Squashed 'third_party/eigen/' content from commit 61d72f6
Change-Id: Iccc90fa0b55ab44037f018046d2fcffd90d9d025
git-subtree-dir: third_party/eigen
git-subtree-split: 61d72f6383cfa842868c53e30e087b0258177257
diff --git a/bench/spbench/CMakeLists.txt b/bench/spbench/CMakeLists.txt
new file mode 100644
index 0000000..6e0e1b1
--- /dev/null
+++ b/bench/spbench/CMakeLists.txt
@@ -0,0 +1,78 @@
+
+
+set(BLAS_FOUND TRUE)
+set(LAPACK_FOUND TRUE)
+set(BLAS_LIBRARIES eigen_blas_static)
+set(LAPACK_LIBRARIES eigen_lapack_static)
+
+set(SPARSE_LIBS "")
+
+# find_library(PARDISO_LIBRARIES pardiso412-GNU450-X86-64)
+# if(PARDISO_LIBRARIES)
+# add_definitions("-DEIGEN_PARDISO_SUPPORT")
+# set(SPARSE_LIBS ${SPARSE_LIBS} ${PARDISO_LIBRARIES})
+# endif(PARDISO_LIBRARIES)
+
+find_package(Cholmod)
+if(CHOLMOD_FOUND AND BLAS_FOUND AND LAPACK_FOUND)
+ add_definitions("-DEIGEN_CHOLMOD_SUPPORT")
+ include_directories(${CHOLMOD_INCLUDES})
+ set(SPARSE_LIBS ${SPARSE_LIBS} ${CHOLMOD_LIBRARIES} ${BLAS_LIBRARIES} ${LAPACK_LIBRARIES})
+ set(CHOLMOD_ALL_LIBS ${CHOLMOD_LIBRARIES} ${BLAS_LIBRARIES} ${LAPACK_LIBRARIES})
+endif()
+
+find_package(Umfpack)
+if(UMFPACK_FOUND AND BLAS_FOUND)
+ add_definitions("-DEIGEN_UMFPACK_SUPPORT")
+ include_directories(${UMFPACK_INCLUDES})
+ set(SPARSE_LIBS ${SPARSE_LIBS} ${UMFPACK_LIBRARIES} ${BLAS_LIBRARIES})
+ set(UMFPACK_ALL_LIBS ${UMFPACK_LIBRARIES} ${BLAS_LIBRARIES})
+endif()
+
+find_package(SuperLU)
+if(SUPERLU_FOUND AND BLAS_FOUND)
+ add_definitions("-DEIGEN_SUPERLU_SUPPORT")
+ include_directories(${SUPERLU_INCLUDES})
+ set(SPARSE_LIBS ${SPARSE_LIBS} ${SUPERLU_LIBRARIES} ${BLAS_LIBRARIES})
+ set(SUPERLU_ALL_LIBS ${SUPERLU_LIBRARIES} ${BLAS_LIBRARIES})
+endif()
+
+
+find_package(Pastix)
+find_package(Scotch)
+find_package(Metis)
+if(PASTIX_FOUND AND BLAS_FOUND)
+ add_definitions("-DEIGEN_PASTIX_SUPPORT")
+ include_directories(${PASTIX_INCLUDES})
+ if(SCOTCH_FOUND)
+ include_directories(${SCOTCH_INCLUDES})
+ set(PASTIX_LIBRARIES ${PASTIX_LIBRARIES} ${SCOTCH_LIBRARIES})
+ elseif(METIS_FOUND)
+ include_directories(${METIS_INCLUDES})
+ set(PASTIX_LIBRARIES ${PASTIX_LIBRARIES} ${METIS_LIBRARIES})
+ endif(SCOTCH_FOUND)
+ set(SPARSE_LIBS ${SPARSE_LIBS} ${PASTIX_LIBRARIES} ${ORDERING_LIBRARIES} ${BLAS_LIBRARIES})
+ set(PASTIX_ALL_LIBS ${PASTIX_LIBRARIES} ${BLAS_LIBRARIES})
+endif(PASTIX_FOUND AND BLAS_FOUND)
+
+if(METIS_FOUND)
+ include_directories(${METIS_INCLUDES})
+ set (SPARSE_LIBS ${SPARSE_LIBS} ${METIS_LIBRARIES})
+ add_definitions("-DEIGEN_METIS_SUPPORT")
+endif(METIS_FOUND)
+
+find_library(RT_LIBRARY rt)
+if(RT_LIBRARY)
+ set(SPARSE_LIBS ${SPARSE_LIBS} ${RT_LIBRARY})
+endif(RT_LIBRARY)
+
+add_executable(spbenchsolver spbenchsolver.cpp)
+target_link_libraries (spbenchsolver ${SPARSE_LIBS})
+
+add_executable(spsolver sp_solver.cpp)
+target_link_libraries (spsolver ${SPARSE_LIBS})
+
+
+add_executable(test_sparseLU test_sparseLU.cpp)
+target_link_libraries (test_sparseLU ${SPARSE_LIBS})
+
diff --git a/bench/spbench/sp_solver.cpp b/bench/spbench/sp_solver.cpp
new file mode 100644
index 0000000..a1f4bac
--- /dev/null
+++ b/bench/spbench/sp_solver.cpp
@@ -0,0 +1,125 @@
+// Small bench routine for Eigen available in Eigen
+// (C) Desire NUENTSA WAKAM, INRIA
+
+#include <iostream>
+#include <fstream>
+#include <iomanip>
+#include <Eigen/Jacobi>
+#include <Eigen/Householder>
+#include <Eigen/IterativeLinearSolvers>
+#include <Eigen/LU>
+#include <unsupported/Eigen/SparseExtra>
+//#include <Eigen/SparseLU>
+#include <Eigen/SuperLUSupport>
+// #include <unsupported/Eigen/src/IterativeSolvers/Scaling.h>
+#include <bench/BenchTimer.h>
+#include <unsupported/Eigen/IterativeSolvers>
+using namespace std;
+using namespace Eigen;
+
+int main(int argc, char **args)
+{
+ SparseMatrix<double, ColMajor> A;
+ typedef SparseMatrix<double, ColMajor>::Index Index;
+ typedef Matrix<double, Dynamic, Dynamic> DenseMatrix;
+ typedef Matrix<double, Dynamic, 1> DenseRhs;
+ VectorXd b, x, tmp;
+ BenchTimer timer,totaltime;
