xref: /petsc/src/mat/impls/aij/mpi/mumps/mumps.c (revision e91c04dfc8a52dee1965211bb1cc8e5bf775178f)
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> /*I  "petscmat.h"  I*/
7 #include <../src/mat/impls/sbaij/mpi/mpisbaij.h>
8 #include <../src/mat/impls/sell/mpi/mpisell.h>
9 
10 #define MUMPS_MANUALS "(see users manual https://mumps-solver.org/index.php?page=doc \"Error and warning diagnostics\")"
11 
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
33 
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
48 
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;
54 
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
64 
65 #define MPIU_MUMPSINT       MPI_INT
66 #define PETSC_MUMPS_INT_MAX 2147483647
67 #define PETSC_MUMPS_INT_MIN -2147483648
68 
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(PetscCount 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 }
79 
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;
85 
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)
94 
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
131 
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
142 
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]
150 
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
166 
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   PetscCount     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   PetscCount     cur_ilen, cur_jlen;  /* current len of ia_alloc[], ja_alloc[] */
192   PetscErrorCode (*ConvertToTriples)(Mat, PetscInt, MatReuse, Mat_MUMPS *);
193 
194   /* Support for MATNEST */
195   PetscErrorCode (**nest_convert_to_triples)(Mat, PetscInt, MatReuse, Mat_MUMPS *);
196   PetscCount  *nest_vals_start;
197   PetscScalar *nest_vals;
198 
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   PetscCount  *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 };
208 
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 PetscCount since mumps only uses PetscMUMPSInt for rhs */
215 
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 }
242 
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 }
254 
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;
262 
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));
305 
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 }
316 
317 static PetscErrorCode MatMumpsHandleSchur_Private(Mat F, PetscBool expansion)
318 {
319   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;
320 
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 }
351 
352 /*
353   MatConvertToTriples_A_B - convert Petsc matrix to triples: row[nz], col[nz], val[nz]
354 
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)
363 
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().
367 
368  */
369 
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   PetscCount         nz, rnz, k;
375   PetscMUMPSInt     *row, *col;
376   Mat_SeqAIJ        *aa = (Mat_SeqAIJ *)A->data;
377 
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 (PetscCount i = k = 0; i < M; i++) {
386       rnz = ai[i + 1] - ai[i];
387       ajj = aj + ai[i];
388       for (PetscCount 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 }
403 
404 static PetscErrorCode MatConvertToTriples_seqsell_seqaij(Mat A, PetscInt shift, MatReuse reuse, Mat_MUMPS *mumps)
405 {
406   PetscCount     nz, i, j, k, r;
407   Mat_SeqSELL   *a = (Mat_SeqSELL *)A->data;
408   PetscMUMPSInt *row, *col;
409 
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 }
426 
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   PetscCount      M, nz = bs2 * aa->nz, idx = 0, rnz, i, j, k, m;
432   PetscInt        bs;
433   PetscMUMPSInt  *row, *col;
434 
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 }
463 
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   PetscCount      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
476 
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 PetscCount alloc_size = aa->nz * bs2;
487 
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;
502 
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 %" PetscCount_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 }
539 
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   PetscCount         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
552 
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;
586 
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 }
648 
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   PetscCount         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
664 
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;
678 
679   garray = mat->garray;
680 
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   }
692 
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;
702 
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       }
718 
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       }
740 
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 }
755 
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   PetscCount         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;
766 
767   PetscFunctionBegin;
768   PetscCall(MatMPIAIJGetSeqAIJ(A, &Ad, &Ao, &garray));
769   PetscCall(MatSeqAIJGetArrayRead(Ad, &av));
770   PetscCall(MatSeqAIJGetArrayRead(Ao, &bv));
771 
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;
778 
779   rstart = A->rmap->rstart;
780   cstart = A->cmap->rstart;
781 
782   if (reuse == MAT_INITIAL_MATRIX) {
783     nz = (PetscCount)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   }
793 
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];
803 
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     }
812 
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 }
827 
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   PetscCount         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;
841 
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   }
855 
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];
865 
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     }
879 
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 }
897 
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   PetscCount         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
911 
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));
920 
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;
928 
929   rstart = A->rmap->rstart;
930 
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     }
942 
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   }
953 
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];
963 
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     }
972 
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 }
989 
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   PetscCount         i;
995   PetscMUMPSInt     *row, *col;
996   Vec                v;
997 
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 }
1016 
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   PetscCount     i, j;
1023   PetscMUMPSInt *row, *col;
1024 
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 }
1056 
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;
1062 
1063   PetscFunctionBegin;
1064   PetscCall(MatNestGetSubMats(A, &nr, &nc, &mats));
1065   if (reuse == MAT_INITIAL_MATRIX) {
1066     PetscMUMPSInt *irns, *jcns;
1067     PetscScalar   *vals;
1068     PetscCount     totnnz, cumnnz, maxnnz;
1069     PetscInt      *pjcns_w;
1070     IS            *rows, *cols;
1071     PetscInt     **rows_idx, **cols_idx;
1072 
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];
1079 
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;
1086 
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));
1101 
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 += (PetscCount)info.nz_used; /* can be overestimated for Cholesky */
1130           maxnnz = PetscMax(maxnnz, info.nz_used);
1131         }
1132       }
1133     }
1134 
1135     /* Allocate total COO */
1136     totnnz = cumnnz;
1137     PetscCall(PetscMalloc2(totnnz, &irns, totnnz, &jcns));
1138     PetscCall(PetscMalloc1(totnnz, &vals));
1139 
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;
1148 
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;
1159         PetscInt        innz;
1160 
1161         mumps->nest_vals_start[r * nc + c] = cumnnz;
1162         if (!mumps->nest_convert_to_triples[r * nc + c]) continue;
1163 
1164         /* Extract inner blocks if needed */
1165         PetscCall(PetscObjectTypeCompare((PetscObject)sub, MATTRANSPOSEVIRTUAL, &isTrans));
1166         if (isTrans) PetscCall(MatTransposeGetMat(sub, &sub));
1167         else {
1168           PetscCall(PetscObjectTypeCompare((PetscObject)sub, MATHERMITIANTRANSPOSEVIRTUAL, &isHTrans));
1169           if (isHTrans) PetscCall(MatHermitianTransposeGetMat(sub, &sub));
1170         }
1171         swap = (PetscBool)(isTrans || isHTrans);
1172 
1173         /* Get column layout to map off-process columns */
1174         PetscCall(MatGetLayouts(sub, NULL, &cmap));
1175 
1176         /* Get row start to map on-process rows */
1177         PetscCall(MatGetOwnershipRange(sub, &rst, NULL));
1178 
1179         /* Directly use the mumps datastructure and use C ordering for now */
1180         PetscCall((*mumps->nest_convert_to_triples[r * nc + c])(sub, 0, MAT_INITIAL_MATRIX, mumps));
1181 
1182         /* Swap the role of rows and columns indices for transposed blocks
1183            since we need values with global final ordering */
1184         if (swap) {
1185           cidx = rows_idx[r];
1186           ridx = cols_idx[c];
1187         }
1188 
1189         /* Communicate column indices
1190            This could have been done with a single SF but it would have complicated the code a lot.
1191            But since we do it only once, we pay the price of setting up an SF for each block */
1192         if (PetscDefined(USE_64BIT_INDICES)) {
1193           for (PetscInt k = 0; k < mumps->nnz; k++) pjcns_w[k] = mumps->jcn[k];
1194         } else pjcns_w = (PetscInt *)mumps->jcn; /* This cast is needed only to silence warnings for 64bit integers builds */
1195         PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &csf));
1196         PetscCall(PetscIntCast(mumps->nnz, &innz));
1197         PetscCall(PetscSFSetGraphLayout(csf, cmap, innz, NULL, PETSC_OWN_POINTER, pjcns_w));
1198         PetscCall(PetscSFBcastBegin(csf, MPIU_INT, cidx, pjcns_w, MPI_REPLACE));
1199         PetscCall(PetscSFBcastEnd(csf, MPIU_INT, cidx, pjcns_w, MPI_REPLACE));
1200         PetscCall(PetscSFDestroy(&csf));
1201 
1202         /* Import indices: use direct map for rows and mapped indices for columns */
1203         if (swap) {
1204           for (PetscInt k = 0; k < mumps->nnz; k++) {
1205             PetscCall(PetscMUMPSIntCast(ridx[mumps->irn[k] - rst] + shift, &jcns[cumnnz + k]));
1206             PetscCall(PetscMUMPSIntCast(pjcns_w[k] + shift, &irns[cumnnz + k]));
1207           }
1208         } else {
1209           for (PetscInt k = 0; k < mumps->nnz; k++) {
1210             PetscCall(PetscMUMPSIntCast(ridx[mumps->irn[k] - rst] + shift, &irns[cumnnz + k]));
1211             PetscCall(PetscMUMPSIntCast(pjcns_w[k] + shift, &jcns[cumnnz + k]));
1212           }
1213         }
1214 
1215         /* Import values to full COO */
1216         PetscCall(PetscArraycpy(vals + cumnnz, mumps->val, mumps->nnz));
1217         if (isHTrans) { /* conjugate the entries */
1218           PetscScalar *v = vals + cumnnz;
1219           for (PetscInt k = 0; k < mumps->nnz; k++) v[k] = PetscConj(v[k]);
1220         }
1221 
1222         /* Shift new starting point and sanity check */
1223         cumnnz += mumps->nnz;
1224         PetscCheck(cumnnz <= totnnz, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unexpected number of nonzeros %" PetscCount_FMT " != %" PetscCount_FMT, cumnnz, totnnz);
1225 
1226         /* Free scratch memory */
1227         PetscCall(PetscFree2(mumps->irn, mumps->jcn));
1228         PetscCall(PetscFree(mumps->val_alloc));
1229         mumps->val = NULL;
1230         mumps->nnz = 0;
1231       }
1232     }
1233     if (PetscDefined(USE_64BIT_INDICES)) PetscCall(PetscFree(pjcns_w));
1234     for (PetscInt r = 0; r < nr; r++) PetscCall(ISRestoreIndices(rows[r], (const PetscInt **)&rows_idx[r]));
1235     for (PetscInt c = 0; c < nc; c++) PetscCall(ISRestoreIndices(cols[c], (const PetscInt **)&cols_idx[c]));
1236     PetscCall(PetscFree4(rows, cols, rows_idx, cols_idx));
1237     if (!chol) PetscCheck(cumnnz == totnnz, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Different number of nonzeros %" PetscCount_FMT " != %" PetscCount_FMT, cumnnz, totnnz);
1238     mumps->nest_vals_start[nr * nc] = cumnnz;
1239 
1240     /* Set pointers for final MUMPS data structure */
1241     mumps->nest_vals = vals;
1242     mumps->val_alloc = NULL; /* do not use val_alloc since it may be reallocated with the OMP callpath */
1243     mumps->val       = vals;
1244     mumps->irn       = irns;
1245     mumps->jcn       = jcns;
1246     mumps->nnz       = cumnnz;
1247   } else {
1248     PetscScalar *oval = mumps->nest_vals;
1249     for (PetscInt r = 0; r < nr; r++) {
1250       for (PetscInt c = 0; c < nc; c++) {
1251         PetscBool isTrans, isHTrans = PETSC_FALSE;
1252         Mat       sub  = mats[r][c];
1253         PetscInt  midx = r * nc + c;
1254 
1255         if (!mumps->nest_convert_to_triples[midx]) continue;
1256         PetscCall(PetscObjectTypeCompare((PetscObject)sub, MATTRANSPOSEVIRTUAL, &isTrans));
1257         if (isTrans) PetscCall(MatTransposeGetMat(sub, &sub));
1258         else {
1259           PetscCall(PetscObjectTypeCompare((PetscObject)sub, MATHERMITIANTRANSPOSEVIRTUAL, &isHTrans));
1260           if (isHTrans) PetscCall(MatHermitianTransposeGetMat(sub, &sub));
1261         }
1262         mumps->val = oval + mumps->nest_vals_start[midx];
1263         PetscCall((*mumps->nest_convert_to_triples[midx])(sub, shift, MAT_REUSE_MATRIX, mumps));
1264         if (isHTrans) {
1265           PetscCount nnz = mumps->nest_vals_start[midx + 1] - mumps->nest_vals_start[midx];
1266           for (PetscCount k = 0; k < nnz; k++) mumps->val[k] = PetscConj(mumps->val[k]);
1267         }
1268       }
1269     }
1270     mumps->val = oval;
1271   }
1272   PetscFunctionReturn(PETSC_SUCCESS);
1273 }
1274 
1275 static PetscErrorCode MatDestroy_MUMPS(Mat A)
1276 {
1277   Mat_MUMPS *mumps = (Mat_MUMPS *)A->data;
1278 
1279   PetscFunctionBegin;
1280   PetscCall(PetscFree2(mumps->id.sol_loc, mumps->id.isol_loc));
1281   PetscCall(VecScatterDestroy(&mumps->scat_rhs));
1282   PetscCall(VecScatterDestroy(&mumps->scat_sol));
1283   PetscCall(VecDestroy(&mumps->b_seq));
1284   PetscCall(VecDestroy(&mumps->x_seq));
1285   PetscCall(PetscFree(mumps->id.perm_in));
1286   PetscCall(PetscFree2(mumps->irn, mumps->jcn));
1287   PetscCall(PetscFree(mumps->val_alloc));
1288   PetscCall(PetscFree(mumps->info));
1289   PetscCall(PetscFree(mumps->ICNTL_pre));
1290   PetscCall(PetscFree(mumps->CNTL_pre));
1291   PetscCall(MatMumpsResetSchur_Private(mumps));
1292   if (mumps->id.job != JOB_NULL) { /* cannot call PetscMUMPS_c() if JOB_INIT has never been called for this instance */
1293     mumps->id.job = JOB_END;
1294     PetscMUMPS_c(mumps);
1295     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));
1296     if (mumps->mumps_comm != MPI_COMM_NULL) {
1297       if (PetscDefined(HAVE_OPENMP_SUPPORT) && mumps->use_petsc_omp_support) PetscCallMPI(MPI_Comm_free(&mumps->mumps_comm));
1298       else PetscCall(PetscCommRestoreComm(PetscObjectComm((PetscObject)A), &mumps->mumps_comm));
1299     }
1300   }
1301 #if defined(PETSC_HAVE_OPENMP_SUPPORT)
1302   if (mumps->use_petsc_omp_support) {
1303     PetscCall(PetscOmpCtrlDestroy(&mumps->omp_ctrl));
1304     PetscCall(PetscFree2(mumps->rhs_loc, mumps->rhs_recvbuf));
1305     PetscCall(PetscFree3(mumps->rhs_nrow, mumps->rhs_recvcounts, mumps->rhs_disps));
1306   }
1307 #endif
1308   PetscCall(PetscFree(mumps->ia_alloc));
1309   PetscCall(PetscFree(mumps->ja_alloc));
1310   PetscCall(PetscFree(mumps->recvcount));
1311   PetscCall(PetscFree(mumps->reqs));
1312   PetscCall(PetscFree(mumps->irhs_loc));
1313   PetscCall(PetscFree2(mumps->nest_vals_start, mumps->nest_convert_to_triples));
1314   PetscCall(PetscFree(mumps->nest_vals));
1315   PetscCall(PetscFree(A->data));
1316 
1317   /* clear composed functions */
1318   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatFactorGetSolverType_C", NULL));
1319   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatFactorSetSchurIS_C", NULL));
1320   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatFactorCreateSchurComplement_C", NULL));
1321   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsSetIcntl_C", NULL));
1322   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetIcntl_C", NULL));
1323   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsSetCntl_C", NULL));
1324   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetCntl_C", NULL));
1325   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetInfo_C", NULL));
1326   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetInfog_C", NULL));
1327   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetRinfo_C", NULL));
1328   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetRinfog_C", NULL));
1329   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetNullPivots_C", NULL));
1330   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetInverse_C", NULL));
1331   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetInverseTranspose_C", NULL));
1332   PetscFunctionReturn(PETSC_SUCCESS);
1333 }
1334 
1335 /* Set up the distributed RHS info for MUMPS. <nrhs> is the number of RHS. <array> points to start of RHS on the local processor. */
1336 static PetscErrorCode MatMumpsSetUpDistRHSInfo(Mat A, PetscInt nrhs, const PetscScalar *array)
1337 {
1338   Mat_MUMPS        *mumps   = (Mat_MUMPS *)A->data;
