add vcglib
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// 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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namespace Eigen {
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namespace internal {
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// FFTW uses non-const arguments
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// so we must use ugly const_cast calls for all the args it uses
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//
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// This should be safe as long as
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// 1. we use FFTW_ESTIMATE for all our planning
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// see the FFTW docs section 4.3.2 "Planner Flags"
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// 2. fftw_complex is compatible with std::complex
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// This assumes std::complex<T> layout is array of size 2 with real,imag
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template <typename T>
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inline
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T * fftw_cast(const T* p)
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{
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return const_cast<T*>( p);
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}
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inline
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fftw_complex * fftw_cast( const std::complex<double> * p)
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{
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return const_cast<fftw_complex*>( reinterpret_cast<const fftw_complex*>(p) );
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}
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inline
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fftwf_complex * fftw_cast( const std::complex<float> * p)
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{
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return const_cast<fftwf_complex*>( reinterpret_cast<const fftwf_complex*>(p) );
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}
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inline
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fftwl_complex * fftw_cast( const std::complex<long double> * p)
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{
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return const_cast<fftwl_complex*>( reinterpret_cast<const fftwl_complex*>(p) );
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}
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template <typename T>
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struct fftw_plan {};
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template <>
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struct fftw_plan<float>
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{
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typedef float scalar_type;
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typedef fftwf_complex complex_type;
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fftwf_plan m_plan;
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fftw_plan() :m_plan(NULL) {}
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~fftw_plan() {if (m_plan) fftwf_destroy_plan(m_plan);}
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inline
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void fwd(complex_type * dst,complex_type * src,int nfft) {
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if (m_plan==NULL) m_plan = fftwf_plan_dft_1d(nfft,src,dst, FFTW_FORWARD, FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
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fftwf_execute_dft( m_plan, src,dst);
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}
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inline
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void inv(complex_type * dst,complex_type * src,int nfft) {
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if (m_plan==NULL) m_plan = fftwf_plan_dft_1d(nfft,src,dst, FFTW_BACKWARD , FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
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fftwf_execute_dft( m_plan, src,dst);
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}
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inline
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void fwd(complex_type * dst,scalar_type * src,int nfft) {
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if (m_plan==NULL) m_plan = fftwf_plan_dft_r2c_1d(nfft,src,dst,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
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fftwf_execute_dft_r2c( m_plan,src,dst);
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}
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inline
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void inv(scalar_type * dst,complex_type * src,int nfft) {
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if (m_plan==NULL)
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m_plan = fftwf_plan_dft_c2r_1d(nfft,src,dst,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
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fftwf_execute_dft_c2r( m_plan, src,dst);
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}
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inline
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void fwd2( complex_type * dst,complex_type * src,int n0,int n1) {
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if (m_plan==NULL) m_plan = fftwf_plan_dft_2d(n0,n1,src,dst,FFTW_FORWARD,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
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fftwf_execute_dft( m_plan, src,dst);
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}
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inline
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void inv2( complex_type * dst,complex_type * src,int n0,int n1) {
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if (m_plan==NULL) m_plan = fftwf_plan_dft_2d(n0,n1,src,dst,FFTW_BACKWARD,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
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fftwf_execute_dft( m_plan, src,dst);
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}
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};
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template <>
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struct fftw_plan<double>
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{
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typedef double scalar_type;
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typedef fftw_complex complex_type;
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::fftw_plan m_plan;
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fftw_plan() :m_plan(NULL) {}
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~fftw_plan() {if (m_plan) fftw_destroy_plan(m_plan);}
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inline
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void fwd(complex_type * dst,complex_type * src,int nfft) {
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if (m_plan==NULL) m_plan = fftw_plan_dft_1d(nfft,src,dst, FFTW_FORWARD, FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
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fftw_execute_dft( m_plan, src,dst);
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}
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inline
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void inv(complex_type * dst,complex_type * src,int nfft) {
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if (m_plan==NULL) m_plan = fftw_plan_dft_1d(nfft,src,dst, FFTW_BACKWARD , FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
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fftw_execute_dft( m_plan, src,dst);
