Amesos2 - Direct Sparse Solver Interfaces Version of the Day
Amesos2_KLU2_def.hpp
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1// @HEADER
2// *****************************************************************************
3// Amesos2: Templated Direct Sparse Solver Package
4//
5// Copyright 2011 NTESS and the Amesos2 contributors.
6// SPDX-License-Identifier: BSD-3-Clause
7// *****************************************************************************
8// @HEADER
9
18#ifndef AMESOS2_KLU2_DEF_HPP
19#define AMESOS2_KLU2_DEF_HPP
20
21#include <Teuchos_Tuple.hpp>
22#include <Teuchos_ParameterList.hpp>
23#include <Teuchos_StandardParameterEntryValidators.hpp>
24
26#include "Amesos2_KLU2_decl.hpp"
27
28namespace Amesos2 {
29
30
31template <class Matrix, class Vector>
33 Teuchos::RCP<const Matrix> A,
34 Teuchos::RCP<Vector> X,
35 Teuchos::RCP<const Vector> B )
36 : SolverCore<Amesos2::KLU2,Matrix,Vector>(A, X, B)
37 , transFlag_(0)
38 , is_contiguous_(true)
39 , use_gather_(true)
40{
41 ::KLU2::klu_defaults<klu2_dtype, local_ordinal_type> (&(data_.common_)) ;
42 data_.symbolic_ = NULL;
43 data_.numeric_ = NULL;
44
45 // Override some default options
46 // TODO: use data_ here to init
47}
48
49
50template <class Matrix, class Vector>
52{
53 /* Free KLU2 data_types
54 * - Matrices
55 * - Vectors
56 * - Other data
57 */
58 if (data_.symbolic_ != NULL)
59 ::KLU2::klu_free_symbolic<klu2_dtype, local_ordinal_type>
60 (&(data_.symbolic_), &(data_.common_)) ;
61 if (data_.numeric_ != NULL)
62 ::KLU2::klu_free_numeric<klu2_dtype, local_ordinal_type>
63 (&(data_.numeric_), &(data_.common_)) ;
64
65 // Storage is initialized in numericFactorization_impl()
66 //if ( data_.A.Store != NULL ){
67 // destoy
68 //}
69
70 // only root allocated these SuperMatrices.
71 //if ( data_.L.Store != NULL ){ // will only be true for this->root_
72 // destroy ..
73 //}
74}
75
76template <class Matrix, class Vector>
77bool
79 return (this->root_ && (this->matrixA_->getComm()->getSize() == 1) && is_contiguous_);
80}
81
82template<class Matrix, class Vector>
83int
85{
86 /* TODO: Define what it means for KLU2
87 */
88#ifdef HAVE_AMESOS2_TIMERS
89 Teuchos::TimeMonitor preOrderTimer(this->timers_.preOrderTime_);
90#endif
91
92 return(0);
93}
94
95
96template <class Matrix, class Vector>
97int
99{
100 if (data_.symbolic_ != NULL) {
101 ::KLU2::klu_free_symbolic<klu2_dtype, local_ordinal_type>
102 (&(data_.symbolic_), &(data_.common_)) ;
103 }
104
105 if ( single_proc_optimization() ) {
106 host_ordinal_type_array host_row_ptr_view;
107 host_ordinal_type_array host_cols_view;
108 this->matrixA_->returnRowPtr_kokkos_view(host_row_ptr_view);
109 this->matrixA_->returnColInd_kokkos_view(host_cols_view);
110 data_.symbolic_ = ::KLU2::klu_analyze<klu2_dtype, local_ordinal_type>
111 ((local_ordinal_type)this->globalNumCols_, host_row_ptr_view.data(),
112 host_cols_view.data(), &(data_.common_)) ;
113 }
114 else
115 {
116 data_.symbolic_ = ::KLU2::klu_analyze<klu2_dtype, local_ordinal_type>
117 ((local_ordinal_type)this->globalNumCols_, host_col_ptr_view_.data(),
118 host_rows_view_.data(), &(data_.common_)) ;
119
120 } //end single_process_optim_check = false
121
122 return(0);
123}
124
125
126template <class Matrix, class Vector>
127int
129{
130 using Teuchos::as;
131
132 // Cleanup old L and U matrices if we are not reusing a symbolic
133 // factorization. Stores and other data will be allocated in gstrf.
