new DFT api

NEWS.md

@@ -193,6 +193,11 @@ Library improvements
 
     * New `vecdot` function, analogous to `vecnorm`, for Euclidean inner products over any iterable container ([#11067]).
 
+  * `p = plan_fft(x)` and similar functions now return a `Base.DFT.Plan` object, rather
+    than an anonymous function.  Calling it via `p(x)` is deprecated in favor of
+    `p * x` or `p \ x` (for the inverse), and it can also be used with `A_mul_B!`
+    to employ pre-allocated output arrays ([#12087]).
+
   * Strings
 
     * NUL-terminated strings should now be passed to C via the new `Cstring` type, not `Ptr{UInt8}` or `Ptr{Cchar}`,
@@ -1519,3 +1524,4 @@ Too numerous to mention.
 [#11922]: https://github.com/JuliaLang/julia/issues/11922
 [#11985]: https://github.com/JuliaLang/julia/issues/11985
 [#12031]: https://github.com/JuliaLang/julia/issues/12031
+[#12087]: https://github.com/JuliaLang/julia/issues/12087

base/complex.jl

@@ -34,6 +34,9 @@ real(x::Real) = x
 imag(x::Real) = zero(x)
 reim(z) = (real(z), imag(z))
 
+real{T<:Real}(::Type{T}) = T
+real{T<:Real}(::Type{Complex{T}}) = T
+
 isreal(x::Real) = true
 isreal(z::Complex) = imag(z) == 0
 isimag(z::Number) = real(z) == 0

base/deprecated.jl

@@ -474,23 +474,31 @@ export float32_isvalid, float64_isvalid
 @deprecate ($)(x::Char, y::Char)  Char(UInt32(x) $ UInt32(y))
 
 # 11241
-
 @deprecate is_valid_char(ch::Char)          isvalid(ch)
 @deprecate is_valid_ascii(str::ASCIIString) isvalid(str)
 @deprecate is_valid_utf8(str::UTF8String)   isvalid(str)
 @deprecate is_valid_utf16(str::UTF16String) isvalid(str)
 @deprecate is_valid_utf32(str::UTF32String) isvalid(str)
-
 @deprecate is_valid_char(ch)   isvalid(Char, ch)
 @deprecate is_valid_ascii(str) isvalid(ASCIIString, str)
 @deprecate is_valid_utf8(str)  isvalid(UTF8String, str)
 @deprecate is_valid_utf16(str) isvalid(UTF16String, str)
 @deprecate is_valid_utf32(str) isvalid(UTF32String, str)
 
 # 11379
-
 @deprecate utf32(c::Integer...)   UTF32String(UInt32[c...,0])
 
+# 12087
+@deprecate call(P::Base.DFT.Plan, A) P * A
+for f in (:plan_fft, :plan_ifft, :plan_bfft, :plan_fft!, :plan_ifft!, :plan_bfft!, :plan_rfft)
+    @eval @deprecate $f(A, dims, flags) $f(A, dims; flags=flags)
+    @eval @deprecate $f(A, dims, flags, tlim) $f(A, dims; flags=flags, timelimit=tlim)
+end
+for f in (:plan_brfft, :plan_irfft)
+    @eval @deprecate $f(A, d, dims, flags) $f(A, d, dims; flags=flags)
+    @eval @deprecate $f(A, d, dims, flags, tlim) $f(A, d, dims; flags=flags, timelimit=tlim)
+end
+
 # 10862
 
 function chol(A::AbstractMatrix, uplo::Symbol)

