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Eigen  3.4.0
 
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SuperLUSupport.h
1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@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#ifndef EIGEN_SUPERLUSUPPORT_H
11#define EIGEN_SUPERLUSUPPORT_H
12
13namespace Eigen {
14
15#if defined(SUPERLU_MAJOR_VERSION) && (SUPERLU_MAJOR_VERSION >= 5)
16#define DECL_GSSVX(PREFIX,FLOATTYPE,KEYTYPE) \
17 extern "C" { \
18 extern void PREFIX##gssvx(superlu_options_t *, SuperMatrix *, int *, int *, int *, \
19 char *, FLOATTYPE *, FLOATTYPE *, SuperMatrix *, SuperMatrix *, \
20 void *, int, SuperMatrix *, SuperMatrix *, \
21 FLOATTYPE *, FLOATTYPE *, FLOATTYPE *, FLOATTYPE *, \
22 GlobalLU_t *, mem_usage_t *, SuperLUStat_t *, int *); \
23 } \
24 inline float SuperLU_gssvx(superlu_options_t *options, SuperMatrix *A, \
25 int *perm_c, int *perm_r, int *etree, char *equed, \
26 FLOATTYPE *R, FLOATTYPE *C, SuperMatrix *L, \
27 SuperMatrix *U, void *work, int lwork, \
28 SuperMatrix *B, SuperMatrix *X, \
29 FLOATTYPE *recip_pivot_growth, \
30 FLOATTYPE *rcond, FLOATTYPE *ferr, FLOATTYPE *berr, \
31 SuperLUStat_t *stats, int *info, KEYTYPE) { \
32 mem_usage_t mem_usage; \
33 GlobalLU_t gLU; \
34 PREFIX##gssvx(options, A, perm_c, perm_r, etree, equed, R, C, L, \
35 U, work, lwork, B, X, recip_pivot_growth, rcond, \
36 ferr, berr, &gLU, &mem_usage, stats, info); \
37 return mem_usage.for_lu; /* bytes used by the factor storage */ \
38 }
39#else // version < 5.0
40#define DECL_GSSVX(PREFIX,FLOATTYPE,KEYTYPE) \
41 extern "C" { \
42 extern void PREFIX##gssvx(superlu_options_t *, SuperMatrix *, int *, int *, int *, \
43 char *, FLOATTYPE *, FLOATTYPE *, SuperMatrix *, SuperMatrix *, \
44 void *, int, SuperMatrix *, SuperMatrix *, \
45 FLOATTYPE *, FLOATTYPE *, FLOATTYPE *, FLOATTYPE *, \
46 mem_usage_t *, SuperLUStat_t *, int *); \
47 } \
48 inline float SuperLU_gssvx(superlu_options_t *options, SuperMatrix *A, \
49 int *perm_c, int *perm_r, int *etree, char *equed, \
50 FLOATTYPE *R, FLOATTYPE *C, SuperMatrix *L, \
51 SuperMatrix *U, void *work, int lwork, \
52 SuperMatrix *B, SuperMatrix *X, \
53 FLOATTYPE *recip_pivot_growth, \
54 FLOATTYPE *rcond, FLOATTYPE *ferr, FLOATTYPE *berr, \
55 SuperLUStat_t *stats, int *info, KEYTYPE) { \
56 mem_usage_t mem_usage; \
57 PREFIX##gssvx(options, A, perm_c, perm_r, etree, equed, R, C, L, \
58 U, work, lwork, B, X, recip_pivot_growth, rcond, \
59 ferr, berr, &mem_usage, stats, info); \
60 return mem_usage.for_lu; /* bytes used by the factor storage */ \
61 }
62#endif
63
64DECL_GSSVX(s,float,float)
65DECL_GSSVX(c,float,std::complex<float>)
66DECL_GSSVX(d,double,double)
67DECL_GSSVX(z,double,std::complex<double>)
68
69#ifdef MILU_ALPHA
70#define EIGEN_SUPERLU_HAS_ILU
71#endif
72
73#ifdef EIGEN_SUPERLU_HAS_ILU
74
75// similarly for the incomplete factorization using gsisx
76#define DECL_GSISX(PREFIX,FLOATTYPE,KEYTYPE) \
77 extern "C" { \
78 extern void PREFIX##gsisx(superlu_options_t *, SuperMatrix *, int *, int *, int *, \
79 char *, FLOATTYPE *, FLOATTYPE *, SuperMatrix *, SuperMatrix *, \
80 void *, int, SuperMatrix *, SuperMatrix *, FLOATTYPE *, FLOATTYPE *, \
81 mem_usage_t *, SuperLUStat_t *, int *); \
82 } \
83 inline float SuperLU_gsisx(superlu_options_t *options, SuperMatrix *A, \
84 int *perm_c, int *perm_r, int *etree, char *equed, \
85 FLOATTYPE *R, FLOATTYPE *C, SuperMatrix *L, \
86 SuperMatrix *U, void *work, int lwork, \
87 SuperMatrix *B, SuperMatrix *X, \
88 FLOATTYPE *recip_pivot_growth, \
89 FLOATTYPE *rcond, \
