250 lines
7.9 KiB
C++
250 lines
7.9 KiB
C++
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/*
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The Evolving Distribution Objects framework (EDO) is a template-based,
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ANSI-C++ evolutionary computation library which helps you to write your
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own estimation of distribution algorithms.
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This library 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 2.1 of the License, or (at your option) any later version.
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This library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with this library; if not, write to the Free Software
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Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
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Copyright (C) 2010 Thales group
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*/
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/*
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Authors:
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Johann Dréo <johann.dreo@thalesgroup.com>
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*/
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//#include <vector>
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#include <cstdlib>
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#include <iostream>
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#include <sstream>
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#include <limits>
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#include <iomanip>
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#include <ctime>
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#include <eo>
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#include <es.h>
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#include <edo>
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typedef eoReal< eoMinimizingFitness > EOT;
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typedef edoNormalMulti<EOT> EOD;
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void setformat( std::ostream& out )
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{
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out << std::right;
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out << std::setfill(' ');
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out << std::setw( 5 + std::numeric_limits<double>::digits10);
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out << std::setprecision(std::numeric_limits<double>::digits10);
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out << std::setiosflags(std::ios_base::showpoint);
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}
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template<typename MT>
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std::string format(const MT& mat )
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{
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std::ostringstream out;
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setformat(out);
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for( unsigned int i=0; i<mat.size1(); ++i) {
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for( unsigned int j=0; j<mat.size2(); ++j) {
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out << mat(i,j) << "\t";
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} // columns
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out << std::endl;
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} // rows
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return out.str();
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}
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template< typename T >
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T round( T val, T prec = 1.0 )
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{
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return (val > 0.0) ?
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floor(val * prec + 0.5) / prec :
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ceil(val * prec - 0.5) / prec ;
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}
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template<typename MT>
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bool equal( const MT& M1, const MT& M2, double prec /* = 1/std::numeric_limits<double>::digits10 ???*/ )
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{
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if( M1.size1() != M2.size1() || M1.size2() != M2.size2() ) {
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return false;
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}
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for( unsigned int i=0; i<M1.size1(); ++i ) {
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for( unsigned int j=0; j<M1.size2(); ++j ) {
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if( round(M1(i,j),prec) != round(M2(i,j),prec) ) {
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std::cout << "round(M(" << i << "," << j << "," << prec << ") == "
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<< round(M1(i,j),prec) << " != " << round(M2(i,j),prec) << std::endl;
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return false;
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}
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}
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}
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return true;
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}
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template<typename MT >
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MT error( const MT& M1, const MT& M2 )
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{
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assert( M1.size1() == M2.size1() && M1.size1() == M2.size2() );
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MT Err = ublas::zero_matrix<double>(M1.size1(),M1.size2());
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for( unsigned int i=0; i<M1.size1(); ++i ) {
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for( unsigned int j=0; j<M1.size2(); ++j ) {
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Err(i,j) = M1(i,j) - M2(i,j);
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}
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}
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return Err;
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}
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template<typename MT >
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double trigsum( const MT& M )
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{
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double sum;
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for( unsigned int i=0; i<M.size1(); ++i ) {
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for( unsigned int j=i; j<M.size2(); ++j ) { // triangular browsing
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sum += fabs( M(i,j) ); // absolute deviation
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}
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}
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return sum;
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}
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template<typename T>
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double sum( const T& c )
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{
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return std::accumulate(c.begin(), c.end(), 0);
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}
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int main(int argc, char** argv)
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{
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srand(time(0));
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unsigned int N = 4; // size of matrix
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unsigned int R = 1000; // nb of repetitions
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if( argc >= 2 ) {
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N = std::atoi(argv[1]);
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}
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if( argc >= 3 ) {
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R = std::atoi(argv[2]);
