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554 lines
17 KiB
554 lines
17 KiB
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#include <iostream>
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#include <fstream>
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#include <Eigen/SparseCore>
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#include <bench/BenchTimer.h>
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#include <cstdlib>
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#include <string>
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#include <Eigen/Cholesky>
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#include <Eigen/Jacobi>
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#include <Eigen/Householder>
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#include <Eigen/IterativeLinearSolvers>
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#include <unsupported/Eigen/IterativeSolvers>
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#include <Eigen/LU>
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#include <unsupported/Eigen/SparseExtra>
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#include <Eigen/SparseLU>
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#include "spbenchstyle.h"
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#ifdef EIGEN_METIS_SUPPORT
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#include <Eigen/MetisSupport>
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#endif
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#ifdef EIGEN_CHOLMOD_SUPPORT
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#include <Eigen/CholmodSupport>
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#endif
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#ifdef EIGEN_UMFPACK_SUPPORT
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#include <Eigen/UmfPackSupport>
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#endif
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#ifdef EIGEN_PARDISO_SUPPORT
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#include <Eigen/PardisoSupport>
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#endif
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#ifdef EIGEN_SUPERLU_SUPPORT
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#include <Eigen/SuperLUSupport>
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#endif
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#ifdef EIGEN_PASTIX_SUPPORT
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#include <Eigen/PaStiXSupport>
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#endif
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// CONSTANTS
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#define EIGEN_UMFPACK 10
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#define EIGEN_SUPERLU 20
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#define EIGEN_PASTIX 30
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#define EIGEN_PARDISO 40
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#define EIGEN_SPARSELU_COLAMD 50
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#define EIGEN_SPARSELU_METIS 51
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#define EIGEN_BICGSTAB 60
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#define EIGEN_BICGSTAB_ILUT 61
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#define EIGEN_GMRES 70
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#define EIGEN_GMRES_ILUT 71
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#define EIGEN_SIMPLICIAL_LDLT 80
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#define EIGEN_CHOLMOD_LDLT 90
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#define EIGEN_PASTIX_LDLT 100
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#define EIGEN_PARDISO_LDLT 110
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#define EIGEN_SIMPLICIAL_LLT 120
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#define EIGEN_CHOLMOD_SUPERNODAL_LLT 130
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#define EIGEN_CHOLMOD_SIMPLICIAL_LLT 140
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#define EIGEN_PASTIX_LLT 150
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#define EIGEN_PARDISO_LLT 160
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#define EIGEN_CG 170
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#define EIGEN_CG_PRECOND 180
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using namespace Eigen;
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using namespace std;
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// Global variables for input parameters
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int MaximumIters; // Maximum number of iterations
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double RelErr; // Relative error of the computed solution
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double best_time_val; // Current best time overall solvers
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int best_time_id; // id of the best solver for the current system
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template<typename T> inline typename NumTraits<T>::Real test_precision() { return NumTraits<T>::dummy_precision(); }
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template<> inline float test_precision<float>() { return 1e-3f; }
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template<> inline double test_precision<double>() { return 1e-6; }
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template<> inline float test_precision<std::complex<float> >() { return test_precision<float>(); }
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template<> inline double test_precision<std::complex<double> >() { return test_precision<double>(); }
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void printStatheader(std::ofstream& out)
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{
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// Print XML header
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// NOTE It would have been much easier to write these XML documents using external libraries like tinyXML or Xerces-C++.
