[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
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| 2 | // for linear algebra.
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| 3 | //
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| 4 | // Copyright (C) 2009 Mark Borgerding mark a borgerding net
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| 5 | //
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| 6 | // This Source Code Form is subject to the terms of the Mozilla
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| 7 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 9 |
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| 10 | #include "main.h"
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| 11 | #include <unsupported/Eigen/FFT>
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| 12 |
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| 13 | template <typename T>
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| 14 | std::complex<T> RandomCpx() { return std::complex<T>( (T)(rand()/(T)RAND_MAX - .5), (T)(rand()/(T)RAND_MAX - .5) ); }
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| 15 |
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| 16 | using namespace std;
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| 17 | using namespace Eigen;
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| 18 |
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| 19 |
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| 20 | template < typename T>
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| 21 | complex<long double> promote(complex<T> x) { return complex<long double>(x.real(),x.imag()); }
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| 22 |
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| 23 | complex<long double> promote(float x) { return complex<long double>( x); }
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| 24 | complex<long double> promote(double x) { return complex<long double>( x); }
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| 25 | complex<long double> promote(long double x) { return complex<long double>( x); }
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| 26 |
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| 27 |
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| 28 | template <typename VT1,typename VT2>
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| 29 | long double fft_rmse( const VT1 & fftbuf,const VT2 & timebuf)
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| 30 | {
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| 31 | long double totalpower=0;
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| 32 | long double difpower=0;
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| 33 | long double pi = acos((long double)-1 );
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| 34 | for (size_t k0=0;k0<(size_t)fftbuf.size();++k0) {
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| 35 | complex<long double> acc = 0;
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| 36 | long double phinc = -2.*k0* pi / timebuf.size();
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| 37 | for (size_t k1=0;k1<(size_t)timebuf.size();++k1) {
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| 38 | acc += promote( timebuf[k1] ) * exp( complex<long double>(0,k1*phinc) );
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| 39 | }
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| 40 | totalpower += numext::abs2(acc);
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| 41 | complex<long double> x = promote(fftbuf[k0]);
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| 42 | complex<long double> dif = acc - x;
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| 43 | difpower += numext::abs2(dif);
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| 44 | //cerr << k0 << "\t" << acc << "\t" << x << "\t" << sqrt(numext::abs2(dif)) << endl;
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| 45 | }
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| 46 | cerr << "rmse:" << sqrt(difpower/totalpower) << endl;
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| 47 | return sqrt(difpower/totalpower);
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| 48 | }
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| 49 |
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| 50 | template <typename VT1,typename VT2>
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| 51 | long double dif_rmse( const VT1 buf1,const VT2 buf2)
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| 52 | {
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| 53 | long double totalpower=0;
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| 54 | long double difpower=0;
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| 55 | size_t n = (min)( buf1.size(),buf2.size() );
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| 56 | for (size_t k=0;k<n;++k) {
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| 57 | totalpower += (numext::abs2( buf1[k] ) + numext::abs2(buf2[k]) )/2.;
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| 58 | difpower += numext::abs2(buf1[k] - buf2[k]);
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| 59 | }
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| 60 | return sqrt(difpower/totalpower);
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| 61 | }
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| 62 |
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| 63 | enum { StdVectorContainer, EigenVectorContainer };
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| 64 |
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| 65 | template<int Container, typename Scalar> struct VectorType;
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| 66 |
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| 67 | template<typename Scalar> struct VectorType<StdVectorContainer,Scalar>
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| 68 | {
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| 69 | typedef vector<Scalar> type;
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| 70 | };
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| 71 |
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| 72 | template<typename Scalar> struct VectorType<EigenVectorContainer,Scalar>
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| 73 | {
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| 74 | typedef Matrix<Scalar,Dynamic,1> type;
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| 75 | };
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| 76 |
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| 77 | template <int Container, typename T>
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| 78 | void test_scalar_generic(int nfft)
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| 79 | {
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| 80 | typedef typename FFT<T>::Complex Complex;
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| 81 | typedef typename FFT<T>::Scalar Scalar;
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| 82 | typedef typename VectorType<Container,Scalar>::type ScalarVector;
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| 83 | typedef typename VectorType<Container,Complex>::type ComplexVector;
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| 84 |
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| 85 | FFT<T> fft;
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| 86 | ScalarVector tbuf(nfft);
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| 87 | ComplexVector freqBuf;
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| 88 | for (int k=0;k<nfft;++k)
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| 89 | tbuf[k]= (T)( rand()/(double)RAND_MAX - .5);
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| 90 |
