1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2009 Mark Borgerding mark a borgerding net 5 // 6 // This Source Code Form is subject to the terms of the Mozilla 7 // Public License v. 2.0. If a copy of the MPL was not distributed 8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 9 10 #include "main.h" 11 #include <unsupported/Eigen/FFT> 12 13 template <typename T> 14 std::complex<T> RandomCpx() { return std::complex<T>( (T)(rand()/(T)RAND_MAX - .5), (T)(rand()/(T)RAND_MAX - .5) ); } 15 16 using namespace std; 17 using namespace Eigen; 18 19 20 template < typename T> 21 complex<long double> promote(complex<T> x) { return complex<long double>(x.real(),x.imag()); } 22 23 complex<long double> promote(float x) { return complex<long double>( x); } 24 complex<long double> promote(double x) { return complex<long double>( x); } 25 complex<long double> promote(long double x) { return complex<long double>( x); } 26 27 28 template <typename VT1,typename VT2> 29 long double fft_rmse( const VT1 & fftbuf,const VT2 & timebuf) 30 { 31 long double totalpower=0; 32 long double difpower=0; 33 long double pi = acos((long double)-1 ); 34 for (size_t k0=0;k0<(size_t)fftbuf.size();++k0) { 35 complex<long double> acc = 0; 36 long double phinc = -2.*k0* pi / timebuf.size(); 37 for (size_t k1=0;k1<(size_t)timebuf.size();++k1) { 38 acc += promote( timebuf[k1] ) * exp( complex<long double>(0,k1*phinc) ); 39 } 40 totalpower += numext::abs2(acc); 41 complex<long double> x = promote(fftbuf[k0]); 42 complex<long double> dif = acc - x; 43 difpower += numext::abs2(dif); 44 //cerr << k0 << "\t" << acc << "\t" << x << "\t" << sqrt(numext::abs2(dif)) << endl; 45 } 46 cerr << "rmse:" << sqrt(difpower/totalpower) << endl; 47 return sqrt(difpower/totalpower); 48 } 49 50 template <typename VT1,typename VT2> 51 long double dif_rmse( const VT1 buf1,const VT2 buf2) 52 { 53 long double totalpower=0; 54 long double difpower=0; 55 size_t n = (min)( buf1.size(),buf2.size() ); 56 for (size_t k=0;k<n;++k) { 57 totalpower += (numext::abs2( buf1[k] ) + numext::abs2(buf2[k]) )/2.; 58 difpower += numext::abs2(buf1[k] - buf2[k]); 59 } 60 return sqrt(difpower/totalpower); 61 } 62 63 enum { StdVectorContainer, EigenVectorContainer }; 64 65 template<int Container, typename Scalar> struct VectorType; 66 67 template<typename Scalar> struct VectorType<StdVectorContainer,Scalar> 68 { 69 typedef vector<Scalar> type; 70 }; 71 72 template<typename Scalar> struct VectorType<EigenVectorContainer,Scalar> 73 { 74 typedef Matrix<Scalar,Dynamic,1> type; 75 }; 76 77 template <int Container, typename T> 78 void test_scalar_generic(int nfft) 79 { 80 typedef typename FFT<T>::Complex Complex; 81 typedef typename FFT<T>::Scalar Scalar; 82 typedef typename VectorType<Container,Scalar>::type ScalarVector; 83 typedef typename VectorType<Container,Complex>::type ComplexVector; 84 85 FFT<T> fft; 86 ScalarVector tbuf(nfft); 87 ComplexVector freqBuf; 88 for (int k=0;k<nfft;++k) 89 tbuf[k]= (T)( rand()/(double)RAND_MAX - .5); 90 91 // make sure it DOESN'T