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Extend FTPlans to Arrays and higher dimensions #252

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merged 8 commits into from
Sep 23, 2024
Merged

Extend FTPlans to Arrays and higher dimensions #252

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04556c5
* and \ for FTPlan applied to an Array
Sep 6, 2024
16b6f43
N-dimensional plan
Sep 6, 2024
87b1924
type-inference
Sep 6, 2024
e0dd9d6
fix N-dimensional transform when dims[1] != 1
Sep 6, 2024
5bdb5e2
perm Vector -> perm Tuple
Sep 6, 2024
b17e76d
use Base.invperm
Sep 6, 2024
1fd17ca
size of plans
Sep 9, 2024
9aca321
bump version number
Sep 23, 2024
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1 change: 1 addition & 0 deletions src/FastTransforms.jl
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Expand Up @@ -128,6 +128,7 @@ for f in (:jac2jac,
@eval $f(x::AbstractArray, y...; z...) = $lib_f(x, y...; z...)
end

include("arrays.jl")
# following use Toeplitz-Hankel to avoid expensive plans
# for f in (:leg2cheb, :cheb2leg, :ultra2ultra)
# th_f = Symbol("th_", f)
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90 changes: 90 additions & 0 deletions src/arrays.jl
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struct ArrayPlan{T, FF<:FTPlan{<:T}, Szs<:Tuple, Dims<:Tuple{<:Int}} <: Plan{T}
F::FF
szs::Szs
dims::Dims
end
size(P::ArrayPlan) = P.szs
size(P::ArrayPlan, k::Int) = P.szs[k]
size(P::ArrayPlan, k...) = P.szs[[k...]]

function ArrayPlan(F::FTPlan{<:T}, c::AbstractArray{T}, dims::Tuple{<:Int}=(1,)) where T
szs = size(c)
@assert F.n == szs[dims[1]]
ArrayPlan(F, size(c), dims)
end

function *(P::ArrayPlan, f::AbstractArray)
F, dims, szs = P.F, P.dims, P.szs
@assert length(dims) == 1
@assert szs == size(f)
d = first(dims)

perm = (d, ntuple(i-> i + (i >= d), ndims(f) -1)...)
fp = permutedims(f, perm)

fr = reshape(fp, size(fp,1), :)

permutedims(reshape(F*fr, size(fp)...), invperm(perm))
end

function \(P::ArrayPlan, f::AbstractArray)
F, dims, szs = P.F, P.dims, P.szs
@assert length(dims) == 1
@assert szs == size(f)
d = first(dims)

perm = (d, ntuple(i-> i + (i >= d), ndims(f) -1)...)
fp = permutedims(f, perm)

fr = reshape(fp, size(fp,1), :)

permutedims(reshape(F\fr, size(fp)...), invperm(perm))
end

struct NDimsPlan{T, FF<:ArrayPlan{<:T}, Szs<:Tuple, Dims<:Tuple} <: Plan{T}
F::FF
szs::Szs
dims::Dims
function NDimsPlan(F, szs, dims)
if length(Set(szs[[dims...]])) > 1
error("Different size in dims axes not yet implemented in N-dimensional transform.")
end
new{eltype(F), typeof(F), typeof(szs), typeof(dims)}(F, szs, dims)
end
end

size(P::NDimsPlan) = P.szs
size(P::NDimsPlan, k::Int) = P.szs[k]
size(P::NDimsPlan, k...) = P.szs[[k...]]
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Why the array construction in the indexing? Shouldn't this just be P.szs[k...]?

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I've probably misunderstood what k is. I copied the size(P, k...) structure from size(P::JacobiTransformPlan, k...) = size(P.chebtransform, k...) and assumed it is a tuple. In which case P.szs[k...] does not work.

e.g.

julia> szs = (10,20,30);
julia> szs[[(1,2)...]]
(10, 20)
julia> szs[(1,2)...]
ERROR: MethodError: no method matching getindex(::Tuple{Int64, Int64, Int64}, ::Int64, ::Int64)

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Perhaps I've misunderstood this. Are you trying to obtain multiple indices in one go?

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That's the intention! Although I don't need that functionality in this PR.

