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This commit is contained in:
Mark Borgerding
@@ -1,245 +1,2 @@
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#if 0
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra. Eigen itself is part of the KDE project.
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//
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// Copyright (C) 2009 Mark Borgerding mark a borgerding net
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//
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// Eigen is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
|
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// License as published by the Free Software Foundation; either
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// version 3 of the License, or (at your option) any later version.
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//
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// Alternatively, you can redistribute it and/or
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// modify it under the terms of the GNU General Public License as
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// published by the Free Software Foundation; either version 2 of
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// the License, or (at your option) any later version.
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//
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// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
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// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
|
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License and a copy of the GNU General Public License along with
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// Eigen. If not, see <http://www.gnu.org/licenses/>.
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#include "main.h"
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#include <unsupported/Eigen/FFT>
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template <typename T>
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std::complex<T> RandomCpx() { return std::complex<T>( (T)(rand()/(T)RAND_MAX - .5), (T)(rand()/(T)RAND_MAX - .5) ); }
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using namespace std;
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using namespace Eigen;
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float norm(float x) {return x*x;}
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double norm(double x) {return x*x;}
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long double norm(long double x) {return x*x;}
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template < typename T>
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complex<long double> promote(complex<T> x) { return complex<long double>(x.real(),x.imag()); }
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complex<long double> promote(float x) { return complex<long double>( x); }
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complex<long double> promote(double x) { return complex<long double>( x); }
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complex<long double> promote(long double x) { return complex<long double>( x); }
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template <typename T1,typename T2>
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long double fft_rmse( const vector<T1> & fftbuf,const vector<T2> & timebuf)
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{
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long double totalpower=0;
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long double difpower=0;
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long double pi = acos((long double)-1 );
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for (size_t k0=0;k0<fftbuf.size();++k0) {
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complex<long double> acc = 0;
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long double phinc = -2.*k0* pi / timebuf.size();
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for (size_t k1=0;k1<timebuf.size();++k1) {
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acc += promote( timebuf[k1] ) * exp( complex<long double>(0,k1*phinc) );
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}
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totalpower += norm(acc);
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complex<long double> x = promote(fftbuf[k0]);
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complex<long double> dif = acc - x;
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difpower += norm(dif);
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cerr << k0 << "\t" << acc << "\t" << x << "\t" << sqrt(norm(dif)) << endl;
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}
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cerr << "rmse:" << sqrt(difpower/totalpower) << endl;
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return sqrt(difpower/totalpower);
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}
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template <typename T1,typename T2>
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long double dif_rmse( const vector<T1> buf1,const vector<T2> buf2)
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{
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long double totalpower=0;
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long double difpower=0;
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size_t n = min( buf1.size(),buf2.size() );
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for (size_t k=0;k<n;++k) {
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totalpower += (norm( buf1[k] ) + norm(buf2[k]) )/2.;
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difpower += norm(buf1[k] - buf2[k]);
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}
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return sqrt(difpower/totalpower);
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}
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enum { StdVectorContainer, EigenVectorContainer };
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template<int Container, typename Scalar> struct VectorType;
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template<typename Scalar> struct VectorType<StdVectorContainer,Scalar>
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{
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typedef vector<Scalar> type;
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};
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template<typename Scalar> struct VectorType<EigenVectorContainer,Scalar>
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{
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typedef Matrix<Scalar,Dynamic,1> type;
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};
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template <int Container, typename T>
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void test_scalar_generic(int nfft)
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{
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typedef typename FFT<T>::Complex Complex;
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typedef typename FFT<T>::Scalar Scalar;
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typedef typename VectorType<Container,Scalar>::type ScalarVector;
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typedef typename VectorType<Container,Complex>::type ComplexVector;
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FFT<T> fft;
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ScalarVector inbuf(nfft);
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ComplexVector outbuf;
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for (int k=0;k<nfft;++k)
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inbuf[k]= (T)(rand()/(double)RAND_MAX - .5);
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// make sure it DOESN'T give the right full spectrum answer
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// if we've asked for half-spectrum
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fft.SetFlag(fft.HalfSpectrum );
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fft.fwd( outbuf,inbuf);
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VERIFY(outbuf.size() == (size_t)( (nfft>>1)+1) );
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VERIFY( fft_rmse(outbuf,inbuf) < test_precision<T>() );// gross check
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fft.ClearFlag(fft.HalfSpectrum );
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fft.fwd( outbuf,inbuf);
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VERIFY( fft_rmse(outbuf,inbuf) < test_precision<T>() );// gross check