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}
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inline
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void fwd(complex_type * dst,scalar_type * src,int nfft) {
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if (m_plan==NULL) m_plan = fftw_plan_dft_r2c_1d(nfft,src,dst,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
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fftw_execute_dft_r2c( m_plan,src,dst);
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}
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inline
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void inv(scalar_type * dst,complex_type * src,int nfft) {
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if (m_plan==NULL)
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m_plan = fftw_plan_dft_c2r_1d(nfft,src,dst,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
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fftw_execute_dft_c2r( m_plan, src,dst);
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}
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inline
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void fwd2( complex_type * dst,complex_type * src,int n0,int n1) {
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if (m_plan==NULL) m_plan = fftw_plan_dft_2d(n0,n1,src,dst,FFTW_FORWARD,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
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fftw_execute_dft( m_plan, src,dst);
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}
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inline
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void inv2( complex_type * dst,complex_type * src,int n0,int n1) {
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if (m_plan==NULL) m_plan = fftw_plan_dft_2d(n0,n1,src,dst,FFTW_BACKWARD,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
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fftw_execute_dft( m_plan, src,dst);
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}
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};
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template <>
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struct fftw_plan<long double>
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{
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typedef long double scalar_type;
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typedef fftwl_complex complex_type;
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fftwl_plan m_plan;
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fftw_plan() :m_plan(NULL) {}
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~fftw_plan() {if (m_plan) fftwl_destroy_plan(m_plan);}
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inline
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void fwd(complex_type * dst,complex_type * src,int nfft) {
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if (m_plan==NULL) m_plan = fftwl_plan_dft_1d(nfft,src,dst, FFTW_FORWARD, FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
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fftwl_execute_dft( m_plan, src,dst);
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}
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inline
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void inv(complex_type * dst,complex_type * src,int nfft) {
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if (m_plan==NULL) m_plan = fftwl_plan_dft_1d(nfft,src,dst, FFTW_BACKWARD , FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
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fftwl_execute_dft( m_plan, src,dst);
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}
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inline
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void fwd(complex_type * dst,scalar_type * src,int nfft) {
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if (m_plan==NULL) m_plan = fftwl_plan_dft_r2c_1d(nfft,src,dst,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
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fftwl_execute_dft_r2c( m_plan,src,dst);
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}
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inline
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void inv(scalar_type * dst,complex_type * src,int nfft) {
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if (m_plan==NULL)
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m_plan = fftwl_plan_dft_c2r_1d(nfft,src,dst,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
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fftwl_execute_dft_c2r( m_plan, src,dst);
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}
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inline
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void fwd2( complex_type * dst,complex_type * src,int n0,int n1) {
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if (m_plan==NULL) m_plan = fftwl_plan_dft_2d(n0,n1,src,dst,FFTW_FORWARD,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
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fftwl_execute_dft( m_plan, src,dst);
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}
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inline
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void inv2( complex_type * dst,complex_type * src,int n0,int n1) {
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if (m_plan==NULL) m_plan = fftwl_plan_dft_2d(n0,n1,src,dst,FFTW_BACKWARD,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
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fftwl_execute_dft( m_plan, src,dst);
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}
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};
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template <typename _Scalar>
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struct fftw_impl
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{
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typedef _Scalar Scalar;
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typedef std::complex<Scalar> Complex;
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inline
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void clear()
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{
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m_plans.clear();
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}
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// complex-to-complex forward FFT
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inline
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void fwd( Complex * dst,const Complex *src,int nfft)
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{
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get_plan(nfft,false,dst,src).fwd(fftw_cast(dst), fftw_cast(src),nfft );
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}
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// real-to-complex forward FFT
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inline
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void fwd( Complex * dst,const Scalar * src,int nfft)
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{
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get_plan(nfft,false,dst,src).fwd(fftw_cast(dst), fftw_cast(src) ,nfft);
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}
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// 2-d complex-to-complex
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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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get_plan(n0,n1,false,dst,src).fwd2(fftw_cast(dst), fftw_cast(src) ,n0,n1);
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}
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// inverse complex-to-complex
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inline
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void inv(Complex * dst,const Complex *src,int nfft)
