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signal_fftw.jl
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signal_fftw.jl
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## FFT: Implement fft by calling fftw.
_jl_libfftw = dlopen("libfftw3")
_jl_libfftwf = dlopen("libfftw3f")
## Direction of FFT
const _jl_FFTW_FORWARD = int32(-1)
const _jl_FFTW_BACKWARD = int32(1)
## _jl_FFTW Flags from fftw3.h
const _jl_FFTW_MEASURE = uint32(0)
const _jl_FFTW_DESTROY_INPUT = uint32(1 << 0)
const _jl_FFTW_UNALIGNED = uint32(1 << 1)
const _jl_FFTW_CONSERVE_MEMORY = uint32(1 << 2)
const _jl_FFTW_EXHAUSTIVE = uint32(1 << 3) # NO_EXHAUSTIVE is default
const _jl_FFTW_PRESERVE_INPUT = uint32(1 << 4) # cancels _jl_FFTW_DESTROY_INPUT
const _jl_FFTW_PATIENT = uint32(1 << 5) # IMPATIENT is default
const _jl_FFTW_ESTIMATE = uint32(1 << 6)
## R2R transform kinds
const _jl_FFTW_R2HC = int32(0)
const _jl_FFTW_HC2R = int32(1)
const _jl_FFTW_DHT = int32(2)
const _jl_FFTW_REDFT00 = int32(3)
const _jl_FFTW_REDFT01 = int32(4)
const _jl_FFTW_REDFT10 = int32(5)
const _jl_FFTW_REDFT11 = int32(6)
const _jl_FFTW_RODFT00 = int32(7)
const _jl_FFTW_RODFT01 = int32(8)
const _jl_FFTW_RODFT10 = int32(9)
const _jl_FFTW_RODFT11 = int32(10)
## Julia wrappers around FFTW functions
# Execute
_jl_fftw_execute(precision::Union(Type{Float64}, Type{Complex128}), plan) =
ccall(dlsym(_jl_libfftw, :fftw_execute), Void, (Ptr{Void},), plan)
_jl_fftw_execute(precision::Union(Type{Float32}, Type{Complex64}), plan) =
ccall(dlsym(_jl_libfftwf, :fftwf_execute), Void, (Ptr{Void},), plan)
# Destroy plan
_jl_fftw_destroy_plan(precision::Union(Type{Float64}, Type{Complex128}), plan) =
ccall(dlsym(_jl_libfftw, :fftw_destroy_plan), Void, (Ptr{Void},), plan)
_jl_fftw_destroy_plan(precision::Union(Type{Float32}, Type{Complex64}), plan) =
ccall(dlsym(_jl_libfftwf, :fftwf_destroy_plan), Void, (Ptr{Void},), plan)
# Create 1d plan
for (libname, fname_complex, fname_real, T_in, T_out) in
((:_jl_libfftw,"fftw_plan_dft_1d","fftw_plan_dft_r2c_1d",:Float64,:Complex128),
(:_jl_libfftwf,"fftwf_plan_dft_1d","fftwf_plan_dft_r2c_1d",:Float32,:Complex64))
@eval begin
function _jl_fftw_plan_dft(X::Vector{$T_out}, Y::Vector{$T_out}, direction::Integer)
ccall(dlsym($libname, $fname_complex),
Ptr{Void},
(Int32, Ptr{$T_out}, Ptr{$T_out}, Int32, Uint32, ),
length(X), X, Y, direction, _jl_FFTW_ESTIMATE)
end
function _jl_fftw_plan_dft(X::Vector{$T_in}, Y::Vector{$T_out})
ccall(dlsym($libname, $fname_real),
Ptr{Void},
(Int32, Ptr{$T_in}, Ptr{$T_out}, Uint32, ),
length(X), X, Y, _jl_FFTW_ESTIMATE)
end
end
end
# Create 2d plan
for (libname, fname_complex, fname_real, T_in, T_out) in
((:_jl_libfftw,"fftw_plan_dft_2d","fftw_plan_dft_r2c_2d",:Float64,:Complex128),
(:_jl_libfftwf,"fftwf_plan_dft_2d","fftwf_plan_dft_r2c_2d",:Float32,:Complex64))
@eval begin
