Actual source code: mumps.c

  1: /*
  2:     Provides an interface to the MUMPS sparse solver
  3: */
  4: #include <petscpkg_version.h>
  5: #include <petscsf.h>
  6: #include <../src/mat/impls/aij/mpi/mpiaij.h>
  7: #include <../src/mat/impls/sbaij/mpi/mpisbaij.h>
  8: #include <../src/mat/impls/sell/mpi/mpisell.h>

 10: #define MUMPS_MANUALS "(see users manual https://mumps-solver.org/index.php?page=doc \"Error and warning diagnostics\")"

 12: EXTERN_C_BEGIN
 13: #if defined(PETSC_USE_COMPLEX)
 14:   #if defined(PETSC_USE_REAL_SINGLE)
 15:     #include <cmumps_c.h>
 16:   #else
 17:     #include <zmumps_c.h>
 18:   #endif
 19: #else
 20:   #if defined(PETSC_USE_REAL_SINGLE)
 21:     #include <smumps_c.h>
 22:   #else
 23:     #include <dmumps_c.h>
 24:   #endif
 25: #endif
 26: EXTERN_C_END
 27: #define JOB_INIT         -1
 28: #define JOB_NULL         0
 29: #define JOB_FACTSYMBOLIC 1
 30: #define JOB_FACTNUMERIC  2
 31: #define JOB_SOLVE        3
 32: #define JOB_END          -2

 34: /* calls to MUMPS */
 35: #if defined(PETSC_USE_COMPLEX)
 36:   #if defined(PETSC_USE_REAL_SINGLE)
 37:     #define MUMPS_c cmumps_c
 38:   #else
 39:     #define MUMPS_c zmumps_c
 40:   #endif
 41: #else
 42:   #if defined(PETSC_USE_REAL_SINGLE)
 43:     #define MUMPS_c smumps_c
 44:   #else
 45:     #define MUMPS_c dmumps_c
 46:   #endif
 47: #endif

 49: /* MUMPS uses MUMPS_INT for nonzero indices such as irn/jcn, irn_loc/jcn_loc and uses int64_t for
 50:    number of nonzeros such as nnz, nnz_loc. We typedef MUMPS_INT to PetscMUMPSInt to follow the
 51:    naming convention in PetscMPIInt, PetscBLASInt etc.
 52: */
 53: typedef MUMPS_INT PetscMUMPSInt;

 55: #if PETSC_PKG_MUMPS_VERSION_GE(5, 3, 0)
 56:   #if defined(MUMPS_INTSIZE64) /* MUMPS_INTSIZE64 is in MUMPS headers if it is built in full 64-bit mode, therefore the macro is more reliable */
 57:     #error "Petsc has not been tested with full 64-bit MUMPS and we choose to error out"
 58:   #endif
 59: #else
 60:   #if defined(INTSIZE64) /* INTSIZE64 is a command line macro one used to build MUMPS in full 64-bit mode */
 61:     #error "Petsc has not been tested with full 64-bit MUMPS and we choose to error out"
 62:   #endif
 63: #endif

 65: #define MPIU_MUMPSINT       MPI_INT
 66: #define PETSC_MUMPS_INT_MAX 2147483647
 67: #define PETSC_MUMPS_INT_MIN -2147483648

 69: /* Cast PetscInt to PetscMUMPSInt. Usually there is no overflow since <a> is row/col indices or some small integers*/
 70: static inline PetscErrorCode PetscMUMPSIntCast(PetscInt a, PetscMUMPSInt *b)
 71: {
 72:   PetscFunctionBegin;
 73: #if PetscDefined(USE_64BIT_INDICES)
 74:   PetscAssert(a <= PETSC_MUMPS_INT_MAX && a >= PETSC_MUMPS_INT_MIN, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "PetscInt too long for PetscMUMPSInt");
 75: #endif
 76:   *b = (PetscMUMPSInt)(a);
 77:   PetscFunctionReturn(PETSC_SUCCESS);
 78: }

 80: /* Put these utility routines here since they are only used in this file */
 81: static inline PetscErrorCode PetscOptionsMUMPSInt_Private(PetscOptionItems *PetscOptionsObject, const char opt[], const char text[], const char man[], PetscMUMPSInt currentvalue, PetscMUMPSInt *value, PetscBool *set, PetscMUMPSInt lb, PetscMUMPSInt ub)
 82: {
 83:   PetscInt  myval;
 84:   PetscBool myset;

 86:   PetscFunctionBegin;
 87:   /* PetscInt's size should be always >= PetscMUMPSInt's. It is safe to call PetscOptionsInt_Private to read a PetscMUMPSInt */
 88:   PetscCall(PetscOptionsInt_Private(PetscOptionsObject, opt, text, man, (PetscInt)currentvalue, &myval, &myset, lb, ub));
 89:   if (myset) PetscCall(PetscMUMPSIntCast(myval, value));
 90:   if (set) *set = myset;
 91:   PetscFunctionReturn(PETSC_SUCCESS);
 92: }
 93: #define PetscOptionsMUMPSInt(a, b, c, d, e, f) PetscOptionsMUMPSInt_Private(PetscOptionsObject, a, b, c, d, e, f, PETSC_MUMPS_INT_MIN, PETSC_MUMPS_INT_MAX)

 95: /* if using PETSc OpenMP support, we only call MUMPS on master ranks. Before/after the call, we change/restore CPUs the master ranks can run on */
 96: #if defined(PETSC_HAVE_OPENMP_SUPPORT)
 97:   #define PetscMUMPS_c(mumps) \
 98:     do { \
 99:       if (mumps->use_petsc_omp_support) { \
100:         if (mumps->is_omp_master) { \
101:           PetscCall(PetscOmpCtrlOmpRegionOnMasterBegin(mumps->omp_ctrl)); \
102:           PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF)); \
103:           PetscStackCallExternalVoid(PetscStringize(MUMPS_c), MUMPS_c(&mumps->id)); \
104:           PetscCall(PetscFPTrapPop()); \
105:           PetscCall(PetscOmpCtrlOmpRegionOnMasterEnd(mumps->omp_ctrl)); \
106:         } \
107:         PetscCall(PetscOmpCtrlBarrier(mumps->omp_ctrl)); \
108:         /* Global info is same on all processes so we Bcast it within omp_comm. Local info is specific      \
109:          to processes, so we only Bcast info[1], an error code and leave others (since they do not have   \
110:          an easy translation between omp_comm and petsc_comm). See MUMPS-5.1.2 manual p82.                   \
111:          omp_comm is a small shared memory communicator, hence doing multiple Bcast as shown below is OK. \
112:       */ \
113:         PetscCallMPI(MPI_Bcast(mumps->id.infog, PETSC_STATIC_ARRAY_LENGTH(mumps->id.infog), MPIU_MUMPSINT, 0, mumps->omp_comm)); \
114:         PetscCallMPI(MPI_Bcast(mumps->id.rinfog, PETSC_STATIC_ARRAY_LENGTH(mumps->id.rinfog), MPIU_REAL, 0, mumps->omp_comm)); \
115:         PetscCallMPI(MPI_Bcast(mumps->id.info, PETSC_STATIC_ARRAY_LENGTH(mumps->id.info), MPIU_MUMPSINT, 0, mumps->omp_comm)); \
116:         PetscCallMPI(MPI_Bcast(mumps->id.rinfo, PETSC_STATIC_ARRAY_LENGTH(mumps->id.rinfo), MPIU_REAL, 0, mumps->omp_comm)); \
117:       } else { \
118:         PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF)); \
119:         PetscStackCallExternalVoid(PetscStringize(MUMPS_c), MUMPS_c(&mumps->id)); \
120:         PetscCall(PetscFPTrapPop()); \
121:       } \
122:     } while (0)
123: #else
124:   #define PetscMUMPS_c(mumps) \
125:     do { \
126:       PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF)); \
127:       PetscStackCallExternalVoid(PetscStringize(MUMPS_c), MUMPS_c(&mumps->id)); \
128:       PetscCall(PetscFPTrapPop()); \
129:     } while (0)
130: #endif

132: /* declare MumpsScalar */
133: #if defined(PETSC_USE_COMPLEX)
134:   #if defined(PETSC_USE_REAL_SINGLE)
135:     #define MumpsScalar mumps_complex
136:   #else
137:     #define MumpsScalar mumps_double_complex
138:   #endif
139: #else
140:   #define MumpsScalar PetscScalar
141: #endif

143: /* macros s.t. indices match MUMPS documentation */
144: #define ICNTL(I)  icntl[(I) - 1]
145: #define CNTL(I)   cntl[(I) - 1]
146: #define INFOG(I)  infog[(I) - 1]
147: #define INFO(I)   info[(I) - 1]
148: #define RINFOG(I) rinfog[(I) - 1]
149: #define RINFO(I)  rinfo[(I) - 1]

151: typedef struct Mat_MUMPS Mat_MUMPS;
152: struct Mat_MUMPS {
153: #if defined(PETSC_USE_COMPLEX)
154:   #if defined(PETSC_USE_REAL_SINGLE)
155:   CMUMPS_STRUC_C id;
156:   #else
157:   ZMUMPS_STRUC_C id;
158:   #endif
159: #else
160:   #if defined(PETSC_USE_REAL_SINGLE)
161:   SMUMPS_STRUC_C id;
162:   #else
163:   DMUMPS_STRUC_C id;
164:   #endif
165: #endif

167:   MatStructure   matstruc;
168:   PetscMPIInt    myid, petsc_size;
169:   PetscMUMPSInt *irn, *jcn;       /* the (i,j,v) triplets passed to mumps. */
170:   PetscScalar   *val, *val_alloc; /* For some matrices, we can directly access their data array without a buffer. For others, we need a buffer. So comes val_alloc. */
171:   PetscInt64     nnz;             /* number of nonzeros. The type is called selective 64-bit in mumps */
172:   PetscMUMPSInt  sym;
173:   MPI_Comm       mumps_comm;
174:   PetscMUMPSInt *ICNTL_pre;
175:   PetscReal     *CNTL_pre;
176:   PetscMUMPSInt  ICNTL9_pre;         /* check if ICNTL(9) is changed from previous MatSolve */
177:   VecScatter     scat_rhs, scat_sol; /* used by MatSolve() */
178:   PetscMUMPSInt  ICNTL20;            /* use centralized (0) or distributed (10) dense RHS */
179:   PetscMUMPSInt  lrhs_loc, nloc_rhs, *irhs_loc;
180: #if defined(PETSC_HAVE_OPENMP_SUPPORT)
181:   PetscInt    *rhs_nrow, max_nrhs;
182:   PetscMPIInt *rhs_recvcounts, *rhs_disps;
183:   PetscScalar *rhs_loc, *rhs_recvbuf;
184: #endif
185:   Vec            b_seq, x_seq;
186:   PetscInt       ninfo, *info; /* which INFO to display */
187:   PetscInt       sizeredrhs;
188:   PetscScalar   *schur_sol;
189:   PetscInt       schur_sizesol;
190:   PetscMUMPSInt *ia_alloc, *ja_alloc; /* work arrays used for the CSR struct for sparse rhs */
191:   PetscInt64     cur_ilen, cur_jlen;  /* current len of ia_alloc[], ja_alloc[] */
192:   PetscErrorCode (*ConvertToTriples)(Mat, PetscInt, MatReuse, Mat_MUMPS *);

194:   /* Support for MATNEST */
195:   PetscErrorCode (**nest_convert_to_triples)(Mat, PetscInt, MatReuse, Mat_MUMPS *);
196:   PetscInt64  *nest_vals_start;
197:   PetscScalar *nest_vals;

199:   /* stuff used by petsc/mumps OpenMP support*/
200:   PetscBool    use_petsc_omp_support;
201:   PetscOmpCtrl omp_ctrl;             /* an OpenMP controller that blocked processes will release their CPU (MPI_Barrier does not have this guarantee) */
202:   MPI_Comm     petsc_comm, omp_comm; /* petsc_comm is petsc matrix's comm */
203:   PetscInt64  *recvcount;            /* a collection of nnz on omp_master */
204:   PetscMPIInt  tag, omp_comm_size;
205:   PetscBool    is_omp_master; /* is this rank the master of omp_comm */
206:   MPI_Request *reqs;
207: };

209: /* Cast a 1-based CSR represented by (nrow, ia, ja) of type PetscInt to a CSR of type PetscMUMPSInt.
210:    Here, nrow is number of rows, ia[] is row pointer and ja[] is column indices.
211:  */
212: static PetscErrorCode PetscMUMPSIntCSRCast(PETSC_UNUSED Mat_MUMPS *mumps, PetscInt nrow, PetscInt *ia, PetscInt *ja, PetscMUMPSInt **ia_mumps, PetscMUMPSInt **ja_mumps, PetscMUMPSInt *nnz_mumps)
213: {
214:   PetscInt nnz = ia[nrow] - 1; /* mumps uses 1-based indices. Uses PetscInt instead of PetscInt64 since mumps only uses PetscMUMPSInt for rhs */

216:   PetscFunctionBegin;
217: #if defined(PETSC_USE_64BIT_INDICES)
218:   {
219:     PetscInt i;
220:     if (nrow + 1 > mumps->cur_ilen) { /* realloc ia_alloc/ja_alloc to fit ia/ja */
221:       PetscCall(PetscFree(mumps->ia_alloc));
222:       PetscCall(PetscMalloc1(nrow + 1, &mumps->ia_alloc));
223:       mumps->cur_ilen = nrow + 1;
224:     }
225:     if (nnz > mumps->cur_jlen) {
226:       PetscCall(PetscFree(mumps->ja_alloc));
227:       PetscCall(PetscMalloc1(nnz, &mumps->ja_alloc));
228:       mumps->cur_jlen = nnz;
229:     }
230:     for (i = 0; i < nrow + 1; i++) PetscCall(PetscMUMPSIntCast(ia[i], &mumps->ia_alloc[i]));
231:     for (i = 0; i < nnz; i++) PetscCall(PetscMUMPSIntCast(ja[i], &mumps->ja_alloc[i]));
232:     *ia_mumps = mumps->ia_alloc;
233:     *ja_mumps = mumps->ja_alloc;
234:   }
235: #else
236:   *ia_mumps = ia;
237:   *ja_mumps = ja;
238: #endif
239:   PetscCall(PetscMUMPSIntCast(nnz, nnz_mumps));
240:   PetscFunctionReturn(PETSC_SUCCESS);
241: }

243: static PetscErrorCode MatMumpsResetSchur_Private(Mat_MUMPS *mumps)
244: {
245:   PetscFunctionBegin;
246:   PetscCall(PetscFree(mumps->id.listvar_schur));
247:   PetscCall(PetscFree(mumps->id.redrhs));
248:   PetscCall(PetscFree(mumps->schur_sol));
249:   mumps->id.size_schur = 0;
250:   mumps->id.schur_lld  = 0;
251:   mumps->id.ICNTL(19)  = 0;
252:   PetscFunctionReturn(PETSC_SUCCESS);
253: }

255: /* solve with rhs in mumps->id.redrhs and return in the same location */
256: static PetscErrorCode MatMumpsSolveSchur_Private(Mat F)
257: {
258:   Mat_MUMPS           *mumps = (Mat_MUMPS *)F->data;
259:   Mat                  S, B, X;
260:   MatFactorSchurStatus schurstatus;
261:   PetscInt             sizesol;

263:   PetscFunctionBegin;
264:   PetscCall(MatFactorFactorizeSchurComplement(F));
265:   PetscCall(MatFactorGetSchurComplement(F, &S, &schurstatus));
266:   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, mumps->id.size_schur, mumps->id.nrhs, (PetscScalar *)mumps->id.redrhs, &B));
267:   PetscCall(MatSetType(B, ((PetscObject)S)->type_name));
268: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
269:   PetscCall(MatBindToCPU(B, S->boundtocpu));
270: #endif
271:   switch (schurstatus) {
272:   case MAT_FACTOR_SCHUR_FACTORED:
273:     PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, mumps->id.size_schur, mumps->id.nrhs, (PetscScalar *)mumps->id.redrhs, &X));
274:     PetscCall(MatSetType(X, ((PetscObject)S)->type_name));
275: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
276:     PetscCall(MatBindToCPU(X, S->boundtocpu));
277: #endif
278:     if (!mumps->id.ICNTL(9)) { /* transpose solve */
279:       PetscCall(MatMatSolveTranspose(S, B, X));
280:     } else {
281:       PetscCall(MatMatSolve(S, B, X));
282:     }
283:     break;
284:   case MAT_FACTOR_SCHUR_INVERTED:
285:     sizesol = mumps->id.nrhs * mumps->id.size_schur;
286:     if (!mumps->schur_sol || sizesol > mumps->schur_sizesol) {
287:       PetscCall(PetscFree(mumps->schur_sol));
288:       PetscCall(PetscMalloc1(sizesol, &mumps->schur_sol));
289:       mumps->schur_sizesol = sizesol;
290:     }
291:     PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, mumps->id.size_schur, mumps->id.nrhs, mumps->schur_sol, &X));
292:     PetscCall(MatSetType(X, ((PetscObject)S)->type_name));
293: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
294:     PetscCall(MatBindToCPU(X, S->boundtocpu));
295: #endif
296:     PetscCall(MatProductCreateWithMat(S, B, NULL, X));
297:     if (!mumps->id.ICNTL(9)) { /* transpose solve */
298:       PetscCall(MatProductSetType(X, MATPRODUCT_AtB));
299:     } else {
300:       PetscCall(MatProductSetType(X, MATPRODUCT_AB));
301:     }
302:     PetscCall(MatProductSetFromOptions(X));
303:     PetscCall(MatProductSymbolic(X));
304:     PetscCall(MatProductNumeric(X));

306:     PetscCall(MatCopy(X, B, SAME_NONZERO_PATTERN));
307:     break;
308:   default:
309:     SETERRQ(PetscObjectComm((PetscObject)F), PETSC_ERR_SUP, "Unhandled MatFactorSchurStatus %d", F->schur_status);
310:   }
311:   PetscCall(MatFactorRestoreSchurComplement(F, &S, schurstatus));
312:   PetscCall(MatDestroy(&B));
313:   PetscCall(MatDestroy(&X));
314:   PetscFunctionReturn(PETSC_SUCCESS);
315: }

317: static PetscErrorCode MatMumpsHandleSchur_Private(Mat F, PetscBool expansion)
318: {
319:   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;

321:   PetscFunctionBegin;
322:   if (!mumps->id.ICNTL(19)) { /* do nothing when Schur complement has not been computed */
323:     PetscFunctionReturn(PETSC_SUCCESS);
324:   }
325:   if (!expansion) { /* prepare for the condensation step */
326:     PetscInt sizeredrhs = mumps->id.nrhs * mumps->id.size_schur;
327:     /* allocate MUMPS internal array to store reduced right-hand sides */
328:     if (!mumps->id.redrhs || sizeredrhs > mumps->sizeredrhs) {
329:       PetscCall(PetscFree(mumps->id.redrhs));
330:       mumps->id.lredrhs = mumps->id.size_schur;
331:       PetscCall(PetscMalloc1(mumps->id.nrhs * mumps->id.lredrhs, &mumps->id.redrhs));
332:       mumps->sizeredrhs = mumps->id.nrhs * mumps->id.lredrhs;
333:     }
334:   } else { /* prepare for the expansion step */
335:     /* solve Schur complement (this has to be done by the MUMPS user, so basically us) */
336:     PetscCall(MatMumpsSolveSchur_Private(F));
337:     mumps->id.ICNTL(26) = 2; /* expansion phase */
338:     PetscMUMPS_c(mumps);
339:     PetscCheck(mumps->id.INFOG(1) >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "MUMPS error in solve: INFOG(1)=%d " MUMPS_MANUALS, mumps->id.INFOG(1));
340:     /* restore defaults */
341:     mumps->id.ICNTL(26) = -1;
342:     /* free MUMPS internal array for redrhs if we have solved for multiple rhs in order to save memory space */
343:     if (mumps->id.nrhs > 1) {
344:       PetscCall(PetscFree(mumps->id.redrhs));
345:       mumps->id.lredrhs = 0;
346:       mumps->sizeredrhs = 0;
347:     }
348:   }
349:   PetscFunctionReturn(PETSC_SUCCESS);
350: }

352: /*
353:   MatConvertToTriples_A_B - convert Petsc matrix to triples: row[nz], col[nz], val[nz]

355:   input:
356:     A       - matrix in aij,baij or sbaij format
357:     shift   - 0: C style output triple; 1: Fortran style output triple.
358:     reuse   - MAT_INITIAL_MATRIX: spaces are allocated and values are set for the triple
359:               MAT_REUSE_MATRIX:   only the values in v array are updated
360:   output:
361:     nnz     - dim of r, c, and v (number of local nonzero entries of A)
362:     r, c, v - row and col index, matrix values (matrix triples)

364:   The returned values r, c, and sometimes v are obtained in a single PetscMalloc(). Then in MatDestroy_MUMPS() it is
365:   freed with PetscFree(mumps->irn);  This is not ideal code, the fact that v is ONLY sometimes part of mumps->irn means
366:   that the PetscMalloc() cannot easily be replaced with a PetscMalloc3().

368:  */

370: static PetscErrorCode MatConvertToTriples_seqaij_seqaij(Mat A, PetscInt shift, MatReuse reuse, Mat_MUMPS *mumps)
371: {
372:   const PetscScalar *av;
373:   const PetscInt    *ai, *aj, *ajj, M = A->rmap->n;
374:   PetscInt64         nz, rnz, i, j, k;
375:   PetscMUMPSInt     *row, *col;
376:   Mat_SeqAIJ        *aa = (Mat_SeqAIJ *)A->data;

378:   PetscFunctionBegin;
379:   PetscCall(MatSeqAIJGetArrayRead(A, &av));
380:   if (reuse == MAT_INITIAL_MATRIX) {
381:     nz = aa->nz;
382:     ai = aa->i;
383:     aj = aa->j;
384:     PetscCall(PetscMalloc2(nz, &row, nz, &col));
385:     for (i = k = 0; i < M; i++) {
386:       rnz = ai[i + 1] - ai[i];
387:       ajj = aj + ai[i];
388:       for (j = 0; j < rnz; j++) {
389:         PetscCall(PetscMUMPSIntCast(i + shift, &row[k]));
390:         PetscCall(PetscMUMPSIntCast(ajj[j] + shift, &col[k]));
391:         k++;
392:       }
393:     }
394:     mumps->val = (PetscScalar *)av;
395:     mumps->irn = row;
396:     mumps->jcn = col;
397:     mumps->nnz = nz;
398:   } else if (mumps->nest_vals) PetscCall(PetscArraycpy(mumps->val, av, aa->nz)); /* MatConvertToTriples_nest_xaij() allocates mumps->val outside of MatConvertToTriples_seqaij_seqaij(), so one needs to copy the memory */
399:   else mumps->val = (PetscScalar *)av;                                           /* in the default case, mumps->val is never allocated, one just needs to update the mumps->val pointer */
400:   PetscCall(MatSeqAIJRestoreArrayRead(A, &av));
401:   PetscFunctionReturn(PETSC_SUCCESS);
402: }

404: static PetscErrorCode MatConvertToTriples_seqsell_seqaij(Mat A, PetscInt shift, MatReuse reuse, Mat_MUMPS *mumps)
405: {
406:   PetscInt64     nz, i, j, k, r;
407:   Mat_SeqSELL   *a = (Mat_SeqSELL *)A->data;
408:   PetscMUMPSInt *row, *col;

410:   PetscFunctionBegin;
411:   nz = a->sliidx[a->totalslices];
412:   if (reuse == MAT_INITIAL_MATRIX) {
413:     PetscCall(PetscMalloc2(nz, &row, nz, &col));
414:     for (i = k = 0; i < a->totalslices; i++) {
415:       for (j = a->sliidx[i], r = 0; j < a->sliidx[i + 1]; j++, r = ((r + 1) & 0x07)) PetscCall(PetscMUMPSIntCast(8 * i + r + shift, &row[k++]));
416:     }
417:     for (i = 0; i < nz; i++) PetscCall(PetscMUMPSIntCast(a->colidx[i] + shift, &col[i]));
418:     mumps->irn = row;
419:     mumps->jcn = col;
420:     mumps->nnz = nz;
421:     mumps->val = a->val;
422:   } else if (mumps->nest_vals) PetscCall(PetscArraycpy(mumps->val, a->val, nz)); /* MatConvertToTriples_nest_xaij() allocates mumps->val outside of MatConvertToTriples_seqsell_seqaij(), so one needs to copy the memory */
423:   else mumps->val = a->val;                                                      /* in the default case, mumps->val is never allocated, one just needs to update the mumps->val pointer */
424:   PetscFunctionReturn(PETSC_SUCCESS);
425: }

427: static PetscErrorCode MatConvertToTriples_seqbaij_seqaij(Mat A, PetscInt shift, MatReuse reuse, Mat_MUMPS *mumps)
428: {
429:   Mat_SeqBAIJ    *aa = (Mat_SeqBAIJ *)A->data;
430:   const PetscInt *ai, *aj, *ajj, bs2 = aa->bs2;
431:   PetscInt64      M, nz = bs2 * aa->nz, idx = 0, rnz, i, j, k, m;
432:   PetscInt        bs;
433:   PetscMUMPSInt  *row, *col;

435:   PetscFunctionBegin;
436:   if (reuse == MAT_INITIAL_MATRIX) {
437:     PetscCall(MatGetBlockSize(A, &bs));
438:     M  = A->rmap->N / bs;
439:     ai = aa->i;
440:     aj = aa->j;
441:     PetscCall(PetscMalloc2(nz, &row, nz, &col));
442:     for (i = 0; i < M; i++) {
443:       ajj = aj + ai[i];
444:       rnz = ai[i + 1] - ai[i];
445:       for (k = 0; k < rnz; k++) {
446:         for (j = 0; j < bs; j++) {
447:           for (m = 0; m < bs; m++) {
448:             PetscCall(PetscMUMPSIntCast(i * bs + m + shift, &row[idx]));
449:             PetscCall(PetscMUMPSIntCast(bs * ajj[k] + j + shift, &col[idx]));
450:             idx++;
451:           }
452:         }
453:       }
454:     }
455:     mumps->irn = row;
456:     mumps->jcn = col;
457:     mumps->nnz = nz;
458:     mumps->val = aa->a;
459:   } else if (mumps->nest_vals) PetscCall(PetscArraycpy(mumps->val, aa->a, nz)); /* MatConvertToTriples_nest_xaij() allocates mumps->val outside of MatConvertToTriples_seqbaij_seqaij(), so one needs to copy the memory */
460:   else mumps->val = aa->a;                                                      /* in the default case, mumps->val is never allocated, one just needs to update the mumps->val pointer */
461:   PetscFunctionReturn(PETSC_SUCCESS);
462: }

464: static PetscErrorCode MatConvertToTriples_seqsbaij_seqsbaij(Mat A, PetscInt shift, MatReuse reuse, Mat_MUMPS *mumps)
465: {
466:   const PetscInt *ai, *aj, *ajj;
467:   PetscInt        bs;
468:   PetscInt64      nz, rnz, i, j, k, m;
469:   PetscMUMPSInt  *row, *col;
470:   PetscScalar    *val;
471:   Mat_SeqSBAIJ   *aa  = (Mat_SeqSBAIJ *)A->data;
472:   const PetscInt  bs2 = aa->bs2, mbs = aa->mbs;
473: #if defined(PETSC_USE_COMPLEX)
474:   PetscBool isset, hermitian;
475: #endif

477:   PetscFunctionBegin;
478: #if defined(PETSC_USE_COMPLEX)
479:   PetscCall(MatIsHermitianKnown(A, &isset, &hermitian));
480:   PetscCheck(!isset || !hermitian, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "MUMPS does not support Hermitian symmetric matrices for Choleksy");
481: #endif
482:   ai = aa->i;
483:   aj = aa->j;
484:   PetscCall(MatGetBlockSize(A, &bs));
485:   if (reuse == MAT_INITIAL_MATRIX) {
486:     const PetscInt64 alloc_size = aa->nz * bs2;

488:     PetscCall(PetscMalloc2(alloc_size, &row, alloc_size, &col));
489:     if (bs > 1) {
490:       PetscCall(PetscMalloc1(alloc_size, &mumps->val_alloc));
491:       mumps->val = mumps->val_alloc;
492:     } else {
493:       mumps->val = aa->a;
494:     }
495:     mumps->irn = row;
496:     mumps->jcn = col;
497:   } else {
498:     row = mumps->irn;
499:     col = mumps->jcn;
500:   }
501:   val = mumps->val;