1339   const PetscMPIInt ompsize = mumps->omp_comm_size;
1340   PetscInt          i, m, M, rstart;
1341 
1342   PetscFunctionBegin;
1343   PetscCall(MatGetSize(A, &M, NULL));
1344   PetscCall(MatGetLocalSize(A, &m, NULL));
1345   PetscCheck(M <= PETSC_MUMPS_INT_MAX, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "PetscInt too long for PetscMUMPSInt");
1346   if (ompsize == 1) {
1347     if (!mumps->irhs_loc) {
1348       mumps->nloc_rhs = (PetscMUMPSInt)m;
1349       PetscCall(PetscMalloc1(m, &mumps->irhs_loc));
1350       PetscCall(MatGetOwnershipRange(A, &rstart, NULL));
1351       for (i = 0; i < m; i++) PetscCall(PetscMUMPSIntCast(rstart + i + 1, &mumps->irhs_loc[i])); /* use 1-based indices */
1352     }
1353     mumps->id.rhs_loc = (MumpsScalar *)array;
1354   } else {
1355 #if defined(PETSC_HAVE_OPENMP_SUPPORT)
1356     const PetscInt *ranges;
1357     PetscMPIInt     j, k, sendcount, *petsc_ranks, *omp_ranks;
1358     MPI_Group       petsc_group, omp_group;
1359     PetscScalar    *recvbuf = NULL;
1360 
1361     if (mumps->is_omp_master) {
1362       /* Lazily initialize the omp stuff for distributed rhs */
1363       if (!mumps->irhs_loc) {
1364         PetscCall(PetscMalloc2(ompsize, &omp_ranks, ompsize, &petsc_ranks));
1365         PetscCall(PetscMalloc3(ompsize, &mumps->rhs_nrow, ompsize, &mumps->rhs_recvcounts, ompsize, &mumps->rhs_disps));
1366         PetscCallMPI(MPI_Comm_group(mumps->petsc_comm, &petsc_group));
1367         PetscCallMPI(MPI_Comm_group(mumps->omp_comm, &omp_group));
1368         for (j = 0; j < ompsize; j++) omp_ranks[j] = j;
1369         PetscCallMPI(MPI_Group_translate_ranks(omp_group, ompsize, omp_ranks, petsc_group, petsc_ranks));
1370 
1371         /* Populate mumps->irhs_loc[], rhs_nrow[] */
1372         mumps->nloc_rhs = 0;
1373         PetscCall(MatGetOwnershipRanges(A, &ranges));
1374         for (j = 0; j < ompsize; j++) {
1375           mumps->rhs_nrow[j] = ranges[petsc_ranks[j] + 1] - ranges[petsc_ranks[j]];
1376           mumps->nloc_rhs += mumps->rhs_nrow[j];
1377         }
1378         PetscCall(PetscMalloc1(mumps->nloc_rhs, &mumps->irhs_loc));
1379         for (j = k = 0; j < ompsize; j++) {
1380           for (i = ranges[petsc_ranks[j]]; i < ranges[petsc_ranks[j] + 1]; i++, k++) mumps->irhs_loc[k] = i + 1; /* uses 1-based indices */
1381         }
1382 
1383         PetscCall(PetscFree2(omp_ranks, petsc_ranks));
1384         PetscCallMPI(MPI_Group_free(&petsc_group));
1385         PetscCallMPI(MPI_Group_free(&omp_group));
1386       }
1387 
1388       /* Realloc buffers when current nrhs is bigger than what we have met */
1389       if (nrhs > mumps->max_nrhs) {
1390         PetscCall(PetscFree2(mumps->rhs_loc, mumps->rhs_recvbuf));
1391         PetscCall(PetscMalloc2(mumps->nloc_rhs * nrhs, &mumps->rhs_loc, mumps->nloc_rhs * nrhs, &mumps->rhs_recvbuf));
1392         mumps->max_nrhs = nrhs;
1393       }
1394 
1395       /* Setup recvcounts[], disps[], recvbuf on omp rank 0 for the upcoming MPI_Gatherv */
1396       for (j = 0; j < ompsize; j++) PetscCall(PetscMPIIntCast(mumps->rhs_nrow[j] * nrhs, &mumps->rhs_recvcounts[j]));
1397       mumps->rhs_disps[0] = 0;
1398       for (j = 1; j < ompsize; j++) {
1399         mumps->rhs_disps[j] = mumps->rhs_disps[j - 1] + mumps->rhs_recvcounts[j - 1];
1400         PetscCheck(mumps->rhs_disps[j] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "PetscMPIInt overflow!");
1401       }
1402       recvbuf = (nrhs == 1) ? mumps->rhs_loc : mumps->rhs_recvbuf; /* Directly use rhs_loc[] as recvbuf. Single rhs is common in Ax=b */
1403     }
1404 
1405     PetscCall(PetscMPIIntCast(m * nrhs, &sendcount));
1406     PetscCallMPI(MPI_Gatherv(array, sendcount, MPIU_SCALAR, recvbuf, mumps->rhs_recvcounts, mumps->rhs_disps, MPIU_SCALAR, 0, mumps->omp_comm));
1407 
1408     if (mumps->is_omp_master) {
1409       if (nrhs > 1) { /* Copy & re-arrange data from rhs_recvbuf[] to mumps->rhs_loc[] only when there are multiple rhs */
1410         PetscScalar *dst, *dstbase = mumps->rhs_loc;
1411         for (j = 0; j < ompsize; j++) {
1412           const PetscScalar *src = mumps->rhs_recvbuf + mumps->rhs_disps[j];
1413           dst                    = dstbase;
1414           for (i = 0; i < nrhs; i++) {
1415             PetscCall(PetscArraycpy(dst, src, mumps->rhs_nrow[j]));
1416             src += mumps->rhs_nrow[j];
1417             dst += mumps->nloc_rhs;
1418           }
1419           dstbase += mumps->rhs_nrow[j];
1420         }
1421       }
1422       mumps->id.rhs_loc = (MumpsScalar *)mumps->rhs_loc;
1423     }
1424 #endif /* PETSC_HAVE_OPENMP_SUPPORT */
1425   }
1426   mumps->id.nrhs     = (PetscMUMPSInt)nrhs;
1427   mumps->id.nloc_rhs = (PetscMUMPSInt)mumps->nloc_rhs;
1428   mumps->id.lrhs_loc = mumps->nloc_rhs;
1429   mumps->id.irhs_loc = mumps->irhs_loc;
1430   PetscFunctionReturn(PETSC_SUCCESS);
1431 }
1432 
1433 static PetscErrorCode MatSolve_MUMPS(Mat A, Vec b, Vec x)
1434 {
1435   Mat_MUMPS         *mumps  = (Mat_MUMPS *)A->data;
1436   const PetscScalar *rarray = NULL;
1437   PetscScalar       *array;
1438   IS                 is_iden, is_petsc;
1439   PetscInt           i;
1440   PetscBool          second_solve = PETSC_FALSE;
1441   static PetscBool   cite1 = PETSC_FALSE, cite2 = PETSC_FALSE;
1442 
1443   PetscFunctionBegin;
1444   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 "
1445                                    "Journal on Matrix Analysis and Applications},\n  volume = {23},\n  number = {1},\n  pages = {15--41},\n  year = {2001}\n}\n",
1446                                    &cite1));
1447   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 "
1448                                    "Computing},\n  volume = {32},\n  number = {2},\n  pages = {136--156},\n  year = {2006}\n}\n",
1449                                    &cite2));
1450 
1451   PetscCall(VecFlag(x, A->factorerrortype));
1452   if (A->factorerrortype) {
1453     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)));
1454     PetscFunctionReturn(PETSC_SUCCESS);
1455   }
1456 
1457   mumps->id.nrhs = 1;
1458   if (mumps->petsc_size > 1) {
1459     if (mumps->ICNTL20 == 10) {
1460       mumps->id.ICNTL(20) = 10; /* dense distributed RHS */
1461       PetscCall(VecGetArrayRead(b, &rarray));
1462       PetscCall(MatMumpsSetUpDistRHSInfo(A, 1, rarray));
1463     } else {
1464       mumps->id.ICNTL(20) = 0; /* dense centralized RHS; Scatter b into a sequential rhs vector*/
1465       PetscCall(VecScatterBegin(mumps->scat_rhs, b, mumps->b_seq, INSERT_VALUES, SCATTER_FORWARD));
1466       PetscCall(VecScatterEnd(mumps->scat_rhs, b, mumps->b_seq, INSERT_VALUES, SCATTER_FORWARD));
1467       if (!mumps->myid) {
1468         PetscCall(VecGetArray(mumps->b_seq, &array));
1469         mumps->id.rhs = (MumpsScalar *)array;
1470       }
1471     }
1472   } else {                   /* petsc_size == 1 */
1473     mumps->id.ICNTL(20) = 0; /* dense centralized RHS */
1474     PetscCall(VecCopy(b, x));
1475     PetscCall(VecGetArray(x, &array));
1476     mumps->id.rhs = (MumpsScalar *)array;
1477   }
1478 
1479   /*
1480      handle condensation step of Schur complement (if any)
1481      We set by default ICNTL(26) == -1 when Schur indices have been provided by the user.
1482      According to MUMPS (5.0.0) manual, any value should be harmful during the factorization phase
1483      Unless the user provides a valid value for ICNTL(26), MatSolve and MatMatSolve routines solve the full system.
1484      This requires an extra call to PetscMUMPS_c and the computation of the factors for S
1485   */
1486   if (mumps->id.size_schur > 0) {
1487     PetscCheck(mumps->petsc_size <= 1, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Parallel Schur complements not yet supported from PETSc");
1488     if (mumps->id.ICNTL(26) < 0 || mumps->id.ICNTL(26) > 2) {
1489       second_solve = PETSC_TRUE;
1490       PetscCall(MatMumpsHandleSchur_Private(A, PETSC_FALSE));
1491       mumps->id.ICNTL(26) = 1; /* condensation phase */
1492     } else if (mumps->id.ICNTL(26) == 1) PetscCall(MatMumpsHandleSchur_Private(A, PETSC_FALSE));
1493   }
1494   /* solve phase */
1495   mumps->id.job = JOB_SOLVE;
1496   PetscMUMPS_c(mumps);
1497   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));
1498 
1499   /* handle expansion step of Schur complement (if any) */
1500   if (second_solve) PetscCall(MatMumpsHandleSchur_Private(A, PETSC_TRUE));
1501   else if (mumps->id.ICNTL(26) == 1) {
1502     PetscCall(MatMumpsSolveSchur_Private(A));
1503     for (i = 0; i < mumps->id.size_schur; ++i) {
1504 #if !defined(PETSC_USE_COMPLEX)
1505       PetscScalar val = mumps->id.redrhs[i];
1506 #else
1507       PetscScalar val = mumps->id.redrhs[i].r + PETSC_i * mumps->id.redrhs[i].i;
1508 #endif
1509       array[mumps->id.listvar_schur[i] - 1] = val;
1510     }
1511   }
1512 
1513   if (mumps->petsc_size > 1) { /* convert mumps distributed solution to petsc mpi x */
1514     if (mumps->scat_sol && mumps->ICNTL9_pre != mumps->id.ICNTL(9)) {
1515       /* when id.ICNTL(9) changes, the contents of lsol_loc may change (not its size, lsol_loc), recreates scat_sol */
1516       PetscCall(VecScatterDestroy(&mumps->scat_sol));
1517     }
1518     if (!mumps->scat_sol) { /* create scatter scat_sol */
1519       PetscInt *isol2_loc = NULL;
1520       PetscCall(ISCreateStride(PETSC_COMM_SELF, mumps->id.lsol_loc, 0, 1, &is_iden)); /* from */
1521       PetscCall(PetscMalloc1(mumps->id.lsol_loc, &isol2_loc));
1522       for (i = 0; i < mumps->id.lsol_loc; i++) isol2_loc[i] = mumps->id.isol_loc[i] - 1;                        /* change Fortran style to C style */
1523       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, mumps->id.lsol_loc, isol2_loc, PETSC_OWN_POINTER, &is_petsc)); /* to */
1524       PetscCall(VecScatterCreate(mumps->x_seq, is_iden, x, is_petsc, &mumps->scat_sol));
1525       PetscCall(ISDestroy(&is_iden));
1526       PetscCall(ISDestroy(&is_petsc));
1527       mumps->ICNTL9_pre = mumps->id.ICNTL(9); /* save current value of id.ICNTL(9) */
1528     }
1529 
1530     PetscCall(VecScatterBegin(mumps->scat_sol, mumps->x_seq, x, INSERT_VALUES, SCATTER_FORWARD));
1531     PetscCall(VecScatterEnd(mumps->scat_sol, mumps->x_seq, x, INSERT_VALUES, SCATTER_FORWARD));
1532   }
1533 
1534   if (mumps->petsc_size > 1) {
1535     if (mumps->ICNTL20 == 10) {
1536       PetscCall(VecRestoreArrayRead(b, &rarray));
1537     } else if (!mumps->myid) {
1538       PetscCall(VecRestoreArray(mumps->b_seq, &array));
1539     }
1540   } else PetscCall(VecRestoreArray(x, &array));
1541 
1542   PetscCall(PetscLogFlops(2.0 * PetscMax(0, (mumps->id.INFO(28) >= 0 ? mumps->id.INFO(28) : -1000000 * mumps->id.INFO(28)) - A->cmap->n)));
1543   PetscFunctionReturn(PETSC_SUCCESS);
1544 }
1545 
1546 static PetscErrorCode MatSolveTranspose_MUMPS(Mat A, Vec b, Vec x)
1547 {
1548   Mat_MUMPS          *mumps = (Mat_MUMPS *)A->data;
1549   const PetscMUMPSInt value = mumps->id.ICNTL(9);
1550 
1551   PetscFunctionBegin;
1552   mumps->id.ICNTL(9) = 0;
1553   PetscCall(MatSolve_MUMPS(A, b, x));
1554   mumps->id.ICNTL(9) = value;
1555   PetscFunctionReturn(PETSC_SUCCESS);
1556 }
1557 
1558 static PetscErrorCode MatMatSolve_MUMPS(Mat A, Mat B, Mat X)
1559 {
1560   Mat                Bt = NULL;
1561   PetscBool          denseX, denseB, flg, flgT;
1562   Mat_MUMPS         *mumps = (Mat_MUMPS *)A->data;
1563   PetscInt           i, nrhs, M;
1564   PetscScalar       *array;
1565   const PetscScalar *rbray;
1566   PetscInt           lsol_loc, nlsol_loc, *idxx, iidx = 0;
1567   PetscMUMPSInt     *isol_loc, *isol_loc_save;
1568   PetscScalar       *bray, *sol_loc, *sol_loc_save;
1569   IS                 is_to, is_from;
1570   PetscInt           k, proc, j, m, myrstart;
1571   const PetscInt    *rstart;
1572   Vec                v_mpi, msol_loc;
1573   VecScatter         scat_sol;
1574   Vec                b_seq;
1575   VecScatter         scat_rhs;
1576   PetscScalar       *aa;
1577   PetscInt           spnr, *ia, *ja;
1578   Mat_MPIAIJ        *b = NULL;
1579 
1580   PetscFunctionBegin;
1581   PetscCall(PetscObjectTypeCompareAny((PetscObject)X, &denseX, MATSEQDENSE, MATMPIDENSE, NULL));
1582   PetscCheck(denseX, PetscObjectComm((PetscObject)X), PETSC_ERR_ARG_WRONG, "Matrix X must be MATDENSE matrix");
1583 
1584   PetscCall(PetscObjectTypeCompareAny((PetscObject)B, &denseB, MATSEQDENSE, MATMPIDENSE, NULL));
1585   if (denseB) {
1586     PetscCheck(B->rmap->n == X->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Matrix B and X must have same row distribution");
1587     mumps->id.ICNTL(20) = 0; /* dense RHS */
1588   } else {                   /* sparse B */
1589     PetscCheck(X != B, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_IDN, "X and B must be different matrices");
1590     PetscCall(PetscObjectTypeCompare((PetscObject)B, MATTRANSPOSEVIRTUAL, &flgT));
1591     if (flgT) { /* input B is transpose of actual RHS matrix,
1592                  because mumps requires sparse compressed COLUMN storage! See MatMatTransposeSolve_MUMPS() */
1593       PetscCall(MatTransposeGetMat(B, &Bt));
1594     } else SETERRQ(PetscObjectComm((PetscObject)B), PETSC_ERR_ARG_WRONG, "Matrix B must be MATTRANSPOSEVIRTUAL matrix");
1595     mumps->id.ICNTL(20) = 1; /* sparse RHS */
1596   }
1597 
1598   PetscCall(MatGetSize(B, &M, &nrhs));
1599   mumps->id.nrhs = (PetscMUMPSInt)nrhs;
1600   mumps->id.lrhs = (PetscMUMPSInt)M;
1601   mumps->id.rhs  = NULL;
1602 
1603   if (mumps->petsc_size == 1) {
1604     PetscScalar *aa;
1605     PetscInt     spnr, *ia, *ja;
1606     PetscBool    second_solve = PETSC_FALSE;
1607 
1608     PetscCall(MatDenseGetArray(X, &array));
1609     mumps->id.rhs = (MumpsScalar *)array;
1610 
1611     if (denseB) {
1612       /* copy B to X */
1613       PetscCall(MatDenseGetArrayRead(B, &rbray));
1614       PetscCall(PetscArraycpy(array, rbray, M * nrhs));
1615       PetscCall(MatDenseRestoreArrayRead(B, &rbray));
1616     } else { /* sparse B */
1617       PetscCall(MatSeqAIJGetArray(Bt, &aa));
1618       PetscCall(MatGetRowIJ(Bt, 1, PETSC_FALSE, PETSC_FALSE, &spnr, (const PetscInt **)&ia, (const PetscInt **)&ja, &flg));
1619       PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot get IJ structure");
1620       PetscCall(PetscMUMPSIntCSRCast(mumps, spnr, ia, ja, &mumps->id.irhs_ptr, &mumps->id.irhs_sparse, &mumps->id.nz_rhs));
1621       mumps->id.rhs_sparse = (MumpsScalar *)aa;
1622     }
1623     /* handle condensation step of Schur complement (if any) */
1624     if (mumps->id.size_schur > 0) {
1625       if (mumps->id.ICNTL(26) < 0 || mumps->id.ICNTL(26) > 2) {
1626         second_solve = PETSC_TRUE;
1627         PetscCall(MatMumpsHandleSchur_Private(A, PETSC_FALSE));
1628         mumps->id.ICNTL(26) = 1; /* condensation phase */
1629       } else if (mumps->id.ICNTL(26) == 1) PetscCall(MatMumpsHandleSchur_Private(A, PETSC_FALSE));
1630     }
1631     /* solve phase */
1632     mumps->id.job = JOB_SOLVE;
1633     PetscMUMPS_c(mumps);
1634     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));
1635 
1636     /* handle expansion step of Schur complement (if any) */
1637     if (second_solve) PetscCall(MatMumpsHandleSchur_Private(A, PETSC_TRUE));
1638     else if (mumps->id.ICNTL(26) == 1) {
1639       PetscCall(MatMumpsSolveSchur_Private(A));
1640       for (j = 0; j < nrhs; ++j)
1641         for (i = 0; i < mumps->id.size_schur; ++i) {
1642 #if !defined(PETSC_USE_COMPLEX)
1643           PetscScalar val = mumps->id.redrhs[i + j * mumps->id.lredrhs];
1644 #else
1645           PetscScalar val = mumps->id.redrhs[i + j * mumps->id.lredrhs].r + PETSC_i * mumps->id.redrhs[i + j * mumps->id.lredrhs].i;
1646 #endif
1647           array[mumps->id.listvar_schur[i] - 1 + j * M] = val;
1648         }
1649     }
1650     if (!denseB) { /* sparse B */
1651       PetscCall(MatSeqAIJRestoreArray(Bt, &aa));
1652       PetscCall(MatRestoreRowIJ(Bt, 1, PETSC_FALSE, PETSC_FALSE, &spnr, (const PetscInt **)&ia, (const PetscInt **)&ja, &flg));
1653       PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot restore IJ structure");
1654     }
1655     PetscCall(MatDenseRestoreArray(X, &array));
1656     PetscFunctionReturn(PETSC_SUCCESS);
1657   }
1658 
1659   /* parallel case: MUMPS requires rhs B to be centralized on the host! */
1660   PetscCheck(!mumps->id.ICNTL(19), PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Parallel Schur complements not yet supported from PETSc");
1661 
1662   /* create msol_loc to hold mumps local solution */
1663   isol_loc_save = mumps->id.isol_loc; /* save it for MatSolve() */
1664   sol_loc_save  = (PetscScalar *)mumps->id.sol_loc;
1665 
1666   lsol_loc  = mumps->id.lsol_loc;
1667   nlsol_loc = nrhs * lsol_loc; /* length of sol_loc */
1668   PetscCall(PetscMalloc2(nlsol_loc, &sol_loc, lsol_loc, &isol_loc));
1669   mumps->id.sol_loc  = (MumpsScalar *)sol_loc;
1670   mumps->id.isol_loc = isol_loc;
1671 
1672   PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, nlsol_loc, (PetscScalar *)sol_loc, &msol_loc));
1673 
1674   if (denseB) {
1675     if (mumps->ICNTL20 == 10) {
1676       mumps->id.ICNTL(20) = 10; /* dense distributed RHS */
1677       PetscCall(MatDenseGetArrayRead(B, &rbray));
1678       PetscCall(MatMumpsSetUpDistRHSInfo(A, nrhs, rbray));
1679       PetscCall(MatDenseRestoreArrayRead(B, &rbray));
1680       PetscCall(MatGetLocalSize(B, &m, NULL));
1681       PetscCall(VecCreateMPIWithArray(PetscObjectComm((PetscObject)B), 1, nrhs * m, nrhs * M, NULL, &v_mpi));
1682     } else {
1683       mumps->id.ICNTL(20) = 0; /* dense centralized RHS */
1684       /* TODO: Because of non-contiguous indices, the created vecscatter scat_rhs is not done in MPI_Gather, resulting in
1685         very inefficient communication. An optimization is to use VecScatterCreateToZero to gather B to rank 0. Then on rank
1686         0, re-arrange B into desired order, which is a local operation.