give the right full spectrum answer 92 // if we've asked for half-spectrum 93 fft.SetFlag(fft.HalfSpectrum ); 94 fft.fwd( freqBuf,tbuf); 95 VERIFY((size_t)freqBuf.size() == (size_t)( (nfft>>1)+1) ); 96 VERIFY( fft_rmse(freqBuf,tbuf) < test_precision<T>() );// gross check 97 98 fft.ClearFlag(fft.HalfSpectrum ); 99 fft.fwd( freqBuf,tbuf); 100 VERIFY( (size_t)freqBuf.size() == (size_t)nfft); 101 VERIFY( fft_rmse(freqBuf,tbuf) < test_precision<T>() );// gross check 102 103 if (nfft&1) 104 return; // odd FFTs get the wrong size inverse FFT 105 106 ScalarVector tbuf2; 107 fft.inv( tbuf2 , freqBuf); 108 VERIFY( dif_rmse(tbuf,tbuf2) < test_precision<T>() );// gross check 109 110 111 // verify that the Unscaled flag takes effect 112 ScalarVector tbuf3; 113 fft.SetFlag(fft.Unscaled); 114 115 fft.inv( tbuf3 , freqBuf); 116 117 for (int k=0;k<nfft;++k) 118 tbuf3[k] *= T(1./nfft); 119 120 121 //for (size_t i=0;i<(size_t) tbuf.size();++i) 122 // cout << "freqBuf=" << freqBuf[i] << " in2=" << tbuf3[i] << " - in=" << tbuf[i] << " => " << (tbuf3[i] - tbuf[i] ) << endl; 123 124 VERIFY( dif_rmse(tbuf,tbuf3) < test_precision<T>() );// gross check 125 126 // verify that ClearFlag works 127 fft.ClearFlag(fft.Unscaled); 128 fft.inv( tbuf2 , freqBuf); 129 VERIFY( dif_rmse(tbuf,tbuf2) < test_precision<T>() );// gross check 130 } 131 132 template <typename T> 133 void test_scalar(int nfft) 134 { 135 test_scalar_generic<StdVectorContainer,T>(nfft); 136 //test_scalar_generic<EigenVectorContainer,T>(nfft); 137 } 138 139 140 template <int Container, typename T> 141 void test_complex_generic(int nfft) 142 { 143 typedef typename FFT<T>::Complex Complex; 144 typedef typename VectorType<Container,Complex>::type ComplexVector; 145 146 FFT<T> fft; 147 148 ComplexVector inbuf(nfft); 149 ComplexVector outbuf; 150 ComplexVector buf3; 151 for (int k=0;k<nfft;++k) 152 inbuf[k]= Complex( (T)(rand()/(double)RAND_MAX - .5), (T)(rand()/(double)RAND_MAX - .5) ); 153 fft.fwd( outbuf , inbuf); 154 155 VERIFY( fft_rmse(outbuf,inbuf) < test_precision<T>() );// gross check 156 fft.inv( buf3 , outbuf); 157 158 VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>() );// gross check 159 160 // verify that the Unscaled flag takes effect 161 ComplexVector buf4; 162 fft.SetFlag(fft.Unscaled); 163 fft.inv( buf4 , outbuf); 164 for (int k=0;k<nfft;++k) 165 buf4[k] *= T(1./nfft); 166 VERIFY( dif_rmse(inbuf,buf4) < test_precision<T>() );// gross check 167 168 // verify that ClearFlag works 169 fft.ClearFlag(fft.Unscaled); 170 fft.inv( buf3 , outbuf); 171 VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>() );// gross check 172 } 173 174 template <typename T> 175 void test_complex(int nfft) 176 { 177 test_complex_generic<StdVectorContainer,T>(nfft); 178 test_complex_generic<EigenVectorContainer,T>(nfft); 179 } 180 /* 181 template <typename T,int nrows,int ncols> 182 void test_complex2d() 183 { 184 typedef typename Eigen::FFT<T>::Complex Complex; 185 FFT<T> fft; 186 Eigen::Matrix<Complex,nrows,ncols> src,src2,dst,dst2; 187 188 src = Eigen::Matrix<Complex,nrows,ncols>::Random(); 189 //src = Eigen::Matrix<Complex,nrows,ncols>::Identity(); 190 191 for (int k=0;k<ncols;k++) { 192 Eigen::Matrix<Complex,nrows,1> tmpOut; 193 fft.fwd( tmpOut,src.col(k) ); 194 dst2.col(k) = tmpOut; 195 } 196 197 for (int k=0;k<nrows;k++) { 198 Eigen::Matrix<Complex,1,ncols> tmpOut; 199 fft.fwd( tmpOut, dst2.row(k) ); 200 dst2.row(k) = tmpOut; 201 } 202 203 fft.fwd2(dst.data(),src.data(),ncols,nrows); 204 fft.inv2(src2.data(),dst.data(),ncols,nrows); 205 VERIFY( (src-src2).norm() < test_precision<T>() ); 206 VERIFY( (dst-dst2).norm() < test_precision<T>() ); 207 } 208 */ 209 210 211 void test_return_by_value(int len) 212 { 213 VectorXf in; 214 VectorXf in1; 215 in.setRandom( len ); 216 VectorXcf out1,out2; 217 FFT<float> fft; 218 219 fft.SetFlag(fft.HalfSpectrum ); 220 221 fft.fwd(out1,in); 222 out2 = fft.fwd(in); 223 VERIFY( (out1-out2).norm() < test_precision<float>() ); 224 in1 = fft.inv(out1); 225 VERIFY( (in1-in).norm() < test_precision<float>() ); 226 } 227 228 void test_FFTW() 229 { 230 CALL_SUBTEST( test_return_by_value(32) ); 231 //CALL_SUBTEST( ( test_complex2d<float,4,8> () ) ); CALL_SUBTEST( ( test_complex2d<double,4,8> () ) ); 232 //CALL_SUBTEST( ( test_complex2d<long double,4,8> () ) ); 233 CALL_SUBTEST( test_complex<float>(32) ); CALL_SUBTEST( test_complex<double>(32) ); 234 CALL_SUBTEST( test_complex<float>(256) ); CALL_SUBTEST( test_complex<double>(256) ); 235 CALL_SUBTEST( test_complex<float>(3*8) ); CALL_SUBTEST( test_complex<double>(3*8) ); 236 CALL_SUBTEST( test_complex<float>(5*32) ); CALL_SUBTEST( test_complex<double>(5*32) ); 237 CALL_SUBTEST( test_complex<float>(2*3*4) ); CALL_SUBTEST( test_complex<double>(2*3*4) ); 238 CALL_SUBTEST( test_complex<float>(2*3*4*5) ); CALL_SUBTEST( test_complex<double>(2*3*4*5) ); 239 CALL_SUBTEST( test_complex<float>(2*3*4*5*7) ); CALL_SUBTEST( test_complex<double>(2*3*4*5*7) ); 240 241 CALL_SUBTEST( test_scalar<float>(32) ); CALL_SUBTEST( test_scalar<double>(32) ); 242 CALL_SUBTEST( test_scalar<float>(45) ); CALL_SUBTEST( test_scalar<double>(45) ); 243 CALL_SUBTEST( test_scalar<float>(50) ); CALL_SUBTEST( test_scalar<double>(50) ); 244 CALL_SUBTEST( test_scalar<float>(256) ); CALL_SUBTEST( test_scalar<double>(256) ); 245 CALL_SUBTEST( test_scalar<float>(2*3*4*5*7) ); CALL_SUBTEST( test_scalar<double>(2*3*4*5*7) ); 246 247 #ifdef EIGEN_HAS_FFTWL 248 CALL_SUBTEST( test_complex<long double>(32) ); 249 CALL_SUBTEST( test_complex<long double>(256) ); 250 CALL_SUBTEST( test_complex<long double>(3*8) ); 251 CALL_SUBTEST( test_complex<long double>(5*32) ); 252 CALL_SUBTEST( test_complex<long double>(2*3*4) ); 253 CALL_SUBTEST( test_complex<long double>(2*3*4*5) ); 254 CALL_SUBTEST( test_complex<long double>(2*3*4*5*7) ); 255 256 CALL_SUBTEST( test_scalar<long double>(32) ); 257 CALL_SUBTEST( test_scalar<long double>(45) ); 258 CALL_SUBTEST( test_scalar<long double>(50) ); 259 CALL_SUBTEST( test_scalar<long double>(256) ); 260 CALL_SUBTEST( test_scalar<long double>(2*3*4*5*7) ); 261 #endif 262 } 263