function _jl_fftw_plan_dft(X::Matrix{$T_out}, Y::Matrix{$T_out}, direction::Integer)
ccall(dlsym($libname, $fname_complex),
Ptr{Void},
(Int32, Int32, Ptr{$T_out}, Ptr{$T_out}, Int32, Uint32, ),
size(X,2), size(X,1), X, Y, direction, _jl_FFTW_ESTIMATE)
end
function _jl_fftw_plan_dft(X::Matrix{$T_in}, Y::Matrix{$T_out})
ccall(dlsym($libname, $fname_real),
Ptr{Void},
(Int32, Int32, Ptr{$T_in}, Ptr{$T_out}, Uint32, ),
size(X,2), size(X,1), X, Y, _jl_FFTW_ESTIMATE)
end
end
end
# Create 3d plan
for (libname, fname_complex, fname_real, T_in, T_out) in
((:_jl_libfftw,"fftw_plan_dft_2d","fftw_plan_dft_r2c_2d",:Float64,:Complex128),
(:_jl_libfftwf,"fftwf_plan_dft_2d","fftwf_plan_dft_r2c_2d",:Float32,:Complex64))
@eval begin
function _jl_fftw_plan_dft(X::Array{$T_out,3}, Y::Array{$T_out,3}, direction::Integer)
ccall(dlsym($libname, $fname_complex),
Ptr{Void},
(Int32, Int32, Int32, Ptr{$T_out}, Ptr{$T_out}, Int32, Uint32, ),
size(X,3), size(X,2), size(X,1), X, Y, direction, _jl_FFTW_ESTIMATE)
end
function _jl_fftw_plan_dft(X::Array{$T_in,3}, Y::Array{$T_out,3})
ccall(dlsym($libname, $fname_real),
Ptr{Void},
(Int32, Int32, Int32, Ptr{$T_in}, Ptr{$T_out}, Uint32, ),
size(X,3), size(X,2), size(X,1), X, Y, _jl_FFTW_ESTIMATE)
end
end
end
# Create nd plan
for (libname, fname_complex, fname_real, T_in, T_out) in
((:_jl_libfftw,"fftw_plan_dft","fftw_plan_dft_r2c",:Float64,:Complex128),
(:_jl_libfftwf,"fftwf_plan_dft","fftwf_plan_dft_r2c",:Float32,:Complex64))
@eval begin
function _jl_fftw_plan_dft(X::Array{$T_out}, Y::Array{$T_out}, direction::Integer)
ccall(dlsym($libname, $fname_complex),
Ptr{Void},
(Int32, Ptr{Int32}, Ptr{$T_out}, Ptr{$T_out}, Int32, Uint32, ),
ndims(X), int32([size(X)...]), X, Y, direction, _jl_FFTW_ESTIMATE)
end
function _jl_fftw_plan_dft(X::Array{$T_in}, Y::Array{$T_out})
ccall(dlsym($libname, $fname_real),
Ptr{Void},
(Int32, Ptr{Int32}, Ptr{$T_in}, Ptr{$T_out}, Uint32, ),
ndims(X), int32([size(X)...]), X, Y, _jl_FFTW_ESTIMATE)
end
end
end
# Complex inputs
function fftn{T<:Union(Complex128,Complex64)}(X::Array{T})
Y = similar(X, T)
plan = _jl_fftw_plan_dft(X, Y, _jl_FFTW_FORWARD)
_jl_fftw_execute(T, plan)
_jl_fftw_destroy_plan(T, plan)
return Y
end
function ifftn{T<:Union(Complex128,Complex64)}(X::Array{T})
Y = similar(X, T)
plan = _jl_fftw_plan_dft(X, Y, _jl_FFTW_BACKWARD)
_jl_fftw_execute(T, plan)
_jl_fftw_destroy_plan(T, plan)
return Y
end
# Real inputs
# This definition can be generalized to fftn, once the code to
# compute the conjugate parts for the nd case is implemented.
function fftn{T<:Union(Float64,Float32)}(X::Vector{T})
T_out = is(T, Float32) ? Complex64 : Complex128
Y = similar(X, T_out)
plan = _jl_fftw_plan_dft(X, Y)
_jl_fftw_execute(T, plan)
_jl_fftw_destroy_plan(T, plan)
n = length(Y)
nconj = int(length(X)/2 - 1)
for i=n:-1:(n-nconj)
Y[i] = conj(Y[n-i+2])