503:   nz = 0;
504:   if (bs > 1) {
505:     for (i = 0; i < mbs; i++) {
506:       rnz = ai[i + 1] - ai[i];
507:       ajj = aj + ai[i];
508:       for (j = 0; j < rnz; j++) {
509:         for (k = 0; k < bs; k++) {
510:           for (m = 0; m < bs; m++) {
511:             if (ajj[j] > i || k >= m) {
512:               if (reuse == MAT_INITIAL_MATRIX) {
513:                 PetscCall(PetscMUMPSIntCast(i * bs + m + shift, &row[nz]));
514:                 PetscCall(PetscMUMPSIntCast(ajj[j] * bs + k + shift, &col[nz]));
515:               }
516:               val[nz++] = aa->a[(ai[i] + j) * bs2 + m + k * bs];
517:             }
518:           }
519:         }
520:       }
521:     }
522:   } else if (reuse == MAT_INITIAL_MATRIX) {
523:     for (i = 0; i < mbs; i++) {
524:       rnz = ai[i + 1] - ai[i];
525:       ajj = aj + ai[i];
526:       for (j = 0; j < rnz; j++) {
527:         PetscCall(PetscMUMPSIntCast(i + shift, &row[nz]));
528:         PetscCall(PetscMUMPSIntCast(ajj[j] + shift, &col[nz]));
529:         nz++;
530:       }
531:     }
532:     PetscCheck(nz == aa->nz, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Different numbers of nonzeros %" PetscInt64_FMT " != %" PetscInt_FMT, nz, aa->nz);
533:   } else if (mumps->nest_vals)
534:     PetscCall(PetscArraycpy(mumps->val, aa->a, aa->nz)); /* bs == 1 and MAT_REUSE_MATRIX, MatConvertToTriples_nest_xaij() allocates mumps->val outside of MatConvertToTriples_seqsbaij_seqsbaij(), so one needs to copy the memory */
535:   else mumps->val = aa->a;                               /* in the default case, mumps->val is never allocated, one just needs to update the mumps->val pointer */
536:   if (reuse == MAT_INITIAL_MATRIX) mumps->nnz = nz;
537:   PetscFunctionReturn(PETSC_SUCCESS);
538: }

540: static PetscErrorCode MatConvertToTriples_seqaij_seqsbaij(Mat A, PetscInt shift, MatReuse reuse, Mat_MUMPS *mumps)
541: {
542:   const PetscInt    *ai, *aj, *ajj, *adiag, M = A->rmap->n;
543:   PetscInt64         nz, rnz, i, j;
544:   const PetscScalar *av, *v1;
545:   PetscScalar       *val;
546:   PetscMUMPSInt     *row, *col;
547:   Mat_SeqAIJ        *aa = (Mat_SeqAIJ *)A->data;
548:   PetscBool          missing;
549: #if defined(PETSC_USE_COMPLEX)
550:   PetscBool hermitian, isset;
551: #endif

553:   PetscFunctionBegin;
554: #if defined(PETSC_USE_COMPLEX)
555:   PetscCall(MatIsHermitianKnown(A, &isset, &hermitian));
556:   PetscCheck(!isset || !hermitian, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "MUMPS does not support Hermitian symmetric matrices for Choleksy");
557: #endif
558:   PetscCall(MatSeqAIJGetArrayRead(A, &av));
559:   ai    = aa->i;
560:   aj    = aa->j;
561:   adiag = aa->diag;
562:   PetscCall(MatMissingDiagonal_SeqAIJ(A, &missing, NULL));
563:   if (reuse == MAT_INITIAL_MATRIX) {
564:     /* count nz in the upper triangular part of A */
565:     nz = 0;
566:     if (missing) {
567:       for (i = 0; i < M; i++) {
568:         if (PetscUnlikely(adiag[i] >= ai[i + 1])) {
569:           for (j = ai[i]; j < ai[i + 1]; j++) {
570:             if (aj[j] < i) continue;
571:             nz++;
572:           }
573:         } else {
574:           nz += ai[i + 1] - adiag[i];
575:         }
576:       }
577:     } else {
578:       for (i = 0; i < M; i++) nz += ai[i + 1] - adiag[i];
579:     }
580:     PetscCall(PetscMalloc2(nz, &row, nz, &col));
581:     PetscCall(PetscMalloc1(nz, &val));
582:     mumps->nnz = nz;
583:     mumps->irn = row;
584:     mumps->jcn = col;
585:     mumps->val = mumps->val_alloc = val;

587:     nz = 0;
588:     if (missing) {
589:       for (i = 0; i < M; i++) {
590:         if (PetscUnlikely(adiag[i] >= ai[i + 1])) {
591:           for (j = ai[i]; j < ai[i + 1]; j++) {
592:             if (aj[j] < i) continue;
593:             PetscCall(PetscMUMPSIntCast(i + shift, &row[nz]));
594:             PetscCall(PetscMUMPSIntCast(aj[j] + shift, &col[nz]));
595:             val[nz] = av[j];
596:             nz++;
597:           }
598:         } else {
599:           rnz = ai[i + 1] - adiag[i];
600:           ajj = aj + adiag[i];
601:           v1  = av + adiag[i];
602:           for (j = 0; j < rnz; j++) {
603:             PetscCall(PetscMUMPSIntCast(i + shift, &row[nz]));
604:             PetscCall(PetscMUMPSIntCast(ajj[j] + shift, &col[nz]));
605:             val[nz++] = v1[j];
606:           }
607:         }
608:       }
609:     } else {
610:       for (i = 0; i < M; i++) {
611:         rnz = ai[i + 1] - adiag[i];
612:         ajj = aj + adiag[i];
613:         v1  = av + adiag[i];
614:         for (j = 0; j < rnz; j++) {
615:           PetscCall(PetscMUMPSIntCast(i + shift, &row[nz]));
616:           PetscCall(PetscMUMPSIntCast(ajj[j] + shift, &col[nz]));
617:           val[nz++] = v1[j];
618:         }
619:       }
620:     }
621:   } else {
622:     nz  = 0;
623:     val = mumps->val;
624:     if (missing) {
625:       for (i = 0; i < M; i++) {
626:         if (PetscUnlikely(adiag[i] >= ai[i + 1])) {
627:           for (j = ai[i]; j < ai[i + 1]; j++) {
628:             if (aj[j] < i) continue;
629:             val[nz++] = av[j];
630:           }
631:         } else {
632:           rnz = ai[i + 1] - adiag[i];
633:           v1  = av + adiag[i];
634:           for (j = 0; j < rnz; j++) val[nz++] = v1[j];
635:         }
636:       }
637:     } else {
638:       for (i = 0; i < M; i++) {
639:         rnz = ai[i + 1] - adiag[i];
640:         v1  = av + adiag[i];
641:         for (j = 0; j < rnz; j++) val[nz++] = v1[j];
642:       }
643:     }
644:   }
645:   PetscCall(MatSeqAIJRestoreArrayRead(A, &av));
646:   PetscFunctionReturn(PETSC_SUCCESS);
647: }

649: static PetscErrorCode MatConvertToTriples_mpisbaij_mpisbaij(Mat A, PetscInt shift, MatReuse reuse, Mat_MUMPS *mumps)
650: {
651:   const PetscInt    *ai, *aj, *bi, *bj, *garray, *ajj, *bjj;
652:   PetscInt           bs;
653:   PetscInt64         rstart, nz, i, j, k, m, jj, irow, countA, countB;
654:   PetscMUMPSInt     *row, *col;
655:   const PetscScalar *av, *bv, *v1, *v2;
656:   PetscScalar       *val;
657:   Mat_MPISBAIJ      *mat = (Mat_MPISBAIJ *)A->data;
658:   Mat_SeqSBAIJ      *aa  = (Mat_SeqSBAIJ *)mat->A->data;
659:   Mat_SeqBAIJ       *bb  = (Mat_SeqBAIJ *)mat->B->data;
660:   const PetscInt     bs2 = aa->bs2, mbs = aa->mbs;
661: #if defined(PETSC_USE_COMPLEX)
662:   PetscBool hermitian, isset;
663: #endif

665:   PetscFunctionBegin;
666: #if defined(PETSC_USE_COMPLEX)
667:   PetscCall(MatIsHermitianKnown(A, &isset, &hermitian));
668:   PetscCheck(!isset || !hermitian, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "MUMPS does not support Hermitian symmetric matrices for Choleksy");
669: #endif
670:   PetscCall(MatGetBlockSize(A, &bs));
671:   rstart = A->rmap->rstart;
672:   ai     = aa->i;
673:   aj     = aa->j;
674:   bi     = bb->i;
675:   bj     = bb->j;
676:   av     = aa->a;
677:   bv     = bb->a;

679:   garray = mat->garray;

681:   if (reuse == MAT_INITIAL_MATRIX) {
682:     nz = (aa->nz + bb->nz) * bs2; /* just a conservative estimate */
683:     PetscCall(PetscMalloc2(nz, &row, nz, &col));
684:     PetscCall(PetscMalloc1(nz, &val));
685:     /* can not decide the exact mumps->nnz now because of the SBAIJ */
686:     mumps->irn = row;
687:     mumps->jcn = col;
688:     mumps->val = mumps->val_alloc = val;
689:   } else {
690:     val = mumps->val;
691:   }

693:   jj   = 0;
694:   irow = rstart;
695:   for (i = 0; i < mbs; i++) {
696:     ajj    = aj + ai[i]; /* ptr to the beginning of this row */
697:     countA = ai[i + 1] - ai[i];
698:     countB = bi[i + 1] - bi[i];
699:     bjj    = bj + bi[i];
700:     v1     = av + ai[i] * bs2;
701:     v2     = bv + bi[i] * bs2;

703:     if (bs > 1) {
704:       /* A-part */
705:       for (j = 0; j < countA; j++) {
706:         for (k = 0; k < bs; k++) {
707:           for (m = 0; m < bs; m++) {
708:             if (rstart + ajj[j] * bs > irow || k >= m) {
709:               if (reuse == MAT_INITIAL_MATRIX) {
710:                 PetscCall(PetscMUMPSIntCast(irow + m + shift, &row[jj]));
711:                 PetscCall(PetscMUMPSIntCast(rstart + ajj[j] * bs + k + shift, &col[jj]));
712:               }
713:               val[jj++] = v1[j * bs2 + m + k * bs];
714:             }
715:           }
716:         }
717:       }

719:       /* B-part */
720:       for (j = 0; j < countB; j++) {
721:         for (k = 0; k < bs; k++) {
722:           for (m = 0; m < bs; m++) {
723:             if (reuse == MAT_INITIAL_MATRIX) {
724:               PetscCall(PetscMUMPSIntCast(irow + m + shift, &row[jj]));
725:               PetscCall(PetscMUMPSIntCast(garray[bjj[j]] * bs + k + shift, &col[jj]));
726:             }
727:             val[jj++] = v2[j * bs2 + m + k * bs];
728:           }
729:         }
730:       }
731:     } else {
732:       /* A-part */
733:       for (j = 0; j < countA; j++) {
734:         if (reuse == MAT_INITIAL_MATRIX) {
735:           PetscCall(PetscMUMPSIntCast(irow + shift, &row[jj]));
736:           PetscCall(PetscMUMPSIntCast(rstart + ajj[j] + shift, &col[jj]));
737:         }
738:         val[jj++] = v1[j];
739:       }

741:       /* B-part */
742:       for (j = 0; j < countB; j++) {
743:         if (reuse == MAT_INITIAL_MATRIX) {
744:           PetscCall(PetscMUMPSIntCast(irow + shift, &row[jj]));
745:           PetscCall(PetscMUMPSIntCast(garray[bjj[j]] + shift, &col[jj]));
746:         }
747:         val[jj++] = v2[j];
748:       }
749:     }
750:     irow += bs;
751:   }
752:   if (reuse == MAT_INITIAL_MATRIX) mumps->nnz = jj;
753:   PetscFunctionReturn(PETSC_SUCCESS);
754: }

756: static PetscErrorCode MatConvertToTriples_mpiaij_mpiaij(Mat A, PetscInt shift, MatReuse reuse, Mat_MUMPS *mumps)
757: {
758:   const PetscInt    *ai, *aj, *bi, *bj, *garray, m = A->rmap->n, *ajj, *bjj;
759:   PetscInt64         rstart, cstart, nz, i, j, jj, irow, countA, countB;
760:   PetscMUMPSInt     *row, *col;
761:   const PetscScalar *av, *bv, *v1, *v2;
762:   PetscScalar       *val;
763:   Mat                Ad, Ao;
764:   Mat_SeqAIJ        *aa;
765:   Mat_SeqAIJ        *bb;

767:   PetscFunctionBegin;
768:   PetscCall(MatMPIAIJGetSeqAIJ(A, &Ad, &Ao, &garray));
769:   PetscCall(MatSeqAIJGetArrayRead(Ad, &av));
770:   PetscCall(MatSeqAIJGetArrayRead(Ao, &bv));

772:   aa = (Mat_SeqAIJ *)(Ad)->data;
773:   bb = (Mat_SeqAIJ *)(Ao)->data;
774:   ai = aa->i;
775:   aj = aa->j;
776:   bi = bb->i;
777:   bj = bb->j;

779:   rstart = A->rmap->rstart;
780:   cstart = A->cmap->rstart;

782:   if (reuse == MAT_INITIAL_MATRIX) {
783:     nz = (PetscInt64)aa->nz + bb->nz; /* make sure the sum won't overflow PetscInt */
784:     PetscCall(PetscMalloc2(nz, &row, nz, &col));
785:     PetscCall(PetscMalloc1(nz, &val));
786:     mumps->nnz = nz;
787:     mumps->irn = row;
788:     mumps->jcn = col;
789:     mumps->val = mumps->val_alloc = val;
790:   } else {
791:     val = mumps->val;
792:   }

794:   jj   = 0;
795:   irow = rstart;
796:   for (i = 0; i < m; i++) {
797:     ajj    = aj + ai[i]; /* ptr to the beginning of this row */
798:     countA = ai[i + 1] - ai[i];
799:     countB = bi[i + 1] - bi[i];
800:     bjj    = bj + bi[i];
801:     v1     = av + ai[i];
802:     v2     = bv + bi[i];

804:     /* A-part */
805:     for (j = 0; j < countA; j++) {
806:       if (reuse == MAT_INITIAL_MATRIX) {
807:         PetscCall(PetscMUMPSIntCast(irow + shift, &row[jj]));
808:         PetscCall(PetscMUMPSIntCast(cstart + ajj[j] + shift, &col[jj]));
809:       }
810:       val[jj++] = v1[j];
811:     }

813:     /* B-part */
814:     for (j = 0; j < countB; j++) {
815:       if (reuse == MAT_INITIAL_MATRIX) {
816:         PetscCall(PetscMUMPSIntCast(irow + shift, &row[jj]));
817:         PetscCall(PetscMUMPSIntCast(garray[bjj[j]] + shift, &col[jj]));
818:       }
819:       val[jj++] = v2[j];
820:     }
821:     irow++;
822:   }
823:   PetscCall(MatSeqAIJRestoreArrayRead(Ad, &av));
824:   PetscCall(MatSeqAIJRestoreArrayRead(Ao, &bv));
825:   PetscFunctionReturn(PETSC_SUCCESS);
826: }

828: static PetscErrorCode MatConvertToTriples_mpibaij_mpiaij(Mat A, PetscInt shift, MatReuse reuse, Mat_MUMPS *mumps)
829: {
830:   Mat_MPIBAIJ       *mat = (Mat_MPIBAIJ *)A->data;
831:   Mat_SeqBAIJ       *aa  = (Mat_SeqBAIJ *)mat->A->data;
832:   Mat_SeqBAIJ       *bb  = (Mat_SeqBAIJ *)mat->B->data;
833:   const PetscInt    *ai = aa->i, *bi = bb->i, *aj = aa->j, *bj = bb->j, *ajj, *bjj;
834:   const PetscInt    *garray = mat->garray, mbs = mat->mbs, rstart = A->rmap->rstart, cstart = A->cmap->rstart;
835:   const PetscInt     bs2 = mat->bs2;
836:   PetscInt           bs;
837:   PetscInt64         nz, i, j, k, n, jj, irow, countA, countB, idx;
838:   PetscMUMPSInt     *row, *col;
839:   const PetscScalar *av = aa->a, *bv = bb->a, *v1, *v2;
840:   PetscScalar       *val;

842:   PetscFunctionBegin;
843:   PetscCall(MatGetBlockSize(A, &bs));
844:   if (reuse == MAT_INITIAL_MATRIX) {
845:     nz = bs2 * (aa->nz + bb->nz);
846:     PetscCall(PetscMalloc2(nz, &row, nz, &col));
847:     PetscCall(PetscMalloc1(nz, &val));
848:     mumps->nnz = nz;
849:     mumps->irn = row;
850:     mumps->jcn = col;
851:     mumps->val = mumps->val_alloc = val;
852:   } else {
853:     val = mumps->val;
854:   }

856:   jj   = 0;
857:   irow = rstart;
858:   for (i = 0; i < mbs; i++) {
859:     countA = ai[i + 1] - ai[i];
860:     countB = bi[i + 1] - bi[i];
861:     ajj    = aj + ai[i];
862:     bjj    = bj + bi[i];
863:     v1     = av + bs2 * ai[i];
864:     v2     = bv + bs2 * bi[i];

866:     idx = 0;
867:     /* A-part */
868:     for (k = 0; k < countA; k++) {
869:       for (j = 0; j < bs; j++) {
870:         for (n = 0; n < bs; n++) {
871:           if (reuse == MAT_INITIAL_MATRIX) {
872:             PetscCall(PetscMUMPSIntCast(irow + n + shift, &row[jj]));
873:             PetscCall(PetscMUMPSIntCast(cstart + bs * ajj[k] + j + shift, &col[jj]));
874:           }
875:           val[jj++] = v1[idx++];
876:         }
877:       }
878:     }

880:     idx = 0;
881:     /* B-part */
882:     for (k = 0; k < countB; k++) {
883:       for (j = 0; j < bs; j++) {
884:         for (n = 0; n < bs; n++) {
885:           if (reuse == MAT_INITIAL_MATRIX) {
886:             PetscCall(PetscMUMPSIntCast(irow + n + shift, &row[jj]));
887:             PetscCall(PetscMUMPSIntCast(bs * garray[bjj[k]] + j + shift, &col[jj]));
888:           }
889:           val[jj++] = v2[idx++];
890:         }
891:       }
892:     }
893:     irow += bs;
894:   }
895:   PetscFunctionReturn(PETSC_SUCCESS);
896: }

898: static PetscErrorCode MatConvertToTriples_mpiaij_mpisbaij(Mat A, PetscInt shift, MatReuse reuse, Mat_MUMPS *mumps)
899: {
900:   const PetscInt    *ai, *aj, *adiag, *bi, *bj, *garray, m = A->rmap->n, *ajj, *bjj;
901:   PetscInt64         rstart, nz, nza, nzb, i, j, jj, irow, countA, countB;
902:   PetscMUMPSInt     *row, *col;
903:   const PetscScalar *av, *bv, *v1, *v2;
904:   PetscScalar       *val;
905:   Mat                Ad, Ao;
906:   Mat_SeqAIJ        *aa;
907:   Mat_SeqAIJ        *bb;
908: #if defined(PETSC_USE_COMPLEX)
909:   PetscBool hermitian, isset;
910: #endif

912:   PetscFunctionBegin;
913: #if defined(PETSC_USE_COMPLEX)
914:   PetscCall(MatIsHermitianKnown(A, &isset, &hermitian));
915:   PetscCheck(!isset || !hermitian, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "MUMPS does not support Hermitian symmetric matrices for Choleksy");
916: #endif
917:   PetscCall(MatMPIAIJGetSeqAIJ(A, &Ad, &Ao, &garray));
918:   PetscCall(MatSeqAIJGetArrayRead(Ad, &av));
919:   PetscCall(MatSeqAIJGetArrayRead(Ao, &bv));

921:   aa    = (Mat_SeqAIJ *)(Ad)->data;
922:   bb    = (Mat_SeqAIJ *)(Ao)->data;
923:   ai    = aa->i;
924:   aj    = aa->j;
925:   adiag = aa->diag;
926:   bi    = bb->i;
927:   bj    = bb->j;

929:   rstart = A->rmap->rstart;

931:   if (reuse == MAT_INITIAL_MATRIX) {
932:     nza = 0; /* num of upper triangular entries in mat->A, including diagonals */
933:     nzb = 0; /* num of upper triangular entries in mat->B */
934:     for (i = 0; i < m; i++) {
935:       nza += (ai[i + 1] - adiag[i]);
936:       countB = bi[i + 1] - bi[i];
937:       bjj    = bj + bi[i];
938:       for (j = 0; j < countB; j++) {
939:         if (garray[bjj[j]] > rstart) nzb++;
940:       }
941:     }

943:     nz = nza + nzb; /* total nz of upper triangular part of mat */
944:     PetscCall(PetscMalloc2(nz, &row, nz, &col));
945:     PetscCall(PetscMalloc1(nz, &val));
946:     mumps->nnz = nz;
947:     mumps->irn = row;
948:     mumps->jcn = col;
949:     mumps->val = mumps->val_alloc = val;
950:   } else {
951:     val = mumps->val;
952:   }

954:   jj   = 0;
955:   irow = rstart;
956:   for (i = 0; i < m; i++) {
957:     ajj    = aj + adiag[i]; /* ptr to the beginning of the diagonal of this row */
958:     v1     = av + adiag[i];
959:     countA = ai[i + 1] - adiag[i];
960:     countB = bi[i + 1] - bi[i];
961:     bjj    = bj + bi[i];
962:     v2     = bv + bi[i];

964:     /* A-part */
965:     for (j = 0; j < countA; j++) {
966:       if (reuse == MAT_INITIAL_MATRIX) {
967:         PetscCall(PetscMUMPSIntCast(irow + shift, &row[jj]));
968:         PetscCall(PetscMUMPSIntCast(rstart + ajj[j] + shift, &col[jj]));
969:       }
970:       val[jj++] = v1[j];
971:     }

973:     /* B-part */
974:     for (j = 0; j < countB; j++) {
975:       if (garray[bjj[j]] > rstart) {
976:         if (reuse == MAT_INITIAL_MATRIX) {
977:           PetscCall(PetscMUMPSIntCast(irow + shift, &row[jj]));
978:           PetscCall(PetscMUMPSIntCast(garray[bjj[j]] + shift, &col[jj]));
979:         }
980:         val[jj++] = v2[j];
981:       }
982:     }
983:     irow++;
984:   }
985:   PetscCall(MatSeqAIJRestoreArrayRead(Ad, &av));
986:   PetscCall(MatSeqAIJRestoreArrayRead(Ao, &bv));
987:   PetscFunctionReturn(PETSC_SUCCESS);
988: }

990: static PetscErrorCode MatConvertToTriples_diagonal_xaij(Mat A, PETSC_UNUSED PetscInt shift, MatReuse reuse, Mat_MUMPS *mumps)
991: {
992:   const PetscScalar *av;
993:   const PetscInt     M = A->rmap->n;
994:   PetscInt64         i;
995:   PetscMUMPSInt     *row, *col;
996:   Vec                v;

998:   PetscFunctionBegin;
999:   PetscCall(MatDiagonalGetDiagonal(A, &v));
1000:   PetscCall(VecGetArrayRead(v, &av));
1001:   if (reuse == MAT_INITIAL_MATRIX) {
1002:     PetscCall(PetscMalloc2(M, &row, M, &col));
1003:     for (i = 0; i < M; i++) {
1004:       PetscCall(PetscMUMPSIntCast(i + A->rmap->rstart, &row[i]));
1005:       col[i] = row[i];
1006:     }
1007:     mumps->val = (PetscScalar *)av;
1008:     mumps->irn = row;
1009:     mumps->jcn = col;
1010:     mumps->nnz = M;
1011:   } else if (mumps->nest_vals) PetscCall(PetscArraycpy(mumps->val, av, M)); /* MatConvertToTriples_nest_xaij() allocates mumps->val outside of MatConvertToTriples_diagonal_xaij(), so one needs to copy the memory */
1012:   else mumps->val = (PetscScalar *)av;                                      /* in the default case, mumps->val is never allocated, one just needs to update the mumps->val pointer */
1013:   PetscCall(VecRestoreArrayRead(v, &av));
1014:   PetscFunctionReturn(PETSC_SUCCESS);
1015: }

1017: static PetscErrorCode MatConvertToTriples_dense_xaij(Mat A, PETSC_UNUSED PetscInt shift, MatReuse reuse, Mat_MUMPS *mumps)
1018: {
1019:   PetscScalar   *v;
1020:   const PetscInt m = A->rmap->n, N = A->cmap->N;
1021:   PetscInt       lda;
1022:   PetscInt64     i, j;
1023:   PetscMUMPSInt *row, *col;

1025:   PetscFunctionBegin;
1026:   PetscCall(MatDenseGetArray(A, &v));
1027:   PetscCall(MatDenseGetLDA(A, &lda));
1028:   if (reuse == MAT_INITIAL_MATRIX) {
1029:     PetscCall(PetscMalloc2(m * N, &row, m * N, &col));
1030:     for (i = 0; i < m; i++) {
1031:       col[i] = 0;
1032:       PetscCall(PetscMUMPSIntCast(i + A->rmap->rstart, &row[i]));
1033:     }
1034:     for (j = 1; j < N; j++) {
1035:       for (i = 0; i < m; i++) PetscCall(PetscMUMPSIntCast(j, col + i + m * j));
1036:       PetscCall(PetscArraycpy(row + m * j, row + m * (j - 1), m));
1037:     }
1038:     if (lda == m) mumps->val = v;
1039:     else {
1040:       PetscCall(PetscMalloc1(m * N, &mumps->val));
1041:       mumps->val_alloc = mumps->val;
1042:       for (j = 0; j < N; j++) PetscCall(PetscArraycpy(mumps->val + m * j, v + lda * j, m));
1043:     }
1044:     mumps->irn = row;
1045:     mumps->jcn = col;
1046:     mumps->nnz = m * N;
1047:   } else {
1048:     if (lda == m && !mumps->nest_vals) mumps->val = v;
1049:     else {
1050:       for (j = 0; j < N; j++) PetscCall(PetscArraycpy(mumps->val + m * j, v + lda * j, m));
1051:     }
1052:   }
1053:   PetscCall(MatDenseRestoreArray(A, &v));
1054:   PetscFunctionReturn(PETSC_SUCCESS);
1055: }

1057: static PetscErrorCode MatConvertToTriples_nest_xaij(Mat A, PetscInt shift, MatReuse reuse, Mat_MUMPS *mumps)
1058: {
1059:   Mat     **mats;
1060:   PetscInt  nr, nc;
1061:   PetscBool chol = mumps->sym ? PETSC_TRUE : PETSC_FALSE;

1063:   PetscFunctionBegin;
1064:   PetscCall(MatNestGetSubMats(A, &nr, &nc, &mats));
1065:   if (reuse == MAT_INITIAL_MATRIX) {
1066:     PetscMUMPSInt *irns, *jcns;
1067:     PetscScalar   *vals;
1068:     PetscInt64     totnnz, cumnnz, maxnnz;
1069:     PetscInt      *pjcns_w;
1070:     IS            *rows, *cols;
1071:     PetscInt     **rows_idx, **cols_idx;

1073:     cumnnz = 0;
1074:     maxnnz = 0;
1075:     PetscCall(PetscMalloc2(nr * nc + 1, &mumps->nest_vals_start, nr * nc, &mumps->nest_convert_to_triples));
1076:     for (PetscInt r = 0; r < nr; r++) {
1077:       for (PetscInt c = 0; c < nc; c++) {
1078:         Mat sub = mats[r][c];

1080:         mumps->nest_convert_to_triples[r * nc + c] = NULL;
1081:         if (chol && c < r) continue; /* skip lower-triangular block for Cholesky */
1082:         if (sub) {
1083:           PetscErrorCode (*convert_to_triples)(Mat, PetscInt, MatReuse, Mat_MUMPS *) = NULL;
1084:           PetscBool isSeqAIJ, isMPIAIJ, isSeqBAIJ, isMPIBAIJ, isSeqSBAIJ, isMPISBAIJ, isTrans, isHTrans = PETSC_FALSE, isDiag, isDense;
1085:           MatInfo   info;

1087:           PetscCall(PetscObjectTypeCompare((PetscObject)sub, MATTRANSPOSEVIRTUAL, &isTrans));
1088:           if (isTrans) PetscCall(MatTransposeGetMat(sub, &sub));
1089:           else {
1090:             PetscCall(PetscObjectTypeCompare((PetscObject)sub, MATHERMITIANTRANSPOSEVIRTUAL, &isHTrans));
1091:             if (isHTrans) PetscCall(MatHermitianTransposeGetMat(sub, &sub));
1092:           }
1093:           PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATSEQAIJ, &isSeqAIJ));
1094:           PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATMPIAIJ, &isMPIAIJ));
1095:           PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATSEQBAIJ, &isSeqBAIJ));
1096:           PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATMPIBAIJ, &isMPIBAIJ));
1097:           PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATSEQSBAIJ, &isSeqSBAIJ));
1098:           PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATMPISBAIJ, &isMPISBAIJ));
1099:           PetscCall(PetscObjectTypeCompare((PetscObject)sub, MATDIAGONAL, &isDiag));
1100:           PetscCall(PetscObjectTypeCompareAny((PetscObject)sub, &isDense, MATSEQDENSE, MATMPIDENSE, NULL));