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out << "<?xml version='1.0' encoding='UTF-8'?> \n";
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out << "<?xml-stylesheet type='text/xsl' href='#stylesheet' ?> \n";
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out << "<!DOCTYPE BENCH [\n<!ATTLIST xsl:stylesheet\n id\t ID #REQUIRED>\n]>";
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out << "\n\n<!-- Generated by the Eigen library -->\n";
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out << "\n<BENCH> \n" ; //root XML element
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// Print the xsl style section
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printBenchStyle(out);
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// List all available solvers
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out << " <AVAILSOLVER> \n";
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#ifdef EIGEN_UMFPACK_SUPPORT
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out <<" <SOLVER ID='" << EIGEN_UMFPACK << "'>\n";
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out << " <TYPE> LU </TYPE> \n";
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out << " <PACKAGE> UMFPACK </PACKAGE> \n";
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out << " </SOLVER> \n";
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#endif
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#ifdef EIGEN_SUPERLU_SUPPORT
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out <<" <SOLVER ID='" << EIGEN_SUPERLU << "'>\n";
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out << " <TYPE> LU </TYPE> \n";
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out << " <PACKAGE> SUPERLU </PACKAGE> \n";
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out << " </SOLVER> \n";
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#endif
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#ifdef EIGEN_CHOLMOD_SUPPORT
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out <<" <SOLVER ID='" << EIGEN_CHOLMOD_SIMPLICIAL_LLT << "'>\n";
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out << " <TYPE> LLT SP</TYPE> \n";
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out << " <PACKAGE> CHOLMOD </PACKAGE> \n";
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out << " </SOLVER> \n";
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out <<" <SOLVER ID='" << EIGEN_CHOLMOD_SUPERNODAL_LLT << "'>\n";
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out << " <TYPE> LLT</TYPE> \n";
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out << " <PACKAGE> CHOLMOD </PACKAGE> \n";
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out << " </SOLVER> \n";
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out <<" <SOLVER ID='" << EIGEN_CHOLMOD_LDLT << "'>\n";
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out << " <TYPE> LDLT </TYPE> \n";
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out << " <PACKAGE> CHOLMOD </PACKAGE> \n";
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out << " </SOLVER> \n";
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#endif
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#ifdef EIGEN_PARDISO_SUPPORT
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out <<" <SOLVER ID='" << EIGEN_PARDISO << "'>\n";
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out << " <TYPE> LU </TYPE> \n";
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out << " <PACKAGE> PARDISO </PACKAGE> \n";
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out << " </SOLVER> \n";
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out <<" <SOLVER ID='" << EIGEN_PARDISO_LLT << "'>\n";
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out << " <TYPE> LLT </TYPE> \n";
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out << " <PACKAGE> PARDISO </PACKAGE> \n";
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out << " </SOLVER> \n";
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out <<" <SOLVER ID='" << EIGEN_PARDISO_LDLT << "'>\n";
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out << " <TYPE> LDLT </TYPE> \n";
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out << " <PACKAGE> PARDISO </PACKAGE> \n";
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out << " </SOLVER> \n";
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#endif
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#ifdef EIGEN_PASTIX_SUPPORT
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out <<" <SOLVER ID='" << EIGEN_PASTIX << "'>\n";
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out << " <TYPE> LU </TYPE> \n";
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out << " <PACKAGE> PASTIX </PACKAGE> \n";
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out << " </SOLVER> \n";
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out <<" <SOLVER ID='" << EIGEN_PASTIX_LLT << "'>\n";
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out << " <TYPE> LLT </TYPE> \n";
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out << " <PACKAGE> PASTIX </PACKAGE> \n";
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out << " </SOLVER> \n";
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out <<" <SOLVER ID='" << EIGEN_PASTIX_LDLT << "'>\n";
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out << " <TYPE> LDLT </TYPE> \n";
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out << " <PACKAGE> PASTIX </PACKAGE> \n";
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out << " </SOLVER> \n";
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#endif
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out <<" <SOLVER ID='" << EIGEN_BICGSTAB << "'>\n";
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out << " <TYPE> BICGSTAB </TYPE> \n";
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out << " <PACKAGE> EIGEN </PACKAGE> \n";
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out << " </SOLVER> \n";
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out <<" <SOLVER ID='" << EIGEN_BICGSTAB_ILUT << "'>\n";
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out << " <TYPE> BICGSTAB_ILUT </TYPE> \n";
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out << " <PACKAGE> EIGEN </PACKAGE> \n";
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out << " </SOLVER> \n";
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out <<" <SOLVER ID='" << EIGEN_GMRES_ILUT << "'>\n";
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out << " <TYPE> GMRES_ILUT </TYPE> \n";
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out << " <PACKAGE> EIGEN </PACKAGE> \n";
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out << " </SOLVER> \n";
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out <<" <SOLVER ID='" << EIGEN_SIMPLICIAL_LDLT << "'>\n";
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out << " <TYPE> LDLT </TYPE> \n";
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out << " <PACKAGE> EIGEN </PACKAGE> \n";