134 // Only rank 0 has valid pointers, TODO: for KLU2
135
136 int info = 0;
137 if ( this->root_ ) {
138
139 { // Do factorization
140#ifdef HAVE_AMESOS2_TIMERS
141 Teuchos::TimeMonitor numFactTimer(this->timers_.numFactTime_);
142#endif
143
144 if (data_.numeric_ != NULL) {
145 ::KLU2::klu_free_numeric<klu2_dtype, local_ordinal_type>
146 (&(data_.numeric_), &(data_.common_));
147 }
148
149 if ( single_proc_optimization() ) {
150 host_ordinal_type_array host_row_ptr_view;
151 host_ordinal_type_array host_cols_view;
152 this->matrixA_->returnRowPtr_kokkos_view(host_row_ptr_view);
153 this->matrixA_->returnColInd_kokkos_view(host_cols_view);
154 this->matrixA_->returnValues_kokkos_view(host_nzvals_view_);
155 klu2_dtype * pValues = function_map::convert_scalar(host_nzvals_view_.data());
156 data_.numeric_ = ::KLU2::klu_factor<klu2_dtype, local_ordinal_type>
157 (host_row_ptr_view.data(), host_cols_view.data(), pValues,
158 data_.symbolic_, &(data_.common_));
159 }
160 else {
161 klu2_dtype * pValues = function_map::convert_scalar(host_nzvals_view_.data());
162 data_.numeric_ = ::KLU2::klu_factor<klu2_dtype, local_ordinal_type>
163 (host_col_ptr_view_.data(), host_rows_view_.data(), pValues,
164 data_.symbolic_, &(data_.common_));
165 } //end single_process_optim_check = false
166
167 // To have a test which confirms a throw, we need MPI to throw on all the
168 // ranks. So we delay and broadcast first. Others throws in Amesos2 which
169 // happen on just the root rank would also have the same problem if we
170 // tested them but we decided to fix just this one for the present. This
171 // is the only error/throw we currently have a unit test for.
172 if(data_.numeric_ == nullptr) {
173 info = 1;
174 }
175
176 // This is set after numeric factorization complete as pivoting can be used;
177 // In this case, a discrepancy between symbolic and numeric nnz total can occur.
178 if(info == 0) { // skip if error code so we don't segfault - will throw
179 this->setNnzLU( as<size_t>((data_.numeric_)->lnz) + as<size_t>((data_.numeric_)->unz) );
180 }
181 } // end scope
182
183 } // end this->root_
184
185 /* All processes should have the same error code */
186 Teuchos::broadcast(*(this->matrixA_->getComm()), 0, &info);
187
188 TEUCHOS_TEST_FOR_EXCEPTION(info > 0, std::runtime_error,
189 "KLU2 numeric factorization failed(info="+std::to_string(info)+")");
190
191 return(info);
192}
193
194template <class Matrix, class Vector>
195int
197 const Teuchos::Ptr<MultiVecAdapter<Vector> > X,
198 const Teuchos::Ptr<const MultiVecAdapter<Vector> > B) const
199{
200 using Teuchos::as;
201 int ierr = 0; // returned error code
202
203 const global_size_type ld_rhs = this->root_ ? X->getGlobalLength() : 0;
204 const size_t nrhs = X->getGlobalNumVectors();
205
206 bool bDidAssignX;
207 bool bDidAssignB;
208 bool use_gather = use_gather_; // user param
209 use_gather = (use_gather && this->matrixA_->getComm()->getSize() > 1); // only with multiple MPIs
210 use_gather = (use_gather && (std::is_same<vector_scalar_type, float>::value ||
211 std::is_same<vector_scalar_type, double>::value)); // only for double or float vectors
212 {
213#ifdef HAVE_AMESOS2_TIMERS
214 Teuchos::TimeMonitor mvConvTimer(this->timers_.vecConvTime_);
215#endif
216 const bool initialize_data = true;
217 const bool do_not_initialize_data = false;