1102:           if (chol) {
1103:             if (r == c) {
1104:               if (isSeqAIJ) convert_to_triples = MatConvertToTriples_seqaij_seqsbaij;
1105:               else if (isMPIAIJ) convert_to_triples = MatConvertToTriples_mpiaij_mpisbaij;
1106:               else if (isSeqSBAIJ) convert_to_triples = MatConvertToTriples_seqsbaij_seqsbaij;
1107:               else if (isMPISBAIJ) convert_to_triples = MatConvertToTriples_mpisbaij_mpisbaij;
1108:               else if (isDiag) convert_to_triples = MatConvertToTriples_diagonal_xaij;
1109:               else if (isDense) convert_to_triples = MatConvertToTriples_dense_xaij;
1110:             } else {
1111:               if (isSeqAIJ) convert_to_triples = MatConvertToTriples_seqaij_seqaij;
1112:               else if (isMPIAIJ) convert_to_triples = MatConvertToTriples_mpiaij_mpiaij;
1113:               else if (isSeqBAIJ) convert_to_triples = MatConvertToTriples_seqbaij_seqaij;
1114:               else if (isMPIBAIJ) convert_to_triples = MatConvertToTriples_mpibaij_mpiaij;
1115:               else if (isDiag) convert_to_triples = MatConvertToTriples_diagonal_xaij;
1116:               else if (isDense) convert_to_triples = MatConvertToTriples_dense_xaij;
1117:             }
1118:           } else {
1119:             if (isSeqAIJ) convert_to_triples = MatConvertToTriples_seqaij_seqaij;
1120:             else if (isMPIAIJ) convert_to_triples = MatConvertToTriples_mpiaij_mpiaij;
1121:             else if (isSeqBAIJ) convert_to_triples = MatConvertToTriples_seqbaij_seqaij;
1122:             else if (isMPIBAIJ) convert_to_triples = MatConvertToTriples_mpibaij_mpiaij;
1123:             else if (isDiag) convert_to_triples = MatConvertToTriples_diagonal_xaij;
1124:             else if (isDense) convert_to_triples = MatConvertToTriples_dense_xaij;
1125:           }
1126:           PetscCheck(convert_to_triples, PetscObjectComm((PetscObject)sub), PETSC_ERR_SUP, "Not for block of type %s", ((PetscObject)sub)->type_name);
1127:           mumps->nest_convert_to_triples[r * nc + c] = convert_to_triples;
1128:           PetscCall(MatGetInfo(sub, MAT_LOCAL, &info));
1129:           cumnnz += (PetscInt64)info.nz_used; /* can be overestimated for Cholesky */
1130:           maxnnz = PetscMax(maxnnz, info.nz_used);
1131:         }
1132:       }
1133:     }

1135:     /* Allocate total COO */
1136:     totnnz = cumnnz;
1137:     PetscCall(PetscMalloc2(totnnz, &irns, totnnz, &jcns));
1138:     PetscCall(PetscMalloc1(totnnz, &vals));

1140:     /* Handle rows and column maps
1141:        We directly map rows and use an SF for the columns */
1142:     PetscCall(PetscMalloc4(nr, &rows, nc, &cols, nr, &rows_idx, nc, &cols_idx));
1143:     PetscCall(MatNestGetISs(A, rows, cols));
1144:     for (PetscInt r = 0; r < nr; r++) PetscCall(ISGetIndices(rows[r], (const PetscInt **)&rows_idx[r]));
1145:     for (PetscInt c = 0; c < nc; c++) PetscCall(ISGetIndices(cols[c], (const PetscInt **)&cols_idx[c]));
1146:     if (PetscDefined(USE_64BIT_INDICES)) PetscCall(PetscMalloc1(maxnnz, &pjcns_w));
1147:     else (void)maxnnz;

1149:     cumnnz = 0;
1150:     for (PetscInt r = 0; r < nr; r++) {
1151:       for (PetscInt c = 0; c < nc; c++) {
1152:         Mat             sub  = mats[r][c];
1153:         const PetscInt *ridx = rows_idx[r];
1154:         const PetscInt *cidx = cols_idx[c];
1155:         PetscInt        rst;
1156:         PetscSF         csf;
1157:         PetscBool       isTrans, isHTrans = PETSC_FALSE, swap;
1158:         PetscLayout     cmap;

1160:         mumps->nest_vals_start[r * nc + c] = cumnnz;
1161:         if (!mumps->nest_convert_to_triples[r * nc + c]) continue;

1163:         /* Extract inner blocks if needed */
1164:         PetscCall(PetscObjectTypeCompare((PetscObject)sub, MATTRANSPOSEVIRTUAL, &isTrans));
1165:         if (isTrans) PetscCall(MatTransposeGetMat(sub, &sub));
1166:         else {
1167:           PetscCall(PetscObjectTypeCompare((PetscObject)sub, MATHERMITIANTRANSPOSEVIRTUAL, &isHTrans));
1168:           if (isHTrans) PetscCall(MatHermitianTransposeGetMat(sub, &sub));
1169:         }
1170:         swap = (PetscBool)(isTrans || isHTrans);

1172:         /* Get column layout to map off-process columns */
1173:         PetscCall(MatGetLayouts(sub, NULL, &cmap));

1175:         /* Get row start to map on-process rows */
1176:         PetscCall(MatGetOwnershipRange(sub, &rst, NULL));

1178:         /* Directly use the mumps datastructure and use C ordering for now */
1179:         PetscCall((*mumps->nest_convert_to_triples[r * nc + c])(sub, 0, MAT_INITIAL_MATRIX, mumps));

1181:         /* Swap the role of rows and columns indices for transposed blocks
1182:            since we need values with global final ordering */
1183:         if (swap) {
1184:           cidx = rows_idx[r];
1185:           ridx = cols_idx[c];
1186:         }

1188:         /* Communicate column indices
1189:            This could have been done with a single SF but it would have complicated the code a lot.
1190:            But since we do it only once, we pay the price of setting up an SF for each block */
1191:         if (PetscDefined(USE_64BIT_INDICES)) {
1192:           for (PetscInt k = 0; k < mumps->nnz; k++) pjcns_w[k] = mumps->jcn[k];
1193:         } else pjcns_w = (PetscInt *)mumps->jcn; /* This cast is needed only to silence warnings for 64bit integers builds */
1194:         PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &csf));
1195:         PetscCall(PetscSFSetGraphLayout(csf, cmap, mumps->nnz, NULL, PETSC_OWN_POINTER, pjcns_w));
1196:         PetscCall(PetscSFBcastBegin(csf, MPIU_INT, cidx, pjcns_w, MPI_REPLACE));
1197:         PetscCall(PetscSFBcastEnd(csf, MPIU_INT, cidx, pjcns_w, MPI_REPLACE));
1198:         PetscCall(PetscSFDestroy(&csf));

1200:         /* Import indices: use direct map for rows and mapped indices for columns */
1201:         if (swap) {
1202:           for (PetscInt k = 0; k < mumps->nnz; k++) {
1203:             PetscCall(PetscMUMPSIntCast(ridx[mumps->irn[k] - rst] + shift, &jcns[cumnnz + k]));
1204:             PetscCall(PetscMUMPSIntCast(pjcns_w[k] + shift, &irns[cumnnz + k]));
1205:           }
1206:         } else {
1207:           for (PetscInt k = 0; k < mumps->nnz; k++) {
1208:             PetscCall(PetscMUMPSIntCast(ridx[mumps->irn[k] - rst] + shift, &irns[cumnnz + k]));
1209:             PetscCall(PetscMUMPSIntCast(pjcns_w[k] + shift, &jcns[cumnnz + k]));
1210:           }
1211:         }

1213:         /* Import values to full COO */
1214:         PetscCall(PetscArraycpy(vals + cumnnz, mumps->val, mumps->nnz));
1215:         if (isHTrans) { /* conjugate the entries */
1216:           PetscScalar *v = vals + cumnnz;
1217:           for (PetscInt k = 0; k < mumps->nnz; k++) v[k] = PetscConj(v[k]);
1218:         }

1220:         /* Shift new starting point and sanity check */
1221:         cumnnz += mumps->nnz;
1222:         PetscCheck(cumnnz <= totnnz, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unexpected number of nonzeros %" PetscInt64_FMT " != %" PetscInt64_FMT, cumnnz, totnnz);

1224:         /* Free scratch memory */
1225:         PetscCall(PetscFree2(mumps->irn, mumps->jcn));
1226:         PetscCall(PetscFree(mumps->val_alloc));
1227:         mumps->val = NULL;
1228:         mumps->nnz = 0;
1229:       }
1230:     }
1231:     if (PetscDefined(USE_64BIT_INDICES)) PetscCall(PetscFree(pjcns_w));
1232:     for (PetscInt r = 0; r < nr; r++) PetscCall(ISRestoreIndices(rows[r], (const PetscInt **)&rows_idx[r]));
1233:     for (PetscInt c = 0; c < nc; c++) PetscCall(ISRestoreIndices(cols[c], (const PetscInt **)&cols_idx[c]));
1234:     PetscCall(PetscFree4(rows, cols, rows_idx, cols_idx));
1235:     if (!chol) PetscCheck(cumnnz == totnnz, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Different number of nonzeros %" PetscInt64_FMT " != %" PetscInt64_FMT, cumnnz, totnnz);
1236:     mumps->nest_vals_start[nr * nc] = cumnnz;

1238:     /* Set pointers for final MUMPS data structure */
1239:     mumps->nest_vals = vals;
1240:     mumps->val_alloc = NULL; /* do not use val_alloc since it may be reallocated with the OMP callpath */
1241:     mumps->val       = vals;
1242:     mumps->irn       = irns;
1243:     mumps->jcn       = jcns;
1244:     mumps->nnz       = cumnnz;
1245:   } else {
1246:     PetscScalar *oval = mumps->nest_vals;
1247:     for (PetscInt r = 0; r < nr; r++) {
1248:       for (PetscInt c = 0; c < nc; c++) {
1249:         PetscBool isTrans, isHTrans = PETSC_FALSE;
1250:         Mat       sub  = mats[r][c];
1251:         PetscInt  midx = r * nc + c;

1253:         if (!mumps->nest_convert_to_triples[midx]) continue;
1254:         PetscCall(PetscObjectTypeCompare((PetscObject)sub, MATTRANSPOSEVIRTUAL, &isTrans));
1255:         if (isTrans) PetscCall(MatTransposeGetMat(sub, &sub));
1256:         else {
1257:           PetscCall(PetscObjectTypeCompare((PetscObject)sub, MATHERMITIANTRANSPOSEVIRTUAL, &isHTrans));
1258:           if (isHTrans) PetscCall(MatHermitianTransposeGetMat(sub, &sub));
1259:         }
1260:         mumps->val = oval + mumps->nest_vals_start[midx];
1261:         PetscCall((*mumps->nest_convert_to_triples[midx])(sub, shift, MAT_REUSE_MATRIX, mumps));
1262:         if (isHTrans) {
1263:           PetscInt nnz = mumps->nest_vals_start[midx + 1] - mumps->nest_vals_start[midx];
1264:           for (PetscInt k = 0; k < nnz; k++) mumps->val[k] = PetscConj(mumps->val[k]);
1265:         }
1266:       }
1267:     }
1268:     mumps->val = oval;
1269:   }
1270:   PetscFunctionReturn(PETSC_SUCCESS);
1271: }

1273: static PetscErrorCode MatDestroy_MUMPS(Mat A)
1274: {
1275:   Mat_MUMPS *mumps = (Mat_MUMPS *)A->data;

1277:   PetscFunctionBegin;
1278:   PetscCall(PetscFree2(mumps->id.sol_loc, mumps->id.isol_loc));
1279:   PetscCall(VecScatterDestroy(&mumps->scat_rhs));
1280:   PetscCall(VecScatterDestroy(&mumps->scat_sol));
1281:   PetscCall(VecDestroy(&mumps->b_seq));
1282:   PetscCall(VecDestroy(&mumps->x_seq));
1283:   PetscCall(PetscFree(mumps->id.perm_in));
1284:   PetscCall(PetscFree2(mumps->irn, mumps->jcn));
1285:   PetscCall(PetscFree(mumps->val_alloc));
1286:   PetscCall(PetscFree(mumps->info));
1287:   PetscCall(PetscFree(mumps->ICNTL_pre));
1288:   PetscCall(PetscFree(mumps->CNTL_pre));
1289:   PetscCall(MatMumpsResetSchur_Private(mumps));
1290:   if (mumps->id.job != JOB_NULL) { /* cannot call PetscMUMPS_c() if JOB_INIT has never been called for this instance */
1291:     mumps->id.job = JOB_END;
1292:     PetscMUMPS_c(mumps);
1293:     PetscCheck(mumps->id.INFOG(1) >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "MUMPS error in termination: INFOG(1)=%d " MUMPS_MANUALS, mumps->id.INFOG(1));
1294:     if (mumps->mumps_comm != MPI_COMM_NULL) {
1295:       if (PetscDefined(HAVE_OPENMP_SUPPORT) && mumps->use_petsc_omp_support) PetscCallMPI(MPI_Comm_free(&mumps->mumps_comm));
1296:       else PetscCall(PetscCommRestoreComm(PetscObjectComm((PetscObject)A), &mumps->mumps_comm));
1297:     }
1298:   }
1299: #if defined(PETSC_HAVE_OPENMP_SUPPORT)
1300:   if (mumps->use_petsc_omp_support) {
1301:     PetscCall(PetscOmpCtrlDestroy(&mumps->omp_ctrl));
1302:     PetscCall(PetscFree2(mumps->rhs_loc, mumps->rhs_recvbuf));
1303:     PetscCall(PetscFree3(mumps->rhs_nrow, mumps->rhs_recvcounts, mumps->rhs_disps));
1304:   }
1305: #endif
1306:   PetscCall(PetscFree(mumps->ia_alloc));
1307:   PetscCall(PetscFree(mumps->ja_alloc));
1308:   PetscCall(PetscFree(mumps->recvcount));
1309:   PetscCall(PetscFree(mumps->reqs));
1310:   PetscCall(PetscFree(mumps->irhs_loc));
1311:   PetscCall(PetscFree2(mumps->nest_vals_start, mumps->nest_convert_to_triples));
1312:   PetscCall(PetscFree(mumps->nest_vals));
1313:   PetscCall(PetscFree(A->data));

1315:   /* clear composed functions */
1316:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatFactorGetSolverType_C", NULL));
1317:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatFactorSetSchurIS_C", NULL));
1318:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatFactorCreateSchurComplement_C", NULL));
1319:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsSetIcntl_C", NULL));
1320:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetIcntl_C", NULL));
1321:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsSetCntl_C", NULL));
1322:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetCntl_C", NULL));
1323:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetInfo_C", NULL));
1324:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetInfog_C", NULL));
1325:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetRinfo_C", NULL));
1326:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetRinfog_C", NULL));
1327:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetNullPivots_C", NULL));
1328:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetInverse_C", NULL));
1329:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetInverseTranspose_C", NULL));
1330:   PetscFunctionReturn(PETSC_SUCCESS);
1331: }

1333: /* Set up the distributed RHS info for MUMPS. <nrhs> is the number of RHS. <array> points to start of RHS on the local processor. */
1334: static PetscErrorCode MatMumpsSetUpDistRHSInfo(Mat A, PetscInt nrhs, const PetscScalar *array)
1335: {
1336:   Mat_MUMPS        *mumps   = (Mat_MUMPS *)A->data;
1337:   const PetscMPIInt ompsize = mumps->omp_comm_size;
1338:   PetscInt          i, m, M, rstart;

1340:   PetscFunctionBegin;
1341:   PetscCall(MatGetSize(A, &M, NULL));
1342:   PetscCall(MatGetLocalSize(A, &m, NULL));
1343:   PetscCheck(M <= PETSC_MUMPS_INT_MAX, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "PetscInt too long for PetscMUMPSInt");
1344:   if (ompsize == 1) {
1345:     if (!mumps->irhs_loc) {
1346:       mumps->nloc_rhs = m;
1347:       PetscCall(PetscMalloc1(m, &mumps->irhs_loc));
1348:       PetscCall(MatGetOwnershipRange(A, &rstart, NULL));
1349:       for (i = 0; i < m; i++) mumps->irhs_loc[i] = rstart + i + 1; /* use 1-based indices */
1350:     }
1351:     mumps->id.rhs_loc = (MumpsScalar *)array;
1352:   } else {
1353: #if defined(PETSC_HAVE_OPENMP_SUPPORT)
1354:     const PetscInt *ranges;
1355:     PetscMPIInt     j, k, sendcount, *petsc_ranks, *omp_ranks;
1356:     MPI_Group       petsc_group, omp_group;
1357:     PetscScalar    *recvbuf = NULL;

1359:     if (mumps->is_omp_master) {
1360:       /* Lazily initialize the omp stuff for distributed rhs */
1361:       if (!mumps->irhs_loc) {
1362:         PetscCall(PetscMalloc2(ompsize, &omp_ranks, ompsize, &petsc_ranks));
1363:         PetscCall(PetscMalloc3(ompsize, &mumps->rhs_nrow, ompsize, &mumps->rhs_recvcounts, ompsize, &mumps->rhs_disps));
1364:         PetscCallMPI(MPI_Comm_group(mumps->petsc_comm, &petsc_group));
1365:         PetscCallMPI(MPI_Comm_group(mumps->omp_comm, &omp_group));
1366:         for (j = 0; j < ompsize; j++) omp_ranks[j] = j;
1367:         PetscCallMPI(MPI_Group_translate_ranks(omp_group, ompsize, omp_ranks, petsc_group, petsc_ranks));

1369:         /* Populate mumps->irhs_loc[], rhs_nrow[] */
1370:         mumps->nloc_rhs = 0;
1371:         PetscCall(MatGetOwnershipRanges(A, &ranges));
1372:         for (j = 0; j < ompsize; j++) {
1373:           mumps->rhs_nrow[j] = ranges[petsc_ranks[j] + 1] - ranges[petsc_ranks[j]];
1374:           mumps->nloc_rhs += mumps->rhs_nrow[j];
1375:         }
1376:         PetscCall(PetscMalloc1(mumps->nloc_rhs, &mumps->irhs_loc));
1377:         for (j = k = 0; j < ompsize; j++) {
1378:           for (i = ranges[petsc_ranks[j]]; i < ranges[petsc_ranks[j] + 1]; i++, k++) mumps->irhs_loc[k] = i + 1; /* uses 1-based indices */
1379:         }

1381:         PetscCall(PetscFree2(omp_ranks, petsc_ranks));
1382:         PetscCallMPI(MPI_Group_free(&petsc_group));
1383:         PetscCallMPI(MPI_Group_free(&omp_group));
1384:       }

1386:       /* Realloc buffers when current nrhs is bigger than what we have met */
1387:       if (nrhs > mumps->max_nrhs) {
1388:         PetscCall(PetscFree2(mumps->rhs_loc, mumps->rhs_recvbuf));
1389:         PetscCall(PetscMalloc2(mumps->nloc_rhs * nrhs, &mumps->rhs_loc, mumps->nloc_rhs * nrhs, &mumps->rhs_recvbuf));
1390:         mumps->max_nrhs = nrhs;
1391:       }

1393:       /* Setup recvcounts[], disps[], recvbuf on omp rank 0 for the upcoming MPI_Gatherv */
1394:       for (j = 0; j < ompsize; j++) PetscCall(PetscMPIIntCast(mumps->rhs_nrow[j] * nrhs, &mumps->rhs_recvcounts[j]));
1395:       mumps->rhs_disps[0] = 0;
1396:       for (j = 1; j < ompsize; j++) {
1397:         mumps->rhs_disps[j] = mumps->rhs_disps[j - 1] + mumps->rhs_recvcounts[j - 1];
1398:         PetscCheck(mumps->rhs_disps[j] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "PetscMPIInt overflow!");
1399:       }
1400:       recvbuf = (nrhs == 1) ? mumps->rhs_loc : mumps->rhs_recvbuf; /* Directly use rhs_loc[] as recvbuf. Single rhs is common in Ax=b */
1401:     }

1403:     PetscCall(PetscMPIIntCast(m * nrhs, &sendcount));
1404:     PetscCallMPI(MPI_Gatherv(array, sendcount, MPIU_SCALAR, recvbuf, mumps->rhs_recvcounts, mumps->rhs_disps, MPIU_SCALAR, 0, mumps->omp_comm));

1406:     if (mumps->is_omp_master) {
1407:       if (nrhs > 1) { /* Copy & re-arrange data from rhs_recvbuf[] to mumps->rhs_loc[] only when there are multiple rhs */
1408:         PetscScalar *dst, *dstbase = mumps->rhs_loc;
1409:         for (j = 0; j < ompsize; j++) {
1410:           const PetscScalar *src = mumps->rhs_recvbuf + mumps->rhs_disps[j];
1411:           dst                    = dstbase;
1412:           for (i = 0; i < nrhs; i++) {
1413:             PetscCall(PetscArraycpy(dst, src, mumps->rhs_nrow[j]));
1414:             src += mumps->rhs_nrow[j];
1415:             dst += mumps->nloc_rhs;
1416:           }
1417:           dstbase += mumps->rhs_nrow[j];
1418:         }
1419:       }
1420:       mumps->id.rhs_loc = (MumpsScalar *)mumps->rhs_loc;
1421:     }
1422: #endif /* PETSC_HAVE_OPENMP_SUPPORT */
1423:   }
1424:   mumps->id.nrhs     = nrhs;
1425:   mumps->id.nloc_rhs = mumps->nloc_rhs;
1426:   mumps->id.lrhs_loc = mumps->nloc_rhs;
1427:   mumps->id.irhs_loc = mumps->irhs_loc;
1428:   PetscFunctionReturn(PETSC_SUCCESS);
1429: }

1431: static PetscErrorCode MatSolve_MUMPS(Mat A, Vec b, Vec x)
1432: {
1433:   Mat_MUMPS         *mumps  = (Mat_MUMPS *)A->data;
1434:   const PetscScalar *rarray = NULL;
1435:   PetscScalar       *array;
1436:   IS                 is_iden, is_petsc;
1437:   PetscInt           i;
1438:   PetscBool          second_solve = PETSC_FALSE;
1439:   static PetscBool   cite1 = PETSC_FALSE, cite2 = PETSC_FALSE;

1441:   PetscFunctionBegin;
1442:   PetscCall(PetscCitationsRegister("@article{MUMPS01,\n  author = {P.~R. Amestoy and I.~S. Duff and J.-Y. L'Excellent and J. Koster},\n  title = {A fully asynchronous multifrontal solver using distributed dynamic scheduling},\n  journal = {SIAM "
1443:                                    "Journal on Matrix Analysis and Applications},\n  volume = {23},\n  number = {1},\n  pages = {15--41},\n  year = {2001}\n}\n",
1444:                                    &cite1));
1445:   PetscCall(PetscCitationsRegister("@article{MUMPS02,\n  author = {P.~R. Amestoy and A. Guermouche and J.-Y. L'Excellent and S. Pralet},\n  title = {Hybrid scheduling for the parallel solution of linear systems},\n  journal = {Parallel "
1446:                                    "Computing},\n  volume = {32},\n  number = {2},\n  pages = {136--156},\n  year = {2006}\n}\n",
1447:                                    &cite2));

1449:   if (A->factorerrortype) {
1450:     PetscCall(PetscInfo(A, "MatSolve is called with singular matrix factor, INFOG(1)=%d, INFO(2)=%d\n", mumps->id.INFOG(1), mumps->id.INFO(2)));
1451:     PetscCall(VecSetInf(x));
1452:     PetscFunctionReturn(PETSC_SUCCESS);
1453:   }

1455:   mumps->id.nrhs = 1;
1456:   if (mumps->petsc_size > 1) {
1457:     if (mumps->ICNTL20 == 10) {
1458:       mumps->id.ICNTL(20) = 10; /* dense distributed RHS */
1459:       PetscCall(VecGetArrayRead(b, &rarray));
1460:       PetscCall(MatMumpsSetUpDistRHSInfo(A, 1, rarray));
1461:     } else {
1462:       mumps->id.ICNTL(20) = 0; /* dense centralized RHS; Scatter b into a sequential rhs vector*/
1463:       PetscCall(VecScatterBegin(mumps->scat_rhs, b, mumps->b_seq, INSERT_VALUES, SCATTER_FORWARD));
1464:       PetscCall(VecScatterEnd(mumps->scat_rhs, b, mumps->b_seq, INSERT_VALUES, SCATTER_FORWARD));
1465:       if (!mumps->myid) {
1466:         PetscCall(VecGetArray(mumps->b_seq, &array));
1467:         mumps->id.rhs = (MumpsScalar *)array;
1468:       }
1469:     }
1470:   } else {                   /* petsc_size == 1 */
1471:     mumps->id.ICNTL(20) = 0; /* dense centralized RHS */
1472:     PetscCall(VecCopy(b, x));
1473:     PetscCall(VecGetArray(x, &array));
1474:     mumps->id.rhs = (MumpsScalar *)array;
1475:   }

1477:   /*
1478:      handle condensation step of Schur complement (if any)
1479:      We set by default ICNTL(26) == -1 when Schur indices have been provided by the user.
1480:      According to MUMPS (5.0.0) manual, any value should be harmful during the factorization phase
1481:      Unless the user provides a valid value for ICNTL(26), MatSolve and MatMatSolve routines solve the full system.
1482:      This requires an extra call to PetscMUMPS_c and the computation of the factors for S
1483:   */
1484:   if (mumps->id.size_schur > 0) {
1485:     PetscCheck(mumps->petsc_size <= 1, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Parallel Schur complements not yet supported from PETSc");
1486:     if (mumps->id.ICNTL(26) < 0 || mumps->id.ICNTL(26) > 2) {
1487:       second_solve = PETSC_TRUE;
1488:       PetscCall(MatMumpsHandleSchur_Private(A, PETSC_FALSE));
1489:       mumps->id.ICNTL(26) = 1; /* condensation phase */
1490:     } else if (mumps->id.ICNTL(26) == 1) PetscCall(MatMumpsHandleSchur_Private(A, PETSC_FALSE));
1491:   }
1492:   /* solve phase */
1493:   mumps->id.job = JOB_SOLVE;
1494:   PetscMUMPS_c(mumps);
1495:   PetscCheck(mumps->id.INFOG(1) >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "MUMPS error in solve: INFOG(1)=%d " MUMPS_MANUALS, mumps->id.INFOG(1));

1497:   /* handle expansion step of Schur complement (if any) */
1498:   if (second_solve) PetscCall(MatMumpsHandleSchur_Private(A, PETSC_TRUE));
1499:   else if (mumps->id.ICNTL(26) == 1) {
1500:     PetscCall(MatMumpsSolveSchur_Private(A));
1501:     for (i = 0; i < mumps->id.size_schur; ++i) {
1502: #if !defined(PETSC_USE_COMPLEX)
1503:       PetscScalar val = mumps->id.redrhs[i];
1504: #else
1505:       PetscScalar val = mumps->id.redrhs[i].r + PETSC_i * mumps->id.redrhs[i].i;
1506: #endif
1507:       array[mumps->id.listvar_schur[i] - 1] = val;
1508:     }
1509:   }

1511:   if (mumps->petsc_size > 1) { /* convert mumps distributed solution to petsc mpi x */
1512:     if (mumps->scat_sol && mumps->ICNTL9_pre != mumps->id.ICNTL(9)) {
1513:       /* when id.ICNTL(9) changes, the contents of lsol_loc may change (not its size, lsol_loc), recreates scat_sol */
1514:       PetscCall(VecScatterDestroy(&mumps->scat_sol));
1515:     }
1516:     if (!mumps->scat_sol) { /* create scatter scat_sol */
1517:       PetscInt *isol2_loc = NULL;
1518:       PetscCall(ISCreateStride(PETSC_COMM_SELF, mumps->id.lsol_loc, 0, 1, &is_iden)); /* from */
1519:       PetscCall(PetscMalloc1(mumps->id.lsol_loc, &isol2_loc));
1520:       for (i = 0; i < mumps->id.lsol_loc; i++) isol2_loc[i] = mumps->id.isol_loc[i] - 1;                        /* change Fortran style to C style */
1521:       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, mumps->id.lsol_loc, isol2_loc, PETSC_OWN_POINTER, &is_petsc)); /* to */
1522:       PetscCall(VecScatterCreate(mumps->x_seq, is_iden, x, is_petsc, &mumps->scat_sol));
1523:       PetscCall(ISDestroy(&is_iden));
1524:       PetscCall(ISDestroy(&is_petsc));
1525:       mumps->ICNTL9_pre = mumps->id.ICNTL(9); /* save current value of id.ICNTL(9) */
1526:     }

1528:     PetscCall(VecScatterBegin(mumps->scat_sol, mumps->x_seq, x, INSERT_VALUES, SCATTER_FORWARD));
1529:     PetscCall(VecScatterEnd(mumps->scat_sol, mumps->x_seq, x, INSERT_VALUES, SCATTER_FORWARD));
1530:   }

1532:   if (mumps->petsc_size > 1) {
1533:     if (mumps->ICNTL20 == 10) {
1534:       PetscCall(VecRestoreArrayRead(b, &rarray));
1535:     } else if (!mumps->myid) {
1536:       PetscCall(VecRestoreArray(mumps->b_seq, &array));
1537:     }
1538:   } else PetscCall(VecRestoreArray(x, &array));

1540:   PetscCall(PetscLogFlops(2.0 * PetscMax(0, (mumps->id.INFO(28) >= 0 ? mumps->id.INFO(28) : -1000000 * mumps->id.INFO(28)) - A->cmap->n)));
1541:   PetscFunctionReturn(PETSC_SUCCESS);
1542: }

1544: static PetscErrorCode MatSolveTranspose_MUMPS(Mat A, Vec b, Vec x)
1545: {
1546:   Mat_MUMPS          *mumps = (Mat_MUMPS *)A->data;
1547:   const PetscMUMPSInt value = mumps->id.ICNTL(9);

1549:   PetscFunctionBegin;
1550:   mumps->id.ICNTL(9) = 0;
1551:   PetscCall(MatSolve_MUMPS(A, b, x));
1552:   mumps->id.ICNTL(9) = value;
1553:   PetscFunctionReturn(PETSC_SUCCESS);
1554: }

