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 float norm(float x) {return x*x;} 20 double norm(double x) {return x*x;} 21 long double norm(long double x) {return x*x;} 22 23 template < typename T> 24 complex<long double> promote(complex<T> x) { return complex<long double>(x.real(),x.imag()); } 25 26 complex<long double> promote(float x) { return complex<long double>( x); } 27 complex<long double> promote(double x) { return complex<long double>( x); } 28 complex<long double> promote(long double x) { return complex<long double>( x); } 29 30 31 template <typename VT1,typename VT2> 32 long double fft_rmse( const VT1 & fftbuf,const VT2 & timebuf) 33 { 34 long double totalpower=0; 35 long double difpower=0; 36 long double pi = acos((long double)-1 ); 37 for (size_t k0=0;k0<(size_t)fftbuf.size();++k0) { 38 complex<long double> acc = 0; 39 long double phinc = -2.*k0* pi / timebuf.size(); 40 for (size_t k1=0;k1<(size_t)timebuf.size();++k1) { 41 acc += promote( timebuf[k1] ) * exp( complex<long double>(0,k1*phinc) ); 42 } 43 totalpower += norm(acc); 44 complex<long double> x = promote(fftbuf[k0]); 45 complex<long double> dif = acc - x; 46 difpower += norm(dif); 47 //cerr << k0 << "\t" << acc << "\t" << x << "\t" << sqrt(norm(dif)) << endl; 48 } 49 cerr << "rmse:" << sqrt(difpower/totalpower) << endl; 50 return sqrt(difpower/totalpower); 51 } 52 53 template <typename VT1,typename VT2> 54 long double dif_rmse( const VT1 buf1,const VT2 buf2) 55 { 56 long double totalpower=0; 57 long double difpower=0; 58 size_t n = (min)( buf1.size(),buf2.size() ); 59 for (size_t k=0;k<n;++k) { 60 totalpower += (norm( buf1[k] ) + norm(buf2[k]) )/2.; 61 difpower += norm(buf1[k] - buf2[k]); 62 } 63 return sqrt(difpower/totalpower); 64 } 65 66 enum { StdVectorContainer, EigenVectorContainer }; 67 68 template<int Container, typename Scalar> struct VectorType; 69 70 template<typename Scalar> struct VectorType<StdVectorContainer,Scalar> 71 { 72 typedef vector<Scalar> type; 73 }; 74 75 template<typename Scalar> struct VectorType<EigenVectorContainer,Scalar> 76 { 77 typedef Matrix<Scalar,Dynamic,1> type; 78 }; 79 80 template <int Container, typename T> 81 void test_scalar_generic(int nfft) 82 { 83 typedef typename FFT<T>::Complex Complex; 84 typedef typename FFT<T>::Scalar Scalar; 85 typedef typename VectorType<Container,Scalar>::type ScalarVector; 86 typedef typename VectorType<Container,Complex>::type ComplexVector; 87 88 FFT<T> fft; 89 ScalarVector tbuf(nfft); 90 ComplexVector freqBuf; 91 for (int k=0;k<nfft;++k) 92 tbuf[k]= (T)( rand()/(double)RAND_MAX - .5); 93 94 // make sure it DOESN'T give the right full spectrum answer 95 // if we've asked for half-spectrum 96 fft.SetFlag(fft.HalfSpectrum ); 97 fft.fwd( freqBuf,tbuf); 98 VERIFY((size_t)freqBuf.size() == (size_t)( (nfft>>1)+1) ); 99 VERIFY( fft_rmse(freqBuf,tbuf) < test_precision<T>() );// gross check 100 101 