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add ultraspherical weight
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@daanhb
daanhb committed Oct 9, 2024
1 parent e9121ce commit 25503b0
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Showing 7 changed files with 131 additions and 51 deletions.
6 changes: 4 additions & 2 deletions Project.toml
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Original file line number Diff line number Diff line change
@@ -1,7 +1,7 @@
name = "DomainIntegrals"
uuid = "cc6bae93-f070-4015-88fd-838f9505a86c"
authors = ["Daan Huybrechs <[email protected]>"]
version = "0.5"
version = "0.5.1"

[deps]
CompositeTypes = "b152e2b5-7a66-4b01-a709-34e65c35f657"
Expand All @@ -12,18 +12,20 @@ HCubature = "19dc6840-f33b-545b-b366-655c7e3ffd49"
IntervalSets = "8197267c-284f-5f27-9208-e0e47529a953"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
QuadGK = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"

[compat]
julia = "1.10"
CompositeTypes = "0.1.3"
DomainSets = "0.7.2"
FastGaussQuadrature = "0.5"
GaussQuadrature = "0.5.7"
HCubature = "1.4.0"
IntervalSets = "0.7"
QuadGK = "2.3.1"
SpecialFunctions = "2"
StaticArrays = "1.0"
julia = "1.10"

[extras]
Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
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1 change: 1 addition & 0 deletions src/DomainIntegrals.jl
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Expand Up @@ -2,6 +2,7 @@ module DomainIntegrals

using QuadGK, LinearAlgebra
using GaussQuadrature, FastGaussQuadrature, HCubature
using SpecialFunctions

using StaticArrays
using IntervalSets, DomainSets
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103 changes: 79 additions & 24 deletions src/weights.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -7,6 +7,7 @@ export LebesgueMeasure,
dx,
LegendreWeight,
JacobiWeight,
UltrasphericalWeight,
ChebyshevWeight,
ChebyshevTWeight,
ChebyshevUWeight,
Expand Down Expand Up @@ -103,6 +104,9 @@ struct LegendreWeight{T} <: LebesgueMeasure{T}
end
LegendreWeight() = LegendreWeight{Float64}()

jacobi_α(μ::LegendreWeight{T}) where {T} = zero(T)
jacobi_β(μ::LegendreWeight{T}) where {T} = zero(T)

similar(μ::LegendreWeight, ::Type{T}) where {T <: Real} = LegendreWeight{T}()
support(μ::LegendreWeight{T}) where {T} = ChebyshevInterval{T}()

Expand All @@ -116,12 +120,23 @@ abstract type AbstractJacobiWeight{T} <: Weight{T} end
==(μ1::AbstractJacobiWeight, μ2::AbstractJacobiWeight) =
jacobi_α(μ1) == jacobi_α(μ2) && jacobi_β(μ1) == jacobi_β(μ2)

support(μ::AbstractJacobiWeight{T}) where {T} = ChebyshevInterval{T}()

jacobi_moment(α, β) = 2^(α+β+1) * gamma(α+1)*gamma(β+1) / gamma(α+β+2)

moment(μ::AbstractJacobiWeight) = jacobi_moment(jacobi_α(μ), jacobi_β(μ))

isnormalized(μ::AbstractJacobiWeight) = moment(μ) ≈ 1

"The Jacobi weight on the interval `[-1,1]`."
struct JacobiWeight{T} <: AbstractJacobiWeight{T}
α :: T
β :: T

JacobiWeight{T}(α = zero(T), β = zero(T)) where {T} = new(α, β)
function JacobiWeight{T}(α = zero(T), β = zero(T)) where {T}
@assert (α > -1) && (β > -1)
new(α, β)
end
end
JacobiWeight() = JacobiWeight{Float64}()
JacobiWeight(α, β) = JacobiWeight(promote(α, β)...)
Expand All @@ -131,7 +146,6 @@ JacobiWeight(α::N, β::N) where {N<:Number} = JacobiWeight(float(α), float(β)
jacobi_weightfun(x, α, β) = (1-x)^α * (1+x)^β

similar(μ::JacobiWeight, ::Type{T}) where {T <: Real} = JacobiWeight{T}(μ.α, μ.β)
support(μ::JacobiWeight{T}) where {T} = ChebyshevInterval{T}()
unsafe_weightfun(μ::JacobiWeight, x) = jacobi_weightfun(x, μ.α, μ.β)

jacobi_α(μ::JacobiWeight) = μ.α
Expand Down Expand Up @@ -189,35 +203,74 @@ Base.show(io::IO, μ::ChebyshevUWeight) = print(io, "√(1+x)^2 dx (ChebyshevU)
Display.object_parentheses(μ::ChebyshevUWeight) = true


convert(::Type{JacobiWeight}, μ::LegendreWeight{T}) where {T} =
JacobiWeight{T}(0, 0)
convert(::Type{JacobiWeight}, μ::ChebyshevTWeight{T}) where {T} =
JacobiWeight{T}(-one(T)/2, -one(T)/2)
convert(::Type{JacobiWeight}, μ::ChebyshevUWeight{T}) where {T} =
JacobiWeight{T}(one(T)/2, one(T)/2)
"""
The `Ultraspherical` (or `Gegenbauer`) weight is the measure on `[-1,1]` with
the weight function `w(x) = (1-x^2)^(λ - 1/2)`.
"""
struct UltrasphericalWeight{T} <: DomainIntegrals.AbstractJacobiWeight{T}
λ :: T