90 SuperLUStat_t *stats, int *info, KEYTYPE) { \
91 mem_usage_t mem_usage; \
92 PREFIX##gsisx(options, A, perm_c, perm_r, etree, equed, R, C, L, \
93 U, work, lwork, B, X, recip_pivot_growth, rcond, \
94 &mem_usage, stats, info); \
95 return mem_usage.for_lu; /* bytes used by the factor storage */ \
96 }
97
98DECL_GSISX(s,float,float)
99DECL_GSISX(c,float,std::complex<float>)
100DECL_GSISX(d,double,double)
101DECL_GSISX(z,double,std::complex<double>)
102
103#endif
104
105template<typename MatrixType>
106struct SluMatrixMapHelper;
107
115struct SluMatrix : SuperMatrix
116{
117 SluMatrix()
118 {
119 Store = &storage;
120 }
121
122 SluMatrix(const SluMatrix& other)
123 : SuperMatrix(other)
124 {
125 Store = &storage;
126 storage = other.storage;
127 }
128
129 SluMatrix& operator=(const SluMatrix& other)
130 {
131 SuperMatrix::operator=(static_cast<const SuperMatrix&>(other));
132 Store = &storage;
133 storage = other.storage;
134 return *this;
135 }
136
137 struct
138 {
139 union {int nnz;int lda;};
140 void *values;
141 int *innerInd;
142 int *outerInd;
143 } storage;
144
145 void setStorageType(Stype_t t)
146 {
147 Stype = t;
148 if (t==SLU_NC || t==SLU_NR || t==SLU_DN)
149 Store = &storage;
150 else
151 {
152 eigen_assert(false && "storage type not supported");
153 Store = 0;
154 }
155 }
156
157 template<typename Scalar>
158 void setScalarType()
159 {
160 if (internal::is_same<Scalar,float>::value)
161 Dtype = SLU_S;
162 else if (internal::is_same<Scalar,double>::value)
163 Dtype = SLU_D;
164 else if (internal::is_same<Scalar,std::complex<float> >::value)
165 Dtype = SLU_C;
166 else if (internal::is_same<Scalar,std::complex<double> >::value)
167 Dtype = SLU_Z;
168 else
169 {
170 eigen_assert(false && "Scalar type not supported by SuperLU");
171 }
172 }
173
174 template<typename MatrixType>
175 static SluMatrix Map(MatrixBase<MatrixType>& _mat)
176 {
177 MatrixType& mat(_mat.derived());
178 eigen_assert( ((MatrixType::Flags&RowMajorBit)!=RowMajorBit) && "row-major dense matrices are not supported by SuperLU");
179 SluMatrix res;
180 res.setStorageType(SLU_DN);
181 res.setScalarType<typename MatrixType::Scalar>();
182 res.Mtype = SLU_GE;
183
184 res.nrow = internal::convert_index<int>(mat.rows());
185 res.ncol = internal::convert_index<int>(mat.cols());
186
187 res.storage.lda = internal::convert_index<int>(MatrixType::IsVectorAtCompileTime ? mat.size() : mat.outerStride());
188 res.storage.values = (void*)(mat.data());
189 return res;
190 }
191
192 template<typename MatrixType>
193 static SluMatrix Map(SparseMatrixBase<MatrixType>& a_mat)
194 {
195 MatrixType &mat(a_mat.derived());
196 SluMatrix res;
197 if ((MatrixType::Flags&RowMajorBit)==RowMajorBit)
198 {
199 res.setStorageType(SLU_NR);
200 res.nrow = internal::convert_index<int>(mat.cols());
201 res.ncol = internal::convert_index<int>(mat.rows());
202 }
203 else
204 {
205 res.setStorageType(SLU_NC);
206 res.nrow = internal::convert_index<int>(mat.rows());
207 res.ncol = internal::convert_index<int>(mat.cols());
208 }
209
210 res.Mtype = SLU_GE;
211
212 res.storage.nnz = internal::convert_index<int>(mat.nonZeros());
213 res.storage.values = mat.valuePtr();
214 res.storage.innerInd = mat.innerIndexPtr();
215 res.storage.outerInd = mat.outerIndexPtr();
216
217 res.setScalarType<typename MatrixType::Scalar>();
218
219 // FIXME the following is not very accurate
220 if (int(MatrixType::Flags) & int(Upper))
221 res.Mtype = SLU_TRU;
222 if (int(MatrixType::Flags) & int(Lower))
223 res.Mtype = SLU_TRL;
224
