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name = "HarmonicOrthogonalPolynomials" | ||
uuid = "e416a80e-9640-42f3-8df8-80a93ca01ea5" | ||
authors = ["Sheehan Olver <[email protected]>"] | ||
version = "0.6.3" | ||
version = "0.7" | ||
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[deps] | ||
BlockArrays = "8e7c35d0-a365-5155-bbbb-fb81a777f24e" | ||
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@@ -20,13 +20,13 @@ StaticArrays = "90137ffa-7385-5640-81b9-e52037218182" | |
[compat] | ||
BlockArrays = "1.0" | ||
BlockBandedMatrices = "0.13" | ||
ClassicalOrthogonalPolynomials = "0.13, 0.14" | ||
ContinuumArrays = "0.18" | ||
ClassicalOrthogonalPolynomials = "0.15" | ||
ContinuumArrays = "0.19" | ||
DomainSets = "0.7" | ||
FastTransforms = "0.15, 0.16, 0.17" | ||
InfiniteArrays = "0.14, 0.15" | ||
IntervalSets = "0.7" | ||
QuasiArrays = "0.11" | ||
QuasiArrays = "0.12" | ||
SpecialFunctions = "1, 2" | ||
StaticArrays = "1" | ||
julia = "1.10" | ||
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# Laplacian | ||
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struct Laplacian{T,D} <: LazyQuasiMatrix{T} | ||
axis::Inclusion{T,D} | ||
end | ||
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Laplacian{T}(axis::Inclusion{<:Any,D}) where {T,D} = Laplacian{T,D}(axis) | ||
# Laplacian{T}(domain) where T = Laplacian{T}(Inclusion(domain)) | ||
# Laplacian(axis) = Laplacian{eltype(axis)}(axis) | ||
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axes(D::Laplacian) = (D.axis, D.axis) | ||
==(a::Laplacian, b::Laplacian) = a.axis == b.axis | ||
copy(D::Laplacian) = Laplacian(copy(D.axis)) | ||
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@simplify function *(Δ::Laplacian, P::AbstractSphericalHarmonic) | ||
function laplacian(P::AbstractSphericalHarmonic; dims...) | ||
# Spherical harmonics are the eigenfunctions of the Laplace operator on the unit sphere | ||
P * Diagonal(mortar(Fill.((-(0:∞)-(0:∞).^2), 1:2:∞))) | ||
end | ||
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# Negative fractional Laplacian (-Δ)^α or equiv. abs(Δ)^α | ||
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struct AbsLaplacianPower{T,D,A} <: LazyQuasiMatrix{T} | ||
axis::Inclusion{T,D} | ||
α::A | ||
end | ||
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AbsLaplacianPower{T}(axis::Inclusion{<:Any,D},α) where {T,D} = AbsLaplacianPower{T,D,typeof(α)}(axis,α) | ||
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axes(D:: AbsLaplacianPower) = (D.axis, D.axis) | ||
==(a:: AbsLaplacianPower, b:: AbsLaplacianPower) = a.axis == b.axis && a.α == b.α | ||
copy(D:: AbsLaplacianPower) = AbsLaplacianPower(copy(D.axis), D.α) | ||
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abs(Δ::Laplacian) = AbsLaplacianPower(axes(Δ,1),1) | ||
-(Δ::Laplacian) = abs(Δ) | ||
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^(D::AbsLaplacianPower, k) = AbsLaplacianPower(D.axis, D.α*k) |
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