is to explain how to embed a logistic regression model from GLM.jl into JuMP.

The data and example in this tutorial comes from the paper: David Bergman, Teng Huang, Philip Brooks, Andrea Lodi, Arvind U. Raghunathan (2021) JANOS: An Integrated Predictive and Prescriptive Modeling Framework. INFORMS Journal on Computing 34(2):807-816. https://doi.org/10.1287/ijoc.2020.1023

Required packages

This tutorial uses the following packages.

julia> using JuMP
julia> import CSV
julia> import DataFrames
julia> import Downloads
julia> import GLM
julia> import Ipopt
julia> import MathOptAI
julia> import Statistics

Data

Here is a function to load the data directly from the JANOS repository:

julia> function read_df(filename)
+           url = "https://raw.githubusercontent.com/INFORMSJoC/2020.1023/master/data/"
+           data = Downloads.download(url * filename)
+           return CSV.read(data, DataFrames.DataFrame)
+       endread_df (generic function with 1 method)

There are two important files. The first, college_student_enroll-s1-1.csv, contains historical admissions data on anonymized students, their SAT score, their GPA, their merit scholarships, and whether the enrolled in the college.

julia> train_df = read_df("college_student_enroll-s1-1.csv")20000×6 DataFrame
+   Row │ Column1  StudentID  SAT    GPA      merit    enroll 
+       │ Int64    Int64      Int64  Float64  Float64  Int64  
+───────┼─────────────────────────────────────────────────────
+     1 │       1          1   1507     3.72     1.64       0
+     2 │       2          2   1532     3.93     0.52       0
+     3 │       3          3   1487     3.77     1.67       0
+     4 │       4          4   1259     3.05     1.21       1
+     5 │       5          5   1354     3.39     1.65       1
+     6 │       6          6   1334     3.22     0.0        0
+     7 │       7          7   1125     2.73     1.68       1
+     8 │       8          8   1180     2.82     0.0        1
+   ⋮   │    ⋮         ⋮        ⋮       ⋮        ⋮       ⋮
+ 19994 │   19994      19994   1185     3.09     1.16       1
+ 19995 │   19995      19995   1471     3.7      1.05       0
+ 19996 │   19996      19996   1139     3.03     1.21       1
+ 19997 │   19997      19997   1371     3.39     1.26       0
+ 19998 │   19998      19998   1424     3.72     0.85       0
+ 19999 │   19999      19999   1170     3.01     0.73       1
+ 20000 │   20000      20000   1389     3.57     0.55       0
+                                           19985 rows omitted

The second, college_applications6000.csv, contains the SAT and GPA data of students who are currently applying:

julia> evaluate_df = read_df("college_applications6000.csv")6000×3 DataFrame
+  Row │ StudentID  SAT    GPA     
+      │ Int64      Int64  Float64 
+──────┼───────────────────────────
+    1 │         1   1240     3.22
+    2 │         2   1206     2.87
+    3 │         3   1520     3.74
+    4 │         4   1238     3.11
+    5 │         5   1142     2.74
+    6 │         6   1086     2.77
+    7 │         7   1367     3.28
+    8 │         8   1034     2.41
+  ⋮   │     ⋮        ⋮       ⋮
+ 5994 │      5994   1121     2.96
+ 5995 │      5995   1564     4.1
+ 5996 │      5996   1332     3.14
+ 5997 │      5997   1228     2.95
+ 5998 │      5998   1165     2.81
+ 5999 │      5999   1400     3.43
+ 6000 │      6000   1097     2.65
+                 5985 rows omitted

There are 6,000 prospective students:

julia> n_students = size(evaluate_df, 1)6000

Prediction model

The first step is to train a logistic regression model to predict the Boolean enroll column based on the SAT, GPA, and merit columns.