fft.ClearFlag(fft.HalfSpectrum ); 102 fft.fwd( freqBuf,tbuf); 103 VERIFY( (size_t)freqBuf.size() == (size_t)nfft); 104 VERIFY( fft_rmse(freqBuf,tbuf) < test_precision<T>() );// gross check 105 106 if (nfft&1) 107 return; // odd FFTs get the wrong size inverse FFT 108 109 ScalarVector tbuf2; 110 fft.inv( tbuf2 , freqBuf); 111 VERIFY( dif_rmse(tbuf,tbuf2) < test_precision<T>() );// gross check 112 113 114 // verify that the Unscaled flag takes effect 115 ScalarVector tbuf3; 116 fft.SetFlag(fft.Unscaled); 117 118 fft.inv( tbuf3 , freqBuf); 119 120 for (int k=0;k<nfft;++k) 121 tbuf3[k] *= T(1./nfft); 122 123 124 //for (size_t i=0;i<(size_t) tbuf.size();++i) 125 // cout << "freqBuf=" << freqBuf[i] << " in2=" << tbuf3[i] << " - in=" << tbuf[i] << " => " << (tbuf3[i] - tbuf[i] ) << endl; 126 127 VERIFY( dif_rmse(tbuf,tbuf3) < test_precision<T>() );// gross check 128 129 // verify that ClearFlag works 130 fft.ClearFlag(fft.Unscaled); 131 fft.inv( tbuf2 , freqBuf); 132 VERIFY( dif_rmse(tbuf,tbuf2) < test_precision<T>() );// gross check 133 } 134 135 template <typename T> 136 void test_scalar(int nfft) 137 { 138 test_scalar_generic<StdVectorContainer,T>(nfft); 139 //test_scalar_generic<EigenVectorContainer,T>(nfft); 140 } 141 142 143 template <int Container, typename T> 144 void test_complex_generic(int nfft) 145 { 146 typedef typename FFT<T>::Complex Complex; 147 typedef typename VectorType<Container,Complex>::type ComplexVector; 148 149 FFT<T> fft; 150 151 ComplexVector inbuf(nfft); 152 ComplexVector outbuf; 153 ComplexVector buf3; 154 for (int k=0;k<nfft;++k) 155 inbuf[k]= Complex( (T)(rand()/(double)RAND_MAX - .5), (T)(rand()/(double)RAND_MAX - .5) ); 156 fft.fwd( outbuf , inbuf); 157 158 VERIFY( fft_rmse(outbuf,inbuf) < test_precision<T>() );// gross check 159 fft.inv( buf3 , outbuf); 160 161 VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>() );// gross check 162 163 // verify that the Unscaled flag takes effect 164 ComplexVector buf4; 165 fft.SetFlag(fft.Unscaled); 166 fft.inv( buf4 , outbuf); 167 for (int k=0;k<nfft;++k) 168 buf4[k] *= T(1./nfft); 169 VERIFY( dif_rmse(inbuf,buf4) < test_precision<T>() );// gross check 170 171 // verify that ClearFlag works 172 fft.ClearFlag(fft.Unscaled); 173 fft.inv( buf3 , outbuf); 174 VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>() );// gross check 175 } 176 177 template <typename T> 178 void test_complex(int nfft) 179 { 180 test_complex_generic<StdVectorContainer,T>(nfft); 181 test_complex_generic<EigenVectorContainer,T>(nfft); 182 } 183 /* 184 template <typename T,int nrows,int ncols> 185 void test_complex2d() 186 { 187 typedef typename Eigen::FFT<T>::Complex Complex; 188 FFT<T> fft; 189 Eigen::Matrix<Complex,nrows,ncols> src,src2,dst,dst2; 190 191 src = Eigen::Matrix<Complex,nrows,ncols>::Random(); 192 //src = Eigen::Matrix<Complex,nrows,ncols>::Identity(); 193 194 for (int k=0;k<ncols;k++) { 195 