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ScalarVector buf3;
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fft.inv( buf3 , outbuf);
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VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>() );// gross check
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// verify that the Unscaled flag takes effect
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ComplexVector buf4;
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fft.SetFlag(fft.Unscaled);
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fft.inv( buf4 , outbuf);
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for (int k=0;k<nfft;++k)
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buf4[k] *= T(1./nfft);
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VERIFY( dif_rmse(inbuf,buf4) < test_precision<T>() );// gross check
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// verify that ClearFlag works
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fft.ClearFlag(fft.Unscaled);
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fft.inv( buf3 , outbuf);
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VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>() );// gross check
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}
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template <typename T>
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void test_scalar(int nfft)
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{
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test_scalar_generic<StdVectorContainer,T>(nfft);
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test_scalar_generic<EigenVectorContainer,T>(nfft);
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}
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template <int Container, typename T>
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void test_complex_generic(int nfft)
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{
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typedef typename FFT<T>::Complex Complex;
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typedef typename VectorType<Container,Complex>::type ComplexVector;
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FFT<T> fft;
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ComplexVector inbuf(nfft);
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ComplexVector outbuf;
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ComplexVector buf3;
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for (int k=0;k<nfft;++k)
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inbuf[k]= Complex( (T)(rand()/(double)RAND_MAX - .5), (T)(rand()/(double)RAND_MAX - .5) );
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fft.fwd( outbuf , inbuf);
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VERIFY( fft_rmse(outbuf,inbuf) < test_precision<T>() );// gross check
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fft.inv( buf3 , outbuf);
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VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>() );// gross check
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// verify that the Unscaled flag takes effect
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ComplexVector buf4;
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fft.SetFlag(fft.Unscaled);
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fft.inv( buf4 , outbuf);
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for (int k=0;k<nfft;++k)
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buf4[k] *= T(1./nfft);
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VERIFY( dif_rmse(inbuf,buf4) < test_precision<T>() );// gross check
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// verify that ClearFlag works
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fft.ClearFlag(fft.Unscaled);
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fft.inv( buf3 , outbuf);
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VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>() );// gross check
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}
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template <typename T>
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void test_complex(int nfft)
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{
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test_complex_generic<StdVectorContainer,T>(nfft);
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test_complex_generic<EigenVectorContainer,T>(nfft);
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}
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void test_FFT()
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{
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CALL_SUBTEST( test_complex<float>(32) );
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CALL_SUBTEST( test_complex<double>(32) );
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CALL_SUBTEST( test_complex<long double>(32) );
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CALL_SUBTEST( test_complex<float>(256) );
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CALL_SUBTEST( test_complex<double>(256) );
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CALL_SUBTEST( test_complex<long double>(256) );
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CALL_SUBTEST( test_complex<float>(3*8) );
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CALL_SUBTEST( test_complex<double>(3*8) );
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CALL_SUBTEST( test_complex<long double>(3*8) );
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CALL_SUBTEST( test_complex<float>(5*32) );
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CALL_SUBTEST( test_complex<double>(5*32) );
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CALL_SUBTEST( test_complex<long double>(5*32) );
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CALL_SUBTEST( test_complex<float>(2*3*4) );
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CALL_SUBTEST( test_complex<double>(2*3*4) );
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CALL_SUBTEST( test_complex<long double>(2*3*4) );
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CALL_SUBTEST( test_complex<float>(2*3*4*5) );
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CALL_SUBTEST( test_complex<double>(2*3*4*5) );
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CALL_SUBTEST( test_complex<long double>(2*3*4*5) );
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CALL_SUBTEST( test_complex<float>(2*3*4*5*7) );
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CALL_SUBTEST( test_complex<double>(2*3*4*5*7) );
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CALL_SUBTEST( test_complex<long double>(2*3*4*5*7) );
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CALL_SUBTEST( test_scalar<float>(32) );
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CALL_SUBTEST( test_scalar<double>(32) );
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CALL_SUBTEST( test_scalar<long double>(32) );
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CALL_SUBTEST( test_scalar<float>(45) );
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CALL_SUBTEST( test_scalar<double>(45) );
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CALL_SUBTEST( test_scalar<long double>(45) );
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CALL_SUBTEST( test_scalar<float>(50) );
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CALL_SUBTEST( test_scalar<double>(50) );
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CALL_SUBTEST( test_scalar<long double>(50) );
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CALL_SUBTEST( test_scalar<float>(256) );
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CALL_SUBTEST( test_scalar<double>(256) );
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CALL_SUBTEST( test_scalar<long double>(256) );
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CALL_SUBTEST( test_scalar<float>(2*3*4*5*7) );
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CALL_SUBTEST( test_scalar<double>(2*3*4*5*7) );
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CALL_SUBTEST( test_scalar<long double>(2*3*4*5*7) );
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}
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#else
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#define test_FFTW test_FFT
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#include "FFTW.cpp"
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#endif
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@@ -23,7 +23,6 @@
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// Eigen. If not, see <http://www.gnu.org/licenses/>.