1687       */
1688 
1689       /* scatter v_mpi to b_seq because MUMPS before 5.3.0 only supports centralized rhs */
1690       /* wrap dense rhs matrix B into a vector v_mpi */
1691       PetscCall(MatGetLocalSize(B, &m, NULL));
1692       PetscCall(MatDenseGetArray(B, &bray));
1693       PetscCall(VecCreateMPIWithArray(PetscObjectComm((PetscObject)B), 1, nrhs * m, nrhs * M, (const PetscScalar *)bray, &v_mpi));
1694       PetscCall(MatDenseRestoreArray(B, &bray));
1695 
1696       /* scatter v_mpi to b_seq in proc[0]. MUMPS requires rhs to be centralized on the host! */
1697       if (!mumps->myid) {
1698         PetscInt *idx;
1699         /* idx: maps from k-th index of v_mpi to (i,j)-th global entry of B */
1700         PetscCall(PetscMalloc1(nrhs * M, &idx));
1701         PetscCall(MatGetOwnershipRanges(B, &rstart));
1702         k = 0;
1703         for (proc = 0; proc < mumps->petsc_size; proc++) {
1704           for (j = 0; j < nrhs; j++) {
1705             for (i = rstart[proc]; i < rstart[proc + 1]; i++) idx[k++] = j * M + i;
1706           }
1707         }
1708 
1709         PetscCall(VecCreateSeq(PETSC_COMM_SELF, nrhs * M, &b_seq));
1710         PetscCall(ISCreateGeneral(PETSC_COMM_SELF, nrhs * M, idx, PETSC_OWN_POINTER, &is_to));
1711         PetscCall(ISCreateStride(PETSC_COMM_SELF, nrhs * M, 0, 1, &is_from));
1712       } else {
1713         PetscCall(VecCreateSeq(PETSC_COMM_SELF, 0, &b_seq));
1714         PetscCall(ISCreateStride(PETSC_COMM_SELF, 0, 0, 1, &is_to));
1715         PetscCall(ISCreateStride(PETSC_COMM_SELF, 0, 0, 1, &is_from));
1716       }
1717       PetscCall(VecScatterCreate(v_mpi, is_from, b_seq, is_to, &scat_rhs));
1718       PetscCall(VecScatterBegin(scat_rhs, v_mpi, b_seq, INSERT_VALUES, SCATTER_FORWARD));
1719       PetscCall(ISDestroy(&is_to));
1720       PetscCall(ISDestroy(&is_from));
1721       PetscCall(VecScatterEnd(scat_rhs, v_mpi, b_seq, INSERT_VALUES, SCATTER_FORWARD));
1722 
1723       if (!mumps->myid) { /* define rhs on the host */
1724         PetscCall(VecGetArray(b_seq, &bray));
1725         mumps->id.rhs = (MumpsScalar *)bray;
1726         PetscCall(VecRestoreArray(b_seq, &bray));
1727       }
1728     }
1729   } else { /* sparse B */
1730     b = (Mat_MPIAIJ *)Bt->data;
1731 
1732     /* wrap dense X into a vector v_mpi */
1733     PetscCall(MatGetLocalSize(X, &m, NULL));
1734     PetscCall(MatDenseGetArray(X, &bray));
1735     PetscCall(VecCreateMPIWithArray(PetscObjectComm((PetscObject)X), 1, nrhs * m, nrhs * M, (const PetscScalar *)bray, &v_mpi));
1736     PetscCall(MatDenseRestoreArray(X, &bray));
1737 
1738     if (!mumps->myid) {
1739       PetscCall(MatSeqAIJGetArray(b->A, &aa));
1740       PetscCall(MatGetRowIJ(b->A, 1, PETSC_FALSE, PETSC_FALSE, &spnr, (const PetscInt **)&ia, (const PetscInt **)&ja, &flg));
1741       PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot get IJ structure");
1742       PetscCall(PetscMUMPSIntCSRCast(mumps, spnr, ia, ja, &mumps->id.irhs_ptr, &mumps->id.irhs_sparse, &mumps->id.nz_rhs));
1743       mumps->id.rhs_sparse = (MumpsScalar *)aa;
1744     } else {
1745       mumps->id.irhs_ptr    = NULL;
1746       mumps->id.irhs_sparse = NULL;
1747       mumps->id.nz_rhs      = 0;
1748       mumps->id.rhs_sparse  = NULL;
1749     }
1750   }
1751 
1752   /* solve phase */
1753   mumps->id.job = JOB_SOLVE;
1754   PetscMUMPS_c(mumps);
1755   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));
1756 
1757   /* scatter mumps distributed solution to petsc vector v_mpi, which shares local arrays with solution matrix X */
1758   PetscCall(MatDenseGetArray(X, &array));
1759   PetscCall(VecPlaceArray(v_mpi, array));
1760 
1761   /* create scatter scat_sol */
1762   PetscCall(MatGetOwnershipRanges(X, &rstart));
1763   /* iidx: index for scatter mumps solution to petsc X */
1764 
1765   PetscCall(ISCreateStride(PETSC_COMM_SELF, nlsol_loc, 0, 1, &is_from));
1766   PetscCall(PetscMalloc1(nlsol_loc, &idxx));
1767   for (i = 0; i < lsol_loc; i++) {
1768     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 */
1769 
1770     for (proc = 0; proc < mumps->petsc_size; proc++) {
1771       if (isol_loc[i] >= rstart[proc] && isol_loc[i] < rstart[proc + 1]) {
1772         myrstart = rstart[proc];
1773         k        = isol_loc[i] - myrstart;          /* local index on 1st column of petsc vector X */
1774         iidx     = k + myrstart * nrhs;             /* maps mumps isol_loc[i] to petsc index in X */
1775         m        = rstart[proc + 1] - rstart[proc]; /* rows of X for this proc */
1776         break;
1777       }
1778     }
1779 
1780     for (j = 0; j < nrhs; j++) idxx[i + j * lsol_loc] = iidx + j * m;
1781   }
1782   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, nlsol_loc, idxx, PETSC_COPY_VALUES, &is_to));
1783   PetscCall(VecScatterCreate(msol_loc, is_from, v_mpi, is_to, &scat_sol));
1784   PetscCall(VecScatterBegin(scat_sol, msol_loc, v_mpi, INSERT_VALUES, SCATTER_FORWARD));
1785   PetscCall(ISDestroy(&is_from));
1786   PetscCall(ISDestroy(&is_to));
1787   PetscCall(VecScatterEnd(scat_sol, msol_loc, v_mpi, INSERT_VALUES, SCATTER_FORWARD));
1788   PetscCall(MatDenseRestoreArray(X, &array));
1789 
1790   /* free spaces */
1791   mumps->id.sol_loc  = (MumpsScalar *)sol_loc_save;
1792   mumps->id.isol_loc = isol_loc_save;
1793 
1794   PetscCall(PetscFree2(sol_loc, isol_loc));
1795   PetscCall(PetscFree(idxx));
1796   PetscCall(VecDestroy(&msol_loc));
1797   PetscCall(VecDestroy(&v_mpi));
1798   if (!denseB) {
1799     if (!mumps->myid) {
1800       b = (Mat_MPIAIJ *)Bt->data;
1801       PetscCall(MatSeqAIJRestoreArray(b->A, &aa));
1802       PetscCall(MatRestoreRowIJ(b->A, 1, PETSC_FALSE, PETSC_FALSE, &spnr, (const PetscInt **)&ia, (const PetscInt **)&ja, &flg));
1803       PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot restore IJ structure");
1804     }
1805   } else {
1806     if (mumps->ICNTL20 == 0) {
1807       PetscCall(VecDestroy(&b_seq));
1808       PetscCall(VecScatterDestroy(&scat_rhs));
1809     }
1810   }
1811   PetscCall(VecScatterDestroy(&scat_sol));
1812   PetscCall(PetscLogFlops(nrhs * PetscMax(0, 2.0 * (mumps->id.INFO(28) >= 0 ? mumps->id.INFO(28) : -1000000 * mumps->id.INFO(28)) - A->cmap->n)));
1813   PetscFunctionReturn(PETSC_SUCCESS);
1814 }
1815 
1816 static PetscErrorCode MatMatSolveTranspose_MUMPS(Mat A, Mat B, Mat X)
1817 {
1818   Mat_MUMPS          *mumps = (Mat_MUMPS *)A->data;
1819   const PetscMUMPSInt value = mumps->id.ICNTL(9);
1820 
1821   PetscFunctionBegin;
1822   mumps->id.ICNTL(9) = 0;
1823   PetscCall(MatMatSolve_MUMPS(A, B, X));
1824   mumps->id.ICNTL(9) = value;
1825   PetscFunctionReturn(PETSC_SUCCESS);
1826 }
1827 
1828 static PetscErrorCode MatMatTransposeSolve_MUMPS(Mat A, Mat Bt, Mat X)
1829 {
1830   PetscBool flg;
1831   Mat       B;
1832 
1833   PetscFunctionBegin;
1834   PetscCall(PetscObjectTypeCompareAny((PetscObject)Bt, &flg, MATSEQAIJ, MATMPIAIJ, NULL));
1835   PetscCheck(flg, PetscObjectComm((PetscObject)Bt), PETSC_ERR_ARG_WRONG, "Matrix Bt must be MATAIJ matrix");
1836 
1837   /* Create B=Bt^T that uses Bt's data structure */
1838   PetscCall(MatCreateTranspose(Bt, &B));
1839 
1840   PetscCall(MatMatSolve_MUMPS(A, B, X));
1841   PetscCall(MatDestroy(&B));
1842   PetscFunctionReturn(PETSC_SUCCESS);
1843 }
1844 
1845 #if !defined(PETSC_USE_COMPLEX)
1846 /*
1847   input:
1848    F:        numeric factor
1849   output:
1850    nneg:     total number of negative pivots
1851    nzero:    total number of zero pivots
1852    npos:     (global dimension of F) - nneg - nzero
1853 */
1854 static PetscErrorCode MatGetInertia_SBAIJMUMPS(Mat F, PetscInt *nneg, PetscInt *nzero, PetscInt *npos)
1855 {
1856   Mat_MUMPS  *mumps = (Mat_MUMPS *)F->data;
1857   PetscMPIInt size;
1858 
1859   PetscFunctionBegin;
1860   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)F), &size));
1861   /* 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 */
1862   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));
1863 
1864   if (nneg) *nneg = mumps->id.INFOG(12);
1865   if (nzero || npos) {
1866     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");
1867     if (nzero) *nzero = mumps->id.INFOG(28);
1868     if (npos) *npos = F->rmap->N - (mumps->id.INFOG(12) + mumps->id.INFOG(28));
1869   }
1870   PetscFunctionReturn(PETSC_SUCCESS);
1871 }
1872 #endif
1873 
1874 static PetscErrorCode MatMumpsGatherNonzerosOnMaster(MatReuse reuse, Mat_MUMPS *mumps)
1875 {
1876   PetscMPIInt    nreqs;
1877   PetscMUMPSInt *irn, *jcn;
1878   PetscMPIInt    count;
1879   PetscCount     totnnz, remain;
1880   const PetscInt osize = mumps->omp_comm_size;
1881   PetscScalar   *val;
1882 
1883   PetscFunctionBegin;
1884   if (osize > 1) {
1885     if (reuse == MAT_INITIAL_MATRIX) {
1886       /* master first gathers counts of nonzeros to receive */
1887       if (mumps->is_omp_master) PetscCall(PetscMalloc1(osize, &mumps->recvcount));
1888       PetscCallMPI(MPI_Gather(&mumps->nnz, 1, MPIU_INT64, mumps->recvcount, 1, MPIU_INT64, 0 /*master*/, mumps->omp_comm));
1889 
1890       /* Then each computes number of send/recvs */
1891       if (mumps->is_omp_master) {
1892         /* Start from 1 since self communication is not done in MPI */
1893         nreqs = 0;
1894         for (PetscMPIInt i = 1; i < osize; i++) nreqs += (mumps->recvcount[i] + PETSC_MPI_INT_MAX - 1) / PETSC_MPI_INT_MAX;
1895       } else {
1896         nreqs = (PetscMPIInt)(((mumps->nnz + PETSC_MPI_INT_MAX - 1) / PETSC_MPI_INT_MAX));
1897       }
1898       PetscCall(PetscMalloc1(nreqs * 3, &mumps->reqs)); /* Triple the requests since we send irn, jcn and val separately */
1899 
1900       /* The following code is doing a very simple thing: omp_master rank gathers irn/jcn/val from others.
1901          MPI_Gatherv would be enough if it supports big counts > 2^31-1. Since it does not, and mumps->nnz
1902          might be a prime number > 2^31-1, we have to slice the message. Note omp_comm_size
1903          is very small, the current approach should have no extra overhead compared to MPI_Gatherv.
