GetFEM  5.4.2
gmm_superlu_interface.h
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30 ===========================================================================*/
31 
32 /**@file gmm_superlu_interface.h
33  @author Yves Renard <Yves.Renard@insa-lyon.fr>
34  @date October 17, 2003.
35  @brief Interface with SuperLU (LU direct solver for sparse matrices).
36 */
37 #if defined(GMM_USES_SUPERLU) && !defined(GETFEM_VERSION)
38 
39 #ifndef GMM_SUPERLU_INTERFACE_H
40 #define GMM_SUPERLU_INTERFACE_H
41 
42 #include "gmm_kernel.h"
43 
44 typedef int int_t;
45 
46 /* because SRC/util.h defines TRUE and FALSE ... */
47 #ifdef TRUE
48 # undef TRUE
49 #endif
50 #ifdef FALSE
51 # undef FALSE
52 #endif
53 
54 #include "superlu/slu_Cnames.h"
55 #include "superlu/supermatrix.h"
56 #include "superlu/slu_util.h"
57 
58 namespace SuperLU_S {
59 #include "superlu/slu_sdefs.h"
60 }
61 namespace SuperLU_D {
62 #include "superlu/slu_ddefs.h"
63 }
64 namespace SuperLU_C {
65 #include "superlu/slu_cdefs.h"
66 }
67 namespace SuperLU_Z {
68 #include "superlu/slu_zdefs.h"
69 }
70 
71 
72 
73 namespace gmm {
74 
75  /* interface for Create_CompCol_Matrix */
76 
77  inline void Create_CompCol_Matrix(SuperMatrix *A, int m, int n, int nnz,
78  float *a, int *ir, int *jc) {
79  SuperLU_S::sCreate_CompCol_Matrix(A, m, n, nnz, a, ir, jc,
80  SLU_NC, SLU_S, SLU_GE);
81  }
82 
83  inline void Create_CompCol_Matrix(SuperMatrix *A, int m, int n, int nnz,
84  double *a, int *ir, int *jc) {
85  SuperLU_D::dCreate_CompCol_Matrix(A, m, n, nnz, a, ir, jc,
86  SLU_NC, SLU_D, SLU_GE);
87  }
88 
89  inline void Create_CompCol_Matrix(SuperMatrix *A, int m, int n, int nnz,
90  std::complex<float> *a, int *ir, int *jc) {
91  SuperLU_C::cCreate_CompCol_Matrix(A, m, n, nnz, (SuperLU_C::complex *)(a),
92  ir, jc, SLU_NC, SLU_C, SLU_GE);
93  }
94 
95  inline void Create_CompCol_Matrix(SuperMatrix *A, int m, int n, int nnz,
96  std::complex<double> *a, int *ir, int *jc) {
97  SuperLU_Z::zCreate_CompCol_Matrix(A, m, n, nnz,
98  (SuperLU_Z::doublecomplex *)(a), ir, jc,
99  SLU_NC, SLU_Z, SLU_GE);
100  }
101 
102  /* interface for Create_Dense_Matrix */
103 
104  inline void Create_Dense_Matrix(SuperMatrix *A, int m, int n, float *a, int k)
105  { SuperLU_S::sCreate_Dense_Matrix(A, m, n, a, k, SLU_DN, SLU_S, SLU_GE); }
106  inline void Create_Dense_Matrix(SuperMatrix *A, int m, int n, double *a, int k)
107  { SuperLU_D::dCreate_Dense_Matrix(A, m, n, a, k, SLU_DN, SLU_D, SLU_GE); }
108  inline void Create_Dense_Matrix(SuperMatrix *A, int m, int n,
109  std::complex<float> *a, int k) {
110  SuperLU_C::cCreate_Dense_Matrix(A, m, n, (SuperLU_C::complex *)(a),
111  k, SLU_DN, SLU_C, SLU_GE);
112  }
113  inline void Create_Dense_Matrix(SuperMatrix *A, int m, int n,
114  std::complex<double> *a, int k) {
115  SuperLU_Z::zCreate_Dense_Matrix(A, m, n, (SuperLU_Z::doublecomplex *)(a),
116  k, SLU_DN, SLU_Z, SLU_GE);
117  }
118 
119  /* interface for gssv */
120 
121 #define DECL_GSSV(NAMESPACE,FNAME,FLOATTYPE,KEYTYPE) \
122  inline void SuperLU_gssv(superlu_options_t *options, SuperMatrix *A, int *p, \