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}
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std::cout << "Usage: t-cholesky [matrix size] [repetitions]" << std::endl;
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std::cout << "matrix size = " << N << std::endl;
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std::cout << "repetitions = " << R << std::endl;
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typedef edoSamplerNormalMulti<EOT,EOD>::Cholesky::CovarMat CovarMat;
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typedef edoSamplerNormalMulti<EOT,EOD>::Cholesky::FactorMat FactorMat;
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edoSamplerNormalMulti<EOT,EOD>::Cholesky LLT( edoSamplerNormalMulti<EOT,EOD>::Cholesky::standard );
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edoSamplerNormalMulti<EOT,EOD>::Cholesky LLTa( edoSamplerNormalMulti<EOT,EOD>::Cholesky::absolute );
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edoSamplerNormalMulti<EOT,EOD>::Cholesky LLTz( edoSamplerNormalMulti<EOT,EOD>::Cholesky::zeroing );
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edoSamplerNormalMulti<EOT,EOD>::Cholesky LDLT( edoSamplerNormalMulti<EOT,EOD>::Cholesky::robust );
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std::vector<double> s0,s1,s2,s3;
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for( unsigned int n=0; n<R; ++n ) {
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// a variance-covariance matrix of size N*N
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CovarMat V(N,N);
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// random covariance matrix
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for( unsigned int i=0; i<N; ++i) {
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V(i,i) = std::pow(rand(),2); // variance should be >= 0
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for( unsigned int j=i+1; j<N; ++j) {
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V(i,j) = rand();
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}
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}
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FactorMat L0 = LLT(V);
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CovarMat V0 = ublas::prod( L0, ublas::trans(L0) );
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s0.push_back( trigsum(error(V,V0)) );
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FactorMat L1 = LLTa(V);
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CovarMat V1 = ublas::prod( L1, ublas::trans(L1) );
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s1.push_back( trigsum(error(V,V1)) );
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FactorMat L2 = LLTz(V);
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CovarMat V2 = ublas::prod( L2, ublas::trans(L2) );
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s2.push_back( trigsum(error(V,V2)) );
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FactorMat L3 = LDLT(V);
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CovarMat V3 = ublas::prod( L3, ublas::trans(L3) );
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s3.push_back( trigsum(error(V,V3)) );
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}
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std::cout << "Average error:" << std::endl;
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std::cout << "\tLLT: " << sum(s0)/R << std::endl;
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std::cout << "\tLLTa: " << sum(s1)/R << std::endl;
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std::cout << "\tLLTz: " << sum(s2)/R << std::endl;
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std::cout << "\tLDLT: " << sum(s3)/R << std::endl;
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// double precision = 1e-15;
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// if( argc >= 4 ) {
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// precision = std::atof(argv[3]);
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// }
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// std::cout << "precision = " << precision << std::endl;
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// std::cout << "usage: t-cholesky [N] [precision]" << std::endl;
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// std::cout << "N = " << N << std::endl;
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// std::cout << "precision = " << precision << std::endl;
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// std::string linesep = "--------------------------------------------------------------------------------------------";
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// std::cout << linesep << std::endl;
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//
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// setformat(std::cout);
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//
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// std::cout << "Covariance matrix" << std::endl << format(V) << std::endl;
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// std::cout << linesep << std::endl;
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//
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// edoSamplerNormalMulti<EOT,EOD>::Cholesky LLT( edoSamplerNormalMulti<EOT,EOD>::Cholesky::standard );
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// FactorMat L0 = LLT(V);
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// CovarMat V0 = ublas::prod( L0, ublas::trans(L0) );
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// CovarMat E0 = error(V,V0);
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// std::cout << "LLT" << std::endl << format(E0) << std::endl;
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// std::cout << trigsum(E0) << std::endl;
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// std::cout << "LLT" << std::endl << format(L0) << std::endl;
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// std::cout << "LLT covar" << std::endl << format(V0) << std::endl;
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// assert( equal(V0,V,precision) );
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// std::cout << linesep << std::endl;
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//
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// edoSamplerNormalMulti<EOT,EOD>::Cholesky LLTa( edoSamplerNormalMulti<EOT,EOD>::Cholesky::absolute );
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// FactorMat L1 = LLTa(V);
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// CovarMat V1 = ublas::prod( L1, ublas::trans(L1) );
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// CovarMat E1 = error(V,V1);
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// std::cout << "LLT abs" << std::endl << format(E1) << std::endl;
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// std::cout << trigsum(E1) << std::endl;
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// std::cout << "LLT abs" << std::endl << format(L1) << std::endl;
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// std::cout << "LLT covar" << std::endl << format(V1) << std::endl;
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// assert( equal(V1,V,precision) );
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// std::cout << linesep << std::endl;
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//
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// edoSamplerNormalMulti<EOT,EOD>::Cholesky LDLT( edoSamplerNormalMulti<EOT,EOD>::Cholesky::robust );
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// FactorMat L2 = LDLT(V);
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// CovarMat V2 = ublas::prod( L2, ublas::trans(L2) );
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// CovarMat E2 = error(V,V2);
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// std::cout << "LDLT" << std::endl << format(E2) << std::endl;
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// std::cout << trigsum(E2) << std::endl;
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// std::cout << "LDLT" << std::endl << format(L2) << std::endl;
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// std::cout << "LDLT covar" << std::endl << format(V2) << std::endl;
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// assert( equal(V2,V,precision) );
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// std::cout << linesep << std::endl;
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}
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