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