1556: static PetscErrorCode MatMatSolve_MUMPS(Mat A, Mat B, Mat X)
1557: {
1558:   Mat                Bt = NULL;
1559:   PetscBool          denseX, denseB, flg, flgT;
1560:   Mat_MUMPS         *mumps = (Mat_MUMPS *)A->data;
1561:   PetscInt           i, nrhs, M;
1562:   PetscScalar       *array;
1563:   const PetscScalar *rbray;
1564:   PetscInt           lsol_loc, nlsol_loc, *idxx, iidx = 0;
1565:   PetscMUMPSInt     *isol_loc, *isol_loc_save;
1566:   PetscScalar       *bray, *sol_loc, *sol_loc_save;
1567:   IS                 is_to, is_from;
1568:   PetscInt           k, proc, j, m, myrstart;
1569:   const PetscInt    *rstart;
1570:   Vec                v_mpi, msol_loc;
1571:   VecScatter         scat_sol;
1572:   Vec                b_seq;
1573:   VecScatter         scat_rhs;
1574:   PetscScalar       *aa;
1575:   PetscInt           spnr, *ia, *ja;
1576:   Mat_MPIAIJ        *b = NULL;

1578:   PetscFunctionBegin;
1579:   PetscCall(PetscObjectTypeCompareAny((PetscObject)X, &denseX, MATSEQDENSE, MATMPIDENSE, NULL));
1580:   PetscCheck(denseX, PetscObjectComm((PetscObject)X), PETSC_ERR_ARG_WRONG, "Matrix X must be MATDENSE matrix");

1582:   PetscCall(PetscObjectTypeCompareAny((PetscObject)B, &denseB, MATSEQDENSE, MATMPIDENSE, NULL));
1583:   if (denseB) {
1584:     PetscCheck(B->rmap->n == X->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Matrix B and X must have same row distribution");
1585:     mumps->id.ICNTL(20) = 0; /* dense RHS */
1586:   } else {                   /* sparse B */
1587:     PetscCheck(X != B, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_IDN, "X and B must be different matrices");
1588:     PetscCall(PetscObjectTypeCompare((PetscObject)B, MATTRANSPOSEVIRTUAL, &flgT));
1589:     if (flgT) { /* input B is transpose of actual RHS matrix,
1590:                  because mumps requires sparse compressed COLUMN storage! See MatMatTransposeSolve_MUMPS() */
1591:       PetscCall(MatTransposeGetMat(B, &Bt));
1592:     } else SETERRQ(PetscObjectComm((PetscObject)B), PETSC_ERR_ARG_WRONG, "Matrix B must be MATTRANSPOSEVIRTUAL matrix");
1593:     mumps->id.ICNTL(20) = 1; /* sparse RHS */
1594:   }

1596:   PetscCall(MatGetSize(B, &M, &nrhs));
1597:   mumps->id.nrhs = nrhs;
1598:   mumps->id.lrhs = M;
1599:   mumps->id.rhs  = NULL;

1601:   if (mumps->petsc_size == 1) {
1602:     PetscScalar *aa;
1603:     PetscInt     spnr, *ia, *ja;
1604:     PetscBool    second_solve = PETSC_FALSE;

1606:     PetscCall(MatDenseGetArray(X, &array));
1607:     mumps->id.rhs = (MumpsScalar *)array;

1609:     if (denseB) {
1610:       /* copy B to X */
1611:       PetscCall(MatDenseGetArrayRead(B, &rbray));
1612:       PetscCall(PetscArraycpy(array, rbray, M * nrhs));
1613:       PetscCall(MatDenseRestoreArrayRead(B, &rbray));
1614:     } else { /* sparse B */
1615:       PetscCall(MatSeqAIJGetArray(Bt, &aa));
1616:       PetscCall(MatGetRowIJ(Bt, 1, PETSC_FALSE, PETSC_FALSE, &spnr, (const PetscInt **)&ia, (const PetscInt **)&ja, &flg));
1617:       PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot get IJ structure");
1618:       PetscCall(PetscMUMPSIntCSRCast(mumps, spnr, ia, ja, &mumps->id.irhs_ptr, &mumps->id.irhs_sparse, &mumps->id.nz_rhs));
1619:       mumps->id.rhs_sparse = (MumpsScalar *)aa;
1620:     }
1621:     /* handle condensation step of Schur complement (if any) */
1622:     if (mumps->id.size_schur > 0) {
1623:       if (mumps->id.ICNTL(26) < 0 || mumps->id.ICNTL(26) > 2) {
1624:         second_solve = PETSC_TRUE;
1625:         PetscCall(MatMumpsHandleSchur_Private(A, PETSC_FALSE));
1626:         mumps->id.ICNTL(26) = 1; /* condensation phase */
1627:       } else if (mumps->id.ICNTL(26) == 1) PetscCall(MatMumpsHandleSchur_Private(A, PETSC_FALSE));
1628:     }
1629:     /* solve phase */
1630:     mumps->id.job = JOB_SOLVE;
1631:     PetscMUMPS_c(mumps);
1632:     PetscCheck(mumps->id.INFOG(1) >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "MUMPS error in solve: INFOG(1)=%d " MUMPS_MANUALS, mumps->id.INFOG(1));

1634:     /* handle expansion step of Schur complement (if any) */
1635:     if (second_solve) PetscCall(MatMumpsHandleSchur_Private(A, PETSC_TRUE));
1636:     else if (mumps->id.ICNTL(26) == 1) {
1637:       PetscCall(MatMumpsSolveSchur_Private(A));
1638:       for (j = 0; j < nrhs; ++j)
1639:         for (i = 0; i < mumps->id.size_schur; ++i) {
1640: #if !defined(PETSC_USE_COMPLEX)
1641:           PetscScalar val = mumps->id.redrhs[i + j * mumps->id.lredrhs];
1642: #else
1643:           PetscScalar val = mumps->id.redrhs[i + j * mumps->id.lredrhs].r + PETSC_i * mumps->id.redrhs[i + j * mumps->id.lredrhs].i;
1644: #endif
1645:           array[mumps->id.listvar_schur[i] - 1 + j * M] = val;
1646:         }
1647:     }
1648:     if (!denseB) { /* sparse B */
1649:       PetscCall(MatSeqAIJRestoreArray(Bt, &aa));
1650:       PetscCall(MatRestoreRowIJ(Bt, 1, PETSC_FALSE, PETSC_FALSE, &spnr, (const PetscInt **)&ia, (const PetscInt **)&ja, &flg));
1651:       PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot restore IJ structure");
1652:     }
1653:     PetscCall(MatDenseRestoreArray(X, &array));
1654:     PetscFunctionReturn(PETSC_SUCCESS);
1655:   }

1657:   /* parallel case: MUMPS requires rhs B to be centralized on the host! */
1658:   PetscCheck(!mumps->id.ICNTL(19), PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Parallel Schur complements not yet supported from PETSc");

1660:   /* create msol_loc to hold mumps local solution */
1661:   isol_loc_save = mumps->id.isol_loc; /* save it for MatSolve() */
1662:   sol_loc_save  = (PetscScalar *)mumps->id.sol_loc;

1664:   lsol_loc  = mumps->id.lsol_loc;
1665:   nlsol_loc = nrhs * lsol_loc; /* length of sol_loc */
1666:   PetscCall(PetscMalloc2(nlsol_loc, &sol_loc, lsol_loc, &isol_loc));
1667:   mumps->id.sol_loc  = (MumpsScalar *)sol_loc;
1668:   mumps->id.isol_loc = isol_loc;

1670:   PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, nlsol_loc, (PetscScalar *)sol_loc, &msol_loc));

1672:   if (denseB) {
1673:     if (mumps->ICNTL20 == 10) {
1674:       mumps->id.ICNTL(20) = 10; /* dense distributed RHS */
1675:       PetscCall(MatDenseGetArrayRead(B, &rbray));
1676:       PetscCall(MatMumpsSetUpDistRHSInfo(A, nrhs, rbray));
1677:       PetscCall(MatDenseRestoreArrayRead(B, &rbray));
1678:       PetscCall(MatGetLocalSize(B, &m, NULL));
1679:       PetscCall(VecCreateMPIWithArray(PetscObjectComm((PetscObject)B), 1, nrhs * m, nrhs * M, NULL, &v_mpi));
1680:     } else {
1681:       mumps->id.ICNTL(20) = 0; /* dense centralized RHS */
1682:       /* TODO: Because of non-contiguous indices, the created vecscatter scat_rhs is not done in MPI_Gather, resulting in
1683:         very inefficient communication. An optimization is to use VecScatterCreateToZero to gather B to rank 0. Then on rank
1684:         0, re-arrange B into desired order, which is a local operation.
1685:       */

1687:       /* scatter v_mpi to b_seq because MUMPS before 5.3.0 only supports centralized rhs */
1688:       /* wrap dense rhs matrix B into a vector v_mpi */
1689:       PetscCall(MatGetLocalSize(B, &m, NULL));
1690:       PetscCall(MatDenseGetArray(B, &bray));
1691:       PetscCall(VecCreateMPIWithArray(PetscObjectComm((PetscObject)B), 1, nrhs * m, nrhs * M, (const PetscScalar *)bray, &v_mpi));
1692:       PetscCall(MatDenseRestoreArray(B, &bray));

1694:       /* scatter v_mpi to b_seq in proc[0]. MUMPS requires rhs to be centralized on the host! */
1695:       if (!mumps->myid) {
1696:         PetscInt *idx;
1697:         /* idx: maps from k-th index of v_mpi to (i,j)-th global entry of B */
1698:         PetscCall(PetscMalloc1(nrhs * M, &idx));
1699:         PetscCall(MatGetOwnershipRanges(B, &rstart));
1700:         k = 0;
1701:         for (proc = 0; proc < mumps->petsc_size; proc++) {
1702:           for (j = 0; j < nrhs; j++) {
1703:             for (i = rstart[proc]; i < rstart[proc + 1]; i++) idx[k++] = j * M + i;
1704:           }
1705:         }

1707:         PetscCall(VecCreateSeq(PETSC_COMM_SELF, nrhs * M, &b_seq));
1708:         PetscCall(ISCreateGeneral(PETSC_COMM_SELF, nrhs * M, idx, PETSC_OWN_POINTER, &is_to));
1709:         PetscCall(ISCreateStride(PETSC_COMM_SELF, nrhs * M, 0, 1, &is_from));
1710:       } else {
1711:         PetscCall(VecCreateSeq(PETSC_COMM_SELF, 0, &b_seq));
1712:         PetscCall(ISCreateStride(PETSC_COMM_SELF, 0, 0, 1, &is_to));
1713:         PetscCall(ISCreateStride(PETSC_COMM_SELF, 0, 0, 1, &is_from));
1714:       }
1715:       PetscCall(VecScatterCreate(v_mpi, is_from, b_seq, is_to, &scat_rhs));
1716:       PetscCall(VecScatterBegin(scat_rhs, v_mpi, b_seq, INSERT_VALUES, SCATTER_FORWARD));
1717:       PetscCall(ISDestroy(&is_to));
1718:       PetscCall(ISDestroy(&is_from));
1719:       PetscCall(VecScatterEnd(scat_rhs, v_mpi, b_seq, INSERT_VALUES, SCATTER_FORWARD));

1721:       if (!mumps->myid) { /* define rhs on the host */
1722:         PetscCall(VecGetArray(b_seq, &bray));
1723:         mumps->id.rhs = (MumpsScalar *)bray;
1724:         PetscCall(VecRestoreArray(b_seq, &bray));
1725:       }
1726:     }
1727:   } else { /* sparse B */
1728:     b = (Mat_MPIAIJ *)Bt->data;

1730:     /* wrap dense X into a vector v_mpi */
1731:     PetscCall(MatGetLocalSize(X, &m, NULL));
1732:     PetscCall(MatDenseGetArray(X, &bray));
1733:     PetscCall(VecCreateMPIWithArray(PetscObjectComm((PetscObject)X), 1, nrhs * m, nrhs * M, (const PetscScalar *)bray, &v_mpi));
1734:     PetscCall(MatDenseRestoreArray(X, &bray));

1736:     if (!mumps->myid) {
1737:       PetscCall(MatSeqAIJGetArray(b->A, &aa));
1738:       PetscCall(MatGetRowIJ(b->A, 1, PETSC_FALSE, PETSC_FALSE, &spnr, (const PetscInt **)&ia, (const PetscInt **)&ja, &flg));
1739:       PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot get IJ structure");
1740:       PetscCall(PetscMUMPSIntCSRCast(mumps, spnr, ia, ja, &mumps->id.irhs_ptr, &mumps->id.irhs_sparse, &mumps->id.nz_rhs));
1741:       mumps->id.rhs_sparse = (MumpsScalar *)aa;
1742:     } else {
1743:       mumps->id.irhs_ptr    = NULL;
1744:       mumps->id.irhs_sparse = NULL;
1745:       mumps->id.nz_rhs      = 0;
1746:       mumps->id.rhs_sparse  = NULL;
1747:     }
1748:   }

1750:   /* solve phase */
1751:   mumps->id.job = JOB_SOLVE;
1752:   PetscMUMPS_c(mumps);
1753:   PetscCheck(mumps->id.INFOG(1) >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "MUMPS error in solve: INFOG(1)=%d " MUMPS_MANUALS, mumps->id.INFOG(1));

1755:   /* scatter mumps distributed solution to petsc vector v_mpi, which shares local arrays with solution matrix X */
1756:   PetscCall(MatDenseGetArray(X, &array));
1757:   PetscCall(VecPlaceArray(v_mpi, array));

1759:   /* create scatter scat_sol */
1760:   PetscCall(MatGetOwnershipRanges(X, &rstart));
1761:   /* iidx: index for scatter mumps solution to petsc X */

1763:   PetscCall(ISCreateStride(PETSC_COMM_SELF, nlsol_loc, 0, 1, &is_from));
1764:   PetscCall(PetscMalloc1(nlsol_loc, &idxx));
1765:   for (i = 0; i < lsol_loc; i++) {
1766:     isol_loc[i] -= 1; /* change Fortran style to C style. isol_loc[i+j*lsol_loc] contains x[isol_loc[i]] in j-th vector */

1768:     for (proc = 0; proc < mumps->petsc_size; proc++) {
1769:       if (isol_loc[i] >= rstart[proc] && isol_loc[i] < rstart[proc + 1]) {
1770:         myrstart = rstart[proc];
1771:         k        = isol_loc[i] - myrstart;          /* local index on 1st column of petsc vector X */
1772:         iidx     = k + myrstart * nrhs;             /* maps mumps isol_loc[i] to petsc index in X */
1773:         m        = rstart[proc + 1] - rstart[proc]; /* rows of X for this proc */
1774:         break;
1775:       }
1776:     }

1778:     for (j = 0; j < nrhs; j++) idxx[i + j * lsol_loc] = iidx + j * m;
1779:   }
1780:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, nlsol_loc, idxx, PETSC_COPY_VALUES, &is_to));
1781:   PetscCall(VecScatterCreate(msol_loc, is_from, v_mpi, is_to, &scat_sol));
1782:   PetscCall(VecScatterBegin(scat_sol, msol_loc, v_mpi, INSERT_VALUES, SCATTER_FORWARD));
1783:   PetscCall(ISDestroy(&is_from));
1784:   PetscCall(ISDestroy(&is_to));
1785:   PetscCall(VecScatterEnd(scat_sol, msol_loc, v_mpi, INSERT_VALUES, SCATTER_FORWARD));
1786:   PetscCall(MatDenseRestoreArray(X, &array));

1788:   /* free spaces */
1789:   mumps->id.sol_loc  = (MumpsScalar *)sol_loc_save;
1790:   mumps->id.isol_loc = isol_loc_save;

1792:   PetscCall(PetscFree2(sol_loc, isol_loc));
1793:   PetscCall(PetscFree(idxx));
1794:   PetscCall(VecDestroy(&msol_loc));
1795:   PetscCall(VecDestroy(&v_mpi));
1796:   if (!denseB) {
1797:     if (!mumps->myid) {
1798:       b = (Mat_MPIAIJ *)Bt->data;
1799:       PetscCall(MatSeqAIJRestoreArray(b->A, &aa));
1800:       PetscCall(MatRestoreRowIJ(b->A, 1, PETSC_FALSE, PETSC_FALSE, &spnr, (const PetscInt **)&ia, (const PetscInt **)&ja, &flg));
1801:       PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot restore IJ structure");
1802:     }
1803:   } else {
1804:     if (mumps->ICNTL20 == 0) {
1805:       PetscCall(VecDestroy(&b_seq));
1806:       PetscCall(VecScatterDestroy(&scat_rhs));
1807:     }
1808:   }
1809:   PetscCall(VecScatterDestroy(&scat_sol));
1810:   PetscCall(PetscLogFlops(nrhs * PetscMax(0, (2.0 * (mumps->id.INFO(28) >= 0 ? mumps->id.INFO(28) : -1000000 * mumps->id.INFO(28)) - A->cmap->n))));
1811:   PetscFunctionReturn(PETSC_SUCCESS);
1812: }

1814: static PetscErrorCode MatMatSolveTranspose_MUMPS(Mat A, Mat B, Mat X)
1815: {
1816:   Mat_MUMPS          *mumps = (Mat_MUMPS *)A->data;
1817:   const PetscMUMPSInt value = mumps->id.ICNTL(9);

1819:   PetscFunctionBegin;
1820:   mumps->id.ICNTL(9) = 0;
1821:   PetscCall(MatMatSolve_MUMPS(A, B, X));
1822:   mumps->id.ICNTL(9) = value;
1823:   PetscFunctionReturn(PETSC_SUCCESS);
1824: }

1826: static PetscErrorCode MatMatTransposeSolve_MUMPS(Mat A, Mat Bt, Mat X)
1827: {
1828:   PetscBool flg;
1829:   Mat       B;

1831:   PetscFunctionBegin;
1832:   PetscCall(PetscObjectTypeCompareAny((PetscObject)Bt, &flg, MATSEQAIJ, MATMPIAIJ, NULL));
1833:   PetscCheck(flg, PetscObjectComm((PetscObject)Bt), PETSC_ERR_ARG_WRONG, "Matrix Bt must be MATAIJ matrix");

1835:   /* Create B=Bt^T that uses Bt's data structure */
1836:   PetscCall(MatCreateTranspose(Bt, &B));

1838:   PetscCall(MatMatSolve_MUMPS(A, B, X));
1839:   PetscCall(MatDestroy(&B));
1840:   PetscFunctionReturn(PETSC_SUCCESS);
1841: }

1843: #if !defined(PETSC_USE_COMPLEX)
1844: /*
1845:   input:
1846:    F:        numeric factor
1847:   output:
1848:    nneg:     total number of negative pivots
1849:    nzero:    total number of zero pivots
1850:    npos:     (global dimension of F) - nneg - nzero
1851: */
1852: static PetscErrorCode MatGetInertia_SBAIJMUMPS(Mat F, PetscInt *nneg, PetscInt *nzero, PetscInt *npos)
1853: {
1854:   Mat_MUMPS  *mumps = (Mat_MUMPS *)F->data;
1855:   PetscMPIInt size;

1857:   PetscFunctionBegin;
1858:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)F), &size));
1859:   /* MUMPS 4.3.1 calls ScaLAPACK when ICNTL(13)=0 (default), which does not offer the possibility to compute the inertia of a dense matrix. Set ICNTL(13)=1 to skip ScaLAPACK */
1860:   PetscCheck(size <= 1 || mumps->id.ICNTL(13) == 1, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "ICNTL(13)=%d. -mat_mumps_icntl_13 must be set as 1 for correct global matrix inertia", mumps->id.INFOG(13));

1862:   if (nneg) *nneg = mumps->id.INFOG(12);
1863:   if (nzero || npos) {
1864:     PetscCheck(mumps->id.ICNTL(24) == 1, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "-mat_mumps_icntl_24 must be set as 1 for null pivot row detection");
1865:     if (nzero) *nzero = mumps->id.INFOG(28);
1866:     if (npos) *npos = F->rmap->N - (mumps->id.INFOG(12) + mumps->id.INFOG(28));
1867:   }
1868:   PetscFunctionReturn(PETSC_SUCCESS);
1869: }
1870: #endif

1872: static PetscErrorCode MatMumpsGatherNonzerosOnMaster(MatReuse reuse, Mat_MUMPS *mumps)
1873: {
1874:   PetscInt       i, nreqs;
1875:   PetscMUMPSInt *irn, *jcn;
1876:   PetscMPIInt    count;
1877:   PetscInt64     totnnz, remain;
1878:   const PetscInt osize = mumps->omp_comm_size;
1879:   PetscScalar   *val;

1881:   PetscFunctionBegin;
1882:   if (osize > 1) {
1883:     if (reuse == MAT_INITIAL_MATRIX) {
1884:       /* master first gathers counts of nonzeros to receive */
1885:       if (mumps->is_omp_master) PetscCall(PetscMalloc1(osize, &mumps->recvcount));
1886:       PetscCallMPI(MPI_Gather(&mumps->nnz, 1, MPIU_INT64, mumps->recvcount, 1, MPIU_INT64, 0 /*master*/, mumps->omp_comm));

1888:       /* Then each computes number of send/recvs */
1889:       if (mumps->is_omp_master) {
1890:         /* Start from 1 since self communication is not done in MPI */
1891:         nreqs = 0;
1892:         for (i = 1; i < osize; i++) nreqs += (mumps->recvcount[i] + PETSC_MPI_INT_MAX - 1) / PETSC_MPI_INT_MAX;
1893:       } else {
1894:         nreqs = (mumps->nnz + PETSC_MPI_INT_MAX - 1) / PETSC_MPI_INT_MAX;
1895:       }
1896:       PetscCall(PetscMalloc1(nreqs * 3, &mumps->reqs)); /* Triple the requests since we send irn, jcn and val separately */

1898:       /* The following code is doing a very simple thing: omp_master rank gathers irn/jcn/val from others.
1899:          MPI_Gatherv would be enough if it supports big counts > 2^31-1. Since it does not, and mumps->nnz
1900:          might be a prime number > 2^31-1, we have to slice the message. Note omp_comm_size
1901:          is very small, the current approach should have no extra overhead compared to MPI_Gatherv.
1902:        */
1903:       nreqs = 0; /* counter for actual send/recvs */
1904:       if (mumps->is_omp_master) {
1905:         for (i = 0, totnnz = 0; i < osize; i++) totnnz += mumps->recvcount[i]; /* totnnz = sum of nnz over omp_comm */
1906:         PetscCall(PetscMalloc2(totnnz, &irn, totnnz, &jcn));
1907:         PetscCall(PetscMalloc1(totnnz, &val));

1909:         /* Self communication */
1910:         PetscCall(PetscArraycpy(irn, mumps->irn, mumps->nnz));
1911:         PetscCall(PetscArraycpy(jcn, mumps->jcn, mumps->nnz));
1912:         PetscCall(PetscArraycpy(val, mumps->val, mumps->nnz));

1914:         /* Replace mumps->irn/jcn etc on master with the newly allocated bigger arrays */
1915:         PetscCall(PetscFree2(mumps->irn, mumps->jcn));
1916:         PetscCall(PetscFree(mumps->val_alloc));
1917:         mumps->nnz = totnnz;
1918:         mumps->irn = irn;
1919:         mumps->jcn = jcn;
1920:         mumps->val = mumps->val_alloc = val;

1922:         irn += mumps->recvcount[0]; /* recvcount[0] is old mumps->nnz on omp rank 0 */
1923:         jcn += mumps->recvcount[0];
1924:         val += mumps->recvcount[0];

1926:         /* Remote communication */
1927:         for (i = 1; i < osize; i++) {
1928:           count  = PetscMin(mumps->recvcount[i], (PetscMPIInt)PETSC_MPI_INT_MAX);
1929:           remain = mumps->recvcount[i] - count;
1930:           while (count > 0) {
1931:             PetscCallMPI(MPI_Irecv(irn, count, MPIU_MUMPSINT, i, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
1932:             PetscCallMPI(MPI_Irecv(jcn, count, MPIU_MUMPSINT, i, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
1933:             PetscCallMPI(MPI_Irecv(val, count, MPIU_SCALAR, i, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
1934:             irn += count;
1935:             jcn += count;
1936:             val += count;
1937:             count = PetscMin(remain, (PetscMPIInt)PETSC_MPI_INT_MAX);
1938:             remain -= count;
1939:           }
1940:         }
1941:       } else {
1942:         irn    = mumps->irn;
1943:         jcn    = mumps->jcn;
1944:         val    = mumps->val;
1945:         count  = PetscMin(mumps->nnz, (PetscMPIInt)PETSC_MPI_INT_MAX);
1946:         remain = mumps->nnz - count;
1947:         while (count > 0) {
1948:           PetscCallMPI(MPI_Isend(irn, count, MPIU_MUMPSINT, 0, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
1949:           PetscCallMPI(MPI_Isend(jcn, count, MPIU_MUMPSINT, 0, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
1950:           PetscCallMPI(MPI_Isend(val, count, MPIU_SCALAR, 0, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
1951:           irn += count;
1952:           jcn += count;
1953:           val += count;
1954:           count = PetscMin(remain, (PetscMPIInt)PETSC_MPI_INT_MAX);
1955:           remain -= count;
1956:         }
1957:       }
1958:     } else {
1959:       nreqs = 0;
1960:       if (mumps->is_omp_master) {
1961:         val = mumps->val + mumps->recvcount[0];
1962:         for (i = 1; i < osize; i++) { /* Remote communication only since self data is already in place */
1963:           count  = PetscMin(mumps->recvcount[i], (PetscMPIInt)PETSC_MPI_INT_MAX);
1964:           remain = mumps->recvcount[i] - count;
1965:           while (count > 0) {
1966:             PetscCallMPI(MPI_Irecv(val, count, MPIU_SCALAR, i, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
1967:             val += count;
1968:             count = PetscMin(remain, (PetscMPIInt)PETSC_MPI_INT_MAX);
1969:             remain -= count;
1970:           }
1971:         }
1972:       } else {
1973:         val    = mumps->val;
1974:         count  = PetscMin(mumps->nnz, (PetscMPIInt)PETSC_MPI_INT_MAX);
1975:         remain = mumps->nnz - count;
1976:         while (count > 0) {
1977:           PetscCallMPI(MPI_Isend(val, count, MPIU_SCALAR, 0, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
1978:           val += count;
1979:           count = PetscMin(remain, (PetscMPIInt)PETSC_MPI_INT_MAX);
1980:           remain -= count;
1981:         }
1982:       }
1983:     }
1984:     PetscCallMPI(MPI_Waitall(nreqs, mumps->reqs, MPI_STATUSES_IGNORE));
1985:     mumps->tag++; /* It is totally fine for above send/recvs to share one mpi tag */
1986:   }
1987:   PetscFunctionReturn(PETSC_SUCCESS);
1988: }

1990: static PetscErrorCode MatFactorNumeric_MUMPS(Mat F, Mat A, PETSC_UNUSED const MatFactorInfo *info)
1991: {
1992:   Mat_MUMPS *mumps = (Mat_MUMPS *)(F)->data;
1993:   PetscBool  isMPIAIJ;

1995:   PetscFunctionBegin;
1996:   if (mumps->id.INFOG(1) < 0 && !(mumps->id.INFOG(1) == -16 && mumps->id.INFOG(1) == 0)) {
1997:     if (mumps->id.INFOG(1) == -6) PetscCall(PetscInfo(A, "MatFactorNumeric is called with singular matrix structure, INFOG(1)=%d, INFO(2)=%d\n", mumps->id.INFOG(1), mumps->id.INFO(2)));
1998:     PetscCall(PetscInfo(A, "MatFactorNumeric is called after analysis phase fails, INFOG(1)=%d, INFO(2)=%d\n", mumps->id.INFOG(1), mumps->id.INFO(2)));
1999:     PetscFunctionReturn(PETSC_SUCCESS);
2000:   }

2002:   PetscCall((*mumps->ConvertToTriples)(A, 1, MAT_REUSE_MATRIX, mumps));
2003:   PetscCall(MatMumpsGatherNonzerosOnMaster(MAT_REUSE_MATRIX, mumps));

2005:   /* numerical factorization phase */
2006:   mumps->id.job = JOB_FACTNUMERIC;
2007:   if (!mumps->id.ICNTL(18)) { /* A is centralized */
2008:     if (!mumps->myid) mumps->id.a = (MumpsScalar *)mumps->val;
2009:   } else {
2010:     mumps->id.a_loc = (MumpsScalar *)mumps->val;
2011:   }
2012:   PetscMUMPS_c(mumps);
2013:   if (mumps->id.INFOG(1) < 0) {
2014:     PetscCheck(!A->erroriffailure, PETSC_COMM_SELF, PETSC_ERR_LIB, "MUMPS error in numerical factorization: INFOG(1)=%d, INFO(2)=%d " MUMPS_MANUALS, mumps->id.INFOG(1), mumps->id.INFO(2));
2015:     if (mumps->id.INFOG(1) == -10) {
2016:       PetscCall(PetscInfo(F, "MUMPS error in numerical factorization: matrix is numerically singular, INFOG(1)=%d, INFO(2)=%d\n", mumps->id.INFOG(1), mumps->id.INFO(2)));
2017:       F->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
2018:     } else if (mumps->id.INFOG(1) == -13) {
2019:       PetscCall(PetscInfo(F, "MUMPS error in numerical factorization: INFOG(1)=%d, cannot allocate required memory %d megabytes\n", mumps->id.INFOG(1), mumps->id.INFO(2)));
2020:       F->factorerrortype = MAT_FACTOR_OUTMEMORY;
2021:     } else if (mumps->id.INFOG(1) == -8 || mumps->id.INFOG(1) == -9 || (-16 < mumps->id.INFOG(1) && mumps->id.INFOG(1) < -10)) {
2022:       PetscCall(PetscInfo(F, "MUMPS error in numerical factorizatione: INFOG(1)=%d, INFO(2)=%d, problem with work array\n", mumps->id.INFOG(1), mumps->id.INFO(2)));
2023:       F->factorerrortype = MAT_FACTOR_OUTMEMORY;
2024:     } else {
2025:       PetscCall(PetscInfo(F, "MUMPS error in numerical factorization: INFOG(1)=%d, INFO(2)=%d\n", mumps->id.INFOG(1), mumps->id.INFO(2)));
2026:       F->factorerrortype = MAT_FACTOR_OTHER;
2027:     }
2028:   }
2029:   PetscCheck(mumps->myid || mumps->id.ICNTL(16) <= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "MUMPS error in numerical factorization: ICNTL(16)=%d " MUMPS_MANUALS, mumps->id.INFOG(16));

