new DFT api

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 +474,23 @@ 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])
 
+# 6193
+@deprecate call(P::Base.DFT.Plan, A) P * A
+
 # 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

base/dsp.jl

@@ -2,16 +2,9 @@
 
 module DSP
 
-importall Base.FFTW
-import Base.FFTW.normalization
 import Base.trailingsize
 
-export FFTW, filt, filt!, deconv, conv, conv2, xcorr, fftshift, ifftshift,
-       dct, idct, dct!, idct!, plan_dct, plan_idct, plan_dct!, plan_idct!,
-       # the rest are defined imported from FFTW:
-       fft, bfft, ifft, rfft, brfft, irfft,
-       plan_fft, plan_bfft, plan_ifft, plan_rfft, plan_brfft, plan_irfft,
-       fft!, bfft!, ifft!, plan_fft!, plan_bfft!, plan_ifft!
+export filt, filt!, deconv, conv, conv2, xcorr
 
 _zerosi(b,a,T) = zeros(promote_type(eltype(b), eltype(a), T), max(length(a), length(b))-1)
 
@@ -117,10 +110,10 @@ function conv{T<:Base.LinAlg.BlasFloat}(u::StridedVector{T}, v::StridedVector{T}
     vpad = [v; zeros(T, np2 - nv)]
     if T <: Real
         p = plan_rfft(upad)
-        y = irfft(p(upad).*p(vpad), np2)
+        y = irfft((p*upad).*(p*vpad), np2)
     else
         p = plan_fft!(upad)
-        y = ifft!(p(upad).*p(vpad))
+        y = ifft!((p*upad).*(p*vpad))
     end
     return y[1:n]
 end
@@ -149,7 +142,7 @@ function conv2{T}(A::StridedMatrix{T}, B::StridedMatrix{T})
     At[1:sa[1], 1:sa[2]] = A
     Bt[1:sb[1], 1:sb[2]] = B
     p = plan_fft(At)
-    C = ifft(p(At).*p(Bt))
+    C = ifft((p*At).*(p*Bt))
     if T <: Real
         return real(C)
     end
@@ -168,124 +161,4 @@ function xcorr(u, v)
     flipdim(conv(flipdim(u, 1), v), 1)
 end
 
-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
-
-# Discrete cosine and sine transforms 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.
-
-fftwcopy{T<:fftwNumber}(X::StridedArray{T}) = copy(X)
-fftwcopy{T<:Real}(X::StridedArray{T}) = float(X)
-fftwcopy{T<:Complex}(X::StridedArray{T}) = map(Complex128,X)
-
-for (f, fr2r, Y, Tx) in ((:dct, :r2r, :Y, :Number),
-                         (:dct!, :r2r!, :X, :fftwNumber))
-    plan_f = symbol("plan_",f)
-    plan_fr2r = symbol("plan_",fr2r)
-    fi = symbol("i",f)
-    plan_fi = symbol("plan_",fi)
-    Ycopy = Y == :X ? 0 : :(Y = fftwcopy(X))
-    @eval begin
-        function $f{T<:$Tx}(X::StridedArray{T}, region)
-            $Y = $fr2r(X, REDFT10, region)
-            scale!($Y, sqrt(0.5^length(region) * normalization(X,region)))
-            sqrthalf = sqrt(0.5)
-            r = map(n -> 1:n, [size(X)...])
-            for d in region
-                r[d] = 1:1
-                $Y[r...] *= sqrthalf
-                r[d] = 1:size(X,d)
-            end
-            return $Y
-        end
-
-        function $plan_f{T<:$Tx}(X::StridedArray{T}, region,
-                                 flags::Unsigned, timelimit::Real)
-            p = $plan_fr2r(X, REDFT10, region, flags, timelimit)
-            sqrthalf = sqrt(0.5)
-            r = map(n -> 1:n, [size(X)...])
-            nrm = sqrt(0.5^length(region) * normalization(X,region))
-            return X::StridedArray{T} -> begin
-                $Y = p(X)
-                scale!($Y, nrm)
-                for d in region
-                    r[d] = 1:1
-                    $Y[r...] *= sqrthalf
-                    r[d] = 1:size(X,d)
-                end
-                return $Y
-            end
-        end
-
-        function $fi{T<:$Tx}(X::StridedArray{T}, region)
-            $Ycopy
-            scale!($Y, sqrt(0.5^length(region) * normalization(X, region)))
-            sqrt2 = sqrt(2)
-            r = map(n -> 1:n, [size(X)...])
-            for d in region
-                r[d] = 1:1
-                $Y[r...] *= sqrt2
-                r[d] = 1:size(X,d)
-            end
-            return r2r!($Y, REDFT01, region)
-        end
-
-        function $plan_fi{T<:$Tx}(X::StridedArray{T}, region,
-                                 flags::Unsigned, timelimit::Real)
-            p = $plan_fr2r(X, REDFT01, region, flags, timelimit)
-            sqrt2 = sqrt(2)
-            r = map(n -> 1:n, [size(X)...])
-            nrm = sqrt(0.5^length(region) * normalization(X,region))
-            return X::StridedArray{T} -> begin
-                $Ycopy
-                scale!($Y, nrm)
-                for d in region
-                    r[d] = 1:1
-                    $Y[r...] *= sqrt2
-                    r[d] = 1:size(X,d)
-                end
-                return p($Y)
-            end
-        end
-
-    end
-    for (g,plan_g) in ((f,plan_f), (fi, plan_fi))
-        @eval begin
-            $g{T<:$Tx}(X::StridedArray{T}) = $g(X, 1:ndims(X))
-
-            $plan_g(X, region, flags::Unsigned) =
-              $plan_g(X, region, flags, NO_TIMELIMIT)
-            $plan_g(X, region) =
-              $plan_g(X, region, ESTIMATE, NO_TIMELIMIT)
-            $plan_g{T<:$Tx}(X::StridedArray{T}) =
-              $plan_g(X, 1:ndims(X), ESTIMATE, NO_TIMELIMIT)
-        end
-    end
-end
-
-# DCT of scalar is just the identity:
-dct(x::Number, dims) = length(dims) == 0 || dims[1] == 1 ? x : throw(BoundsError())
-idct(x::Number, dims) = dct(x, dims)
-dct(x::Number) = x
-idct(x::Number) = x
-plan_dct(x::Number, dims, flags, tlim) = length(dims) == 0 || dims[1] == 1 ? y::Number -> y : throw(BoundsError())
-plan_idct(x::Number, dims, flags, tlim) = plan_dct(x, dims)
-plan_dct(x::Number) = y::Number -> y
-plan_idct(x::Number) = y::Number -> y
-
 end # module