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#include "main.h"
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#include <iostream>
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#include <unsupported/Eigen/FFT>
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template <typename T>
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@@ -107,8 +106,6 @@ void test_scalar_generic(int nfft)
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for (int k=0;k<nfft;++k)
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tbuf[k]= (T)( rand()/(double)RAND_MAX - .5);
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cout << "tbuf=["; for (size_t i=0;i<(size_t) tbuf.size();++i) {cout << tbuf[i] << " ";} cout << "];\n";
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// make sure it DOESN'T give the right full spectrum answer
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// if we've asked for half-spectrum
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fft.SetFlag(fft.HalfSpectrum );
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@@ -125,9 +122,7 @@ void test_scalar_generic(int nfft)
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return; // odd FFTs get the wrong size inverse FFT
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ScalarVector tbuf2;
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cout << "freqBuf=["; for (size_t i=0;i<(size_t) freqBuf.size();++i) {cout << freqBuf[i] << " ";} cout << "];\n";
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fft.inv( tbuf2 , freqBuf);
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cout << "tbuf2=["; for (size_t i=0;i<(size_t) tbuf2.size();++i) {cout << tbuf2[i] << " ";} cout << "];\n";
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VERIFY( dif_rmse(tbuf,tbuf2) < test_precision<T>() );// gross check
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@@ -135,9 +130,7 @@ void test_scalar_generic(int nfft)
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ScalarVector tbuf3;
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fft.SetFlag(fft.Unscaled);
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cout << "freqBuf=["; for (size_t i=0;i<(size_t) freqBuf.size();++i) {cout << freqBuf[i] << " ";} cout << "];\n";
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fft.inv( tbuf3 , freqBuf);
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cout << "tbuf3=["; for (size_t i=0;i<(size_t) tbuf3.size();++i) {cout << tbuf3[i] << " ";} cout << "];\n";
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for (int k=0;k<nfft;++k)
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tbuf3[k] *= T(1./nfft);
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@@ -146,8 +139,6 @@ void test_scalar_generic(int nfft)
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//for (size_t i=0;i<(size_t) tbuf.size();++i)
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// cout << "freqBuf=" << freqBuf[i] << " in2=" << tbuf3[i] << " - in=" << tbuf[i] << " => " << (tbuf3[i] - tbuf[i] ) << endl;
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cout << "dif_rmse = " << dif_rmse(tbuf,tbuf3) << endl;
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cout << "test_precision = " << test_precision<T>() << endl;
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VERIFY( dif_rmse(tbuf,tbuf3) < test_precision<T>() );// gross check
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// verify that ClearFlag works
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@@ -216,7 +216,7 @@ void testLmder()
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// check covariance
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covfac = fnorm*fnorm/(m-n);
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ei_covar(lm.fjac, lm.ipvt); // TODO : move this as a function of lm
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ei_covar(lm.fjac, lm.permutation.indices()); // TODO : move this as a function of lm
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MatrixXd cov_ref(n,n);
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cov_ref <<
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@@ -605,7 +605,7 @@ void testLmdif()
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// check covariance
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covfac = fnorm*fnorm/(m-n);