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{
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get_plan(nfft,true,dst,src).inv(fftw_cast(dst), fftw_cast(src),nfft );
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}
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// half-complex to scalar
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inline
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void inv( Scalar * dst,const Complex * src,int nfft)
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{
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get_plan(nfft,true,dst,src).inv(fftw_cast(dst), fftw_cast(src),nfft );
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}
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// 2-d complex-to-complex
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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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get_plan(n0,n1,true,dst,src).inv2(fftw_cast(dst), fftw_cast(src) ,n0,n1);
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}
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protected:
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typedef fftw_plan<Scalar> PlanData;
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typedef Eigen::numext::int64_t int64_t;
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typedef std::map<int64_t,PlanData> PlanMap;
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PlanMap m_plans;
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inline
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PlanData & get_plan(int nfft,bool inverse,void * dst,const void * src)
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{
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bool inplace = (dst==src);
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bool aligned = ( (reinterpret_cast<size_t>(src)&15) | (reinterpret_cast<size_t>(dst)&15) ) == 0;
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int64_t key = ( (nfft<<3 ) | (inverse<<2) | (inplace<<1) | aligned ) << 1;
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return m_plans[key];
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}
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inline
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PlanData & get_plan(int n0,int n1,bool inverse,void * dst,const void * src)
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{
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bool inplace = (dst==src);
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bool aligned = ( (reinterpret_cast<size_t>(src)&15) | (reinterpret_cast<size_t>(dst)&15) ) == 0;
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int64_t key = ( ( (((int64_t)n0) << 30)|(n1<<3 ) | (inverse<<2) | (inplace<<1) | aligned ) << 1 ) + 1;
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return m_plans[key];
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}
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};
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} // end namespace internal
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} // end namespace Eigen
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@@ -0,0 +1,449 @@
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// 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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namespace Eigen {
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namespace internal {
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// This FFT implementation was derived from kissfft xxxp:sourceforge.net/projects/kissfft
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// Copyright 2003-2009 Mark Borgerding
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template <typename _Scalar>
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struct kiss_cpx_fft
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{
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typedef _Scalar Scalar;
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typedef std::complex<Scalar> Complex;
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std::vector<Complex> m_twiddles;
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std::vector<int> m_stageRadix;
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std::vector<int> m_stageRemainder;
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std::vector<Complex> m_scratchBuf;
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bool m_inverse;
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inline void make_twiddles(int nfft, bool inverse)
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{
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using numext::sin;
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using numext::cos;
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m_inverse = inverse;
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m_twiddles.resize(nfft);
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double phinc = 0.25 * double(EIGEN_PI) / nfft;
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Scalar flip = inverse ? Scalar(1) : Scalar(-1);
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m_twiddles[0] = Complex(Scalar(1), Scalar(0));
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if ((nfft&1)==0)
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m_twiddles[nfft/2] = Complex(Scalar(-1), Scalar(0));
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int i=1;
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for (;i*8<nfft;++i)
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{
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Scalar c = Scalar(cos(i*8*phinc));
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Scalar s = Scalar(sin(i*8*phinc));
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m_twiddles[i] = Complex(c, s*flip);
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m_twiddles[nfft-i] = Complex(c, -s*flip);
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}
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for (;i*4<nfft;++i)
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{
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Scalar c = Scalar(cos((2*nfft-8*i)*phinc));
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Scalar s = Scalar(sin((2*nfft-8*i)*phinc));
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m_twiddles[i] = Complex(s, c*flip);
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m_twiddles[nfft-i] = Complex(s, -c*flip);
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}
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for (;i*8<3*nfft;++i)
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{
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Scalar c = Scalar(cos((8*i-2*nfft)*phinc));
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Scalar s = Scalar(sin((8*i-2*nfft)*phinc));
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m_twiddles[i] = Complex(-s, c*flip);
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m_twiddles[nfft-i] = Complex(-s, -c*flip);
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}
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for (;i*2<nfft;++i)
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{
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Scalar c = Scalar(cos((4*nfft-8*i)*phinc));
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Scalar s = Scalar(sin((4*nfft-8*i)*phinc));
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m_twiddles[i] = Complex(-c, s*flip);
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m_twiddles[nfft-i] = Complex(-c, -s*flip);
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}
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}
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void factorize(int nfft)
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{
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//start factoring out 4's, then 2's, then 3,5,7,9,...