1904        */
1905       nreqs = 0; /* counter for actual send/recvs */
1906       if (mumps->is_omp_master) {
1907         totnnz = 0;
1908 
1909         for (PetscMPIInt i = 0; i < osize; i++) totnnz += mumps->recvcount[i]; /* totnnz = sum of nnz over omp_comm */
1910         PetscCall(PetscMalloc2(totnnz, &irn, totnnz, &jcn));
1911         PetscCall(PetscMalloc1(totnnz, &val));
1912 
1913         /* Self communication */
1914         PetscCall(PetscArraycpy(irn, mumps->irn, mumps->nnz));
1915         PetscCall(PetscArraycpy(jcn, mumps->jcn, mumps->nnz));
1916         PetscCall(PetscArraycpy(val, mumps->val, mumps->nnz));
1917 
1918         /* Replace mumps->irn/jcn etc on master with the newly allocated bigger arrays */
1919         PetscCall(PetscFree2(mumps->irn, mumps->jcn));
1920         PetscCall(PetscFree(mumps->val_alloc));
1921         mumps->nnz = totnnz;
1922         mumps->irn = irn;
1923         mumps->jcn = jcn;
1924         mumps->val = mumps->val_alloc = val;
1925 
1926         irn += mumps->recvcount[0]; /* recvcount[0] is old mumps->nnz on omp rank 0 */
1927         jcn += mumps->recvcount[0];
1928         val += mumps->recvcount[0];
1929 
1930         /* Remote communication */
1931         for (PetscMPIInt i = 1; i < osize; i++) {
1932           count  = (PetscMPIInt)PetscMin(mumps->recvcount[i], (PetscMPIInt)PETSC_MPI_INT_MAX);
1933           remain = mumps->recvcount[i] - count;
1934           while (count > 0) {
1935             PetscCallMPI(MPIU_Irecv(irn, count, MPIU_MUMPSINT, i, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
1936             PetscCallMPI(MPIU_Irecv(jcn, count, MPIU_MUMPSINT, i, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
1937             PetscCallMPI(MPIU_Irecv(val, count, MPIU_SCALAR, i, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
1938             irn += count;
1939             jcn += count;
1940             val += count;
1941             count = (PetscMPIInt)PetscMin(remain, (PetscMPIInt)PETSC_MPI_INT_MAX);
1942             remain -= count;
1943           }
1944         }
1945       } else {
1946         irn    = mumps->irn;
1947         jcn    = mumps->jcn;
1948         val    = mumps->val;
1949         count  = (PetscMPIInt)PetscMin(mumps->nnz, (PetscMPIInt)PETSC_MPI_INT_MAX);
1950         remain = mumps->nnz - count;
1951         while (count > 0) {
1952           PetscCallMPI(MPIU_Isend(irn, count, MPIU_MUMPSINT, 0, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
1953           PetscCallMPI(MPIU_Isend(jcn, count, MPIU_MUMPSINT, 0, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
1954           PetscCallMPI(MPIU_Isend(val, count, MPIU_SCALAR, 0, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
1955           irn += count;
1956           jcn += count;
1957           val += count;
1958           count = (PetscMPIInt)PetscMin(remain, (PetscMPIInt)PETSC_MPI_INT_MAX);
1959           remain -= count;
1960         }
1961       }
1962     } else {
1963       nreqs = 0;
1964       if (mumps->is_omp_master) {
1965         val = mumps->val + mumps->recvcount[0];
1966         for (PetscMPIInt i = 1; i < osize; i++) { /* Remote communication only since self data is already in place */
1967           count  = (PetscMPIInt)PetscMin(mumps->recvcount[i], (PetscMPIInt)PETSC_MPI_INT_MAX);
1968           remain = mumps->recvcount[i] - count;
1969           while (count > 0) {
1970             PetscCallMPI(MPIU_Irecv(val, count, MPIU_SCALAR, i, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
1971             val += count;
1972             count = (PetscMPIInt)PetscMin(remain, (PetscMPIInt)PETSC_MPI_INT_MAX);
1973             remain -= count;
1974           }
1975         }
1976       } else {
1977         val    = mumps->val;
1978         count  = (PetscMPIInt)PetscMin(mumps->nnz, (PetscMPIInt)PETSC_MPI_INT_MAX);
1979         remain = mumps->nnz - count;
1980         while (count > 0) {
1981           PetscCallMPI(MPIU_Isend(val, count, MPIU_SCALAR, 0, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
1982           val += count;
1983           count = (PetscMPIInt)PetscMin(remain, (PetscMPIInt)PETSC_MPI_INT_MAX);
1984           remain -= count;
1985         }
1986       }
1987     }
1988     PetscCallMPI(MPI_Waitall(nreqs, mumps->reqs, MPI_STATUSES_IGNORE));
1989     mumps->tag++; /* It is totally fine for above send/recvs to share one mpi tag */
1990   }
1991   PetscFunctionReturn(PETSC_SUCCESS);
1992 }
1993 
1994 static PetscErrorCode MatFactorNumeric_MUMPS(Mat F, Mat A, PETSC_UNUSED const MatFactorInfo *info)
1995 {
1996   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;
1997   PetscBool  isMPIAIJ;
1998 
1999   PetscFunctionBegin;
2000   if (mumps->id.INFOG(1) < 0 && !(mumps->id.INFOG(1) == -16 && mumps->id.INFOG(1) == 0)) {
2001     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)));
2002     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)));
2003     PetscFunctionReturn(PETSC_SUCCESS);
2004   }
2005 
2006   PetscCall((*mumps->ConvertToTriples)(A, 1, MAT_REUSE_MATRIX, mumps));
2007   PetscCall(MatMumpsGatherNonzerosOnMaster(MAT_REUSE_MATRIX, mumps));
2008 
2009   /* numerical factorization phase */
2010   mumps->id.job = JOB_FACTNUMERIC;
2011   if (!mumps->id.ICNTL(18)) { /* A is centralized */
2012     if (!mumps->myid) mumps->id.a = (MumpsScalar *)mumps->val;
2013   } else {
2014     mumps->id.a_loc = (MumpsScalar *)mumps->val;
2015   }
2016   PetscMUMPS_c(mumps);
2017   if (mumps->id.INFOG(1) < 0) {
2018     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));
2019     if (mumps->id.INFOG(1) == -10) {
2020       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)));
2021       F->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
2022     } else if (mumps->id.INFOG(1) == -13) {
2023       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)));
2024       F->factorerrortype = MAT_FACTOR_OUTMEMORY;
2025     } else if (mumps->id.INFOG(1) == -8 || mumps->id.INFOG(1) == -9 || (-16 < mumps->id.INFOG(1) && mumps->id.INFOG(1) < -10)) {
2026       PetscCall(PetscInfo(F, "MUMPS error in numerical factorization: INFOG(1)=%d, INFO(2)=%d, problem with work array\n", mumps->id.INFOG(1), mumps->id.INFO(2)));
2027       F->factorerrortype = MAT_FACTOR_OUTMEMORY;
2028     } else {
2029       PetscCall(PetscInfo(F, "MUMPS error in numerical factorization: INFOG(1)=%d, INFO(2)=%d\n", mumps->id.INFOG(1), mumps->id.INFO(2)));
2030       F->factorerrortype = MAT_FACTOR_OTHER;
2031     }
2032   }
2033   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));
2034 
2035   F->assembled = PETSC_TRUE;
2036 
2037   if (F->schur) { /* reset Schur status to unfactored */
2038 #if defined(PETSC_HAVE_CUDA)
2039     F->schur->offloadmask = PETSC_OFFLOAD_CPU;
2040 #endif
2041     if (mumps->id.ICNTL(19) == 1) { /* stored by rows */
2042       mumps->id.ICNTL(19) = 2;
2043       PetscCall(MatTranspose(F->schur, MAT_INPLACE_MATRIX, &F->schur));
2044     }
2045     PetscCall(MatFactorRestoreSchurComplement(F, NULL, MAT_FACTOR_SCHUR_UNFACTORED));
2046   }
2047 
2048   /* just to be sure that ICNTL(19) value returned by a call from MatMumpsGetIcntl is always consistent */
2049   if (!mumps->sym && mumps->id.ICNTL(19) && mumps->id.ICNTL(19) != 1) mumps->id.ICNTL(19) = 3;
2050 
2051   if (!mumps->is_omp_master) mumps->id.INFO(23) = 0;
2052   if (mumps->petsc_size > 1) {
2053     PetscInt     lsol_loc;
2054     PetscScalar *sol_loc;
2055 
2056     PetscCall(PetscObjectTypeCompare((PetscObject)A, MATMPIAIJ, &isMPIAIJ));
2057 
2058     /* distributed solution; Create x_seq=sol_loc for repeated use */
2059     if (mumps->x_seq) {
2060       PetscCall(VecScatterDestroy(&mumps->scat_sol));
2061       PetscCall(PetscFree2(mumps->id.sol_loc, mumps->id.isol_loc));
2062       PetscCall(VecDestroy(&mumps->x_seq));
2063     }
2064     lsol_loc = mumps->id.INFO(23); /* length of sol_loc */
2065     PetscCall(PetscMalloc2(lsol_loc, &sol_loc, lsol_loc, &mumps->id.isol_loc));
2066     mumps->id.lsol_loc = (PetscMUMPSInt)lsol_loc;
2067     mumps->id.sol_loc  = (MumpsScalar *)sol_loc;
2068     PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, lsol_loc, sol_loc, &mumps->x_seq));
2069   }
2070   PetscCall(PetscLogFlops((double)mumps->id.RINFO(2)));
2071   PetscFunctionReturn(PETSC_SUCCESS);
2072 }
2073 
2074 /* Sets MUMPS options from the options database */
2075 static PetscErrorCode MatSetFromOptions_MUMPS(Mat F, Mat A)
2076 {
2077   Mat_MUMPS    *mumps = (Mat_MUMPS *)F->data;
2078   PetscMUMPSInt icntl = 0, size, *listvar_schur;
2079   PetscInt      info[80], i, ninfo = 80, rbs, cbs;
2080   PetscBool     flg = PETSC_FALSE, schur = (PetscBool)(mumps->id.ICNTL(26) == -1);
2081   MumpsScalar  *arr;
2082 
2083   PetscFunctionBegin;
2084   PetscOptionsBegin(PetscObjectComm((PetscObject)F), ((PetscObject)F)->prefix, "MUMPS Options", "Mat");
2085   if (mumps->id.job == JOB_NULL) { /* MatSetFromOptions_MUMPS() has never been called before */
2086     PetscInt nthreads   = 0;
2087     PetscInt nCNTL_pre  = mumps->CNTL_pre ? mumps->CNTL_pre[0] : 0;
2088     PetscInt nICNTL_pre = mumps->ICNTL_pre ? mumps->ICNTL_pre[0] : 0;
2089 
2090     mumps->petsc_comm = PetscObjectComm((PetscObject)A);
2091     PetscCallMPI(MPI_Comm_size(mumps->petsc_comm, &mumps->petsc_size));
2092     PetscCallMPI(MPI_Comm_rank(mumps->petsc_comm, &mumps->myid)); /* "if (!myid)" still works even if mumps_comm is different */
2093 
2094     PetscCall(PetscOptionsName("-mat_mumps_use_omp_threads", "Convert MPI processes into OpenMP threads", "None", &mumps->use_petsc_omp_support));
2095     if (mumps->use_petsc_omp_support) nthreads = -1; /* -1 will let PetscOmpCtrlCreate() guess a proper value when user did not supply one */
2096     /* do not use PetscOptionsInt() so that the option -mat_mumps_use_omp_threads is not displayed twice in the help */
2097     PetscCall(PetscOptionsGetInt(NULL, ((PetscObject)F)->prefix, "-mat_mumps_use_omp_threads", &nthreads, NULL));
2098     if (mumps->use_petsc_omp_support) {
2099       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 : "");
2100 #if defined(PETSC_HAVE_OPENMP_SUPPORT)
2101       PetscCall(PetscOmpCtrlCreate(mumps->petsc_comm, nthreads, &mumps->omp_ctrl));
2102       PetscCall(PetscOmpCtrlGetOmpComms(mumps->omp_ctrl, &mumps->omp_comm, &mumps->mumps_comm, &mumps->is_omp_master));
2103 #else
2104       SETERRQ(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",
2105               ((PetscObject)F)->prefix ? ((PetscObject)F)->prefix : "");
2106 #endif
2107     } else {
2108       mumps->omp_comm      = PETSC_COMM_SELF;
2109       mumps->mumps_comm    = mumps->petsc_comm;
2110       mumps->is_omp_master = PETSC_TRUE;
2111     }
2112     PetscCallMPI(MPI_Comm_size(mumps->omp_comm, &mumps->omp_comm_size));
2113     mumps->reqs = NULL;
2114     mumps->tag  = 0;
2115 
2116     if (mumps->mumps_comm != MPI_COMM_NULL) {
2117       if (PetscDefined(HAVE_OPENMP_SUPPORT) && mumps->use_petsc_omp_support) {
2118         /* It looks like MUMPS does not dup the input comm. Dup a new comm for MUMPS to avoid any tag mismatches. */
2119         MPI_Comm comm;
2120         PetscCallMPI(MPI_Comm_dup(mumps->mumps_comm, &comm));
2121         mumps->mumps_comm = comm;
2122       } else PetscCall(PetscCommGetComm(mumps->petsc_comm, &mumps->mumps_comm));
2123     }
2124 
2125     mumps->id.comm_fortran = MPI_Comm_c2f(mumps->mumps_comm);
2126     mumps->id.job          = JOB_INIT;
2127     mumps->id.par          = 1; /* host participates factorizaton and solve */
2128     mumps->id.sym          = mumps->sym;
2129 
2130     size          = mumps->id.size_schur;
2131     arr           = mumps->id.schur;
2132     listvar_schur = mumps->id.listvar_schur;
2133     PetscMUMPS_c(mumps);
2134     PetscCheck(mumps->id.INFOG(1) >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "MUMPS error: INFOG(1)=%d " MUMPS_MANUALS, mumps->id.INFOG(1));
2135 
2136     /* set PETSc-MUMPS default options - override MUMPS default */
2137     mumps->id.ICNTL(3) = 0;
2138     mumps->id.ICNTL(4) = 0;
2139     if (mumps->petsc_size == 1) {
2140       mumps->id.ICNTL(18) = 0; /* centralized assembled matrix input */
2141       mumps->id.ICNTL(7)  = 7; /* automatic choice of ordering done by the package */
2142     } else {
2143       mumps->id.ICNTL(18) = 3; /* distributed assembled matrix input */
2144       mumps->id.ICNTL(21) = 1; /* distributed solution */
2145     }
2146 
2147     /* restore cached ICNTL and CNTL values */
2148     for (icntl = 0; icntl < nICNTL_pre; ++icntl) mumps->id.ICNTL(mumps->ICNTL_pre[1 + 2 * icntl]) = mumps->ICNTL_pre[2 + 2 * icntl];
2149     for (icntl = 0; icntl < nCNTL_pre; ++icntl) mumps->id.CNTL((PetscInt)mumps->CNTL_pre[1 + 2 * icntl]) = mumps->CNTL_pre[2 + 2 * icntl];
2150     PetscCall(PetscFree(mumps->ICNTL_pre));
2151     PetscCall(PetscFree(mumps->CNTL_pre));
2152 
2153     if (schur) {
2154       mumps->id.size_schur    = size;
2155       mumps->id.schur_lld     = size;
2156       mumps->id.schur         = arr;
2157       mumps->id.listvar_schur = listvar_schur;
2158       if (mumps->petsc_size > 1) {
2159         PetscBool gs; /* gs is false if any rank other than root has non-empty IS */
2160 
2161         mumps->id.ICNTL(19) = 1;                                                                            /* MUMPS returns Schur centralized on the host */
2162         gs                  = mumps->myid ? (mumps->id.size_schur ? PETSC_FALSE : PETSC_TRUE) : PETSC_TRUE; /* always true on root; false on others if their size != 0 */
2163         PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &gs, 1, MPIU_BOOL, MPI_LAND, mumps->petsc_comm));
2164         PetscCheck(gs, PETSC_COMM_SELF, PETSC_ERR_SUP, "MUMPS distributed parallel Schur complements not yet supported from PETSc");
2165       } else {
2166         if (F->factortype == MAT_FACTOR_LU) {
2167           mumps->id.ICNTL(19) = 3; /* MUMPS returns full matrix */
2168         } else {
2169           mumps->id.ICNTL(19) = 2; /* MUMPS returns lower triangular part */
2170         }
2171       }
2172       mumps->id.ICNTL(26) = -1;
2173     }
2174 
2175     /* copy MUMPS default control values from master to slaves. Although slaves do not call MUMPS, they may access these values in code.
2176        For example, ICNTL(9) is initialized to 1 by MUMPS and slaves check ICNTL(9) in MatSolve_MUMPS.
2177      */
2178     PetscCallMPI(MPI_Bcast(mumps->id.icntl, 40, MPI_INT, 0, mumps->omp_comm));
2179     PetscCallMPI(MPI_Bcast(mumps->id.cntl, 15, MPIU_REAL, 0, mumps->omp_comm));
2180 
2181     mumps->scat_rhs = NULL;
2182     mumps->scat_sol = NULL;
2183   }
2184   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_1", "ICNTL(1): output stream for error messages", "None", mumps->id.ICNTL(1), &icntl, &flg));
2185   if (flg) mumps->id.ICNTL(1) = icntl;
2186   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_2", "ICNTL(2): output stream for diagnostic printing, statistics, and warning", "None", mumps->id.ICNTL(2), &icntl, &flg));
2187   if (flg) mumps->id.ICNTL(2) = icntl;
2188   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_3", "ICNTL(3): output stream for global information, collected on the host", "None", mumps->id.ICNTL(3), &icntl, &flg));
2189   if (flg) mumps->id.ICNTL(3) = icntl;
2190 
2191   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_4", "ICNTL(4): level of printing (0 to 4)", "None", mumps->id.ICNTL(4), &icntl, &flg));
2192   if (flg) mumps->id.ICNTL(4) = icntl;
2193   if (mumps->id.ICNTL(4) || PetscLogPrintInfo) mumps->id.ICNTL(3) = 6; /* resume MUMPS default id.ICNTL(3) = 6 */
2194 
2195   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));
2196   if (flg) mumps->id.ICNTL(6) = icntl;
2197 
2198   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));
2199   if (flg) {
2200     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");
2201     mumps->id.ICNTL(7) = icntl;
2202   }
2203 
2204   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));
2205   /* 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() */
2206   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_10", "ICNTL(10): max num of refinements", "None", mumps->id.ICNTL(10), &mumps->id.ICNTL(10), NULL));
2207   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));
2208   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));
2209   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));
2210   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));
2211   PetscCall(MatGetBlockSizes(A, &rbs, &cbs));
2212   if (rbs == cbs && rbs > 1) mumps->id.ICNTL(15) = (PetscMUMPSInt)-rbs;
2213   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));
2214   if (flg) {
2215     PetscCheck(mumps->id.ICNTL(15) <= 0, PETSC_COMM_SELF, PETSC_ERR_SUP, "Positive -mat_mumps_icntl_15 not handled");
2216     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");
2217   }
2218   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_19", "ICNTL(19): computes the Schur complement", "None", mumps->id.ICNTL(19), &mumps->id.ICNTL(19), NULL));
2219   if (mumps->id.ICNTL(19) <= 0 || mumps->id.ICNTL(19) > 3) { /* reset any schur data (if any) */
2220     PetscCall(MatDestroy(&F->schur));
2221     PetscCall(MatMumpsResetSchur_Private(mumps));
2222   }
2223 
2224   /* Two MPICH Fortran MPI_IN_PLACE binding bugs prevented the use of 'mpich + mumps'. One happened with "mpi4py + mpich + mumps",
2225      and was reported by Firedrake. See https://bitbucket.org/mpi4py/mpi4py/issues/162/mpi4py-initialization-breaks-fortran
2226      and a petsc-maint mailing list thread with subject 'MUMPS segfaults in parallel because of ...'
2227      This bug was fixed by https://github.com/pmodels/mpich/pull/4149. But the fix brought a new bug,
2228      see https://github.com/pmodels/mpich/issues/5589. This bug was fixed by https://github.com/pmodels/mpich/pull/5590.