218 if ( single_proc_optimization() && nrhs == 1 ) {
219 // no msp creation
220 bDidAssignB = Util::get_1d_copy_helper_kokkos_view<MultiVecAdapter<Vector>,
221 host_solve_array_t>::do_get(initialize_data, B, bValues_, as<size_t>(ld_rhs));
222
223 bDidAssignX = Util::get_1d_copy_helper_kokkos_view<MultiVecAdapter<Vector>,
224 host_solve_array_t>::do_get(do_not_initialize_data, X, xValues_, as<size_t>(ld_rhs));
225 }
226 else {
227 if (use_gather) {
228 int rval = B->gather(bValues_, this->perm_g2l, this->recvCountRows, this->recvDisplRows,
229 (is_contiguous_ == true) ? ROOTED : CONTIGUOUS_AND_ROOTED);
230 if (rval == 0) {
231 X->gather(xValues_, this->perm_g2l, this->recvCountRows, this->recvDisplRows,
232 (is_contiguous_ == true) ? ROOTED : CONTIGUOUS_AND_ROOTED);
233 bDidAssignB = true; // TODO : find when we can avoid deep-copy
234 bDidAssignX = false; // TODO : find when we can avoid scatter
235 } else {
236 use_gather = false;
237 }
238 }
239 if (!use_gather) {
240 bDidAssignB = Util::get_1d_copy_helper_kokkos_view<MultiVecAdapter<Vector>,
241 host_solve_array_t>::do_get(initialize_data, B, bValues_,
242 as<size_t>(ld_rhs),
243 (is_contiguous_ == true) ? ROOTED : CONTIGUOUS_AND_ROOTED,
244 this->rowIndexBase_);
245 // see Amesos2_Tacho_def.hpp for an explanation of why we 'get' X
246 bDidAssignX = Util::get_1d_copy_helper_kokkos_view<MultiVecAdapter<Vector>,
247 host_solve_array_t>::do_get(do_not_initialize_data, X, xValues_,
248 as<size_t>(ld_rhs),
249 (is_contiguous_ == true) ? ROOTED : CONTIGUOUS_AND_ROOTED,
250 this->rowIndexBase_);
251 }
252
253 // klu_tsolve is going to put the solution x into the input b.
254 // Copy b to x then solve in x.
255 // We do not want to solve in b, then copy to x, because if b was assigned
256 // then the solve will change b permanently and mess up the next test cycle.
257 // However if b was actually a copy (bDidAssignB = false) then we can avoid
258 // this deep_copy and just assign xValues_ = bValues_.
259 if(bDidAssignB) {
260 Kokkos::deep_copy(xValues_, bValues_); // need deep_copy or solve will change adapter's b memory which should never happen
261 }
262 else {
263 xValues_ = bValues_; // safe because bValues_ does not point straight to adapter's memory space
264 }
265 }
266 }
267
268 klu2_dtype * pxValues = function_map::convert_scalar(xValues_.data());
269 klu2_dtype * pbValues = function_map::convert_scalar(bValues_.data());
270
271 // can be null for non root
272 if( this->root_) {
273 TEUCHOS_TEST_FOR_EXCEPTION(pbValues == nullptr,
274 std::runtime_error, "Amesos2 Runtime Error: b_vector returned null ");
275
276 TEUCHOS_TEST_FOR_EXCEPTION(pxValues == nullptr,
277 std::runtime_error, "Amesos2 Runtime Error: x_vector returned null ");
278 }
279
280 if ( single_proc_optimization() && nrhs == 1 ) {
281#ifdef HAVE_AMESOS2_TIMERS
282 Teuchos::TimeMonitor solveTimer(this->timers_.solveTime_);
283#endif
284
285 // For this case, Crs matrix raw pointers were used, so the non-transpose default solve
286 // is actually the transpose solve as klu_solve expects Ccs matrix pointers
287 // Thus, if the transFlag_ is true, the non-transpose solve should be used
288 if (transFlag_ == 0)
289 {
290 ::KLU2::klu_tsolve2<klu2_dtype, local_ordinal_type>
291 (data_.symbolic_, data_.numeric_,
292 (local_ordinal_type)this->globalNumCols_,