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| 91 | // make sure it DOESN'T give the right full spectrum answer
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| 92 | // if we've asked for half-spectrum
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| 93 | fft.SetFlag(fft.HalfSpectrum );
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| 94 | fft.fwd( freqBuf,tbuf);
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| 95 | VERIFY((size_t)freqBuf.size() == (size_t)( (nfft>>1)+1) );
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| 96 | VERIFY( fft_rmse(freqBuf,tbuf) < test_precision<T>() );// gross check
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| 97 |
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| 98 | fft.ClearFlag(fft.HalfSpectrum );
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| 99 | fft.fwd( freqBuf,tbuf);
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| 100 | VERIFY( (size_t)freqBuf.size() == (size_t)nfft);
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| 101 | VERIFY( fft_rmse(freqBuf,tbuf) < test_precision<T>() );// gross check
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| 102 |
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| 103 | if (nfft&1)
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| 104 | return; // odd FFTs get the wrong size inverse FFT
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| 105 |
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| 106 | ScalarVector tbuf2;
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| 107 | fft.inv( tbuf2 , freqBuf);
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| 108 | VERIFY( dif_rmse(tbuf,tbuf2) < test_precision<T>() );// gross check
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| 109 |
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| 110 |
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| 111 | // verify that the Unscaled flag takes effect
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| 112 | ScalarVector tbuf3;
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| 113 | fft.SetFlag(fft.Unscaled);
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| 114 |
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| 115 | fft.inv( tbuf3 , freqBuf);
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| 116 |
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| 117 | for (int k=0;k<nfft;++k)
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| 118 | tbuf3[k] *= T(1./nfft);
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| 119 |
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| 120 |
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| 121 | //for (size_t i=0;i<(size_t) tbuf.size();++i)
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| 122 | // cout << "freqBuf=" << freqBuf[i] << " in2=" << tbuf3[i] << " - in=" << tbuf[i] << " => " << (tbuf3[i] - tbuf[i] ) << endl;
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| 123 |
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| 124 | VERIFY( dif_rmse(tbuf,tbuf3) < test_precision<T>() );// gross check
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| 125 |
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| 126 | // verify that ClearFlag works
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| 127 | fft.ClearFlag(fft.Unscaled);
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| 128 | fft.inv( tbuf2 , freqBuf);
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| 129 | VERIFY( dif_rmse(tbuf,tbuf2) < test_precision<T>() );// gross check
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| 130 | }
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| 131 |
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| 132 | template <typename T>
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| 133 | void test_scalar(int nfft)
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| 134 | {
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| 135 | test_scalar_generic<StdVectorContainer,T>(nfft);
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| 136 | //test_scalar_generic<EigenVectorContainer,T>(nfft);
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| 137 | }
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| 138 |
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| 139 |
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| 140 | template <int Container, typename T>
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| 141 | void test_complex_generic(int nfft)
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| 142 | {
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| 143 | typedef typename FFT<T>::Complex Complex;
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| 144 | typedef typename VectorType<Container,Complex>::type ComplexVector;
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| 145 |
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| 146 | FFT<T> fft;
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| 147 |
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| 148 | ComplexVector inbuf(nfft);
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| 149 | ComplexVector outbuf;
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| 150 | ComplexVector buf3;
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| 151 | for (int k=0;k<nfft;++k)
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| 152 | inbuf[k]= Complex( (T)(rand()/(double)RAND_MAX - .5), (T)(rand()/(double)RAND_MAX - .5) );
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| 153 | fft.fwd( outbuf , inbuf);
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| 154 |
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| 155 | VERIFY( fft_rmse(outbuf,inbuf) < test_precision<T>() );// gross check
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| 156 | fft.inv( buf3 , outbuf);
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| 157 |
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| 158 | VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>() );// gross check
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| 159 |
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| 160 | // verify that the Unscaled flag takes effect
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| 161 | ComplexVector buf4;
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| 162 | fft.SetFlag(fft.Unscaled);
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| 163 | fft.inv( buf4 , outbuf);
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| 164 | for (int k=0;k<nfft;++k)
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| 165 | buf4[k] *= T(1./nfft);
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| 166 | VERIFY( dif_rmse(inbuf,buf4) < test_precision<T>() );// gross check
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| 167 |
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| 168 | // verify that ClearFlag works
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| 169 | fft.ClearFlag(fft.Unscaled);
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| 170 | fft.inv( buf3 , outbuf);
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| 171 | VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>() );// gross check
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| 172 | }
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| 173 |
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| 174 | template <typename T>
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| 175 | void test_complex(int nfft)
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| 176 | {
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| 177 | test_complex_generic<StdVectorContainer,T>(nfft);
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| 178 | test_complex_generic<EigenVectorContainer,T>(nfft);
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| 179 | }
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| 180 | /*