function UltrasphericalWeight{T}(λ) where T
@assert λ > -one(T)/2
new(λ)
end
end

const GegenbauerWeight = UltrasphericalWeight

UltrasphericalWeight(α::T) where {T<:AbstractFloat} = UltrasphericalWeight{T}(α)
UltrasphericalWeight(α::N) where {N<:Number} = UltrasphericalWeight(float(α), float(β))

ultraspherical_weightfun(x, λ::T) where T = (1-x^2)^(λ - one(T)/2)

jacobi_α(μ::UltrasphericalWeight{T}) where {T} = μ.λ-one(T)/2
jacobi_β(μ::UltrasphericalWeight{T}) where {T} = μ.λ-one(T)/2

similar(μ::UltrasphericalWeight, ::Type{T}) where {T <: Real} =
UltrasphericalWeight{T}(μ.λ)
unsafe_weightfun(μ::UltrasphericalWeight, x) = ultraspherical_weightfun(x, μ.λ)

Base.show(io::IO, μ::UltrasphericalWeight) = print(io, "(1-x^2)^(λ - 1/2) dx (Ultraspherical)")
Display.object_parentheses(μ::UltrasphericalWeight) = true


convert(::Type{JacobiWeight}, μ::AbstractJacobiWeight{T}) where T =
JacobiWeight{T}(jacobi_α(μ), jacobi_β(μ))
convert(::Type{JacobiWeight{T}}, μ::AbstractJacobiWeight) where T =
JacobiWeight{T}(jacobi_α(μ), jacobi_β(μ))

function convert(::Type{ChebyshevTWeight}, μ::JacobiWeight{T}) where {T}
function convert(::Type{ChebyshevTWeight}, μ::AbstractJacobiWeight{T}) where T
(jacobi_α(μ) ≈ -one(T)/2 && jacobi_β(μ) ≈ -one(T)/2) || throw(InexactError(:convert, ChebyshevTWeight, μ))
ChebyshevTWeight{T}()
end

function convert(::Type{ChebyshevUWeight}, μ::JacobiWeight{T}) where {T}
function convert(::Type{ChebyshevTWeight{T}}, μ::AbstractJacobiWeight) where T
(jacobi_α(μ) ≈ -one(T)/2 && jacobi_β(μ) ≈ -one(T)/2) || throw(InexactError(:convert, ChebyshevTWeight, μ))
ChebyshevTWeight{T}()
end
function convert(::Type{ChebyshevUWeight}, μ::AbstractJacobiWeight{T}) where T
(jacobi_α(μ) ≈ one(T)/2 && jacobi_β(μ) ≈ one(T)/2) || throw(InexactError(:convert, ChebyshevUWeight, μ))
ChebyshevUWeight{T}()
end

function convert(::Type{LegendreWeight}, μ::JacobiWeight{T}) where {T}
(μ.α ≈ 0 && μ.β ≈ 0) || throw(InexactError(:convert, LegendreWeight, μ))
function convert(::Type{ChebyshevUWeight{T}}, μ::AbstractJacobiWeight) where T
(jacobi_α(μ) ≈ one(T)/2 && jacobi_β(μ) ≈ one(T)/2) || throw(InexactError(:convert, ChebyshevUWeight, μ))
ChebyshevUWeight{T}()
end
function convert(::Type{LegendreWeight}, μ::AbstractJacobiWeight{T}) where {T}
(jacobi_α(μ) == 0 && jacobi_β(μ) == 0) || throw(InexactError(:convert, LegendreWeight, μ))
LegendreWeight{T}()
end

jacobi_α(μ::LegendreWeight{T}) where {T} = zero(T)
jacobi_β(μ::LegendreWeight{T}) where {T} = zero(T)

==(μ1::AbstractJacobiWeight, μ2::LegendreWeight) =
jacobi_α(μ1) == jacobi_α(μ2) && jacobi_β(μ1) == jacobi_β(μ2)
==(μ1::LegendreWeight, μ2::AbstractJacobiWeight) =
jacobi_α(μ1) == jacobi_α(μ2) && jacobi_β(μ1) == jacobi_β(μ2)
function convert(::Type{LegendreWeight{T}}, μ::AbstractJacobiWeight) where T
(jacobi_α(μ) == 0 && jacobi_β(μ) == 0) || throw(InexactError(:convert, LegendreWeight, μ))
LegendreWeight{T}()
end
function convert(::Type{UltrasphericalWeight}, μ::AbstractJacobiWeight{T}) where T
(jacobi_α(μ) == jacobi_β(μ)) || throw(InexactError(:convert, UltrasphericalWeight, μ))
UltrasphericalWeight{T}(jacobi_α(μ)+one(T)/2)
end
function convert(::Type{UltrasphericalWeight{T}}, μ::AbstractJacobiWeight) where T
(jacobi_α(μ) == jacobi_β(μ)) || throw(InexactError(:convert, UltrasphericalWeight, μ))
UltrasphericalWeight{T}(jacobi_α(μ)+one(T)/2)
end