293 (local_ordinal_type)nrhs,
294 pbValues, pxValues, &(data_.common_)) ;
295 }
296 else {
297 ::KLU2::klu_solve2<klu2_dtype, local_ordinal_type>
298 (data_.symbolic_, data_.numeric_,
299 (local_ordinal_type)this->globalNumCols_,
300 (local_ordinal_type)nrhs,
301 pbValues, pxValues, &(data_.common_)) ;
302 }
303
304 /* All processes should have the same error code */
305 // Teuchos::broadcast(*(this->getComm()), 0, &ierr);
306
307 } // end single_process_optim_check && nrhs == 1
308 else // single proc optimizations but nrhs > 1,
309 // or distributed over processes case
310 {
311 if ( this->root_ ) {
312#ifdef HAVE_AMESOS2_TIMERS
313 Teuchos::TimeMonitor solveTimer(this->timers_.solveTime_);
314#endif
315 if (transFlag_ == 0)
316 {
317 // For this case, Crs matrix raw pointers were used, so the non-transpose default solve
318 // is actually the transpose solve as klu_solve expects Ccs matrix pointers
319 // Thus, if the transFlag_ is true, the non-transpose solve should be used
320 if ( single_proc_optimization() ) {
321 ::KLU2::klu_tsolve<klu2_dtype, local_ordinal_type>
322 (data_.symbolic_, data_.numeric_,
323 (local_ordinal_type)this->globalNumCols_,
324 (local_ordinal_type)nrhs,
325 pxValues, &(data_.common_)) ;
326 }
327 else {
328 ::KLU2::klu_solve<klu2_dtype, local_ordinal_type>
329 (data_.symbolic_, data_.numeric_,
330 (local_ordinal_type)this->globalNumCols_,
331 (local_ordinal_type)nrhs,
332 pxValues, &(data_.common_)) ;
333 }
334 }
335 else
336 {
337 // For this case, Crs matrix raw pointers were used, so the non-transpose default solve
338 // is actually the transpose solve as klu_solve expects Ccs matrix pointers
339 // Thus, if the transFlag_ is true, the non- transpose solve should be used
340 if ( single_proc_optimization() ) {
341 ::KLU2::klu_solve<klu2_dtype, local_ordinal_type>
342 (data_.symbolic_, data_.numeric_,
343 (local_ordinal_type)this->globalNumCols_,
344 (local_ordinal_type)nrhs,
345 pxValues, &(data_.common_)) ;
346 }
347 else {
348 ::KLU2::klu_tsolve<klu2_dtype, local_ordinal_type>
349 (data_.symbolic_, data_.numeric_,
350 (local_ordinal_type)this->globalNumCols_,
351 (local_ordinal_type)nrhs,
352 pxValues, &(data_.common_)) ;
353 }
354 }
355 } // end root_
356 } //end else
357
358 // if bDidAssignX, then we solved straight to the adapter's X memory space without
359 // requiring additional memory allocation, so the x data is already in place.
360 if(!bDidAssignX) {
361#ifdef HAVE_AMESOS2_TIMERS
362 Teuchos::TimeMonitor redistTimer( this->timers_.vecRedistTime_ );
363#endif
364 if (use_gather) {
365 int rval = X->scatter(xValues_, this->perm_g2l, this->recvCountRows, this->recvDisplRows,
366 (is_contiguous_ == true) ? ROOTED : CONTIGUOUS_AND_ROOTED);
367 if (rval != 0) use_gather = false;
368 }
369 if (!use_gather) {
370 Util::put_1d_data_helper_kokkos_view<
371 MultiVecAdapter<Vector>,host_solve_array_t>::do_put(X, xValues_,
372 as<size_t>(ld_rhs),
373 (is_contiguous_ == true) ? ROOTED : CONTIGUOUS_AND_ROOTED,
374 this->rowIndexBase_);
375 }
376 }
377 return(ierr);
378}
379
380
381template <class Matrix, class Vector>
382bool
384{
385 // The KLU2 factorization routines can handle square as well as
386 // rectangular matrices, but KLU2 can only apply the solve routines to
387 // square matrices, so we check the matrix for squareness.