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ei_covar(lm.fjac, lm.ipvt);
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ei_covar(lm.fjac, lm.permutation.indices()); // TODO : move this as a function of lm
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MatrixXd cov_ref(n,n);
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cov_ref <<
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@@ -692,8 +692,8 @@ void testNistChwirut2(void)
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x<< 0.15, 0.008, 0.010;
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// do the computation
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lm.resetParameters();
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lm.parameters.ftol = 1.E6*epsilon<double>();
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lm.parameters.xtol = 1.E6*epsilon<double>();
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lm.parameters.ftol = 1.E6*NumTraits<double>::epsilon();
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lm.parameters.xtol = 1.E6*NumTraits<double>::epsilon();
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info = lm.minimize(x);
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|
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// check return value
|
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@@ -1010,7 +1010,7 @@ void testNistLanczos1(void)
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VERIFY( 79 == lm.nfev);
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VERIFY( 72 == lm.njev);
|
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// check norm^2
|
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VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.429604433690E-25); // should be 1.4307867721E-25, but nist results are on 128-bit floats
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VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.430899764097e-25); // should be 1.4307867721E-25, but nist results are on 128-bit floats
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// check x
|
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VERIFY_IS_APPROX(x[0], 9.5100000027E-02 );
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VERIFY_IS_APPROX(x[1], 1.0000000001E+00 );
|
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@@ -1031,7 +1031,7 @@ void testNistLanczos1(void)
|
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VERIFY( 9 == lm.nfev);
|
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VERIFY( 8 == lm.njev);
|
||||
// check norm^2
|
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VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.43049947737308E-25); // should be 1.4307867721E-25, but nist results are on 128-bit floats
|
||||
VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.428595533845e-25); // should be 1.4307867721E-25, but nist results are on 128-bit floats
|
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// check x
|
||||
VERIFY_IS_APPROX(x[0], 9.5100000027E-02 );
|
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VERIFY_IS_APPROX(x[1], 1.0000000001E+00 );
|
||||
@@ -1170,9 +1170,9 @@ void testNistMGH10(void)
|
||||
info = lm.minimize(x);
|
||||
|
||||
// check return value
|
||||
VERIFY( 2 == info);
|
||||
VERIFY( 285 == lm.nfev);
|
||||
VERIFY( 250 == lm.njev);
|
||||
VERIFY( 2 == info);
|
||||
VERIFY( 284 == lm.nfev);
|
||||
VERIFY( 249 == lm.njev);
|
||||
// check norm^2
|
||||
VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 8.7945855171E+01);
|
||||
// check x
|
||||
@@ -1188,7 +1188,7 @@ void testNistMGH10(void)
|
||||
info = lm.minimize(x);
|
||||
|
||||
// check return value
|
||||
VERIFY( 2 == info);
|
||||
VERIFY( 3 == info);
|
||||
VERIFY( 126 == lm.nfev);
|
||||
VERIFY( 116 == lm.njev);
|
||||
// check norm^2
|
||||
@@ -1243,8 +1243,8 @@ void testNistBoxBOD(void)
|
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// do the computation
|
||||
BoxBOD_functor functor;
|
||||
LevenbergMarquardt<BoxBOD_functor> lm(functor);
|
||||
lm.parameters.ftol = 1.E6*epsilon<double>();
|
||||
lm.parameters.xtol = 1.E6*epsilon<double>();
|
||||
lm.parameters.ftol = 1.E6*NumTraits<double>::epsilon();
|
||||
lm.parameters.xtol = 1.E6*NumTraits<double>::epsilon();
|
||||
lm.parameters.factor = 10.;
|
||||
info = lm.minimize(x);
|
||||
|
||||
@@ -1264,14 +1264,14 @@ void testNistBoxBOD(void)
|
||||
x<< 100., 0.75;
|
||||