123  int *q, SuperMatrix *L, SuperMatrix *U, SuperMatrix *B, \
124  SuperLUStat_t *stats, int *info, KEYTYPE) { \
125  NAMESPACE::FNAME(options, A, p, q, L, U, B, stats, info); \
126  }
127 
128  DECL_GSSV(SuperLU_S,sgssv,float,float)
129  DECL_GSSV(SuperLU_C,cgssv,float,std::complex<float>)
130  DECL_GSSV(SuperLU_D,dgssv,double,double)
131  DECL_GSSV(SuperLU_Z,zgssv,double,std::complex<double>)
132 
133  /* interface for gssvx */
134 
135 #define DECL_GSSVX(NAMESPACE,FNAME,FLOATTYPE,KEYTYPE) \
136  inline float SuperLU_gssvx(superlu_options_t *options, SuperMatrix *A, \
137  int *perm_c, int *perm_r, int *etree, char *equed, \
138  FLOATTYPE *R, FLOATTYPE *C, SuperMatrix *L, \
139  SuperMatrix *U, void *work, int lwork, \
140  SuperMatrix *B, SuperMatrix *X, \
141  FLOATTYPE *recip_pivot_growth, \
142  FLOATTYPE *rcond, FLOATTYPE *ferr, FLOATTYPE *berr, \
143  SuperLUStat_t *stats, int *info, KEYTYPE) { \
144  NAMESPACE::mem_usage_t mem_usage; \
145  NAMESPACE::FNAME(options, A, perm_c, perm_r, etree, equed, R, C, L, \
146  U, work, lwork, B, X, recip_pivot_growth, rcond, \
147  ferr, berr, &mem_usage, stats, info); \
148  return mem_usage.for_lu; /* bytes used by the factor storage */ \
149  }
150 
151  DECL_GSSVX(SuperLU_S,sgssvx,float,float)
152  DECL_GSSVX(SuperLU_C,cgssvx,float,std::complex<float>)
153  DECL_GSSVX(SuperLU_D,dgssvx,double,double)
154  DECL_GSSVX(SuperLU_Z,zgssvx,double,std::complex<double>)
155 
156  /* ********************************************************************* */
157  /* SuperLU solve interface */
158  /* ********************************************************************* */
159 
160  template <typename MAT, typename VECTX, typename VECTB>
161  int SuperLU_solve(const MAT &A, const VECTX &X_, const VECTB &B,
162  double& rcond_, int permc_spec = 3) {
163  VECTX &X = const_cast<VECTX &>(X_);
164  /*
165  * Get column permutation vector perm_c[], according to permc_spec:
166  * permc_spec = 0: use the natural ordering
167  * permc_spec = 1: use minimum degree ordering on structure of A'*A
168  * permc_spec = 2: use minimum degree ordering on structure of A'+A
169  * permc_spec = 3: use approximate minimum degree column ordering
170  */
171  typedef typename linalg_traits<MAT>::value_type T;
172  typedef typename number_traits<T>::magnitude_type R;
173 
174  int m = mat_nrows(A), n = mat_ncols(A), nrhs = 1, info = 0;
175 
176  csc_matrix<T> csc_A(m, n); gmm::copy(A, csc_A);
177  std::vector<T> rhs(m), sol(m);
178  gmm::copy(B, rhs);
179 
180  int nz = nnz(csc_A);
181  if ((2 * nz / n) >= m)
182  GMM_WARNING2("CAUTION : it seems that SuperLU has a problem"
183  " for nearly dense sparse matrices");
184 
185  superlu_options_t options;
186  set_default_options(&options);
187  options.ColPerm = NATURAL;
188  options.PrintStat = NO;
189  options.ConditionNumber = YES;
190  switch (permc_spec) {
191  case 1 : options.ColPerm = MMD_ATA; break;
192  case 2 : options.ColPerm = MMD_AT_PLUS_A; break;
193  case 3 : options.ColPerm = COLAMD; break;