base/dft.jl

@@ -0,0 +1,195 @@
+# This file is a part of Julia. License is MIT: http://julialang.org/license
+
+module DFT
+
+# DFT plan where the inputs are an array of eltype T
+abstract Plan{T}
+
+import Base: show, summary, size, ndims, length, eltype,
+             *, A_mul_B!, inv, \, A_ldiv_B!
+
+eltype{T}(::Plan{T}) = T
+eltype{P<:Plan}(T::Type{P}) = T.parameters[1]
+
+# size(p) should return the size of the input array for p
+size(p::Plan, d) = size(p)[d]
+ndims(p::Plan) = length(size(p))
+length(p::Plan) = prod(size(p))::Int
+
+##############################################################################
+export fft, ifft, bfft, fft!, ifft!, bfft!,
+       plan_fft, plan_ifft, plan_bfft, plan_fft!, plan_ifft!, plan_bfft!,
+       rfft, irfft, brfft, plan_rfft, plan_irfft, plan_brfft
+
+complexfloat{T<:FloatingPoint}(x::AbstractArray{Complex{T}}) = x
+
+# return an Array, rather than similar(x), to avoid an extra copy for FFTW
+# (which only works on StridedArray types).
+complexfloat{T<:Complex}(x::AbstractArray{T}) = copy!(Array(typeof(float(one(T))), size(x)), x)
+complexfloat{T<:FloatingPoint}(x::AbstractArray{T}) = copy!(Array(typeof(complex(one(T))), size(x)), x)
+complexfloat{T<:Real}(x::AbstractArray{T}) = copy!(Array(typeof(complex(float(one(T)))), size(x)), x)
+
+# implementations only need to provide plan_X(x, region)
+# for X in (:fft, :bfft, ...):
+for f in (:fft, :bfft, :ifft, :fft!, :bfft!, :ifft!, :rfft)
+    pf = symbol(string("plan_", f))
+    @eval begin
+        $f(x::AbstractArray) = $pf(x) * x
+        $f(x::AbstractArray, region) = $pf(x, region) * x
+        $pf(x::AbstractArray; kws...) = $pf(x, 1:ndims(x); kws...)
+    end
+end
+
+# promote to a complex floating-point type (out-of-place only),
+# so implementations only need Complex{Float} methods
+for f in (:fft, :bfft, :ifft)
+    pf = symbol(string("plan_", f))
+    @eval begin
+        $f{T<:Real}(x::AbstractArray{T}, region=1:ndims(x)) = $f(complexfloat(x), region)
+        $pf{T<:Real}(x::AbstractArray{T}, region; kws...) = $pf(complexfloat(x), region; kws...)
+        $f{T<:Union(Integer,Rational)}(x::AbstractArray{Complex{T}}, region=1:ndims(x)) = $f(complexfloat(x), region)
+        $pf{T<:Union(Integer,Rational)}(x::AbstractArray{Complex{T}}, region; kws...) = $pf(complexfloat(x), region; kws...)
+    end
+end
+rfft{T<:Union(Integer,Rational)}(x::AbstractArray{T}, region=1:ndims(x)) = rfft(float(x), region)
+plan_rfft{T<:Union(Integer,Rational)}(x::AbstractArray{T}, region; kws...) = plan_rfft(float(x), region; kws...)
+
+# only require implementation to provide *(::Plan{T}, ::Array{T})
+*{T}(p::Plan{T}, x::AbstractArray) = p * copy!(Array(T, size(x)), x)
+
+# Implementations should also implement A_mul_B!(Y, plan, X) so as to support
+# pre-allocated output arrays.  We don't define * in terms of A_mul_B!
+# generically here, however, because of subtleties for in-place and rfft plans.
+
+##############################################################################
+# To support inv, \, and A_ldiv_B!(y, p, x), we require Plan subtypes
+# to have a pinv::Plan field, which caches the inverse plan, and which
+# should be initially undefined.  They should also implement
+# plan_inv(p) to construct the inverse of a plan p.
+
+# hack from @simonster (in #6193) to compute the return type of plan_inv
+# without actually calling it or even constructing the empty arrays.
+_pinv_type(p::Plan) = typeof([plan_inv(x) for x in typeof(p)[]])
+pinv_type(p::Plan) = eltype(_pinv_type(p))
+
+inv(p::Plan) =
+    isdefined(p, :pinv) ? p.pinv::pinv_type(p) : (p.pinv = plan_inv(p))
+\(p::Plan, x::AbstractArray) = inv(p) * x
+A_ldiv_B!(y::AbstractArray, p::Plan, x::AbstractArray) = A_mul_B!(y, inv(p), x)
+
+##############################################################################
+# implementations only need to provide the unnormalized backwards FFT,
+# similar to FFTW, and we do the scaling generically to get the ifft:
+