// do the computation
|
||||
lm.resetParameters();
|
||||
lm.parameters.ftol = epsilon<double>();
|
||||
lm.parameters.xtol = epsilon<double>();
|
||||
lm.parameters.ftol = NumTraits<double>::epsilon();
|
||||
lm.parameters.xtol = NumTraits<double>::epsilon();
|
||||
info = lm.minimize(x);
|
||||
|
||||
// check return value
|
||||
VERIFY( 1 == info);
|
||||
VERIFY( 15 == lm.nfev);
|
||||
VERIFY( 14 == lm.njev);
|
||||
VERIFY( 1 == info);
|
||||
VERIFY( 15 == lm.nfev);
|
||||
VERIFY( 14 == lm.njev);
|
||||
// check norm^2
|
||||
VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.1680088766E+03);
|
||||
// check x
|
||||
@@ -1325,15 +1325,15 @@ void testNistMGH17(void)
|
||||
// do the computation
|
||||
MGH17_functor functor;
|
||||
LevenbergMarquardt<MGH17_functor> lm(functor);
|
||||
lm.parameters.ftol = epsilon<double>();
|
||||
lm.parameters.xtol = epsilon<double>();
|
||||
lm.parameters.ftol = NumTraits<double>::epsilon();
|
||||
lm.parameters.xtol = NumTraits<double>::epsilon();
|
||||
lm.parameters.maxfev = 1000;
|
||||
info = lm.minimize(x);
|
||||
|
||||
// check return value
|
||||
VERIFY( 1 == info);
|
||||
VERIFY( 599 == lm.nfev);
|
||||
VERIFY( 544 == lm.njev);
|
||||
VERIFY( 2 == info);
|
||||
VERIFY( 602 == lm.nfev);
|
||||
VERIFY( 545 == lm.njev);
|
||||
// check norm^2
|
||||
VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.4648946975E-05);
|
||||
// check x
|
||||
@@ -1418,16 +1418,16 @@ void testNistMGH09(void)
|
||||
info = lm.minimize(x);
|
||||
|
||||
// check return value
|
||||
VERIFY( 1 == info);
|
||||
VERIFY( 503== lm.nfev);
|
||||
VERIFY( 385 == lm.njev);
|
||||
VERIFY( 1 == info);
|
||||
VERIFY( 490 == lm.nfev);
|
||||
VERIFY( 376 == lm.njev);
|
||||
// check norm^2
|
||||
VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 3.0750560385E-04);
|
||||
// check x
|
||||
VERIFY_IS_APPROX(x[0], 0.19280624); // should be 1.9280693458E-01
|
||||
VERIFY_IS_APPROX(x[1], 0.19129774); // should be 1.9128232873E-01
|
||||
VERIFY_IS_APPROX(x[2], 0.12305940); // should be 1.2305650693E-01
|
||||
VERIFY_IS_APPROX(x[3], 0.13606946); // should be 1.3606233068E-01
|
||||
VERIFY_IS_APPROX(x[0], 0.1928077089); // should be 1.9280693458E-01
|
||||
VERIFY_IS_APPROX(x[1], 0.19126423573); // should be 1.9128232873E-01
|
||||
VERIFY_IS_APPROX(x[2], 0.12305309914); // should be 1.2305650693E-01
|
||||
VERIFY_IS_APPROX(x[3], 0.13605395375); // should be 1.3606233068E-01
|
||||
|
||||
/*
|
||||
* Second try
|
||||
@@ -1584,8 +1584,8 @@ void testNistThurber(void)
|
||||
// do the computation
|
||||
thurber_functor functor;
|
||||
LevenbergMarquardt<thurber_functor> lm(functor);
|
||||
lm.parameters.ftol = 1.E4*epsilon<double>();
|
||||
lm.parameters.xtol = 1.E4*epsilon<double>();
|
||||
lm.parameters.ftol = 1.E4*NumTraits<double>::epsilon();
|
||||
lm.parameters.xtol = 1.E4*NumTraits<double>::epsilon();
|
||||
info = lm.minimize(x);
|
||||
|
||||
// check return value
|
||||
@@ -1609,8 +1609,8 @@ void testNistThurber(void)
|
||||
x<< 1300 ,1500 ,500 ,75 ,1 ,0.4 ,0.05 ;
|
||||
// do the computation
|
||||
lm.resetParameters();
|
||||
lm.parameters.ftol = 1.E4*epsilon<double>();
|
||||
lm.parameters.xtol = 1.E4*epsilon<double>();
|
||||
lm.parameters.ftol = 1.E4*NumTraits<double>::epsilon();
|
||||
lm.parameters.xtol = 1.E4*NumTraits<double>::epsilon();
|
||||
info = lm.minimize(x);
|
||||
|
||||
// check return value
|
||||
@@ -1676,8 +1676,8 @@ void testNistRat43(void)
|
||||
// do the computation
|
||||
rat43_functor functor;
|
||||
LevenbergMarquardt<rat43_functor> lm(functor);
|
||||
lm.parameters.ftol = 1.E6*epsilon<double>();
|
||||
lm.parameters.xtol = 1.E6*epsilon<double>();
|
||||
lm.parameters.ftol = 1.E6*NumTraits<double>::epsilon();
|
||||
lm.parameters.xtol = 1.E6*NumTraits<double>::epsilon();
|
||||
info = lm.minimize(x);
|
||||
|
||||
// check return value
|
||||
@@ -1698,8 +1698,8 @@ void testNistRat43(void)
|
||||
x<< 700., 5., 0.75, 1.3;
|
||||
// do the computation
|
||||
lm.resetParameters();
|
||||
lm.parameters.ftol = 1.E5*epsilon<double>();
|
||||
lm.parameters.xtol = 1.E5*epsilon<double>();
|
||||
lm.parameters.ftol = 1.E5*NumTraits<double>::epsilon();
|
||||
lm.parameters.xtol = 1.E5*NumTraits<double>::epsilon();
|
||||
info = lm.minimize(x);
|
||||
|
||||
// check return value
|
||||
@@ -1833,7 +1833,6 @@ void test_NonLinearOptimization()
|
||||
|
||||
/*
|
||||
* Can be useful for debugging...