+ //SparseLU<SparseMatrix<double, ColMajor> > solver;
+// SuperLU<SparseMatrix<double, ColMajor> > solver;
+ ConjugateGradient<SparseMatrix<double, ColMajor>, Lower,IncompleteCholesky<double,Lower> > solver;
+ ifstream matrix_file;
+ string line;
+ int n;
+ // Set parameters
+// solver.iparm(IPARM_THREAD_NBR) = 4;
+ /* Fill the matrix with sparse matrix stored in Matrix-Market coordinate column-oriented format */
+ if (argc < 2) assert(false && "please, give the matrix market file ");
+
+ timer.start();
+ totaltime.start();
+ loadMarket(A, args[1]);
+ cout << "End charging matrix " << endl;
+ bool iscomplex=false, isvector=false;
+ int sym;
+ getMarketHeader(args[1], sym, iscomplex, isvector);
+ if (iscomplex) { cout<< " Not for complex matrices \n"; return -1; }
+ if (isvector) { cout << "The provided file is not a matrix file\n"; return -1;}
+ if (sym != 0) { // symmetric matrices, only the lower part is stored
+ SparseMatrix<double, ColMajor> temp;
+ temp = A;
+ A = temp.selfadjointView<Lower>();
+ }
+ timer.stop();
+
+ n = A.cols();
+ // ====== TESTS FOR SPARSE TUTORIAL ======
+// cout<< "OuterSize " << A.outerSize() << " inner " << A.innerSize() << endl;
+// SparseMatrix<double, RowMajor> mat1(A);
+// SparseMatrix<double, RowMajor> mat2;
+// cout << " norm of A " << mat1.norm() << endl; ;
+// PermutationMatrix<Dynamic, Dynamic, int> perm(n);
+// perm.resize(n,1);
+// perm.indices().setLinSpaced(n, 0, n-1);
+// mat2 = perm * mat1;
+// mat.subrows();
+// mat2.resize(n,n);
+// mat2.reserve(10);
+// mat2.setConstant();
+// std::cout<< "NORM " << mat1.squaredNorm()<< endl;
+
+ cout<< "Time to load the matrix " << timer.value() <<endl;
+ /* Fill the right hand side */
+
+// solver.set_restart(374);
+ if (argc > 2)
+ loadMarketVector(b, args[2]);
+ else
+ {
+ b.resize(n);
+ tmp.resize(n);
+// tmp.setRandom();
+ for (int i = 0; i < n; i++) tmp(i) = i;
+ b = A * tmp ;
+ }
+// Scaling<SparseMatrix<double> > scal;
+// scal.computeRef(A);
+// b = scal.LeftScaling().cwiseProduct(b);
+
+ /* Compute the factorization */
+ cout<< "Starting the factorization "<< endl;
+ timer.reset();
+ timer.start();
+ cout<< "Size of Input Matrix "<< b.size()<<"\n\n";
+ cout<< "Rows and columns "<< A.rows() <<" " <<A.cols() <<"\n";
+ solver.compute(A);
+// solver.analyzePattern(A);
+// solver.factorize(A);
+ if (solver.info() != Success) {
+ std::cout<< "The solver failed \n";
+ return -1;
+ }
+ timer.stop();
+ float time_comp = timer.value();
+ cout <<" Compute Time " << time_comp<< endl;
+
+ timer.reset();
+ timer.start();
+ x = solver.solve(b);
+// x = scal.RightScaling().cwiseProduct(x);
+ timer.stop();
+ float time_solve = timer.value();
+ cout<< " Time to solve " << time_solve << endl;
+
+ /* Check the accuracy */
+ VectorXd tmp2 = b - A*x;
+ double tempNorm = tmp2.norm()/b.norm();
+ cout << "Relative norm of the computed solution : " << tempNorm <<"\n";
+// cout << "Iterations : " << solver.iterations() << "\n";
+
+ totaltime.stop();
+ cout << "Total time " << totaltime.value() << "\n";
+// std::cout<<x.transpose()<<"\n";
+
+ return 0;
+}
\ No newline at end of file
diff --git a/bench/spbench/spbench.dtd b/bench/spbench/spbench.dtd
new file mode 100644
index 0000000..0fb51b8
--- /dev/null
+++ b/bench/spbench/spbench.dtd
@@ -0,0 +1,31 @@
+<!ELEMENT BENCH (AVAILSOLVER+,LINEARSYSTEM+)>
+ <!ELEMENT AVAILSOLVER (SOLVER+)>
+ <!ELEMENT SOLVER (TYPE,PACKAGE)>
+ <!ELEMENT TYPE (#PCDATA)> <!-- One of LU, LLT, LDLT, ITER -->
+ <!ELEMENT PACKAGE (#PCDATA)> <!-- Derived from a library -->
+ <!ELEMENT LINEARSYSTEM (MATRIX,SOLVER_STAT+,BEST_SOLVER,GLOBAL_PARAMS*)>
+ <!ELEMENT MATRIX (NAME,SIZE,ENTRIES,PATTERN?,SYMMETRY,POSDEF?,ARITHMETIC,RHS*)>
+ <!ELEMENT NAME (#PCDATA)>
+ <!ELEMENT SIZE (#PCDATA)>
+ <!ELEMENT ENTRIES (#PCDATA)> <!-- The number of nonzeros elements -->
+ <!ELEMENT PATTERN (#PCDATA)> <!-- Is structural pattern symmetric or not -->
+ <!ELEMENT SYMMETRY (#PCDATA)> <!-- symmmetry with numerical values -->