388 return( this->matrixA_->getGlobalNumRows() == this->matrixA_->getGlobalNumCols() );
389}
390
391
392template <class Matrix, class Vector>
393void
394KLU2<Matrix,Vector>::setParameters_impl(const Teuchos::RCP<Teuchos::ParameterList> & parameterList )
395{
396 using Teuchos::RCP;
397 using Teuchos::getIntegralValue;
398 using Teuchos::ParameterEntryValidator;
399
400 RCP<const Teuchos::ParameterList> valid_params = getValidParameters_impl();
401
402 transFlag_ = this->control_.useTranspose_ ? 1: 0;
403 // The KLU2 transpose option can override the Amesos2 option
404 if( parameterList->isParameter("Trans") ){
405 RCP<const ParameterEntryValidator> trans_validator = valid_params->getEntry("Trans").validator();
406 parameterList->getEntry("Trans").setValidator(trans_validator);
407
408 transFlag_ = getIntegralValue<int>(*parameterList, "Trans");
409 }
410
411 if( parameterList->isParameter("IsContiguous") ){
412 is_contiguous_ = parameterList->get<bool>("IsContiguous");
413 }
414 if( parameterList->isParameter("UseCustomGather") ){
415 use_gather_ = parameterList->get<bool>("UseCustomGather");
416 }
417}
418
419
420template <class Matrix, class Vector>
421Teuchos::RCP<const Teuchos::ParameterList>
423{
424 using std::string;
425 using Teuchos::tuple;
426 using Teuchos::ParameterList;
427 using Teuchos::setStringToIntegralParameter;
428
429 static Teuchos::RCP<const Teuchos::ParameterList> valid_params;
430
431 if( is_null(valid_params) )
432 {
433 Teuchos::RCP<Teuchos::ParameterList> pl = Teuchos::parameterList();
434
435 pl->set("Equil", true, "Whether to equilibrate the system before solve, does nothing now");
436 pl->set("IsContiguous", true, "Whether GIDs contiguous");
437 pl->set("UseCustomGather", true, "Whether to use new matrix-gather routine");
438
439 setStringToIntegralParameter<int>("Trans", "NOTRANS",
440 "Solve for the transpose system or not",
441 tuple<string>("NOTRANS","TRANS","CONJ"),
442 tuple<string>("Solve with transpose",
443 "Do not solve with transpose",
444 "Solve with the conjugate transpose"),
445 tuple<int>(0, 1, 2),
446 pl.getRawPtr());
447 valid_params = pl;
448 }
449
450 return valid_params;
451}
452
453
454template <class Matrix, class Vector>
455bool
457{
458 using Teuchos::as;
459#ifdef HAVE_AMESOS2_TIMERS
460 Teuchos::TimeMonitor convTimer(this->timers_.mtxConvTime_);
461#endif
462
463 if(current_phase == SOLVE)return(false);
464
465 if ( single_proc_optimization() ) {
466 // Do nothing in this case - Crs raw pointers will be used
467 }
468 else
469 {
470 // Only the root image needs storage allocated
471 if( this->root_ ) {
472 if (host_nzvals_view_.extent(0) != this->globalNumNonZeros_)
473 Kokkos::resize(host_nzvals_view_, this->globalNumNonZeros_);
474 if (host_rows_view_.extent(0) != this->globalNumNonZeros_)
475 Kokkos::resize(host_rows_view_, this->globalNumNonZeros_);
476 if (host_col_ptr_view_.extent(0) != (this->globalNumRows_ + 1))
477 Kokkos::resize(host_col_ptr_view_, this->globalNumRows_ + 1);
478 }
479 local_ordinal_type nnz_ret = -1;
480 bool use_gather = use_gather_; // user param
481 use_gather = (use_gather && this->matrixA_->getComm()->getSize() > 1); // only with multiple MPIs
482 use_gather = (use_gather && (std::is_same<scalar_type, float>::value || std::is_same<scalar_type, double>::value)); // only for double or float
483 {
484#ifdef HAVE_AMESOS2_TIMERS
485 Teuchos::TimeMonitor mtxRedistTimer( this->timers_.mtxRedistTime_ );
486#endif
487 if (use_gather) {
488 bool column_major = true;
489 if (!is_contiguous_) {
490 auto contig_mat = this->matrixA_->reindex(this->contig_rowmap_, this->contig_colmap_, current_phase);
491 nnz_ret = contig_mat->gather(host_nzvals_view_, host_rows_view_, host_col_ptr_view_, this->perm_g2l, this->recvCountRows, this->recvDisplRows, this->recvCounts, this->recvDispls,