julia> predictor = GLM.glm(
+           GLM.@formula(enroll ~ 0 + SAT + GPA + merit),
+           train_df,
+           GLM.Bernoulli(),
+       )StatsModels.TableRegressionModel{GLM.GeneralizedLinearModel{GLM.GlmResp{Vector{Float64}, Distributions.Bernoulli{Float64}, GLM.LogitLink}, GLM.DensePredChol{Float64, LinearAlgebra.CholeskyPivoted{Float64, Matrix{Float64}, Vector{Int64}}}}, Matrix{Float64}}
+
+enroll ~ 0 + SAT + GPA + merit
+
+Coefficients:
+──────────────────────────────────────────────────────────────────────────
+             Coef.   Std. Error      z  Pr(>|z|)    Lower 95%    Upper 95%
+──────────────────────────────────────────────────────────────────────────
+SAT     0.00243882  0.000309312   7.88    <1e-14   0.00183258   0.00304506
+GPA    -1.09868     0.123796     -8.87    <1e-18  -1.34132     -0.856045
+merit   0.248294    0.0191086    12.99    <1e-37   0.210842     0.285747
+──────────────────────────────────────────────────────────────────────────

Decision model

Now that we have a trained logistic regression model, we want a decision model that chooses the optimal merit scholarship for each student in

julia> evaluate_df6000×3 DataFrame
+  Row │ StudentID  SAT    GPA     
+      │ Int64      Int64  Float64 
+──────┼───────────────────────────
+    1 │         1   1240     3.22
+    2 │         2   1206     2.87
+    3 │         3   1520     3.74
+    4 │         4   1238     3.11
+    5 │         5   1142     2.74
+    6 │         6   1086     2.77
+    7 │         7   1367     3.28
+    8 │         8   1034     2.41
+  ⋮   │     ⋮        ⋮       ⋮
+ 5994 │      5994   1121     2.96
+ 5995 │      5995   1564     4.1
+ 5996 │      5996   1332     3.14
+ 5997 │      5997   1228     2.95
+ 5998 │      5998   1165     2.81
+ 5999 │      5999   1400     3.43
+ 6000 │      6000   1097     2.65
+                 5985 rows omitted

Here's an empty JuMP model to start:

julia> model = Model()A JuMP Model
+├ solver: none
+├ objective_sense: FEASIBILITY_SENSE
+├ num_variables: 0
+├ num_constraints: 0
+└ Names registered in the model: none

First, we add a new column to evaluate_df, with one JuMP decision variable for each row. It is important the .merit column name in evaluate_df matches the name in train_df.

julia> evaluate_df.merit = @variable(model, 0 <= x_merit[1:n_students] <= 2.5);
julia> evaluate_df6000×4 DataFrame
+  Row │ StudentID  SAT    GPA      merit         
+      │ Int64      Int64  Float64  GenericV…     
+──────┼──────────────────────────────────────────
+    1 │         1   1240     3.22  x_merit[1]
+    2 │         2   1206     2.87  x_merit[2]
+    3 │         3   1520     3.74  x_merit[3]
+    4 │         4   1238     3.11  x_merit[4]
+    5 │         5   1142     2.74  x_merit[5]
+    6 │         6   1086     2.77  x_merit[6]
+    7 │         7   1367     3.28  x_merit[7]
+    8 │         8   1034     2.41  x_merit[8]
+  ⋮   │     ⋮        ⋮       ⋮           ⋮
+ 5994 │      5994   1121     2.96  x_merit[5994]
+ 5995 │      5995   1564     4.1   x_merit[5995]
+ 5996 │      5996   1332     3.14  x_merit[5996]
+ 5997 │      5997   1228     2.95  x_merit[5997]
+ 5998 │      5998   1165     2.81  x_merit[5998]
+ 5999 │      5999   1400     3.43  x_merit[5999]
+ 6000 │      6000   1097     2.65  x_merit[6000]
+                                5985 rows omitted

Then, we use MathOptAI.add_predictor to embed predictor into the JuMP model. MathOptAI.add_predictor returns a vector of variables, one for each row inn evaluate_df, corresponding to the output enroll of our logistic regression.