2031:   F->assembled = PETSC_TRUE;

2033:   if (F->schur) { /* reset Schur status to unfactored */
2034: #if defined(PETSC_HAVE_CUDA)
2035:     F->schur->offloadmask = PETSC_OFFLOAD_CPU;
2036: #endif
2037:     if (mumps->id.ICNTL(19) == 1) { /* stored by rows */
2038:       mumps->id.ICNTL(19) = 2;
2039:       PetscCall(MatTranspose(F->schur, MAT_INPLACE_MATRIX, &F->schur));
2040:     }
2041:     PetscCall(MatFactorRestoreSchurComplement(F, NULL, MAT_FACTOR_SCHUR_UNFACTORED));
2042:   }

2044:   /* just to be sure that ICNTL(19) value returned by a call from MatMumpsGetIcntl is always consistent */
2045:   if (!mumps->sym && mumps->id.ICNTL(19) && mumps->id.ICNTL(19) != 1) mumps->id.ICNTL(19) = 3;

2047:   if (!mumps->is_omp_master) mumps->id.INFO(23) = 0;
2048:   if (mumps->petsc_size > 1) {
2049:     PetscInt     lsol_loc;
2050:     PetscScalar *sol_loc;

2052:     PetscCall(PetscObjectTypeCompare((PetscObject)A, MATMPIAIJ, &isMPIAIJ));

2054:     /* distributed solution; Create x_seq=sol_loc for repeated use */
2055:     if (mumps->x_seq) {
2056:       PetscCall(VecScatterDestroy(&mumps->scat_sol));
2057:       PetscCall(PetscFree2(mumps->id.sol_loc, mumps->id.isol_loc));
2058:       PetscCall(VecDestroy(&mumps->x_seq));
2059:     }
2060:     lsol_loc = mumps->id.INFO(23); /* length of sol_loc */
2061:     PetscCall(PetscMalloc2(lsol_loc, &sol_loc, lsol_loc, &mumps->id.isol_loc));
2062:     mumps->id.lsol_loc = lsol_loc;
2063:     mumps->id.sol_loc  = (MumpsScalar *)sol_loc;
2064:     PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, lsol_loc, sol_loc, &mumps->x_seq));
2065:   }
2066:   PetscCall(PetscLogFlops((double)mumps->id.RINFO(2)));
2067:   PetscFunctionReturn(PETSC_SUCCESS);
2068: }

2070: /* Sets MUMPS options from the options database */
2071: static PetscErrorCode MatSetFromOptions_MUMPS(Mat F, Mat A)
2072: {
2073:   Mat_MUMPS    *mumps = (Mat_MUMPS *)F->data;
2074:   PetscMUMPSInt icntl = 0, size, *listvar_schur;
2075:   PetscInt      info[80], i, ninfo = 80, rbs, cbs;
2076:   PetscBool     flg = PETSC_FALSE, schur = (PetscBool)(mumps->id.ICNTL(26) == -1);
2077:   MumpsScalar  *arr;

2079:   PetscFunctionBegin;
2080:   PetscOptionsBegin(PetscObjectComm((PetscObject)F), ((PetscObject)F)->prefix, "MUMPS Options", "Mat");
2081:   if (mumps->id.job == JOB_NULL) { /* MatSetFromOptions_MUMPS() has never been called before */
2082:     PetscInt nthreads   = 0;
2083:     PetscInt nCNTL_pre  = mumps->CNTL_pre ? mumps->CNTL_pre[0] : 0;
2084:     PetscInt nICNTL_pre = mumps->ICNTL_pre ? mumps->ICNTL_pre[0] : 0;

2086:     mumps->petsc_comm = PetscObjectComm((PetscObject)A);
2087:     PetscCallMPI(MPI_Comm_size(mumps->petsc_comm, &mumps->petsc_size));
2088:     PetscCallMPI(MPI_Comm_rank(mumps->petsc_comm, &mumps->myid)); /* "if (!myid)" still works even if mumps_comm is different */

2090:     PetscCall(PetscOptionsName("-mat_mumps_use_omp_threads", "Convert MPI processes into OpenMP threads", "None", &mumps->use_petsc_omp_support));
2091:     if (mumps->use_petsc_omp_support) nthreads = -1; /* -1 will let PetscOmpCtrlCreate() guess a proper value when user did not supply one */
2092:     /* do not use PetscOptionsInt() so that the option -mat_mumps_use_omp_threads is not displayed twice in the help */
2093:     PetscCall(PetscOptionsGetInt(NULL, ((PetscObject)F)->prefix, "-mat_mumps_use_omp_threads", &nthreads, NULL));
2094:     if (mumps->use_petsc_omp_support) {
2095:       PetscCheck(PetscDefined(HAVE_OPENMP_SUPPORT), PETSC_COMM_SELF, PETSC_ERR_SUP_SYS, "The system does not have PETSc OpenMP support but you added the -%smat_mumps_use_omp_threads option. Configure PETSc with --with-openmp --download-hwloc (or --with-hwloc) to enable it, see more in MATSOLVERMUMPS manual",
2096:                  ((PetscObject)F)->prefix ? ((PetscObject)F)->prefix : "");
2097:       PetscCheck(!schur, PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot use -%smat_mumps_use_omp_threads with the Schur complement feature", ((PetscObject)F)->prefix ? ((PetscObject)F)->prefix : "");
2098: #if defined(PETSC_HAVE_OPENMP_SUPPORT)
2099:       PetscCall(PetscOmpCtrlCreate(mumps->petsc_comm, nthreads, &mumps->omp_ctrl));
2100:       PetscCall(PetscOmpCtrlGetOmpComms(mumps->omp_ctrl, &mumps->omp_comm, &mumps->mumps_comm, &mumps->is_omp_master));
2101: #endif
2102:     } else {
2103:       mumps->omp_comm      = PETSC_COMM_SELF;
2104:       mumps->mumps_comm    = mumps->petsc_comm;
2105:       mumps->is_omp_master = PETSC_TRUE;
2106:     }
2107:     PetscCallMPI(MPI_Comm_size(mumps->omp_comm, &mumps->omp_comm_size));
2108:     mumps->reqs = NULL;
2109:     mumps->tag  = 0;

2111:     if (mumps->mumps_comm != MPI_COMM_NULL) {
2112:       if (PetscDefined(HAVE_OPENMP_SUPPORT) && mumps->use_petsc_omp_support) {
2113:         /* It looks like MUMPS does not dup the input comm. Dup a new comm for MUMPS to avoid any tag mismatches. */
2114:         MPI_Comm comm;
2115:         PetscCallMPI(MPI_Comm_dup(mumps->mumps_comm, &comm));
2116:         mumps->mumps_comm = comm;
2117:       } else PetscCall(PetscCommGetComm(mumps->petsc_comm, &mumps->mumps_comm));
2118:     }

2120:     mumps->id.comm_fortran = MPI_Comm_c2f(mumps->mumps_comm);
2121:     mumps->id.job          = JOB_INIT;
2122:     mumps->id.par          = 1; /* host participates factorizaton and solve */
2123:     mumps->id.sym          = mumps->sym;

2125:     size          = mumps->id.size_schur;
2126:     arr           = mumps->id.schur;
2127:     listvar_schur = mumps->id.listvar_schur;
2128:     PetscMUMPS_c(mumps);
2129:     PetscCheck(mumps->id.INFOG(1) >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "MUMPS error: INFOG(1)=%d " MUMPS_MANUALS, mumps->id.INFOG(1));

2131:     /* set PETSc-MUMPS default options - override MUMPS default */
2132:     mumps->id.ICNTL(3) = 0;
2133:     mumps->id.ICNTL(4) = 0;
2134:     if (mumps->petsc_size == 1) {
2135:       mumps->id.ICNTL(18) = 0; /* centralized assembled matrix input */
2136:       mumps->id.ICNTL(7)  = 7; /* automatic choice of ordering done by the package */
2137:     } else {
2138:       mumps->id.ICNTL(18) = 3; /* distributed assembled matrix input */
2139:       mumps->id.ICNTL(21) = 1; /* distributed solution */
2140:     }

2142:     /* restore cached ICNTL and CNTL values */
2143:     for (icntl = 0; icntl < nICNTL_pre; ++icntl) mumps->id.ICNTL(mumps->ICNTL_pre[1 + 2 * icntl]) = mumps->ICNTL_pre[2 + 2 * icntl];
2144:     for (icntl = 0; icntl < nCNTL_pre; ++icntl) mumps->id.CNTL((PetscInt)mumps->CNTL_pre[1 + 2 * icntl]) = mumps->CNTL_pre[2 + 2 * icntl];
2145:     PetscCall(PetscFree(mumps->ICNTL_pre));
2146:     PetscCall(PetscFree(mumps->CNTL_pre));

2148:     if (schur) {
2149:       mumps->id.size_schur    = size;
2150:       mumps->id.schur_lld     = size;
2151:       mumps->id.schur         = arr;
2152:       mumps->id.listvar_schur = listvar_schur;
2153:       if (mumps->petsc_size > 1) {
2154:         PetscBool gs; /* gs is false if any rank other than root has non-empty IS */

2156:         mumps->id.ICNTL(19) = 1;                                                                            /* MUMPS returns Schur centralized on the host */
2157:         gs                  = mumps->myid ? (mumps->id.size_schur ? PETSC_FALSE : PETSC_TRUE) : PETSC_TRUE; /* always true on root; false on others if their size != 0 */
2158:         PetscCall(MPIU_Allreduce(MPI_IN_PLACE, &gs, 1, MPIU_BOOL, MPI_LAND, mumps->petsc_comm));
2159:         PetscCheck(gs, PETSC_COMM_SELF, PETSC_ERR_SUP, "MUMPS distributed parallel Schur complements not yet supported from PETSc");
2160:       } else {
2161:         if (F->factortype == MAT_FACTOR_LU) {
2162:           mumps->id.ICNTL(19) = 3; /* MUMPS returns full matrix */
2163:         } else {
2164:           mumps->id.ICNTL(19) = 2; /* MUMPS returns lower triangular part */
2165:         }
2166:       }
2167:       mumps->id.ICNTL(26) = -1;
2168:     }

2170:     /* copy MUMPS default control values from master to slaves. Although slaves do not call MUMPS, they may access these values in code.
2171:        For example, ICNTL(9) is initialized to 1 by MUMPS and slaves check ICNTL(9) in MatSolve_MUMPS.
2172:      */
2173:     PetscCallMPI(MPI_Bcast(mumps->id.icntl, 40, MPI_INT, 0, mumps->omp_comm));
2174:     PetscCallMPI(MPI_Bcast(mumps->id.cntl, 15, MPIU_REAL, 0, mumps->omp_comm));

2176:     mumps->scat_rhs = NULL;
2177:     mumps->scat_sol = NULL;
2178:   }
2179:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_1", "ICNTL(1): output stream for error messages", "None", mumps->id.ICNTL(1), &icntl, &flg));
2180:   if (flg) mumps->id.ICNTL(1) = icntl;
2181:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_2", "ICNTL(2): output stream for diagnostic printing, statistics, and warning", "None", mumps->id.ICNTL(2), &icntl, &flg));
2182:   if (flg) mumps->id.ICNTL(2) = icntl;
2183:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_3", "ICNTL(3): output stream for global information, collected on the host", "None", mumps->id.ICNTL(3), &icntl, &flg));
2184:   if (flg) mumps->id.ICNTL(3) = icntl;

2186:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_4", "ICNTL(4): level of printing (0 to 4)", "None", mumps->id.ICNTL(4), &icntl, &flg));
2187:   if (flg) mumps->id.ICNTL(4) = icntl;
2188:   if (mumps->id.ICNTL(4) || PetscLogPrintInfo) mumps->id.ICNTL(3) = 6; /* resume MUMPS default id.ICNTL(3) = 6 */

2190:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_6", "ICNTL(6): permutes to a zero-free diagonal and/or scale the matrix (0 to 7)", "None", mumps->id.ICNTL(6), &icntl, &flg));
2191:   if (flg) mumps->id.ICNTL(6) = icntl;

2193:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_7", "ICNTL(7): computes a symmetric permutation in sequential analysis. 0=AMD, 2=AMF, 3=Scotch, 4=PORD, 5=Metis, 6=QAMD, and 7=auto(default)", "None", mumps->id.ICNTL(7), &icntl, &flg));
2194:   if (flg) {
2195:     PetscCheck(icntl != 1 && icntl >= 0 && icntl <= 7, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Valid values are 0=AMD, 2=AMF, 3=Scotch, 4=PORD, 5=Metis, 6=QAMD, and 7=auto");
2196:     mumps->id.ICNTL(7) = icntl;
2197:   }

2199:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_8", "ICNTL(8): scaling strategy (-2 to 8 or 77)", "None", mumps->id.ICNTL(8), &mumps->id.ICNTL(8), NULL));
2200:   /* PetscCall(PetscOptionsInt("-mat_mumps_icntl_9","ICNTL(9): computes the solution using A or A^T","None",mumps->id.ICNTL(9),&mumps->id.ICNTL(9),NULL)); handled by MatSolveTranspose_MUMPS() */
2201:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_10", "ICNTL(10): max num of refinements", "None", mumps->id.ICNTL(10), &mumps->id.ICNTL(10), NULL));
2202:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_11", "ICNTL(11): statistics related to an error analysis (via -ksp_view)", "None", mumps->id.ICNTL(11), &mumps->id.ICNTL(11), NULL));
2203:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_12", "ICNTL(12): an ordering strategy for symmetric matrices (0 to 3)", "None", mumps->id.ICNTL(12), &mumps->id.ICNTL(12), NULL));
2204:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_13", "ICNTL(13): parallelism of the root node (enable ScaLAPACK) and its splitting", "None", mumps->id.ICNTL(13), &mumps->id.ICNTL(13), NULL));
2205:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_14", "ICNTL(14): percentage increase in the estimated working space", "None", mumps->id.ICNTL(14), &mumps->id.ICNTL(14), NULL));
2206:   PetscCall(MatGetBlockSizes(A, &rbs, &cbs));
2207:   if (rbs == cbs && rbs > 1) mumps->id.ICNTL(15) = -rbs;
2208:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_15", "ICNTL(15): compression of the input matrix resulting from a block format", "None", mumps->id.ICNTL(15), &mumps->id.ICNTL(15), &flg));
2209:   if (flg) {
2210:     PetscCheck(mumps->id.ICNTL(15) <= 0, PETSC_COMM_SELF, PETSC_ERR_SUP, "Positive -mat_mumps_icntl_15 not handled");
2211:     PetscCheck((-mumps->id.ICNTL(15) % cbs == 0) && (-mumps->id.ICNTL(15) % rbs == 0), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The opposite of -mat_mumps_icntl_15 must be a multiple of the column and row blocksizes");
2212:   }
2213:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_19", "ICNTL(19): computes the Schur complement", "None", mumps->id.ICNTL(19), &mumps->id.ICNTL(19), NULL));
2214:   if (mumps->id.ICNTL(19) <= 0 || mumps->id.ICNTL(19) > 3) { /* reset any schur data (if any) */
2215:     PetscCall(MatDestroy(&F->schur));
2216:     PetscCall(MatMumpsResetSchur_Private(mumps));
2217:   }

2219:   /* Two MPICH Fortran MPI_IN_PLACE binding bugs prevented the use of 'mpich + mumps'. One happened with "mpi4py + mpich + mumps",
2220:      and was reported by Firedrake. See https://bitbucket.org/mpi4py/mpi4py/issues/162/mpi4py-initialization-breaks-fortran
2221:      and a petsc-maint mailing list thread with subject 'MUMPS segfaults in parallel because of ...'
2222:      This bug was fixed by https://github.com/pmodels/mpich/pull/4149. But the fix brought a new bug,
2223:      see https://github.com/pmodels/mpich/issues/5589. This bug was fixed by https://github.com/pmodels/mpich/pull/5590.
2224:      In short, we could not use distributed RHS until with MPICH v4.0b1 or we enabled a workaround in mumps-5.6.2+
2225:    */
2226: #if PETSC_PKG_MUMPS_VERSION_GE(5, 6, 2) && defined(PETSC_HAVE_MUMPS_AVOID_MPI_IN_PLACE)
2227:   mumps->ICNTL20 = 10;
2228: #elif PETSC_PKG_MUMPS_VERSION_LT(5, 3, 0) || (defined(PETSC_HAVE_MPICH_NUMVERSION) && (PETSC_HAVE_MPICH_NUMVERSION < 40000101))
2229:   mumps->ICNTL20 = 0; /* Centralized dense RHS*/
2230: #else
2231:   mumps->ICNTL20 = 10; /* Distributed dense RHS*/
2232: #endif
2233:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_20", "ICNTL(20): give mumps centralized (0) or distributed (10) dense right-hand sides", "None", mumps->ICNTL20, &mumps->ICNTL20, &flg));
2234:   PetscCheck(!flg || mumps->ICNTL20 == 10 || mumps->ICNTL20 == 0, PETSC_COMM_SELF, PETSC_ERR_SUP, "ICNTL(20)=%d is not supported by the PETSc/MUMPS interface. Allowed values are 0, 10", (int)mumps->ICNTL20);
2235: #if PETSC_PKG_MUMPS_VERSION_LT(5, 3, 0)
2236:   PetscCheck(!flg || mumps->ICNTL20 != 10, PETSC_COMM_SELF, PETSC_ERR_SUP, "ICNTL(20)=10 is not supported before MUMPS-5.3.0");
2237: #endif
2238:   /* PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_21","ICNTL(21): the distribution (centralized or distributed) of the solution vectors","None",mumps->id.ICNTL(21),&mumps->id.ICNTL(21),NULL)); we only use distributed solution vector */

2240:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_22", "ICNTL(22): in-core/out-of-core factorization and solve (0 or 1)", "None", mumps->id.ICNTL(22), &mumps->id.ICNTL(22), NULL));
2241:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_23", "ICNTL(23): max size of the working memory (MB) that can allocate per processor", "None", mumps->id.ICNTL(23), &mumps->id.ICNTL(23), NULL));
2242:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_24", "ICNTL(24): detection of null pivot rows (0 or 1)", "None", mumps->id.ICNTL(24), &mumps->id.ICNTL(24), NULL));
2243:   if (mumps->id.ICNTL(24)) { mumps->id.ICNTL(13) = 1; /* turn-off ScaLAPACK to help with the correct detection of null pivots */ }

2245:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_25", "ICNTL(25): computes a solution of a deficient matrix and a null space basis", "None", mumps->id.ICNTL(25), &mumps->id.ICNTL(25), NULL));
2246:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_26", "ICNTL(26): drives the solution phase if a Schur complement matrix", "None", mumps->id.ICNTL(26), &mumps->id.ICNTL(26), NULL));
2247:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_27", "ICNTL(27): controls the blocking size for multiple right-hand sides", "None", mumps->id.ICNTL(27), &mumps->id.ICNTL(27), NULL));
2248:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_28", "ICNTL(28): use 1 for sequential analysis and ICNTL(7) ordering, or 2 for parallel analysis and ICNTL(29) ordering", "None", mumps->id.ICNTL(28), &mumps->id.ICNTL(28), NULL));
2249:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_29", "ICNTL(29): parallel ordering 1 = ptscotch, 2 = parmetis", "None", mumps->id.ICNTL(29), &mumps->id.ICNTL(29), NULL));
2250:   /* PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_30","ICNTL(30): compute user-specified set of entries in inv(A)","None",mumps->id.ICNTL(30),&mumps->id.ICNTL(30),NULL)); */ /* call MatMumpsGetInverse() directly */
2251:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_31", "ICNTL(31): indicates which factors may be discarded during factorization", "None", mumps->id.ICNTL(31), &mumps->id.ICNTL(31), NULL));
2252:   /* PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_32","ICNTL(32): performs the forward elimination of the right-hand sides during factorization","None",mumps->id.ICNTL(32),&mumps->id.ICNTL(32),NULL));  -- not supported by PETSc API */
2253:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_33", "ICNTL(33): compute determinant", "None", mumps->id.ICNTL(33), &mumps->id.ICNTL(33), NULL));
2254:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_35", "ICNTL(35): activates Block Low Rank (BLR) based factorization", "None", mumps->id.ICNTL(35), &mumps->id.ICNTL(35), NULL));
2255:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_36", "ICNTL(36): choice of BLR factorization variant", "None", mumps->id.ICNTL(36), &mumps->id.ICNTL(36), NULL));
2256:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_38", "ICNTL(38): estimated compression rate of LU factors with BLR", "None", mumps->id.ICNTL(38), &mumps->id.ICNTL(38), NULL));
2257:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_58", "ICNTL(58): defines options for symbolic factorization", "None", mumps->id.ICNTL(58), &mumps->id.ICNTL(58), NULL));

2259:   PetscCall(PetscOptionsReal("-mat_mumps_cntl_1", "CNTL(1): relative pivoting threshold", "None", mumps->id.CNTL(1), &mumps->id.CNTL(1), NULL));
2260:   PetscCall(PetscOptionsReal("-mat_mumps_cntl_2", "CNTL(2): stopping criterion of refinement", "None", mumps->id.CNTL(2), &mumps->id.CNTL(2), NULL));
2261:   PetscCall(PetscOptionsReal("-mat_mumps_cntl_3", "CNTL(3): absolute pivoting threshold", "None", mumps->id.CNTL(3), &mumps->id.CNTL(3), NULL));
2262:   PetscCall(PetscOptionsReal("-mat_mumps_cntl_4", "CNTL(4): value for static pivoting", "None", mumps->id.CNTL(4), &mumps->id.CNTL(4), NULL));
2263:   PetscCall(PetscOptionsReal("-mat_mumps_cntl_5", "CNTL(5): fixation for null pivots", "None", mumps->id.CNTL(5), &mumps->id.CNTL(5), NULL));
2264:   PetscCall(PetscOptionsReal("-mat_mumps_cntl_7", "CNTL(7): dropping parameter used during BLR", "None", mumps->id.CNTL(7), &mumps->id.CNTL(7), NULL));

2266:   PetscCall(PetscOptionsString("-mat_mumps_ooc_tmpdir", "out of core directory", "None", mumps->id.ooc_tmpdir, mumps->id.ooc_tmpdir, sizeof(mumps->id.ooc_tmpdir), NULL));

2268:   PetscCall(PetscOptionsIntArray("-mat_mumps_view_info", "request INFO local to each processor", "", info, &ninfo, NULL));
2269:   if (ninfo) {
2270:     PetscCheck(ninfo <= 80, PETSC_COMM_SELF, PETSC_ERR_USER, "number of INFO %" PetscInt_FMT " must <= 80", ninfo);
2271:     PetscCall(PetscMalloc1(ninfo, &mumps->info));
2272:     mumps->ninfo = ninfo;
2273:     for (i = 0; i < ninfo; i++) {
2274:       PetscCheck(info[i] >= 0 && info[i] <= 80, PETSC_COMM_SELF, PETSC_ERR_USER, "index of INFO %" PetscInt_FMT " must between 1 and 80", ninfo);
2275:       mumps->info[i] = info[i];
2276:     }
2277:   }
2278:   PetscOptionsEnd();
2279:   PetscFunctionReturn(PETSC_SUCCESS);
2280: }

2282: static PetscErrorCode MatFactorSymbolic_MUMPS_ReportIfError(Mat F, Mat A, PETSC_UNUSED const MatFactorInfo *info, Mat_MUMPS *mumps)
2283: {
2284:   PetscFunctionBegin;
2285:   if (mumps->id.INFOG(1) < 0) {
2286:     PetscCheck(!A->erroriffailure, PETSC_COMM_SELF, PETSC_ERR_LIB, "MUMPS error in analysis: INFOG(1)=%d " MUMPS_MANUALS, mumps->id.INFOG(1));
2287:     if (mumps->id.INFOG(1) == -6) {
2288:       PetscCall(PetscInfo(F, "MUMPS error in analysis: matrix is singular, INFOG(1)=%d, INFO(2)=%d\n", mumps->id.INFOG(1), mumps->id.INFO(2)));
2289:       F->factorerrortype = MAT_FACTOR_STRUCT_ZEROPIVOT;
2290:     } else if (mumps->id.INFOG(1) == -5 || mumps->id.INFOG(1) == -7) {
2291:       PetscCall(PetscInfo(F, "MUMPS error in analysis: problem with work array, INFOG(1)=%d, INFO(2)=%d\n", mumps->id.INFOG(1), mumps->id.INFO(2)));
2292:       F->factorerrortype = MAT_FACTOR_OUTMEMORY;
2293:     } else if (mumps->id.INFOG(1) == -16 && mumps->id.INFOG(1) == 0) {
2294:       PetscCall(PetscInfo(F, "MUMPS error in analysis: empty matrix\n"));
2295:     } else {
2296:       PetscCall(PetscInfo(F, "MUMPS error in analysis: INFOG(1)=%d, INFO(2)=%d " MUMPS_MANUALS "\n", mumps->id.INFOG(1), mumps->id.INFO(2)));
2297:       F->factorerrortype = MAT_FACTOR_OTHER;
2298:     }
2299:   }
2300:   PetscFunctionReturn(PETSC_SUCCESS);
2301: }

2303: static PetscErrorCode MatLUFactorSymbolic_AIJMUMPS(Mat F, Mat A, IS r, PETSC_UNUSED IS c, const MatFactorInfo *info)
2304: {
2305:   Mat_MUMPS     *mumps = (Mat_MUMPS *)F->data;
2306:   Vec            b;
2307:   const PetscInt M = A->rmap->N;

2309:   PetscFunctionBegin;
2310:   if (mumps->matstruc == SAME_NONZERO_PATTERN) {
2311:     /* F is assembled by a previous call of MatLUFactorSymbolic_AIJMUMPS() */
2312:     PetscFunctionReturn(PETSC_SUCCESS);
2313:   }

2315:   /* Set MUMPS options from the options database */
2316:   PetscCall(MatSetFromOptions_MUMPS(F, A));

2318:   PetscCall((*mumps->ConvertToTriples)(A, 1, MAT_INITIAL_MATRIX, mumps));
2319:   PetscCall(MatMumpsGatherNonzerosOnMaster(MAT_INITIAL_MATRIX, mumps));

2321:   /* analysis phase */
2322:   mumps->id.job = JOB_FACTSYMBOLIC;
2323:   mumps->id.n   = M;
2324:   switch (mumps->id.ICNTL(18)) {
2325:   case 0: /* centralized assembled matrix input */
2326:     if (!mumps->myid) {
2327:       mumps->id.nnz = mumps->nnz;
2328:       mumps->id.irn = mumps->irn;
2329:       mumps->id.jcn = mumps->jcn;
2330:       if (mumps->id.ICNTL(6) > 1) mumps->id.a = (MumpsScalar *)mumps->val;
2331:       if (r && mumps->id.ICNTL(7) == 7) {
2332:         mumps->id.ICNTL(7) = 1;
2333:         if (!mumps->myid) {
2334:           const PetscInt *idx;
2335:           PetscInt        i;

2337:           PetscCall(PetscMalloc1(M, &mumps->id.perm_in));
2338:           PetscCall(ISGetIndices(r, &idx));
2339:           for (i = 0; i < M; i++) PetscCall(PetscMUMPSIntCast(idx[i] + 1, &mumps->id.perm_in[i])); /* perm_in[]: start from 1, not 0! */
2340:           PetscCall(ISRestoreIndices(r, &idx));
2341:         }
2342:       }
2343:     }
2344:     break;
2345:   case 3: /* distributed assembled matrix input (size>1) */
2346:     mumps->id.nnz_loc = mumps->nnz;
2347:     mumps->id.irn_loc = mumps->irn;
2348:     mumps->id.jcn_loc = mumps->jcn;
2349:     if (mumps->id.ICNTL(6) > 1) mumps->id.a_loc = (MumpsScalar *)mumps->val;
2350:     if (mumps->ICNTL20 == 0) { /* Centralized rhs. Create scatter scat_rhs for repeated use in MatSolve() */
2351:       PetscCall(MatCreateVecs(A, NULL, &b));
2352:       PetscCall(VecScatterCreateToZero(b, &mumps->scat_rhs, &mumps->b_seq));
2353:       PetscCall(VecDestroy(&b));
2354:     }
2355:     break;
2356:   }
2357:   PetscMUMPS_c(mumps);
2358:   PetscCall(MatFactorSymbolic_MUMPS_ReportIfError(F, A, info, mumps));

