xref: /aosp_15_r20/external/eigen/bench/spbench/spbenchsolver.h (revision bf2c37156dfe67e5dfebd6d394bad8b2ab5804d4)
1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2012 Désiré Nuentsa-Wakam <[email protected]>
5 //
6 // This Source Code Form is subject to the terms of the Mozilla
7 // Public License v. 2.0. If a copy of the MPL was not distributed
8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9 
10 
11 #include <iostream>
12 #include <fstream>
13 #include <Eigen/SparseCore>
14 #include <bench/BenchTimer.h>
15 #include <cstdlib>
16 #include <string>
17 #include <Eigen/Cholesky>
18 #include <Eigen/Jacobi>
19 #include <Eigen/Householder>
20 #include <Eigen/IterativeLinearSolvers>
21 #include <unsupported/Eigen/IterativeSolvers>
22 #include <Eigen/LU>
23 #include <unsupported/Eigen/SparseExtra>
24 #include <Eigen/SparseLU>
25 
26 #include "spbenchstyle.h"
27 
28 #ifdef EIGEN_METIS_SUPPORT
29 #include <Eigen/MetisSupport>
30 #endif
31 
32 #ifdef EIGEN_CHOLMOD_SUPPORT
33 #include <Eigen/CholmodSupport>
34 #endif
35 
36 #ifdef EIGEN_UMFPACK_SUPPORT
37 #include <Eigen/UmfPackSupport>
38 #endif
39 
40 #ifdef EIGEN_KLU_SUPPORT
41 #include <Eigen/KLUSupport>
42 #endif
43 
44 #ifdef EIGEN_PARDISO_SUPPORT
45 #include <Eigen/PardisoSupport>
46 #endif
47 
48 #ifdef EIGEN_SUPERLU_SUPPORT
49 #include <Eigen/SuperLUSupport>
50 #endif
51 
52 #ifdef EIGEN_PASTIX_SUPPORT
53 #include <Eigen/PaStiXSupport>
54 #endif
55 
56 // CONSTANTS
57 #define EIGEN_UMFPACK  10
58 #define EIGEN_KLU  11
59 #define EIGEN_SUPERLU  20
60 #define EIGEN_PASTIX  30
61 #define EIGEN_PARDISO  40
62 #define EIGEN_SPARSELU_COLAMD 50
63 #define EIGEN_SPARSELU_METIS 51
64 #define EIGEN_BICGSTAB  60
65 #define EIGEN_BICGSTAB_ILUT  61
66 #define EIGEN_GMRES 70
67 #define EIGEN_GMRES_ILUT 71
68 #define EIGEN_SIMPLICIAL_LDLT  80
69 #define EIGEN_CHOLMOD_LDLT  90
70 #define EIGEN_PASTIX_LDLT  100
71 #define EIGEN_PARDISO_LDLT  110
72 #define EIGEN_SIMPLICIAL_LLT  120
73 #define EIGEN_CHOLMOD_SUPERNODAL_LLT  130
74 #define EIGEN_CHOLMOD_SIMPLICIAL_LLT  140
75 #define EIGEN_PASTIX_LLT  150
76 #define EIGEN_PARDISO_LLT  160
77 #define EIGEN_CG  170
78 #define EIGEN_CG_PRECOND  180
79 
80 using namespace Eigen;
81 using namespace std;
82 
83 
84 // Global variables for input parameters
85 int MaximumIters; // Maximum number of iterations
86 double RelErr; // Relative error of the computed solution
87 double best_time_val; // Current best time overall solvers
88 int best_time_id; //  id of the best solver for the current system
89 
test_precision()90 template<typename T> inline typename NumTraits<T>::Real test_precision() { return NumTraits<T>::dummy_precision(); }
91 template<> inline float test_precision<float>() { return 1e-3f; }
92 template<> inline double test_precision<double>() { return 1e-6; }
93 template<> inline float test_precision<std::complex<float> >() { return test_precision<float>(); }
94 template<> inline double test_precision<std::complex<double> >() { return test_precision<double>(); }
95 
printStatheader(std::ofstream & out)96 void printStatheader(std::ofstream& out)
97 {
98   // Print XML header
99   // NOTE It would have been much easier to write these XML documents using external libraries like tinyXML or Xerces-C++.