2229      In short, we could not use distributed RHS until with MPICH v4.0b1 or we enabled a workaround in mumps-5.6.2+
2230    */
2231 #if PETSC_PKG_MUMPS_VERSION_GE(5, 6, 2) && defined(PETSC_HAVE_MUMPS_AVOID_MPI_IN_PLACE)
2232   mumps->ICNTL20 = 10;
2233 #elif PETSC_PKG_MUMPS_VERSION_LT(5, 3, 0) || (defined(PETSC_HAVE_MPICH) && (MPICH_NUMVERSION < 40000101))
2234   mumps->ICNTL20 = 0; /* Centralized dense RHS*/
2235 #else
2236   mumps->ICNTL20 = 10; /* Distributed dense RHS*/
2237 #endif
2238   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));
2239   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);
2240 #if PETSC_PKG_MUMPS_VERSION_LT(5, 3, 0)
2241   PetscCheck(!flg || mumps->ICNTL20 != 10, PETSC_COMM_SELF, PETSC_ERR_SUP, "ICNTL(20)=10 is not supported before MUMPS-5.3.0");
2242 #endif
2243   /* 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 */
2244 
2245   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));
2246   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));
2247   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));
2248   if (mumps->id.ICNTL(24)) { mumps->id.ICNTL(13) = 1; /* turn-off ScaLAPACK to help with the correct detection of null pivots */ }
2249 
2250   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));
2251   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));
2252   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));
2253   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));
2254   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_29", "ICNTL(29): parallel ordering 1 = ptscotch, 2 = parmetis", "None", mumps->id.ICNTL(29), &mumps->id.ICNTL(29), NULL));
2255   /* 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 */
2256   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));
2257   /* 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 */
2258   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_33", "ICNTL(33): compute determinant", "None", mumps->id.ICNTL(33), &mumps->id.ICNTL(33), NULL));
2259   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));
2260   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_36", "ICNTL(36): choice of BLR factorization variant", "None", mumps->id.ICNTL(36), &mumps->id.ICNTL(36), NULL));
2261   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));
2262   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_48", "ICNTL(48): multithreading with tree parallelism", "None", mumps->id.ICNTL(48), &mumps->id.ICNTL(48), NULL));
2263   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_58", "ICNTL(58): defines options for symbolic factorization", "None", mumps->id.ICNTL(58), &mumps->id.ICNTL(58), NULL));
2264 
2265   PetscCall(PetscOptionsReal("-mat_mumps_cntl_1", "CNTL(1): relative pivoting threshold", "None", mumps->id.CNTL(1), &mumps->id.CNTL(1), NULL));
2266   PetscCall(PetscOptionsReal("-mat_mumps_cntl_2", "CNTL(2): stopping criterion of refinement", "None", mumps->id.CNTL(2), &mumps->id.CNTL(2), NULL));
2267   PetscCall(PetscOptionsReal("-mat_mumps_cntl_3", "CNTL(3): absolute pivoting threshold", "None", mumps->id.CNTL(3), &mumps->id.CNTL(3), NULL));
2268   PetscCall(PetscOptionsReal("-mat_mumps_cntl_4", "CNTL(4): value for static pivoting", "None", mumps->id.CNTL(4), &mumps->id.CNTL(4), NULL));
2269   PetscCall(PetscOptionsReal("-mat_mumps_cntl_5", "CNTL(5): fixation for null pivots", "None", mumps->id.CNTL(5), &mumps->id.CNTL(5), NULL));
2270   PetscCall(PetscOptionsReal("-mat_mumps_cntl_7", "CNTL(7): dropping parameter used during BLR", "None", mumps->id.CNTL(7), &mumps->id.CNTL(7), NULL));
2271 
2272   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));
2273 
2274   PetscCall(PetscOptionsIntArray("-mat_mumps_view_info", "request INFO local to each processor", "", info, &ninfo, NULL));
2275   if (ninfo) {
2276     PetscCheck(ninfo <= 80, PETSC_COMM_SELF, PETSC_ERR_USER, "number of INFO %" PetscInt_FMT " must <= 80", ninfo);
2277     PetscCall(PetscMalloc1(ninfo, &mumps->info));
2278     mumps->ninfo = ninfo;
2279     for (i = 0; i < ninfo; i++) {
2280       PetscCheck(info[i] >= 0 && info[i] <= 80, PETSC_COMM_SELF, PETSC_ERR_USER, "index of INFO %" PetscInt_FMT " must between 1 and 80", ninfo);
2281       mumps->info[i] = info[i];
2282     }
2283   }
2284   PetscOptionsEnd();
2285   PetscFunctionReturn(PETSC_SUCCESS);
2286 }
2287 
2288 static PetscErrorCode MatFactorSymbolic_MUMPS_ReportIfError(Mat F, Mat A, PETSC_UNUSED const MatFactorInfo *info, Mat_MUMPS *mumps)
2289 {
2290   PetscFunctionBegin;
2291   if (mumps->id.INFOG(1) < 0) {
2292     PetscCheck(!A->erroriffailure, PETSC_COMM_SELF, PETSC_ERR_LIB, "MUMPS error in analysis: INFOG(1)=%d " MUMPS_MANUALS, mumps->id.INFOG(1));
2293     if (mumps->id.INFOG(1) == -6) {
2294       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)));
2295       F->factorerrortype = MAT_FACTOR_STRUCT_ZEROPIVOT;
2296     } else if (mumps->id.INFOG(1) == -5 || mumps->id.INFOG(1) == -7) {
2297       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)));
2298       F->factorerrortype = MAT_FACTOR_OUTMEMORY;
2299     } else if (mumps->id.INFOG(1) == -16 && mumps->id.INFOG(1) == 0) {
2300       PetscCall(PetscInfo(F, "MUMPS error in analysis: empty matrix\n"));
2301     } else {
2302       PetscCall(PetscInfo(F, "MUMPS error in analysis: INFOG(1)=%d, INFO(2)=%d " MUMPS_MANUALS "\n", mumps->id.INFOG(1), mumps->id.INFO(2)));
2303       F->factorerrortype = MAT_FACTOR_OTHER;
2304     }
2305   }
2306   if (!mumps->id.n) F->factorerrortype = MAT_FACTOR_NOERROR;
2307   PetscFunctionReturn(PETSC_SUCCESS);
2308 }
2309 
2310 static PetscErrorCode MatLUFactorSymbolic_AIJMUMPS(Mat F, Mat A, IS r, PETSC_UNUSED IS c, const MatFactorInfo *info)
2311 {
2312   Mat_MUMPS     *mumps = (Mat_MUMPS *)F->data;
2313   Vec            b;
2314   const PetscInt M = A->rmap->N;
2315 
2316   PetscFunctionBegin;
2317   if (mumps->matstruc == SAME_NONZERO_PATTERN) {
2318     /* F is assembled by a previous call of MatLUFactorSymbolic_AIJMUMPS() */
2319     PetscFunctionReturn(PETSC_SUCCESS);
2320   }
2321 
2322   /* Set MUMPS options from the options database */
2323   PetscCall(MatSetFromOptions_MUMPS(F, A));
2324 
2325   PetscCall((*mumps->ConvertToTriples)(A, 1, MAT_INITIAL_MATRIX, mumps));
2326   PetscCall(MatMumpsGatherNonzerosOnMaster(MAT_INITIAL_MATRIX, mumps));
2327 
2328   /* analysis phase */
2329   mumps->id.job = JOB_FACTSYMBOLIC;
2330   PetscCall(PetscMUMPSIntCast(M, &mumps->id.n));
2331   switch (mumps->id.ICNTL(18)) {
2332   case 0: /* centralized assembled matrix input */
2333     if (!mumps->myid) {
2334       mumps->id.nnz = mumps->nnz;
2335       mumps->id.irn = mumps->irn;
2336       mumps->id.jcn = mumps->jcn;
2337       if (mumps->id.ICNTL(6) > 1) mumps->id.a = (MumpsScalar *)mumps->val;
2338       if (r && mumps->id.ICNTL(7) == 7) {
2339         mumps->id.ICNTL(7) = 1;
2340         if (!mumps->myid) {
2341           const PetscInt *idx;
2342           PetscInt        i;
2343 
2344           PetscCall(PetscMalloc1(M, &mumps->id.perm_in));
2345           PetscCall(ISGetIndices(r, &idx));
2346           for (i = 0; i < M; i++) PetscCall(PetscMUMPSIntCast(idx[i] + 1, &mumps->id.perm_in[i])); /* perm_in[]: start from 1, not 0! */
2347           PetscCall(ISRestoreIndices(r, &idx));
2348         }
2349       }
2350     }
2351     break;
2352   case 3: /* distributed assembled matrix input (size>1) */
2353     mumps->id.nnz_loc = mumps->nnz;
2354     mumps->id.irn_loc = mumps->irn;
2355     mumps->id.jcn_loc = mumps->jcn;
2356     if (mumps->id.ICNTL(6) > 1) mumps->id.a_loc = (MumpsScalar *)mumps->val;
2357     if (mumps->ICNTL20 == 0) { /* Centralized rhs. Create scatter scat_rhs for repeated use in MatSolve() */
2358       PetscCall(MatCreateVecs(A, NULL, &b));
2359       PetscCall(VecScatterCreateToZero(b, &mumps->scat_rhs, &mumps->b_seq));
2360       PetscCall(VecDestroy(&b));
2361     }
2362     break;
2363   }
2364   PetscMUMPS_c(mumps);
2365   PetscCall(MatFactorSymbolic_MUMPS_ReportIfError(F, A, info, mumps));
2366 
2367   F->ops->lufactornumeric   = MatFactorNumeric_MUMPS;
2368   F->ops->solve             = MatSolve_MUMPS;
2369   F->ops->solvetranspose    = MatSolveTranspose_MUMPS;
2370   F->ops->matsolve          = MatMatSolve_MUMPS;
2371   F->ops->mattransposesolve = MatMatTransposeSolve_MUMPS;
2372   F->ops->matsolvetranspose = MatMatSolveTranspose_MUMPS;
2373 
2374   mumps->matstruc = SAME_NONZERO_PATTERN;
2375   PetscFunctionReturn(PETSC_SUCCESS);
2376 }
2377 
2378 /* Note the Petsc r and c permutations are ignored */
2379 static PetscErrorCode MatLUFactorSymbolic_BAIJMUMPS(Mat F, Mat A, PETSC_UNUSED IS r, PETSC_UNUSED IS c, const MatFactorInfo *info)
2380 {
2381   Mat_MUMPS     *mumps = (Mat_MUMPS *)F->data;
2382   Vec            b;
2383   const PetscInt M = A->rmap->N;
2384 
2385   PetscFunctionBegin;
2386   if (mumps->matstruc == SAME_NONZERO_PATTERN) {
2387     /* F is assembled by a previous call of MatLUFactorSymbolic_BAIJMUMPS() */
2388     PetscFunctionReturn(PETSC_SUCCESS);
2389   }
2390 
2391   /* Set MUMPS options from the options database */
2392   PetscCall(MatSetFromOptions_MUMPS(F, A));
2393 
2394   PetscCall((*mumps->ConvertToTriples)(A, 1, MAT_INITIAL_MATRIX, mumps));
2395   PetscCall(MatMumpsGatherNonzerosOnMaster(MAT_INITIAL_MATRIX, mumps));
2396 
2397   /* analysis phase */
2398   mumps->id.job = JOB_FACTSYMBOLIC;
2399   PetscCall(PetscMUMPSIntCast(M, &mumps->id.n));
2400   switch (mumps->id.ICNTL(18)) {
2401   case 0: /* centralized assembled matrix input */
2402     if (!mumps->myid) {
2403       mumps->id.nnz = mumps->nnz;
2404       mumps->id.irn = mumps->irn;
2405       mumps->id.jcn = mumps->jcn;
2406       if (mumps->id.ICNTL(6) > 1) mumps->id.a = (MumpsScalar *)mumps->val;
2407     }
2408     break;
2409   case 3: /* distributed assembled matrix input (size>1) */
2410     mumps->id.nnz_loc = mumps->nnz;
2411     mumps->id.irn_loc = mumps->irn;
2412     mumps->id.jcn_loc = mumps->jcn;
2413     if (mumps->id.ICNTL(6) > 1) mumps->id.a_loc = (MumpsScalar *)mumps->val;
2414     if (mumps->ICNTL20 == 0) { /* Centralized rhs. Create scatter scat_rhs for repeated use in MatSolve() */
2415       PetscCall(MatCreateVecs(A, NULL, &b));
2416       PetscCall(VecScatterCreateToZero(b, &mumps->scat_rhs, &mumps->b_seq));
2417       PetscCall(VecDestroy(&b));
2418     }
2419     break;
2420   }
2421   PetscMUMPS_c(mumps);
2422   PetscCall(MatFactorSymbolic_MUMPS_ReportIfError(F, A, info, mumps));
2423 
2424   F->ops->lufactornumeric   = MatFactorNumeric_MUMPS;
2425   F->ops->solve             = MatSolve_MUMPS;
2426   F->ops->solvetranspose    = MatSolveTranspose_MUMPS;
2427   F->ops->matsolvetranspose = MatMatSolveTranspose_MUMPS;
2428 
2429   mumps->matstruc = SAME_NONZERO_PATTERN;
2430   PetscFunctionReturn(PETSC_SUCCESS);
2431 }
2432 
2433 /* Note the Petsc r permutation and factor info are ignored */
2434 static PetscErrorCode MatCholeskyFactorSymbolic_MUMPS(Mat F, Mat A, PETSC_UNUSED IS r, const MatFactorInfo *info)
2435 {
2436   Mat_MUMPS     *mumps = (Mat_MUMPS *)F->data;
2437   Vec            b;
2438   const PetscInt M = A->rmap->N;
2439 
2440   PetscFunctionBegin;
2441   if (mumps->matstruc == SAME_NONZERO_PATTERN) {
2442     /* F is assembled by a previous call of MatCholeskyFactorSymbolic_MUMPS() */
2443     PetscFunctionReturn(PETSC_SUCCESS);
2444   }
2445 
2446   /* Set MUMPS options from the options database */
2447   PetscCall(MatSetFromOptions_MUMPS(F, A));
2448 
2449   PetscCall((*mumps->ConvertToTriples)(A, 1, MAT_INITIAL_MATRIX, mumps));
2450   PetscCall(MatMumpsGatherNonzerosOnMaster(MAT_INITIAL_MATRIX, mumps));
2451 
2452   /* analysis phase */
2453   mumps->id.job = JOB_FACTSYMBOLIC;
2454   PetscCall(PetscMUMPSIntCast(M, &mumps->id.n));
2455   switch (mumps->id.ICNTL(18)) {
2456   case 0: /* centralized assembled matrix input */
2457     if (!mumps->myid) {
2458       mumps->id.nnz = mumps->nnz;
2459       mumps->id.irn = mumps->irn;
2460       mumps->id.jcn = mumps->jcn;
2461       if (mumps->id.ICNTL(6) > 1) mumps->id.a = (MumpsScalar *)mumps->val;
2462     }
2463     break;
2464   case 3: /* distributed assembled matrix input (size>1) */
2465     mumps->id.nnz_loc = mumps->nnz;
2466     mumps->id.irn_loc = mumps->irn;
2467     mumps->id.jcn_loc = mumps->jcn;
2468     if (mumps->id.ICNTL(6) > 1) mumps->id.a_loc = (MumpsScalar *)mumps->val;
2469     if (mumps->ICNTL20 == 0) { /* Centralized rhs. Create scatter scat_rhs for repeated use in MatSolve() */
2470       PetscCall(MatCreateVecs(A, NULL, &b));
2471       PetscCall(VecScatterCreateToZero(b, &mumps->scat_rhs, &mumps->b_seq));
2472       PetscCall(VecDestroy(&b));
2473     }
2474     break;
2475   }
2476   PetscMUMPS_c(mumps);
2477   PetscCall(MatFactorSymbolic_MUMPS_ReportIfError(F, A, info, mumps));
2478 
2479   F->ops->choleskyfactornumeric = MatFactorNumeric_MUMPS;
2480   F->ops->solve                 = MatSolve_MUMPS;
2481   F->ops->solvetranspose        = MatSolve_MUMPS;
2482   F->ops->matsolve              = MatMatSolve_MUMPS;
2483   F->ops->mattransposesolve     = MatMatTransposeSolve_MUMPS;
2484   F->ops->matsolvetranspose     = MatMatSolveTranspose_MUMPS;
2485 #if defined(PETSC_USE_COMPLEX)
2486   F->ops->getinertia = NULL;
2487 #else
2488   F->ops->getinertia = MatGetInertia_SBAIJMUMPS;
2489 #endif
2490 
2491   mumps->matstruc = SAME_NONZERO_PATTERN;
2492   PetscFunctionReturn(PETSC_SUCCESS);
2493 }
2494 
2495 static PetscErrorCode MatView_MUMPS(Mat A, PetscViewer viewer)
2496 {
2497   PetscBool         iascii;
2498   PetscViewerFormat format;
2499   Mat_MUMPS        *mumps = (Mat_MUMPS *)A->data;
2500 
2501   PetscFunctionBegin;
2502   /* check if matrix is mumps type */
2503   if (A->ops->solve != MatSolve_MUMPS) PetscFunctionReturn(PETSC_SUCCESS);
2504 
2505   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
2506   if (iascii) {
2507     PetscCall(PetscViewerGetFormat(viewer, &format));
2508     if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
2509       PetscCall(PetscViewerASCIIPrintf(viewer, "MUMPS run parameters:\n"));
2510       if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
2511         PetscCall(PetscViewerASCIIPrintf(viewer, "  SYM (matrix type):                   %d\n", mumps->id.sym));
2512         PetscCall(PetscViewerASCIIPrintf(viewer, "  PAR (host participation):            %d\n", mumps->id.par));
2513         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(1) (output for error):         %d\n", mumps->id.ICNTL(1)));
2514         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(2) (output of diagnostic msg): %d\n", mumps->id.ICNTL(2)));
2515         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(3) (output for global info):   %d\n", mumps->id.ICNTL(3)));
2516         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(4) (level of printing):        %d\n", mumps->id.ICNTL(4)));
2517         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(5) (input mat struct):         %d\n", mumps->id.ICNTL(5)));
2518         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(6) (matrix prescaling):        %d\n", mumps->id.ICNTL(6)));
2519         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(7) (sequential matrix ordering):%d\n", mumps->id.ICNTL(7)));
2520         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(8) (scaling strategy):         %d\n", mumps->id.ICNTL(8)));
2521         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(10) (max num of refinements):  %d\n", mumps->id.ICNTL(10)));
2522         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(11) (error analysis):          %d\n", mumps->id.ICNTL(11)));
2523         if (mumps->id.ICNTL(11) > 0) {
2524           PetscCall(PetscViewerASCIIPrintf(viewer, "    RINFOG(4) (inf norm of input mat):        %g\n", (double)mumps->id.RINFOG(4)));
2525           PetscCall(PetscViewerASCIIPrintf(viewer, "    RINFOG(5) (inf norm of solution):         %g\n", (double)mumps->id.RINFOG(5)));
2526           PetscCall(PetscViewerASCIIPrintf(viewer, "    RINFOG(6) (inf norm of residual):         %g\n", (double)mumps->id.RINFOG(6)));
2527           PetscCall(PetscViewerASCIIPrintf(viewer, "    RINFOG(7),RINFOG(8) (backward error est): %g, %g\n", (double)mumps->id.RINFOG(7), (double)mumps->id.RINFOG(8)));
2528           PetscCall(PetscViewerASCIIPrintf(viewer, "    RINFOG(9) (error estimate):               %g\n", (double)mumps->id.RINFOG(9)));
2529           PetscCall(PetscViewerASCIIPrintf(viewer, "    RINFOG(10),RINFOG(11)(condition numbers): %g, %g\n", (double)mumps->id.RINFOG(10), (double)mumps->id.RINFOG(11)));
2530         }
2531         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(12) (efficiency control):                         %d\n", mumps->id.ICNTL(12)));
2532         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(13) (sequential factorization of the root node):  %d\n", mumps->id.ICNTL(13)));
2533         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(14) (percentage of estimated workspace increase): %d\n", mumps->id.ICNTL(14)));
2534         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(15) (compression of the input matrix):            %d\n", mumps->id.ICNTL(15)));
2535         /* ICNTL(15-17) not used */
2536         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(18) (input mat struct):                           %d\n", mumps->id.ICNTL(18)));
2537         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(19) (Schur complement info):                      %d\n", mumps->id.ICNTL(19)));
2538         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(20) (RHS sparse pattern):                         %d\n", mumps->id.ICNTL(20)));