2360:   F->ops->lufactornumeric   = MatFactorNumeric_MUMPS;
2361:   F->ops->solve             = MatSolve_MUMPS;
2362:   F->ops->solvetranspose    = MatSolveTranspose_MUMPS;
2363:   F->ops->matsolve          = MatMatSolve_MUMPS;
2364:   F->ops->mattransposesolve = MatMatTransposeSolve_MUMPS;
2365:   F->ops->matsolvetranspose = MatMatSolveTranspose_MUMPS;

2367:   mumps->matstruc = SAME_NONZERO_PATTERN;
2368:   PetscFunctionReturn(PETSC_SUCCESS);
2369: }

2371: /* Note the Petsc r and c permutations are ignored */
2372: static PetscErrorCode MatLUFactorSymbolic_BAIJMUMPS(Mat F, Mat A, PETSC_UNUSED IS r, PETSC_UNUSED IS c, const MatFactorInfo *info)
2373: {
2374:   Mat_MUMPS     *mumps = (Mat_MUMPS *)F->data;
2375:   Vec            b;
2376:   const PetscInt M = A->rmap->N;

2378:   PetscFunctionBegin;
2379:   if (mumps->matstruc == SAME_NONZERO_PATTERN) {
2380:     /* F is assembled by a previous call of MatLUFactorSymbolic_BAIJMUMPS() */
2381:     PetscFunctionReturn(PETSC_SUCCESS);
2382:   }

2384:   /* Set MUMPS options from the options database */
2385:   PetscCall(MatSetFromOptions_MUMPS(F, A));

2387:   PetscCall((*mumps->ConvertToTriples)(A, 1, MAT_INITIAL_MATRIX, mumps));
2388:   PetscCall(MatMumpsGatherNonzerosOnMaster(MAT_INITIAL_MATRIX, mumps));

2390:   /* analysis phase */
2391:   mumps->id.job = JOB_FACTSYMBOLIC;
2392:   mumps->id.n   = M;
2393:   switch (mumps->id.ICNTL(18)) {
2394:   case 0: /* centralized assembled matrix input */
2395:     if (!mumps->myid) {
2396:       mumps->id.nnz = mumps->nnz;
2397:       mumps->id.irn = mumps->irn;
2398:       mumps->id.jcn = mumps->jcn;
2399:       if (mumps->id.ICNTL(6) > 1) mumps->id.a = (MumpsScalar *)mumps->val;
2400:     }
2401:     break;
2402:   case 3: /* distributed assembled matrix input (size>1) */
2403:     mumps->id.nnz_loc = mumps->nnz;
2404:     mumps->id.irn_loc = mumps->irn;
2405:     mumps->id.jcn_loc = mumps->jcn;
2406:     if (mumps->id.ICNTL(6) > 1) mumps->id.a_loc = (MumpsScalar *)mumps->val;
2407:     if (mumps->ICNTL20 == 0) { /* Centralized rhs. Create scatter scat_rhs for repeated use in MatSolve() */
2408:       PetscCall(MatCreateVecs(A, NULL, &b));
2409:       PetscCall(VecScatterCreateToZero(b, &mumps->scat_rhs, &mumps->b_seq));
2410:       PetscCall(VecDestroy(&b));
2411:     }
2412:     break;
2413:   }
2414:   PetscMUMPS_c(mumps);
2415:   PetscCall(MatFactorSymbolic_MUMPS_ReportIfError(F, A, info, mumps));

2417:   F->ops->lufactornumeric   = MatFactorNumeric_MUMPS;
2418:   F->ops->solve             = MatSolve_MUMPS;
2419:   F->ops->solvetranspose    = MatSolveTranspose_MUMPS;
2420:   F->ops->matsolvetranspose = MatMatSolveTranspose_MUMPS;

2422:   mumps->matstruc = SAME_NONZERO_PATTERN;
2423:   PetscFunctionReturn(PETSC_SUCCESS);
2424: }

2426: /* Note the Petsc r permutation and factor info are ignored */
2427: static PetscErrorCode MatCholeskyFactorSymbolic_MUMPS(Mat F, Mat A, PETSC_UNUSED IS r, const MatFactorInfo *info)
2428: {
2429:   Mat_MUMPS     *mumps = (Mat_MUMPS *)F->data;
2430:   Vec            b;
2431:   const PetscInt M = A->rmap->N;

2433:   PetscFunctionBegin;
2434:   if (mumps->matstruc == SAME_NONZERO_PATTERN) {
2435:     /* F is assembled by a previous call of MatCholeskyFactorSymbolic_MUMPS() */
2436:     PetscFunctionReturn(PETSC_SUCCESS);
2437:   }

2439:   /* Set MUMPS options from the options database */
2440:   PetscCall(MatSetFromOptions_MUMPS(F, A));

2442:   PetscCall((*mumps->ConvertToTriples)(A, 1, MAT_INITIAL_MATRIX, mumps));
2443:   PetscCall(MatMumpsGatherNonzerosOnMaster(MAT_INITIAL_MATRIX, mumps));

2445:   /* analysis phase */
2446:   mumps->id.job = JOB_FACTSYMBOLIC;
2447:   mumps->id.n   = M;
2448:   switch (mumps->id.ICNTL(18)) {
2449:   case 0: /* centralized assembled matrix input */
2450:     if (!mumps->myid) {
2451:       mumps->id.nnz = mumps->nnz;
2452:       mumps->id.irn = mumps->irn;
2453:       mumps->id.jcn = mumps->jcn;
2454:       if (mumps->id.ICNTL(6) > 1) mumps->id.a = (MumpsScalar *)mumps->val;
2455:     }
2456:     break;
2457:   case 3: /* distributed assembled matrix input (size>1) */
2458:     mumps->id.nnz_loc = mumps->nnz;
2459:     mumps->id.irn_loc = mumps->irn;
2460:     mumps->id.jcn_loc = mumps->jcn;
2461:     if (mumps->id.ICNTL(6) > 1) mumps->id.a_loc = (MumpsScalar *)mumps->val;
2462:     if (mumps->ICNTL20 == 0) { /* Centralized rhs. Create scatter scat_rhs for repeated use in MatSolve() */
2463:       PetscCall(MatCreateVecs(A, NULL, &b));
2464:       PetscCall(VecScatterCreateToZero(b, &mumps->scat_rhs, &mumps->b_seq));
2465:       PetscCall(VecDestroy(&b));
2466:     }
2467:     break;
2468:   }
2469:   PetscMUMPS_c(mumps);
2470:   PetscCall(MatFactorSymbolic_MUMPS_ReportIfError(F, A, info, mumps));

2472:   F->ops->choleskyfactornumeric = MatFactorNumeric_MUMPS;
2473:   F->ops->solve                 = MatSolve_MUMPS;
2474:   F->ops->solvetranspose        = MatSolve_MUMPS;
2475:   F->ops->matsolve              = MatMatSolve_MUMPS;
2476:   F->ops->mattransposesolve     = MatMatTransposeSolve_MUMPS;
2477:   F->ops->matsolvetranspose     = MatMatSolveTranspose_MUMPS;
2478: #if defined(PETSC_USE_COMPLEX)
2479:   F->ops->getinertia = NULL;
2480: #else
2481:   F->ops->getinertia = MatGetInertia_SBAIJMUMPS;
2482: #endif

2484:   mumps->matstruc = SAME_NONZERO_PATTERN;
2485:   PetscFunctionReturn(PETSC_SUCCESS);
2486: }

2488: static PetscErrorCode MatView_MUMPS(Mat A, PetscViewer viewer)
2489: {
2490:   PetscBool         iascii;
2491:   PetscViewerFormat format;
2492:   Mat_MUMPS        *mumps = (Mat_MUMPS *)A->data;

2494:   PetscFunctionBegin;
2495:   /* check if matrix is mumps type */
2496:   if (A->ops->solve != MatSolve_MUMPS) PetscFunctionReturn(PETSC_SUCCESS);

2498:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
2499:   if (iascii) {
2500:     PetscCall(PetscViewerGetFormat(viewer, &format));
2501:     if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
2502:       PetscCall(PetscViewerASCIIPrintf(viewer, "MUMPS run parameters:\n"));
2503:       if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
2504:         PetscCall(PetscViewerASCIIPrintf(viewer, "  SYM (matrix type):                   %d\n", mumps->id.sym));
2505:         PetscCall(PetscViewerASCIIPrintf(viewer, "  PAR (host participation):            %d\n", mumps->id.par));
2506:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(1) (output for error):         %d\n", mumps->id.ICNTL(1)));
2507:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(2) (output of diagnostic msg): %d\n", mumps->id.ICNTL(2)));
2508:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(3) (output for global info):   %d\n", mumps->id.ICNTL(3)));
2509:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(4) (level of printing):        %d\n", mumps->id.ICNTL(4)));
2510:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(5) (input mat struct):         %d\n", mumps->id.ICNTL(5)));
2511:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(6) (matrix prescaling):        %d\n", mumps->id.ICNTL(6)));
2512:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(7) (sequential matrix ordering):%d\n", mumps->id.ICNTL(7)));
2513:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(8) (scaling strategy):         %d\n", mumps->id.ICNTL(8)));
2514:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(10) (max num of refinements):  %d\n", mumps->id.ICNTL(10)));
2515:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(11) (error analysis):          %d\n", mumps->id.ICNTL(11)));
2516:         if (mumps->id.ICNTL(11) > 0) {
2517:           PetscCall(PetscViewerASCIIPrintf(viewer, "    RINFOG(4) (inf norm of input mat):        %g\n", (double)mumps->id.RINFOG(4)));
2518:           PetscCall(PetscViewerASCIIPrintf(viewer, "    RINFOG(5) (inf norm of solution):         %g\n", (double)mumps->id.RINFOG(5)));
2519:           PetscCall(PetscViewerASCIIPrintf(viewer, "    RINFOG(6) (inf norm of residual):         %g\n", (double)mumps->id.RINFOG(6)));
2520:           PetscCall(PetscViewerASCIIPrintf(viewer, "    RINFOG(7),RINFOG(8) (backward error est): %g, %g\n", (double)mumps->id.RINFOG(7), (double)mumps->id.RINFOG(8)));
2521:           PetscCall(PetscViewerASCIIPrintf(viewer, "    RINFOG(9) (error estimate):               %g\n", (double)mumps->id.RINFOG(9)));
2522:           PetscCall(PetscViewerASCIIPrintf(viewer, "    RINFOG(10),RINFOG(11)(condition numbers): %g, %g\n", (double)mumps->id.RINFOG(10), (double)mumps->id.RINFOG(11)));
2523:         }
2524:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(12) (efficiency control):                         %d\n", mumps->id.ICNTL(12)));
2525:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(13) (sequential factorization of the root node):  %d\n", mumps->id.ICNTL(13)));
2526:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(14) (percentage of estimated workspace increase): %d\n", mumps->id.ICNTL(14)));
2527:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(15) (compression of the input matrix):            %d\n", mumps->id.ICNTL(15)));
2528:         /* ICNTL(15-17) not used */
2529:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(18) (input mat struct):                           %d\n", mumps->id.ICNTL(18)));
2530:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(19) (Schur complement info):                      %d\n", mumps->id.ICNTL(19)));
2531:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(20) (RHS sparse pattern):                         %d\n", mumps->id.ICNTL(20)));
2532:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(21) (solution struct):                            %d\n", mumps->id.ICNTL(21)));
2533:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(22) (in-core/out-of-core facility):               %d\n", mumps->id.ICNTL(22)));
2534:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(23) (max size of memory can be allocated locally):%d\n", mumps->id.ICNTL(23)));

2536:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(24) (detection of null pivot rows):               %d\n", mumps->id.ICNTL(24)));
2537:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(25) (computation of a null space basis):          %d\n", mumps->id.ICNTL(25)));
2538:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(26) (Schur options for RHS or solution):          %d\n", mumps->id.ICNTL(26)));
2539:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(27) (blocking size for multiple RHS):             %d\n", mumps->id.ICNTL(27)));
2540:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(28) (use parallel or sequential ordering):        %d\n", mumps->id.ICNTL(28)));
2541:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(29) (parallel ordering):                          %d\n", mumps->id.ICNTL(29)));

2543:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(30) (user-specified set of entries in inv(A)):    %d\n", mumps->id.ICNTL(30)));
2544:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(31) (factors is discarded in the solve phase):    %d\n", mumps->id.ICNTL(31)));
2545:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(33) (compute determinant):                        %d\n", mumps->id.ICNTL(33)));
2546:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(35) (activate BLR based factorization):           %d\n", mumps->id.ICNTL(35)));
2547:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(36) (choice of BLR factorization variant):        %d\n", mumps->id.ICNTL(36)));
2548:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(38) (estimated compression rate of LU factors):   %d\n", mumps->id.ICNTL(38)));
2549:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(58) (options for symbolic factorization):         %d\n", mumps->id.ICNTL(58)));

2551:         PetscCall(PetscViewerASCIIPrintf(viewer, "  CNTL(1) (relative pivoting threshold):      %g\n", (double)mumps->id.CNTL(1)));
2552:         PetscCall(PetscViewerASCIIPrintf(viewer, "  CNTL(2) (stopping criterion of refinement): %g\n", (double)mumps->id.CNTL(2)));
2553:         PetscCall(PetscViewerASCIIPrintf(viewer, "  CNTL(3) (absolute pivoting threshold):      %g\n", (double)mumps->id.CNTL(3)));
2554:         PetscCall(PetscViewerASCIIPrintf(viewer, "  CNTL(4) (value of static pivoting):         %g\n", (double)mumps->id.CNTL(4)));
2555:         PetscCall(PetscViewerASCIIPrintf(viewer, "  CNTL(5) (fixation for null pivots):         %g\n", (double)mumps->id.CNTL(5)));
2556:         PetscCall(PetscViewerASCIIPrintf(viewer, "  CNTL(7) (dropping parameter for BLR):       %g\n", (double)mumps->id.CNTL(7)));

2558:         /* information local to each processor */
2559:         PetscCall(PetscViewerASCIIPrintf(viewer, "  RINFO(1) (local estimated flops for the elimination after analysis):\n"));
2560:         PetscCall(PetscViewerASCIIPushSynchronized(viewer));
2561:         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %g\n", mumps->myid, (double)mumps->id.RINFO(1)));
2562:         PetscCall(PetscViewerFlush(viewer));
2563:         PetscCall(PetscViewerASCIIPrintf(viewer, "  RINFO(2) (local estimated flops for the assembly after factorization):\n"));
2564:         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %g\n", mumps->myid, (double)mumps->id.RINFO(2)));
2565:         PetscCall(PetscViewerFlush(viewer));
2566:         PetscCall(PetscViewerASCIIPrintf(viewer, "  RINFO(3) (local estimated flops for the elimination after factorization):\n"));
2567:         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %g\n", mumps->myid, (double)mumps->id.RINFO(3)));
2568:         PetscCall(PetscViewerFlush(viewer));

2570:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFO(15) (estimated size of (in MB) MUMPS internal data for running numerical factorization):\n"));
2571:         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %d\n", mumps->myid, mumps->id.INFO(15)));
2572:         PetscCall(PetscViewerFlush(viewer));

2574:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFO(16) (size of (in MB) MUMPS internal data used during numerical factorization):\n"));
2575:         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %d\n", mumps->myid, mumps->id.INFO(16)));
2576:         PetscCall(PetscViewerFlush(viewer));

2578:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFO(23) (num of pivots eliminated on this processor after factorization):\n"));
2579:         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %d\n", mumps->myid, mumps->id.INFO(23)));
2580:         PetscCall(PetscViewerFlush(viewer));

2582:         if (mumps->ninfo && mumps->ninfo <= 80) {
2583:           PetscInt i;
2584:           for (i = 0; i < mumps->ninfo; i++) {
2585:             PetscCall(PetscViewerASCIIPrintf(viewer, "  INFO(%" PetscInt_FMT "):\n", mumps->info[i]));
2586:             PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %d\n", mumps->myid, mumps->id.INFO(mumps->info[i])));
2587:             PetscCall(PetscViewerFlush(viewer));
2588:           }
2589:         }
2590:         PetscCall(PetscViewerASCIIPopSynchronized(viewer));
2591:       } else PetscCall(PetscViewerASCIIPrintf(viewer, "  Use -%sksp_view ::ascii_info_detail to display information for all processes\n", ((PetscObject)A)->prefix ? ((PetscObject)A)->prefix : ""));

2593:       if (mumps->myid == 0) { /* information from the host */
2594:         PetscCall(PetscViewerASCIIPrintf(viewer, "  RINFOG(1) (global estimated flops for the elimination after analysis): %g\n", (double)mumps->id.RINFOG(1)));
2595:         PetscCall(PetscViewerASCIIPrintf(viewer, "  RINFOG(2) (global estimated flops for the assembly after factorization): %g\n", (double)mumps->id.RINFOG(2)));
2596:         PetscCall(PetscViewerASCIIPrintf(viewer, "  RINFOG(3) (global estimated flops for the elimination after factorization): %g\n", (double)mumps->id.RINFOG(3)));
2597:         PetscCall(PetscViewerASCIIPrintf(viewer, "  (RINFOG(12) RINFOG(13))*2^INFOG(34) (determinant): (%g,%g)*(2^%d)\n", (double)mumps->id.RINFOG(12), (double)mumps->id.RINFOG(13), mumps->id.INFOG(34)));

2599:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(3) (estimated real workspace for factors on all processors after analysis): %d\n", mumps->id.INFOG(3)));
2600:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(4) (estimated integer workspace for factors on all processors after analysis): %d\n", mumps->id.INFOG(4)));
2601:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(5) (estimated maximum front size in the complete tree): %d\n", mumps->id.INFOG(5)));
2602:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(6) (number of nodes in the complete tree): %d\n", mumps->id.INFOG(6)));
2603:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(7) (ordering option effectively used after analysis): %d\n", mumps->id.INFOG(7)));
2604:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(8) (structural symmetry in percent of the permuted matrix after analysis): %d\n", mumps->id.INFOG(8)));
2605:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(9) (total real/complex workspace to store the matrix factors after factorization): %d\n", mumps->id.INFOG(9)));
2606:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(10) (total integer space store the matrix factors after factorization): %d\n", mumps->id.INFOG(10)));
2607:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(11) (order of largest frontal matrix after factorization): %d\n", mumps->id.INFOG(11)));
2608:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(12) (number of off-diagonal pivots): %d\n", mumps->id.INFOG(12)));
2609:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(13) (number of delayed pivots after factorization): %d\n", mumps->id.INFOG(13)));
2610:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(14) (number of memory compress after factorization): %d\n", mumps->id.INFOG(14)));
2611:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(15) (number of steps of iterative refinement after solution): %d\n", mumps->id.INFOG(15)));
2612:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(16) (estimated size (in MB) of all MUMPS internal data for factorization after analysis: value on the most memory consuming processor): %d\n", mumps->id.INFOG(16)));
2613:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(17) (estimated size of all MUMPS internal data for factorization after analysis: sum over all processors): %d\n", mumps->id.INFOG(17)));
2614:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(18) (size of all MUMPS internal data allocated during factorization: value on the most memory consuming processor): %d\n", mumps->id.INFOG(18)));
2615:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(19) (size of all MUMPS internal data allocated during factorization: sum over all processors): %d\n", mumps->id.INFOG(19)));
2616:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(20) (estimated number of entries in the factors): %d\n", mumps->id.INFOG(20)));
2617:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(21) (size in MB of memory effectively used during factorization - value on the most memory consuming processor): %d\n", mumps->id.INFOG(21)));
2618:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(22) (size in MB of memory effectively used during factorization - sum over all processors): %d\n", mumps->id.INFOG(22)));
2619:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(23) (after analysis: value of ICNTL(6) effectively used): %d\n", mumps->id.INFOG(23)));
2620:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(24) (after analysis: value of ICNTL(12) effectively used): %d\n", mumps->id.INFOG(24)));
2621:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(25) (after factorization: number of pivots modified by static pivoting): %d\n", mumps->id.INFOG(25)));
2622:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(28) (after factorization: number of null pivots encountered): %d\n", mumps->id.INFOG(28)));
2623:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(29) (after factorization: effective number of entries in the factors (sum over all processors)): %d\n", mumps->id.INFOG(29)));
2624:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(30, 31) (after solution: size in Mbytes of memory used during solution phase): %d, %d\n", mumps->id.INFOG(30), mumps->id.INFOG(31)));
2625:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(32) (after analysis: type of analysis done): %d\n", mumps->id.INFOG(32)));
2626:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(33) (value used for ICNTL(8)): %d\n", mumps->id.INFOG(33)));
2627:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(34) (exponent of the determinant if determinant is requested): %d\n", mumps->id.INFOG(34)));
2628:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(35) (after factorization: number of entries taking into account BLR factor compression - sum over all processors): %d\n", mumps->id.INFOG(35)));
2629:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(36) (after analysis: estimated size of all MUMPS internal data for running BLR in-core - value on the most memory consuming processor): %d\n", mumps->id.INFOG(36)));
2630:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(37) (after analysis: estimated size of all MUMPS internal data for running BLR in-core - sum over all processors): %d\n", mumps->id.INFOG(37)));
2631:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(38) (after analysis: estimated size of all MUMPS internal data for running BLR out-of-core - value on the most memory consuming processor): %d\n", mumps->id.INFOG(38)));
2632:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(39) (after analysis: estimated size of all MUMPS internal data for running BLR out-of-core - sum over all processors): %d\n", mumps->id.INFOG(39)));
2633:       }
2634:     }
2635:   }
2636:   PetscFunctionReturn(PETSC_SUCCESS);
2637: }

2639: static PetscErrorCode MatGetInfo_MUMPS(Mat A, PETSC_UNUSED MatInfoType flag, MatInfo *info)
2640: {
2641:   Mat_MUMPS *mumps = (Mat_MUMPS *)A->data;

2643:   PetscFunctionBegin;
2644:   info->block_size        = 1.0;
2645:   info->nz_allocated      = mumps->id.INFOG(20) >= 0 ? mumps->id.INFOG(20) : -1000000 * mumps->id.INFOG(20);
2646:   info->nz_used           = mumps->id.INFOG(20) >= 0 ? mumps->id.INFOG(20) : -1000000 * mumps->id.INFOG(20);
2647:   info->nz_unneeded       = 0.0;
2648:   info->assemblies        = 0.0;
2649:   info->mallocs           = 0.0;
2650:   info->memory            = 0.0;
2651:   info->fill_ratio_given  = 0;
2652:   info->fill_ratio_needed = 0;
2653:   info->factor_mallocs    = 0;
2654:   PetscFunctionReturn(PETSC_SUCCESS);
2655: }

2657: static PetscErrorCode MatFactorSetSchurIS_MUMPS(Mat F, IS is)
2658: {
2659:   Mat_MUMPS         *mumps = (Mat_MUMPS *)F->data;
2660:   const PetscScalar *arr;
2661:   const PetscInt    *idxs;
2662:   PetscInt           size, i;

2664:   PetscFunctionBegin;
2665:   PetscCall(ISGetLocalSize(is, &size));
2666:   /* Schur complement matrix */
2667:   PetscCall(MatDestroy(&F->schur));
2668:   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, size, size, NULL, &F->schur));
2669:   PetscCall(MatDenseGetArrayRead(F->schur, &arr));
2670:   mumps->id.schur      = (MumpsScalar *)arr;
2671:   mumps->id.size_schur = size;
2672:   mumps->id.schur_lld  = size;
2673:   PetscCall(MatDenseRestoreArrayRead(F->schur, &arr));
2674:   if (mumps->sym == 1) PetscCall(MatSetOption(F->schur, MAT_SPD, PETSC_TRUE));

2676:   /* MUMPS expects Fortran style indices */
2677:   PetscCall(PetscFree(mumps->id.listvar_schur));
2678:   PetscCall(PetscMalloc1(size, &mumps->id.listvar_schur));
2679:   PetscCall(ISGetIndices(is, &idxs));
2680:   for (i = 0; i < size; i++) PetscCall(PetscMUMPSIntCast(idxs[i] + 1, &mumps->id.listvar_schur[i]));
2681:   PetscCall(ISRestoreIndices(is, &idxs));
2682:   /* set a special value of ICNTL (not handled my MUMPS) to be used in the solve phase by PETSc */
2683:   mumps->id.ICNTL(26) = -1;
2684:   PetscFunctionReturn(PETSC_SUCCESS);
2685: }

2687: static PetscErrorCode MatFactorCreateSchurComplement_MUMPS(Mat F, Mat *S)
2688: {
2689:   Mat          St;
2690:   Mat_MUMPS   *mumps = (Mat_MUMPS *)F->data;
2691:   PetscScalar *array;

2693:   PetscFunctionBegin;
2694:   PetscCheck(mumps->id.ICNTL(19), PetscObjectComm((PetscObject)F), PETSC_ERR_ORDER, "Schur complement mode not selected! Call MatFactorSetSchurIS() to enable it");
2695:   PetscCall(MatCreate(PETSC_COMM_SELF, &St));
2696:   PetscCall(MatSetSizes(St, PETSC_DECIDE, PETSC_DECIDE, mumps->id.size_schur, mumps->id.size_schur));
2697:   PetscCall(MatSetType(St, MATDENSE));
2698:   PetscCall(MatSetUp(St));
2699:   PetscCall(MatDenseGetArray(St, &array));
2700:   if (!mumps->sym) {                /* MUMPS always return a full matrix */
2701:     if (mumps->id.ICNTL(19) == 1) { /* stored by rows */
2702:       PetscInt i, j, N = mumps->id.size_schur;
2703:       for (i = 0; i < N; i++) {
2704:         for (j = 0; j < N; j++) {
2705: #if !defined(PETSC_USE_COMPLEX)
2706:           PetscScalar val = mumps->id.schur[i * N + j];
2707: #else
2708:           PetscScalar val = mumps->id.schur[i * N + j].r + PETSC_i * mumps->id.schur[i * N + j].i;
2709: #endif
2710:           array[j * N + i] = val;
2711:         }
2712:       }
2713:     } else { /* stored by columns */
2714:       PetscCall(PetscArraycpy(array, mumps->id.schur, mumps->id.size_schur * mumps->id.size_schur));
2715:     }
2716:   } else {                          /* either full or lower-triangular (not packed) */
2717:     if (mumps->id.ICNTL(19) == 2) { /* lower triangular stored by columns */
2718:       PetscInt i, j, N = mumps->id.size_schur;
2719:       for (i = 0; i < N; i++) {
2720:         for (j = i; j < N; j++) {
2721: #if !defined(PETSC_USE_COMPLEX)
2722:           PetscScalar val = mumps->id.schur[i * N + j];
2723: #else
2724:           PetscScalar val = mumps->id.schur[i * N + j].r + PETSC_i * mumps->id.schur[i * N + j].i;
2725: #endif
2726:           array[i * N + j] = array[j * N + i] = val;
2727:         }
2728:       }
2729:     } else if (mumps->id.ICNTL(19) == 3) { /* full matrix */
2730:       PetscCall(PetscArraycpy(array, mumps->id.schur, mumps->id.size_schur * mumps->id.size_schur));
2731:     } else { /* ICNTL(19) == 1 lower triangular stored by rows */
2732:       PetscInt i, j, N = mumps->id.size_schur;
2733:       for (i = 0; i < N; i++) {
2734:         for (j = 0; j < i + 1; j++) {
2735: #if !defined(PETSC_USE_COMPLEX)
2736:           PetscScalar val = mumps->id.schur[i * N + j];
2737: #else
2738:           PetscScalar val = mumps->id.schur[i * N + j].r + PETSC_i * mumps->id.schur[i * N + j].i;
2739: #endif
2740:           array[i * N + j] = array[j * N + i] = val;
2741:         }
2742:       }
2743:     }
2744:   }
2745:   PetscCall(MatDenseRestoreArray(St, &array));
2746:   *S = St;
2747:   PetscFunctionReturn(PETSC_SUCCESS);
2748: }

2750: static PetscErrorCode MatMumpsSetIcntl_MUMPS(Mat F, PetscInt icntl, PetscInt ival)
2751: {
2752:   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;

2754:   PetscFunctionBegin;
2755:   if (mumps->id.job == JOB_NULL) {                                       /* need to cache icntl and ival since PetscMUMPS_c() has never been called */
2756:     PetscInt i, nICNTL_pre = mumps->ICNTL_pre ? mumps->ICNTL_pre[0] : 0; /* number of already cached ICNTL */
2757:     for (i = 0; i < nICNTL_pre; ++i)
2758:       if (mumps->ICNTL_pre[1 + 2 * i] == icntl) break; /* is this ICNTL already cached? */
2759:     if (i == nICNTL_pre) {                             /* not already cached */
2760:       if (i > 0) PetscCall(PetscRealloc(sizeof(PetscMUMPSInt) * (2 * nICNTL_pre + 3), &mumps->ICNTL_pre));
2761:       else PetscCall(PetscCalloc(sizeof(PetscMUMPSInt) * 3, &mumps->ICNTL_pre));
2762:       mumps->ICNTL_pre[0]++;
2763:     }
2764:     mumps->ICNTL_pre[1 + 2 * i] = icntl;
2765:     PetscCall(PetscMUMPSIntCast(ival, mumps->ICNTL_pre + 2 + 2 * i));
2766:   } else PetscCall(PetscMUMPSIntCast(ival, &mumps->id.ICNTL(icntl)));
2767:   PetscFunctionReturn(PETSC_SUCCESS);
2768: }

2770: static PetscErrorCode MatMumpsGetIcntl_MUMPS(Mat F, PetscInt icntl, PetscInt *ival)
2771: {
2772:   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;

