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265 lines
8.9 KiB
265 lines
8.9 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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#include "main.h"
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#include <unsupported/Eigen/FFT>
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template <typename T>
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std::complex<T> RandomCpx() { return std::complex<T>( (T)(rand()/(T)RAND_MAX - .5), (T)(rand()/(T)RAND_MAX - .5) ); }
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using namespace std;
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using namespace Eigen;
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float norm(float x) {return x*x;}
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double norm(double x) {return x*x;}
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long double norm(long double x) {return x*x;}
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template < typename T>
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complex<long double> promote(complex<T> x) { return complex<long double>(x.real(),x.imag()); }
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complex<long double> promote(float x) { return complex<long double>( x); }
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complex<long double> promote(double x) { return complex<long double>( x); }
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complex<long double> promote(long double x) { return complex<long double>( x); }
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template <typename VT1,typename VT2>
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long double fft_rmse( const VT1 & fftbuf,const VT2 & timebuf)
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{
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long double totalpower=0;
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long double difpower=0;
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long double pi = acos((long double)-1 );
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for (size_t k0=0;k0<(size_t)fftbuf.size();++k0) {
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complex<long double> acc = 0;
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long double phinc = -2.*k0* pi / timebuf.size();
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for (size_t k1=0;k1<(size_t)timebuf.size();++k1) {
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acc += promote( timebuf[k1] ) * exp( complex<long double>(0,k1*phinc) );
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}
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totalpower += norm(acc);
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complex<long double> x = promote(fftbuf[k0]);
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complex<long double> dif = acc - x;
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difpower += norm(dif);
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//cerr << k0 << "\t" << acc << "\t" << x << "\t" << sqrt(norm(dif)) << endl;
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}
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cerr << "rmse:" << sqrt(difpower/totalpower) << endl;
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return sqrt(difpower/totalpower);
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}
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template <typename VT1,typename VT2>
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long double dif_rmse( const VT1 buf1,const VT2 buf2)
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{
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long double totalpower=0;
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long double difpower=0;
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size_t n = (min)( buf1.size(),buf2.size() );
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for (size_t k=0;k<n;++k) {
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totalpower += (norm( buf1[k] ) + norm(buf2[k]) )/2.;
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difpower += norm(buf1[k] - buf2[k]);
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}
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return sqrt(difpower/totalpower);
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}
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enum { StdVectorContainer, EigenVectorContainer };
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template<int Container, typename Scalar> struct VectorType;
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template<typename Scalar> struct VectorType<StdVectorContainer,Scalar>
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{
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typedef vector<Scalar> type;
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};
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template<typename Scalar> struct VectorType<EigenVectorContainer,Scalar>
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{
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typedef Matrix<Scalar,Dynamic,1> type;
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};
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template <int Container, typename T>
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void test_scalar_generic(int nfft)
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{
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typedef typename FFT<T>::Complex Complex;
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typedef typename FFT<T>::Scalar Scalar;
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typedef typename VectorType<Container,Scalar>::type ScalarVector;
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typedef typename VectorType<Container,Complex>::type ComplexVector;
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FFT<T> fft;
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ScalarVector tbuf(nfft);
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ComplexVector freqBuf;
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for (int k=0;k<nfft;++k)
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tbuf[k]= (T)( rand()/(double)RAND_MAX - .5);
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// make sure it DOESN'T give the right full spectrum answer
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// if we've asked for half-spectrum
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fft.SetFlag(fft.HalfSpectrum );
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fft.fwd( freqBuf,tbuf);
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VERIFY((size_t)freqBuf.size() == (size_t)( (nfft>>1)+1) );
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VERIFY( fft_rmse(freqBuf,tbuf) < test_precision<T>() );// gross check
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fft.ClearFlag(fft.HalfSpectrum );
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fft.fwd( freqBuf,tbuf);
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VERIFY( (size_t)freqBuf.size() == (size_t)nfft);
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VERIFY( fft_rmse(freqBuf,tbuf) < test_precision<T>() );// gross check
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if (nfft&1)
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return; // odd FFTs get the wrong size inverse FFT
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ScalarVector tbuf2;
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fft.inv( tbuf2 , freqBuf);
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VERIFY( dif_rmse(tbuf,tbuf2) < test_precision<T>() );// gross check
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// verify that the Unscaled flag takes effect
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ScalarVector tbuf3;
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fft.SetFlag(fft.Unscaled);
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fft.inv( tbuf3 , freqBuf);
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for (int k=0;k<nfft;++k)
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tbuf3[k] *= T(1./nfft);
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//for (size_t i=0;i<(size_t) tbuf.size();++i)
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// cout << "freqBuf=" << freqBuf[i] << " in2=" << tbuf3[i] << " - in=" << tbuf[i] << " => " << (tbuf3[i] - tbuf[i] ) << endl;
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VERIFY( dif_rmse(tbuf,tbuf3) < test_precision<T>() );// gross check
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// verify that ClearFlag works
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fft.ClearFlag(fft.Unscaled);
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fft.inv( tbuf2 , freqBuf);
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VERIFY( dif_rmse(tbuf,tbuf2) < test_precision<T>() );// gross check
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}
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template <typename T>
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void test_scalar(int nfft)
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{
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test_scalar_generic<StdVectorContainer,T>(nfft);
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//test_scalar_generic<EigenVectorContainer,T>(nfft);
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}