100 
101   out << "<?xml version='1.0' encoding='UTF-8'?> \n";
102   out << "<?xml-stylesheet type='text/xsl' href='#stylesheet' ?> \n";
103   out << "<!DOCTYPE BENCH  [\n<!ATTLIST xsl:stylesheet\n id\t ID  #REQUIRED>\n]>";
104   out << "\n\n<!-- Generated by the Eigen library -->\n";
105 
106   out << "\n<BENCH> \n" ; //root XML element
107   // Print the xsl style section
108   printBenchStyle(out);
109   // List all available solvers
110   out << " <AVAILSOLVER> \n";
111 #ifdef EIGEN_UMFPACK_SUPPORT
112   out <<"  <SOLVER ID='" << EIGEN_UMFPACK << "'>\n";
113   out << "   <TYPE> LU </TYPE> \n";
114   out << "   <PACKAGE> UMFPACK </PACKAGE> \n";
115   out << "  </SOLVER> \n";
116 #endif
117 #ifdef EIGEN_KLU_SUPPORT
118   out <<"  <SOLVER ID='" << EIGEN_KLU << "'>\n";
119   out << "   <TYPE> LU </TYPE> \n";
120   out << "   <PACKAGE> KLU </PACKAGE> \n";
121   out << "  </SOLVER> \n";
122 #endif
123 #ifdef EIGEN_SUPERLU_SUPPORT
124   out <<"  <SOLVER ID='" << EIGEN_SUPERLU << "'>\n";
125   out << "   <TYPE> LU </TYPE> \n";
126   out << "   <PACKAGE> SUPERLU </PACKAGE> \n";
127   out << "  </SOLVER> \n";
128 #endif
129 #ifdef EIGEN_CHOLMOD_SUPPORT
130   out <<"  <SOLVER ID='" << EIGEN_CHOLMOD_SIMPLICIAL_LLT << "'>\n";
131   out << "   <TYPE> LLT SP</TYPE> \n";
132   out << "   <PACKAGE> CHOLMOD </PACKAGE> \n";
133   out << "  </SOLVER> \n";
134 
135   out <<"  <SOLVER ID='" << EIGEN_CHOLMOD_SUPERNODAL_LLT << "'>\n";
136   out << "   <TYPE> LLT</TYPE> \n";
137   out << "   <PACKAGE> CHOLMOD </PACKAGE> \n";
138   out << "  </SOLVER> \n";
139 
140   out <<"  <SOLVER ID='" << EIGEN_CHOLMOD_LDLT << "'>\n";
141   out << "   <TYPE> LDLT </TYPE> \n";
142   out << "   <PACKAGE> CHOLMOD </PACKAGE> \n";
143   out << "  </SOLVER> \n";
144 #endif
145 #ifdef EIGEN_PARDISO_SUPPORT
146   out <<"  <SOLVER ID='" << EIGEN_PARDISO << "'>\n";
147   out << "   <TYPE> LU </TYPE> \n";
148   out << "   <PACKAGE> PARDISO </PACKAGE> \n";
149   out << "  </SOLVER> \n";
150 
151   out <<"  <SOLVER ID='" << EIGEN_PARDISO_LLT << "'>\n";
152   out << "   <TYPE> LLT </TYPE> \n";
153   out << "   <PACKAGE> PARDISO </PACKAGE> \n";
154   out << "  </SOLVER> \n";
155 
156   out <<"  <SOLVER ID='" << EIGEN_PARDISO_LDLT << "'>\n";
157   out << "   <TYPE> LDLT </TYPE> \n";
158   out << "   <PACKAGE> PARDISO </PACKAGE> \n";
159   out << "  </SOLVER> \n";
160 #endif
161 #ifdef EIGEN_PASTIX_SUPPORT
162   out <<"  <SOLVER ID='" << EIGEN_PASTIX << "'>\n";
163   out << "   <TYPE> LU </TYPE> \n";
164   out << "   <PACKAGE> PASTIX </PACKAGE> \n";
165   out << "  </SOLVER> \n";
166 
167   out <<"  <SOLVER ID='" << EIGEN_PASTIX_LLT << "'>\n";
168   out << "   <TYPE> LLT </TYPE> \n";
169   out << "   <PACKAGE> PASTIX </PACKAGE> \n";
170   out << "  </SOLVER> \n";
171 
172   out <<"  <SOLVER ID='" << EIGEN_PASTIX_LDLT << "'>\n";
173   out << "   <TYPE> LDLT </TYPE> \n";
174   out << "   <PACKAGE> PASTIX </PACKAGE> \n";
175   out << "  </SOLVER> \n";
176 #endif
177 
178   out <<"  <SOLVER ID='" << EIGEN_BICGSTAB << "'>\n";
179   out << "   <TYPE> BICGSTAB </TYPE> \n";
180   out << "   <PACKAGE> EIGEN </PACKAGE> \n";
181   out << "  </SOLVER> \n";
182 
183   out <<"  <SOLVER ID='" << EIGEN_BICGSTAB_ILUT << "'>\n";
184   out << "   <TYPE> BICGSTAB_ILUT </TYPE> \n";
185   out << "   <PACKAGE> EIGEN </PACKAGE> \n";
186   out << "  </SOLVER> \n";
187 
