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419 lines
14 KiB
419 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 the mozilla.org home page |
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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 (xxxp://www.fftw.org) : faster, GPL -- incompatible with Eigen in LGPL form, bigger code size. |
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* - MKL (xxxp://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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#include "../../Eigen/src/Core/util/DisableStupidWarnings.h" |
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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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}; |
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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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}; |
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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 ComplexDerived::RealScalar real_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 ) )*real_type(.5); |
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}else{ // expanding -- split the old Nyquist bin into two halves |
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tmp(nhead) = src(nhead) * real_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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#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h" |
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#endif
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