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template <int Container, typename T>
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void test_complex_generic(int nfft)
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{
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typedef typename FFT<T>::Complex Complex;
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typedef typename VectorType<Container,Complex>::type ComplexVector;
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FFT<T> fft;
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ComplexVector inbuf(nfft);
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ComplexVector outbuf;
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ComplexVector buf3;
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for (int k=0;k<nfft;++k)
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inbuf[k]= Complex( (T)(rand()/(double)RAND_MAX - .5), (T)(rand()/(double)RAND_MAX - .5) );
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fft.fwd( outbuf , inbuf);
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VERIFY( fft_rmse(outbuf,inbuf) < test_precision<T>() );// gross check
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fft.inv( buf3 , outbuf);
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VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>() );// gross check
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// verify that the Unscaled flag takes effect
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ComplexVector buf4;
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fft.SetFlag(fft.Unscaled);
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fft.inv( buf4 , outbuf);
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for (int k=0;k<nfft;++k)
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buf4[k] *= T(1./nfft);
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VERIFY( dif_rmse(inbuf,buf4) < test_precision<T>() );// gross check
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// verify that ClearFlag works
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fft.ClearFlag(fft.Unscaled);
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fft.inv( buf3 , outbuf);
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VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>() );// gross check
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}
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template <typename T>
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void test_complex(int nfft)
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{
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test_complex_generic<StdVectorContainer,T>(nfft);
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test_complex_generic<EigenVectorContainer,T>(nfft);
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}
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/*
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template <typename T,int nrows,int ncols>
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void test_complex2d()
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{
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typedef typename Eigen::FFT<T>::Complex Complex;
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FFT<T> fft;
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Eigen::Matrix<Complex,nrows,ncols> src,src2,dst,dst2;
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src = Eigen::Matrix<Complex,nrows,ncols>::Random();
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//src = Eigen::Matrix<Complex,nrows,ncols>::Identity();
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for (int k=0;k<ncols;k++) {
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Eigen::Matrix<Complex,nrows,1> tmpOut;
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fft.fwd( tmpOut,src.col(k) );
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dst2.col(k) = tmpOut;
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}
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for (int k=0;k<nrows;k++) {
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Eigen::Matrix<Complex,1,ncols> tmpOut;
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fft.fwd( tmpOut, dst2.row(k) );
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dst2.row(k) = tmpOut;
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}
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fft.fwd2(dst.data(),src.data(),ncols,nrows);
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fft.inv2(src2.data(),dst.data(),ncols,nrows);
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VERIFY( (src-src2).norm() < test_precision<T>() );
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VERIFY( (dst-dst2).norm() < test_precision<T>() );
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}
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*/
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void test_return_by_value(int len)
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{
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VectorXf in;
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VectorXf in1;
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in.setRandom( len );
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VectorXcf out1,out2;
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FFT<float> fft;
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fft.SetFlag(fft.HalfSpectrum );
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fft.fwd(out1,in);
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out2 = fft.fwd(in);
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VERIFY( (out1-out2).norm() < test_precision<float>() );
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in1 = fft.inv(out1);
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VERIFY( (in1-in).norm() < test_precision<float>() );
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}
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void test_FFTW()
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{
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CALL_SUBTEST( test_return_by_value(32) );
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//CALL_SUBTEST( ( test_complex2d<float,4,8> () ) ); CALL_SUBTEST( ( test_complex2d<double,4,8> () ) );
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//CALL_SUBTEST( ( test_complex2d<long double,4,8> () ) );
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CALL_SUBTEST( test_complex<float>(32) ); CALL_SUBTEST( test_complex<double>(32) );
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CALL_SUBTEST( test_complex<float>(256) ); CALL_SUBTEST( test_complex<double>(256) );
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CALL_SUBTEST( test_complex<float>(3*8) ); CALL_SUBTEST( test_complex<double>(3*8) );
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CALL_SUBTEST( test_complex<float>(5*32) ); CALL_SUBTEST( test_complex<double>(5*32) );
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CALL_SUBTEST( test_complex<float>(2*3*4) ); CALL_SUBTEST( test_complex<double>(2*3*4) );
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CALL_SUBTEST( test_complex<float>(2*3*4*5) ); CALL_SUBTEST( test_complex<double>(2*3*4*5) );
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CALL_SUBTEST( test_complex<float>(2*3*4*5*7) ); CALL_SUBTEST( test_complex<double>(2*3*4*5*7) );
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CALL_SUBTEST( test_scalar<float>(32) ); CALL_SUBTEST( test_scalar<double>(32) );
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CALL_SUBTEST( test_scalar<float>(45) ); CALL_SUBTEST( test_scalar<double>(45) );
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CALL_SUBTEST( test_scalar<float>(50) ); CALL_SUBTEST( test_scalar<double>(50) );
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CALL_SUBTEST( test_scalar<float>(256) ); CALL_SUBTEST( test_scalar<double>(256) );
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CALL_SUBTEST( test_scalar<float>(2*3*4*5*7) ); CALL_SUBTEST( test_scalar<double>(2*3*4*5*7) );
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#ifdef EIGEN_HAS_FFTWL
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CALL_SUBTEST( test_complex<long double>(32) );
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CALL_SUBTEST( test_complex<long double>(256) );
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CALL_SUBTEST( test_complex<long double>(3*8) );
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CALL_SUBTEST( test_complex<long double>(5*32) );
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CALL_SUBTEST( test_complex<long double>(2*3*4) );
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CALL_SUBTEST( test_complex<long double>(2*3*4*5) );
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CALL_SUBTEST( test_complex<long double>(2*3*4*5*7) );
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CALL_SUBTEST( test_scalar<long double>(32) );
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CALL_SUBTEST( test_scalar<long double>(45) );
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CALL_SUBTEST( test_scalar<long double>(50) );
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CALL_SUBTEST( test_scalar<long double>(256) );
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CALL_SUBTEST( test_scalar<long double>(2*3*4*5*7) );
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#endif
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}
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