188   out <<"  <SOLVER ID='" << EIGEN_GMRES_ILUT << "'>\n";
189   out << "   <TYPE> GMRES_ILUT </TYPE> \n";
190   out << "   <PACKAGE> EIGEN </PACKAGE> \n";
191   out << "  </SOLVER> \n";
192 
193   out <<"  <SOLVER ID='" << EIGEN_SIMPLICIAL_LDLT << "'>\n";
194   out << "   <TYPE> LDLT </TYPE> \n";
195   out << "   <PACKAGE> EIGEN </PACKAGE> \n";
196   out << "  </SOLVER> \n";
197 
198   out <<"  <SOLVER ID='" << EIGEN_SIMPLICIAL_LLT << "'>\n";
199   out << "   <TYPE> LLT </TYPE> \n";
200   out << "   <PACKAGE> EIGEN </PACKAGE> \n";
201   out << "  </SOLVER> \n";
202 
203   out <<"  <SOLVER ID='" << EIGEN_CG << "'>\n";
204   out << "   <TYPE> CG </TYPE> \n";
205   out << "   <PACKAGE> EIGEN </PACKAGE> \n";
206   out << "  </SOLVER> \n";
207 
208   out <<"  <SOLVER ID='" << EIGEN_SPARSELU_COLAMD << "'>\n";
209   out << "   <TYPE> LU_COLAMD </TYPE> \n";
210   out << "   <PACKAGE> EIGEN </PACKAGE> \n";
211   out << "  </SOLVER> \n";
212 
213 #ifdef EIGEN_METIS_SUPPORT
214   out <<"  <SOLVER ID='" << EIGEN_SPARSELU_METIS << "'>\n";
215   out << "   <TYPE> LU_METIS </TYPE> \n";
216   out << "   <PACKAGE> EIGEN </PACKAGE> \n";
217   out << "  </SOLVER> \n";
218 #endif
219   out << " </AVAILSOLVER> \n";
220 
221 }
222 
223 
224 template<typename Solver, typename Scalar>
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)225 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)
226 {
227 
228   double total_time;
229   double compute_time;
230   double solve_time;
231   double rel_error;
232   Matrix<Scalar, Dynamic, 1> x;
233   BenchTimer timer;
234   timer.reset();
235   timer.start();
236   solver.compute(A);
237   if (solver.info() != Success)
238   {
239     std::cerr << "Solver failed ... \n";
240     return;
241   }
242   timer.stop();
243   compute_time = timer.value();
244   statbuf << "    <TIME>\n";
245   statbuf << "     <COMPUTE> " << timer.value() << "</COMPUTE>\n";
246   std::cout<< "COMPUTE TIME : " << timer.value() <<std::endl;
247 
248   timer.reset();
249   timer.start();
250   x = solver.solve(b);
251   if (solver.info() == NumericalIssue)
252   {
253     std::cerr << "Solver failed ... \n";
254     return;
255   }
256   timer.stop();
257   solve_time = timer.value();
258   statbuf << "     <SOLVE> " << timer.value() << "</SOLVE>\n";
259   std::cout<< "SOLVE TIME : " << timer.value() <<std::endl;
260 
261   total_time = solve_time + compute_time;
262   statbuf << "     <TOTAL> " << total_time << "</TOTAL>\n";
263   std::cout<< "TOTAL TIME : " << total_time <<std::endl;
264   statbuf << "    </TIME>\n";
265 
266   // Verify the relative error
267   if(refX.size() != 0)
268     rel_error = (refX - x).norm()/refX.norm();
269   else
270   {
271     // Compute the relative residual norm
272     Matrix<Scalar, Dynamic, 1> temp;
273     temp = A * x;
274     rel_error = (b-temp).norm()/b.norm();
275   }
276   statbuf << "    <ERROR> " << rel_error << "</ERROR>\n";
277   std::cout<< "REL. ERROR : " << rel_error << "\n\n" ;
278   if ( rel_error <= RelErr )
279   {
280     // check the best time if convergence
281     if(!best_time_val || (best_time_val > total_time))
282     {
283       best_time_val = total_time;
284       best_time_id = solver_id;
285     }
286   }
287 }
288 
289 template<typename Solver, typename Scalar>
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)290 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)