194  }
195  SuperLUStat_t stat;
196  StatInit(&stat);
197 
198  SuperMatrix SA, SL, SU, SB, SX; // SuperLU format.
199  Create_CompCol_Matrix(&SA, m, n, nz, (double *)(&(csc_A.pr[0])),
200  (int *)(&(csc_A.ir[0])), (int *)(&(csc_A.jc[0])));
201  Create_Dense_Matrix(&SB, m, nrhs, &rhs[0], m);
202  Create_Dense_Matrix(&SX, m, nrhs, &sol[0], m);
203  memset(&SL,0,sizeof SL);
204  memset(&SU,0,sizeof SU);
205 
206  std::vector<int> etree(n);
207  char equed[] = "B";
208  std::vector<R> Rscale(m),Cscale(n); // row scale factors
209  std::vector<R> ferr(nrhs), berr(nrhs);
210  R recip_pivot_gross, rcond;
211  std::vector<int> perm_r(m), perm_c(n);
212 
213  SuperLU_gssvx(&options, &SA, &perm_c[0], &perm_r[0],
214  &etree[0] /* output */, equed /* output */,
215  &Rscale[0] /* row scale factors (output) */,
216  &Cscale[0] /* col scale factors (output) */,
217  &SL /* fact L (output)*/, &SU /* fact U (output)*/,
218  NULL /* work */,
219  0 /* lwork: superlu auto allocates (input) */,
220  &SB /* rhs */, &SX /* solution */,
221  &recip_pivot_gross /* reciprocal pivot growth */
222  /* factor max_j( norm(A_j)/norm(U_j) ). */,
223  &rcond /*estimate of the reciprocal condition */
224  /* number of the matrix A after equilibration */,
225  &ferr[0] /* estimated forward error */,
226  &berr[0] /* relative backward error */,
227  &stat, &info, T());
228  rcond_ = rcond;
229  Destroy_SuperMatrix_Store(&SB);
230  Destroy_SuperMatrix_Store(&SX);
231  Destroy_SuperMatrix_Store(&SA);
232  Destroy_SuperNode_Matrix(&SL);
233  Destroy_CompCol_Matrix(&SU);
234  StatFree(&stat);
235  GMM_ASSERT1(info >= 0, "SuperLU solve failed: info =" << info);
236  if (info > 0) GMM_WARNING1("SuperLU solve failed: info =" << info);
237  gmm::copy(sol, X);
238  return info;
239  }
240 
241  template <class T> class SuperLU_factor {
242  typedef typename number_traits<T>::magnitude_type R;
243 
244  csc_matrix<T> csc_A;
245  mutable SuperMatrix SA, SL, SB, SU, SX;
246  mutable SuperLUStat_t stat;
247  mutable superlu_options_t options;
248  float memory_used;
249  mutable std::vector<int> etree, perm_r, perm_c;
250  mutable std::vector<R> Rscale, Cscale;
251  mutable std::vector<R> ferr, berr;
252  mutable std::vector<T> rhs;
253  mutable std::vector<T> sol;
254  mutable bool is_init;
255  mutable char equed;
256 
257  public :
258  enum { LU_NOTRANSP, LU_TRANSP, LU_CONJUGATED };
259  void free_supermatrix(void);
260  template <class MAT> void build_with(const MAT &A, int permc_spec = 3);
261  template <typename VECTX, typename VECTB>
262  /* transp = LU_NOTRANSP -> solves Ax = B
263  transp = LU_TRANSP -> solves A'x = B
264  transp = LU_CONJUGATED -> solves conj(A)X = B */
265  void solve(const VECTX &X_, const VECTB &B, int transp=LU_NOTRANSP) const;
266  SuperLU_factor(void) { is_init = false; }
267  SuperLU_factor(const SuperLU_factor& other) {
268  GMM_ASSERT2(!(other.is_init),