2539         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(21) (solution struct):                            %d\n", mumps->id.ICNTL(21)));
2540         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(22) (in-core/out-of-core facility):               %d\n", mumps->id.ICNTL(22)));
2541         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(23) (max size of memory can be allocated locally):%d\n", mumps->id.ICNTL(23)));
2542 
2543         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(24) (detection of null pivot rows):               %d\n", mumps->id.ICNTL(24)));
2544         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(25) (computation of a null space basis):          %d\n", mumps->id.ICNTL(25)));
2545         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(26) (Schur options for RHS or solution):          %d\n", mumps->id.ICNTL(26)));
2546         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(27) (blocking size for multiple RHS):             %d\n", mumps->id.ICNTL(27)));
2547         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(28) (use parallel or sequential ordering):        %d\n", mumps->id.ICNTL(28)));
2548         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(29) (parallel ordering):                          %d\n", mumps->id.ICNTL(29)));
2549 
2550         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(30) (user-specified set of entries in inv(A)):    %d\n", mumps->id.ICNTL(30)));
2551         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(31) (factors is discarded in the solve phase):    %d\n", mumps->id.ICNTL(31)));
2552         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(33) (compute determinant):                        %d\n", mumps->id.ICNTL(33)));
2553         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(35) (activate BLR based factorization):           %d\n", mumps->id.ICNTL(35)));
2554         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(36) (choice of BLR factorization variant):        %d\n", mumps->id.ICNTL(36)));
2555         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(38) (estimated compression rate of LU factors):   %d\n", mumps->id.ICNTL(38)));
2556         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(48) (multithreading with tree parallelism):       %d\n", mumps->id.ICNTL(48)));
2557         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(58) (options for symbolic factorization):         %d\n", mumps->id.ICNTL(58)));
2558 
2559         PetscCall(PetscViewerASCIIPrintf(viewer, "  CNTL(1) (relative pivoting threshold):      %g\n", (double)mumps->id.CNTL(1)));
2560         PetscCall(PetscViewerASCIIPrintf(viewer, "  CNTL(2) (stopping criterion of refinement): %g\n", (double)mumps->id.CNTL(2)));
2561         PetscCall(PetscViewerASCIIPrintf(viewer, "  CNTL(3) (absolute pivoting threshold):      %g\n", (double)mumps->id.CNTL(3)));
2562         PetscCall(PetscViewerASCIIPrintf(viewer, "  CNTL(4) (value of static pivoting):         %g\n", (double)mumps->id.CNTL(4)));
2563         PetscCall(PetscViewerASCIIPrintf(viewer, "  CNTL(5) (fixation for null pivots):         %g\n", (double)mumps->id.CNTL(5)));
2564         PetscCall(PetscViewerASCIIPrintf(viewer, "  CNTL(7) (dropping parameter for BLR):       %g\n", (double)mumps->id.CNTL(7)));
2565 
2566         /* information local to each processor */
2567         PetscCall(PetscViewerASCIIPrintf(viewer, "  RINFO(1) (local estimated flops for the elimination after analysis):\n"));
2568         PetscCall(PetscViewerASCIIPushSynchronized(viewer));
2569         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %g\n", mumps->myid, (double)mumps->id.RINFO(1)));
2570         PetscCall(PetscViewerFlush(viewer));
2571         PetscCall(PetscViewerASCIIPrintf(viewer, "  RINFO(2) (local estimated flops for the assembly after factorization):\n"));
2572         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %g\n", mumps->myid, (double)mumps->id.RINFO(2)));
2573         PetscCall(PetscViewerFlush(viewer));
2574         PetscCall(PetscViewerASCIIPrintf(viewer, "  RINFO(3) (local estimated flops for the elimination after factorization):\n"));
2575         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %g\n", mumps->myid, (double)mumps->id.RINFO(3)));
2576         PetscCall(PetscViewerFlush(viewer));
2577 
2578         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFO(15) (estimated size of (in MB) MUMPS internal data for running numerical factorization):\n"));
2579         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %d\n", mumps->myid, mumps->id.INFO(15)));
2580         PetscCall(PetscViewerFlush(viewer));
2581 
2582         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFO(16) (size of (in MB) MUMPS internal data used during numerical factorization):\n"));
2583         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %d\n", mumps->myid, mumps->id.INFO(16)));
2584         PetscCall(PetscViewerFlush(viewer));
2585 
2586         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFO(23) (num of pivots eliminated on this processor after factorization):\n"));
2587         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %d\n", mumps->myid, mumps->id.INFO(23)));
2588         PetscCall(PetscViewerFlush(viewer));
2589 
2590         if (mumps->ninfo && mumps->ninfo <= 80) {
2591           PetscInt i;
2592           for (i = 0; i < mumps->ninfo; i++) {
2593             PetscCall(PetscViewerASCIIPrintf(viewer, "  INFO(%" PetscInt_FMT "):\n", mumps->info[i]));
2594             PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %d\n", mumps->myid, mumps->id.INFO(mumps->info[i])));
2595             PetscCall(PetscViewerFlush(viewer));
2596           }
2597         }
2598         PetscCall(PetscViewerASCIIPopSynchronized(viewer));
2599       } else PetscCall(PetscViewerASCIIPrintf(viewer, "  Use -%sksp_view ::ascii_info_detail to display information for all processes\n", ((PetscObject)A)->prefix ? ((PetscObject)A)->prefix : ""));
2600 
2601       if (mumps->myid == 0) { /* information from the host */
2602         PetscCall(PetscViewerASCIIPrintf(viewer, "  RINFOG(1) (global estimated flops for the elimination after analysis): %g\n", (double)mumps->id.RINFOG(1)));
2603         PetscCall(PetscViewerASCIIPrintf(viewer, "  RINFOG(2) (global estimated flops for the assembly after factorization): %g\n", (double)mumps->id.RINFOG(2)));
2604         PetscCall(PetscViewerASCIIPrintf(viewer, "  RINFOG(3) (global estimated flops for the elimination after factorization): %g\n", (double)mumps->id.RINFOG(3)));
2605         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)));
2606 
2607         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(3) (estimated real workspace for factors on all processors after analysis): %d\n", mumps->id.INFOG(3)));
2608         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(4) (estimated integer workspace for factors on all processors after analysis): %d\n", mumps->id.INFOG(4)));
2609         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(5) (estimated maximum front size in the complete tree): %d\n", mumps->id.INFOG(5)));
2610         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(6) (number of nodes in the complete tree): %d\n", mumps->id.INFOG(6)));
2611         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(7) (ordering option effectively used after analysis): %d\n", mumps->id.INFOG(7)));
2612         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(8) (structural symmetry in percent of the permuted matrix after analysis): %d\n", mumps->id.INFOG(8)));
2613         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(9) (total real/complex workspace to store the matrix factors after factorization): %d\n", mumps->id.INFOG(9)));
2614         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(10) (total integer space store the matrix factors after factorization): %d\n", mumps->id.INFOG(10)));
2615         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(11) (order of largest frontal matrix after factorization): %d\n", mumps->id.INFOG(11)));
2616         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(12) (number of off-diagonal pivots): %d\n", mumps->id.INFOG(12)));
2617         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(13) (number of delayed pivots after factorization): %d\n", mumps->id.INFOG(13)));
2618         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(14) (number of memory compress after factorization): %d\n", mumps->id.INFOG(14)));
2619         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(15) (number of steps of iterative refinement after solution): %d\n", mumps->id.INFOG(15)));
2620         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)));
2621         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)));
2622         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)));
2623         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(19) (size of all MUMPS internal data allocated during factorization: sum over all processors): %d\n", mumps->id.INFOG(19)));
2624         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(20) (estimated number of entries in the factors): %d\n", mumps->id.INFOG(20)));
2625         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)));
2626         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(22) (size in MB of memory effectively used during factorization - sum over all processors): %d\n", mumps->id.INFOG(22)));
2627         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(23) (after analysis: value of ICNTL(6) effectively used): %d\n", mumps->id.INFOG(23)));
2628         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(24) (after analysis: value of ICNTL(12) effectively used): %d\n", mumps->id.INFOG(24)));
2629         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(25) (after factorization: number of pivots modified by static pivoting): %d\n", mumps->id.INFOG(25)));
2630         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(28) (after factorization: number of null pivots encountered): %d\n", mumps->id.INFOG(28)));
2631         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(29) (after factorization: effective number of entries in the factors (sum over all processors)): %d\n", mumps->id.INFOG(29)));
2632         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)));
2633         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(32) (after analysis: type of analysis done): %d\n", mumps->id.INFOG(32)));
2634         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(33) (value used for ICNTL(8)): %d\n", mumps->id.INFOG(33)));
2635         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(34) (exponent of the determinant if determinant is requested): %d\n", mumps->id.INFOG(34)));
2636         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)));
2637         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)));
2638         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)));
2639         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)));
2640         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)));
2641       }
2642     }
2643   }
2644   PetscFunctionReturn(PETSC_SUCCESS);
2645 }
2646 
2647 static PetscErrorCode MatGetInfo_MUMPS(Mat A, PETSC_UNUSED MatInfoType flag, MatInfo *info)
2648 {
2649   Mat_MUMPS *mumps = (Mat_MUMPS *)A->data;
2650 
2651   PetscFunctionBegin;
2652   info->block_size        = 1.0;
2653   info->nz_allocated      = mumps->id.INFOG(20) >= 0 ? mumps->id.INFOG(20) : -1000000 * mumps->id.INFOG(20);
2654   info->nz_used           = mumps->id.INFOG(20) >= 0 ? mumps->id.INFOG(20) : -1000000 * mumps->id.INFOG(20);
2655   info->nz_unneeded       = 0.0;
2656   info->assemblies        = 0.0;
2657   info->mallocs           = 0.0;
2658   info->memory            = 0.0;
2659   info->fill_ratio_given  = 0;
2660   info->fill_ratio_needed = 0;
2661   info->factor_mallocs    = 0;
2662   PetscFunctionReturn(PETSC_SUCCESS);
2663 }
2664 
2665 static PetscErrorCode MatFactorSetSchurIS_MUMPS(Mat F, IS is)
2666 {
2667   Mat_MUMPS         *mumps = (Mat_MUMPS *)F->data;
2668   const PetscScalar *arr;
2669   const PetscInt    *idxs;
2670   PetscInt           size, i;
2671 
2672   PetscFunctionBegin;
2673   PetscCall(ISGetLocalSize(is, &size));
2674   /* Schur complement matrix */
2675   PetscCall(MatDestroy(&F->schur));
2676   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, size, size, NULL, &F->schur));
2677   PetscCall(MatDenseGetArrayRead(F->schur, &arr));
2678   mumps->id.schur = (MumpsScalar *)arr;
2679   PetscCall(PetscMUMPSIntCast(size, &mumps->id.size_schur));
2680   PetscCall(PetscMUMPSIntCast(size, &mumps->id.schur_lld));
2681   PetscCall(MatDenseRestoreArrayRead(F->schur, &arr));
2682   if (mumps->sym == 1) PetscCall(MatSetOption(F->schur, MAT_SPD, PETSC_TRUE));
2683 
2684   /* MUMPS expects Fortran style indices */
2685   PetscCall(PetscFree(mumps->id.listvar_schur));
2686   PetscCall(PetscMalloc1(size, &mumps->id.listvar_schur));
2687   PetscCall(ISGetIndices(is, &idxs));
2688   for (i = 0; i < size; i++) PetscCall(PetscMUMPSIntCast(idxs[i] + 1, &mumps->id.listvar_schur[i]));
2689   PetscCall(ISRestoreIndices(is, &idxs));
2690   /* set a special value of ICNTL (not handled my MUMPS) to be used in the solve phase by PETSc */
2691   mumps->id.ICNTL(26) = -1;
2692   PetscFunctionReturn(PETSC_SUCCESS);
2693 }
2694 
2695 static PetscErrorCode MatFactorCreateSchurComplement_MUMPS(Mat F, Mat *S)
2696 {
2697   Mat          St;
2698   Mat_MUMPS   *mumps = (Mat_MUMPS *)F->data;
2699   PetscScalar *array;
2700 
2701   PetscFunctionBegin;
2702   PetscCheck(mumps->id.ICNTL(19), PetscObjectComm((PetscObject)F), PETSC_ERR_ORDER, "Schur complement mode not selected! Call MatFactorSetSchurIS() to enable it");
2703   PetscCall(MatCreate(PETSC_COMM_SELF, &St));
2704   PetscCall(MatSetSizes(St, PETSC_DECIDE, PETSC_DECIDE, mumps->id.size_schur, mumps->id.size_schur));
2705   PetscCall(MatSetType(St, MATDENSE));
2706   PetscCall(MatSetUp(St));
2707   PetscCall(MatDenseGetArray(St, &array));
2708   if (!mumps->sym) {                /* MUMPS always return a full matrix */
2709     if (mumps->id.ICNTL(19) == 1) { /* stored by rows */
2710       PetscInt i, j, N = mumps->id.size_schur;
2711       for (i = 0; i < N; i++) {
2712         for (j = 0; j < N; j++) {
2713 #if !defined(PETSC_USE_COMPLEX)
2714           PetscScalar val = mumps->id.schur[i * N + j];
2715 #else
2716           PetscScalar val = mumps->id.schur[i * N + j].r + PETSC_i * mumps->id.schur[i * N + j].i;
2717 #endif
2718           array[j * N + i] = val;
2719         }
2720       }
2721     } else { /* stored by columns */
2722       PetscCall(PetscArraycpy(array, mumps->id.schur, mumps->id.size_schur * mumps->id.size_schur));
2723     }
2724   } else {                          /* either full or lower-triangular (not packed) */
2725     if (mumps->id.ICNTL(19) == 2) { /* lower triangular stored by columns */
2726       PetscInt i, j, N = mumps->id.size_schur;
2727       for (i = 0; i < N; i++) {
2728         for (j = i; j < N; j++) {
2729 #if !defined(PETSC_USE_COMPLEX)
2730           PetscScalar val = mumps->id.schur[i * N + j];
2731 #else
2732           PetscScalar val = mumps->id.schur[i * N + j].r + PETSC_i * mumps->id.schur[i * N + j].i;
2733 #endif
2734           array[i * N + j] = array[j * N + i] = val;
2735         }
2736       }
2737     } else if (mumps->id.ICNTL(19) == 3) { /* full matrix */
2738       PetscCall(PetscArraycpy(array, mumps->id.schur, mumps->id.size_schur * mumps->id.size_schur));
2739     } else { /* ICNTL(19) == 1 lower triangular stored by rows */
2740       PetscInt i, j, N = mumps->id.size_schur;
2741       for (i = 0; i < N; i++) {
2742         for (j = 0; j < i + 1; j++) {
2743 #if !defined(PETSC_USE_COMPLEX)
2744           PetscScalar val = mumps->id.schur[i * N + j];
2745 #else
2746           PetscScalar val = mumps->id.schur[i * N + j].r + PETSC_i * mumps->id.schur[i * N + j].i;
2747 #endif
2748           array[i * N + j] = array[j * N + i] = val;
2749         }
2750       }
2751     }
2752   }
2753   PetscCall(MatDenseRestoreArray(St, &array));
2754   *S = St;
2755   PetscFunctionReturn(PETSC_SUCCESS);
2756 }
2757 
2758 static PetscErrorCode MatMumpsSetIcntl_MUMPS(Mat F, PetscInt icntl, PetscInt ival)
2759 {
2760   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;
2761 
2762   PetscFunctionBegin;
2763   if (mumps->id.job == JOB_NULL) {                                            /* need to cache icntl and ival since PetscMUMPS_c() has never been called */
2764     PetscMUMPSInt i, nICNTL_pre = mumps->ICNTL_pre ? mumps->ICNTL_pre[0] : 0; /* number of already cached ICNTL */
2765     for (i = 0; i < nICNTL_pre; ++i)
2766       if (mumps->ICNTL_pre[1 + 2 * i] == icntl) break; /* is this ICNTL already cached? */
2767     if (i == nICNTL_pre) {                             /* not already cached */
2768       if (i > 0) PetscCall(PetscRealloc(sizeof(PetscMUMPSInt) * (2 * nICNTL_pre + 3), &mumps->ICNTL_pre));
2769       else PetscCall(PetscCalloc(sizeof(PetscMUMPSInt) * 3, &mumps->ICNTL_pre));
2770       mumps->ICNTL_pre[0]++;
2771     }
2772     mumps->ICNTL_pre[1 + 2 * i] = (PetscMUMPSInt)icntl;
2773     PetscCall(PetscMUMPSIntCast(ival, mumps->ICNTL_pre + 2 + 2 * i));
2774   } else PetscCall(PetscMUMPSIntCast(ival, &mumps->id.ICNTL(icntl)));
2775   PetscFunctionReturn(PETSC_SUCCESS);
2776 }
2777 
2778 static PetscErrorCode MatMumpsGetIcntl_MUMPS(Mat F, PetscInt icntl, PetscInt *ival)
2779 {
2780   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;
2781 
2782   PetscFunctionBegin;