julia> evaluate_df.enroll, _ = MathOptAI.add_predictor(model, predictor, evaluate_df);
julia> evaluate_df6000×5 DataFrame
+  Row │ StudentID  SAT    GPA      merit          enroll          
+      │ Int64      Int64  Float64  GenericV…      GenericV…       
+──────┼───────────────────────────────────────────────────────────
+    1 │         1   1240     3.22  x_merit[1]     moai_Sigmoid[1]
+    2 │         2   1206     2.87  x_merit[2]     moai_Sigmoid[1]
+    3 │         3   1520     3.74  x_merit[3]     moai_Sigmoid[1]
+    4 │         4   1238     3.11  x_merit[4]     moai_Sigmoid[1]
+    5 │         5   1142     2.74  x_merit[5]     moai_Sigmoid[1]
+    6 │         6   1086     2.77  x_merit[6]     moai_Sigmoid[1]
+    7 │         7   1367     3.28  x_merit[7]     moai_Sigmoid[1]
+    8 │         8   1034     2.41  x_merit[8]     moai_Sigmoid[1]
+  ⋮   │     ⋮        ⋮       ⋮           ⋮               ⋮
+ 5994 │      5994   1121     2.96  x_merit[5994]  moai_Sigmoid[1]
+ 5995 │      5995   1564     4.1   x_merit[5995]  moai_Sigmoid[1]
+ 5996 │      5996   1332     3.14  x_merit[5996]  moai_Sigmoid[1]
+ 5997 │      5997   1228     2.95  x_merit[5997]  moai_Sigmoid[1]
+ 5998 │      5998   1165     2.81  x_merit[5998]  moai_Sigmoid[1]
+ 5999 │      5999   1400     3.43  x_merit[5999]  moai_Sigmoid[1]
+ 6000 │      6000   1097     2.65  x_merit[6000]  moai_Sigmoid[1]
+                                                 5985 rows omitted

The .enroll column name in evaluate_df is just a name. It doesn't have to match the name in train_df.

The objective of our problem is to maximize the expected number of students who enroll:

julia> @objective(model, Max, sum(evaluate_df.enroll))moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + [[...5940 terms omitted...]] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1] + moai_Sigmoid[1]

Subject to the constraint that we can spend at most 0.2 * n_students on merit scholarships:

julia> @constraint(model, sum(evaluate_df.merit) <= 0.2 * n_students)x_merit[1] + x_merit[2] + x_merit[3] + x_merit[4] + x_merit[5] + x_merit[6] + x_merit[7] + x_merit[8] + x_merit[9] + x_merit[10] + x_merit[11] + x_merit[12] + x_merit[13] + x_merit[14] + x_merit[15] + x_merit[16] + x_merit[17] + x_merit[18] + x_merit[19] + x_merit[20] + x_merit[21] + x_merit[22] + x_merit[23] + x_merit[24] + x_merit[25] + x_merit[26] + x_merit[27] + x_merit[28] + x_merit[29] + x_merit[30] + [[...5940 terms omitted...]] + x_merit[5971] + x_merit[5972] + x_merit[5973] + x_merit[5974] + x_merit[5975] + x_merit[5976] + x_merit[5977] + x_merit[5978] + x_merit[5979] + x_merit[5980] + x_merit[5981] + x_merit[5982] + x_merit[5983] + x_merit[5984] + x_merit[5985] + x_merit[5986] + x_merit[5987] + x_merit[5988] + x_merit[5989] + x_merit[5990] + x_merit[5991] + x_merit[5992] + x_merit[5993] + x_merit[5994] + x_merit[5995] + x_merit[5996] + x_merit[5997] + x_merit[5998] + x_merit[5999] + x_merit[6000] ≤ 1200

