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dct.jl
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dct.jl
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# This file is a part of Julia. License is MIT: https://julialang.org/license
# (This is part of the FFTW module.)
export dct, idct, dct!, idct!, plan_dct, plan_idct, plan_dct!, plan_idct!
# Discrete cosine transforms (type II/III) via FFTW's r2r transforms;
# we follow the Matlab convention and adopt a unitary normalization here.
# Unlike Matlab we compute the multidimensional transform by default,
# similar to the Julia fft functions.
type DCTPlan{T<:fftwNumber,K,inplace} <: Plan{T}
plan::r2rFFTWPlan{T}
r::Array{UnitRange{Int}} # array of indices for rescaling
nrm::Float64 # normalization factor
region::Dims # dimensions being transformed
pinv::DCTPlan{T}
DCTPlan{T,K,inplace}(plan,r,nrm,region) where {T<:fftwNumber,K,inplace} = new(plan,r,nrm,region)
end
size(p::DCTPlan) = size(p.plan)
function show{T,K,inplace}(io::IO, p::DCTPlan{T,K,inplace})
print(io, inplace ? "FFTW in-place " : "FFTW ",
K == REDFT10 ? "DCT (DCT-II)" : "IDCT (DCT-III)", " plan for ")
showfftdims(io, p.plan.sz, p.plan.istride, eltype(p))
end
for (pf, pfr, K, inplace) in ((:plan_dct, :plan_r2r, REDFT10, false),
(:plan_dct!, :plan_r2r!, REDFT10, true),
(:plan_idct, :plan_r2r, REDFT01, false),
(:plan_idct!, :plan_r2r!, REDFT01, true))
@eval function $pf{T<:fftwNumber}(X::StridedArray{T}, region; kws...)
r = [1:n for n in size(X)]
nrm = sqrt(0.5^length(region) * normalization(X,region))
DCTPlan{T,$K,$inplace}($pfr(X, $K, region; kws...), r, nrm,
ntuple(i -> Int(region[i]), length(region)))
end
end
"""
plan_dct!(A [, dims [, flags [, timelimit]]])
Same as [`plan_dct`](@ref), but operates in-place on `A`.
"""
plan_dct!
"""
plan_idct(A [, dims [, flags [, timelimit]]])
Pre-plan an optimized inverse discrete cosine transform (DCT), similar to
[`plan_fft`](@ref) except producing a function that computes
[`idct`](@ref). The first two arguments have the same meaning as for
[`idct`](@ref).
"""
plan_idct
"""