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out << " </SOLVER> \n";
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out <<" <SOLVER ID='" << EIGEN_SIMPLICIAL_LLT << "'>\n";
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out << " <TYPE> LLT </TYPE> \n";
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out << " <PACKAGE> EIGEN </PACKAGE> \n";
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out << " </SOLVER> \n";
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out <<" <SOLVER ID='" << EIGEN_CG << "'>\n";
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out << " <TYPE> CG </TYPE> \n";
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out << " <PACKAGE> EIGEN </PACKAGE> \n";
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out << " </SOLVER> \n";
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out <<" <SOLVER ID='" << EIGEN_SPARSELU_COLAMD << "'>\n";
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out << " <TYPE> LU_COLAMD </TYPE> \n";
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out << " <PACKAGE> EIGEN </PACKAGE> \n";
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out << " </SOLVER> \n";
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#ifdef EIGEN_METIS_SUPPORT
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out <<" <SOLVER ID='" << EIGEN_SPARSELU_METIS << "'>\n";
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out << " <TYPE> LU_METIS </TYPE> \n";
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out << " <PACKAGE> EIGEN </PACKAGE> \n";
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out << " </SOLVER> \n";
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#endif
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out << " </AVAILSOLVER> \n";
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}
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template<typename Solver, typename Scalar>
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void call_solver(Solver &solver, const int solver_id, const typename Solver::MatrixType& A, const Matrix<Scalar, Dynamic, 1>& b, const Matrix<Scalar, Dynamic, 1>& refX,std::ofstream& statbuf)
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{
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double total_time;
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double compute_time;
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double solve_time;
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double rel_error;
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Matrix<Scalar, Dynamic, 1> x;
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BenchTimer timer;
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timer.reset();
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timer.start();
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solver.compute(A);
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if (solver.info() != Success)
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{
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std::cerr << "Solver failed ... \n";
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return;
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}
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timer.stop();
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compute_time = timer.value();
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statbuf << " <TIME>\n";
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statbuf << " <COMPUTE> " << timer.value() << "</COMPUTE>\n";
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std::cout<< "COMPUTE TIME : " << timer.value() <<std::endl;
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timer.reset();
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timer.start();
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x = solver.solve(b);
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if (solver.info() == NumericalIssue)
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{
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std::cerr << "Solver failed ... \n";
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return;
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}
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timer.stop();
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solve_time = timer.value();
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statbuf << " <SOLVE> " << timer.value() << "</SOLVE>\n";
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std::cout<< "SOLVE TIME : " << timer.value() <<std::endl;
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total_time = solve_time + compute_time;
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statbuf << " <TOTAL> " << total_time << "</TOTAL>\n";
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std::cout<< "TOTAL TIME : " << total_time <<std::endl;
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statbuf << " </TIME>\n";
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// Verify the relative error
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if(refX.size() != 0)
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rel_error = (refX - x).norm()/refX.norm();
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else
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{
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// Compute the relative residual norm
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Matrix<Scalar, Dynamic, 1> temp;
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temp = A * x;
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rel_error = (b-temp).norm()/b.norm();
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}
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statbuf << " <ERROR> " << rel_error << "</ERROR>\n";
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std::cout<< "REL. ERROR : " << rel_error << "\n\n" ;
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if ( rel_error <= RelErr )
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{
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// check the best time if convergence
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if(!best_time_val || (best_time_val > total_time))
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{
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best_time_val = total_time;
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best_time_id = solver_id;
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}
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}
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}
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template<typename Solver, typename Scalar>
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void call_directsolver(Solver& solver, const int solver_id, const typename Solver::MatrixType& A, const Matrix<Scalar, Dynamic, 1>& b, const Matrix<Scalar, Dynamic, 1>& refX, std::string& statFile)
