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Add th_cheb2jac and th_jac2cheb (#229)
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* Add Cheb2Jac and Jac2Cheb

* seed random nums

* Update toeplitzhankeltests.jl
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@dlfivefifty
dlfivefifty authored Oct 21, 2023
1 parent 5028278 commit 2dcabeb
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Showing 3 changed files with 99 additions and 6 deletions.
9 changes: 8 additions & 1 deletion Project.toml
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Original file line number Diff line number Diff line change
Expand Up @@ -13,7 +13,6 @@ Libdl = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
ToeplitzMatrices = "c751599d-da0a-543b-9d20-d0a503d91d24"

[compat]
Expand All @@ -27,3 +26,11 @@ Reexport = "0.2, 1.0"
SpecialFunctions = "0.10, 1, 2"
ToeplitzMatrices = "0.7.1, 0.8"
julia = "1.7"


[extras]
Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[targets]
test = ["Test", "Random"]
72 changes: 70 additions & 2 deletions src/toeplitzhankel.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -448,7 +448,7 @@ Jac2JacPlanTH(plans, α, β, γ, δ, dims) = Jac2JacPlanTH(plans, promote(α, β

function *(P::Jac2JacPlanTH, A::AbstractArray)
if P.α + P.β ≤ -1
_jacobi_raise_a!(A, P.α, P.β)
_jacobi_raise_a!(A, P.α, P.β, P.dims)
c,d = _nearest_jacobi_par(P.α+1, P.γ), _nearest_jacobi_par(P.β, P.δ)
else
c,d = _nearest_jacobi_par(P.α, P.γ), _nearest_jacobi_par(P.β, P.δ)
Expand Down Expand Up @@ -690,4 +690,72 @@ plan_th_jac2jac!(::Type{S}, mn::NTuple{N,Int}, α, β, γ, δ, dims::UnitRange)
plan_th_jac2jac!(::Type{S}, mn::Tuple{Int}, α, β, γ, δ, dims::Tuple{Int}=(1,)) where {S} = plan_th_jac2jac!(S, mn, α, β, γ, δ, dims...)
plan_th_jac2jac!(::Type{S}, (m,n)::NTuple{2,Int}, α, β, γ, δ) where {S} = plan_th_jac2jac!(S, (m,n), α, β, γ, δ, (1,2))
plan_th_jac2jac!(arr::AbstractArray{T}, α, β, γ, δ, dims...) where T = plan_th_jac2jac!(T, size(arr), α, β, γ, δ, dims...)
th_jac2jac(v, α, β, γ, δ, dims...) = plan_th_jac2jac!(eltype(v), size(v), α, β, γ, δ, dims...)*copy(v)
th_jac2jac(v, α, β, γ, δ, dims...) = plan_th_jac2jac!(eltype(v), size(v), α, β, γ, δ, dims...)*copy(v)


####
# cheb2jac
####

struct Cheb2JacPlanTH{T, Pl<:Jac2JacPlanTH{T}} <: Plan{T}
jac2jac::Pl
end


struct Jac2ChebPlanTH{T, Pl<:Jac2JacPlanTH{T}} <: Plan{T}
jac2jac::Pl
end


function jac_cheb_recurrencecoefficients(T, N)
n = 0:N
h = one(T)/2
A = (2n .+ one(T)) ./ (n .+ one(T))
A[1] /= 2
A, Zeros(n),
((n .- h) .* (n .- h) .* (2n .+ one(T))) ./ ((n .+ one(T)) .* n .* (2n .- one(T)))
end


function *(P::Cheb2JacPlanTH{T}, X::AbstractArray) where T
A,B,C = jac_cheb_recurrencecoefficients(T, max(size(X)...))

for d in P.jac2jac.dims
if d == 1
p = forwardrecurrence(size(X,1), A,B,C, one(T))
X .= p .\ X
else
@assert d == 2
n = size(X,2)
p = forwardrecurrence(size(X,2), A,B,C, one(T))
X .= X ./ transpose(p)
end
end
P.jac2jac*X
end

function *(P::Jac2ChebPlanTH{T}, X::AbstractArray) where T
X = P.jac2jac*X
A,B,C = jac_cheb_recurrencecoefficients(T, max(size(X)...))

for d in P.jac2jac.dims
if d == 1
p = forwardrecurrence(size(X,1), A,B,C, one(T))
X .= p .* X
else
@assert d == 2
n = size(X,2)
p = forwardrecurrence(size(X,2), A,B,C, one(T))
X .= X .* transpose(p)
end
end
X
end

plan_th_cheb2jac!(::Type{T}, mn, α, β, dims...) where T = Cheb2JacPlanTH(plan_th_jac2jac!(T, mn, -one(α)/2, -one(α)/2, α, β, dims...))
plan_th_cheb2jac!(arr::AbstractArray{T}, α, β, dims...) where T = plan_th_cheb2jac!(T, size(arr), α, β, dims...)
th_cheb2jac(v, α, β, dims...) = plan_th_cheb2jac!(eltype(v), size(v), α, β, dims...)*copy(v)

