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>
RandomCpx()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>
promote(complex<T> x)21 complex<long double> promote(complex<T> x) { return complex<long double>((long double)x.real(),(long double)x.imag()); }
22
promote(float x)23 complex<long double> promote(float x) { return complex<long double>((long double)x); }
promote(double x)24 complex<long double> promote(double x) { return complex<long double>((long double)x); }
promote(long double x)25 complex<long double> promote(long double x) { return complex<long double>((long double)x); }
26
27
28 template <typename VT1,typename VT2>
fft_rmse(const VT1 & fftbuf,const VT2 & timebuf)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 = (long double)(-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>
dif_rmse(const VT1 buf1,const VT2 buf2)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 += (long double)((numext::abs2( buf1[k] ) + numext::abs2(buf2[k]) )/2);
58 difpower += (long double)(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>
test_scalar_generic(int nfft)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( T(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( T(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( T(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( T(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( T(dif_rmse(tbuf,tbuf2)) < test_precision<T>() );// gross check
130 }
131
132 template <typename T>
test_scalar(int nfft)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>
test_complex_generic(int nfft)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( T(fft_rmse(outbuf,inbuf)) < test_precision<T>() );// gross check
156 fft.inv( buf3 , outbuf);
157
158 VERIFY( T(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( T(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( T(dif_rmse(inbuf,buf3)) < test_precision<T>() );// gross check
172 }
173
174 template <typename T>
test_complex(int nfft)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
test_return_by_value(int len)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
test_FFTW()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