Because logistic regression involves a Sigmoid layer, we need to use a smooth nonlinear optimizer. A common choice is Ipopt. Solve and check the optimizer found a feasible solution:

julia> set_optimizer(model, Ipopt.Optimizer)
julia> set_silent(model)
julia> optimize!(model)
julia> @assert is_solved_and_feasible(model)
julia> solution_summary(model)* Solver : Ipopt
+
+* Status
+  Result count       : 1
+  Termination status : LOCALLY_SOLVED
+  Message from the solver:
+  "Solve_Succeeded"
+
+* Candidate solution (result #1)
+  Primal status      : FEASIBLE_POINT
+  Dual status        : FEASIBLE_POINT
+  Objective value    : 2.48820e+03
+  Dual objective value : -4.91918e+02
+
+* Work counters
+  Solve time (sec)   : 5.91986e+00
+  Barrier iterations : 142

Let's store the solution in evaluate_df for analysis:

julia> evaluate_df.merit_sol = value.(evaluate_df.merit);
julia> evaluate_df.enroll_sol = value.(evaluate_df.enroll);
julia> evaluate_df6000×7 DataFrame
+  Row │ StudentID  SAT    GPA      merit          enroll           merit_sol   ⋯
+      │ Int64      Int64  Float64  GenericV…      GenericV…        Float64     ⋯
+──────┼─────────────────────────────────────────────────────────────────────────
+    1 │         1   1240     3.22  x_merit[1]     moai_Sigmoid[1]  6.37389e-7  ⋯
+    2 │         2   1206     2.87  x_merit[2]     moai_Sigmoid[1]  1.08151
+    3 │         3   1520     3.74  x_merit[3]     moai_Sigmoid[1]  1.03717e-6
+    4 │         4   1238     3.11  x_merit[4]     moai_Sigmoid[1]  1.06046e-6
+    5 │         5   1142     2.74  x_merit[5]     moai_Sigmoid[1]  1.13489     ⋯
+    6 │         6   1086     2.77  x_merit[6]     moai_Sigmoid[1]  1.0759e-6
+    7 │         7   1367     3.28  x_merit[7]     moai_Sigmoid[1]  2.33948e-6
+    8 │         8   1034     2.41  x_merit[8]     moai_Sigmoid[1]  0.735482
+  ⋮   │     ⋮        ⋮       ⋮           ⋮               ⋮             ⋮       ⋱
+ 5994 │      5994   1121     2.96  x_merit[5994]  moai_Sigmoid[1]  6.26387e-7  ⋯
+ 5995 │      5995   1564     4.1   x_merit[5995]  moai_Sigmoid[1]  3.58792e-7
+ 5996 │      5996   1332     3.14  x_merit[5996]  moai_Sigmoid[1]  1.03863
+ 5997 │      5997   1228     2.95  x_merit[5997]  moai_Sigmoid[1]  1.21941
+ 5998 │      5998   1165     2.81  x_merit[5998]  moai_Sigmoid[1]  1.21872     ⋯
+ 5999 │      5999   1400     3.43  x_merit[5999]  moai_Sigmoid[1]  1.33971e-6
+ 6000 │      6000   1097     2.65  x_merit[6000]  moai_Sigmoid[1]  1.17865
+                                                  1 column and 5985 rows omitted

Solution analysis

We expect that just under 2,500 students will enroll:

julia> sum(evaluate_df.enroll_sol)2488.1951671444017

We awarded merit scholarships to approximately 1 in 6 students:

julia> count(evaluate_df.merit_sol .> 1e-5)1152

The average merit scholarship was worth just over $1,000:

julia> 1_000 * Statistics.mean(evaluate_df.merit_sol[evaluate_df.merit_sol.>1e-5])1041.6622990671967

This page was generated using Literate.jl.

diff --git a/versions.js b/versions.js new file mode 100644 index 00000000..268b25c8 --- /dev/null +++ b/versions.js @@ -0,0 +1,7 @@ +var DOC_VERSIONS = [ + "stable", + "v0.1", + "dev", +]; +var DOCUMENTER_NEWEST = "v0.1.4"; +var DOCUMENTER_STABLE = "stable";