GetFEM  5.4.4
gmm_superlu_interface.h
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30 ===========================================================================*/
31 
32 /**@file gmm_superlu_interface.h
33  @author Yves Renard <[email protected]>
34  @date October 17, 2003.
35  @brief Interface with SuperLU (LU direct solver for sparse matrices).
36 */
37 #if defined(GMM_USES_SUPERLU)
38 
39 #ifndef GMM_SUPERLU_INTERFACE_H
40 #define GMM_SUPERLU_INTERFACE_H
41 
42 #include "gmm_kernel.h"
43 
44 
45 typedef int int_t;
46 
47 /* because slu_util.h defines TRUE, FALSE, EMPTY ... */
48 #ifdef TRUE
49 # undef TRUE
50 #endif
51 #ifdef FALSE
52 # undef FALSE
53 #endif
54 #ifdef EMPTY
55 # undef EMPTY
56 #endif
57 
58 namespace SuperLU {
59 #if defined(GMM_NO_SUPERLU_INCLUDE_SUBDIR)
60  #include "slu_Cnames.h"
61  #include "supermatrix.h"
62  #include "slu_util.h"
63  #include "slu_scomplex.h"
64  #include "slu_dcomplex.h"
65 #else
66  #include "superlu/slu_Cnames.h"
67  #include "superlu/supermatrix.h"
68  #include "superlu/slu_util.h"
69  #include "superlu/slu_scomplex.h"
70  #include "superlu/slu_dcomplex.h"
71 #endif
72 
73 #if (SUPERLU_MAJOR_VERSION <= 6)
74 # define singlecomplex complex
75 #endif
76 
77 
78  // Hard copy from {s,d,c,z}lu_sdefs.h headers from SuperLU version 7
79  // This is a fragile solution, but SuperLU headers contaminate the
80  // global namespace too much (breaking linking with BLAS for clang).
81 
82  // static_assert(SUPERLU_MAJOR_VERSION >= 6,
83  // "GMM library supports only SuperLU version 7 or later");
84 
85  extern "C"{
86  extern void
87  sgssv(superlu_options_t *, SuperMatrix *, int *, int *, SuperMatrix *,
88  SuperMatrix *, SuperMatrix *, SuperLUStat_t *, int_t *info);
89  extern void
90  dgssv(superlu_options_t *, SuperMatrix *, int *, int *, SuperMatrix *,
91  SuperMatrix *, SuperMatrix *, SuperLUStat_t *, int_t *info);
92  extern void
93  cgssv(superlu_options_t *, SuperMatrix *, int *, int *, SuperMatrix *,
94  SuperMatrix *, SuperMatrix *, SuperLUStat_t *, int_t *info);
95  extern void
96  zgssv(superlu_options_t *, SuperMatrix *, int *, int *, SuperMatrix *,
97  SuperMatrix *, SuperMatrix *, SuperLUStat_t *, int_t *info);
98  extern void
99  sgssvx(superlu_options_t *, SuperMatrix *, int *, int *, int *,
100  char *, float *, float *, SuperMatrix *, SuperMatrix *,
101  void *, int_t lwork, SuperMatrix *, SuperMatrix *,
102  float *, float *, float *, float *,
103  GlobalLU_t *, mem_usage_t *, SuperLUStat_t *, int_t *info);
104  extern void
105  dgssvx(superlu_options_t *, SuperMatrix *, int *, int *, int *,
106  char *, double *, double *, SuperMatrix *, SuperMatrix *,
107  void *, int_t lwork, SuperMatrix *, SuperMatrix *,
108  double *, double *, double *, double *,
109  GlobalLU_t *, mem_usage_t *, SuperLUStat_t *, int_t *info);
110  extern void
111  cgssvx(superlu_options_t *, SuperMatrix *, int *, int *, int *,
112  char *, float *, float *, SuperMatrix *, SuperMatrix *,
113  void *, int_t lwork, SuperMatrix *, SuperMatrix *,
114  float *, float *, float *, float *,
115  GlobalLU_t *, mem_usage_t *, SuperLUStat_t *, int_t *info);
116  extern void
117  zgssvx(superlu_options_t *, SuperMatrix *, int *, int *, int *,
118  char *, double *, double *, SuperMatrix *, SuperMatrix *,
119  void *, int_t lwork, SuperMatrix *, SuperMatrix *,
