source: pacpussensors/trunk/Vislab/lib3dv/eigen/bench/spbench/spbenchsolver.h@ 139

Last change on this file since 139 was 136, checked in by ldecherf, 8 years ago

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