|
||||
printf("info, nfev, njev : %d, %d, %d\n", info, lm.nfev, lm.njev);
|
||||
printf("info, nfev : %d, %d\n", info, lm.nfev);
|
||||
printf("info, nfev, njev : %d, %d, %d\n", info, solver.nfev, solver.njev);
|
||||
printf("info, nfev : %d, %d\n", info, solver.nfev);
|
||||
@@ -1843,5 +1842,14 @@ void test_NonLinearOptimization()
|
||||
printf("x[3] : %.32g\n", x[3]);
|
||||
printf("fvec.blueNorm() : %.32g\n", solver.fvec.blueNorm());
|
||||
printf("fvec.blueNorm() : %.32g\n", lm.fvec.blueNorm());
|
||||
|
||||
printf("info, nfev, njev : %d, %d, %d\n", info, lm.nfev, lm.njev);
|
||||
printf("fvec.squaredNorm() : %.13g\n", lm.fvec.squaredNorm());
|
||||
std::cout << x << std::endl;
|
||||
std::cout.precision(9);
|
||||
std::cout << x[0] << std::endl;
|
||||
std::cout << x[1] << std::endl;
|
||||
std::cout << x[2] << std::endl;
|
||||
std::cout << x[3] << std::endl;
|
||||
*/
|
||||
|
||||
|
||||
@@ -61,7 +61,7 @@ void test2dRotation(double tol)
|
||||
std::cout << "test2dRotation: i = " << i << " error funm = " << relerr(C, B);
|
||||
VERIFY(C.isApprox(B, static_cast<T>(tol)));
|
||||
|
||||
ei_matrix_exponential(angle*A, &C);
|
||||
C = ei_matrix_exponential(angle*A);
|
||||
std::cout << " error expm = " << relerr(C, B) << "\n";
|
||||
VERIFY(C.isApprox(B, static_cast<T>(tol)));
|
||||
}
|
||||
@@ -86,7 +86,7 @@ void test2dHyperbolicRotation(double tol)
|
||||
std::cout << "test2dHyperbolicRotation: i = " << i << " error funm = " << relerr(C, B);
|
||||
VERIFY(C.isApprox(B, static_cast<T>(tol)));
|
||||
|
||||
ei_matrix_exponential(A, &C);
|
||||
C = ei_matrix_exponential(A);
|
||||
std::cout << " error expm = " << relerr(C, B) << "\n";
|
||||
VERIFY(C.isApprox(B, static_cast<T>(tol)));
|
||||
}
|
||||
@@ -110,7 +110,7 @@ void testPascal(double tol)
|
||||
std::cout << "testPascal: size = " << size << " error funm = " << relerr(C, B);
|
||||
VERIFY(C.isApprox(B, static_cast<T>(tol)));
|
||||
|
||||
ei_matrix_exponential(A, &C);
|
||||
C = ei_matrix_exponential(A);
|
||||
std::cout << " error expm = " << relerr(C, B) << "\n";
|
||||
VERIFY(C.isApprox(B, static_cast<T>(tol)));
|
||||
}
|
||||
@@ -137,10 +137,9 @@ void randomTest(const MatrixType& m, double tol)
|
||||
std::cout << "randomTest: error funm = " << relerr(identity, m2 * m3);
|
||||
VERIFY(identity.isApprox(m2 * m3, static_cast<RealScalar>(tol)));
|
||||
|
||||
ei_matrix_exponential(m1, &m2);
|
||||
ei_matrix_exponential(-m1, &m3);
|
||||
std::cout << " error expm = " << relerr(identity, m2 * m3) << "\n";
|
||||
VERIFY(identity.isApprox(m2 * m3, static_cast<RealScalar>(tol)));
|
||||
m2 = ei_matrix_exponential(m1) * ei_matrix_exponential(-m1);
|
||||
std::cout << " error expm = " << relerr(identity, m2) << "\n";
|
||||
VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol)));
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
@@ -25,44 +25,100 @@
|
||||
#include "main.h"
|
||||
#include <unsupported/Eigen/MatrixFunctions>
|
||||
|
||||
// Returns a matrix with eigenvalues clustered around 0, 1 and 2.
