FFTW.cpp
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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>((long double)x.real(),(long double)x.imag()); }
22 
23 complex<long double> promote(float x) { return complex<long double>((long double)x); }
24 complex<long double> promote(double x) { return complex<long double>((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>
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>
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>
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>
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( 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>
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 EIGEN_DECLARE_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 }
Complex
std::complex< RealScalar > Complex
Definition: gtsam/3rdparty/Eigen/blas/common.h:94
dif_rmse
long double dif_rmse(const VT1 buf1, const VT2 buf2)
Definition: FFTW.cpp:51
Eigen
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EIGEN_DEVICE_FUNC const EIGEN_STRONG_INLINE Abs2ReturnType abs2() const
Definition: ArrayCwiseUnaryOps.h:80
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complex< long double > promote(complex< T > x)
Definition: FFTW.cpp:21
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const EIGEN_DEVICE_FUNC ExpReturnType exp() const
Definition: ArrayCwiseUnaryOps.h:97
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Jet< T, N > acos(const Jet< T, N > &f)
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Definition: spbenchsolver.h:91
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std::complex< T > RandomCpx()
Definition: FFTW.cpp:14
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long double fft_rmse(const VT1 &fftbuf, const VT2 &timebuf)
Definition: FFTW.cpp:29
EigenVectorContainer
@ EigenVectorContainer
Definition: FFTW.cpp:63
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Definition: k1.c:133
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void test_scalar_generic(int nfft)
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Definition: FFTW.cpp:69
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A small structure to hold a non zero as a triplet (i,j,value).
Definition: SparseUtil.h:162
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VectorType< EigenVectorContainer, Scalar >::type
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void test_complex_generic(int nfft)
Definition: FFTW.cpp:141
len
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Get the length of a Python object.
Definition: pytypes.h:2446
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@ StdVectorContainer
Definition: FFTW.cpp:63
EIGEN_DECLARE_TEST
EIGEN_DECLARE_TEST(FFTW)
Definition: FFTW.cpp:228
test_return_by_value
void test_return_by_value(int len)
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Definition: jet.h:418
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#define CALL_SUBTEST(FUNC)
Definition: main.h:399
VERIFY
#define VERIFY(a)
Definition: main.h:380

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