+ <!ELEMENT POSDEF (#PCDATA)> <!-- Is the matrix positive definite or not -->
+ <!ELEMENT ARITHMETIC (#PCDATA)>
+ <!ELEMENT RHS (SOURCE)> <!-- A matrix can have one or more right hand side associated. -->
+ <!ELEMENT SOURCE (#PCDATA)> <!-- Source of the right hand side, either generated or provided -->
+ <!ELEMENT SOLVER_STAT (PARAMS*,TIME,ERROR,ITER?)>
+ <!ELEMENT PARAMS (#PCDATA)>
+ <!ELEMENT TIME (COMPUTE,SOLVE,TOTAL)>
+ <!ELEMENT COMPUTE (#PCDATA)> <!-- Time to analyze,to factorize, or to setup the preconditioner-->
+ <!ELEMENT SOLVE (#PCDATA)> <!-- Time to solve with all the available rhs -->
+ <!ELEMENT TOTAL (#PCDATA)>
+ <!ELEMENT ERROR (#PCDATA)> <!-- Either the relative error or the relative residual norm -->
+ <!ELEMENT ITER (#PCDATA)> <!-- Number of iterations -->
+ <!ELEMENT BEST_SOLVER CDATA> <!-- Id of the best solver -->
+ <!ELEMENT GLOBAL_PARAMS (#PCDATA)> <!-- Parameters shared by all solvers -->
+
+<!ATTLIST SOLVER ID CDATA #REQUIRED>
+<!ATTLIST SOLVER_STAT ID CDATA #REQUIRED>
+<!ATTLIST BEST_SOLVER ID CDATA #REQUIRED>
+<!ATTLIST RHS ID CDATA #IMPLIED>
\ No newline at end of file
diff --git a/bench/spbench/spbenchsolver.cpp b/bench/spbench/spbenchsolver.cpp
new file mode 100644
index 0000000..4acd003
--- /dev/null
+++ b/bench/spbench/spbenchsolver.cpp
@@ -0,0 +1,87 @@
+#include <bench/spbench/spbenchsolver.h>
+
+void bench_printhelp()
+{
+ cout<< " \nbenchsolver : performs a benchmark of all the solvers available in Eigen \n\n";
+ cout<< " MATRIX FOLDER : \n";
+ cout<< " The matrices for the benchmark should be collected in a folder specified with an environment variable EIGEN_MATRIXDIR \n";
+ cout<< " The matrices are stored using the matrix market coordinate format \n";
+ cout<< " The matrix and associated right-hand side (rhs) files are named respectively \n";
+ cout<< " as MatrixName.mtx and MatrixName_b.mtx. If the rhs does not exist, a random one is generated. \n";
+ cout<< " If a matrix is SPD, the matrix should be named as MatrixName_SPD.mtx \n";
+ cout<< " If a true solution exists, it should be named as MatrixName_x.mtx; \n" ;
+ cout<< " it will be used to compute the norm of the error relative to the computed solutions\n\n";
+ cout<< " OPTIONS : \n";
+ cout<< " -h or --help \n print this help and return\n\n";
+ cout<< " -d matrixdir \n Use matrixdir as the matrix folder instead of the one specified in the environment variable EIGEN_MATRIXDIR\n\n";
+ cout<< " -o outputfile.xml \n Output the statistics to a xml file \n\n";
+ cout<< " --eps <RelErr> Sets the relative tolerance for iterative solvers (default 1e-08) \n\n";
+ cout<< " --maxits <MaxIts> Sets the maximum number of iterations (default 1000) \n\n";
+
+}
+int main(int argc, char ** args)
+{
+
+ bool help = ( get_options(argc, args, "-h") || get_options(argc, args, "--help") );
+ if(help) {
+ bench_printhelp();
+ return 0;
+ }
+
+ // Get the location of the test matrices
+ string matrix_dir;
+ if (!get_options(argc, args, "-d", &matrix_dir))
+ {
+ if(getenv("EIGEN_MATRIXDIR") == NULL){
+ std::cerr << "Please, specify the location of the matrices with -d mat_folder or the environment variable EIGEN_MATRIXDIR \n";
+ std::cerr << " Run with --help to see the list of all the available options \n";
+ return -1;
+ }
+ matrix_dir = getenv("EIGEN_MATRIXDIR");
+ }
+
+ std::ofstream statbuf;
+ string statFile ;
+
+ // Get the file to write the statistics
+ bool statFileExists = get_options(argc, args, "-o", &statFile);
+ if(statFileExists)
+ {
+ statbuf.open(statFile.c_str(), std::ios::out);
+ if(statbuf.good()){
+ statFileExists = true;
+ printStatheader(statbuf);
+ statbuf.close();
+ }
+ else
+ std::cerr << "Unable to open the provided file for writting... \n";
+ }
+
+ // Get the maximum number of iterations and the tolerance
+ int maxiters = 1000;
+ double tol = 1e-08;
+ string inval;
+ if (get_options(argc, args, "--eps", &inval))
+ tol = atof(inval.c_str());
+ if(get_options(argc, args, "--maxits", &inval))
