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eigen/unsupported/Eigen/FFT

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Mark Borgerding mark a borgerding net
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#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>
namespace Eigen {
# include "src/FFT/ei_fftw_impl.h"
//template <typename T> typedef struct ei_fftw_impl default_fft_impl; this does not work
template <typename T> struct default_fft_impl : public ei_fftw_impl<T> {};
}
#elif defined EIGEN_MKL_DEFAULT
// TODO
// intel Math Kernel Library: fastest, commercial -- may be incompatible with Eigen in GPL form
namespace Eigen {
# include "src/FFT/ei_imklfft_impl.h"
template <typename T> struct default_fft_impl : public ei_imklfft_impl {};
}
#else
// ei_kissfft_impl: small, free, reasonably efficient default, derived from kissfft
//
namespace Eigen {
# include "src/FFT/ei_kissfft_impl.h"
template <typename T>
struct default_fft_impl : public ei_kissfft_impl<T> {};
}
#endif
namespace Eigen {
template <typename _Scalar,
typename _Impl=default_fft_impl<_Scalar> >
class FFT
{
public:
typedef _Impl impl_type;
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, int nfft)
{
m_impl.fwd(dst,src,nfft);
if ( HasFlag(HalfSpectrum) == false)
ReflectSpectrum(dst,nfft);
}
inline
void fwd( Complex * dst, const Complex * src, int nfft)
{
m_impl.fwd(dst,src,nfft);
}
inline
void fwd2(Complex * dst, const Complex * src, int nrows,int ncols)
{
m_impl.fwd2(dst,src,nrows,ncols);
}
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);
else
dst->resize(src.size());
fwd(&(*dst)[0],&src[0],static_cast<int>(src.size()));
}
template<typename InputDerived, typename ComplexDerived>
inline
void fwd( MatrixBase<ComplexDerived> * dst, const MatrixBase<InputDerived> & src)
{
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((ei_is_same_type<typename ComplexDerived::Scalar, Complex>::ret),
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 ( NumTraits< typename InputDerived::Scalar >::IsComplex == 0 && HasFlag(HalfSpectrum) )
dst->derived().resize( (src.size()>>1)+1);
else
dst->derived().resize(src.size());
if (src.stride() != 1) {
Matrix<typename InputDerived::Scalar,1,Dynamic> tmp = src;
fwd( &(*dst)[0],&tmp[0],src.size() );
}else{
fwd( &(*dst)[0],&src[0],src.size() );
}
}
inline
void inv( Complex * dst, const Complex * src, int nfft)
{
m_impl.inv( dst,src,nfft );
if ( HasFlag( Unscaled ) == false)
scale(dst,1./nfft,nfft);
}
inline
void inv( Scalar * dst, const Complex * src, int nfft)
{
m_impl.inv( dst,src,nfft );
if ( HasFlag( Unscaled ) == false)
scale(dst,1./nfft,nfft);
}
template<typename OutputDerived, typename ComplexDerived>
inline
void inv( MatrixBase<OutputDerived> * dst, const MatrixBase<ComplexDerived> & src)
{
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((ei_is_same_type<typename ComplexDerived::Scalar, Complex>::ret),
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)
int nfft = src.size();
int nout = HasFlag(HalfSpectrum) ? ((nfft>>1)+1) : nfft;
dst->derived().resize( nout );
if (src.stride() != 1) {
Matrix<typename ComplexDerived::Scalar,1,Dynamic> 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)
{
if ( NumTraits<_Output>::IsComplex == 0 && HasFlag(HalfSpectrum) )
dst->resize( 2*(src.size()-1) );
else
dst->resize( src.size() );
inv( &(*dst)[0],&src[0],static_cast<int>(dst->size()) );
}
inline
void inv2(Complex * dst, const Complex * src, int nrows,int ncols)
{
m_impl.inv2(dst,src,nrows,ncols);
if ( HasFlag( Unscaled ) == false)
scale(dst,1./(nrows*ncols),nrows*ncols);
}
// TODO: multi-dimensional FFTs
inline
impl_type & impl() {return m_impl;}
private:
template <typename T_Data>
inline
void scale(T_Data * x,Scalar s,int 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,int nfft)
{
// create the implicit right-half spectrum (conjugate-mirror of the left-half)
int nhbins=(nfft>>1)+1;
for (int k=nhbins;k < nfft; ++k )
freq[k] = conj(freq[nfft-k]);
}
impl_type m_impl;
int m_flag;
};
}
#endif
/* vim: set filetype=cpp et sw=2 ts=2 ai: */
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