492 this->transpose_map, this->nzvals_t, column_major, current_phase);
493 } else {
494 nnz_ret = this->matrixA_->gather(host_nzvals_view_, host_rows_view_, host_col_ptr_view_, this->perm_g2l, this->recvCountRows, this->recvDisplRows, this->recvCounts, this->recvDispls,
495 this->transpose_map, this->nzvals_t, column_major, current_phase);
496 }
497 // gather failed (e.g., not implemened for KokkosCrsMatrix)
498 // in case of the failure, it falls back to the original "do_get"
499 if (nnz_ret < 0) use_gather = false;
500 }
501 if (!use_gather) {
503 MatrixAdapter<Matrix>,host_value_type_array,host_ordinal_type_array,host_ordinal_type_array>
504 ::do_get(this->matrixA_.ptr(), host_nzvals_view_, host_rows_view_, host_col_ptr_view_, nnz_ret,
505 (is_contiguous_ == true) ? ROOTED : CONTIGUOUS_AND_ROOTED,
506 ARBITRARY,
507 this->rowIndexBase_);
508 }
509 }
510
511 // gather return the total nnz_ret on every MPI process
512 if (use_gather || this->root_) {
513 TEUCHOS_TEST_FOR_EXCEPTION( nnz_ret != as<local_ordinal_type>(this->globalNumNonZeros_),
514 std::runtime_error,
515 "Amesos2_KLU2 loadA_impl: Did not get the expected number of non-zero vals("
516 +std::to_string(nnz_ret)+" vs "+std::to_string(this->globalNumNonZeros_)+")");
517 }
518 } //end else single_process_optim_check = false
519
520 return true;
521}
522
523
524template<class Matrix, class Vector>
525const char* KLU2<Matrix,Vector>::name = "KLU2";
526
527
528} // end namespace Amesos2
529
530#endif // AMESOS2_KLU2_DEF_HPP
Amesos2 KLU2 declarations.
@ ROOTED
Definition Amesos2_TypeDecl.hpp:93
@ CONTIGUOUS_AND_ROOTED
Definition Amesos2_TypeDecl.hpp:94
@ ARBITRARY
Definition Amesos2_TypeDecl.hpp:109
Amesos2 interface to the KLU2 package.
Definition Amesos2_KLU2_decl.hpp:39
KLU2(Teuchos::RCP< const Matrix > A, Teuchos::RCP< Vector > X, Teuchos::RCP< const Vector > B)
Initialize from Teuchos::RCP.
Definition Amesos2_KLU2_def.hpp:32
Teuchos::RCP< const Teuchos::ParameterList > getValidParameters_impl() const
Definition Amesos2_KLU2_def.hpp:422
bool single_proc_optimization() const
can we optimize size_type and ordinal_type for straight pass through, also check that is_contiguous_ ...
Definition Amesos2_KLU2_def.hpp:78
bool matrixShapeOK_impl() const
Determines whether the shape of the matrix is OK for this solver.
Definition Amesos2_KLU2_def.hpp:383
int symbolicFactorization_impl()
Perform symbolic factorization of the matrix using KLU2.
Definition Amesos2_KLU2_def.hpp:98
int preOrdering_impl()
Performs pre-ordering on the matrix to increase efficiency.
Definition Amesos2_KLU2_def.hpp:84
int solve_impl(const Teuchos::Ptr< MultiVecAdapter< Vector > > X, const Teuchos::Ptr< const MultiVecAdapter< Vector > > B) const
KLU2 specific solve.
Definition Amesos2_KLU2_def.hpp:196
~KLU2()
Destructor.
Definition Amesos2_KLU2_def.hpp:51
bool loadA_impl(EPhase current_phase)
Reads matrix data into internal structures.
Definition Amesos2_KLU2_def.hpp:456
int numericFactorization_impl()
KLU2 specific numeric factorization.
Definition Amesos2_KLU2_def.hpp:128
void setParameters_impl(const Teuchos::RCP< Teuchos::ParameterList > &parameterList)
Definition Amesos2_KLU2_def.hpp:394
A Matrix adapter interface for Amesos2.
Definition Amesos2_MatrixAdapter_decl.hpp:42
Amesos2::SolverCore: A templated interface for interaction with third-party direct sparse solvers.
Definition Amesos2_SolverCore_decl.hpp:72
EPhase
Used to indicate a phase in the direct solution.
Definition Amesos2_TypeDecl.hpp:31
A templated MultiVector class adapter for Amesos2.
Definition Amesos2_MultiVecAdapter_decl.hpp:142
A generic helper class for getting a CCS representation of a Matrix.
Definition Amesos2_Util.hpp:633