120  double *, double *, double *, double *,
121  GlobalLU_t *, mem_usage_t *, SuperLUStat_t *, int_t *info);
122  extern void
123  sCreate_CompCol_Matrix(SuperMatrix *, int, int, int_t, float *,
124  int_t *, int_t *, Stype_t, Dtype_t, Mtype_t);
125  extern void
126  dCreate_CompCol_Matrix(SuperMatrix *, int, int, int_t, double *,
127  int_t *, int_t *, Stype_t, Dtype_t, Mtype_t);
128  extern void
129  cCreate_CompCol_Matrix(SuperMatrix *, int, int, int_t, singlecomplex *,
130  int_t *, int_t *, Stype_t, Dtype_t, Mtype_t);
131  extern void
132  zCreate_CompCol_Matrix(SuperMatrix *, int, int, int_t, doublecomplex *,
133  int_t *, int_t *, Stype_t, Dtype_t, Mtype_t);
134  extern void
135  sCreate_Dense_Matrix(SuperMatrix *, int, int, float *, int,
136  Stype_t, Dtype_t, Mtype_t);
137  extern void
138  dCreate_Dense_Matrix(SuperMatrix *, int, int, double *, int,
139  Stype_t, Dtype_t, Mtype_t);
140  extern void
141  cCreate_Dense_Matrix(SuperMatrix *, int, int, singlecomplex *, int,
142  Stype_t, Dtype_t, Mtype_t);
143  extern void
144  zCreate_Dense_Matrix(SuperMatrix *, int, int, doublecomplex *, int,
145  Stype_t, Dtype_t, Mtype_t);
146  }
147 }
148 
149 namespace gmm {
150 
151  /* interface for Create_CompCol_Matrix */
152 
153  inline void Create_CompCol_Matrix(SuperLU::SuperMatrix *A, int m, int n,
154  int nnz, float *a, int *ir, int *jc) {
155  SuperLU::sCreate_CompCol_Matrix(A, m, n, nnz, a, ir, jc,
156  SuperLU::SLU_NC, SuperLU::SLU_S,
157  SuperLU::SLU_GE);
158  }
159 
160  inline void Create_CompCol_Matrix(SuperLU::SuperMatrix *A, int m, int n,
161  int nnz, double *a, int *ir, int *jc) {
162  SuperLU::dCreate_CompCol_Matrix(A, m, n, nnz, a, ir, jc,
163  SuperLU::SLU_NC, SuperLU::SLU_D,
164  SuperLU::SLU_GE);
165  }
166 
167  inline void Create_CompCol_Matrix(SuperLU::SuperMatrix *A, int m, int n,
168  int nnz, std::complex<float> *a,
169  int *ir, int *jc) {
170  SuperLU::cCreate_CompCol_Matrix(A, m, n, nnz,
171  (SuperLU::singlecomplex *)(a),
172  ir, jc, SuperLU::SLU_NC, SuperLU::SLU_C,
173  SuperLU::SLU_GE);
174  }
175 
176  inline void Create_CompCol_Matrix(SuperLU::SuperMatrix *A, int m, int n,
177  int nnz, std::complex<double> *a,
178  int *ir, int *jc) {
179  SuperLU::zCreate_CompCol_Matrix(A, m, n, nnz,
180  (SuperLU::doublecomplex *)(a), ir, jc,
181  SuperLU::SLU_NC, SuperLU::SLU_Z,
182  SuperLU::SLU_GE);
183  }
184 
185  /* interface for Create_Dense_Matrix */
186 
187  inline void Create_Dense_Matrix(SuperLU::SuperMatrix *A, int m, int n,
188  float *a, int k) {
189  SuperLU::sCreate_Dense_Matrix(A, m, n, a, k, SuperLU::SLU_DN,
190  SuperLU::SLU_S,
191  SuperLU::SLU_GE);
192  }
193  inline void Create_Dense_Matrix(SuperLU::SuperMatrix *A, int m, int n,
194  double *a, int k) {
195  SuperLU::dCreate_Dense_Matrix(A, m, n, a, k, SuperLU::SLU_DN,
196  SuperLU::SLU_D,
197  SuperLU::SLU_GE);
198  }
199  inline void Create_Dense_Matrix(SuperLU::SuperMatrix *A, int m, int n,
200  std::complex<float> *a, int k) {
201  SuperLU::cCreate_Dense_Matrix(A, m, n,
202  (SuperLU::singlecomplex *)(a),
203  k, SuperLU::SLU_DN, SuperLU::SLU_C,
204  SuperLU::SLU_GE);
205  }
206  inline void Create_Dense_Matrix(SuperLU::SuperMatrix *A, int m, int n,
207  std::complex<double> *a, int k) {
208  SuperLU::zCreate_Dense_Matrix(A, m, n, (SuperLU::doublecomplex *)(a),
209  k, SuperLU::SLU_DN, SuperLU::SLU_Z,
210  SuperLU::SLU_GE);