225 eigen_assert(((int(MatrixType::Flags) & int(SelfAdjoint))==0) && "SelfAdjoint matrix shape not supported by SuperLU");
226
227 return res;
228 }
229};
230
231template<typename Scalar, int Rows, int Cols, int Options, int MRows, int MCols>
232struct SluMatrixMapHelper<Matrix<Scalar,Rows,Cols,Options,MRows,MCols> >
233{
234 typedef Matrix<Scalar,Rows,Cols,Options,MRows,MCols> MatrixType;
235 static void run(MatrixType& mat, SluMatrix& res)
236 {
237 eigen_assert( ((Options&RowMajor)!=RowMajor) && "row-major dense matrices is not supported by SuperLU");
238 res.setStorageType(SLU_DN);
239 res.setScalarType<Scalar>();
240 res.Mtype = SLU_GE;
241
242 res.nrow = mat.rows();
243 res.ncol = mat.cols();
244
245 res.storage.lda = mat.outerStride();
246 res.storage.values = mat.data();
247 }
248};
249
250template<typename Derived>
251struct SluMatrixMapHelper<SparseMatrixBase<Derived> >
252{
253 typedef Derived MatrixType;
254 static void run(MatrixType& mat, SluMatrix& res)
255 {
256 if ((MatrixType::Flags&RowMajorBit)==RowMajorBit)
257 {
258 res.setStorageType(SLU_NR);
259 res.nrow = mat.cols();
260 res.ncol = mat.rows();
261 }
262 else
263 {
264 res.setStorageType(SLU_NC);
265 res.nrow = mat.rows();
266 res.ncol = mat.cols();
267 }
268
269 res.Mtype = SLU_GE;
270
271 res.storage.nnz = mat.nonZeros();
272 res.storage.values = mat.valuePtr();
273 res.storage.innerInd = mat.innerIndexPtr();
274 res.storage.outerInd = mat.outerIndexPtr();
275
276 res.setScalarType<typename MatrixType::Scalar>();
277
278 // FIXME the following is not very accurate
279 if (MatrixType::Flags & Upper)
280 res.Mtype = SLU_TRU;
281 if (MatrixType::Flags & Lower)
282 res.Mtype = SLU_TRL;
283
284 eigen_assert(((MatrixType::Flags & SelfAdjoint)==0) && "SelfAdjoint matrix shape not supported by SuperLU");
285 }
286};
287
288namespace internal {
289
290template<typename MatrixType>
291SluMatrix asSluMatrix(MatrixType& mat)
292{
293 return SluMatrix::Map(mat);
294}
295
297template<typename Scalar, int Flags, typename Index>
298MappedSparseMatrix<Scalar,Flags,Index> map_superlu(SluMatrix& sluMat)
299{
300 eigen_assert(((Flags&RowMajor)==RowMajor && sluMat.Stype == SLU_NR)
301 || ((Flags&ColMajor)==ColMajor && sluMat.Stype == SLU_NC));
302
303 Index outerSize = (Flags&RowMajor)==RowMajor ? sluMat.ncol : sluMat.nrow;
304
305 return MappedSparseMatrix<Scalar,Flags,Index>(
306 sluMat.nrow, sluMat.ncol, sluMat.storage.outerInd[outerSize],
307 sluMat.storage.outerInd, sluMat.storage.innerInd, reinterpret_cast<Scalar*>(sluMat.storage.values) );
308}
309
310} // end namespace internal
311
316template<typename _MatrixType, typename Derived>
317class SuperLUBase : public SparseSolverBase<Derived>
318{
319 protected:
321 using Base::derived;
322 using Base::m_isInitialized;
323 public:
324 typedef _MatrixType MatrixType;
325 typedef typename MatrixType::Scalar Scalar;
326 typedef typename MatrixType::RealScalar RealScalar;
327 typedef typename MatrixType::StorageIndex StorageIndex;
333 enum {
334 ColsAtCompileTime = MatrixType::ColsAtCompileTime,
335 MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
336 };
337
338 public:
339
340 SuperLUBase() {}
341
343 {
344 clearFactors();
345 }
346
347 inline Index rows() const { return m_matrix.rows(); }
348 inline Index cols() const { return m_matrix.cols(); }
349
351 inline superlu_options_t& options() { return m_sluOptions; }
352
359 {
360 eigen_assert(m_isInitialized && "Decomposition is not initialized.");
361 return m_info;
362 }
363
365 void compute(const MatrixType& matrix)
366 {
367 derived().analyzePattern(matrix);
