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
13template <typename T>
14std::complex<T> RandomCpx() { return std::complex<T>( (T)(rand()/(T)RAND_MAX - .5), (T)(rand()/(T)RAND_MAX - .5) ); }
15
16using namespace std;
17using namespace Eigen;
18
19
20template < typename T>
21complex<long double>  promote(complex<T> x) { return complex<long double>((long double)x.real(),(long double)x.imag()); }
22
23complex<long double>  promote(float x) { return complex<long double>((long double)x); }
24complex<long double>  promote(double x) { return complex<long double>((long double)x); }
25complex<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
63enum { StdVectorContainer, EigenVectorContainer };
64
65template<int Container, typename Scalar> struct VectorType;
66
67template<typename Scalar> struct VectorType<StdVectorContainer,Scalar>
68{
69  typedef vector<Scalar> type;
70};
71
72template<typename Scalar> struct VectorType<EigenVectorContainer,Scalar>
73{
74  typedef Matrix<Scalar,Dynamic,1> type;
75};
76
77template <int Container, typename T>
78void 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
132template <typename T>
133void test_scalar(int nfft)
134{
135  test_scalar_generic<StdVectorContainer,T>(nfft);
136  //test_scalar_generic<EigenVectorContainer,T>(nfft);
137}
138
139
140template <int Container, typename T>
141void 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
174template <typename T>
175void test_complex(int nfft)
176{
177  test_complex_generic<StdVectorContainer,T>(nfft);
178  test_complex_generic<EigenVectorContainer,T>(nfft);
179}
180/*
181template <typename T,int nrows,int ncols>
182void 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
211void 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
228void 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