269  "copy of initialized SuperLU_factor is forbidden");
270  is_init = false;
271  }
272  SuperLU_factor& operator=(const SuperLU_factor& other) {
273  GMM_ASSERT2(!(other.is_init) && !is_init,
274  "assignment of initialized SuperLU_factor is forbidden");
275  return *this;
276  }
277  ~SuperLU_factor() { free_supermatrix(); }
278  float memsize() { return memory_used; }
279  };
280 
281 
282  template <class T> void SuperLU_factor<T>::free_supermatrix(void) {
283  if (is_init) {
284  if (SB.Store) Destroy_SuperMatrix_Store(&SB);
285  if (SX.Store) Destroy_SuperMatrix_Store(&SX);
286  if (SA.Store) Destroy_SuperMatrix_Store(&SA);
287  if (SL.Store) Destroy_SuperNode_Matrix(&SL);
288  if (SU.Store) Destroy_CompCol_Matrix(&SU);
289  }
290  }
291 
292 
293  template <class T> template <class MAT>
294  void SuperLU_factor<T>::build_with(const MAT &A, int permc_spec) {
295  /*
296  * Get column permutation vector perm_c[], according to permc_spec:
297  * permc_spec = 0: use the natural ordering
298  * permc_spec = 1: use minimum degree ordering on structure of A'*A
299  * permc_spec = 2: use minimum degree ordering on structure of A'+A
300  * permc_spec = 3: use approximate minimum degree column ordering
301  */
302  free_supermatrix();
303  int n = mat_nrows(A), m = mat_ncols(A), info = 0;
304  csc_A.init_with(A);
305 
306  rhs.resize(m); sol.resize(m);
307  gmm::clear(rhs);
308  int nz = nnz(csc_A);
309 
310  set_default_options(&options);
311  options.ColPerm = NATURAL;
312  options.PrintStat = NO;
313  options.ConditionNumber = NO;
314  switch (permc_spec) {
315  case 1 : options.ColPerm = MMD_ATA; break;
316  case 2 : options.ColPerm = MMD_AT_PLUS_A; break;
317  case 3 : options.ColPerm = COLAMD; break;
318  }
319  StatInit(&stat);
320 
321  Create_CompCol_Matrix(&SA, m, n, nz, (double *)(&(csc_A.pr[0])),
322  (int *)(&(csc_A.ir[0])), (int *)(&(csc_A.jc[0])));
323 
324  Create_Dense_Matrix(&SB, m, 0, &rhs[0], m);
325  Create_Dense_Matrix(&SX, m, 0, &sol[0], m);
326  memset(&SL,0,sizeof SL);
327  memset(&SU,0,sizeof SU);
328  equed = 'B';
329  Rscale.resize(m); Cscale.resize(n); etree.resize(n);
330  ferr.resize(1); berr.resize(1);
331  R recip_pivot_gross, rcond;
332  perm_r.resize(m); perm_c.resize(n);
333  memory_used = SuperLU_gssvx(&options, &SA, &perm_c[0], &perm_r[0],
334  &etree[0] /* output */, &equed /* output */,
335  &Rscale[0] /* row scale factors (output) */,
336  &Cscale[0] /* col scale factors (output) */,
337  &SL /* fact L (output)*/, &SU /* fact U (output)*/,
338  NULL /* work */,
339  0 /* lwork: superlu auto allocates (input) */,
340  &SB /* rhs */, &SX /* solution */,
341  &recip_pivot_gross /* reciprocal pivot growth */
342  /* factor max_j( norm(A_j)/norm(U_j) ). */,
343  &rcond /*estimate of the reciprocal condition */
344  /* number of the matrix A after equilibration */,
345  &ferr[0] /* estimated forward error */,