291 {
292     std::ofstream statbuf(statFile.c_str(), std::ios::app);
293     statbuf << "   <SOLVER_STAT ID='" << solver_id <<"'>\n";
294     call_solver(solver, solver_id, A, b, refX,statbuf);
295     statbuf << "   </SOLVER_STAT>\n";
296     statbuf.close();
297 }
298 
299 template<typename Solver, typename Scalar>
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)300 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)
301 {
302   solver.setTolerance(RelErr);
303   solver.setMaxIterations(MaximumIters);
304 
305   std::ofstream statbuf(statFile.c_str(), std::ios::app);
306   statbuf << " <SOLVER_STAT ID='" << solver_id <<"'>\n";
307   call_solver(solver, solver_id, A, b, refX,statbuf);
308   statbuf << "   <ITER> "<< solver.iterations() << "</ITER>\n";
309   statbuf << " </SOLVER_STAT>\n";
310   std::cout << "ITERATIONS : " << solver.iterations() <<"\n\n\n";
311 
312 }
313 
314 
315 template <typename Scalar>
SelectSolvers(const SparseMatrix<Scalar> & A,unsigned int sym,Matrix<Scalar,Dynamic,1> & b,const Matrix<Scalar,Dynamic,1> & refX,std::string & statFile)316 void SelectSolvers(const SparseMatrix<Scalar>&A, unsigned int sym, Matrix<Scalar, Dynamic, 1>& b, const Matrix<Scalar, Dynamic, 1>& refX, std::string& statFile)
317 {
318   typedef SparseMatrix<Scalar, ColMajor> SpMat;
319   // First, deal with Nonsymmetric and symmetric matrices
320   best_time_id = 0;
321   best_time_val = 0.0;
322   //UMFPACK
323   #ifdef EIGEN_UMFPACK_SUPPORT
324   {
325     cout << "Solving with UMFPACK LU ... \n";
326     UmfPackLU<SpMat> solver;
327     call_directsolver(solver, EIGEN_UMFPACK, A, b, refX,statFile);
328   }
329   #endif
330   //KLU
331   #ifdef EIGEN_KLU_SUPPORT
332   {
333     cout << "Solving with KLU LU ... \n";
334     KLU<SpMat> solver;
335     call_directsolver(solver, EIGEN_KLU, A, b, refX,statFile);
336   }
337   #endif
338     //SuperLU
339   #ifdef EIGEN_SUPERLU_SUPPORT
340   {
341     cout << "\nSolving with SUPERLU ... \n";
342     SuperLU<SpMat> solver;
343     call_directsolver(solver, EIGEN_SUPERLU, A, b, refX,statFile);
344   }
345   #endif
346 
347    // PaStix LU
348   #ifdef EIGEN_PASTIX_SUPPORT
349   {
350     cout << "\nSolving with PASTIX LU ... \n";
351     PastixLU<SpMat> solver;
352     call_directsolver(solver, EIGEN_PASTIX, A, b, refX,statFile) ;
353   }
354   #endif
355 
356    //PARDISO LU
357   #ifdef EIGEN_PARDISO_SUPPORT
358   {
359     cout << "\nSolving with PARDISO LU ... \n";
360     PardisoLU<SpMat>  solver;
361     call_directsolver(solver, EIGEN_PARDISO, A, b, refX,statFile);
362   }
363   #endif
364 
365   // Eigen SparseLU METIS
366   cout << "\n Solving with Sparse LU AND COLAMD ... \n";
367   SparseLU<SpMat, COLAMDOrdering<int> >   solver;
368   call_directsolver(solver, EIGEN_SPARSELU_COLAMD, A, b, refX, statFile);
369   // Eigen SparseLU METIS
370   #ifdef EIGEN_METIS_SUPPORT
371   {
372     cout << "\n Solving with Sparse LU AND METIS ... \n";
373     SparseLU<SpMat, MetisOrdering<int> >   solver;
374     call_directsolver(solver, EIGEN_SPARSELU_METIS, A, b, refX, statFile);
375   }
376   #endif
377 
378   //BiCGSTAB
379   {
380     cout << "\nSolving with BiCGSTAB ... \n";
381     BiCGSTAB<SpMat> solver;
382     call_itersolver(solver, EIGEN_BICGSTAB, A, b, refX,statFile);
383   }
384   //BiCGSTAB+ILUT