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int n= nfft;
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int p=4;
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do {
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while (n % p) {
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switch (p) {
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case 4: p = 2; break;
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case 2: p = 3; break;
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default: p += 2; break;
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}
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if (p*p>n)
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p=n;// impossible to have a factor > sqrt(n)
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}
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n /= p;
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m_stageRadix.push_back(p);
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m_stageRemainder.push_back(n);
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if ( p > 5 )
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m_scratchBuf.resize(p); // scratchbuf will be needed in bfly_generic
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}while(n>1);
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}
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template <typename _Src>
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inline
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void work( int stage,Complex * xout, const _Src * xin, size_t fstride,size_t in_stride)
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{
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int p = m_stageRadix[stage];
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int m = m_stageRemainder[stage];
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Complex * Fout_beg = xout;
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Complex * Fout_end = xout + p*m;
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if (m>1) {
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do{
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// recursive call:
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// DFT of size m*p performed by doing
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// p instances of smaller DFTs of size m,
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// each one takes a decimated version of the input
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work(stage+1, xout , xin, fstride*p,in_stride);
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xin += fstride*in_stride;
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}while( (xout += m) != Fout_end );
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}else{
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do{
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*xout = *xin;
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xin += fstride*in_stride;
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}while(++xout != Fout_end );
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}
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xout=Fout_beg;
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// recombine the p smaller DFTs
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switch (p) {
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case 2: bfly2(xout,fstride,m); break;
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case 3: bfly3(xout,fstride,m); break;
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case 4: bfly4(xout,fstride,m); break;