2774:   PetscFunctionBegin;
2775:   if (mumps->id.job == JOB_NULL) {
2776:     PetscInt i, nICNTL_pre = mumps->ICNTL_pre ? mumps->ICNTL_pre[0] : 0;
2777:     *ival = 0;
2778:     for (i = 0; i < nICNTL_pre; ++i) {
2779:       if (mumps->ICNTL_pre[1 + 2 * i] == icntl) *ival = mumps->ICNTL_pre[2 + 2 * i];
2780:     }
2781:   } else *ival = mumps->id.ICNTL(icntl);
2782:   PetscFunctionReturn(PETSC_SUCCESS);
2783: }

2785: /*@
2786:   MatMumpsSetIcntl - Set MUMPS parameter ICNTL() <https://mumps-solver.org/index.php?page=doc>

2788:   Logically Collective

2790:   Input Parameters:
2791: + F     - the factored matrix obtained by calling `MatGetFactor()` from PETSc-MUMPS interface
2792: . icntl - index of MUMPS parameter array ICNTL()
2793: - ival  - value of MUMPS ICNTL(icntl)

2795:   Options Database Key:
2796: . -mat_mumps_icntl_<icntl> <ival> - change the option numbered icntl to ival

2798:   Level: beginner

2800: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`
2801: @*/
2802: PetscErrorCode MatMumpsSetIcntl(Mat F, PetscInt icntl, PetscInt ival)
2803: {
2804:   PetscFunctionBegin;
2806:   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
2809:   PetscCheck((icntl >= 1 && icntl <= 38) || icntl == 58, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONG, "Unsupported ICNTL value %" PetscInt_FMT, icntl);
2810:   PetscTryMethod(F, "MatMumpsSetIcntl_C", (Mat, PetscInt, PetscInt), (F, icntl, ival));
2811:   PetscFunctionReturn(PETSC_SUCCESS);
2812: }

2814: /*@
2815:   MatMumpsGetIcntl - Get MUMPS parameter ICNTL() <https://mumps-solver.org/index.php?page=doc>

2817:   Logically Collective

2819:   Input Parameters:
2820: + F     - the factored matrix obtained by calling `MatGetFactor()` from PETSc-MUMPS interface
2821: - icntl - index of MUMPS parameter array ICNTL()

2823:   Output Parameter:
2824: . ival - value of MUMPS ICNTL(icntl)

2826:   Level: beginner

2828: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`
2829: @*/
2830: PetscErrorCode MatMumpsGetIcntl(Mat F, PetscInt icntl, PetscInt *ival)
2831: {
2832:   PetscFunctionBegin;
2834:   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
2836:   PetscAssertPointer(ival, 3);
2837:   PetscCheck((icntl >= 1 && icntl <= 38) || icntl == 58, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONG, "Unsupported ICNTL value %" PetscInt_FMT, icntl);
2838:   PetscUseMethod(F, "MatMumpsGetIcntl_C", (Mat, PetscInt, PetscInt *), (F, icntl, ival));
2839:   PetscFunctionReturn(PETSC_SUCCESS);
2840: }

2842: static PetscErrorCode MatMumpsSetCntl_MUMPS(Mat F, PetscInt icntl, PetscReal val)
2843: {
2844:   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;

2846:   PetscFunctionBegin;
2847:   if (mumps->id.job == JOB_NULL) {
2848:     PetscInt i, nCNTL_pre = mumps->CNTL_pre ? mumps->CNTL_pre[0] : 0;
2849:     for (i = 0; i < nCNTL_pre; ++i)
2850:       if (mumps->CNTL_pre[1 + 2 * i] == icntl) break;
2851:     if (i == nCNTL_pre) {
2852:       if (i > 0) PetscCall(PetscRealloc(sizeof(PetscReal) * (2 * nCNTL_pre + 3), &mumps->CNTL_pre));
2853:       else PetscCall(PetscCalloc(sizeof(PetscReal) * 3, &mumps->CNTL_pre));
2854:       mumps->CNTL_pre[0]++;
2855:     }
2856:     mumps->CNTL_pre[1 + 2 * i] = icntl;
2857:     mumps->CNTL_pre[2 + 2 * i] = val;
2858:   } else mumps->id.CNTL(icntl) = val;
2859:   PetscFunctionReturn(PETSC_SUCCESS);
2860: }

2862: static PetscErrorCode MatMumpsGetCntl_MUMPS(Mat F, PetscInt icntl, PetscReal *val)
2863: {
2864:   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;

2866:   PetscFunctionBegin;
2867:   if (mumps->id.job == JOB_NULL) {
2868:     PetscInt i, nCNTL_pre = mumps->CNTL_pre ? mumps->CNTL_pre[0] : 0;
2869:     *val = 0.0;
2870:     for (i = 0; i < nCNTL_pre; ++i) {
2871:       if (mumps->CNTL_pre[1 + 2 * i] == icntl) *val = mumps->CNTL_pre[2 + 2 * i];
2872:     }
2873:   } else *val = mumps->id.CNTL(icntl);
2874:   PetscFunctionReturn(PETSC_SUCCESS);
2875: }

2877: /*@
2878:   MatMumpsSetCntl - Set MUMPS parameter CNTL() <https://mumps-solver.org/index.php?page=doc>

2880:   Logically Collective

2882:   Input Parameters:
2883: + F     - the factored matrix obtained by calling `MatGetFactor()` from PETSc-MUMPS interface
2884: . icntl - index of MUMPS parameter array CNTL()
2885: - val   - value of MUMPS CNTL(icntl)

2887:   Options Database Key:
2888: . -mat_mumps_cntl_<icntl> <val> - change the option numbered icntl to ival

2890:   Level: beginner

2892: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`
2893: @*/
2894: PetscErrorCode MatMumpsSetCntl(Mat F, PetscInt icntl, PetscReal val)
2895: {
2896:   PetscFunctionBegin;
2898:   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
2901:   PetscCheck(icntl >= 1 && icntl <= 7, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONG, "Unsupported CNTL value %" PetscInt_FMT, icntl);
2902:   PetscTryMethod(F, "MatMumpsSetCntl_C", (Mat, PetscInt, PetscReal), (F, icntl, val));
2903:   PetscFunctionReturn(PETSC_SUCCESS);
2904: }

2906: /*@
2907:   MatMumpsGetCntl - Get MUMPS parameter CNTL() <https://mumps-solver.org/index.php?page=doc>

2909:   Logically Collective

2911:   Input Parameters:
2912: + F     - the factored matrix obtained by calling `MatGetFactor()` from PETSc-MUMPS interface
2913: - icntl - index of MUMPS parameter array CNTL()

2915:   Output Parameter:
2916: . val - value of MUMPS CNTL(icntl)

2918:   Level: beginner

2920: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`
2921: @*/
2922: PetscErrorCode MatMumpsGetCntl(Mat F, PetscInt icntl, PetscReal *val)
2923: {
2924:   PetscFunctionBegin;
2926:   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
2928:   PetscAssertPointer(val, 3);
2929:   PetscCheck(icntl >= 1 && icntl <= 7, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONG, "Unsupported CNTL value %" PetscInt_FMT, icntl);
2930:   PetscUseMethod(F, "MatMumpsGetCntl_C", (Mat, PetscInt, PetscReal *), (F, icntl, val));
2931:   PetscFunctionReturn(PETSC_SUCCESS);
2932: }

2934: static PetscErrorCode MatMumpsGetInfo_MUMPS(Mat F, PetscInt icntl, PetscInt *info)
2935: {
2936:   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;

2938:   PetscFunctionBegin;
2939:   *info = mumps->id.INFO(icntl);
2940:   PetscFunctionReturn(PETSC_SUCCESS);
2941: }

2943: static PetscErrorCode MatMumpsGetInfog_MUMPS(Mat F, PetscInt icntl, PetscInt *infog)
2944: {
2945:   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;

2947:   PetscFunctionBegin;
2948:   *infog = mumps->id.INFOG(icntl);
2949:   PetscFunctionReturn(PETSC_SUCCESS);
2950: }

2952: static PetscErrorCode MatMumpsGetRinfo_MUMPS(Mat F, PetscInt icntl, PetscReal *rinfo)
2953: {
2954:   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;

2956:   PetscFunctionBegin;
2957:   *rinfo = mumps->id.RINFO(icntl);
2958:   PetscFunctionReturn(PETSC_SUCCESS);
2959: }

2961: static PetscErrorCode MatMumpsGetRinfog_MUMPS(Mat F, PetscInt icntl, PetscReal *rinfog)
2962: {
2963:   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;

2965:   PetscFunctionBegin;
2966:   *rinfog = mumps->id.RINFOG(icntl);
2967:   PetscFunctionReturn(PETSC_SUCCESS);
2968: }

2970: static PetscErrorCode MatMumpsGetNullPivots_MUMPS(Mat F, PetscInt *size, PetscInt **array)
2971: {
2972:   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;

2974:   PetscFunctionBegin;
2975:   PetscCheck(mumps->id.ICNTL(24) == 1, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "-mat_mumps_icntl_24 must be set as 1 for null pivot row detection");
2976:   *size  = 0;
2977:   *array = NULL;
2978:   if (!mumps->myid) {
2979:     *size = mumps->id.INFOG(28);
2980:     PetscCall(PetscMalloc1(*size, array));
2981:     for (int i = 0; i < *size; i++) (*array)[i] = mumps->id.pivnul_list[i] - 1;
2982:   }
2983:   PetscFunctionReturn(PETSC_SUCCESS);
2984: }

2986: static PetscErrorCode MatMumpsGetInverse_MUMPS(Mat F, Mat spRHS)
2987: {
2988:   Mat          Bt = NULL, Btseq = NULL;
2989:   PetscBool    flg;
2990:   Mat_MUMPS   *mumps = (Mat_MUMPS *)F->data;
2991:   PetscScalar *aa;
2992:   PetscInt     spnr, *ia, *ja, M, nrhs;

2994:   PetscFunctionBegin;
2995:   PetscAssertPointer(spRHS, 2);
2996:   PetscCall(PetscObjectTypeCompare((PetscObject)spRHS, MATTRANSPOSEVIRTUAL, &flg));
2997:   if (flg) {
2998:     PetscCall(MatTransposeGetMat(spRHS, &Bt));
2999:   } else SETERRQ(PetscObjectComm((PetscObject)spRHS), PETSC_ERR_ARG_WRONG, "Matrix spRHS must be type MATTRANSPOSEVIRTUAL matrix");

3001:   PetscCall(MatMumpsSetIcntl(F, 30, 1));

3003:   if (mumps->petsc_size > 1) {
3004:     Mat_MPIAIJ *b = (Mat_MPIAIJ *)Bt->data;
3005:     Btseq         = b->A;
3006:   } else {
3007:     Btseq = Bt;
3008:   }

3010:   PetscCall(MatGetSize(spRHS, &M, &nrhs));
3011:   mumps->id.nrhs = nrhs;
3012:   mumps->id.lrhs = M;
3013:   mumps->id.rhs  = NULL;

3015:   if (!mumps->myid) {
3016:     PetscCall(MatSeqAIJGetArray(Btseq, &aa));
3017:     PetscCall(MatGetRowIJ(Btseq, 1, PETSC_FALSE, PETSC_FALSE, &spnr, (const PetscInt **)&ia, (const PetscInt **)&ja, &flg));
3018:     PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot get IJ structure");
3019:     PetscCall(PetscMUMPSIntCSRCast(mumps, spnr, ia, ja, &mumps->id.irhs_ptr, &mumps->id.irhs_sparse, &mumps->id.nz_rhs));
3020:     mumps->id.rhs_sparse = (MumpsScalar *)aa;
3021:   } else {
3022:     mumps->id.irhs_ptr    = NULL;
3023:     mumps->id.irhs_sparse = NULL;
3024:     mumps->id.nz_rhs      = 0;
3025:     mumps->id.rhs_sparse  = NULL;
3026:   }
3027:   mumps->id.ICNTL(20) = 1; /* rhs is sparse */
3028:   mumps->id.ICNTL(21) = 0; /* solution is in assembled centralized format */

3030:   /* solve phase */
3031:   mumps->id.job = JOB_SOLVE;
3032:   PetscMUMPS_c(mumps);
3033:   PetscCheck(mumps->id.INFOG(1) >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "MUMPS error in solve: INFOG(1)=%d INFO(2)=%d " MUMPS_MANUALS, mumps->id.INFOG(1), mumps->id.INFO(2));

3035:   if (!mumps->myid) {
3036:     PetscCall(MatSeqAIJRestoreArray(Btseq, &aa));
3037:     PetscCall(MatRestoreRowIJ(Btseq, 1, PETSC_FALSE, PETSC_FALSE, &spnr, (const PetscInt **)&ia, (const PetscInt **)&ja, &flg));
3038:     PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot get IJ structure");
3039:   }
3040:   PetscFunctionReturn(PETSC_SUCCESS);
3041: }

3043: /*@
3044:   MatMumpsGetInverse - Get user-specified set of entries in inverse of `A` <https://mumps-solver.org/index.php?page=doc>

3046:   Logically Collective

3048:   Input Parameter:
3049: . F - the factored matrix obtained by calling `MatGetFactor()` from PETSc-MUMPS interface

3051:   Output Parameter:
3052: . spRHS - sequential sparse matrix in `MATTRANSPOSEVIRTUAL` format with requested entries of inverse of `A`

3054:   Level: beginner

3056: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatCreateTranspose()`
3057: @*/
3058: PetscErrorCode MatMumpsGetInverse(Mat F, Mat spRHS)
3059: {
3060:   PetscFunctionBegin;
3062:   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
3063:   PetscUseMethod(F, "MatMumpsGetInverse_C", (Mat, Mat), (F, spRHS));
3064:   PetscFunctionReturn(PETSC_SUCCESS);
3065: }

3067: static PetscErrorCode MatMumpsGetInverseTranspose_MUMPS(Mat F, Mat spRHST)
3068: {
3069:   Mat spRHS;

3071:   PetscFunctionBegin;
3072:   PetscCall(MatCreateTranspose(spRHST, &spRHS));
3073:   PetscCall(MatMumpsGetInverse_MUMPS(F, spRHS));
3074:   PetscCall(MatDestroy(&spRHS));
3075:   PetscFunctionReturn(PETSC_SUCCESS);
3076: }

3078: /*@
3079:   MatMumpsGetInverseTranspose - Get user-specified set of entries in inverse of matrix $A^T $ <https://mumps-solver.org/index.php?page=doc>

3081:   Logically Collective

3083:   Input Parameter:
3084: . F - the factored matrix of A obtained by calling `MatGetFactor()` from PETSc-MUMPS interface

3086:   Output Parameter:
3087: . spRHST - sequential sparse matrix in `MATAIJ` format containing the requested entries of inverse of `A`^T

3089:   Level: beginner

3091: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatCreateTranspose()`, `MatMumpsGetInverse()`
3092: @*/
3093: PetscErrorCode MatMumpsGetInverseTranspose(Mat F, Mat spRHST)
3094: {
3095:   PetscBool flg;

3097:   PetscFunctionBegin;
3099:   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
3100:   PetscCall(PetscObjectTypeCompareAny((PetscObject)spRHST, &flg, MATSEQAIJ, MATMPIAIJ, NULL));
3101:   PetscCheck(flg, PetscObjectComm((PetscObject)spRHST), PETSC_ERR_ARG_WRONG, "Matrix spRHST must be MATAIJ matrix");

3103:   PetscUseMethod(F, "MatMumpsGetInverseTranspose_C", (Mat, Mat), (F, spRHST));
3104:   PetscFunctionReturn(PETSC_SUCCESS);
3105: }

3107: /*@
3108:   MatMumpsGetInfo - Get MUMPS parameter INFO() <https://mumps-solver.org/index.php?page=doc>

3110:   Logically Collective

3112:   Input Parameters:
3113: + F     - the factored matrix obtained by calling `MatGetFactor()` from PETSc-MUMPS interface
3114: - icntl - index of MUMPS parameter array INFO()

3116:   Output Parameter:
3117: . ival - value of MUMPS INFO(icntl)

3119:   Level: beginner

3121: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`
3122: @*/
3123: PetscErrorCode MatMumpsGetInfo(Mat F, PetscInt icntl, PetscInt *ival)
3124: {
3125:   PetscFunctionBegin;
3127:   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
3128:   PetscAssertPointer(ival, 3);
3129:   PetscUseMethod(F, "MatMumpsGetInfo_C", (Mat, PetscInt, PetscInt *), (F, icntl, ival));
3130:   PetscFunctionReturn(PETSC_SUCCESS);
3131: }

3133: /*@
3134:   MatMumpsGetInfog - Get MUMPS parameter INFOG() <https://mumps-solver.org/index.php?page=doc>

3136:   Logically Collective

3138:   Input Parameters:
3139: + F     - the factored matrix obtained by calling `MatGetFactor()` from PETSc-MUMPS interface
3140: - icntl - index of MUMPS parameter array INFOG()

3142:   Output Parameter:
3143: . ival - value of MUMPS INFOG(icntl)

3145:   Level: beginner

3147: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`
3148: @*/
3149: PetscErrorCode MatMumpsGetInfog(Mat F, PetscInt icntl, PetscInt *ival)
3150: {
3151:   PetscFunctionBegin;
3153:   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
3154:   PetscAssertPointer(ival, 3);
3155:   PetscUseMethod(F, "MatMumpsGetInfog_C", (Mat, PetscInt, PetscInt *), (F, icntl, ival));
3156:   PetscFunctionReturn(PETSC_SUCCESS);
3157: }

3159: /*@
3160:   MatMumpsGetRinfo - Get MUMPS parameter RINFO() <https://mumps-solver.org/index.php?page=doc>

3162:   Logically Collective

3164:   Input Parameters:
3165: + F     - the factored matrix obtained by calling `MatGetFactor()` from PETSc-MUMPS interface
3166: - icntl - index of MUMPS parameter array RINFO()

3168:   Output Parameter:
3169: . val - value of MUMPS RINFO(icntl)

3171:   Level: beginner

3173: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfog()`
3174: @*/
3175: PetscErrorCode MatMumpsGetRinfo(Mat F, PetscInt icntl, PetscReal *val)
3176: {
3177:   PetscFunctionBegin;
3179:   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
3180:   PetscAssertPointer(val, 3);
3181:   PetscUseMethod(F, "MatMumpsGetRinfo_C", (Mat, PetscInt, PetscReal *), (F, icntl, val));
3182:   PetscFunctionReturn(PETSC_SUCCESS);
3183: }

3185: /*@
3186:   MatMumpsGetRinfog - Get MUMPS parameter RINFOG() <https://mumps-solver.org/index.php?page=doc>

3188:   Logically Collective

3190:   Input Parameters:
3191: + F     - the factored matrix obtained by calling `MatGetFactor()` from PETSc-MUMPS interface
3192: - icntl - index of MUMPS parameter array RINFOG()

3194:   Output Parameter:
3195: . val - value of MUMPS RINFOG(icntl)

3197:   Level: beginner

3199: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`
3200: @*/
3201: PetscErrorCode MatMumpsGetRinfog(Mat F, PetscInt icntl, PetscReal *val)
3202: {
3203:   PetscFunctionBegin;
3205:   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
3206:   PetscAssertPointer(val, 3);
3207:   PetscUseMethod(F, "MatMumpsGetRinfog_C", (Mat, PetscInt, PetscReal *), (F, icntl, val));
3208:   PetscFunctionReturn(PETSC_SUCCESS);
3209: }

3211: /*@
3212:   MatMumpsGetNullPivots - Get MUMPS parameter PIVNUL_LIST() <https://mumps-solver.org/index.php?page=doc>

3214:   Logically Collective

3216:   Input Parameter:
3217: . F - the factored matrix obtained by calling `MatGetFactor()` from PETSc-MUMPS interface

3219:   Output Parameters:
3220: + size  - local size of the array. The size of the array is non-zero only on the host.
3221: - array - array of rows with null pivot, these rows follow 0-based indexing. The array gets allocated within the function and the user is responsible
3222:            for freeing this array.

3224:   Level: beginner

3226: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`
3227: @*/
3228: PetscErrorCode MatMumpsGetNullPivots(Mat F, PetscInt *size, PetscInt **array)
3229: {
3230:   PetscFunctionBegin;
3232:   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
3233:   PetscAssertPointer(size, 2);
3234:   PetscAssertPointer(array, 3);
3235:   PetscUseMethod(F, "MatMumpsGetNullPivots_C", (Mat, PetscInt *, PetscInt **), (F, size, array));
3236:   PetscFunctionReturn(PETSC_SUCCESS);
3237: }

3239: /*MC
3240:   MATSOLVERMUMPS -  A matrix type providing direct solvers (LU and Cholesky) for
3241:   distributed and sequential matrices via the external package MUMPS <https://mumps-solver.org/index.php?page=doc>

3243:   Works with `MATAIJ` and `MATSBAIJ` matrices

3245:   Use ./configure --download-mumps --download-scalapack --download-parmetis --download-metis --download-ptscotch to have PETSc installed with MUMPS

3247:   Use ./configure --with-openmp --download-hwloc (or --with-hwloc) to enable running MUMPS in MPI+OpenMP hybrid mode and non-MUMPS in flat-MPI mode.
3248:   See details below.

3250:   Use `-pc_type cholesky` or `lu` `-pc_factor_mat_solver_type mumps` to use this direct solver

3252:   Options Database Keys:
3253: +  -mat_mumps_icntl_1   - ICNTL(1): output stream for error messages
3254: .  -mat_mumps_icntl_2   - ICNTL(2): output stream for diagnostic printing, statistics, and warning
3255: .  -mat_mumps_icntl_3   -  ICNTL(3): output stream for global information, collected on the host
3256: .  -mat_mumps_icntl_4   -  ICNTL(4): level of printing (0 to 4)
3257: .  -mat_mumps_icntl_6   - ICNTL(6): permutes to a zero-free diagonal and/or scale the matrix (0 to 7)
3258: .  -mat_mumps_icntl_7   - ICNTL(7): computes a symmetric permutation in sequential analysis, 0=AMD, 2=AMF, 3=Scotch, 4=PORD, 5=Metis, 6=QAMD, and 7=auto
3259:                           Use -pc_factor_mat_ordering_type <type> to have PETSc perform the ordering (sequential only)
3260: .  -mat_mumps_icntl_8   - ICNTL(8): scaling strategy (-2 to 8 or 77)
3261: .  -mat_mumps_icntl_10  - ICNTL(10): max num of refinements
3262: .  -mat_mumps_icntl_11  - ICNTL(11): statistics related to an error analysis (via -ksp_view)
3263: .  -mat_mumps_icntl_12  - ICNTL(12): an ordering strategy for symmetric matrices (0 to 3)
3264: .  -mat_mumps_icntl_13  - ICNTL(13): parallelism of the root node (enable ScaLAPACK) and its splitting
3265: .  -mat_mumps_icntl_14  - ICNTL(14): percentage increase in the estimated working space
3266: .  -mat_mumps_icntl_15  - ICNTL(15): compression of the input matrix resulting from a block format
3267: .  -mat_mumps_icntl_19  - ICNTL(19): computes the Schur complement
3268: .  -mat_mumps_icntl_20  - ICNTL(20): give MUMPS centralized (0) or distributed (10) dense RHS
3269: .  -mat_mumps_icntl_22  - ICNTL(22): in-core/out-of-core factorization and solve (0 or 1)
3270: .  -mat_mumps_icntl_23  - ICNTL(23): max size of the working memory (MB) that can allocate per processor
3271: .  -mat_mumps_icntl_24  - ICNTL(24): detection of null pivot rows (0 or 1)
3272: .  -mat_mumps_icntl_25  - ICNTL(25): compute a solution of a deficient matrix and a null space basis
3273: .  -mat_mumps_icntl_26  - ICNTL(26): drives the solution phase if a Schur complement matrix
3274: .  -mat_mumps_icntl_28  - ICNTL(28): use 1 for sequential analysis and ICNTL(7) ordering, or 2 for parallel analysis and ICNTL(29) ordering
3275: .  -mat_mumps_icntl_29 - ICNTL(29): parallel ordering 1 = ptscotch, 2 = parmetis
3276: .  -mat_mumps_icntl_30 - ICNTL(30): compute user-specified set of entries in inv(A)
3277: .  -mat_mumps_icntl_31 - ICNTL(31): indicates which factors may be discarded during factorization
3278: .  -mat_mumps_icntl_33 - ICNTL(33): compute determinant
3279: .  -mat_mumps_icntl_35 - ICNTL(35): level of activation of BLR (Block Low-Rank) feature
3280: .  -mat_mumps_icntl_36 - ICNTL(36): controls the choice of BLR factorization variant
3281: .  -mat_mumps_icntl_38 - ICNTL(38): sets the estimated compression rate of LU factors with BLR
3282: .  -mat_mumps_icntl_58 - ICNTL(58): options for symbolic factorization
3283: .  -mat_mumps_cntl_1   - CNTL(1): relative pivoting threshold
3284: .  -mat_mumps_cntl_2   -  CNTL(2): stopping criterion of refinement
3285: .  -mat_mumps_cntl_3   - CNTL(3): absolute pivoting threshold
3286: .  -mat_mumps_cntl_4   - CNTL(4): value for static pivoting
3287: .  -mat_mumps_cntl_5   - CNTL(5): fixation for null pivots
3288: .  -mat_mumps_cntl_7   - CNTL(7): precision of the dropping parameter used during BLR factorization
3289: -  -mat_mumps_use_omp_threads [m] - run MUMPS in MPI+OpenMP hybrid mode as if omp_set_num_threads(m) is called before calling MUMPS.
3290:                                    Default might be the number of cores per CPU package (socket) as reported by hwloc and suggested by the MUMPS manual.

3292:   Level: beginner

3294:   Notes:
3295:   MUMPS Cholesky does not handle (complex) Hermitian matrices (see User's Guide at <https://mumps-solver.org/index.php?page=doc>) so using it will
3296:   error if the matrix is Hermitian.

3298:   When used within a `KSP`/`PC` solve the options are prefixed with that of the `PC`. Otherwise one can set the options prefix by calling
3299:   `MatSetOptionsPrefixFactor()` on the matrix from which the factor was obtained or `MatSetOptionsPrefix()` on the factor matrix.

3301:   When a MUMPS factorization fails inside a KSP solve, for example with a `KSP_DIVERGED_PC_FAILED`, one can find the MUMPS information about
3302:   the failure with
3303: .vb
3304:           KSPGetPC(ksp,&pc);
3305:           PCFactorGetMatrix(pc,&mat);
3306:           MatMumpsGetInfo(mat,....);
3307:           MatMumpsGetInfog(mat,....); etc.
3308: .ve
3309:     Or run with `-ksp_error_if_not_converged` and the program will be stopped and the information printed in the error message.

3311:   MUMPS provides 64-bit integer support in two build modes:
3312:   full 64-bit: here MUMPS is built with C preprocessing flag -DINTSIZE64 and Fortran compiler option -i8, -fdefault-integer-8 or equivalent, and
3313:   requires all dependent libraries MPI, ScaLAPACK, LAPACK and BLAS built the same way with 64-bit integers (for example ILP64 Intel MKL and MPI).

3315:   selective 64-bit: with the default MUMPS build, 64-bit integers have been introduced where needed. In compressed sparse row (CSR) storage of matrices,
3316:   MUMPS stores column indices in 32-bit, but row offsets in 64-bit, so you can have a huge number of non-zeros, but must have less than 2^31 rows and
3317:   columns. This can lead to significant memory and performance gains with respect to a full 64-bit integer MUMPS version. This requires a regular (32-bit
3318:   integer) build of all dependent libraries MPI, ScaLAPACK, LAPACK and BLAS.

3320:   With --download-mumps=1, PETSc always build MUMPS in selective 64-bit mode, which can be used by both --with-64-bit-indices=0/1 variants of PETSc.

3322:   Two modes to run MUMPS/PETSc with OpenMP
3323: .vb
3324:      Set OMP_NUM_THREADS and run with fewer MPI ranks than cores. For example, if you want to have 16 OpenMP
3325:      threads per rank, then you may use "export OMP_NUM_THREADS=16 && mpirun -n 4 ./test".
3326: .ve

3328: .vb
3329:      -mat_mumps_use_omp_threads [m] and run your code with as many MPI ranks as the number of cores. For example,
3330:     if a compute node has 32 cores and you run on two nodes, you may use "mpirun -n 64 ./test -mat_mumps_use_omp_threads 16"
3331: .ve

3333:    To run MUMPS in MPI+OpenMP hybrid mode (i.e., enable multithreading in MUMPS), but still run the non-MUMPS part
3334:    (i.e., PETSc part) of your code in the so-called flat-MPI (aka pure-MPI) mode, you need to configure PETSc with `--with-openmp` `--download-hwloc`
3335:    (or `--with-hwloc`), and have an MPI that supports MPI-3.0's process shared memory (which is usually available). Since MUMPS calls BLAS
3336:    libraries, to really get performance, you should have multithreaded BLAS libraries such as Intel MKL, AMD ACML, Cray libSci or OpenBLAS
3337:    (PETSc will automatically try to utilized a threaded BLAS if --with-openmp is provided).