+ maxiters = atoi(inval.c_str());
+
+ string current_dir;
+ // Test the real-arithmetics matrices
+ Browse_Matrices<double>(matrix_dir, statFileExists, statFile,maxiters, tol);
+
+ // Test the complex-arithmetics matrices
+ Browse_Matrices<std::complex<double> >(matrix_dir, statFileExists, statFile, maxiters, tol);
+
+ if(statFileExists)
+ {
+ statbuf.open(statFile.c_str(), std::ios::app);
+ statbuf << "</BENCH> \n";
+ cout << "\n Output written in " << statFile << " ...\n";
+ statbuf.close();
+ }
+
+ return 0;
+}
+
+
diff --git a/bench/spbench/spbenchsolver.h b/bench/spbench/spbenchsolver.h
new file mode 100644
index 0000000..19c719c
--- /dev/null
+++ b/bench/spbench/spbenchsolver.h
@@ -0,0 +1,554 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+#include <iostream>
+#include <fstream>
+#include <Eigen/SparseCore>
+#include <bench/BenchTimer.h>
+#include <cstdlib>
+#include <string>
+#include <Eigen/Cholesky>
+#include <Eigen/Jacobi>
+#include <Eigen/Householder>
+#include <Eigen/IterativeLinearSolvers>
+#include <unsupported/Eigen/IterativeSolvers>
+#include <Eigen/LU>
+#include <unsupported/Eigen/SparseExtra>
+#include <Eigen/SparseLU>
+
+#include "spbenchstyle.h"
+
+#ifdef EIGEN_METIS_SUPPORT
+#include <Eigen/MetisSupport>
+#endif
+
+#ifdef EIGEN_CHOLMOD_SUPPORT
+#include <Eigen/CholmodSupport>
+#endif
+
+#ifdef EIGEN_UMFPACK_SUPPORT
+#include <Eigen/UmfPackSupport>
+#endif
+
+#ifdef EIGEN_PARDISO_SUPPORT
+#include <Eigen/PardisoSupport>
+#endif
+
+#ifdef EIGEN_SUPERLU_SUPPORT
+#include <Eigen/SuperLUSupport>
+#endif
+
+#ifdef EIGEN_PASTIX_SUPPORT
+#include <Eigen/PaStiXSupport>
+#endif
+
+// CONSTANTS
+#define EIGEN_UMFPACK 10
+#define EIGEN_SUPERLU 20
+#define EIGEN_PASTIX 30
+#define EIGEN_PARDISO 40
+#define EIGEN_SPARSELU_COLAMD 50
+#define EIGEN_SPARSELU_METIS 51
+#define EIGEN_BICGSTAB 60
+#define EIGEN_BICGSTAB_ILUT 61
+#define EIGEN_GMRES 70
+#define EIGEN_GMRES_ILUT 71
+#define EIGEN_SIMPLICIAL_LDLT 80
+#define EIGEN_CHOLMOD_LDLT 90
+#define EIGEN_PASTIX_LDLT 100
+#define EIGEN_PARDISO_LDLT 110
+#define EIGEN_SIMPLICIAL_LLT 120
+#define EIGEN_CHOLMOD_SUPERNODAL_LLT 130
+#define EIGEN_CHOLMOD_SIMPLICIAL_LLT 140
+#define EIGEN_PASTIX_LLT 150
+#define EIGEN_PARDISO_LLT 160
+#define EIGEN_CG 170
+#define EIGEN_CG_PRECOND 180
+
+using namespace Eigen;
+using namespace std;
+
+
+// Global variables for input parameters
+int MaximumIters; // Maximum number of iterations
+double RelErr; // Relative error of the computed solution
+double best_time_val; // Current best time overall solvers
+int best_time_id; // id of the best solver for the current system
+
+template<typename T> inline typename NumTraits<T>::Real test_precision() { return NumTraits<T>::dummy_precision(); }
+template<> inline float test_precision<float>() { return 1e-3f; }
+template<> inline double test_precision<double>() { return 1e-6; }
+template<> inline float test_precision<std::complex<float> >() { return test_precision<float>(); }
+template<> inline double test_precision<std::complex<double> >() { return test_precision<double>(); }
+
+void printStatheader(std::ofstream& out)
+{
+ // Print XML header
+ // NOTE It would have been much easier to write these XML documents using external libraries like tinyXML or Xerces-C++.
+
+ out << "<?xml version='1.0' encoding='UTF-8'?> \n";
+ out << "<?xml-stylesheet type='text/xsl' href='#stylesheet' ?> \n";
+ out << "<!DOCTYPE BENCH [\n<!ATTLIST xsl:stylesheet\n id\t ID #REQUIRED>\n]>";
+ out << "\n\n<!-- Generated by the Eigen library -->\n";
+
+ out << "\n<BENCH> \n" ; //root XML element
+ // Print the xsl style section
+ printBenchStyle(out);
+ // List all available solvers
+ out << " <AVAILSOLVER> \n";
+#ifdef EIGEN_UMFPACK_SUPPORT
+ out <<" <SOLVER ID='" << EIGEN_UMFPACK << "'>\n";
+ out << " <TYPE> LU </TYPE> \n";
+ out << " <PACKAGE> UMFPACK </PACKAGE> \n";
+ out << " </SOLVER> \n";
+#endif
+#ifdef EIGEN_SUPERLU_SUPPORT
+ out <<" <SOLVER ID='" << EIGEN_SUPERLU << "'>\n";