211  }
212 
213  /* interface for gssv */
214 
215 #define DECL_GSSV(FNAME,KEYTYPE) \
216  inline void SuperLU_gssv(SuperLU::superlu_options_t *options, \
217  SuperLU::SuperMatrix *A, int *p, int *q, \
218  SuperLU::SuperMatrix *L, \
219  SuperLU::SuperMatrix *U, \
220  SuperLU::SuperMatrix *B, \
221  SuperLU::SuperLUStat_t *stats, \
222  int *info, KEYTYPE) { \
223  SuperLU::FNAME(options, A, p, q, L, U, B, stats, info); \
224  }
225 
226  DECL_GSSV(sgssv, float)
227  DECL_GSSV(cgssv, std::complex<float>)
228  DECL_GSSV(dgssv, double)
229  DECL_GSSV(zgssv, std::complex<double>)
230 
231  /* interface for gssvx */
232 
233 #define DECL_GSSVX(FNAME,FLOATTYPE,KEYTYPE) \
234  inline float SuperLU_gssvx(SuperLU::superlu_options_t *options, \
235  SuperLU::SuperMatrix *A, \
236  int *perm_c, int *perm_r, int *etree, \
237  char *equed, \
238  FLOATTYPE *R, FLOATTYPE *C, \
239  SuperLU::SuperMatrix *L, \
240  SuperLU::SuperMatrix *U, \
241  void *work, int lwork, \
242  SuperLU::SuperMatrix *B, \
243  SuperLU::SuperMatrix *X, \
244  FLOATTYPE *recip_pivot_growth, \
245  FLOATTYPE *rcond, FLOATTYPE *ferr, \
246  FLOATTYPE *berr, \
247  SuperLU::SuperLUStat_t *stats, \
248  int *info, KEYTYPE) { \
249  SuperLU::mem_usage_t mem_usage; \
250  SuperLU::GlobalLU_t Glu; \
251  SuperLU::FNAME(options, A, perm_c, perm_r, etree, equed, R, C, L, \
252  U, work, lwork, B, X, recip_pivot_growth, rcond, \
253  ferr, berr, &Glu, &mem_usage, stats, info); \
254  return mem_usage.for_lu; /* bytes used by the factor storage */ \
255  }
256 
257  DECL_GSSVX(sgssvx, float, float)
258  DECL_GSSVX(cgssvx, float, std::complex<float>)
259  DECL_GSSVX(dgssvx, double, double)
260  DECL_GSSVX(zgssvx, double, std::complex<double>)
261 
262  /* ********************************************************************* */
263  /* SuperLU solve interface */
264  /* ********************************************************************* */
265 
266  template <typename MAT, typename VECTX, typename VECTB>
267  int SuperLU_solve(const MAT &A, const VECTX &X, const VECTB &B,
268  double& rcond_, int permc_spec = 3) {
269  /*
270  * Get column permutation vector perm_c[], according to permc_spec:
271  * permc_spec = 0: use the natural ordering
272  * permc_spec = 1: use minimum degree ordering on structure of A'*A
273  * permc_spec = 2: use minimum degree ordering on structure of A'+A
274  * permc_spec = 3: use approximate minimum degree column ordering
275  */
276  typedef typename linalg_traits<MAT>::value_type T;
277  typedef typename number_traits<T>::magnitude_type R;
278 
279  int m = int(mat_nrows(A)), n = int(mat_ncols(A)), nrhs = 1, info = 0;
280 
281  csc_matrix<T> csc_A(m, n);
282  gmm::copy(A, csc_A);
283  std::vector<T> rhs(m), sol(m);
284  gmm::copy(B, rhs);
285 
286  int nz = int(nnz(csc_A));
287  if ((2 * nz / n) >= m)
288  GMM_WARNING2("CAUTION : it seems that SuperLU has a problem"
289  " for nearly dense sparse matrices");
290 
291  SuperLU::superlu_options_t options;
292  set_default_options(&options);
293  options.ColPerm = SuperLU::NATURAL;
294  options.PrintStat = SuperLU::NO;
295  options.ConditionNumber = SuperLU::YES;
296  switch (permc_spec) {
297  case 1 : options.ColPerm = SuperLU::MMD_ATA; break;
298  case 2 : options.ColPerm = SuperLU::MMD_AT_PLUS_A; break;
299  case 3 : options.ColPerm = SuperLU::COLAMD; break;
