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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
"""
plan_dct(A [, dims [, flags [, timelimit]]])
Pre-plan an optimized discrete cosine transform (DCT), similar to
[`plan_fft`](@ref) except producing a function that computes
[`dct`](@ref). The first two arguments have the same meaning as for
[`dct`](@ref).
"""
plan_dct
"""
plan_idct!(A [, dims [, flags [, timelimit]]])
Same as [`plan_idct`](@ref), but operates in-place on `A`.
"""
plan_idct!
function plan_inv{T,K,inplace}(p::DCTPlan{T,K,inplace})
X = Array{T}(p.plan.sz)
iK = inv_kind[K]
DCTPlan{T,iK,inplace}(inplace ?
plan_r2r!(X, iK, p.region, flags=p.plan.flags) :
plan_r2r(X, iK, p.region, flags=p.plan.flags),
p.r, p.nrm, p.region)
end
for f in (:dct, :dct!, :idct, :idct!)
pf = Symbol("plan_", f)
@eval begin
$f{T<:fftwNumber}(x::AbstractArray{T}) = $pf(x) * x
$f{T<:fftwNumber}(x::AbstractArray{T}, region) = $pf(x, region) * x
$pf(x::AbstractArray; kws...) = $pf(x, 1:ndims(x); kws...)
$f{T<:Real}(x::AbstractArray{T}, region=1:ndims(x)) = $f(fftwfloat(x), region)
$pf{T<:Real}(x::AbstractArray{T}, region; kws...) = $pf(fftwfloat(x), region; kws...)
$pf{T<:Complex}(x::AbstractArray{T}, region; kws...) = $pf(fftwcomplex(x), region; kws...)
end
end
"""
dct(A [, dims])
Performs a multidimensional type-II discrete cosine transform (DCT) of the array `A`, using
the unitary normalization of the DCT. The optional `dims` argument specifies an iterable
subset of dimensions (e.g. an integer, range, tuple, or array) to transform along. Most
efficient if the size of `A` along the transformed dimensions is a product of small primes;
see [`nextprod`](@ref). See also [`plan_dct`](@ref) for even greater
efficiency.
"""
dct
"""
idct(A [, dims])
Computes the multidimensional inverse discrete cosine transform (DCT) of the array `A`
(technically, a type-III DCT with the unitary normalization). The optional `dims` argument
specifies an iterable subset of dimensions (e.g. an integer, range, tuple, or array) to
transform along. Most efficient if the size of `A` along the transformed dimensions is a
product of small primes; see [`nextprod`](@ref). See also
[`plan_idct`](@ref) for even greater efficiency.
"""
idct
"""
dct!(A [, dims])
Same as [`dct!`](@ref), except that it operates in-place on `A`, which must be an
array of real or complex floating-point values.
"""
dct!
"""
idct!(A [, dims])
Same as [`idct!`](@ref), but operates in-place on `A`.
"""
idct!
const sqrthalf = sqrt(0.5)
const sqrt2 = sqrt(2.0)
const onerange = 1:1
function A_mul_B!{T}(y::StridedArray{T}, p::DCTPlan{T,REDFT10},
x::StridedArray{T})
assert_applicable(p.plan, x, y)
unsafe_execute!(p.plan, x, y)
scale!(y, p.nrm)
r = p.r
for d in p.region
oldr = r[d]
r[d] = onerange
y[r...] *= sqrthalf
r[d] = oldr
end
return y
end
# note: idct changes input data
function A_mul_B!{T}(y::StridedArray{T}, p::DCTPlan{T,REDFT01},
x::StridedArray{T})
assert_applicable(p.plan, x, y)
scale!(x, p.nrm)
r = p.r
for d in p.region
oldr = r[d]
r[d] = onerange
x[r...] *= sqrt2
r[d] = oldr
end
unsafe_execute!(p.plan, x, y)
return y
end
*{T}(p::DCTPlan{T,REDFT10,false}, x::StridedArray{T}) =
A_mul_B!(Array{T}(p.plan.osz), p, x)
*{T}(p::DCTPlan{T,REDFT01,false}, x::StridedArray{T}) =
A_mul_B!(Array{T}(p.plan.osz), p, copy(x)) # need copy to preserve input
*{T,K}(p::DCTPlan{T,K,true}, x::StridedArray{T}) = A_mul_B!(x, p, x)