2783   if (mumps->id.job == JOB_NULL) {
2784     PetscInt i, nICNTL_pre = mumps->ICNTL_pre ? mumps->ICNTL_pre[0] : 0;
2785     *ival = 0;
2786     for (i = 0; i < nICNTL_pre; ++i) {
2787       if (mumps->ICNTL_pre[1 + 2 * i] == icntl) *ival = mumps->ICNTL_pre[2 + 2 * i];
2788     }
2789   } else *ival = mumps->id.ICNTL(icntl);
2790   PetscFunctionReturn(PETSC_SUCCESS);
2791 }
2792 
2793 /*@
2794   MatMumpsSetIcntl - Set MUMPS parameter ICNTL() <https://mumps-solver.org/index.php?page=doc>
2795 
2796   Logically Collective
2797 
2798   Input Parameters:
2799 + F     - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
2800 . icntl - index of MUMPS parameter array ICNTL()
2801 - ival  - value of MUMPS ICNTL(icntl)
2802 
2803   Options Database Key:
2804 . -mat_mumps_icntl_<icntl> <ival> - change the option numbered icntl to ival
2805 
2806   Level: beginner
2807 
2808 .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`
2809 @*/
2810 PetscErrorCode MatMumpsSetIcntl(Mat F, PetscInt icntl, PetscInt ival)
2811 {
2812   PetscFunctionBegin;
2813   PetscValidType(F, 1);
2814   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
2815   PetscValidLogicalCollectiveInt(F, icntl, 2);
2816   PetscValidLogicalCollectiveInt(F, ival, 3);
2817   PetscCheck((icntl >= 1 && icntl <= 38) || icntl == 48 || icntl == 58, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONG, "Unsupported ICNTL value %" PetscInt_FMT, icntl);
2818   PetscTryMethod(F, "MatMumpsSetIcntl_C", (Mat, PetscInt, PetscInt), (F, icntl, ival));
2819   PetscFunctionReturn(PETSC_SUCCESS);
2820 }
2821 
2822 /*@
2823   MatMumpsGetIcntl - Get MUMPS parameter ICNTL() <https://mumps-solver.org/index.php?page=doc>
2824 
2825   Logically Collective
2826 
2827   Input Parameters:
2828 + F     - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
2829 - icntl - index of MUMPS parameter array ICNTL()
2830 
2831   Output Parameter:
2832 . ival - value of MUMPS ICNTL(icntl)
2833 
2834   Level: beginner
2835 
2836 .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`
2837 @*/
2838 PetscErrorCode MatMumpsGetIcntl(Mat F, PetscInt icntl, PetscInt *ival)
2839 {
2840   PetscFunctionBegin;
2841   PetscValidType(F, 1);
2842   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
2843   PetscValidLogicalCollectiveInt(F, icntl, 2);
2844   PetscAssertPointer(ival, 3);
2845   PetscCheck((icntl >= 1 && icntl <= 38) || icntl == 48 || icntl == 58, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONG, "Unsupported ICNTL value %" PetscInt_FMT, icntl);
2846   PetscUseMethod(F, "MatMumpsGetIcntl_C", (Mat, PetscInt, PetscInt *), (F, icntl, ival));
2847   PetscFunctionReturn(PETSC_SUCCESS);
2848 }
2849 
2850 static PetscErrorCode MatMumpsSetCntl_MUMPS(Mat F, PetscInt icntl, PetscReal val)
2851 {
2852   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;
2853 
2854   PetscFunctionBegin;
2855   if (mumps->id.job == JOB_NULL) {
2856     PetscInt i, nCNTL_pre = mumps->CNTL_pre ? mumps->CNTL_pre[0] : 0;
2857     for (i = 0; i < nCNTL_pre; ++i)
2858       if (mumps->CNTL_pre[1 + 2 * i] == icntl) break;
2859     if (i == nCNTL_pre) {
2860       if (i > 0) PetscCall(PetscRealloc(sizeof(PetscReal) * (2 * nCNTL_pre + 3), &mumps->CNTL_pre));
2861       else PetscCall(PetscCalloc(sizeof(PetscReal) * 3, &mumps->CNTL_pre));
2862       mumps->CNTL_pre[0]++;
2863     }
2864     mumps->CNTL_pre[1 + 2 * i] = icntl;
2865     mumps->CNTL_pre[2 + 2 * i] = val;
2866   } else mumps->id.CNTL(icntl) = val;
2867   PetscFunctionReturn(PETSC_SUCCESS);
2868 }
2869 
2870 static PetscErrorCode MatMumpsGetCntl_MUMPS(Mat F, PetscInt icntl, PetscReal *val)
2871 {
2872   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;
2873 
2874   PetscFunctionBegin;
2875   if (mumps->id.job == JOB_NULL) {
2876     PetscInt i, nCNTL_pre = mumps->CNTL_pre ? mumps->CNTL_pre[0] : 0;
2877     *val = 0.0;
2878     for (i = 0; i < nCNTL_pre; ++i) {
2879       if (mumps->CNTL_pre[1 + 2 * i] == icntl) *val = mumps->CNTL_pre[2 + 2 * i];
2880     }
2881   } else *val = mumps->id.CNTL(icntl);
2882   PetscFunctionReturn(PETSC_SUCCESS);
2883 }
2884 
2885 /*@
2886   MatMumpsSetCntl - Set MUMPS parameter CNTL() <https://mumps-solver.org/index.php?page=doc>
2887 
2888   Logically Collective
2889 
2890   Input Parameters:
2891 + F     - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
2892 . icntl - index of MUMPS parameter array CNTL()
2893 - val   - value of MUMPS CNTL(icntl)
2894 
2895   Options Database Key:
2896 . -mat_mumps_cntl_<icntl> <val> - change the option numbered icntl to ival
2897 
2898   Level: beginner
2899 
2900 .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`
2901 @*/
2902 PetscErrorCode MatMumpsSetCntl(Mat F, PetscInt icntl, PetscReal val)
2903 {
2904   PetscFunctionBegin;
2905   PetscValidType(F, 1);
2906   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
2907   PetscValidLogicalCollectiveInt(F, icntl, 2);
2908   PetscValidLogicalCollectiveReal(F, val, 3);
2909   PetscCheck(icntl >= 1 && icntl <= 7, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONG, "Unsupported CNTL value %" PetscInt_FMT, icntl);
2910   PetscTryMethod(F, "MatMumpsSetCntl_C", (Mat, PetscInt, PetscReal), (F, icntl, val));
2911   PetscFunctionReturn(PETSC_SUCCESS);
2912 }
2913 
2914 /*@
2915   MatMumpsGetCntl - Get MUMPS parameter CNTL() <https://mumps-solver.org/index.php?page=doc>
2916 
2917   Logically Collective
2918 
2919   Input Parameters:
2920 + F     - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
2921 - icntl - index of MUMPS parameter array CNTL()
2922 
2923   Output Parameter:
2924 . val - value of MUMPS CNTL(icntl)
2925 
2926   Level: beginner
2927 
2928 .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`
2929 @*/
2930 PetscErrorCode MatMumpsGetCntl(Mat F, PetscInt icntl, PetscReal *val)
2931 {
2932   PetscFunctionBegin;
2933   PetscValidType(F, 1);
2934   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
2935   PetscValidLogicalCollectiveInt(F, icntl, 2);
2936   PetscAssertPointer(val, 3);
2937   PetscCheck(icntl >= 1 && icntl <= 7, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONG, "Unsupported CNTL value %" PetscInt_FMT, icntl);
2938   PetscUseMethod(F, "MatMumpsGetCntl_C", (Mat, PetscInt, PetscReal *), (F, icntl, val));
2939   PetscFunctionReturn(PETSC_SUCCESS);
2940 }
2941 
2942 static PetscErrorCode MatMumpsGetInfo_MUMPS(Mat F, PetscInt icntl, PetscInt *info)
2943 {
2944   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;
2945 
2946   PetscFunctionBegin;
2947   *info = mumps->id.INFO(icntl);
2948   PetscFunctionReturn(PETSC_SUCCESS);
2949 }
2950 
2951 static PetscErrorCode MatMumpsGetInfog_MUMPS(Mat F, PetscInt icntl, PetscInt *infog)
2952 {
2953   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;
2954 
2955   PetscFunctionBegin;
2956   *infog = mumps->id.INFOG(icntl);
2957   PetscFunctionReturn(PETSC_SUCCESS);
2958 }
2959 
2960 static PetscErrorCode MatMumpsGetRinfo_MUMPS(Mat F, PetscInt icntl, PetscReal *rinfo)
2961 {
2962   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;
2963 
2964   PetscFunctionBegin;
2965   *rinfo = mumps->id.RINFO(icntl);
2966   PetscFunctionReturn(PETSC_SUCCESS);
2967 }
2968 
2969 static PetscErrorCode MatMumpsGetRinfog_MUMPS(Mat F, PetscInt icntl, PetscReal *rinfog)
2970 {
2971   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;
2972 
2973   PetscFunctionBegin;
2974   *rinfog = mumps->id.RINFOG(icntl);
2975   PetscFunctionReturn(PETSC_SUCCESS);
2976 }
2977 
2978 static PetscErrorCode MatMumpsGetNullPivots_MUMPS(Mat F, PetscInt *size, PetscInt **array)
2979 {
2980   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;
2981 
2982   PetscFunctionBegin;
2983   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");
2984   *size  = 0;
2985   *array = NULL;
2986   if (!mumps->myid) {
2987     *size = mumps->id.INFOG(28);
2988     PetscCall(PetscMalloc1(*size, array));
2989     for (int i = 0; i < *size; i++) (*array)[i] = mumps->id.pivnul_list[i] - 1;
2990   }
2991   PetscFunctionReturn(PETSC_SUCCESS);
2992 }
2993 
2994 static PetscErrorCode MatMumpsGetInverse_MUMPS(Mat F, Mat spRHS)
2995 {
2996   Mat          Bt = NULL, Btseq = NULL;
2997   PetscBool    flg;
2998   Mat_MUMPS   *mumps = (Mat_MUMPS *)F->data;
2999   PetscScalar *aa;
3000   PetscInt     spnr, *ia, *ja, M, nrhs;
3001 
3002   PetscFunctionBegin;
3003   PetscAssertPointer(spRHS, 2);
3004   PetscCall(PetscObjectTypeCompare((PetscObject)spRHS, MATTRANSPOSEVIRTUAL, &flg));
3005   if (flg) {
3006     PetscCall(MatTransposeGetMat(spRHS, &Bt));
3007   } else SETERRQ(PetscObjectComm((PetscObject)spRHS), PETSC_ERR_ARG_WRONG, "Matrix spRHS must be type MATTRANSPOSEVIRTUAL matrix");
3008 
3009   PetscCall(MatMumpsSetIcntl(F, 30, 1));
3010 
3011   if (mumps->petsc_size > 1) {
3012     Mat_MPIAIJ *b = (Mat_MPIAIJ *)Bt->data;
3013     Btseq         = b->A;
3014   } else {
3015     Btseq = Bt;
3016   }
3017 
3018   PetscCall(MatGetSize(spRHS, &M, &nrhs));
3019   mumps->id.nrhs = (PetscMUMPSInt)nrhs;
3020   PetscCall(PetscMUMPSIntCast(M, &mumps->id.lrhs));
3021   mumps->id.rhs = NULL;
3022 
3023   if (!mumps->myid) {
3024     PetscCall(MatSeqAIJGetArray(Btseq, &aa));
3025     PetscCall(MatGetRowIJ(Btseq, 1, PETSC_FALSE, PETSC_FALSE, &spnr, (const PetscInt **)&ia, (const PetscInt **)&ja, &flg));
3026     PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot get IJ structure");
3027     PetscCall(PetscMUMPSIntCSRCast(mumps, spnr, ia, ja, &mumps->id.irhs_ptr, &mumps->id.irhs_sparse, &mumps->id.nz_rhs));
3028     mumps->id.rhs_sparse = (MumpsScalar *)aa;
3029   } else {
3030     mumps->id.irhs_ptr    = NULL;
3031     mumps->id.irhs_sparse = NULL;
3032     mumps->id.nz_rhs      = 0;
3033     mumps->id.rhs_sparse  = NULL;
3034   }
3035   mumps->id.ICNTL(20) = 1; /* rhs is sparse */
3036   mumps->id.ICNTL(21) = 0; /* solution is in assembled centralized format */
3037 
3038   /* solve phase */
3039   mumps->id.job = JOB_SOLVE;
3040   PetscMUMPS_c(mumps);
3041   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));
3042 
3043   if (!mumps->myid) {
3044     PetscCall(MatSeqAIJRestoreArray(Btseq, &aa));
3045     PetscCall(MatRestoreRowIJ(Btseq, 1, PETSC_FALSE, PETSC_FALSE, &spnr, (const PetscInt **)&ia, (const PetscInt **)&ja, &flg));
3046     PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot get IJ structure");
3047   }
3048   PetscFunctionReturn(PETSC_SUCCESS);
3049 }
3050 
3051 /*@
3052   MatMumpsGetInverse - Get user-specified set of entries in inverse of `A` <https://mumps-solver.org/index.php?page=doc>
3053 
3054   Logically Collective
3055 
3056   Input Parameter:
3057 . F - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
3058 
3059   Output Parameter:
3060 . spRHS - sequential sparse matrix in `MATTRANSPOSEVIRTUAL` format with requested entries of inverse of `A`
3061 
3062   Level: beginner
3063 
3064 .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatCreateTranspose()`
3065 @*/
3066 PetscErrorCode MatMumpsGetInverse(Mat F, Mat spRHS)
3067 {
3068   PetscFunctionBegin;
3069   PetscValidType(F, 1);
3070   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
3071   PetscUseMethod(F, "MatMumpsGetInverse_C", (Mat, Mat), (F, spRHS));
3072   PetscFunctionReturn(PETSC_SUCCESS);
3073 }
3074 
3075 static PetscErrorCode MatMumpsGetInverseTranspose_MUMPS(Mat F, Mat spRHST)
3076 {
3077   Mat spRHS;
3078 
3079   PetscFunctionBegin;
3080   PetscCall(MatCreateTranspose(spRHST, &spRHS));
3081   PetscCall(MatMumpsGetInverse_MUMPS(F, spRHS));
3082   PetscCall(MatDestroy(&spRHS));
3083   PetscFunctionReturn(PETSC_SUCCESS);
3084 }
3085 
3086 /*@
3087   MatMumpsGetInverseTranspose - Get user-specified set of entries in inverse of matrix $A^T $ <https://mumps-solver.org/index.php?page=doc>
3088 
3089   Logically Collective
3090 
3091   Input Parameter:
3092 . F - the factored matrix of A obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
3093 
3094   Output Parameter:
3095 . spRHST - sequential sparse matrix in `MATAIJ` format containing the requested entries of inverse of `A`^T
3096 
3097   Level: beginner
3098 
3099 .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatCreateTranspose()`, `MatMumpsGetInverse()`
3100 @*/
3101 PetscErrorCode MatMumpsGetInverseTranspose(Mat F, Mat spRHST)
3102 {
3103   PetscBool flg;
3104 
3105   PetscFunctionBegin;
3106   PetscValidType(F, 1);
3107   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
3108   PetscCall(PetscObjectTypeCompareAny((PetscObject)spRHST, &flg, MATSEQAIJ, MATMPIAIJ, NULL));
3109   PetscCheck(flg, PetscObjectComm((PetscObject)spRHST), PETSC_ERR_ARG_WRONG, "Matrix spRHST must be MATAIJ matrix");
3110 
3111   PetscUseMethod(F, "MatMumpsGetInverseTranspose_C", (Mat, Mat), (F, spRHST));
3112   PetscFunctionReturn(PETSC_SUCCESS);
3113 }
3114 
3115 /*@
3116   MatMumpsGetInfo - Get MUMPS parameter INFO() <https://mumps-solver.org/index.php?page=doc>
3117 
3118   Logically Collective
3119 
3120   Input Parameters:
3121 + F     - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
3122 - icntl - index of MUMPS parameter array INFO()
3123 
3124   Output Parameter:
3125 . ival - value of MUMPS INFO(icntl)
3126 
3127   Level: beginner
3128 
3129 .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`
3130 @*/
3131 PetscErrorCode MatMumpsGetInfo(Mat F, PetscInt icntl, PetscInt *ival)
3132 {
3133   PetscFunctionBegin;
3134   PetscValidType(F, 1);
3135   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
3136   PetscAssertPointer(ival, 3);
3137   PetscUseMethod(F, "MatMumpsGetInfo_C", (Mat, PetscInt, PetscInt *), (F, icntl, ival));
3138   PetscFunctionReturn(PETSC_SUCCESS);
3139 }
3140 
3141 /*@
3142   MatMumpsGetInfog - Get MUMPS parameter INFOG() <https://mumps-solver.org/index.php?page=doc>
3143 
3144   Logically Collective
3145 
3146   Input Parameters:
3147 + F     - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
3148 - icntl - index of MUMPS parameter array INFOG()
3149 
3150   Output Parameter:
3151 . ival - value of MUMPS INFOG(icntl)
3152 
3153   Level: beginner
3154 
3155 .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`
3156 @*/
3157 PetscErrorCode MatMumpsGetInfog(Mat F, PetscInt icntl, PetscInt *ival)
3158 {
3159   PetscFunctionBegin;
3160   PetscValidType(F, 1);
3161   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
3162   PetscAssertPointer(ival, 3);
3163   PetscUseMethod(F, "MatMumpsGetInfog_C", (Mat, PetscInt, PetscInt *), (F, icntl, ival));
3164   PetscFunctionReturn(PETSC_SUCCESS);
3165 }
3166 
3167 /*@
3168   MatMumpsGetRinfo - Get MUMPS parameter RINFO() <https://mumps-solver.org/index.php?page=doc>
3169 
3170   Logically Collective
3171 
3172   Input Parameters:
3173 + F     - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
3174 - icntl - index of MUMPS parameter array RINFO()
3175 
3176   Output Parameter:
3177 . val - value of MUMPS RINFO(icntl)
3178 
3179   Level: beginner
3180 
3181 .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfog()`
3182 @*/
3183 PetscErrorCode MatMumpsGetRinfo(Mat F, PetscInt icntl, PetscReal *val)
3184 {
3185   PetscFunctionBegin;
3186   PetscValidType(F, 1);
3187   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
3188   PetscAssertPointer(val, 3);
3189   PetscUseMethod(F, "MatMumpsGetRinfo_C", (Mat, PetscInt, PetscReal *), (F, icntl, val));
3190   PetscFunctionReturn(PETSC_SUCCESS);
3191 }
3192 
3193 /*@
3194   MatMumpsGetRinfog - Get MUMPS parameter RINFOG() <https://mumps-solver.org/index.php?page=doc>
3195 
3196   Logically Collective
3197 
3198   Input Parameters:
3199 + F     - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
3200 - icntl - index of MUMPS parameter array RINFOG()
3201 
3202   Output Parameter:
3203 . val - value of MUMPS RINFOG(icntl)
3204 
3205   Level: beginner
3206 
3207 .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`
3208 @*/
3209 PetscErrorCode MatMumpsGetRinfog(Mat F, PetscInt icntl, PetscReal *val)
3210 {
3211   PetscFunctionBegin;
3212   PetscValidType(F, 1);
3213   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
3214   PetscAssertPointer(val, 3);
3215   PetscUseMethod(F, "MatMumpsGetRinfog_C", (Mat, PetscInt, PetscReal *), (F, icntl, val));
3216   PetscFunctionReturn(PETSC_SUCCESS);
3217 }
3218 
3219 /*@
3220   MatMumpsGetNullPivots - Get MUMPS parameter PIVNUL_LIST() <https://mumps-solver.org/index.php?page=doc>
3221 
3222   Logically Collective
3223 
3224   Input Parameter:
3225 . F - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
3226 
3227   Output Parameters:
3228 + size  - local size of the array. The size of the array is non-zero only on MPI rank 0
3229 - 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
3230           for freeing this array.
3231 
3232   Level: beginner
3233 
3234 .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`
3235 @*/
3236 PetscErrorCode MatMumpsGetNullPivots(Mat F, PetscInt *size, PetscInt **array)
3237 {
3238   PetscFunctionBegin;
3239   PetscValidType(F, 1);
3240   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
3241   PetscAssertPointer(size, 2);
3242   PetscAssertPointer(array, 3);
3243   PetscUseMethod(F, "MatMumpsGetNullPivots_C", (Mat, PetscInt *, PetscInt **), (F, size, array));
3244   PetscFunctionReturn(PETSC_SUCCESS);
3245 }
3246 
3247 /*MC
3248   MATSOLVERMUMPS -  A matrix type providing direct solvers (LU and Cholesky) for
3249   MPI distributed and sequential matrices via the external package MUMPS <https://mumps-solver.org/index.php?page=doc>
3250 
3251   Works with `MATAIJ` and `MATSBAIJ` matrices
3252 
3253   Use ./configure --download-mumps --download-scalapack --download-parmetis --download-metis --download-ptscotch to have PETSc installed with MUMPS
3254 
3255   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.