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{
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std::ofstream statbuf(statFile.c_str(), std::ios::app);
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statbuf << " <SOLVER_STAT ID='" << solver_id <<"'>\n";
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call_solver(solver, solver_id, A, b, refX,statbuf);
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statbuf << " </SOLVER_STAT>\n";
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statbuf.close();
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}
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template<typename Solver, typename Scalar>
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void call_itersolver(Solver &solver, const int solver_id, const typename Solver::MatrixType& A, const Matrix<Scalar, Dynamic, 1>& b, const Matrix<Scalar, Dynamic, 1>& refX, std::string& statFile)
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{
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solver.setTolerance(RelErr);
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solver.setMaxIterations(MaximumIters);
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std::ofstream statbuf(statFile.c_str(), std::ios::app);
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statbuf << " <SOLVER_STAT ID='" << solver_id <<"'>\n";
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call_solver(solver, solver_id, A, b, refX,statbuf);
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statbuf << " <ITER> "<< solver.iterations() << "</ITER>\n";
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statbuf << " </SOLVER_STAT>\n";
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std::cout << "ITERATIONS : " << solver.iterations() <<"\n\n\n";
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}
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template <typename Scalar>
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void SelectSolvers(const SparseMatrix<Scalar>&A, unsigned int sym, Matrix<Scalar, Dynamic, 1>& b, const Matrix<Scalar, Dynamic, 1>& refX, std::string& statFile)
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{
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typedef SparseMatrix<Scalar, ColMajor> SpMat;
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// First, deal with Nonsymmetric and symmetric matrices
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best_time_id = 0;
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best_time_val = 0.0;
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//UMFPACK
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#ifdef EIGEN_UMFPACK_SUPPORT
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{
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cout << "Solving with UMFPACK LU ... \n";
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UmfPackLU<SpMat> solver;
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call_directsolver(solver, EIGEN_UMFPACK, A, b, refX,statFile);
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}
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#endif
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//SuperLU
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#ifdef EIGEN_SUPERLU_SUPPORT
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{
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cout << "\nSolving with SUPERLU ... \n";
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SuperLU<SpMat> solver;
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call_directsolver(solver, EIGEN_SUPERLU, A, b, refX,statFile);
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}
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#endif
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// PaStix LU
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#ifdef EIGEN_PASTIX_SUPPORT
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{
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cout << "\nSolving with PASTIX LU ... \n";
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PastixLU<SpMat> solver;
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call_directsolver(solver, EIGEN_PASTIX, A, b, refX,statFile) ;
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}
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#endif
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//PARDISO LU
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#ifdef EIGEN_PARDISO_SUPPORT
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{
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cout << "\nSolving with PARDISO LU ... \n";
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PardisoLU<SpMat> solver;
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call_directsolver(solver, EIGEN_PARDISO, A, b, refX,statFile);
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}
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#endif
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// Eigen SparseLU METIS
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cout << "\n Solving with Sparse LU AND COLAMD ... \n";
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SparseLU<SpMat, COLAMDOrdering<int> > solver;
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call_directsolver(solver, EIGEN_SPARSELU_COLAMD, A, b, refX, statFile);
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// Eigen SparseLU METIS
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#ifdef EIGEN_METIS_SUPPORT
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{
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cout << "\n Solving with Sparse LU AND METIS ... \n";
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SparseLU<SpMat, MetisOrdering<int> > solver;
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call_directsolver(solver, EIGEN_SPARSELU_METIS, A, b, refX, statFile);
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}
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#endif
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//BiCGSTAB
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{
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cout << "\nSolving with BiCGSTAB ... \n";
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BiCGSTAB<SpMat> solver;
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call_itersolver(solver, EIGEN_BICGSTAB, A, b, refX,statFile);
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}
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//BiCGSTAB+ILUT
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{
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cout << "\nSolving with BiCGSTAB and ILUT ... \n";
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BiCGSTAB<SpMat, IncompleteLUT<Scalar> > solver;
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call_itersolver(solver, EIGEN_BICGSTAB_ILUT, A, b, refX,statFile);
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}