300  }
301  SuperLU::SuperLUStat_t stat;
302  StatInit(&stat);
303 
304  SuperLU::SuperMatrix SA, SL, SU, SB, SX; // SuperLU format.
305  Create_CompCol_Matrix(&SA, m, n, nz, (T *)(&csc_A.pr[0]),
306  (int *)(&csc_A.ir[0]),
307  (int *)(&csc_A.jc[0]));
308  Create_Dense_Matrix(&SB, m, nrhs, &rhs[0], m);
309  Create_Dense_Matrix(&SX, m, nrhs, &sol[0], m);
310  memset(&SL,0,sizeof SL);
311  memset(&SU,0,sizeof SU);
312 
313  std::vector<int> etree(n);
314  char equed[] = "B";
315  std::vector<R> Rscale(m),Cscale(n); // row scale factors
316  std::vector<R> ferr(nrhs), berr(nrhs);
317  R recip_pivot_gross, rcond;
318  std::vector<int> perm_r(m), perm_c(n);
319 
320  SuperLU_gssvx(&options, &SA, &perm_c[0], &perm_r[0],
321  &etree[0] /* output */, equed /* output */,
322  &Rscale[0] /* row scale factors (output) */,
323  &Cscale[0] /* col scale factors (output) */,
324  &SL /* fact L (output)*/, &SU /* fact U (output)*/,
325  NULL /* work */,
326  0 /* lwork: superlu auto allocates (input) */,
327  &SB /* rhs */, &SX /* solution */,
328  &recip_pivot_gross /* reciprocal pivot growth */
329  /* factor max_j( norm(A_j)/norm(U_j) ). */,
330  &rcond /*estimate of the reciprocal condition */
331  /* number of the matrix A after equilibration */,
332  &ferr[0] /* estimated forward error */,
333  &berr[0] /* relative backward error */,
334  &stat, &info, T());
335  rcond_ = rcond;
336  if (SB.Store) Destroy_SuperMatrix_Store(&SB);
337  if (SX.Store) Destroy_SuperMatrix_Store(&SX);
338  if (SA.Store) Destroy_SuperMatrix_Store(&SA);
339  if (SL.Store) Destroy_SuperNode_Matrix(&SL);
340  if (SU.Store) Destroy_CompCol_Matrix(&SU);
341  StatFree(&stat);
342  GMM_ASSERT1(info != -333333333, "SuperLU was cancelled."); // user interruption (for matlab interface)
343 
344  GMM_ASSERT1(info >= 0, "SuperLU solve failed: info =" << info);
345  if (info > 0) GMM_WARNING1("SuperLU solve failed: info =" << info);
346  gmm::copy(sol, const_cast<VECTX &>(X));
347  return info;
348  }
349 
350  template <class T>
351  class SuperLU_factor {
352  typedef typename number_traits<T>::magnitude_type R;
353 
354  csc_matrix<T> csc_A;
355  mutable SuperLU::SuperMatrix SA, SL, SB, SU, SX;
356  mutable SuperLU::SuperLUStat_t stat;
357  mutable SuperLU::superlu_options_t options;
358  float memory_used;
359  mutable std::vector<int> etree, perm_r, perm_c;
360  mutable std::vector<R> Rscale, Cscale;
361  mutable std::vector<R> ferr, berr;
362  mutable std::vector<T> rhs;
363  mutable std::vector<T> sol;
364  mutable bool is_init;
365  mutable char equed;
366 
367  public :
368  enum { LU_NOTRANSP, LU_TRANSP, LU_CONJUGATED };
369  void free_supermatrix() {
370  if (is_init) {
371  if (SB.Store) Destroy_SuperMatrix_Store(&SB);
372  if (SX.Store) Destroy_SuperMatrix_Store(&SX);
373  if (SA.Store) Destroy_SuperMatrix_Store(&SA);
374  if (SL.Store) Destroy_SuperNode_Matrix(&SL);
375  if (SU.Store) Destroy_CompCol_Matrix(&SU);
376  }
377  }