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case 5: bfly5(xout,fstride,m); break;
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default: bfly_generic(xout,fstride,m,p); break;
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}
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}
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inline
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void bfly2( Complex * Fout, const size_t fstride, int m)
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{
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for (int k=0;k<m;++k) {
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Complex t = Fout[m+k] * m_twiddles[k*fstride];
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Fout[m+k] = Fout[k] - t;
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Fout[k] += t;
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}
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}
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inline
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void bfly4( Complex * Fout, const size_t fstride, const size_t m)
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{
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Complex scratch[6];
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int negative_if_inverse = m_inverse * -2 +1;
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for (size_t k=0;k<m;++k) {
|
||||
scratch[0] = Fout[k+m] * m_twiddles[k*fstride];
|
||||
scratch[1] = Fout[k+2*m] * m_twiddles[k*fstride*2];
|
||||
scratch[2] = Fout[k+3*m] * m_twiddles[k*fstride*3];
|
||||
scratch[5] = Fout[k] - scratch[1];
|
||||
|
||||
Fout[k] += scratch[1];
|
||||
scratch[3] = scratch[0] + scratch[2];
|
||||
scratch[4] = scratch[0] - scratch[2];
|
||||
scratch[4] = Complex( scratch[4].imag()*negative_if_inverse , -scratch[4].real()* negative_if_inverse );
|
||||
|
||||
Fout[k+2*m] = Fout[k] - scratch[3];
|
||||
Fout[k] += scratch[3];
|
||||
Fout[k+m] = scratch[5] + scratch[4];
|
||||
Fout[k+3*m] = scratch[5] - scratch[4];
|
||||
}
|
||||
}
|
||||
|
||||
inline
|
||||
void bfly3( Complex * Fout, const size_t fstride, const size_t m)
|
||||
{
|
||||
size_t k=m;
|
||||
const size_t m2 = 2*m;
|
||||
Complex *tw1,*tw2;
|
||||
Complex scratch[5];
|
||||
Complex epi3;
|
||||
epi3 = m_twiddles[fstride*m];
|
||||
|
||||
tw1=tw2=&m_twiddles[0];
|
||||
|
||||
do{
|
||||
scratch[1]=Fout[m] * *tw1;
|
||||
scratch[2]=Fout[m2] * *tw2;
|
||||
|
||||
scratch[3]=scratch[1]+scratch[2];
|
||||
scratch[0]=scratch[1]-scratch[2];
|
||||
tw1 += fstride;
|
||||
tw2 += fstride*2;
|
||||
Fout[m] = Complex( Fout->real() - Scalar(.5)*scratch[3].real() , Fout->imag() - Scalar(.5)*scratch[3].imag() );
|
||||
scratch[0] *= epi3.imag();
|
||||
*Fout += scratch[3];
|
||||
Fout[m2] = Complex( Fout[m].real() + scratch[0].imag() , Fout[m].imag() - scratch[0].real() );
|
||||
Fout[m] += Complex( -scratch[0].imag(),scratch[0].real() );
|
||||
++Fout;
|
||||
}while(--k);
|
||||
}
|
||||
|
||||
inline
|
||||
void bfly5( Complex * Fout, const size_t fstride, const size_t m)
|
||||
{
|
||||
Complex *Fout0,*Fout1,*Fout2,*Fout3,*Fout4;
|
||||
size_t u;
|
||||
Complex scratch[13];
|
||||
Complex * twiddles = &m_twiddles[0];
|
||||
Complex *tw;
|
||||
Complex ya,yb;
|
||||
ya = twiddles[fstride*m];
|
||||
yb = twiddles[fstride*2*m];
|
||||
|
||||
Fout0=Fout;
|
||||
Fout1=Fout0+m;
|
||||
Fout2=Fout0+2*m;
|
||||
Fout3=Fout0+3*m;
|
||||
Fout4=Fout0+4*m;
|
||||
|
||||
tw=twiddles;
|
||||
for ( u=0; u<m; ++u ) {
|
||||
scratch[0] = *Fout0;
|
||||
|
||||