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//GMRES
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// {
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// cout << "\nSolving with GMRES ... \n";
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// GMRES<SpMat> solver;
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// call_itersolver(solver, EIGEN_GMRES, A, b, refX,statFile);
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// }
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//GMRES+ILUT
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{
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cout << "\nSolving with GMRES and ILUT ... \n";
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GMRES<SpMat, IncompleteLUT<Scalar> > solver;
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call_itersolver(solver, EIGEN_GMRES_ILUT, A, b, refX,statFile);
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}
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// Hermitian and not necessarily positive-definites
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if (sym != NonSymmetric)
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{
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// Internal Cholesky
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{
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cout << "\nSolving with Simplicial LDLT ... \n";
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SimplicialLDLT<SpMat, Lower> solver;
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call_directsolver(solver, EIGEN_SIMPLICIAL_LDLT, A, b, refX,statFile);
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}
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// CHOLMOD
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#ifdef EIGEN_CHOLMOD_SUPPORT
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{
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cout << "\nSolving with CHOLMOD LDLT ... \n";
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CholmodDecomposition<SpMat, Lower> solver;
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solver.setMode(CholmodLDLt);
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call_directsolver(solver,EIGEN_CHOLMOD_LDLT, A, b, refX,statFile);
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}
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#endif
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//PASTIX LLT
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#ifdef EIGEN_PASTIX_SUPPORT
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{
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cout << "\nSolving with PASTIX LDLT ... \n";
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PastixLDLT<SpMat, Lower> solver;
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call_directsolver(solver,EIGEN_PASTIX_LDLT, A, b, refX,statFile);
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}
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#endif
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//PARDISO LLT
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#ifdef EIGEN_PARDISO_SUPPORT
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{
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cout << "\nSolving with PARDISO LDLT ... \n";
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PardisoLDLT<SpMat, Lower> solver;
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call_directsolver(solver,EIGEN_PARDISO_LDLT, A, b, refX,statFile);
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}
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#endif
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}
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// Now, symmetric POSITIVE DEFINITE matrices
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if (sym == SPD)
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{
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//Internal Sparse Cholesky
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{
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cout << "\nSolving with SIMPLICIAL LLT ... \n";
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SimplicialLLT<SpMat, Lower> solver;
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call_directsolver(solver,EIGEN_SIMPLICIAL_LLT, A, b, refX,statFile);
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}
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// CHOLMOD
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#ifdef EIGEN_CHOLMOD_SUPPORT
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{
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// CholMOD SuperNodal LLT
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cout << "\nSolving with CHOLMOD LLT (Supernodal)... \n";
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CholmodDecomposition<SpMat, Lower> solver;
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solver.setMode(CholmodSupernodalLLt);
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call_directsolver(solver,EIGEN_CHOLMOD_SUPERNODAL_LLT, A, b, refX,statFile);
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// CholMod Simplicial LLT
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cout << "\nSolving with CHOLMOD LLT (Simplicial) ... \n";
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solver.setMode(CholmodSimplicialLLt);
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call_directsolver(solver,EIGEN_CHOLMOD_SIMPLICIAL_LLT, A, b, refX,statFile);
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}
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#endif
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//PASTIX LLT
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#ifdef EIGEN_PASTIX_SUPPORT
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{
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cout << "\nSolving with PASTIX LLT ... \n";
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PastixLLT<SpMat, Lower> solver;
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call_directsolver(solver,EIGEN_PASTIX_LLT, A, b, refX,statFile);
|
|
}
|
|
#endif
|
|
|
|
//PARDISO LLT
|
|
#ifdef EIGEN_PARDISO_SUPPORT
|
|
{
|
|
cout << "\nSolving with PARDISO LLT ... \n";
|
|
PardisoLLT<SpMat, Lower> solver;
|
|
call_directsolver(solver,EIGEN_PARDISO_LLT, A, b, refX,statFile);
|
|
}
|
|
#endif
|
|
|
|
// Internal CG
|
|
{
|
|
cout << "\nSolving with CG ... \n";
|
|
ConjugateGradient<SpMat, Lower> solver;
|
|
call_itersolver(solver,EIGEN_CG, A, b, refX,statFile);
|
|
}
|
|
//CG+IdentityPreconditioner
|
|
// {
|
|
// cout << "\nSolving with CG and IdentityPreconditioner ... \n";
|
|
// ConjugateGradient<SpMat, Lower, IdentityPreconditioner> solver;
|
|
// call_itersolver(solver,EIGEN_CG_PRECOND, A, b, refX,statFile);
|
|
// }
|
|
} // End SPD matrices
|
|
}
|
|
|
|
/* Browse all the matrices available in the specified folder
|
|
* and solve the associated linear system.
