unsupported/Eigen/FFT

// 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, either using a built-in implementation
  * or as a frontend to various FFT libraries.
  *
  * The build-in implementation is based on kissfft. It is a small, free, and
  * reasonably efficient default.
  *
  * There are currently two frontends:
  *
  * - fftw (http://www.fftw.org) : faster, GPL -- incompatible with Eigen in LGPL form, bigger code size.
  * - MLK (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);
    }

    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());
      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 );
        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()) );
    }

    // TODO: multi-dimensional FFTs
    
    // TODO: handle Eigen MatrixBase
     // ---> i added fwd and inv specializations above + unit test, is this enough? (bjacob)

    inline
    impl_type & impl() {return m_impl;}
  private:

    template <typename _It,typename _Val>
    inline
    void scale(_It x,_Val s,int nx)
    {
      for (int k=0;k<nx;++k)
        *x++ *= s;
    }

    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: */