3339:    If you run your code through a job submission system, there are caveats in MPI rank mapping. We use MPI_Comm_split_type() to obtain MPI
3340:    processes on each compute node. Listing the processes in rank ascending order, we split processes on a node into consecutive groups of
3341:    size m and create a communicator called omp_comm for each group. Rank 0 in an omp_comm is called the master rank, and others in the omp_comm
3342:    are called slave ranks (or slaves). Only master ranks are seen to MUMPS and slaves are not. We will free CPUs assigned to slaves (might be set
3343:    by CPU binding policies in job scripts) and make the CPUs available to the master so that OMP threads spawned by MUMPS can run on the CPUs.
3344:    In a multi-socket compute node, MPI rank mapping is an issue. Still use the above example and suppose your compute node has two sockets,
3345:    if you interleave MPI ranks on the two sockets, in other words, even ranks are placed on socket 0, and odd ranks are on socket 1, and bind
3346:    MPI ranks to cores, then with -mat_mumps_use_omp_threads 16, a master rank (and threads it spawns) will use half cores in socket 0, and half
3347:    cores in socket 1, that definitely hurts locality. On the other hand, if you map MPI ranks consecutively on the two sockets, then the
3348:    problem will not happen. Therefore, when you use -mat_mumps_use_omp_threads, you need to keep an eye on your MPI rank mapping and CPU binding.
3349:    For example, with the Slurm job scheduler, one can use srun --cpu-bind=verbose -m block:block to map consecutive MPI ranks to sockets and
3350:    examine the mapping result.

3352:    PETSc does not control thread binding in MUMPS. So to get best performance, one still has to set `OMP_PROC_BIND` and `OMP_PLACES` in job scripts,
3353:    for example, export `OMP_PLACES`=threads and export `OMP_PROC_BIND`=spread. One does not need to export `OMP_NUM_THREADS`=m in job scripts as PETSc
3354:    calls `omp_set_num_threads`(m) internally before calling MUMPS.

3356:    See {cite}`heroux2011bi` and {cite}`gutierrez2017accommodating`

3358: .seealso: [](ch_matrices), `Mat`, `PCFactorSetMatSolverType()`, `MatSolverType`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`, `KSPGetPC()`, `PCFactorGetMatrix()`
3359: M*/

3361: static PetscErrorCode MatFactorGetSolverType_mumps(PETSC_UNUSED Mat A, MatSolverType *type)
3362: {
3363:   PetscFunctionBegin;
3364:   *type = MATSOLVERMUMPS;
3365:   PetscFunctionReturn(PETSC_SUCCESS);
3366: }

3368: /* MatGetFactor for Seq and MPI AIJ matrices */
3369: static PetscErrorCode MatGetFactor_aij_mumps(Mat A, MatFactorType ftype, Mat *F)
3370: {
3371:   Mat         B;
3372:   Mat_MUMPS  *mumps;
3373:   PetscBool   isSeqAIJ, isDiag, isDense;
3374:   PetscMPIInt size;

3376:   PetscFunctionBegin;
3377: #if defined(PETSC_USE_COMPLEX)
3378:   if (ftype == MAT_FACTOR_CHOLESKY && A->hermitian == PETSC_BOOL3_TRUE && A->symmetric != PETSC_BOOL3_TRUE) {
3379:     PetscCall(PetscInfo(A, "Hermitian MAT_FACTOR_CHOLESKY is not supported. Use MAT_FACTOR_LU instead.\n"));
3380:     *F = NULL;
3381:     PetscFunctionReturn(PETSC_SUCCESS);
3382:   }
3383: #endif
3384:   /* Create the factorization matrix */
3385:   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATSEQAIJ, &isSeqAIJ));
3386:   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATDIAGONAL, &isDiag));
3387:   PetscCall(PetscObjectTypeCompareAny((PetscObject)A, &isDense, MATSEQDENSE, MATMPIDENSE, NULL));
3388:   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
3389:   PetscCall(MatSetSizes(B, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
3390:   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &((PetscObject)B)->type_name));
3391:   PetscCall(MatSetUp(B));

3393:   PetscCall(PetscNew(&mumps));

3395:   B->ops->view    = MatView_MUMPS;
3396:   B->ops->getinfo = MatGetInfo_MUMPS;

3398:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorGetSolverType_C", MatFactorGetSolverType_mumps));
3399:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorSetSchurIS_C", MatFactorSetSchurIS_MUMPS));
3400:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorCreateSchurComplement_C", MatFactorCreateSchurComplement_MUMPS));
3401:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetIcntl_C", MatMumpsSetIcntl_MUMPS));
3402:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetIcntl_C", MatMumpsGetIcntl_MUMPS));
3403:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetCntl_C", MatMumpsSetCntl_MUMPS));
3404:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetCntl_C", MatMumpsGetCntl_MUMPS));
3405:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfo_C", MatMumpsGetInfo_MUMPS));
3406:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfog_C", MatMumpsGetInfog_MUMPS));
3407:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfo_C", MatMumpsGetRinfo_MUMPS));
3408:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfog_C", MatMumpsGetRinfog_MUMPS));
3409:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetNullPivots_C", MatMumpsGetNullPivots_MUMPS));
3410:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverse_C", MatMumpsGetInverse_MUMPS));
3411:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverseTranspose_C", MatMumpsGetInverseTranspose_MUMPS));

3413:   if (ftype == MAT_FACTOR_LU) {
3414:     B->ops->lufactorsymbolic = MatLUFactorSymbolic_AIJMUMPS;
3415:     B->factortype            = MAT_FACTOR_LU;
3416:     if (isSeqAIJ) mumps->ConvertToTriples = MatConvertToTriples_seqaij_seqaij;
3417:     else if (isDiag) mumps->ConvertToTriples = MatConvertToTriples_diagonal_xaij;
3418:     else if (isDense) mumps->ConvertToTriples = MatConvertToTriples_dense_xaij;
3419:     else mumps->ConvertToTriples = MatConvertToTriples_mpiaij_mpiaij;
3420:     PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&B->preferredordering[MAT_FACTOR_LU]));
3421:     mumps->sym = 0;
3422:   } else {
3423:     B->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_MUMPS;
3424:     B->factortype                  = MAT_FACTOR_CHOLESKY;
3425:     if (isSeqAIJ) mumps->ConvertToTriples = MatConvertToTriples_seqaij_seqsbaij;
3426:     else if (isDiag) mumps->ConvertToTriples = MatConvertToTriples_diagonal_xaij;
3427:     else if (isDense) mumps->ConvertToTriples = MatConvertToTriples_dense_xaij;
3428:     else mumps->ConvertToTriples = MatConvertToTriples_mpiaij_mpisbaij;
3429:     PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&B->preferredordering[MAT_FACTOR_CHOLESKY]));
3430: #if defined(PETSC_USE_COMPLEX)
3431:     mumps->sym = 2;
3432: #else
3433:     if (A->spd == PETSC_BOOL3_TRUE) mumps->sym = 1;
3434:     else mumps->sym = 2;
3435: #endif
3436:   }

3438:   /* set solvertype */
3439:   PetscCall(PetscFree(B->solvertype));
3440:   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &B->solvertype));
3441:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
3442:   if (size == 1) {
3443:     /* MUMPS option -mat_mumps_icntl_7 1 is automatically set if PETSc ordering is passed into symbolic factorization */
3444:     B->canuseordering = PETSC_TRUE;
3445:   }
3446:   B->ops->destroy = MatDestroy_MUMPS;
3447:   B->data         = (void *)mumps;

3449:   *F               = B;
3450:   mumps->id.job    = JOB_NULL;
3451:   mumps->ICNTL_pre = NULL;
3452:   mumps->CNTL_pre  = NULL;
3453:   mumps->matstruc  = DIFFERENT_NONZERO_PATTERN;
3454:   PetscFunctionReturn(PETSC_SUCCESS);
3455: }

3457: /* MatGetFactor for Seq and MPI SBAIJ matrices */
3458: static PetscErrorCode MatGetFactor_sbaij_mumps(Mat A, PETSC_UNUSED MatFactorType ftype, Mat *F)
3459: {
3460:   Mat         B;
3461:   Mat_MUMPS  *mumps;
3462:   PetscBool   isSeqSBAIJ;
3463:   PetscMPIInt size;

3465:   PetscFunctionBegin;
3466: #if defined(PETSC_USE_COMPLEX)
3467:   if (ftype == MAT_FACTOR_CHOLESKY && A->hermitian == PETSC_BOOL3_TRUE && A->symmetric != PETSC_BOOL3_TRUE) {
3468:     PetscCall(PetscInfo(A, "Hermitian MAT_FACTOR_CHOLESKY is not supported. Use MAT_FACTOR_LU instead.\n"));
3469:     *F = NULL;
3470:     PetscFunctionReturn(PETSC_SUCCESS);
3471:   }
3472: #endif
3473:   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
3474:   PetscCall(MatSetSizes(B, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
3475:   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &((PetscObject)B)->type_name));
3476:   PetscCall(MatSetUp(B));

3478:   PetscCall(PetscNew(&mumps));
3479:   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQSBAIJ, &isSeqSBAIJ));
3480:   if (isSeqSBAIJ) {
3481:     mumps->ConvertToTriples = MatConvertToTriples_seqsbaij_seqsbaij;
3482:   } else {
3483:     mumps->ConvertToTriples = MatConvertToTriples_mpisbaij_mpisbaij;
3484:   }

3486:   B->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_MUMPS;
3487:   B->ops->view                   = MatView_MUMPS;
3488:   B->ops->getinfo                = MatGetInfo_MUMPS;

3490:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorGetSolverType_C", MatFactorGetSolverType_mumps));
3491:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorSetSchurIS_C", MatFactorSetSchurIS_MUMPS));
3492:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorCreateSchurComplement_C", MatFactorCreateSchurComplement_MUMPS));
3493:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetIcntl_C", MatMumpsSetIcntl_MUMPS));
3494:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetIcntl_C", MatMumpsGetIcntl_MUMPS));
3495:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetCntl_C", MatMumpsSetCntl_MUMPS));
3496:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetCntl_C", MatMumpsGetCntl_MUMPS));
3497:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfo_C", MatMumpsGetInfo_MUMPS));
3498:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfog_C", MatMumpsGetInfog_MUMPS));
3499:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfo_C", MatMumpsGetRinfo_MUMPS));
3500:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfog_C", MatMumpsGetRinfog_MUMPS));
3501:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetNullPivots_C", MatMumpsGetNullPivots_MUMPS));
3502:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverse_C", MatMumpsGetInverse_MUMPS));
3503:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverseTranspose_C", MatMumpsGetInverseTranspose_MUMPS));

3505:   B->factortype = MAT_FACTOR_CHOLESKY;
3506: #if defined(PETSC_USE_COMPLEX)
3507:   mumps->sym = 2;
3508: #else
3509:   if (A->spd == PETSC_BOOL3_TRUE) mumps->sym = 1;
3510:   else mumps->sym = 2;
3511: #endif

3513:   /* set solvertype */
3514:   PetscCall(PetscFree(B->solvertype));
3515:   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &B->solvertype));
3516:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
3517:   if (size == 1) {
3518:     /* MUMPS option -mat_mumps_icntl_7 1 is automatically set if PETSc ordering is passed into symbolic factorization */
3519:     B->canuseordering = PETSC_TRUE;
3520:   }
3521:   PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&B->preferredordering[MAT_FACTOR_CHOLESKY]));
3522:   B->ops->destroy = MatDestroy_MUMPS;
3523:   B->data         = (void *)mumps;

3525:   *F               = B;
3526:   mumps->id.job    = JOB_NULL;
3527:   mumps->ICNTL_pre = NULL;
3528:   mumps->CNTL_pre  = NULL;
3529:   mumps->matstruc  = DIFFERENT_NONZERO_PATTERN;
3530:   PetscFunctionReturn(PETSC_SUCCESS);
3531: }

3533: static PetscErrorCode MatGetFactor_baij_mumps(Mat A, MatFactorType ftype, Mat *F)
3534: {
3535:   Mat         B;
3536:   Mat_MUMPS  *mumps;
3537:   PetscBool   isSeqBAIJ;
3538:   PetscMPIInt size;

3540:   PetscFunctionBegin;
3541:   /* Create the factorization matrix */
3542:   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQBAIJ, &isSeqBAIJ));
3543:   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
3544:   PetscCall(MatSetSizes(B, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
3545:   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &((PetscObject)B)->type_name));
3546:   PetscCall(MatSetUp(B));

3548:   PetscCall(PetscNew(&mumps));
3549:   if (ftype == MAT_FACTOR_LU) {
3550:     B->ops->lufactorsymbolic = MatLUFactorSymbolic_BAIJMUMPS;
3551:     B->factortype            = MAT_FACTOR_LU;
3552:     if (isSeqBAIJ) mumps->ConvertToTriples = MatConvertToTriples_seqbaij_seqaij;
3553:     else mumps->ConvertToTriples = MatConvertToTriples_mpibaij_mpiaij;
3554:     mumps->sym = 0;
3555:     PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&B->preferredordering[MAT_FACTOR_LU]));
3556:   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot use PETSc BAIJ matrices with MUMPS Cholesky, use SBAIJ or AIJ matrix instead");

3558:   B->ops->view    = MatView_MUMPS;
3559:   B->ops->getinfo = MatGetInfo_MUMPS;

3561:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorGetSolverType_C", MatFactorGetSolverType_mumps));
3562:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorSetSchurIS_C", MatFactorSetSchurIS_MUMPS));
3563:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorCreateSchurComplement_C", MatFactorCreateSchurComplement_MUMPS));
3564:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetIcntl_C", MatMumpsSetIcntl_MUMPS));
3565:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetIcntl_C", MatMumpsGetIcntl_MUMPS));
3566:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetCntl_C", MatMumpsSetCntl_MUMPS));
3567:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetCntl_C", MatMumpsGetCntl_MUMPS));
3568:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfo_C", MatMumpsGetInfo_MUMPS));
3569:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfog_C", MatMumpsGetInfog_MUMPS));
3570:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfo_C", MatMumpsGetRinfo_MUMPS));
3571:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfog_C", MatMumpsGetRinfog_MUMPS));
3572:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetNullPivots_C", MatMumpsGetNullPivots_MUMPS));
3573:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverse_C", MatMumpsGetInverse_MUMPS));
3574:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverseTranspose_C", MatMumpsGetInverseTranspose_MUMPS));

3576:   /* set solvertype */
3577:   PetscCall(PetscFree(B->solvertype));
3578:   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &B->solvertype));
3579:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
3580:   if (size == 1) {
3581:     /* MUMPS option -mat_mumps_icntl_7 1 is automatically set if PETSc ordering is passed into symbolic factorization */
3582:     B->canuseordering = PETSC_TRUE;
3583:   }
3584:   B->ops->destroy = MatDestroy_MUMPS;
3585:   B->data         = (void *)mumps;

3587:   *F               = B;
3588:   mumps->id.job    = JOB_NULL;
3589:   mumps->ICNTL_pre = NULL;
3590:   mumps->CNTL_pre  = NULL;
3591:   mumps->matstruc  = DIFFERENT_NONZERO_PATTERN;
3592:   PetscFunctionReturn(PETSC_SUCCESS);
3593: }

3595: /* MatGetFactor for Seq and MPI SELL matrices */
3596: static PetscErrorCode MatGetFactor_sell_mumps(Mat A, MatFactorType ftype, Mat *F)
3597: {
3598:   Mat         B;
3599:   Mat_MUMPS  *mumps;
3600:   PetscBool   isSeqSELL;
3601:   PetscMPIInt size;

3603:   PetscFunctionBegin;
3604:   /* Create the factorization matrix */
3605:   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQSELL, &isSeqSELL));
3606:   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
3607:   PetscCall(MatSetSizes(B, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
3608:   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &((PetscObject)B)->type_name));
3609:   PetscCall(MatSetUp(B));

3611:   PetscCall(PetscNew(&mumps));

3613:   B->ops->view    = MatView_MUMPS;
3614:   B->ops->getinfo = MatGetInfo_MUMPS;

3616:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorGetSolverType_C", MatFactorGetSolverType_mumps));
3617:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorSetSchurIS_C", MatFactorSetSchurIS_MUMPS));
3618:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorCreateSchurComplement_C", MatFactorCreateSchurComplement_MUMPS));
3619:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetIcntl_C", MatMumpsSetIcntl_MUMPS));
3620:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetIcntl_C", MatMumpsGetIcntl_MUMPS));
3621:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetCntl_C", MatMumpsSetCntl_MUMPS));
3622:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetCntl_C", MatMumpsGetCntl_MUMPS));
3623:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfo_C", MatMumpsGetInfo_MUMPS));
3624:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfog_C", MatMumpsGetInfog_MUMPS));
3625:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfo_C", MatMumpsGetRinfo_MUMPS));
3626:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfog_C", MatMumpsGetRinfog_MUMPS));
3627:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetNullPivots_C", MatMumpsGetNullPivots_MUMPS));

3629:   if (ftype == MAT_FACTOR_LU) {
3630:     B->ops->lufactorsymbolic = MatLUFactorSymbolic_AIJMUMPS;
3631:     B->factortype            = MAT_FACTOR_LU;
3632:     if (isSeqSELL) mumps->ConvertToTriples = MatConvertToTriples_seqsell_seqaij;
3633:     else SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "To be implemented");
3634:     mumps->sym = 0;
3635:     PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&B->preferredordering[MAT_FACTOR_LU]));
3636:   } else SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "To be implemented");

3638:   /* set solvertype */
3639:   PetscCall(PetscFree(B->solvertype));
3640:   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &B->solvertype));
3641:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
3642:   if (size == 1) {
3643:     /* MUMPS option -mat_mumps_icntl_7 1 is automatically set if PETSc ordering is passed into symbolic factorization  */
3644:     B->canuseordering = PETSC_TRUE;
3645:   }
3646:   B->ops->destroy = MatDestroy_MUMPS;
3647:   B->data         = (void *)mumps;

3649:   *F               = B;
3650:   mumps->id.job    = JOB_NULL;
3651:   mumps->ICNTL_pre = NULL;
3652:   mumps->CNTL_pre  = NULL;
3653:   mumps->matstruc  = DIFFERENT_NONZERO_PATTERN;
3654:   PetscFunctionReturn(PETSC_SUCCESS);
3655: }

3657: /* MatGetFactor for MATNEST matrices */
3658: static PetscErrorCode MatGetFactor_nest_mumps(Mat A, MatFactorType ftype, Mat *F)
3659: {
3660:   Mat         B, **mats;
3661:   Mat_MUMPS  *mumps;
3662:   PetscInt    nr, nc;
3663:   PetscMPIInt size;
3664:   PetscBool   flg = PETSC_TRUE;

3666:   PetscFunctionBegin;
3667: #if defined(PETSC_USE_COMPLEX)
3668:   if (ftype == MAT_FACTOR_CHOLESKY && A->hermitian == PETSC_BOOL3_TRUE && A->symmetric != PETSC_BOOL3_TRUE) {
3669:     PetscCall(PetscInfo(A, "Hermitian MAT_FACTOR_CHOLESKY is not supported. Use MAT_FACTOR_LU instead.\n"));
3670:     *F = NULL;
3671:     PetscFunctionReturn(PETSC_SUCCESS);
3672:   }
3673: #endif

3675:   /* Return if some condition is not satisfied */
3676:   *F = NULL;
3677:   PetscCall(MatNestGetSubMats(A, &nr, &nc, &mats));
3678:   if (ftype == MAT_FACTOR_CHOLESKY) {
3679:     IS       *rows, *cols;
3680:     PetscInt *m, *M;

3682:     PetscCheck(nr == nc, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "MAT_FACTOR_CHOLESKY not supported for nest sizes %" PetscInt_FMT " != %" PetscInt_FMT ". Use MAT_FACTOR_LU.", nr, nc);
3683:     PetscCall(PetscMalloc2(nr, &rows, nc, &cols));
3684:     PetscCall(MatNestGetISs(A, rows, cols));
3685:     for (PetscInt r = 0; flg && r < nr; r++) PetscCall(ISEqualUnsorted(rows[r], cols[r], &flg));
3686:     if (!flg) {
3687:       PetscCall(PetscFree2(rows, cols));
3688:       PetscCall(PetscInfo(A, "MAT_FACTOR_CHOLESKY not supported for unequal row and column maps. Use MAT_FACTOR_LU.\n"));
3689:       PetscFunctionReturn(PETSC_SUCCESS);
3690:     }
3691:     PetscCall(PetscMalloc2(nr, &m, nr, &M));
3692:     for (PetscInt r = 0; r < nr; r++) PetscCall(ISGetMinMax(rows[r], &m[r], &M[r]));
3693:     for (PetscInt r = 0; flg && r < nr; r++)
3694:       for (PetscInt k = r + 1; flg && k < nr; k++)
3695:         if ((m[k] <= m[r] && m[r] <= M[k]) || (m[k] <= M[r] && M[r] <= M[k])) flg = PETSC_FALSE;
3696:     PetscCall(PetscFree2(m, M));
3697:     PetscCall(PetscFree2(rows, cols));
3698:     if (!flg) {
3699:       PetscCall(PetscInfo(A, "MAT_FACTOR_CHOLESKY not supported for intersecting row maps. Use MAT_FACTOR_LU.\n"));
3700:       PetscFunctionReturn(PETSC_SUCCESS);
3701:     }
3702:   }

3704:   for (PetscInt r = 0; r < nr; r++) {
3705:     for (PetscInt c = 0; c < nc; c++) {
3706:       Mat       sub = mats[r][c];
3707:       PetscBool isSeqAIJ, isMPIAIJ, isSeqBAIJ, isMPIBAIJ, isSeqSBAIJ, isMPISBAIJ, isTrans, isDiag, isDense;

3709:       if (!sub || (ftype == MAT_FACTOR_CHOLESKY && c < r)) continue;
3710:       PetscCall(PetscObjectTypeCompare((PetscObject)sub, MATTRANSPOSEVIRTUAL, &isTrans));
3711:       if (isTrans) PetscCall(MatTransposeGetMat(sub, &sub));
3712:       else {
3713:         PetscCall(PetscObjectTypeCompare((PetscObject)sub, MATHERMITIANTRANSPOSEVIRTUAL, &isTrans));
3714:         if (isTrans) PetscCall(MatHermitianTransposeGetMat(sub, &sub));
3715:       }
3716:       PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATSEQAIJ, &isSeqAIJ));
3717:       PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATMPIAIJ, &isMPIAIJ));
3718:       PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATSEQBAIJ, &isSeqBAIJ));
3719:       PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATMPIBAIJ, &isMPIBAIJ));
3720:       PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATSEQSBAIJ, &isSeqSBAIJ));
3721:       PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATMPISBAIJ, &isMPISBAIJ));
3722:       PetscCall(PetscObjectTypeCompare((PetscObject)sub, MATDIAGONAL, &isDiag));
3723:       PetscCall(PetscObjectTypeCompareAny((PetscObject)sub, &isDense, MATSEQDENSE, MATMPIDENSE, NULL));
3724:       if (ftype == MAT_FACTOR_CHOLESKY) {
3725:         if (r == c) {
3726:           if (!isSeqAIJ && !isMPIAIJ && !isSeqBAIJ && !isMPIBAIJ && !isSeqSBAIJ && !isMPISBAIJ && !isDiag && !isDense) {
3727:             PetscCall(PetscInfo(sub, "MAT_FACTOR_CHOLESKY not supported for diagonal block of type %s.\n", ((PetscObject)sub)->type_name));
3728:             flg = PETSC_FALSE;
3729:           }
3730:         } else if (!isSeqAIJ && !isMPIAIJ && !isSeqBAIJ && !isMPIBAIJ && !isDiag && !isDense) {
3731:           PetscCall(PetscInfo(sub, "MAT_FACTOR_CHOLESKY not supported for off-diagonal block of type %s.\n", ((PetscObject)sub)->type_name));
3732:           flg = PETSC_FALSE;
3733:         }
3734:       } else if (!isSeqAIJ && !isMPIAIJ && !isSeqBAIJ && !isMPIBAIJ && !isDiag && !isDense) {
3735:         PetscCall(PetscInfo(sub, "MAT_FACTOR_LU not supported for block of type %s.\n", ((PetscObject)sub)->type_name));
3736:         flg = PETSC_FALSE;
3737:       }
3738:     }
3739:   }
3740:   if (!flg) PetscFunctionReturn(PETSC_SUCCESS);

3742:   /* Create the factorization matrix */
3743:   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
3744:   PetscCall(MatSetSizes(B, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
3745:   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &((PetscObject)B)->type_name));
3746:   PetscCall(MatSetUp(B));

3748:   PetscCall(PetscNew(&mumps));

3750:   B->ops->view    = MatView_MUMPS;
3751:   B->ops->getinfo = MatGetInfo_MUMPS;

3753:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorGetSolverType_C", MatFactorGetSolverType_mumps));
3754:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorSetSchurIS_C", MatFactorSetSchurIS_MUMPS));
3755:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorCreateSchurComplement_C", MatFactorCreateSchurComplement_MUMPS));
3756:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetIcntl_C", MatMumpsSetIcntl_MUMPS));
3757:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetIcntl_C", MatMumpsGetIcntl_MUMPS));
3758:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetCntl_C", MatMumpsSetCntl_MUMPS));
3759:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetCntl_C", MatMumpsGetCntl_MUMPS));
3760:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfo_C", MatMumpsGetInfo_MUMPS));
3761:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfog_C", MatMumpsGetInfog_MUMPS));
3762:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfo_C", MatMumpsGetRinfo_MUMPS));
3763:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfog_C", MatMumpsGetRinfog_MUMPS));
3764:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetNullPivots_C", MatMumpsGetNullPivots_MUMPS));
3765:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverse_C", MatMumpsGetInverse_MUMPS));
3766:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverseTranspose_C", MatMumpsGetInverseTranspose_MUMPS));

3768:   if (ftype == MAT_FACTOR_LU) {
3769:     B->ops->lufactorsymbolic = MatLUFactorSymbolic_AIJMUMPS;
3770:     B->factortype            = MAT_FACTOR_LU;
3771:     mumps->sym               = 0;
3772:   } else {
3773:     B->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_MUMPS;
3774:     B->factortype                  = MAT_FACTOR_CHOLESKY;
3775: #if defined(PETSC_USE_COMPLEX)
3776:     mumps->sym = 2;
3777: #else
3778:     if (A->spd == PETSC_BOOL3_TRUE) mumps->sym = 1;
3779:     else mumps->sym = 2;
3780: #endif
3781:   }
3782:   mumps->ConvertToTriples = MatConvertToTriples_nest_xaij;
3783:   PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&B->preferredordering[ftype]));

3785:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
3786:   if (size == 1) {
3787:     /* MUMPS option -mat_mumps_icntl_7 1 is automatically set if PETSc ordering is passed into symbolic factorization */
3788:     B->canuseordering = PETSC_TRUE;
3789:   }

3791:   /* set solvertype */
3792:   PetscCall(PetscFree(B->solvertype));
3793:   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &B->solvertype));
3794:   B->ops->destroy = MatDestroy_MUMPS;
3795:   B->data         = (void *)mumps;

3797:   *F               = B;
3798:   mumps->id.job    = JOB_NULL;
3799:   mumps->ICNTL_pre = NULL;
3800:   mumps->CNTL_pre  = NULL;
3801:   mumps->matstruc  = DIFFERENT_NONZERO_PATTERN;
3802:   PetscFunctionReturn(PETSC_SUCCESS);
3803: }

3805: PETSC_EXTERN PetscErrorCode MatSolverTypeRegister_MUMPS(void)
3806: {
3807:   PetscFunctionBegin;
3808:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPIAIJ, MAT_FACTOR_LU, MatGetFactor_aij_mumps));
3809:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPIAIJ, MAT_FACTOR_CHOLESKY, MatGetFactor_aij_mumps));
3810:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPIBAIJ, MAT_FACTOR_LU, MatGetFactor_baij_mumps));
3811:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPIBAIJ, MAT_FACTOR_CHOLESKY, MatGetFactor_baij_mumps));
3812:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPISBAIJ, MAT_FACTOR_CHOLESKY, MatGetFactor_sbaij_mumps));
3813:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQAIJ, MAT_FACTOR_LU, MatGetFactor_aij_mumps));
3814:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQAIJ, MAT_FACTOR_CHOLESKY, MatGetFactor_aij_mumps));
3815:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQBAIJ, MAT_FACTOR_LU, MatGetFactor_baij_mumps));
3816:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQBAIJ, MAT_FACTOR_CHOLESKY, MatGetFactor_baij_mumps));
3817:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQSBAIJ, MAT_FACTOR_CHOLESKY, MatGetFactor_sbaij_mumps));
3818:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQSELL, MAT_FACTOR_LU, MatGetFactor_sell_mumps));
3819:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATDIAGONAL, MAT_FACTOR_LU, MatGetFactor_aij_mumps));
3820:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATDIAGONAL, MAT_FACTOR_CHOLESKY, MatGetFactor_aij_mumps));
3821:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQDENSE, MAT_FACTOR_LU, MatGetFactor_aij_mumps));
3822:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQDENSE, MAT_FACTOR_CHOLESKY, MatGetFactor_aij_mumps));
3823:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPIDENSE, MAT_FACTOR_LU, MatGetFactor_aij_mumps));
3824:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPIDENSE, MAT_FACTOR_CHOLESKY, MatGetFactor_aij_mumps));
3825:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATNEST, MAT_FACTOR_LU, MatGetFactor_nest_mumps));
3826:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATNEST, MAT_FACTOR_CHOLESKY, MatGetFactor_nest_mumps));
3827:   PetscFunctionReturn(PETSC_SUCCESS);
3828: }