385   {
386     cout << "\nSolving with BiCGSTAB and ILUT ... \n";
387     BiCGSTAB<SpMat, IncompleteLUT<Scalar> > solver;
388     call_itersolver(solver, EIGEN_BICGSTAB_ILUT, A, b, refX,statFile);
389   }
390 
391 
392   //GMRES
393 //   {
394 //     cout << "\nSolving with GMRES ... \n";
395 //     GMRES<SpMat> solver;
396 //     call_itersolver(solver, EIGEN_GMRES, A, b, refX,statFile);
397 //   }
398   //GMRES+ILUT
399   {
400     cout << "\nSolving with GMRES and ILUT ... \n";
401     GMRES<SpMat, IncompleteLUT<Scalar> > solver;
402     call_itersolver(solver, EIGEN_GMRES_ILUT, A, b, refX,statFile);
403   }
404 
405   // Hermitian and not necessarily positive-definites
406   if (sym != NonSymmetric)
407   {
408     // Internal Cholesky
409     {
410       cout << "\nSolving with Simplicial LDLT ... \n";
411       SimplicialLDLT<SpMat, Lower> solver;
412       call_directsolver(solver, EIGEN_SIMPLICIAL_LDLT, A, b, refX,statFile);
413     }
414 
415     // CHOLMOD
416     #ifdef EIGEN_CHOLMOD_SUPPORT
417     {
418       cout << "\nSolving with CHOLMOD LDLT ... \n";
419       CholmodDecomposition<SpMat, Lower> solver;
420       solver.setMode(CholmodLDLt);
421        call_directsolver(solver,EIGEN_CHOLMOD_LDLT, A, b, refX,statFile);
422     }
423     #endif
424 
425     //PASTIX LLT
426     #ifdef EIGEN_PASTIX_SUPPORT
427     {
428       cout << "\nSolving with PASTIX LDLT ... \n";
429       PastixLDLT<SpMat, Lower> solver;
430       call_directsolver(solver,EIGEN_PASTIX_LDLT, A, b, refX,statFile);
431     }
432     #endif
433 
434     //PARDISO LLT
435     #ifdef EIGEN_PARDISO_SUPPORT
436     {
437       cout << "\nSolving with PARDISO LDLT ... \n";
438       PardisoLDLT<SpMat, Lower> solver;
439       call_directsolver(solver,EIGEN_PARDISO_LDLT, A, b, refX,statFile);
440     }
441     #endif
442   }
443 
444    // Now, symmetric POSITIVE DEFINITE matrices
445   if (sym == SPD)
446   {
447 
448     //Internal Sparse Cholesky
449     {
450       cout << "\nSolving with SIMPLICIAL LLT ... \n";
451       SimplicialLLT<SpMat, Lower> solver;
452       call_directsolver(solver,EIGEN_SIMPLICIAL_LLT, A, b, refX,statFile);
453     }
454 
455     // CHOLMOD
456     #ifdef EIGEN_CHOLMOD_SUPPORT
457     {
458       // CholMOD SuperNodal LLT
459       cout << "\nSolving with CHOLMOD LLT (Supernodal)... \n";
460       CholmodDecomposition<SpMat, Lower> solver;
461       solver.setMode(CholmodSupernodalLLt);
462        call_directsolver(solver,EIGEN_CHOLMOD_SUPERNODAL_LLT, A, b, refX,statFile);
463       // CholMod Simplicial LLT
464       cout << "\nSolving with CHOLMOD LLT (Simplicial) ... \n";
465       solver.setMode(CholmodSimplicialLLt);
466       call_directsolver(solver,EIGEN_CHOLMOD_SIMPLICIAL_LLT, A, b, refX,statFile);
467     }
468     #endif
469 
470     //PASTIX LLT
471     #ifdef EIGEN_PASTIX_SUPPORT
472     {
473       cout << "\nSolving with PASTIX LLT ... \n";
474       PastixLLT<SpMat, Lower> solver;
475       call_directsolver(solver,EIGEN_PASTIX_LLT, A, b, refX,statFile);
476     }
477     #endif
478 
479     //PARDISO LLT
480     #ifdef EIGEN_PARDISO_SUPPORT
481     {
482       cout << "\nSolving with PARDISO LLT ... \n";
483       PardisoLLT<SpMat, Lower> solver;
484       call_directsolver(solver,EIGEN_PARDISO_LLT, A, b, refX,statFile);
485     }
486     #endif
487 
488     // Internal CG