+ out << " <TYPE> LU </TYPE> \n";
+ out << " <PACKAGE> SUPERLU </PACKAGE> \n";
+ out << " </SOLVER> \n";
+#endif
+#ifdef EIGEN_CHOLMOD_SUPPORT
+ out <<" <SOLVER ID='" << EIGEN_CHOLMOD_SIMPLICIAL_LLT << "'>\n";
+ out << " <TYPE> LLT SP</TYPE> \n";
+ out << " <PACKAGE> CHOLMOD </PACKAGE> \n";
+ out << " </SOLVER> \n";
+
+ out <<" <SOLVER ID='" << EIGEN_CHOLMOD_SUPERNODAL_LLT << "'>\n";
+ out << " <TYPE> LLT</TYPE> \n";
+ out << " <PACKAGE> CHOLMOD </PACKAGE> \n";
+ out << " </SOLVER> \n";
+
+ out <<" <SOLVER ID='" << EIGEN_CHOLMOD_LDLT << "'>\n";
+ out << " <TYPE> LDLT </TYPE> \n";
+ out << " <PACKAGE> CHOLMOD </PACKAGE> \n";
+ out << " </SOLVER> \n";
+#endif
+#ifdef EIGEN_PARDISO_SUPPORT
+ out <<" <SOLVER ID='" << EIGEN_PARDISO << "'>\n";
+ out << " <TYPE> LU </TYPE> \n";
+ out << " <PACKAGE> PARDISO </PACKAGE> \n";
+ out << " </SOLVER> \n";
+
+ out <<" <SOLVER ID='" << EIGEN_PARDISO_LLT << "'>\n";
+ out << " <TYPE> LLT </TYPE> \n";
+ out << " <PACKAGE> PARDISO </PACKAGE> \n";
+ out << " </SOLVER> \n";
+
+ out <<" <SOLVER ID='" << EIGEN_PARDISO_LDLT << "'>\n";
+ out << " <TYPE> LDLT </TYPE> \n";
+ out << " <PACKAGE> PARDISO </PACKAGE> \n";
+ out << " </SOLVER> \n";
+#endif
+#ifdef EIGEN_PASTIX_SUPPORT
+ out <<" <SOLVER ID='" << EIGEN_PASTIX << "'>\n";
+ out << " <TYPE> LU </TYPE> \n";
+ out << " <PACKAGE> PASTIX </PACKAGE> \n";
+ out << " </SOLVER> \n";
+
+ out <<" <SOLVER ID='" << EIGEN_PASTIX_LLT << "'>\n";
+ out << " <TYPE> LLT </TYPE> \n";
+ out << " <PACKAGE> PASTIX </PACKAGE> \n";
+ out << " </SOLVER> \n";
+
+ out <<" <SOLVER ID='" << EIGEN_PASTIX_LDLT << "'>\n";
+ out << " <TYPE> LDLT </TYPE> \n";
+ out << " <PACKAGE> PASTIX </PACKAGE> \n";
+ out << " </SOLVER> \n";
+#endif
+
+ out <<" <SOLVER ID='" << EIGEN_BICGSTAB << "'>\n";
+ out << " <TYPE> BICGSTAB </TYPE> \n";
+ out << " <PACKAGE> EIGEN </PACKAGE> \n";
+ out << " </SOLVER> \n";
+
+ out <<" <SOLVER ID='" << EIGEN_BICGSTAB_ILUT << "'>\n";
+ out << " <TYPE> BICGSTAB_ILUT </TYPE> \n";
+ out << " <PACKAGE> EIGEN </PACKAGE> \n";
+ out << " </SOLVER> \n";
+
+ out <<" <SOLVER ID='" << EIGEN_GMRES_ILUT << "'>\n";
+ out << " <TYPE> GMRES_ILUT </TYPE> \n";
+ out << " <PACKAGE> EIGEN </PACKAGE> \n";
+ out << " </SOLVER> \n";
+
+ out <<" <SOLVER ID='" << EIGEN_SIMPLICIAL_LDLT << "'>\n";
+ out << " <TYPE> LDLT </TYPE> \n";
+ out << " <PACKAGE> EIGEN </PACKAGE> \n";
+ out << " </SOLVER> \n";
+
+ out <<" <SOLVER ID='" << EIGEN_SIMPLICIAL_LLT << "'>\n";
+ out << " <TYPE> LLT </TYPE> \n";
+ out << " <PACKAGE> EIGEN </PACKAGE> \n";
+ out << " </SOLVER> \n";
+
+ out <<" <SOLVER ID='" << EIGEN_CG << "'>\n";
+ out << " <TYPE> CG </TYPE> \n";
+ out << " <PACKAGE> EIGEN </PACKAGE> \n";
+ out << " </SOLVER> \n";
+
+ out <<" <SOLVER ID='" << EIGEN_SPARSELU_COLAMD << "'>\n";
+ out << " <TYPE> LU_COLAMD </TYPE> \n";
+ out << " <PACKAGE> EIGEN </PACKAGE> \n";
+ out << " </SOLVER> \n";
+
+#ifdef EIGEN_METIS_SUPPORT
+ out <<" <SOLVER ID='" << EIGEN_SPARSELU_METIS << "'>\n";
+ out << " <TYPE> LU_METIS </TYPE> \n";
+ out << " <PACKAGE> EIGEN </PACKAGE> \n";
+ out << " </SOLVER> \n";
+#endif
+ out << " </AVAILSOLVER> \n";
+
+}
+
+
+template<typename Solver, typename Scalar>
+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)
+{
+
+ double total_time;
+ double compute_time;
+ double solve_time;
+ double rel_error;
+ Matrix<Scalar, Dynamic, 1> x;
+ BenchTimer timer;
+ timer.reset();
+ timer.start();
+ solver.compute(A);
+ if (solver.info() != Success)
+ {
+ std::cerr << "Solver failed ... \n";
+ return;
+ }
+ timer.stop();
+ compute_time = timer.value();
+ statbuf << " <TIME>\n";
+ statbuf << " <COMPUTE> " << timer.value() << "</COMPUTE>\n";
+ std::cout<< "COMPUTE TIME : " << timer.value() <<std::endl;
+
+ timer.reset();
+ timer.start();
+ x = solver.solve(b);
+ if (solver.info() == NumericalIssue)
+ {
+ std::cerr << "Solver failed ... \n";
+ return;
+ }
+ timer.stop();
+ solve_time = timer.value();
+ statbuf << " <SOLVE> " << timer.value() << "</SOLVE>\n";