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| 181 | template <typename T,int nrows,int ncols>
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| 182 | void test_complex2d()
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| 183 | {
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| 184 | typedef typename Eigen::FFT<T>::Complex Complex;
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| 185 | FFT<T> fft;
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| 186 | Eigen::Matrix<Complex,nrows,ncols> src,src2,dst,dst2;
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| 187 |
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| 188 | src = Eigen::Matrix<Complex,nrows,ncols>::Random();
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| 189 | //src = Eigen::Matrix<Complex,nrows,ncols>::Identity();
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| 190 |
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| 191 | for (int k=0;k<ncols;k++) {
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| 192 | Eigen::Matrix<Complex,nrows,1> tmpOut;
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| 193 | fft.fwd( tmpOut,src.col(k) );
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| 194 | dst2.col(k) = tmpOut;
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| 195 | }
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| 196 |
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| 197 | for (int k=0;k<nrows;k++) {
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| 198 | Eigen::Matrix<Complex,1,ncols> tmpOut;
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| 199 | fft.fwd( tmpOut, dst2.row(k) );
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| 200 | dst2.row(k) = tmpOut;
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| 201 | }
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| 202 |
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| 203 | fft.fwd2(dst.data(),src.data(),ncols,nrows);
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| 204 | fft.inv2(src2.data(),dst.data(),ncols,nrows);
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| 205 | VERIFY( (src-src2).norm() < test_precision<T>() );
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| 206 | VERIFY( (dst-dst2).norm() < test_precision<T>() );
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| 207 | }
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| 208 | */
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| 209 |
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| 210 |
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| 211 | void test_return_by_value(int len)
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| 212 | {
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| 213 | VectorXf in;
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| 214 | VectorXf in1;
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| 215 | in.setRandom( len );
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| 216 | VectorXcf out1,out2;
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| 217 | FFT<float> fft;
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| 218 |
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| 219 | fft.SetFlag(fft.HalfSpectrum );
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| 220 |
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| 221 | fft.fwd(out1,in);
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| 222 | out2 = fft.fwd(in);
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| 223 | VERIFY( (out1-out2).norm() < test_precision<float>() );
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| 224 | in1 = fft.inv(out1);
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| 225 | VERIFY( (in1-in).norm() < test_precision<float>() );
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| 226 | }
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| 227 |
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| 228 | void test_FFTW()
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| 229 | {
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| 230 | CALL_SUBTEST( test_return_by_value(32) );
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| 231 | //CALL_SUBTEST( ( test_complex2d<float,4,8> () ) ); CALL_SUBTEST( ( test_complex2d<double,4,8> () ) );
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| 232 | //CALL_SUBTEST( ( test_complex2d<long double,4,8> () ) );
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| 233 | CALL_SUBTEST( test_complex<float>(32) ); CALL_SUBTEST( test_complex<double>(32) );
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| 234 | CALL_SUBTEST( test_complex<float>(256) ); CALL_SUBTEST( test_complex<double>(256) );
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| 235 | CALL_SUBTEST( test_complex<float>(3*8) ); CALL_SUBTEST( test_complex<double>(3*8) );
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| 236 | CALL_SUBTEST( test_complex<float>(5*32) ); CALL_SUBTEST( test_complex<double>(5*32) );
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| 237 | CALL_SUBTEST( test_complex<float>(2*3*4) ); CALL_SUBTEST( test_complex<double>(2*3*4) );
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| 238 | CALL_SUBTEST( test_complex<float>(2*3*4*5) ); CALL_SUBTEST( test_complex<double>(2*3*4*5) );
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| 239 | CALL_SUBTEST( test_complex<float>(2*3*4*5*7) ); CALL_SUBTEST( test_complex<double>(2*3*4*5*7) );
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| 240 |
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| 241 | CALL_SUBTEST( test_scalar<float>(32) ); CALL_SUBTEST( test_scalar<double>(32) );
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| 242 | CALL_SUBTEST( test_scalar<float>(45) ); CALL_SUBTEST( test_scalar<double>(45) );
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| 243 | CALL_SUBTEST( test_scalar<float>(50) ); CALL_SUBTEST( test_scalar<double>(50) );
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| 244 | CALL_SUBTEST( test_scalar<float>(256) ); CALL_SUBTEST( test_scalar<double>(256) );
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| 245 | CALL_SUBTEST( test_scalar<float>(2*3*4*5*7) ); CALL_SUBTEST( test_scalar<double>(2*3*4*5*7) );
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| 246 |
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| 247 | #ifdef EIGEN_HAS_FFTWL
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| 248 | CALL_SUBTEST( test_complex<long double>(32) );
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| 249 | CALL_SUBTEST( test_complex<long double>(256) );
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| 250 | CALL_SUBTEST( test_complex<long double>(3*8) );
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| 251 | CALL_SUBTEST( test_complex<long double>(5*32) );
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| 252 | CALL_SUBTEST( test_complex<long double>(2*3*4) );
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| 253 | CALL_SUBTEST( test_complex<long double>(2*3*4*5) );
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| 254 | CALL_SUBTEST( test_complex<long double>(2*3*4*5*7) );
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| 255 |
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| 256 | CALL_SUBTEST( test_scalar<long double>(32) );
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| 257 | CALL_SUBTEST( test_scalar<long double>(45) );
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| 258 | CALL_SUBTEST( test_scalar<long double>(50) );
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| 259 | CALL_SUBTEST( test_scalar<long double>(256) );
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| 260 | CALL_SUBTEST( test_scalar<long double>(2*3*4*5*7) );
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| 261 | #endif
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| 262 | }
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