489     {
490       cout << "\nSolving with CG ... \n";
491       ConjugateGradient<SpMat, Lower> solver;
492       call_itersolver(solver,EIGEN_CG, A, b, refX,statFile);
493     }
494     //CG+IdentityPreconditioner
495 //     {
496 //       cout << "\nSolving with CG and IdentityPreconditioner ... \n";
497 //       ConjugateGradient<SpMat, Lower, IdentityPreconditioner> solver;
498 //       call_itersolver(solver,EIGEN_CG_PRECOND, A, b, refX,statFile);
499 //     }
500   } // End SPD matrices
501 }
502 
503 /* Browse all the matrices available in the specified folder
504  * and solve the associated linear system.
505  * The results of each solve are printed in the standard output
506  * and optionally in the provided html file
507  */
508 template <typename Scalar>
Browse_Matrices(const string folder,bool statFileExists,std::string & statFile,int maxiters,double tol)509 void Browse_Matrices(const string folder, bool statFileExists, std::string& statFile, int maxiters, double tol)
510 {
511   MaximumIters = maxiters; // Maximum number of iterations, global variable
512   RelErr = tol;  //Relative residual error  as stopping criterion for iterative solvers
513   MatrixMarketIterator<Scalar> it(folder);
514   for ( ; it; ++it)
515   {
516     //print the infos for this linear system
517     if(statFileExists)
518     {
519       std::ofstream statbuf(statFile.c_str(), std::ios::app);
520       statbuf << "<LINEARSYSTEM> \n";
521       statbuf << "   <MATRIX> \n";
522       statbuf << "     <NAME> " << it.matname() << " </NAME>\n";
523       statbuf << "     <SIZE> " << it.matrix().rows() << " </SIZE>\n";
524       statbuf << "     <ENTRIES> " << it.matrix().nonZeros() << "</ENTRIES>\n";
525       if (it.sym()!=NonSymmetric)
526       {
527         statbuf << "     <SYMMETRY> Symmetric </SYMMETRY>\n" ;
528         if (it.sym() == SPD)
529           statbuf << "     <POSDEF> YES </POSDEF>\n";
530         else
531           statbuf << "     <POSDEF> NO </POSDEF>\n";
532 
533       }
534       else
535       {
536         statbuf << "     <SYMMETRY> NonSymmetric </SYMMETRY>\n" ;
537         statbuf << "     <POSDEF> NO </POSDEF>\n";
538       }
539       statbuf << "   </MATRIX> \n";
540       statbuf.close();
541     }
542 
543     cout<< "\n\n===================================================== \n";
544     cout<< " ======  SOLVING WITH MATRIX " << it.matname() << " ====\n";
545     cout<< " =================================================== \n\n";
546     Matrix<Scalar, Dynamic, 1> refX;
547     if(it.hasrefX()) refX = it.refX();
548     // Call all suitable solvers for this linear system
549     SelectSolvers<Scalar>(it.matrix(), it.sym(), it.rhs(), refX, statFile);
550 
551     if(statFileExists)
552     {
553       std::ofstream statbuf(statFile.c_str(), std::ios::app);
554       statbuf << "  <BEST_SOLVER ID='"<< best_time_id
555               << "'></BEST_SOLVER>\n";
556       statbuf << " </LINEARSYSTEM> \n";
557       statbuf.close();
558     }
559   }
560 }
561 
562 bool get_options(int argc, char **args, string option, string* value=0)
563 {
564   int idx = 1, found=false;
565   while (idx<argc && !found){
566     if (option.compare(args[idx]) == 0){
567       found = true;
568       if(value) *value = args[idx+1];
569     }
570     idx+=2;
571   }
572   return found;
573 }
574