+ std::cout<< "SOLVE TIME : " << timer.value() <<std::endl;
+
+ total_time = solve_time + compute_time;
+ statbuf << " <TOTAL> " << total_time << "</TOTAL>\n";
+ std::cout<< "TOTAL TIME : " << total_time <<std::endl;
+ statbuf << " </TIME>\n";
+
+ // Verify the relative error
+ if(refX.size() != 0)
+ rel_error = (refX - x).norm()/refX.norm();
+ else
+ {
+ // Compute the relative residual norm
+ Matrix<Scalar, Dynamic, 1> temp;
+ temp = A * x;
+ rel_error = (b-temp).norm()/b.norm();
+ }
+ statbuf << " <ERROR> " << rel_error << "</ERROR>\n";
+ std::cout<< "REL. ERROR : " << rel_error << "\n\n" ;
+ if ( rel_error <= RelErr )
+ {
+ // check the best time if convergence
+ if(!best_time_val || (best_time_val > total_time))
+ {
+ best_time_val = total_time;
+ best_time_id = solver_id;
+ }
+ }
+}
+
+template<typename Solver, typename Scalar>
+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)
+{
+ std::ofstream statbuf(statFile.c_str(), std::ios::app);
+ statbuf << " <SOLVER_STAT ID='" << solver_id <<"'>\n";
+ call_solver(solver, solver_id, A, b, refX,statbuf);
+ statbuf << " </SOLVER_STAT>\n";
+ statbuf.close();
+}
+
+template<typename Solver, typename Scalar>
+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)
+{
+ solver.setTolerance(RelErr);
+ solver.setMaxIterations(MaximumIters);
+
+ std::ofstream statbuf(statFile.c_str(), std::ios::app);
+ statbuf << " <SOLVER_STAT ID='" << solver_id <<"'>\n";
+ call_solver(solver, solver_id, A, b, refX,statbuf);
+ statbuf << " <ITER> "<< solver.iterations() << "</ITER>\n";
+ statbuf << " </SOLVER_STAT>\n";
+ std::cout << "ITERATIONS : " << solver.iterations() <<"\n\n\n";
+
+}
+
+
+template <typename Scalar>
+void SelectSolvers(const SparseMatrix<Scalar>&A, unsigned int sym, Matrix<Scalar, Dynamic, 1>& b, const Matrix<Scalar, Dynamic, 1>& refX, std::string& statFile)
+{
+ typedef SparseMatrix<Scalar, ColMajor> SpMat;
+ // First, deal with Nonsymmetric and symmetric matrices
+ best_time_id = 0;
+ best_time_val = 0.0;
+ //UMFPACK
+ #ifdef EIGEN_UMFPACK_SUPPORT
+ {
+ cout << "Solving with UMFPACK LU ... \n";
+ UmfPackLU<SpMat> solver;
+ call_directsolver(solver, EIGEN_UMFPACK, A, b, refX,statFile);
+ }
+ #endif
+ //SuperLU
+ #ifdef EIGEN_SUPERLU_SUPPORT
+ {
+ cout << "\nSolving with SUPERLU ... \n";
+ SuperLU<SpMat> solver;
+ call_directsolver(solver, EIGEN_SUPERLU, A, b, refX,statFile);
+ }
+ #endif
+
+ // PaStix LU
+ #ifdef EIGEN_PASTIX_SUPPORT
+ {
+ cout << "\nSolving with PASTIX LU ... \n";
+ PastixLU<SpMat> solver;
+ call_directsolver(solver, EIGEN_PASTIX, A, b, refX,statFile) ;
+ }
+ #endif
+
+ //PARDISO LU
+ #ifdef EIGEN_PARDISO_SUPPORT
+ {
+ cout << "\nSolving with PARDISO LU ... \n";
+ PardisoLU<SpMat> solver;
+ call_directsolver(solver, EIGEN_PARDISO, A, b, refX,statFile);
+ }
+ #endif
+
+ // Eigen SparseLU METIS
+ cout << "\n Solving with Sparse LU AND COLAMD ... \n";
+ SparseLU<SpMat, COLAMDOrdering<int> > solver;
+ call_directsolver(solver, EIGEN_SPARSELU_COLAMD, A, b, refX, statFile);
+ // Eigen SparseLU METIS
+ #ifdef EIGEN_METIS_SUPPORT
+ {
+ cout << "\n Solving with Sparse LU AND METIS ... \n";
+ SparseLU<SpMat, MetisOrdering<int> > solver;
+ call_directsolver(solver, EIGEN_SPARSELU_METIS, A, b, refX, statFile);
+ }
+ #endif
+
+ //BiCGSTAB
+ {
+ cout << "\nSolving with BiCGSTAB ... \n";
+ BiCGSTAB<SpMat> solver;
+ call_itersolver(solver, EIGEN_BICGSTAB, A, b, refX,statFile);
+ }
+ //BiCGSTAB+ILUT
+ {
+ cout << "\nSolving with BiCGSTAB and ILUT ... \n";
+ BiCGSTAB<SpMat, IncompleteLUT<Scalar> > solver;
+ call_itersolver(solver, EIGEN_BICGSTAB_ILUT, A, b, refX,statFile);
+ }
+
+
+ //GMRES
+// {
+// cout << "\nSolving with GMRES ... \n";
+// GMRES<SpMat> solver;
+// call_itersolver(solver, EIGEN_GMRES, A, b, refX,statFile);
+// }
+ //GMRES+ILUT
+ {
+ cout << "\nSolving with GMRES and ILUT ... \n";
+ GMRES<SpMat, IncompleteLUT<Scalar> > solver;
+ call_itersolver(solver, EIGEN_GMRES_ILUT, A, b, refX,statFile);
+ }
+
+ // Hermitian and not necessarily positive-definites