346  &berr[0] /* relative backward error */,
347  &stat, &info, T());
348 
349  Destroy_SuperMatrix_Store(&SB);
350  Destroy_SuperMatrix_Store(&SX);
351  Create_Dense_Matrix(&SB, m, 1, &rhs[0], m);
352  Create_Dense_Matrix(&SX, m, 1, &sol[0], m);
353  StatFree(&stat);
354 
355  GMM_ASSERT1(info == 0, "SuperLU solve failed: info=" << info);
356  is_init = true;
357  }
358 
359  template <class T> template <typename VECTX, typename VECTB>
360  void SuperLU_factor<T>::solve(const VECTX &X_, const VECTB &B,
361  int transp) const {
362  VECTX &X = const_cast<VECTX &>(X_);
363  gmm::copy(B, rhs);
364  options.Fact = FACTORED;
365  options.IterRefine = NOREFINE;
366  switch (transp) {
367  case LU_NOTRANSP: options.Trans = NOTRANS; break;
368  case LU_TRANSP: options.Trans = TRANS; break;
369  case LU_CONJUGATED: options.Trans = CONJ; break;
370  default: GMM_ASSERT1(false, "invalid value for transposition option");
371  }
372  StatInit(&stat);
373  int info = 0;
374  R recip_pivot_gross, rcond;
375  SuperLU_gssvx(&options, &SA, &perm_c[0], &perm_r[0],
376  &etree[0] /* output */, &equed /* output */,
377  &Rscale[0] /* row scale factors (output) */,
378  &Cscale[0] /* col scale factors (output) */,
379  &SL /* fact L (output)*/, &SU /* fact U (output)*/,
380  NULL /* work */,
381  0 /* lwork: superlu auto allocates (input) */,
382  &SB /* rhs */, &SX /* solution */,
383  &recip_pivot_gross /* reciprocal pivot growth */
384  /* factor max_j( norm(A_j)/norm(U_j) ). */,
385  &rcond /*estimate of the reciprocal condition */
386  /* number of the matrix A after equilibration */,
387  &ferr[0] /* estimated forward error */,
388  &berr[0] /* relative backward error */,
389  &stat, &info, T());
390  StatFree(&stat);
391  GMM_ASSERT1(info == 0, "SuperLU solve failed: info=" << info);
392  gmm::copy(sol, X);
393  }
394 
395  template <typename T, typename V1, typename V2> inline
396  void mult(const SuperLU_factor<T>& P, const V1 &v1, const V2 &v2) {
397  P.solve(v2,v1);
398  }
399 
400  template <typename T, typename V1, typename V2> inline
401  void transposed_mult(const SuperLU_factor<T>& P,const V1 &v1,const V2 &v2) {
402  P.solve(v2, v1, SuperLU_factor<T>::LU_TRANSP);
403  }
404 
405 }
406 
407 
408 #endif // GMM_SUPERLU_INTERFACE_H
409 
410 #endif // GMM_USES_SUPERLU
gmm::clear
void clear(L &l)
clear (fill with zeros) a vector or matrix.
Definition: gmm_blas.h:59
gmm::nnz
size_type nnz(const L &l)
count the number of non-zero entries of a vector or matrix.
Definition: gmm_blas.h:68
gmm::SuperLU_factor::build_with
void build_with(const MAT &A, int permc_spec=3)
Do the factorization of the supplied sparse matrix.
Definition: getfem_superlu.h:90
gmm_kernel.h
Include the base gmm files.
gmm::SuperLU_factor::solve
void solve(const VECTX &X, const VECTB &B, int transp=LU_NOTRANSP) const
After factorization, do the triangular solves.
Definition: getfem_superlu.h:103