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