plan_th_jac2cheb!(::Type{T}, mn, α, β, dims...) where T = Jac2ChebPlanTH(plan_th_jac2jac!(T, mn, α, β, -one(α)/2, -one(α)/2, dims...))
plan_th_jac2cheb!(arr::AbstractArray{T}, α, β, dims...) where T = plan_th_jac2cheb!(T, size(arr), α, β, dims...)
th_jac2cheb(v, α, β, dims...) = plan_th_jac2cheb!(eltype(v), size(v), α, β, dims...)*copy(v)
24 changes: 21 additions & 3 deletions test/toeplitzhankeltests.jl
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Original file line number Diff line number Diff line change
@@ -1,7 +1,10 @@
using FastTransforms, Test
using FastTransforms, Test, Random
import FastTransforms: th_leg2cheb, th_cheb2leg, th_leg2chebu, th_ultra2ultra,th_jac2jac, th_leg2chebu,
lib_leg2cheb, lib_cheb2leg, lib_ultra2ultra, lib_jac2jac,
plan_th_cheb2leg!, plan_th_leg2chebu!, plan_th_leg2cheb!, plan_th_ultra2ultra!, plan_th_jac2jac!
plan_th_cheb2leg!, plan_th_leg2chebu!, plan_th_leg2cheb!, plan_th_ultra2ultra!, plan_th_jac2jac!,
th_cheb2jac, th_jac2cheb

Random.seed!(0)

@testset "ToeplitzHankel" begin
for x in ([1.0], [1.0,2,3,4,5], [1.0+im,2-3im,3+4im,4-5im,5+10im], collect(1.0:1000))
Expand All @@ -26,11 +29,14 @@ import FastTransforms: th_leg2cheb, th_cheb2leg, th_leg2chebu, th_ultra2ultra,th
@test th_jac2jac(x, -1/2,-1/2,1/2,0) ≈ lib_jac2jac(x, -1/2,-1/2,1/2,0)
@test th_jac2jac(x, -1/2,-1/2,0,1/2) ≈ lib_jac2jac(x, -1/2,-1/2,0,1/2)
@test th_jac2jac(x, -3/4,-3/4,0,3/4) ≈ lib_jac2jac(x, -3/4,-3/4,0,3/4)
@test th_jac2jac(x,0, 0, 5, 5) ≈ lib_jac2jac(x, 0, 0, 5, 5)
if length(x) < 10
@test th_jac2jac(x,0, 0, 5, 5) ≈ lib_jac2jac(x, 0, 0, 5, 5)
@test th_jac2jac(x, 5, 5, 0, 0) ≈ lib_jac2jac(x, 5, 5, 0, 0)
end

@test th_cheb2jac(x, 0.2, 0.3) ≈ cheb2jac(x, 0.2, 0.3)
@test th_jac2cheb(x, 0.2, 0.3) ≈ jac2cheb(x, 0.2, 0.3)

@test th_cheb2leg(th_leg2cheb(x)) ≈ x
@test th_leg2cheb(th_cheb2leg(x)) ≈ x
@test th_ultra2ultra(th_ultra2ultra(x, 0.1, 0.6), 0.6, 0.1) ≈ x
Expand Down Expand Up @@ -93,6 +99,18 @@ import FastTransforms: th_leg2cheb, th_cheb2leg, th_leg2chebu, th_ultra2ultra,th
@test th_jac2jac(X, 0.1, 0.6, 3.1, 2.8, 1) ≈ hcat([jac2jac(X[:,j], 0.1, 0.6, 3.1, 2.8) for j=1:size(X,2)]...)
@test th_jac2jac(X, 0.1, 0.6, 3.1, 2.8, 2) ≈ vcat([permutedims(jac2jac(X[k,:], 0.1, 0.6, 3.1, 2.8)) for k=1:size(X,1)]...)
@test th_jac2jac(X, 0.1, 0.6, 3.1, 2.8) ≈ th_jac2jac(th_jac2jac(X, 0.1, 0.6, 3.1, 2.8, 1), 0.1, 0.6, 3.1, 2.8, 2)

@test th_jac2jac(X, -0.5, -0.5, 3.1, 2.8, 1) ≈ hcat([jac2jac(X[:,j], -0.5, -0.5, 3.1, 2.8) for j=1:size(X,2)]...)
@test th_jac2jac(X, -0.5, -0.5, 3.1, 2.8, 2) ≈ vcat([permutedims(jac2jac(X[k,:], -0.5, -0.5, 3.1, 2.8)) for k=1:size(X,1)]...)
@test th_jac2jac(X, -0.5, -0.5, 3.1, 2.8) ≈ th_jac2jac(th_jac2jac(X, -0.5, -0.5, 3.1, 2.8, 1), -0.5, -0.5, 3.1, 2.8, 2)

@test th_cheb2jac(X, 3.1, 2.8, 1) ≈ hcat([cheb2jac(X[:,j], 3.1, 2.8) for j=1:size(X,2)]...)
@test th_cheb2jac(X, 3.1, 2.8, 2) ≈ vcat([permutedims(cheb2jac(X[k,:], 3.1, 2.8)) for k=1:size(X,1)]...)
@test th_cheb2jac(X, 3.1, 2.8) ≈ th_cheb2jac(th_cheb2jac(X, 3.1, 2.8, 1), 3.1, 2.8, 2)

@test th_jac2cheb(X, 3.1, 2.8, 1) ≈ hcat([jac2cheb(X[:,j], 3.1, 2.8) for j=1:size(X,2)]...)
@test th_jac2cheb(X, 3.1, 2.8, 2) ≈ vcat([permutedims(jac2cheb(X[k,:], 3.1, 2.8)) for k=1:size(X,1)]...)
@test th_jac2cheb(X, 3.1, 2.8) ≈ th_jac2cheb(th_jac2cheb(X, 3.1, 2.8, 1), 3.1, 2.8, 2)
end

@testset "BigFloat" begin
Expand Down

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Registration pull request created: JuliaRegistries/General/93856

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 v0.15.9 -m "<description of version>" 2dcabebd3b31a59b3ece09e390e127a279a941c8
git push origin v0.15.9

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