// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Mark Borgerding mark a borgerding net
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_FFT_H
#define EIGEN_FFT_H
#include <complex>
#include <vector>
#include <map>
#include <Eigen/Core>
/** \ingroup Unsupported_modules
* \defgroup FFT_Module Fast Fourier Transform module
*
* \code
* #include <unsupported/Eigen/FFT>
* \endcode
*
* This module provides Fast Fourier transformation, with a configurable backend
* implementation.
*
* The default implementation is based on kissfft. It is a small, free, and
* reasonably efficient default.
*
* There are currently two implementation backend:
*
* - fftw (http://www.fftw.org) : faster, GPL -- incompatible with Eigen in LGPL form, bigger code size.
* - MKL (http://en.wikipedia.org/wiki/Math_Kernel_Library) : fastest, commercial -- may be incompatible with Eigen in GPL form.
*
* \section FFTDesign Design
*
* The following design decisions were made concerning scaling and
* half-spectrum for real FFT.
*
* The intent is to facilitate generic programming and ease migrating code
* from Matlab/octave.
* We think the default behavior of Eigen/FFT should favor correctness and
* generality over speed. Of course, the caller should be able to "opt-out" from this
* behavior and get the speed increase if they want it.
*
* 1) %Scaling:
* Other libraries (FFTW,IMKL,KISSFFT) do not perform scaling, so there
* is a constant gain incurred after the forward&inverse transforms , so
* IFFT(FFT(x)) = Kx; this is done to avoid a vector-by-value multiply.
* The downside is that algorithms that worked correctly in Matlab/octave
* don't behave the same way once implemented in C++.
*
* How Eigen/FFT differs: invertible scaling is performed so IFFT( FFT(x) ) = x.
*
* 2) Real FFT half-spectrum
* Other libraries use only half the frequency spectrum (plus one extra
* sample for the Nyquist bin) for a real FFT, the other half is the
* conjugate-symmetric of the first half. This saves them a copy and some
* memory. The downside is the caller needs to have special logic for the
* number of bins in complex vs real.
*
* How Eigen/FFT differs: The full spectrum is returned from the forward
* transform. This facilitates generic template programming by obviating
* separate specializations for real vs complex. On the inverse
* transform, only half the spectrum is actually used if the output type is real.
*/
#ifdef EIGEN_FFTW_DEFAULT
// FFTW: faster, GPL -- incompatible with Eigen in LGPL form, bigger code size
# include <fftw3.h>
# include "src/FFT/ei_fftw_impl.h"
namespace Eigen {
//template <typename T> typedef struct internal::fftw_impl default_fft_impl; this does not work
template <typename T> struct default_fft_impl : public internal::fftw_impl<T> {};
}
#elif defined EIGEN_MKL_DEFAULT
// TODO
// intel Math Kernel Library: fastest, commercial -- may be incompatible with Eigen in GPL form
# include "src/FFT/ei_imklfft_impl.h"
namespace Eigen {
template <typename T> struct default_fft_impl : public internal::imklfft_impl {};
}
#else
// internal::kissfft_impl: small, free, reasonably efficient default, derived from kissfft
//
# include "src/FFT/ei_kissfft_impl.h"
namespace Eigen {
template <typename T>
struct default_fft_impl : public internal::kissfft_impl<T> {};
}
#endif
namespace Eigen {
//
template<typename T_SrcMat,typename T_FftIfc> struct fft_fwd_proxy;
template<typename T_SrcMat,typename T_FftIfc> struct fft_inv_proxy;
namespace internal {
template<typename T_SrcMat,typename T_FftIfc>
struct traits< fft_fwd_proxy<T_SrcMat,T_FftIfc> >
{
typedef typename T_SrcMat::PlainObject ReturnType;
};
template<typename T_SrcMat,typename T_FftIfc>
struct traits< fft_inv_proxy<T_SrcMat,T_FftIfc> >
{
typedef typename T_SrcMat::PlainObject ReturnType;
};
}
template<typename T_SrcMat,typename T_FftIfc>
struct fft_fwd_proxy
: public ReturnByValue<fft_fwd_proxy<T_SrcMat,T_FftIfc> >
{
typedef DenseIndex Index;
fft_fwd_proxy(const T_SrcMat& src,T_FftIfc & fft, Index nfft) : m_src(src),m_ifc(fft), m_nfft(nfft) {}