end
return Y
end
# TODO: Can be computed efficiently without converting to complex
# if the conjugate pairs are checked for.
ifftn{T<:Union(Float64,Float32)}(X::Array{T}) = ifftn(complex(X))
# Convenience functions
fft2{T<:Union(Float64,Float32)}(X::Matrix{T}) = fftn(complex(X))
fft3{T<:Union(Float64,Float32)}(X::Array{T}) = fftn(complex(X))
fft2{T<:Union(Complex128,Complex64)}(X::Matrix{T}) = fftn(X)
fft3{T<:Union(Complex128,Complex64)}(X::Array{T}) = fftn(X)
ifft{T<:Union(Float64,Float32,Complex128,Complex64)}(X::Vector{T}) = ifftn(X)
ifft2{T<:Union(Float64,Float32,Complex128,Complex64)}(X::Matrix{T}) = ifftn(X)
ifft3{T<:Union(Float64,Float32,Complex128,Complex64)}(X::Array{T}) = ifftn(X)
# Compute fft and ifft of slices of arrays
fft(X) = fft(X, (), 1)
ifft(X) = ifft(X, (), 1)
# TODO: This is inefficient. Advanced interfaces of _jl_FFTW should be used
for (fname, fname_compute) in ((:fft,:fftn), (:ifft,:ifftn))
@eval begin
function ($fname){T<:Union(Float64,Float32,Complex128,Complex64),n}(
X::Array{T,n}, npoints, dim::Integer
)
if npoints != (); error("the npoints option is not yet supported"); end
if dim > 2; error("only 2d arrays are supported for now"); end
if n == 1; return fftn(X); end
Y = similar(X, (is(T,Float32)||is(T,Complex64)) ? Complex64 : Complex128)
if dim == 2; X = X.'; Y = reshape(Y, size(X)); end
for i=1:size(X,1):numel(X)
R = i:(i+size(X,1)-1)
Y[R] = ($fname_compute)(X[R])
end
if dim == 2; Y = Y.'; end
return Y
end
end
end
# Transpose
# NOTE: Using _jl_FFTW_MEASURE and _jl_FFTW_PATIENT zeros out the input the
# first time it is used for a particular size. Use _jl_FFTW_ESTIMATE
for (libname, fname, elty) in ((:_jl_libfftw ,"fftw_plan_guru_r2r",:Float64),
(:_jl_libfftwf,"fftwf_plan_guru_r2r",:Float32))
@eval begin
function _jl_fftw_transpose(X::Matrix{$elty})
P = similar(X)
(n1, n2) = size(X)
plan = ccall(dlsym($libname, $fname), Ptr{Void},
(Int32, Ptr{Int32}, Int32, Ptr{Int32}, Ptr{$elty}, Ptr{$elty}, Ptr{Int32}, Uint32),
0, C_NULL, 2, int32([n1,n2,1,n2,1,n1]), X, P, [_jl_FFTW_HC2R], _jl_FFTW_ESTIMATE | _jl_FFTW_PRESERVE_INPUT)
_jl_fftw_execute($elty, plan)
_jl_fftw_destroy_plan($elty, plan)
return P
end
end
end
for (libname, fname, celty) in ((:_jl_libfftw ,"fftw_plan_guru_dft",:Complex128),
(:_jl_libfftwf,"fftwf_plan_guru_dft",:Complex64))
@eval begin
function _jl_fftw_transpose(X::Matrix{$celty})
P = similar(X)
(n1, n2) = size(X)
plan = ccall(dlsym($libname, $fname), Ptr{Void},
(Int32, Ptr{Int32}, Int32, Ptr{Int32}, Ptr{$celty}, Ptr{$celty}, Int32, Uint32),
0, C_NULL, 2, int32([n1,n2,1,n2,1,n1]), X, P, _jl_FFTW_FORWARD, _jl_FFTW_ESTIMATE | _jl_FFTW_PRESERVE_INPUT)
_jl_fftw_execute($celty, plan)
_jl_fftw_destroy_plan($celty, plan)
return P
end
end
end