+ if (sym != NonSymmetric)
+ {
+ // Internal Cholesky
+ {
+ cout << "\nSolving with Simplicial LDLT ... \n";
+ SimplicialLDLT<SpMat, Lower> solver;
+ call_directsolver(solver, EIGEN_SIMPLICIAL_LDLT, A, b, refX,statFile);
+ }
+
+ // CHOLMOD
+ #ifdef EIGEN_CHOLMOD_SUPPORT
+ {
+ cout << "\nSolving with CHOLMOD LDLT ... \n";
+ CholmodDecomposition<SpMat, Lower> solver;
+ solver.setMode(CholmodLDLt);
+ call_directsolver(solver,EIGEN_CHOLMOD_LDLT, A, b, refX,statFile);
+ }
+ #endif
+
+ //PASTIX LLT
+ #ifdef EIGEN_PASTIX_SUPPORT
+ {
+ cout << "\nSolving with PASTIX LDLT ... \n";
+ PastixLDLT<SpMat, Lower> solver;
+ call_directsolver(solver,EIGEN_PASTIX_LDLT, A, b, refX,statFile);
+ }
+ #endif
+
+ //PARDISO LLT
+ #ifdef EIGEN_PARDISO_SUPPORT
+ {
+ cout << "\nSolving with PARDISO LDLT ... \n";
+ PardisoLDLT<SpMat, Lower> solver;
+ call_directsolver(solver,EIGEN_PARDISO_LDLT, A, b, refX,statFile);
+ }
+ #endif
+ }
+
+ // Now, symmetric POSITIVE DEFINITE matrices
+ if (sym == SPD)
+ {
+
+ //Internal Sparse Cholesky
+ {
+ cout << "\nSolving with SIMPLICIAL LLT ... \n";
+ SimplicialLLT<SpMat, Lower> solver;
+ call_directsolver(solver,EIGEN_SIMPLICIAL_LLT, A, b, refX,statFile);
+ }
+
+ // CHOLMOD
+ #ifdef EIGEN_CHOLMOD_SUPPORT
+ {
+ // CholMOD SuperNodal LLT
+ cout << "\nSolving with CHOLMOD LLT (Supernodal)... \n";
+ CholmodDecomposition<SpMat, Lower> solver;
+ solver.setMode(CholmodSupernodalLLt);
+ call_directsolver(solver,EIGEN_CHOLMOD_SUPERNODAL_LLT, A, b, refX,statFile);
+ // CholMod Simplicial LLT
+ cout << "\nSolving with CHOLMOD LLT (Simplicial) ... \n";
+ solver.setMode(CholmodSimplicialLLt);
+ call_directsolver(solver,EIGEN_CHOLMOD_SIMPLICIAL_LLT, A, b, refX,statFile);
+ }
+ #endif
+
+ //PASTIX LLT
+ #ifdef EIGEN_PASTIX_SUPPORT
+ {
+ cout << "\nSolving with PASTIX LLT ... \n";
+ PastixLLT<SpMat, Lower> solver;
+ 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;
+}
diff --git a/bench/spbench/spbenchstyle.h b/bench/spbench/spbenchstyle.h
new file mode 100644
index 0000000..17a05ce
--- /dev/null
+++ b/bench/spbench/spbenchstyle.h
@@ -0,0 +1,94 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef SPBENCHSTYLE_H
+#define SPBENCHSTYLE_H
+
+void printBenchStyle(std::ofstream& out)
+{
+ out << "<xsl:stylesheet id='stylesheet' version='1.0' \
+ xmlns:xsl='http://www.w3.org/1999/XSL/Transform' >\n \
+ <xsl:template match='xsl:stylesheet' />\n \
+ <xsl:template match='/'> <!-- Root of the document -->\n \
+ <html>\n \
+ <head> \n \
+ <style type='text/css'> \n \
+ td { white-space: nowrap;}\n \
+ </style>\n \
+ </head>\n \
+ <body>";
+ out<<"<table border='1' width='100%' height='100%'>\n \
+ <TR> <!-- Write the table header -->\n \
+ <TH>Matrix</TH> <TH>N</TH> <TH> NNZ</TH> <TH> Sym</TH> <TH> SPD</TH> <TH> </TH>\n \
+ <xsl:for-each select='BENCH/AVAILSOLVER/SOLVER'>\n \
+ <xsl:sort select='@ID' data-type='number'/>\n \
+ <TH>\n \
+ <xsl:value-of select='TYPE' />\n \
+ <xsl:text></xsl:text>\n \
+ <xsl:value-of select='PACKAGE' />\n \
+ <xsl:text></xsl:text>\n \
+ </TH>\n \
+ </xsl:for-each>\n \
+ </TR>";
+
+ out<<" <xsl:for-each select='BENCH/LINEARSYSTEM'>\n \
+ <TR> <!-- print statistics for one linear system-->\n \
+ <TH rowspan='4'> <xsl:value-of select='MATRIX/NAME' /> </TH>\n \
+ <TD rowspan='4'> <xsl:value-of select='MATRIX/SIZE' /> </TD>\n \
+ <TD rowspan='4'> <xsl:value-of select='MATRIX/ENTRIES' /> </TD>\n \
+ <TD rowspan='4'> <xsl:value-of select='MATRIX/SYMMETRY' /> </TD>\n \
+ <TD rowspan='4'> <xsl:value-of select='MATRIX/POSDEF' /> </TD>\n \
+ <TH> Compute Time </TH>\n \
+ <xsl:for-each select='SOLVER_STAT'>\n \
+ <xsl:sort select='@ID' data-type='number'/>\n \
+ <TD> <xsl:value-of select='TIME/COMPUTE' /> </TD>\n \
+ </xsl:for-each>\n \
+ </TR>";
+ out<<" <TR>\n \
+ <TH> Solve Time </TH>\n \
+ <xsl:for-each select='SOLVER_STAT'>\n \
+ <xsl:sort select='@ID' data-type='number'/>\n \
+ <TD> <xsl:value-of select='TIME/SOLVE' /> </TD>\n \
+ </xsl:for-each>\n \
+ </TR>\n \
+ <TR>\n \
