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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