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Perhaps best to remove it then, as it's not the conventional usage of size. One may broadcast size over indices to obtain the sizes along multiple dimensions at once.

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Note sizes of plans and arrays behave differently

compare w FFT

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judging by this line here https://github.com/JuliaMath/FFTW.jl/blob/f888022d7a1ff78491abf8f33f1055cc52a68f0a/src/fft.jl#L254 I think I should only really keep size(P::NDimsPlan) = P.szs

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...or maybe I should keep size(P::NDimsPlan, k::Int) = P.szs[k]?


function NDimsPlan(F::FTPlan, szs::Tuple, dims::Tuple)
NDimsPlan(ArrayPlan(F, szs, (first(dims),)), szs, dims)
end

function *(P::NDimsPlan, f::AbstractArray)
F, dims = P.F, P.dims
@assert size(P) == size(f)
g = copy(f)
t = 1:ndims(g)
d1 = dims[1]
for d in dims
perm = ntuple(k -> k == d1 ? t[d] : k == d ? t[d1] : t[k], ndims(g))
gp = permutedims(g, perm)
g = permutedims(F*gp, invperm(perm))
end
return g
end

function \(P::NDimsPlan, f::AbstractArray)
F, dims = P.F, P.dims
@assert size(P) == size(f)
g = copy(f)
t = 1:ndims(g)
d1 = dims[1]
for d in dims
perm = ntuple(k -> k == d1 ? t[d] : k == d ? t[d1] : t[k], ndims(g))
gp = permutedims(g, perm)
g = permutedims(F\gp, invperm(perm))
end
return g
end
68 changes: 68 additions & 0 deletions test/arraystests.jl
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using FastTransforms, Test
import FastTransforms: ArrayPlan, NDimsPlan

@testset "Array transform" begin
@testset "ArrayPlan" begin
c = randn(5,20,10)
F = plan_cheb2leg(c)
FT = ArrayPlan(F, c)

@test size(FT) == size(c)
@test size(FT,1) == size(c,1)
@test size(FT,1,2) == (size(c,1), size(c,2))

f = similar(c);
for k in axes(c,3)
f[:,:,k] = (F*c[:,:,k])
end
@test f ≈ FT*c
@test c ≈ FT\f

F = plan_cheb2leg(Vector{Float64}(axes(c,2)))
FT = ArrayPlan(F, c, (2,))
for k in axes(c,3)
f[:,:,k] = (F*c[:,:,k]')'
end
@test f ≈ FT*c
@test c ≈ FT\f
end

@testset "NDimsPlan" begin
c = randn(20,10,20)
@test_throws ErrorException("Different size in dims axes not yet implemented in N-dimensional transform.") NDimsPlan(ArrayPlan(plan_cheb2leg(c), c), size(c), (1,2))

c = randn(5,20)
F = plan_cheb2leg(c)
FT = ArrayPlan(F, c)
P = NDimsPlan(F, size(c), (1,))
@test F*c ≈ FT*c ≈ P*c

c = randn(20,20,5);
F = plan_cheb2leg(c)
FT = ArrayPlan(F, c)
P = NDimsPlan(FT, size(c), (1,2))

@test size(P) == size(c)
@test size(P,1) == size(c,1)
@test size(P,1,2) == (size(c,1), size(c,2))

f = similar(c);
for k in axes(f,3)
f[:,:,k] = (F*(F*c[:,:,k])')'
end
@test f ≈ P*c
@test c ≈ P\f

c = randn(5,10,10,60)
F = plan_cheb2leg(randn(10))
P = NDimsPlan(F, size(c), (2,3))
f = similar(c)
for i in axes(f,1), j in axes(f,4)
f[i,:,:,j] = (F*(F*c[i,:,:,j])')'
end
@test f ≈ P*c
@test c ≈ P\f
end
end


1 change: 1 addition & 0 deletions test/runtests.jl
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Expand Up @@ -12,3 +12,4 @@ include("clenshawtests.jl")
include("toeplitzplanstests.jl")
include("toeplitzhankeltests.jl")
include("symmetrictoeplitzplushankeltests.jl")
include("arraystests.jl")
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