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Merged
merged 2 commits into from
Mar 11, 2024
Merged

add Jacobi matrices for RectPolynomial #174

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c7329f1
Revert "Revert "add Jacobi matrices for RectPolynomial""
dlfivefifty Mar 11, 2024
bee0ad7
fix tests
dlfivefifty Mar 11, 2024
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14 changes: 13 additions & 1 deletion src/rect.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -36,6 +36,18 @@ function getindex(P::RectPolynomial, xy::StaticVector{2}, JR::BlockOneTo)
N = size(JR,1)
DiagTrav(A[x,OneTo(N)] .* B[y,OneTo(N)]')
end
# Actually Jxᵀ
function jacobimatrix(::Val{1}, P::RectPolynomial)
A,B = P.args
X = jacobimatrix(A)
KronTrav(Eye{eltype(X)}(∞), X)
end
# Actually Jyᵀ
function jacobimatrix(::Val{2}, P::RectPolynomial)
A,B = P.args
Y = jacobimatrix(B)
KronTrav(Y, Eye{eltype(Y)}(∞))
end
@simplify function *(Dx::PartialDerivative{1}, P::RectPolynomial)
A,B = P.args
U,M = (Derivative(axes(A,1))*A).args
Expand Down Expand Up @@ -150,4 +162,4 @@ function transform_ldiv(K::KronPolynomial{d,V,<:Fill{<:Legendre}}, f::Union{Abst
T = KronPolynomial{d}(Fill(ChebyshevT{V}(), size(K.args)...))
dat = (T \ f).array
DiagTrav(pad(FastTransforms.th_cheb2leg(paddeddata(dat)), axes(dat)...))
end
end
21 changes: 20 additions & 1 deletion test/test_rect.jl
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Expand Up @@ -43,6 +43,25 @@ using ContinuumArrays: plotgridvalues
@test f[SVector(0.1,0.2)] ≈ exp(0.1*cos(0.1))
end

@testset "Jacobi matrices" begin
T = ChebyshevT()
U = ChebyshevU()
TU = RectPolynomial(T, U)
X = jacobimatrix(Val{1}(), TU)
Y = jacobimatrix(Val{2}(), TU)
𝐱 = axes(TU, 1)
x, y = first.(𝐱), last.(𝐱)
N = 10
KR = Block.(1:N)
@test (TU \ (x .* TU))[KR,KR] == X[KR,KR]
@test (TU \ (y .* TU))[KR,KR] == Y[KR,KR]
f = expand(TU, splat((x,y) -> exp(x*cos(y-0.1))))
g = expand(TU, splat((x,y) -> x*exp(x*cos(y-0.1))))
h = expand(TU, splat((x,y) -> y*exp(x*cos(y-0.1))))
@test (X * (TU \ f))[KR] ≈ (TU \ g)[KR]
@test (Y * (TU \ f))[KR] ≈ (TU \ h)[KR]
end

@testset "Conversion" begin
T = ChebyshevT()
U = ChebyshevU()
Expand Down Expand Up @@ -119,4 +138,4 @@ using ContinuumArrays: plotgridvalues
@test x == SVector.(ChebyshevGrid{2}(40), ChebyshevGrid{2}(40)')
@test F == ones(40,40)
end
end
end