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Support more Lanczos singularitities #7

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Merged
merged 2 commits into from
Feb 11, 2021
Merged

Support more Lanczos singularitities #7

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c46aed0
Support more Lanczos singularitities
dlfivefifty Feb 11, 2021
f361227
v0.1.2
dlfivefifty Feb 11, 2021
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2 changes: 1 addition & 1 deletion Project.toml
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Original file line number Diff line number Diff line change
@@ -1,7 +1,7 @@
name = "ClassicalOrthogonalPolynomials"
uuid = "b30e2e7b-c4ee-47da-9d5f-2c5c27239acd"
authors = ["Sheehan Olver <[email protected]>"]
version = "0.1.1"
version = "0.1.2"

[deps]
ArrayLayouts = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"
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5 changes: 3 additions & 2 deletions src/jacobi.jl
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Expand Up @@ -68,6 +68,7 @@ for op in (:+, :-, :*)
singularitiesbroadcast(::typeof($op), ::NoSingularities, L::LegendreWeight) = L
end
end
singularitiesbroadcast(::typeof(^), L::LegendreWeight, ::NoSingularities) = L
singularitiesbroadcast(::typeof(/), ::NoSingularities, L::LegendreWeight) = L # can't find roots

_parent(::NoSingularities) = NoSingularities()
Expand All @@ -78,8 +79,8 @@ singularitiesbroadcast(F::Function, G::Function, V::SubQuasiArray, K) = singular
singularitiesbroadcast(F, V::Union{NoSingularities,SubQuasiArray}...) = singularitiesbroadcast(F, map(_parent,V)...)[_parentindices(V...)...]


singularitiesbroadcast(::typeof(*), ::LegendreWeight, b::JacobiWeight) = b
singularitiesbroadcast(::typeof(*), a::JacobiWeight, ::LegendreWeight) = a
singularitiesbroadcast(::typeof(*), ::LegendreWeight, b::AbstractJacobiWeight) = b
singularitiesbroadcast(::typeof(*), a::AbstractJacobiWeight, ::LegendreWeight) = a

abstract type AbstractJacobi{T} <: OrthogonalPolynomial{T} end

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15 changes: 15 additions & 0 deletions test/test_lanczos.jl
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Expand Up @@ -183,4 +183,19 @@ import ClassicalOrthogonalPolynomials: recurrencecoefficients, PaddedLayout
@test (pϕ.P' * (ϕw .* pϕ.P))[1:3,1:3] ≈ [2 -0.5 0; -0.5 2 -0.5; 0 -0.5 2]
@test (pϕ' * (ϕw .* pϕ))[1:5,1:5] ≈ I
end

@testset "weighted Chebyshev" begin
T = ChebyshevT()
x = axes(T,1)
t = 2
Q = LanczosPolynomial((t .- x).^(-1) .* ChebyshevWeight())
# perturbation of Toeplitz
@test jacobimatrix(Q)[3:10,3:10] ≈ Symmetric(BandedMatrix(1 => Fill(0.5,7)))

Q = LanczosPolynomial((t .- x) .^ (-1))
@test Q[0.1,2] ≈ -0.1327124082839674

R = LanczosPolynomial((t .- x).^(-1/2) .* ChebyshevWeight())
@test R[0.1,2] ≈ -0.03269577983003056
end
end