|
|
* The results of each solve are printed in the standard output
|
|
* and optionally in the provided html file
|
|
*/
|
|
template <typename Scalar>
|
|
void Browse_Matrices(const string folder, bool statFileExists, std::string& statFile, int maxiters, double tol)
|
|
{
|
|
MaximumIters = maxiters; // Maximum number of iterations, global variable
|
|
RelErr = tol; //Relative residual error as stopping criterion for iterative solvers
|
|
MatrixMarketIterator<Scalar> it(folder);
|
|
for ( ; it; ++it)
|
|
{
|
|
//print the infos for this linear system
|
|
if(statFileExists)
|
|
{
|
|
std::ofstream statbuf(statFile.c_str(), std::ios::app);
|
|
statbuf << "<LINEARSYSTEM> \n";
|
|
statbuf << " <MATRIX> \n";
|
|
statbuf << " <NAME> " << it.matname() << " </NAME>\n";
|
|
statbuf << " <SIZE> " << it.matrix().rows() << " </SIZE>\n";
|
|
statbuf << " <ENTRIES> " << it.matrix().nonZeros() << "</ENTRIES>\n";
|
|
if (it.sym()!=NonSymmetric)
|
|
{
|
|
statbuf << " <SYMMETRY> Symmetric </SYMMETRY>\n" ;
|
|
if (it.sym() == SPD)
|
|
statbuf << " <POSDEF> YES </POSDEF>\n";
|
|
else
|
|
statbuf << " <POSDEF> NO </POSDEF>\n";
|
|
|
|
}
|
|
else
|
|
{
|
|
statbuf << " <SYMMETRY> NonSymmetric </SYMMETRY>\n" ;
|
|
statbuf << " <POSDEF> NO </POSDEF>\n";
|
|
}
|
|
statbuf << " </MATRIX> \n";
|
|
statbuf.close();
|
|
}
|
|
|
|
cout<< "\n\n===================================================== \n";
|
|
cout<< " ====== SOLVING WITH MATRIX " << it.matname() << " ====\n";
|
|
cout<< " =================================================== \n\n";
|
|
Matrix<Scalar, Dynamic, 1> refX;
|
|
if(it.hasrefX()) refX = it.refX();
|
|
// Call all suitable solvers for this linear system
|
|
SelectSolvers<Scalar>(it.matrix(), it.sym(), it.rhs(), refX, statFile);
|
|
|
|
if(statFileExists)
|
|
{
|
|
std::ofstream statbuf(statFile.c_str(), std::ios::app);
|
|
statbuf << " <BEST_SOLVER ID='"<< best_time_id
|
|
<< "'></BEST_SOLVER>\n";
|
|
statbuf << " </LINEARSYSTEM> \n";
|
|
statbuf.close();
|
|
}
|
|
}
|
|
}
|
|
|
|
bool get_options(int argc, char **args, string option, string* value=0)
|
|
{
|
|
int idx = 1, found=false;
|
|
while (idx<argc && !found){
|
|
if (option.compare(args[idx]) == 0){
|
|
found = true;
|
|
if(value) *value = args[idx+1];
|
|
}
|
|
idx+=2;
|
|
}
|
|
return found;
|
|
}
|