template<typename T_DestMat> void evalTo(T_DestMat& dst) const;
Index rows() const { return m_src.rows(); }
Index cols() const { return m_src.cols(); }
protected:
const T_SrcMat & m_src;
T_FftIfc & m_ifc;
Index m_nfft;
private:
fft_fwd_proxy& operator=(const fft_fwd_proxy&);
};
template<typename T_SrcMat,typename T_FftIfc>
struct fft_inv_proxy
: public ReturnByValue<fft_inv_proxy<T_SrcMat,T_FftIfc> >
{
typedef DenseIndex Index;
fft_inv_proxy(const T_SrcMat& src,T_FftIfc & fft, Index nfft) : m_src(src),m_ifc(fft), m_nfft(nfft) {}
template<typename T_DestMat> void evalTo(T_DestMat& dst) const;
Index rows() const { return m_src.rows(); }
Index cols() const { return m_src.cols(); }
protected:
const T_SrcMat & m_src;
T_FftIfc & m_ifc;
Index m_nfft;
private:
fft_inv_proxy& operator=(const fft_inv_proxy&);
};
template <typename T_Scalar,
typename T_Impl=default_fft_impl<T_Scalar> >
class FFT
{
public:
typedef T_Impl impl_type;
typedef DenseIndex Index;
typedef typename impl_type::Scalar Scalar;
typedef typename impl_type::Complex Complex;
enum Flag {
Default=0, // goof proof
Unscaled=1,
HalfSpectrum=2,
// SomeOtherSpeedOptimization=4
Speedy=32767
};
FFT( const impl_type & impl=impl_type() , Flag flags=Default ) :m_impl(impl),m_flag(flags) { }
inline
bool HasFlag(Flag f) const { return (m_flag & (int)f) == f;}
inline
void SetFlag(Flag f) { m_flag |= (int)f;}
inline
void ClearFlag(Flag f) { m_flag &= (~(int)f);}
inline
void fwd( Complex * dst, const Scalar * src, Index nfft)
{
m_impl.fwd(dst,src,static_cast<int>(nfft));
if ( HasFlag(HalfSpectrum) == false)
ReflectSpectrum(dst,nfft);
}
inline
void fwd( Complex * dst, const Complex * src, Index nfft)
{
m_impl.fwd(dst,src,static_cast<int>(nfft));
}
/*
inline
void fwd2(Complex * dst, const Complex * src, int n0,int n1)
{
m_impl.fwd2(dst,src,n0,n1);
}
*/
template <typename _Input>
inline
void fwd( std::vector<Complex> & dst, const std::vector<_Input> & src)
{
if ( NumTraits<_Input>::IsComplex == 0 && HasFlag(HalfSpectrum) )
dst.resize( (src.size()>>1)+1); // half the bins + Nyquist bin
else
dst.resize(src.size());
fwd(&dst[0],&src[0],src.size());
}
template<typename InputDerived, typename ComplexDerived>
inline
void fwd( MatrixBase<ComplexDerived> & dst, const MatrixBase<InputDerived> & src, Index nfft=-1)
{
typedef typename ComplexDerived::Scalar dst_type;
typedef typename InputDerived::Scalar src_type;
EIGEN_STATIC_ASSERT_VECTOR_ONLY(InputDerived)
EIGEN_STATIC_ASSERT_VECTOR_ONLY(ComplexDerived)
EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(ComplexDerived,InputDerived) // size at compile-time
EIGEN_STATIC_ASSERT((internal::is_same<dst_type, Complex>::value),
YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
EIGEN_STATIC_ASSERT(int(InputDerived::Flags)&int(ComplexDerived::Flags)&DirectAccessBit,
THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_WITH_DIRECT_MEMORY_ACCESS_SUCH_AS_MAP_OR_PLAIN_MATRICES)
if (nfft<1)
nfft = src.size();
if ( NumTraits< src_type >::IsComplex == 0 && HasFlag(HalfSpectrum) )
dst.derived().resize( (nfft>>1)+1);
else
dst.derived().resize(nfft);
if ( src.innerStride() != 1 || src.size() < nfft ) {
Matrix<src_type,1,Dynamic> tmp;
if (src.size()<nfft) {
tmp.setZero(nfft);
tmp.block(0,0,src.size(),1 ) = src;
}else{
tmp = src;
}
fwd( &dst[0],&tmp[0],nfft );
}else{
fwd( &dst[0],&src[0],nfft );
}
}
template<typename InputDerived>
inline
fft_fwd_proxy< MatrixBase<InputDerived>, FFT<T_Scalar,T_Impl> >
fwd( const MatrixBase<InputDerived> & src, Index nfft=-1)
{
return fft_fwd_proxy< MatrixBase<InputDerived> ,FFT<T_Scalar,T_Impl> >( src, *this,nfft );
}
template<typename InputDerived>
inline
fft_inv_proxy< MatrixBase<InputDerived>, FFT<T_Scalar,T_Impl> >
inv( const MatrixBase<InputDerived> & src, Index nfft=-1)
{
return fft_inv_proxy< MatrixBase<InputDerived> ,FFT<T_Scalar,T_Impl> >( src, *this,nfft );
}
inline
void inv( Complex * dst, const Complex * src, Index nfft)
{
m_impl.inv( dst,src,static_cast<int>(nfft) );
if ( HasFlag( Unscaled ) == false)
scale(dst,Scalar(1./nfft),nfft); // scale the time series