|
||||
template<typename MatrixType>
|
||||
void testMatrixExponential(const MatrixType& m)
|
||||
MatrixType randomMatrixWithRealEivals(const int size)
|
||||
{
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename MatrixType::RealScalar RealScalar;
|
||||
MatrixType diag = MatrixType::Zero(size, size);
|
||||
for (int i = 0; i < size; ++i) {
|
||||
diag(i, i) = Scalar(RealScalar(ei_random<int>(0,2)))
|
||||
+ ei_random<Scalar>() * Scalar(RealScalar(0.01));
|
||||
}
|
||||
MatrixType A = MatrixType::Random(size, size);
|
||||
return A.inverse() * diag * A;
|
||||
}
|
||||
|
||||
template <typename MatrixType, int IsComplex = NumTraits<typename ei_traits<MatrixType>::Scalar>::IsComplex>
|
||||
struct randomMatrixWithImagEivals
|
||||
{
|
||||
// Returns a matrix with eigenvalues clustered around 0 and +/- i.
|
||||
static MatrixType run(const int size);
|
||||
};
|
||||
|
||||
// Partial specialization for real matrices
|
||||
template<typename MatrixType>
|
||||
struct randomMatrixWithImagEivals<MatrixType, 0>
|
||||
{
|
||||
static MatrixType run(const int size)
|
||||
{
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
MatrixType diag = MatrixType::Zero(size, size);
|
||||
int i = 0;
|
||||
while (i < size) {
|
||||
int randomInt = ei_random<int>(-1, 1);
|
||||
if (randomInt == 0 || i == size-1) {
|
||||
diag(i, i) = ei_random<Scalar>() * Scalar(0.01);
|
||||
++i;
|
||||
} else {
|
||||
Scalar alpha = Scalar(randomInt) + ei_random<Scalar>() * Scalar(0.01);
|
||||
diag(i, i+1) = alpha;
|
||||
diag(i+1, i) = -alpha;
|
||||
i += 2;
|
||||
}
|
||||
}
|
||||
MatrixType A = MatrixType::Random(size, size);
|
||||
return A.inverse() * diag * A;
|
||||
}
|
||||
};
|
||||
|
||||
// Partial specialization for complex matrices
|
||||
template<typename MatrixType>
|
||||
struct randomMatrixWithImagEivals<MatrixType, 1>
|
||||
{
|
||||
static MatrixType run(const int size)
|
||||
{
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename MatrixType::RealScalar RealScalar;
|
||||
const Scalar imagUnit(0, 1);
|
||||
MatrixType diag = MatrixType::Zero(size, size);
|
||||
for (int i = 0; i < size; ++i) {
|
||||
diag(i, i) = Scalar(RealScalar(ei_random<int>(-1, 1))) * imagUnit
|
||||
+ ei_random<Scalar>() * Scalar(RealScalar(0.01));
|
||||
}
|
||||
MatrixType A = MatrixType::Random(size, size);
|
||||
return A.inverse() * diag * A;
|
||||
}
|
||||
};
|
||||
|
||||
template<typename MatrixType>
|
||||
void testMatrixExponential(const MatrixType& A)
|
||||
{
|
||||
typedef typename ei_traits<MatrixType>::Scalar Scalar;
|
||||
typedef typename NumTraits<Scalar>::Real RealScalar;
|
||||
typedef std::complex<RealScalar> ComplexScalar;
|
||||
|
||||
const int rows = m.rows();
|
||||
const int cols = m.cols();
|
||||
|
||||
for (int i = 0; i < g_repeat; i++) {
|
||||
MatrixType A = MatrixType::Random(rows, cols);
|
||||
MatrixType expA1, expA2;
|
||||
ei_matrix_exponential(A, &expA1);
|
||||
ei_matrix_function(A, StdStemFunctions<ComplexScalar>::exp, &expA2);
|
||||
VERIFY_IS_APPROX(expA1, expA2);
|
||||
VERIFY_IS_APPROX(ei_matrix_exponential(A),
|
||||
ei_matrix_function(A, StdStemFunctions<ComplexScalar>::exp));