368 derived().factorize(matrix);
369 }
370
377 void analyzePattern(const MatrixType& /*matrix*/)
378 {
379 m_isInitialized = true;
380 m_info = Success;
381 m_analysisIsOk = true;
382 m_factorizationIsOk = false;
383 }
384
385 template<typename Stream>
386 void dumpMemory(Stream& /*s*/)
387 {}
388
389 protected:
390
391 void initFactorization(const MatrixType& a)
392 {
393 set_default_options(&this->m_sluOptions);
394
395 const Index size = a.rows();
396 m_matrix = a;
397
398 m_sluA = internal::asSluMatrix(m_matrix);
399 clearFactors();
400
401 m_p.resize(size);
402 m_q.resize(size);
403 m_sluRscale.resize(size);
404 m_sluCscale.resize(size);
405 m_sluEtree.resize(size);
406
407 // set empty B and X
408 m_sluB.setStorageType(SLU_DN);
409 m_sluB.setScalarType<Scalar>();
410 m_sluB.Mtype = SLU_GE;
411 m_sluB.storage.values = 0;
412 m_sluB.nrow = 0;
413 m_sluB.ncol = 0;
414 m_sluB.storage.lda = internal::convert_index<int>(size);
415 m_sluX = m_sluB;
416
417 m_extractedDataAreDirty = true;
418 }
419
420 void init()
421 {
422 m_info = InvalidInput;
423 m_isInitialized = false;
424 m_sluL.Store = 0;
425 m_sluU.Store = 0;
426 }
427
428 void extractData() const;
429
430 void clearFactors()
431 {
432 if(m_sluL.Store)
433 Destroy_SuperNode_Matrix(&m_sluL);
434 if(m_sluU.Store)
435 Destroy_CompCol_Matrix(&m_sluU);
436
437 m_sluL.Store = 0;
438 m_sluU.Store = 0;
439
440 memset(&m_sluL,0,sizeof m_sluL);
441 memset(&m_sluU,0,sizeof m_sluU);
442 }
443
444 // cached data to reduce reallocation, etc.
445 mutable LUMatrixType m_l;
446 mutable LUMatrixType m_u;
447 mutable IntColVectorType m_p;
448 mutable IntRowVectorType m_q;
449
450 mutable LUMatrixType m_matrix; // copy of the factorized matrix
451 mutable SluMatrix m_sluA;
452 mutable SuperMatrix m_sluL, m_sluU;
453 mutable SluMatrix m_sluB, m_sluX;
454 mutable SuperLUStat_t m_sluStat;
455 mutable superlu_options_t m_sluOptions;
456 mutable std::vector<int> m_sluEtree;
457 mutable Matrix<RealScalar,Dynamic,1> m_sluRscale, m_sluCscale;
458 mutable Matrix<RealScalar,Dynamic,1> m_sluFerr, m_sluBerr;
459 mutable char m_sluEqued;
460
461 mutable ComputationInfo m_info;
462 int m_factorizationIsOk;
463 int m_analysisIsOk;
464 mutable bool m_extractedDataAreDirty;
465
466 private:
467 SuperLUBase(SuperLUBase& ) { }
468};
469
470
487template<typename _MatrixType>
488class SuperLU : public SuperLUBase<_MatrixType,SuperLU<_MatrixType> >
489{
490 public:
492 typedef _MatrixType MatrixType;
493 typedef typename Base::Scalar Scalar;
494 typedef typename Base::RealScalar RealScalar;
495 typedef typename Base::StorageIndex StorageIndex;
498 typedef typename Base::PermutationMap PermutationMap;
499 typedef typename Base::LUMatrixType LUMatrixType;
502
503 public:
504 using Base::_solve_impl;
505
506 SuperLU() : Base() { init(); }
507
508 explicit SuperLU(const MatrixType& matrix) : Base()
509 {
510 init();
511 Base::compute(matrix);
512 }
513
514 ~SuperLU()
515 {
516 }
517
524 void analyzePattern(const MatrixType& matrix)
525 {
526 m_info = InvalidInput;
527 m_isInitialized = false;
528 Base::analyzePattern(matrix);
529 }
530
537 void factorize(const MatrixType& matrix);
538
540 template<typename Rhs,typename Dest>
541 void _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const;
542
543 inline const LMatrixType& matrixL() const
544 {
545 if (m_extractedDataAreDirty) this->extractData();
546 return m_l;
547 }
548
549 inline const UMatrixType& matrixU() const
550 {
551 if (m_extractedDataAreDirty) this->extractData();
552 return m_u;
553 }
554
555 inline const IntColVectorType& permutationP() const