Eigen::Matrix<Complex,nrows,1> tmpOut; 196 fft.fwd( tmpOut,src.col(k) ); 197 dst2.col(k) = tmpOut; 198 } 199 200 for (int k=0;k<nrows;k++) { 201 Eigen::Matrix<Complex,1,ncols> tmpOut; 202 fft.fwd( tmpOut, dst2.row(k) ); 203 dst2.row(k) = tmpOut; 204 } 205 206 fft.fwd2(dst.data(),src.data(),ncols,nrows); 207 fft.inv2(src2.data(),dst.data(),ncols,nrows); 208 VERIFY( (src-src2).norm() < test_precision<T>() ); 209 VERIFY( (dst-dst2).norm() < test_precision<T>() ); 210 } 211 */ 212 213 214 void test_return_by_value(int len) 215 { 216 VectorXf in; 217 VectorXf in1; 218 in.setRandom( len ); 219 VectorXcf out1,out2; 220 FFT<float> fft; 221 222 fft.SetFlag(fft.HalfSpectrum ); 223 224 fft.fwd(out1,in); 225 out2 = fft.fwd(in); 226 VERIFY( (out1-out2).norm() < test_precision<float>() ); 227 in1 = fft.inv(out1); 228 VERIFY( (in1-in).norm() < test_precision<float>() ); 229 } 230 231 void test_FFTW() 232 { 233 CALL_SUBTEST( test_return_by_value(32) ); 234 //CALL_SUBTEST( ( test_complex2d<float,4,8> () ) ); CALL_SUBTEST( ( test_complex2d<double,4,8> () ) ); 235 //CALL_SUBTEST( ( test_complex2d<long double,4,8> () ) ); 236 CALL_SUBTEST( test_complex<float>(32) ); CALL_SUBTEST( test_complex<double>(32) ); 237 CALL_SUBTEST( test_complex<float>(256) ); CALL_SUBTEST( test_complex<double>(256) ); 238 CALL_SUBTEST( test_complex<float>(3*8) ); CALL_SUBTEST( test_complex<double>(3*8) ); 239 CALL_SUBTEST( test_complex<float>(5*32) ); CALL_SUBTEST( test_complex<double>(5*32) ); 240 CALL_SUBTEST( test_complex<float>(2*3*4) ); CALL_SUBTEST( test_complex<double>(2*3*4) ); 241 CALL_SUBTEST( test_complex<float>(2*3*4*5) ); CALL_SUBTEST( test_complex<double>(2*3*4*5) ); 242 CALL_SUBTEST( test_complex<float>(2*3*4*5*7) ); CALL_SUBTEST( test_complex<double>(2*3*4*5*7) ); 243 244 CALL_SUBTEST( test_scalar<float>(32) ); CALL_SUBTEST( test_scalar<double>(32) ); 245 CALL_SUBTEST( test_scalar<float>(45) ); CALL_SUBTEST( test_scalar<double>(45) ); 246 CALL_SUBTEST( test_scalar<float>(50) ); CALL_SUBTEST( test_scalar<double>(50) ); 247 CALL_SUBTEST( test_scalar<float>(256) ); CALL_SUBTEST( test_scalar<double>(256) ); 248 CALL_SUBTEST( test_scalar<float>(2*3*4*5*7) ); CALL_SUBTEST( test_scalar<double>(2*3*4*5*7) ); 249 250 #ifdef EIGEN_HAS_FFTWL 251 CALL_SUBTEST( test_complex<long double>(32) ); 252 CALL_SUBTEST( test_complex<long double>(256) ); 253 CALL_SUBTEST( test_complex<long double>(3*8) ); 254 CALL_SUBTEST( test_complex<long double>(5*32) ); 255 CALL_SUBTEST( test_complex<long double>(2*3*4) ); 256 CALL_SUBTEST( test_complex<long double>(2*3*4*5) ); 257 CALL_SUBTEST( test_complex<long double>(2*3*4*5*7) ); 258 259 CALL_SUBTEST( test_scalar<long double>(32) ); 260 CALL_SUBTEST( test_scalar<long double>(45) ); 261 CALL_SUBTEST( test_scalar<long double>(50) ); 262 CALL_SUBTEST( test_scalar<long double>(256) ); 263 CALL_SUBTEST( test_scalar<long double>(2*3*4*5*7) ); 264 #endif 265 } 266