+ <TH> Total Time </TH>\n \
+ <xsl:for-each select='SOLVER_STAT'>\n \
+ <xsl:sort select='@ID' data-type='number'/>\n \
+ <xsl:choose>\n \
+ <xsl:when test='@ID=../BEST_SOLVER/@ID'>\n \
+ <TD style='background-color:red'> <xsl:value-of select='TIME/TOTAL' /> </TD>\n \
+ </xsl:when>\n \
+ <xsl:otherwise>\n \
+ <TD> <xsl:value-of select='TIME/TOTAL' /></TD>\n \
+ </xsl:otherwise>\n \
+ </xsl:choose>\n \
+ </xsl:for-each>\n \
+ </TR>";
+ out<<" <TR>\n \
+ <TH> Error </TH>\n \
+ <xsl:for-each select='SOLVER_STAT'>\n \
+ <xsl:sort select='@ID' data-type='number'/>\n \
+ <TD> <xsl:value-of select='ERROR' />\n \
+ <xsl:if test='ITER'>\n \
+ <xsl:text>(</xsl:text>\n \
+ <xsl:value-of select='ITER' />\n \
+ <xsl:text>)</xsl:text>\n \
+ </xsl:if> </TD>\n \
+ </xsl:for-each>\n \
+ </TR>\n \
+ </xsl:for-each>\n \
+ </table>\n \
+ </body>\n \
+ </html>\n \
+ </xsl:template>\n \
+ </xsl:stylesheet>\n\n";
+
+}
+#endif
\ No newline at end of file
diff --git a/bench/spbench/test_sparseLU.cpp b/bench/spbench/test_sparseLU.cpp
new file mode 100644
index 0000000..f8ecbe6
--- /dev/null
+++ b/bench/spbench/test_sparseLU.cpp
@@ -0,0 +1,93 @@
+// Small bench routine for Eigen available in Eigen
+// (C) Desire NUENTSA WAKAM, INRIA
+
+#include <iostream>
+#include <fstream>
+#include <iomanip>
+#include <unsupported/Eigen/SparseExtra>
+#include <Eigen/SparseLU>
+#include <bench/BenchTimer.h>
+#ifdef EIGEN_METIS_SUPPORT
+#include <Eigen/MetisSupport>
+#endif
+
+using namespace std;
+using namespace Eigen;
+
+int main(int argc, char **args)
+{
+// typedef complex<double> scalar;
+ typedef double scalar;
+ SparseMatrix<scalar, ColMajor> A;
+ typedef SparseMatrix<scalar, ColMajor>::Index Index;
+ typedef Matrix<scalar, Dynamic, Dynamic> DenseMatrix;
+ typedef Matrix<scalar, Dynamic, 1> DenseRhs;
+ Matrix<scalar, Dynamic, 1> b, x, tmp;
+// SparseLU<SparseMatrix<scalar, ColMajor>, AMDOrdering<int> > solver;
+// #ifdef EIGEN_METIS_SUPPORT
+// SparseLU<SparseMatrix<scalar, ColMajor>, MetisOrdering<int> > solver;
+// std::cout<< "ORDERING : METIS\n";
+// #else
+ SparseLU<SparseMatrix<scalar, ColMajor>, COLAMDOrdering<int> > solver;
+ std::cout<< "ORDERING : COLAMD\n";
+// #endif
+
+ ifstream matrix_file;
+ string line;
+ int n;
+ BenchTimer timer;
+
+ // Set parameters
+ /* Fill the matrix with sparse matrix stored in Matrix-Market coordinate column-oriented format */
+ if (argc < 2) assert(false && "please, give the matrix market file ");
+ loadMarket(A, args[1]);
+ cout << "End charging matrix " << endl;
+ bool iscomplex=false, isvector=false;
+ int sym;
+ getMarketHeader(args[1], sym, iscomplex, isvector);
+// if (iscomplex) { cout<< " Not for complex matrices \n"; return -1; }
+ if (isvector) { cout << "The provided file is not a matrix file\n"; return -1;}
+ if (sym != 0) { // symmetric matrices, only the lower part is stored
+ SparseMatrix<scalar, ColMajor> temp;
+ temp = A;
+ A = temp.selfadjointView<Lower>();
+ }
+ n = A.cols();
+ /* Fill the right hand side */
+
+ if (argc > 2)
+ loadMarketVector(b, args[2]);
+ else
+ {
+ b.resize(n);
+ tmp.resize(n);
+// tmp.setRandom();
+ for (int i = 0; i < n; i++) tmp(i) = i;
+ b = A * tmp ;
+ }
+
+ /* Compute the factorization */
+// solver.isSymmetric(true);
+ timer.start();
+// solver.compute(A);
+ solver.analyzePattern(A);
+ timer.stop();
+ cout << "Time to analyze " << timer.value() << std::endl;
+ timer.reset();
+ timer.start();
+ solver.factorize(A);
+ timer.stop();
+ cout << "Factorize Time " << timer.value() << std::endl;
+ timer.reset();
+ timer.start();
+ x = solver.solve(b);
+ timer.stop();
+ cout << "solve time " << timer.value() << std::endl;
+ /* Check the accuracy */
+ Matrix<scalar, Dynamic, 1> tmp2 = b - A*x;
+ scalar tempNorm = tmp2.norm()/b.norm();
+ cout << "Relative norm of the computed solution : " << tempNorm <<"\n";
+ cout << "Number of nonzeros in the factor : " << solver.nnzL() + solver.nnzU() << std::endl;
+
+ return 0;
+}
\ No newline at end of file