556 {
557 if (m_extractedDataAreDirty) this->extractData();
558 return m_p;
559 }
560
561 inline const IntRowVectorType& permutationQ() const
562 {
563 if (m_extractedDataAreDirty) this->extractData();
564 return m_q;
565 }
566
567 Scalar determinant() const;
568
569 protected:
570
571 using Base::m_matrix;
572 using Base::m_sluOptions;
573 using Base::m_sluA;
574 using Base::m_sluB;
575 using Base::m_sluX;
576 using Base::m_p;
577 using Base::m_q;
578 using Base::m_sluEtree;
579 using Base::m_sluEqued;
580 using Base::m_sluRscale;
581 using Base::m_sluCscale;
582 using Base::m_sluL;
583 using Base::m_sluU;
584 using Base::m_sluStat;
585 using Base::m_sluFerr;
586 using Base::m_sluBerr;
587 using Base::m_l;
588 using Base::m_u;
589
590 using Base::m_analysisIsOk;
591 using Base::m_factorizationIsOk;
592 using Base::m_extractedDataAreDirty;
593 using Base::m_isInitialized;
594 using Base::m_info;
595
596 void init()
597 {
598 Base::init();
599
600 set_default_options(&this->m_sluOptions);
601 m_sluOptions.PrintStat = NO;
602 m_sluOptions.ConditionNumber = NO;
603 m_sluOptions.Trans = NOTRANS;
604 m_sluOptions.ColPerm = COLAMD;
605 }
606
607
608 private:
609 SuperLU(SuperLU& ) { }
610};
611
612template<typename MatrixType>
613void SuperLU<MatrixType>::factorize(const MatrixType& a)
614{
615 eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
616 if(!m_analysisIsOk)
617 {
618 m_info = InvalidInput;
619 return;
620 }
621
622 this->initFactorization(a);
623
624 m_sluOptions.ColPerm = COLAMD;
625 int info = 0;
626 RealScalar recip_pivot_growth, rcond;
627 RealScalar ferr, berr;
628
629 StatInit(&m_sluStat);
630 SuperLU_gssvx(&m_sluOptions, &m_sluA, m_q.data(), m_p.data(), &m_sluEtree[0],
631 &m_sluEqued, &m_sluRscale[0], &m_sluCscale[0],
632 &m_sluL, &m_sluU,
633 NULL, 0,
634 &m_sluB, &m_sluX,
635 &recip_pivot_growth, &rcond,
636 &ferr, &berr,
637 &m_sluStat, &info, Scalar());
638 StatFree(&m_sluStat);
639
640 m_extractedDataAreDirty = true;
641
642 // FIXME how to better check for errors ???
643 m_info = info == 0 ? Success : NumericalIssue;
644 m_factorizationIsOk = true;
645}
646
647template<typename MatrixType>
648template<typename Rhs,typename Dest>
650{
651 eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or analyzePattern()/factorize()");
652
653 const Index rhsCols = b.cols();
654 eigen_assert(m_matrix.rows()==b.rows());
655
656 m_sluOptions.Trans = NOTRANS;
657 m_sluOptions.Fact = FACTORED;
658 m_sluOptions.IterRefine = NOREFINE;
659
660
661 m_sluFerr.resize(rhsCols);
662 m_sluBerr.resize(rhsCols);
663
666
667 m_sluB = SluMatrix::Map(b_ref.const_cast_derived());
668 m_sluX = SluMatrix::Map(x_ref.const_cast_derived());
669
670 typename Rhs::PlainObject b_cpy;
671 if(m_sluEqued!='N')
672 {
673 b_cpy = b;
674 m_sluB = SluMatrix::Map(b_cpy.const_cast_derived());
675 }
676
677 StatInit(&m_sluStat);
678 int info = 0;
679 RealScalar recip_pivot_growth, rcond;
680 SuperLU_gssvx(&m_sluOptions, &m_sluA,
681 m_q.data(), m_p.data(),
682 &m_sluEtree[0], &m_sluEqued,
683 &m_sluRscale[0], &m_sluCscale[0],
684 &m_sluL, &m_sluU,
685 NULL, 0,
686 &m_sluB, &m_sluX,
687 &recip_pivot_growth, &rcond,
688 &m_sluFerr[0], &m_sluBerr[0],
689 &m_sluStat, &info, Scalar());
690 StatFree(&m_sluStat);
691
692 if(x.derived().data() != x_ref.data())
693 x = x_ref;
694
695 m_info = info==0 ? Success : NumericalIssue;
696}
697
698// the code of this extractData() function has been adapted from the SuperLU's Matlab support code,
699//
700// Copyright (c) 1994 by Xerox Corporation. All rights reserved.