|
||||
}
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
void testHyperbolicFunctions(const MatrixType& m)
|
||||
void testHyperbolicFunctions(const MatrixType& A)
|
||||
{
|
||||
const int rows = m.rows();
|
||||
const int cols = m.cols();
|
||||
|
||||
for (int i = 0; i < g_repeat; i++) {
|
||||
MatrixType A = MatrixType::Random(rows, cols);
|
||||
MatrixType sinhA, coshA, expA;
|
||||
ei_matrix_sinh(A, &sinhA);
|
||||
ei_matrix_cosh(A, &coshA);
|
||||
ei_matrix_exponential(A, &expA);
|
||||
MatrixType sinhA = ei_matrix_sinh(A);
|
||||
MatrixType coshA = ei_matrix_cosh(A);
|
||||
MatrixType expA = ei_matrix_exponential(A);
|
||||
VERIFY_IS_APPROX(sinhA, (expA - expA.inverse())/2);
|
||||
VERIFY_IS_APPROX(coshA, (expA + expA.inverse())/2);
|
||||
}
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
void testGonioFunctions(const MatrixType& m)
|
||||
void testGonioFunctions(const MatrixType& A)
|
||||
{
|
||||
typedef ei_traits<MatrixType> Traits;
|
||||
typedef typename Traits::Scalar Scalar;
|
||||
@@ -71,36 +127,44 @@ void testGonioFunctions(const MatrixType& m)
|
||||
typedef Matrix<ComplexScalar, Traits::RowsAtCompileTime,
|
||||
Traits::ColsAtCompileTime, MatrixType::Options> ComplexMatrix;
|
||||
|
||||
const int rows = m.rows();
|
||||
const int cols = m.cols();
|
||||
ComplexScalar imagUnit(0,1);
|
||||
ComplexScalar two(2,0);
|
||||
|
||||
for (int i = 0; i < g_repeat; i++) {
|
||||
MatrixType A = MatrixType::Random(rows, cols);
|
||||
ComplexMatrix Ac = A.template cast<ComplexScalar>();
|
||||
|
||||
ComplexMatrix exp_iA;
|
||||
ei_matrix_exponential(imagUnit * Ac, &exp_iA);
|
||||
ComplexMatrix exp_iA = ei_matrix_exponential(imagUnit * Ac);
|
||||
|
||||
MatrixType sinA;
|
||||
ei_matrix_sin(A, &sinA);
|
||||
MatrixType sinA = ei_matrix_sin(A);
|
||||
ComplexMatrix sinAc = sinA.template cast<ComplexScalar>();
|
||||
VERIFY_IS_APPROX(sinAc, (exp_iA - exp_iA.inverse()) / (two*imagUnit));
|
||||
|
||||
MatrixType cosA;
|
||||
ei_matrix_cos(A, &cosA);
|
||||
MatrixType cosA = ei_matrix_cos(A);
|
||||
ComplexMatrix cosAc = cosA.template cast<ComplexScalar>();
|
||||
VERIFY_IS_APPROX(cosAc, (exp_iA + exp_iA.inverse()) / 2);
|
||||
}
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
void testMatrix(const MatrixType& A)
|
||||
{
|
||||
testMatrixExponential(A);
|
||||
testHyperbolicFunctions(A);
|
||||
testGonioFunctions(A);
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
void testMatrixType(const MatrixType& m)
|
||||
{
|
||||
testMatrixExponential(m);
|
||||
testHyperbolicFunctions(m);
|
||||
testGonioFunctions(m);
|
||||
// Matrices with clustered eigenvalue lead to different code paths
|
||||
// in MatrixFunction.h and are thus useful for testing.
|
||||
|
||||
const int size = m.rows();
|
||||
for (int i = 0; i < g_repeat; i++) {
|
||||
testMatrix(MatrixType::Random(size, size).eval());
|
||||
testMatrix(randomMatrixWithRealEivals<MatrixType>(size));
|
||||
testMatrix(randomMatrixWithImagEivals<MatrixType>::run(size));
|
||||
}
|
||||
}
|
||||
|
||||
void test_matrix_function()
|
||||
|
||||
Reference in New Issue
Block a user