scratch[1] = *Fout1 * tw[u*fstride];
|
||||
scratch[2] = *Fout2 * tw[2*u*fstride];
|
||||
scratch[3] = *Fout3 * tw[3*u*fstride];
|
||||
scratch[4] = *Fout4 * tw[4*u*fstride];
|
||||
|
||||
scratch[7] = scratch[1] + scratch[4];
|
||||
scratch[10] = scratch[1] - scratch[4];
|
||||
scratch[8] = scratch[2] + scratch[3];
|
||||
scratch[9] = scratch[2] - scratch[3];
|
||||
|
||||
*Fout0 += scratch[7];
|
||||
*Fout0 += scratch[8];
|
||||
|
||||
scratch[5] = scratch[0] + Complex(
|
||||
(scratch[7].real()*ya.real() ) + (scratch[8].real() *yb.real() ),
|
||||
(scratch[7].imag()*ya.real()) + (scratch[8].imag()*yb.real())
|
||||
);
|
||||
|
||||
scratch[6] = Complex(
|
||||
(scratch[10].imag()*ya.imag()) + (scratch[9].imag()*yb.imag()),
|
||||
-(scratch[10].real()*ya.imag()) - (scratch[9].real()*yb.imag())
|
||||
);
|
||||
|
||||
*Fout1 = scratch[5] - scratch[6];
|
||||
*Fout4 = scratch[5] + scratch[6];
|
||||
|
||||
scratch[11] = scratch[0] +
|
||||
Complex(
|
||||
(scratch[7].real()*yb.real()) + (scratch[8].real()*ya.real()),
|
||||
(scratch[7].imag()*yb.real()) + (scratch[8].imag()*ya.real())
|
||||
);
|
||||
|
||||
scratch[12] = Complex(
|
||||
-(scratch[10].imag()*yb.imag()) + (scratch[9].imag()*ya.imag()),
|
||||
(scratch[10].real()*yb.imag()) - (scratch[9].real()*ya.imag())
|
||||
);
|
||||
|
||||
*Fout2=scratch[11]+scratch[12];
|
||||
*Fout3=scratch[11]-scratch[12];
|
||||
|
||||
++Fout0;++Fout1;++Fout2;++Fout3;++Fout4;
|
||||
}
|
||||
}
|
||||
|
||||
/* perform the butterfly for one stage of a mixed radix FFT */
|
||||
inline
|
||||
void bfly_generic(
|
||||
Complex * Fout,
|
||||
const size_t fstride,
|
||||
int m,
|
||||
int p
|
||||
)
|
||||
{
|
||||
int u,k,q1,q;
|
||||
Complex * twiddles = &m_twiddles[0];
|
||||
Complex t;
|
||||
int Norig = static_cast<int>(m_twiddles.size());
|
||||
Complex * scratchbuf = &m_scratchBuf[0];
|
||||
|
||||
for ( u=0; u<m; ++u ) {
|
||||
k=u;
|
||||
for ( q1=0 ; q1<p ; ++q1 ) {
|
||||
scratchbuf[q1] = Fout[ k ];
|
||||
k += m;
|
||||
}
|
||||
|
||||
k=u;
|
||||
for ( q1=0 ; q1<p ; ++q1 ) {
|
||||
int twidx=0;
|
||||
Fout[ k ] = scratchbuf[0];
|
||||
for (q=1;q<p;++q ) {
|
||||
twidx += static_cast<int>(fstride) * k;
|
||||
if (twidx>=Norig) twidx-=Norig;
|
||||
t=scratchbuf[q] * twiddles[twidx];
|
||||
Fout[ k ] += t;
|
||||
}
|
||||
k += m;
|
||||
}
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
template <typename _Scalar>
|
||||
struct kissfft_impl
|
||||
{
|
||||
typedef _Scalar Scalar;
|
||||
typedef std::complex<Scalar> Complex;
|
||||
|
||||
void clear()
|
||||
{
|
||||
m_plans.clear();
|
||||
m_realTwiddles.clear();
|
||||
}
|
||||
|
||||
inline
|
||||
void fwd( Complex * dst,const Complex *src,int nfft)
|
||||
{
|
||||
get_plan(nfft,false).work(0, dst, src, 1,1);
|
||||
}
|
||||
|
||||
inline
|
||||
void fwd2( Complex * dst,const Complex *src,int n0,int n1)
|
||||
{
|
||||
EIGEN_UNUSED_VARIABLE(dst);
|
||||
EIGEN_UNUSED_VARIABLE(src);
|
||||
EIGEN_UNUSED_VARIABLE(n0);
|
||||
EIGEN_UNUSED_VARIABLE(n1);
|
||||
}
|
||||
|
||||
inline
|
||||
void inv2( Complex * dst,const Complex *src,int n0,int n1)
|
||||
{
|
||||
EIGEN_UNUSED_VARIABLE(dst);
|
||||
EIGEN_UNUSED_VARIABLE(src);
|
||||
EIGEN_UNUSED_VARIABLE(n0);
|
||||
EIGEN_UNUSED_VARIABLE(n1);
|
||||
}
|
||||
|
||||
// real-to-complex forward FFT
|
||||
// perform two FFTs of src even and src odd
|
||||
// then twiddle to recombine them into the half-spectrum format
|
||||
// then fill in the conjugate symmetric half
|
||||
inline
|
||||
void fwd( Complex * dst,const Scalar * src,int nfft)
|
||||
{
|
||||
if ( nfft&3 ) {
|
||||
// use generic mode for odd
|
||||