701//
702// THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
703// EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
704//
705template<typename MatrixType, typename Derived>
706void SuperLUBase<MatrixType,Derived>::extractData() const
707{
708 eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for extracting factors, you must first call either compute() or analyzePattern()/factorize()");
709 if (m_extractedDataAreDirty)
710 {
711 int upper;
712 int fsupc, istart, nsupr;
713 int lastl = 0, lastu = 0;
714 SCformat *Lstore = static_cast<SCformat*>(m_sluL.Store);
715 NCformat *Ustore = static_cast<NCformat*>(m_sluU.Store);
716 Scalar *SNptr;
717
718 const Index size = m_matrix.rows();
719 m_l.resize(size,size);
720 m_l.resizeNonZeros(Lstore->nnz);
721 m_u.resize(size,size);
722 m_u.resizeNonZeros(Ustore->nnz);
723
724 int* Lcol = m_l.outerIndexPtr();
725 int* Lrow = m_l.innerIndexPtr();
726 Scalar* Lval = m_l.valuePtr();
727
728 int* Ucol = m_u.outerIndexPtr();
729 int* Urow = m_u.innerIndexPtr();
730 Scalar* Uval = m_u.valuePtr();
731
732 Ucol[0] = 0;
733 Ucol[0] = 0;
734
735 /* for each supernode */
736 for (int k = 0; k <= Lstore->nsuper; ++k)
737 {
738 fsupc = L_FST_SUPC(k);
739 istart = L_SUB_START(fsupc);
740 nsupr = L_SUB_START(fsupc+1) - istart;
741 upper = 1;
742
743 /* for each column in the supernode */
744 for (int j = fsupc; j < L_FST_SUPC(k+1); ++j)
745 {
746 SNptr = &((Scalar*)Lstore->nzval)[L_NZ_START(j)];
747
748 /* Extract U */
749 for (int i = U_NZ_START(j); i < U_NZ_START(j+1); ++i)
750 {
751 Uval[lastu] = ((Scalar*)Ustore->nzval)[i];
752 /* Matlab doesn't like explicit zero. */
753 if (Uval[lastu] != 0.0)
754 Urow[lastu++] = U_SUB(i);
755 }
756 for (int i = 0; i < upper; ++i)
757 {
758 /* upper triangle in the supernode */
759 Uval[lastu] = SNptr[i];
760 /* Matlab doesn't like explicit zero. */
761 if (Uval[lastu] != 0.0)
762 Urow[lastu++] = L_SUB(istart+i);
763 }
764 Ucol[j+1] = lastu;
765
766 /* Extract L */
767 Lval[lastl] = 1.0; /* unit diagonal */
768 Lrow[lastl++] = L_SUB(istart + upper - 1);
769 for (int i = upper; i < nsupr; ++i)
770 {
771 Lval[lastl] = SNptr[i];
772 /* Matlab doesn't like explicit zero. */
773 if (Lval[lastl] != 0.0)
774 Lrow[lastl++] = L_SUB(istart+i);
775 }
776 Lcol[j+1] = lastl;
777
778 ++upper;
779 } /* for j ... */
780
781 } /* for k ... */
782
783 // squeeze the matrices :
784 m_l.resizeNonZeros(lastl);
785 m_u.resizeNonZeros(lastu);
786
787 m_extractedDataAreDirty = false;
788 }
789}
790
791template<typename MatrixType>
792typename SuperLU<MatrixType>::Scalar SuperLU<MatrixType>::determinant() const
793{
794 eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for computing the determinant, you must first call either compute() or analyzePattern()/factorize()");
795
796 if (m_extractedDataAreDirty)
797 this->extractData();
798
799 Scalar det = Scalar(1);
800 for (int j=0; j<m_u.cols(); ++j)
801 {
802 if (m_u.outerIndexPtr()[j+1]-m_u.outerIndexPtr()[j] > 0)
803 {
804 int lastId = m_u.outerIndexPtr()[j+1]-1;
805 eigen_assert(m_u.innerIndexPtr()[lastId]<=j);
806 if (m_u.innerIndexPtr()[lastId]==j)
807 det *= m_u.valuePtr()[lastId];
808 }
809 }
