ASP

Project.toml

@@ -4,6 +4,7 @@ authors = ["William C Witt <[email protected]>, Christoph Ortner <christophor
 version = "0.2.0"
 
 [deps]
+ActiveSetPursuit = "d86c1dc8-ba26-4c98-b330-3a8efc174d20"
 Distributed = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 IterativeSolvers = "42fd0dbc-a981-5370-80f2-aaf504508153"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
@@ -21,25 +22,25 @@ MLJScikitLearnInterface = "5ae90465-5518-4432-b9d2-8a1def2f0cab"
 PythonCall = "6099a3de-0909-46bc-b1f4-468b9a2dfc0d"
 
 [extensions]
-ACEfit_PythonCall_ext = "PythonCall"
-ACEfit_MLJLinearModels_ext = [ "MLJ", "MLJLinearModels" ]
+ACEfit_MLJLinearModels_ext = ["MLJ", "MLJLinearModels"]
 ACEfit_MLJScikitLearnInterface_ext = ["MLJScikitLearnInterface", "PythonCall", "MLJ"]
+ACEfit_PythonCall_ext = "PythonCall"
 
 [compat]
-julia = "1.9"
 IterativeSolvers = "0.9.2"
+LowRankApprox = "0.5.3"
 MLJ = "0.19"
 MLJLinearModels = "0.9"
 MLJScikitLearnInterface = "0.7"
-LowRankApprox = "0.5.3"
 Optim = "1.7"
 ParallelDataTransfer = "0.5.0"
 ProgressMeter = "1.7"
 PythonCall = "0.9"
 StaticArrays = "1.5"
+julia = "1.9"
 
 [extras]
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Test", ]
+test = ["Test"]

src/solvers.jl

@@ -3,6 +3,7 @@ using LowRankApprox: pqrfact
 using IterativeSolvers
 using .BayesianLinear
 using LinearAlgebra: SVD, svd
+using ActiveSetPursuit
 
 @doc raw"""
 `struct QR` : linear least squares solver, using standard QR factorisation; 
@@ -195,3 +196,95 @@ function solve(solver::TruncatedSVD, A, y)
     return Dict{String, Any}("C" => solver.P \ θP)
 end
 
+
+@doc raw"""
+`struct ASP` : Active Set Pursuit sparse solver
+    solves the following optimization problem using the homotopy approach:
+
+    ```math 
+    \max_{y} \left( b^T y - \frac{1}{2} λ y^T y \right)
+    ```
+        subject to
+
+    ```math
+        \|A^T y\|_{\infty} \leq 1.
+    ```
+
+    * Input
+    * `A` : `m`-by-`n` explicit matrix or linear operator.
+    * `b` : `m`-vector.
+
+    * Solver parameters
+    * `min_lambda` : Minimum value for `λ`. Defaults to zero if not provided.
+    * `loglevel` : Logging level.
+    * `itnMax` : Maximum number of iterations.
+    * `actMax` : Maximum number of active constraints.
+
+    Constructor
+    ```julia
+    ACEfit.ASP(; P = I, select, params)
+    ``` 
+    where 
+    - `P` : right-preconditioner / tychonov operator
+    - `select`: Selection mode for the final solution.
+    - `(:byerror, th)`: Selects the smallest active set fit within a factor `th` of the smallest fit error.
+    - `(:final, nothing)`: Returns the final iterate.
+    - `params`: The solver parameters, passed as named arguments.
+"""
+struct ASP
+    P::Any
+    select::Tuple
+    params::NamedTuple
+end
+
+function ASP(; P = I, select, params...)
+    params_tuple = NamedTuple(params)
+    return ASP(P, select, params_tuple)
+end
+
+function solve(solver::ASP, A, y)
+    # Apply preconditioning
+    AP = A / solver.P
+
+    tracer = asp_homotopy(AP, y; solver.params[1]...)
+
+    new_tracer = Vector{NamedTuple{(:solution, :λ), Tuple{Any, Any}}}(undef, length(tracer))
+
+    for i in 1:length(tracer)
+        new_tracer[i] = (solution = solver.P \ tracer[i][1], λ = tracer[i][2])
+    end
+
+    # Select the final solution based on the criterion
+    xs, in = select_solution(new_tracer, solver, A, y)
+
+    println("done.")
+    return Dict("C" => xs, "path" => new_tracer, "nnzs" => length((tracer[in][1]).nzind) )
+end
+
+function select_solution(tracer, solver, A, y)
+    criterion, threshold = solver.select
+
+    if criterion == :final
+        return tracer[end][1], length(tracer)
+
+    elseif criterion == :byerror
+        errors = [norm(A * t[1] - y) for t in tracer]
+        min_error = minimum(errors)
+
+        # Find the solution with the smallest error within the threshold
+        for (i, error) in enumerate(errors)
+            if error <= threshold * min_error
+                return tracer[i][1], i
+            end
+        end
+    elseif criterion == :bysize
+        for i in 1:length(tracer)
+            if length((tracer[i][1]).nzind) == threshold
+                return tracer[i][1], i
+            end
+        end
+    else
+        @error("Unknown selection criterion: $criterion")
+    end
+end
+

test/test_linearsolvers.jl

@@ -111,3 +111,32 @@ C = results["C"]
 @show norm(C)
 @show norm(C - c_ref)
 
+@info(" ... ASP_homotopy selected by error")
+solver = ACEfit.ASP(P = P, select = (:byerror,1.5), params = (loglevel=0, traceFlag=true))
+results = ACEfit.solve(solver, A, y)
+C = results["C"]
+full_path = results["path"]
+@show results["nnzs"]
+@show norm(A * C - y)
+@show norm(C)
+@show norm(C - c_ref)
+
+@info(" ... ASP_homotopy selected by size")
+solver = ACEfit.ASP(P = P, select = (:bysize,50), params = (loglevel=0, traceFlag=true))
+results = ACEfit.solve(solver, A, y)
+C = results["C"]
+full_path = results["path"]
+@show results["nnzs"]
+@show norm(A * C - y)
+@show norm(C)
+@show norm(C - c_ref)
+
+@info(" ... ASP_homotopy final solution")
+solver = ACEfit.ASP(P = P, select = (:final,nothing), params = (loglevel=0, traceFlag=true))
+results = ACEfit.solve(solver, A, y)
+C = results["C"]
+full_path = results["path"]
+@show results["nnzs"]
+@show norm(A * C - y)
+@show norm(C)
+@show norm(C - c_ref)