378  template <class MAT> void build_with(const MAT &A, int permc_spec = 3);
379  template <typename VECTX, typename VECTB>
380  /* transp = LU_NOTRANSP -> solves Ax = B
381  transp = LU_TRANSP -> solves A'x = B
382  transp = LU_CONJUGATED -> solves conj(A)X = B */
383  void solve(const VECTX &X_, const VECTB &B, int transp=LU_NOTRANSP) const;
384  SuperLU_factor() { is_init = false; }
385  SuperLU_factor(const SuperLU_factor& other) {
386  GMM_ASSERT2(!(other.is_init),
387  "copy of initialized SuperLU_factor is forbidden");
388  is_init = false;
389  }
390  SuperLU_factor& operator=(const SuperLU_factor& other) {
391  GMM_ASSERT2(!(other.is_init) && !is_init,
392  "assignment of initialized SuperLU_factor is forbidden");
393  return *this;
394  }
395  ~SuperLU_factor() { free_supermatrix(); }
396  float memsize() { return memory_used; }
397  };
398 
399 
400  template <class T> template <class MAT>
401  void SuperLU_factor<T>::build_with(const MAT &A, int permc_spec) {
402  /*
403  * Get column permutation vector perm_c[], according to permc_spec:
404  * permc_spec = 0: use the natural ordering
405  * permc_spec = 1: use minimum degree ordering on structure of A'*A
406  * permc_spec = 2: use minimum degree ordering on structure of A'+A
407  * permc_spec = 3: use approximate minimum degree column ordering
408  */
409  free_supermatrix();
410  int n = int(mat_nrows(A)), m = int(mat_ncols(A)), info = 0;
411  csc_A.init_with(A);
412 
413  rhs.resize(m); sol.resize(m);
414  gmm::clear(rhs);
415  int nz = int(nnz(csc_A));
416 
417  set_default_options(&options);
418  options.ColPerm = SuperLU::NATURAL;
419  options.PrintStat = SuperLU::NO;
420  options.ConditionNumber = SuperLU::NO;
421  switch (permc_spec) {
422  case 1 : options.ColPerm = SuperLU::MMD_ATA; break;
423  case 2 : options.ColPerm = SuperLU::MMD_AT_PLUS_A; break;
424  case 3 : options.ColPerm = SuperLU::COLAMD; break;
425  }
426  StatInit(&stat);
427 
428  Create_CompCol_Matrix(&SA, m, n, nz, (T *)(&csc_A.pr[0]),
429  (int *)(&csc_A.ir[0]),
430  (int *)(&csc_A.jc[0]));
431  Create_Dense_Matrix(&SB, m, 0, &rhs[0], m);
432  Create_Dense_Matrix(&SX, m, 0, &sol[0], m);
433  memset(&SL,0,sizeof SL);
434  memset(&SU,0,sizeof SU);
435  equed = 'B';
436  Rscale.resize(m); Cscale.resize(n); etree.resize(n);
437  ferr.resize(1); berr.resize(1);
438  R recip_pivot_gross, rcond;
439  perm_r.resize(m); perm_c.resize(n);
440  memory_used = SuperLU_gssvx(&options, &SA, &perm_c[0], &perm_r[0],
441  &etree[0] /* output */, &equed /* output */,
442  &Rscale[0] /* row scale factors (output) */,
443  &Cscale[0] /* col scale factors (output) */,
444  &SL /* fact L (output) */,
445  &SU /* fact U (output) */,
446  NULL /* work */,
447  0 /* lwork: superlu auto allocates (input) */,
448  &SB /* rhs */, &SX /* solution */,
449  &recip_pivot_gross /* reciprocal pivot growth*/
450  /* factor max_j(norm(A_j)/norm(U_j)). */,
451  &rcond /*estimate of the reciprocal condition*/
452  /* number of the matrix A after equilibration*/,