}
inline
void inv( Scalar * dst, const Complex * src, Index nfft)
{
m_impl.inv( dst,src,static_cast<int>(nfft) );
if ( HasFlag( Unscaled ) == false)
scale(dst,Scalar(1./nfft),nfft); // scale the time series
}
template<typename OutputDerived, typename ComplexDerived>
inline
void inv( MatrixBase<OutputDerived> & dst, const MatrixBase<ComplexDerived> & src, Index nfft=-1)
{
typedef typename ComplexDerived::Scalar src_type;
typedef typename OutputDerived::Scalar dst_type;
const bool realfft= (NumTraits<dst_type>::IsComplex == 0);
EIGEN_STATIC_ASSERT_VECTOR_ONLY(OutputDerived)
EIGEN_STATIC_ASSERT_VECTOR_ONLY(ComplexDerived)
EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(ComplexDerived,OutputDerived) // size at compile-time
EIGEN_STATIC_ASSERT((internal::is_same<src_type, Complex>::value),
YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
EIGEN_STATIC_ASSERT(int(OutputDerived::Flags)&int(ComplexDerived::Flags)&DirectAccessBit,
THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_WITH_DIRECT_MEMORY_ACCESS_SUCH_AS_MAP_OR_PLAIN_MATRICES)
if (nfft<1) { //automatic FFT size determination
if ( realfft && HasFlag(HalfSpectrum) )
nfft = 2*(src.size()-1); //assume even fft size
else
nfft = src.size();
}
dst.derived().resize( nfft );
// check for nfft that does not fit the input data size
Index resize_input= ( realfft && HasFlag(HalfSpectrum) )
? ( (nfft/2+1) - src.size() )
: ( nfft - src.size() );
if ( src.innerStride() != 1 || resize_input ) {
// if the vector is strided, then we need to copy it to a packed temporary
Matrix<src_type,1,Dynamic> tmp;
if ( resize_input ) {
size_t ncopy = (std::min)(src.size(),src.size() + resize_input);
tmp.setZero(src.size() + resize_input);
if ( realfft && HasFlag(HalfSpectrum) ) {
// pad at the Nyquist bin
tmp.head(ncopy) = src.head(ncopy);
tmp(ncopy-1) = real(tmp(ncopy-1)); // enforce real-only Nyquist bin
}else{
size_t nhead,ntail;
nhead = 1+ncopy/2-1; // range [0:pi)
ntail = ncopy/2-1; // range (-pi:0)
tmp.head(nhead) = src.head(nhead);
tmp.tail(ntail) = src.tail(ntail);
if (resize_input<0) { //shrinking -- create the Nyquist bin as the average of the two bins that fold into it
tmp(nhead) = ( src(nfft/2) + src( src.size() - nfft/2 ) )*src_type(.5);
}else{ // expanding -- split the old Nyquist bin into two halves
tmp(nhead) = src(nhead) * src_type(.5);
tmp(tmp.size()-nhead) = tmp(nhead);
}
}
}else{
tmp = src;
}
inv( &dst[0],&tmp[0], nfft);
}else{
inv( &dst[0],&src[0], nfft);
}
}
template <typename _Output>
inline
void inv( std::vector<_Output> & dst, const std::vector<Complex> & src,Index nfft=-1)
{
if (nfft<1)
nfft = ( NumTraits<_Output>::IsComplex == 0 && HasFlag(HalfSpectrum) ) ? 2*(src.size()-1) : src.size();
dst.resize( nfft );
inv( &dst[0],&src[0],nfft);
}
/*
// TODO: multi-dimensional FFTs
inline
void inv2(Complex * dst, const Complex * src, int n0,int n1)
{
m_impl.inv2(dst,src,n0,n1);
if ( HasFlag( Unscaled ) == false)
scale(dst,1./(n0*n1),n0*n1);
}
*/
inline
impl_type & impl() {return m_impl;}
private:
template <typename T_Data>
inline
void scale(T_Data * x,Scalar s,Index nx)
{
#if 1
for (int k=0;k<nx;++k)
*x++ *= s;
#else
if ( ((ptrdiff_t)x) & 15 )
Matrix<T_Data, Dynamic, 1>::Map(x,nx) *= s;
else
Matrix<T_Data, Dynamic, 1>::MapAligned(x,nx) *= s;
//Matrix<T_Data, Dynamic, Dynamic>::Map(x,nx) * s;
#endif
}
inline
void ReflectSpectrum(Complex * freq, Index nfft)
{
// create the implicit right-half spectrum (conjugate-mirror of the left-half)
Index nhbins=(nfft>>1)+1;
for (Index k=nhbins;k < nfft; ++k )
freq[k] = conj(freq[nfft-k]);
}
impl_type m_impl;
int m_flag;
};
template<typename T_SrcMat,typename T_FftIfc>
template<typename T_DestMat> inline
void fft_fwd_proxy<T_SrcMat,T_FftIfc>::evalTo(T_DestMat& dst) const
{
m_ifc.fwd( dst, m_src, m_nfft);
}
template<typename T_SrcMat,typename T_FftIfc>
template<typename T_DestMat> inline
void fft_inv_proxy<T_SrcMat,T_FftIfc>::evalTo(T_DestMat& dst) const
{
m_ifc.inv( dst, m_src, m_nfft);
}
}
#endif
/* vim: set filetype=cpp et sw=2 ts=2 ai: */