m_tmpBuf1.resize(nfft);
|
||||
get_plan(nfft,false).work(0, &m_tmpBuf1[0], src, 1,1);
|
||||
std::copy(m_tmpBuf1.begin(),m_tmpBuf1.begin()+(nfft>>1)+1,dst );
|
||||
}else{
|
||||
int ncfft = nfft>>1;
|
||||
int ncfft2 = nfft>>2;
|
||||
Complex * rtw = real_twiddles(ncfft2);
|
||||
|
||||
// use optimized mode for even real
|
||||
fwd( dst, reinterpret_cast<const Complex*> (src), ncfft);
|
||||
Complex dc(dst[0].real() + dst[0].imag());
|
||||
Complex nyquist(dst[0].real() - dst[0].imag());
|
||||
int k;
|
||||
for ( k=1;k <= ncfft2 ; ++k ) {
|
||||
Complex fpk = dst[k];
|
||||
Complex fpnk = conj(dst[ncfft-k]);
|
||||
Complex f1k = fpk + fpnk;
|
||||
Complex f2k = fpk - fpnk;
|
||||
Complex tw= f2k * rtw[k-1];
|
||||
dst[k] = (f1k + tw) * Scalar(.5);
|
||||
dst[ncfft-k] = conj(f1k -tw)*Scalar(.5);
|
||||
}
|
||||
dst[0] = dc;
|
||||
dst[ncfft] = nyquist;
|
||||
}
|
||||
}
|
||||
|
||||
// inverse complex-to-complex
|
||||
inline
|
||||
void inv(Complex * dst,const Complex *src,int nfft)
|
||||
{
|
||||
get_plan(nfft,true).work(0, dst, src, 1,1);
|
||||
}
|
||||
|
||||
// half-complex to scalar
|
||||
inline
|
||||
void inv( Scalar * dst,const Complex * src,int nfft)
|
||||
{
|
||||
if (nfft&3) {
|
||||
m_tmpBuf1.resize(nfft);
|
||||
m_tmpBuf2.resize(nfft);
|
||||
std::copy(src,src+(nfft>>1)+1,m_tmpBuf1.begin() );
|
||||
for (int k=1;k<(nfft>>1)+1;++k)
|
||||
m_tmpBuf1[nfft-k] = conj(m_tmpBuf1[k]);
|
||||
inv(&m_tmpBuf2[0],&m_tmpBuf1[0],nfft);
|
||||
for (int k=0;k<nfft;++k)
|
||||
dst[k] = m_tmpBuf2[k].real();
|
||||
}else{
|
||||
// optimized version for multiple of 4
|
||||
int ncfft = nfft>>1;
|
||||
int ncfft2 = nfft>>2;
|
||||
Complex * rtw = real_twiddles(ncfft2);
|
||||
m_tmpBuf1.resize(ncfft);
|
||||
m_tmpBuf1[0] = Complex( src[0].real() + src[ncfft].real(), src[0].real() - src[ncfft].real() );
|
||||
for (int k = 1; k <= ncfft / 2; ++k) {
|
||||
Complex fk = src[k];
|
||||
Complex fnkc = conj(src[ncfft-k]);
|
||||
Complex fek = fk + fnkc;
|
||||
Complex tmp = fk - fnkc;
|
||||
Complex fok = tmp * conj(rtw[k-1]);
|
||||
m_tmpBuf1[k] = fek + fok;
|
||||
m_tmpBuf1[ncfft-k] = conj(fek - fok);
|
||||
}
|
||||
get_plan(ncfft,true).work(0, reinterpret_cast<Complex*>(dst), &m_tmpBuf1[0], 1,1);
|
||||
}
|
||||
}
|
||||
|
||||
protected:
|
||||
typedef kiss_cpx_fft<Scalar> PlanData;
|
||||
typedef std::map<int,PlanData> PlanMap;
|
||||
|
||||
PlanMap m_plans;
|
||||
std::map<int, std::vector<Complex> > m_realTwiddles;
|
||||
std::vector<Complex> m_tmpBuf1;
|
||||
std::vector<Complex> m_tmpBuf2;
|
||||
|
||||
inline
|
||||
int PlanKey(int nfft, bool isinverse) const { return (nfft<<1) | int(isinverse); }
|
||||
|
||||
inline
|
||||
PlanData & get_plan(int nfft, bool inverse)
|
||||
{
|
||||
// TODO look for PlanKey(nfft, ! inverse) and conjugate the twiddles
|
||||
PlanData & pd = m_plans[ PlanKey(nfft,inverse) ];
|
||||
if ( pd.m_twiddles.size() == 0 ) {
|
||||
pd.make_twiddles(nfft,inverse);
|
||||
pd.factorize(nfft);
|
||||
}
|
||||
return pd;
|
||||
}
|
||||
|
||||
inline
|
||||
Complex * real_twiddles(int ncfft2)
|
||||
{
|
||||
using std::acos;
|
||||
std::vector<Complex> & twidref = m_realTwiddles[ncfft2];// creates new if not there
|
||||
if ( (int)twidref.size() != ncfft2 ) {
|
||||
twidref.resize(ncfft2);
|
||||
int ncfft= ncfft2<<1;
|
||||
Scalar pi = acos( Scalar(-1) );
|
||||
for (int k=1;k<=ncfft2;++k)
|
||||
twidref[k-1] = exp( Complex(0,-pi * (Scalar(k) / ncfft + Scalar(.5)) ) );
|
||||
}
|
||||
return &twidref[0];
|
||||
}
|
||||
};
|
||||
|
||||
} // end namespace internal
|
||||
|
||||
} // end namespace Eigen
|
||||
Reference in new issue
Block a user