810 if(PermutationMap(m_p.data(),m_p.size()).determinant()*PermutationMap(m_q.data(),m_q.size()).determinant()<0)
811 det = -det;
812 if(m_sluEqued!='N')
813 return det/m_sluRscale.prod()/m_sluCscale.prod();
814 else
815 return det;
816}
817
818#ifdef EIGEN_PARSED_BY_DOXYGEN
819#define EIGEN_SUPERLU_HAS_ILU
820#endif
821
822#ifdef EIGEN_SUPERLU_HAS_ILU
823
840template<typename _MatrixType>
841class SuperILU : public SuperLUBase<_MatrixType,SuperILU<_MatrixType> >
842{
843 public:
845 typedef _MatrixType MatrixType;
846 typedef typename Base::Scalar Scalar;
847 typedef typename Base::RealScalar RealScalar;
848
849 public:
850 using Base::_solve_impl;
851
852 SuperILU() : Base() { init(); }
853
854 SuperILU(const MatrixType& matrix) : Base()
855 {
856 init();
857 Base::compute(matrix);
858 }
859
860 ~SuperILU()
861 {
862 }
863
870 void analyzePattern(const MatrixType& matrix)
871 {
872 Base::analyzePattern(matrix);
873 }
874
881 void factorize(const MatrixType& matrix);
882
883 #ifndef EIGEN_PARSED_BY_DOXYGEN
885 template<typename Rhs,typename Dest>
886 void _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const;
887 #endif // EIGEN_PARSED_BY_DOXYGEN
888
889 protected:
890
891 using Base::m_matrix;
892 using Base::m_sluOptions;
893 using Base::m_sluA;
894 using Base::m_sluB;
895 using Base::m_sluX;
896 using Base::m_p;
897 using Base::m_q;
898 using Base::m_sluEtree;
899 using Base::m_sluEqued;
900 using Base::m_sluRscale;
901 using Base::m_sluCscale;
902 using Base::m_sluL;
903 using Base::m_sluU;
904 using Base::m_sluStat;
905 using Base::m_sluFerr;
906 using Base::m_sluBerr;
907 using Base::m_l;
908 using Base::m_u;
909
910 using Base::m_analysisIsOk;
911 using Base::m_factorizationIsOk;
912 using Base::m_extractedDataAreDirty;
913 using Base::m_isInitialized;
914 using Base::m_info;
915
916 void init()
917 {
918 Base::init();
919
920 ilu_set_default_options(&m_sluOptions);
921 m_sluOptions.PrintStat = NO;
922 m_sluOptions.ConditionNumber = NO;
923 m_sluOptions.Trans = NOTRANS;
924 m_sluOptions.ColPerm = MMD_AT_PLUS_A;
925
926 // no attempt to preserve column sum
927 m_sluOptions.ILU_MILU = SILU;
928 // only basic ILU(k) support -- no direct control over memory consumption
929 // better to use ILU_DropRule = DROP_BASIC | DROP_AREA
930 // and set ILU_FillFactor to max memory growth
931 m_sluOptions.ILU_DropRule = DROP_BASIC;
932 m_sluOptions.ILU_DropTol = NumTraits<Scalar>::dummy_precision()*10;
933 }
934
935 private:
936 SuperILU(SuperILU& ) { }
937};
938
939template<typename MatrixType>
940void SuperILU<MatrixType>::factorize(const MatrixType& a)
941{
942 eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
943 if(!m_analysisIsOk)
944 {
945 m_info = InvalidInput;
946 return;
947 }
948
949 this->initFactorization(a);
950
951 int info = 0;
952 RealScalar recip_pivot_growth, rcond;
953
954 StatInit(&m_sluStat);
955 SuperLU_gsisx(&m_sluOptions, &m_sluA, m_q.data(), m_p.data(), &m_sluEtree[0],
956 &m_sluEqued, &m_sluRscale[0], &m_sluCscale[0],
957 &m_sluL, &m_sluU,
958 NULL, 0,
959 &m_sluB, &m_sluX,
960 &recip_pivot_growth, &rcond,
961 &m_sluStat, &info, Scalar());
962 StatFree(&m_sluStat);
963
964 // FIXME how to better check for errors ???
