Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 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 | |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 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 | } |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 40 | totalpower += numext::abs2(acc); |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 41 | complex<long double> x = promote(fftbuf[k0]); |
| 42 | complex<long double> dif = acc - x; |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 43 | difpower += numext::abs2(dif); |
| 44 | //cerr << k0 << "\t" << acc << "\t" << x << "\t" << sqrt(numext::abs2(dif)) << endl; |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 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) { |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 57 | totalpower += (numext::abs2( buf1[k] ) + numext::abs2(buf2[k]) )/2.; |
| 58 | difpower += numext::abs2(buf1[k] - buf2[k]); |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 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 | } |