"The generalised Laguerre measure on the halfline `[0,∞)`."
Expand All @@ -240,6 +293,8 @@ unsafe_weightfun(μ::LaguerreWeight, x) = laguerre_weightfun(x, μ.α)

laguerre_α(μ::LaguerreWeight) = μ.α

==(μ1::LaguerreWeight, μ2::LaguerreWeight) = laguerre_α(μ1) == laguerre_α(μ2)

Base.show(io::IO, μ::LaguerreWeight) =
laguerre_α(μ) == 0 ? print(io, "exp(-x)dx (Laguerre)") : print(io, "x^$(laguerre_α(μ))exp(-x)dx (Laguerre)")
Display.object_parentheses(μ::LaguerreWeight) = true
Expand All @@ -262,13 +317,13 @@ Base.show(io::IO, μ::HermiteWeight) = print(io, "exp(-x^2)dx (Hermite)")
Display.object_parentheses(μ::HermiteWeight) = true


"The Gaussian measure with weight exp(-|x|^2/2)."
"The Gaussian measure with weight 1/sqrt(2π)^(n/2)*exp(-|x|^2/2)."
struct GaussianWeight{T} <: Weight{T}
end
GaussianWeight() = GaussianWeight{Float64}()

gaussian_weightfun(x, ::Type{T} = prectype(x)) where {T} =
1/(2*convert(T, pi))^(length(x)/2) * exp(-norm(x)^2)
1/(2*T(pi))^(length(x)/2) * exp(-norm(x)^2)

similar(μ::GaussianWeight, ::Type{T}) where {T} = GaussianWeight{T}()
isnormalized(μ::GaussianWeight) = true
Expand Down
23 changes: 22 additions & 1 deletion test/runtests.jl
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@@ -1 +1,22 @@
include("test_suite.jl")

using Test
using DomainSets, HCubature, LinearAlgebra, StaticArrays

using DomainIntegrals

include("test_measures.jl")
include("test_integrals.jl")
include("test_gauss.jl")

@testset "Measures" begin
test_measures()
test_discrete_measures()
end

@testset "Quadrature rules" begin
test_gauss()
end

@testset "Selected integrals" begin
test_integrals()
end
5 changes: 3 additions & 2 deletions test/test_integrals.jl
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Expand Up @@ -71,12 +71,13 @@ function test_some_integrals()
@test abs(integral(strategy, x->1, UnitDisk()) - pi) < 1e-5
end

function test_discrete_measures()
function test_integrals_with_discrete_measures()
m1 = DomainIntegrals.GenericDiscreteWeight([0.2], [0.5])
@test integral(exp, m1) == 0.5*exp(0.2)
@test integral(exp, m1) ≈ 0.5*exp(0.2)
end

function test_integrals()
test_some_integrals()
test_readme_examples()
test_integrals_with_discrete_measures()
end
22 changes: 22 additions & 0 deletions test/test_measures.jl
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Expand Up @@ -84,6 +84,28 @@ function test_measures()
@test jacobi_α(m8) == 1/2
@test jacobi_β(m8) == 1/2
@test m8 == JacobiWeight(1/2, 1/2)

m9 = JacobiWeight(0.4, 0.7)
@test support(m9) == (-1..1)
@test !isdiscrete(m9)
@test iscontinuous(m9)
@test !isnormalized(m9)
@test domaintype(m8) == Float64
@test jacobi_α(m9) == 0.4
@test jacobi_β(m9) == 0.7
@test weightfun(m9, 0.22) ≈ (1-0.22)^0.4 * (1+0.22)^0.7
@test_throws AssertionError JacobiWeight(-2, 0)
@test_throws AssertionError JacobiWeight(0, -1)

m10 = UltrasphericalWeight(0.3)
@test support(m10) == (-1..1)
@test !isdiscrete(m10)
@test iscontinuous(m10)
@test !isnormalized(m10)
@test domaintype(m10) == Float64
@test jacobi_α(m10) == 0.3-0.5
@test jacobi_β(m10) == 0.3-0.5
@test weightfun(m10, 0.22) ≈ (1-0.22^2)^(0.3-0.5)
end

function test_discrete_measures()
Expand Down
22 changes: 0 additions & 22 deletions test/test_suite.jl
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2 comments on commit 25503b0

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@daanhb daanhb commented on 25503b0 Oct 10, 2024

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Registration pull request created: JuliaRegistries/General/116951

Tip: Release Notes

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Release notes:

## Breaking changes

- blah

To add them here just re-invoke and the PR will be updated.

Tagging

After the above pull request is merged, it is recommended that a tag is created on this repository for the registered package version.

This will be done automatically if the Julia TagBot GitHub Action is installed, or can be done manually through the github interface, or via:

git tag -a v0.5.1 -m "<description of version>" 25503b0c82c9e8541b2ea0782e1f1628e0c1b082
git push origin v0.5.1

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