965 m_info = info == 0 ? Success : NumericalIssue;
966 m_factorizationIsOk = true;
967}
968
969#ifndef EIGEN_PARSED_BY_DOXYGEN
970template<typename MatrixType>
971template<typename Rhs,typename Dest>
973{
974 eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or analyzePattern()/factorize()");
975
976 const int rhsCols = b.cols();
977 eigen_assert(m_matrix.rows()==b.rows());
978
979 m_sluOptions.Trans = NOTRANS;
980 m_sluOptions.Fact = FACTORED;
981 m_sluOptions.IterRefine = NOREFINE;
982
983 m_sluFerr.resize(rhsCols);
984 m_sluBerr.resize(rhsCols);
985
988
989 m_sluB = SluMatrix::Map(b_ref.const_cast_derived());
990 m_sluX = SluMatrix::Map(x_ref.const_cast_derived());
991
992 typename Rhs::PlainObject b_cpy;
993 if(m_sluEqued!='N')
994 {
995 b_cpy = b;
996 m_sluB = SluMatrix::Map(b_cpy.const_cast_derived());
997 }
998
999 int info = 0;
1000 RealScalar recip_pivot_growth, rcond;
1001
1002 StatInit(&m_sluStat);
1003 SuperLU_gsisx(&m_sluOptions, &m_sluA,
1004 m_q.data(), m_p.data(),
1005 &m_sluEtree[0], &m_sluEqued,
1006 &m_sluRscale[0], &m_sluCscale[0],
1007 &m_sluL, &m_sluU,
1008 NULL, 0,
1009 &m_sluB, &m_sluX,
1010 &recip_pivot_growth, &rcond,
1011 &m_sluStat, &info, Scalar());
1012 StatFree(&m_sluStat);
1013
1014 if(x.derived().data() != x_ref.data())
1015 x = x_ref;
1016
1017 m_info = info==0 ? Success : NumericalIssue;
1018}
1019#endif
1020
1021#endif
1022
1023} // end namespace Eigen
1024
1025#endif // EIGEN_SUPERLUSUPPORT_H
EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT
Definition: EigenBase.h:63
Derived & derived()
Definition: EigenBase.h:46
EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT
Definition: EigenBase.h:60
A matrix or vector expression mapping an existing array of data.
Definition: Map.h:96
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:50
The matrix class, also used for vectors and row-vectors.
Definition: Matrix.h:180
void resize(Index rows, Index cols)
Definition: PlainObjectBase.h:271
A matrix or vector expression mapping an existing expression.
Definition: Ref.h:283
A versatible sparse matrix representation.
Definition: SparseMatrix.h:98
Index rows() const
Definition: SparseMatrix.h:138
Index cols() const
Definition: SparseMatrix.h:140
A base class for sparse solvers.
Definition: SparseSolverBase.h:68
A sparse direct incomplete LU factorization and solver based on the SuperLU library.
Definition: SuperLUSupport.h:842
void analyzePattern(const MatrixType &matrix)
Definition: SuperLUSupport.h:870
void factorize(const MatrixType &matrix)
Definition: SuperLUSupport.h:940
The base class for the direct and incomplete LU factorization of SuperLU.
Definition: SuperLUSupport.h:318
void compute(const MatrixType &matrix)
Definition: SuperLUSupport.h:365
void analyzePattern(const MatrixType &)
Definition: SuperLUSupport.h:377
superlu_options_t & options()
Definition: SuperLUSupport.h:351
ComputationInfo info() const
Reports whether previous computation was successful.
Definition: SuperLUSupport.h:358
A sparse direct LU factorization and solver based on the SuperLU library.
Definition: SuperLUSupport.h:489
void factorize(const MatrixType &matrix)
Definition: SuperLUSupport.h:613
void analyzePattern(const MatrixType &matrix)
Definition: SuperLUSupport.h:524
Expression of a triangular part in a matrix.
Definition: TriangularMatrix.h:189
ComputationInfo
Definition: Constants.h:440
@ SelfAdjoint
Definition: Constants.h:225
@ Lower
Definition: Constants.h:209
@ Upper
Definition: Constants.h:211
@ NumericalIssue
Definition: Constants.h:444
@ InvalidInput
Definition: Constants.h:449
@ Success
Definition: Constants.h:442
@ ColMajor
Definition: Constants.h:319
@ RowMajor
Definition: Constants.h:321
const unsigned int RowMajorBit
Definition: Constants.h:66
Namespace containing all symbols from the Eigen library.
Definition: Core:141
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:74
Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
Definition: NumTraits.h:233