453  &ferr[0] /* estimated forward error */,
454  &berr[0] /* relative backward error */,
455  &stat, &info, T());
456 
457  Destroy_SuperMatrix_Store(&SB);
458  Destroy_SuperMatrix_Store(&SX);
459  Create_Dense_Matrix(&SB, m, 1, &rhs[0], m);
460  Create_Dense_Matrix(&SX, m, 1, &sol[0], m);
461  StatFree(&stat);
462 
463  GMM_ASSERT1(info != -333333333, "SuperLU was cancelled.");
464  GMM_ASSERT1(info == 0, "SuperLU solve failed: info=" << info);
465  is_init = true;
466  }
467 
468  template <class T> template <typename VECTX, typename VECTB>
469  void SuperLU_factor<T>::solve(const VECTX &X, const VECTB &B,
470  int transp) const {
471  gmm::copy(B, rhs);
472  options.Fact = SuperLU::FACTORED;
473  options.IterRefine = SuperLU::NOREFINE;
474  switch (transp) {
475  case LU_NOTRANSP: options.Trans = SuperLU::NOTRANS; break;
476  case LU_TRANSP: options.Trans = SuperLU::TRANS; break;
477  case LU_CONJUGATED: options.Trans = SuperLU::CONJ; break;
478  default: GMM_ASSERT1(false, "invalid value for transposition option");
479  }
480  StatInit(&stat);
481  int info = 0;
482  R recip_pivot_gross, rcond;
483  SuperLU_gssvx(&options, &SA, &perm_c[0], &perm_r[0],
484  &etree[0] /* output */, &equed /* output */,
485  &Rscale[0] /* row scale factors (output) */,
486  &Cscale[0] /* col scale factors (output) */,
487  &SL /* fact L (output)*/, &SU /* fact U (output)*/,
488  NULL /* work */,
489  0 /* lwork: superlu auto allocates (input) */,
490  &SB /* rhs */, &SX /* solution */,
491  &recip_pivot_gross /* reciprocal pivot growth */
492  /* factor max_j( norm(A_j)/norm(U_j) ). */,
493  &rcond /*estimate of the reciprocal condition */
494  /* number of the matrix A after equilibration */,
495  &ferr[0] /* estimated forward error */,
496  &berr[0] /* relative backward error */,
497  &stat, &info, T());
498  StatFree(&stat);
499  GMM_ASSERT1(info == 0, "SuperLU solve failed: info=" << info);
500  gmm::copy(sol, const_cast<VECTX &>(X));
501  }
502 
503  template <typename T, typename V1, typename V2> inline
504  void mult(const SuperLU_factor<T>& P, const V1 &v1, const V2 &v2) {
505  P.solve(v2,v1);
506  }
507 
508  template <typename T, typename V1, typename V2> inline
509  void transposed_mult(const SuperLU_factor<T>& P,const V1 &v1,const V2 &v2) {
510  P.solve(v2, v1, SuperLU_factor<T>::LU_TRANSP);
511  }
512 
513 }
514 
515 #ifdef TRUE
516 # undef TRUE
517 #endif
518 #ifdef FALSE
519 # undef FALSE
520 #endif
521 #ifdef EMPTY
522 # undef EMPTY
523 #endif
524 
525 #endif // GMM_SUPERLU_INTERFACE_H
526 
527 #endif // GMM_USES_SUPERLU
gmm::nnz
size_type nnz(const L &l)
count the number of non-zero entries of a vector or matrix.
Definition: gmm_blas.h:69
gmm::copy
void copy(const L1 &l1, L2 &l2)
*‍/
Definition: gmm_blas.h:977
gmm::clear
void clear(L &l)
clear (fill with zeros) a vector or matrix.
Definition: gmm_blas.h:59
gmm::mult
void mult(const L1 &l1, const L2 &l2, L3 &l3)
*‍/
Definition: gmm_blas.h:1664
gmm_kernel.h
Include the base gmm files.