+type ScaledPlan{T,P,N} <: Plan{T}
+    p::P
+    scale::N # not T, to avoid unnecessary promotion to Complex
+    pinv::Plan
+    ScaledPlan(p, scale) = new(p, scale)
+end
+ScaledPlan{P<:Plan,N<:Number}(p::P, scale::N) = ScaledPlan{eltype(P),P,N}(p, scale)
+ScaledPlan(p::ScaledPlan, α::Number) = ScaledPlan(p.p, p.scale * α)
+
+size(p::ScaledPlan) = size(p.p)
+
+show(io::IO, p::ScaledPlan) = print(io, p.scale, " * ", p.p)
+summary(p::ScaledPlan) = string(p.scale, " * ", summary(p.p))
+
+*(p::ScaledPlan, x::AbstractArray) = scale!(p.p * x, p.scale)
+
+*(α::Number, p::Plan) = ScaledPlan(p, α)
+*(p::Plan, α::Number) = ScaledPlan(p, α)
+*(I::UniformScaling, p::ScaledPlan) = ScaledPlan(p, I.λ)
+*(p::ScaledPlan, I::UniformScaling) = ScaledPlan(p, I.λ)
+*(I::UniformScaling, p::Plan) = ScaledPlan(p, I.λ)
+*(p::Plan, I::UniformScaling) = ScaledPlan(p, I.λ)
+
+# Normalization for ifft, given unscaled bfft, is 1/prod(dimensions)
+normalization(T, sz, region) = one(T) / prod([sz...][[region...]])
+normalization(X, region) = normalization(real(eltype(X)), size(X), region)
+
+plan_ifft(x::AbstractArray, region; kws...) =
+    ScaledPlan(plan_bfft(x, region; kws...), normalization(x, region))
+plan_ifft!(x::AbstractArray, region; kws...) =
+    ScaledPlan(plan_bfft!(x, region; kws...), normalization(x, region))
+
+plan_inv(p::ScaledPlan) = ScaledPlan(plan_inv(p.p), inv(p.scale))
+
+A_mul_B!(y::AbstractArray, p::ScaledPlan, x::AbstractArray) =
+    scale!(p.scale, A_mul_B!(y, p.p, x))
+
+##############################################################################
+# Real-input DFTs are annoying because the output has a different size
+# than the input if we want to gain the full factor-of-two(ish) savings
+# For backward real-data transforms, we must specify the original length
+# of the first dimension, since there is no reliable way to detect this
+# from the data (we can't detect whether the dimension was originally even
+# or odd).
+
+for f in (:brfft, :irfft)
+    pf = symbol(string("plan_", f))
+    @eval begin
+        $f(x::AbstractArray, d::Integer) = $pf(x, d) * x
+        $f(x::AbstractArray, d::Integer, region) = $pf(x, d, region) * x
+        $pf(x::AbstractArray, d::Integer;kws...) = $pf(x, d, 1:ndims(x);kws...)
+    end
+end
+
+for f in (:brfft, :irfft)
+    @eval begin
+        $f{T<:Real}(x::AbstractArray{T}, d::Integer, region=1:ndims(x)) = $f(complexfloat(x), d, region)
+        $f{T<:Union(Integer,Rational)}(x::AbstractArray{Complex{T}}, d::Integer, region=1:ndims(x)) = $f(complexfloat(x), d, region)
+    end
+end
+
+function rfft_output_size(x::AbstractArray, region)
+    d1 = first(region)
+    osize = [size(x)...]
+    osize[d1] = osize[d1]>>1 + 1
+    return osize
+end
+
+function brfft_output_size(x::AbstractArray, d::Integer, region)
+    d1 = first(region)
+    osize = [size(x)...]
+    @assert osize[d1] == d>>1 + 1
+    osize[d1] = d
+    return osize
+end
+
+plan_irfft{T}(x::AbstractArray{Complex{T}}, d::Integer, region; kws...) =
+    ScaledPlan(plan_brfft(x, d, region; kws...),
+               normalization(T, brfft_output_size(x, d, region), region))
+
+##############################################################################
+
+export fftshift, ifftshift
+
+fftshift(x) = circshift(x, div([size(x)...],2))
+
+function fftshift(x,dim)
+    s = zeros(Int,ndims(x))
+    s[dim] = div(size(x,dim),2)
+    circshift(x, s)
+end
+
+ifftshift(x) = circshift(x, div([size(x)...],-2))
+
+function ifftshift(x,dim)
+    s = zeros(Int,ndims(x))
+    s[dim] = -div(size(x,dim),2)
+    circshift(x, s)
+end
+
+##############################################################################
+
+# FFTW module (may move to an external package at some point):
+if Base.USE_GPL_LIBS
+    include("fft/FFTW.jl")
+    importall .FFTW
+    export FFTW, dct, idct, dct!, idct!, plan_dct, plan_idct, plan_dct!, plan_idct!
+end
+
+##############################################################################
+
+end