3256   See details below.
3257 
3258   Use `-pc_type cholesky` or `lu` `-pc_factor_mat_solver_type mumps` to use this direct solver
3259 
3260   Options Database Keys:
3261 +  -mat_mumps_icntl_1  - ICNTL(1): output stream for error messages
3262 .  -mat_mumps_icntl_2  - ICNTL(2): output stream for diagnostic printing, statistics, and warning
3263 .  -mat_mumps_icntl_3  - ICNTL(3): output stream for global information, collected on the host
3264 .  -mat_mumps_icntl_4  - ICNTL(4): level of printing (0 to 4)
3265 .  -mat_mumps_icntl_6  - ICNTL(6): permutes to a zero-free diagonal and/or scale the matrix (0 to 7)
3266 .  -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
3267                           Use -pc_factor_mat_ordering_type <type> to have PETSc perform the ordering (sequential only)
3268 .  -mat_mumps_icntl_8  - ICNTL(8): scaling strategy (-2 to 8 or 77)
3269 .  -mat_mumps_icntl_10 - ICNTL(10): max num of refinements
3270 .  -mat_mumps_icntl_11 - ICNTL(11): statistics related to an error analysis (via -ksp_view)
3271 .  -mat_mumps_icntl_12 - ICNTL(12): an ordering strategy for symmetric matrices (0 to 3)
3272 .  -mat_mumps_icntl_13 - ICNTL(13): parallelism of the root node (enable ScaLAPACK) and its splitting
3273 .  -mat_mumps_icntl_14 - ICNTL(14): percentage increase in the estimated working space
3274 .  -mat_mumps_icntl_15 - ICNTL(15): compression of the input matrix resulting from a block format
3275 .  -mat_mumps_icntl_19 - ICNTL(19): computes the Schur complement
3276 .  -mat_mumps_icntl_20 - ICNTL(20): give MUMPS centralized (0) or distributed (10) dense RHS
3277 .  -mat_mumps_icntl_22 - ICNTL(22): in-core/out-of-core factorization and solve (0 or 1)
3278 .  -mat_mumps_icntl_23 - ICNTL(23): max size of the working memory (MB) that can allocate per processor
3279 .  -mat_mumps_icntl_24 - ICNTL(24): detection of null pivot rows (0 or 1)
3280 .  -mat_mumps_icntl_25 - ICNTL(25): compute a solution of a deficient matrix and a null space basis
3281 .  -mat_mumps_icntl_26 - ICNTL(26): drives the solution phase if a Schur complement matrix
3282 .  -mat_mumps_icntl_28 - ICNTL(28): use 1 for sequential analysis and ICNTL(7) ordering, or 2 for parallel analysis and ICNTL(29) ordering
3283 .  -mat_mumps_icntl_29 - ICNTL(29): parallel ordering 1 = ptscotch, 2 = parmetis
3284 .  -mat_mumps_icntl_30 - ICNTL(30): compute user-specified set of entries in inv(A)
3285 .  -mat_mumps_icntl_31 - ICNTL(31): indicates which factors may be discarded during factorization
3286 .  -mat_mumps_icntl_33 - ICNTL(33): compute determinant
3287 .  -mat_mumps_icntl_35 - ICNTL(35): level of activation of BLR (Block Low-Rank) feature
3288 .  -mat_mumps_icntl_36 - ICNTL(36): controls the choice of BLR factorization variant
3289 .  -mat_mumps_icntl_38 - ICNTL(38): sets the estimated compression rate of LU factors with BLR
3290 .  -mat_mumps_icntl_48 - ICNTL(48): multithreading with tree parallelism
3291 .  -mat_mumps_icntl_58 - ICNTL(58): options for symbolic factorization
3292 .  -mat_mumps_cntl_1   - CNTL(1): relative pivoting threshold
3293 .  -mat_mumps_cntl_2   - CNTL(2): stopping criterion of refinement
3294 .  -mat_mumps_cntl_3   - CNTL(3): absolute pivoting threshold
3295 .  -mat_mumps_cntl_4   - CNTL(4): value for static pivoting
3296 .  -mat_mumps_cntl_5   - CNTL(5): fixation for null pivots
3297 .  -mat_mumps_cntl_7   - CNTL(7): precision of the dropping parameter used during BLR factorization
3298 -  -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.
3299                                     Default might be the number of cores per CPU package (socket) as reported by hwloc and suggested by the MUMPS manual.
3300 
3301   Level: beginner
3302 
3303   Notes:
3304   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
3305   error if the matrix is Hermitian.
3306 
3307   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
3308   `MatSetOptionsPrefixFactor()` on the matrix from which the factor was obtained or `MatSetOptionsPrefix()` on the factor matrix.
3309 
3310   When a MUMPS factorization fails inside a KSP solve, for example with a `KSP_DIVERGED_PC_FAILED`, one can find the MUMPS information about
3311   the failure with
3312 .vb
3313           KSPGetPC(ksp,&pc);
3314           PCFactorGetMatrix(pc,&mat);
3315           MatMumpsGetInfo(mat,....);
3316           MatMumpsGetInfog(mat,....); etc.
3317 .ve
3318   Or run with `-ksp_error_if_not_converged` and the program will be stopped and the information printed in the error message.
3319 
3320   MUMPS provides 64-bit integer support in two build modes:
3321   full 64-bit: here MUMPS is built with C preprocessing flag -DINTSIZE64 and Fortran compiler option -i8, -fdefault-integer-8 or equivalent, and
3322   requires all dependent libraries MPI, ScaLAPACK, LAPACK and BLAS built the same way with 64-bit integers (for example ILP64 Intel MKL and MPI).
3323 
3324   selective 64-bit: with the default MUMPS build, 64-bit integers have been introduced where needed. In compressed sparse row (CSR) storage of matrices,
3325   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
3326   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
3327   integer) build of all dependent libraries MPI, ScaLAPACK, LAPACK and BLAS.
3328 
3329   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.
3330 
3331   Two modes to run MUMPS/PETSc with OpenMP
3332 .vb
3333    Set `OMP_NUM_THREADS` and run with fewer MPI ranks than cores. For example, if you want to have 16 OpenMP
3334    threads per rank, then you may use "export `OMP_NUM_THREADS` = 16 && mpirun -n 4 ./test".
3335 .ve
3336 
3337 .vb
3338    `-mat_mumps_use_omp_threads` [m] and run your code with as many MPI ranks as the number of cores. For example,
3339    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"
3340 .ve
3341 
3342    To run MUMPS in MPI+OpenMP hybrid mode (i.e., enable multithreading in MUMPS), but still run the non-MUMPS part
3343    (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`
3344    (or `--with-hwloc`), and have an MPI that supports MPI-3.0's process shared memory (which is usually available). Since MUMPS calls BLAS
3345    libraries, to really get performance, you should have multithreaded BLAS libraries such as Intel MKL, AMD ACML, Cray libSci or OpenBLAS
3346    (PETSc will automatically try to utilized a threaded BLAS if `--with-openmp` is provided).
3347 
3348    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
3349    processes on each compute node. Listing the processes in rank ascending order, we split processes on a node into consecutive groups of
3350    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
3351    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
3352    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.
3353    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,
3354    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
3355    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
3356    cores in socket 1, that definitely hurts locality. On the other hand, if you map MPI ranks consecutively on the two sockets, then the
3357    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.
3358    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
3359    examine the mapping result.
3360 
3361    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,
3362    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
3363    calls `omp_set_num_threads`(m) internally before calling MUMPS.
3364 
3365    See {cite}`heroux2011bi` and {cite}`gutierrez2017accommodating`
3366 
3367 .seealso: [](ch_matrices), `Mat`, `PCFactorSetMatSolverType()`, `MatSolverType`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`, `KSPGetPC()`, `PCFactorGetMatrix()`
3368 M*/
3369 
3370 static PetscErrorCode MatFactorGetSolverType_mumps(PETSC_UNUSED Mat A, MatSolverType *type)
3371 {
3372   PetscFunctionBegin;
3373   *type = MATSOLVERMUMPS;
3374   PetscFunctionReturn(PETSC_SUCCESS);
3375 }
3376 
3377 /* MatGetFactor for Seq and MPI AIJ matrices */
3378 static PetscErrorCode MatGetFactor_aij_mumps(Mat A, MatFactorType ftype, Mat *F)
3379 {
3380   Mat         B;
3381   Mat_MUMPS  *mumps;
3382   PetscBool   isSeqAIJ, isDiag, isDense;
3383   PetscMPIInt size;
3384 
3385   PetscFunctionBegin;
3386 #if defined(PETSC_USE_COMPLEX)
3387   if (ftype == MAT_FACTOR_CHOLESKY && A->hermitian == PETSC_BOOL3_TRUE && A->symmetric != PETSC_BOOL3_TRUE) {
3388     PetscCall(PetscInfo(A, "Hermitian MAT_FACTOR_CHOLESKY is not supported. Use MAT_FACTOR_LU instead.\n"));
3389     *F = NULL;
3390     PetscFunctionReturn(PETSC_SUCCESS);
3391   }
3392 #endif
3393   /* Create the factorization matrix */
3394   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATSEQAIJ, &isSeqAIJ));
3395   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATDIAGONAL, &isDiag));
3396   PetscCall(PetscObjectTypeCompareAny((PetscObject)A, &isDense, MATSEQDENSE, MATMPIDENSE, NULL));
3397   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
3398   PetscCall(MatSetSizes(B, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
3399   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &((PetscObject)B)->type_name));
3400   PetscCall(MatSetUp(B));
3401 
3402   PetscCall(PetscNew(&mumps));
3403 
3404   B->ops->view    = MatView_MUMPS;
3405   B->ops->getinfo = MatGetInfo_MUMPS;
3406 
3407   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorGetSolverType_C", MatFactorGetSolverType_mumps));
3408   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorSetSchurIS_C", MatFactorSetSchurIS_MUMPS));
3409   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorCreateSchurComplement_C", MatFactorCreateSchurComplement_MUMPS));
3410   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetIcntl_C", MatMumpsSetIcntl_MUMPS));
3411   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetIcntl_C", MatMumpsGetIcntl_MUMPS));
3412   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetCntl_C", MatMumpsSetCntl_MUMPS));
3413   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetCntl_C", MatMumpsGetCntl_MUMPS));
3414   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfo_C", MatMumpsGetInfo_MUMPS));
3415   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfog_C", MatMumpsGetInfog_MUMPS));
3416   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfo_C", MatMumpsGetRinfo_MUMPS));
3417   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfog_C", MatMumpsGetRinfog_MUMPS));
3418   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetNullPivots_C", MatMumpsGetNullPivots_MUMPS));
3419   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverse_C", MatMumpsGetInverse_MUMPS));
3420   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverseTranspose_C", MatMumpsGetInverseTranspose_MUMPS));
3421 
3422   if (ftype == MAT_FACTOR_LU) {
3423     B->ops->lufactorsymbolic = MatLUFactorSymbolic_AIJMUMPS;
3424     B->factortype            = MAT_FACTOR_LU;
3425     if (isSeqAIJ) mumps->ConvertToTriples = MatConvertToTriples_seqaij_seqaij;
3426     else if (isDiag) mumps->ConvertToTriples = MatConvertToTriples_diagonal_xaij;
3427     else if (isDense) mumps->ConvertToTriples = MatConvertToTriples_dense_xaij;
3428     else mumps->ConvertToTriples = MatConvertToTriples_mpiaij_mpiaij;
3429     PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&B->preferredordering[MAT_FACTOR_LU]));
3430     mumps->sym = 0;
3431   } else {
3432     B->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_MUMPS;
3433     B->factortype                  = MAT_FACTOR_CHOLESKY;
3434     if (isSeqAIJ) mumps->ConvertToTriples = MatConvertToTriples_seqaij_seqsbaij;
3435     else if (isDiag) mumps->ConvertToTriples = MatConvertToTriples_diagonal_xaij;
3436     else if (isDense) mumps->ConvertToTriples = MatConvertToTriples_dense_xaij;
3437     else mumps->ConvertToTriples = MatConvertToTriples_mpiaij_mpisbaij;
3438     PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&B->preferredordering[MAT_FACTOR_CHOLESKY]));
3439 #if defined(PETSC_USE_COMPLEX)
3440     mumps->sym = 2;
3441 #else
3442     if (A->spd == PETSC_BOOL3_TRUE) mumps->sym = 1;
3443     else mumps->sym = 2;
3444 #endif
3445   }
3446 
3447   /* set solvertype */
3448   PetscCall(PetscFree(B->solvertype));
3449   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &B->solvertype));
3450   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
3451   if (size == 1) {
3452     /* MUMPS option -mat_mumps_icntl_7 1 is automatically set if PETSc ordering is passed into symbolic factorization */
3453     B->canuseordering = PETSC_TRUE;
3454   }
3455   B->ops->destroy = MatDestroy_MUMPS;
3456   B->data         = (void *)mumps;
3457 
3458   *F               = B;
3459   mumps->id.job    = JOB_NULL;
3460   mumps->ICNTL_pre = NULL;
3461   mumps->CNTL_pre  = NULL;
3462   mumps->matstruc  = DIFFERENT_NONZERO_PATTERN;
3463   PetscFunctionReturn(PETSC_SUCCESS);
3464 }
3465 
3466 /* MatGetFactor for Seq and MPI SBAIJ matrices */
3467 static PetscErrorCode MatGetFactor_sbaij_mumps(Mat A, PETSC_UNUSED MatFactorType ftype, Mat *F)
3468 {
3469   Mat         B;
3470   Mat_MUMPS  *mumps;
3471   PetscBool   isSeqSBAIJ;
3472   PetscMPIInt size;
3473 
3474   PetscFunctionBegin;
3475 #if defined(PETSC_USE_COMPLEX)
3476   if (ftype == MAT_FACTOR_CHOLESKY && A->hermitian == PETSC_BOOL3_TRUE && A->symmetric != PETSC_BOOL3_TRUE) {
3477     PetscCall(PetscInfo(A, "Hermitian MAT_FACTOR_CHOLESKY is not supported. Use MAT_FACTOR_LU instead.\n"));
3478     *F = NULL;
3479     PetscFunctionReturn(PETSC_SUCCESS);
3480   }
3481 #endif
3482   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
3483   PetscCall(MatSetSizes(B, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
3484   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &((PetscObject)B)->type_name));
3485   PetscCall(MatSetUp(B));
3486 
3487   PetscCall(PetscNew(&mumps));
3488   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQSBAIJ, &isSeqSBAIJ));
3489   if (isSeqSBAIJ) {
3490     mumps->ConvertToTriples = MatConvertToTriples_seqsbaij_seqsbaij;
3491   } else {
3492     mumps->ConvertToTriples = MatConvertToTriples_mpisbaij_mpisbaij;
3493   }
3494 
3495   B->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_MUMPS;
3496   B->ops->view                   = MatView_MUMPS;
3497   B->ops->getinfo                = MatGetInfo_MUMPS;
3498 
3499   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorGetSolverType_C", MatFactorGetSolverType_mumps));
3500   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorSetSchurIS_C", MatFactorSetSchurIS_MUMPS));
3501   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorCreateSchurComplement_C", MatFactorCreateSchurComplement_MUMPS));
3502   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetIcntl_C", MatMumpsSetIcntl_MUMPS));
3503   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetIcntl_C", MatMumpsGetIcntl_MUMPS));
3504   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetCntl_C", MatMumpsSetCntl_MUMPS));
3505   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetCntl_C", MatMumpsGetCntl_MUMPS));
3506   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfo_C", MatMumpsGetInfo_MUMPS));
3507   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfog_C", MatMumpsGetInfog_MUMPS));
3508   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfo_C", MatMumpsGetRinfo_MUMPS));
3509   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfog_C", MatMumpsGetRinfog_MUMPS));
3510   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetNullPivots_C", MatMumpsGetNullPivots_MUMPS));
3511   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverse_C", MatMumpsGetInverse_MUMPS));
3512   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverseTranspose_C", MatMumpsGetInverseTranspose_MUMPS));
3513 
3514   B->factortype = MAT_FACTOR_CHOLESKY;
3515 #if defined(PETSC_USE_COMPLEX)
3516   mumps->sym = 2;
3517 #else
3518   if (A->spd == PETSC_BOOL3_TRUE) mumps->sym = 1;
3519   else mumps->sym = 2;
3520 #endif
3521 
3522   /* set solvertype */
3523   PetscCall(PetscFree(B->solvertype));
3524   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &B->solvertype));
3525   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
3526   if (size == 1) {
3527     /* MUMPS option -mat_mumps_icntl_7 1 is automatically set if PETSc ordering is passed into symbolic factorization */
3528     B->canuseordering = PETSC_TRUE;
3529   }
3530   PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&B->preferredordering[MAT_FACTOR_CHOLESKY]));
3531   B->ops->destroy = MatDestroy_MUMPS;
3532   B->data         = (void *)mumps;
3533 
3534   *F               = B;
3535   mumps->id.job    = JOB_NULL;
3536   mumps->ICNTL_pre = NULL;
3537   mumps->CNTL_pre  = NULL;
3538   mumps->matstruc  = DIFFERENT_NONZERO_PATTERN;
3539   PetscFunctionReturn(PETSC_SUCCESS);
3540 }
3541 
3542 static PetscErrorCode MatGetFactor_baij_mumps(Mat A, MatFactorType ftype, Mat *F)
3543 {
3544   Mat         B;
3545   Mat_MUMPS  *mumps;
3546   PetscBool   isSeqBAIJ;
3547   PetscMPIInt size;
3548 
3549   PetscFunctionBegin;
3550   /* Create the factorization matrix */
3551   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQBAIJ, &isSeqBAIJ));
3552   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
3553   PetscCall(MatSetSizes(B, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
3554   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &((PetscObject)B)->type_name));
3555   PetscCall(MatSetUp(B));
3556 
3557   PetscCall(PetscNew(&mumps));
3558   if (ftype == MAT_FACTOR_LU) {
3559     B->ops->lufactorsymbolic = MatLUFactorSymbolic_BAIJMUMPS;
3560     B->factortype            = MAT_FACTOR_LU;
3561     if (isSeqBAIJ) mumps->ConvertToTriples = MatConvertToTriples_seqbaij_seqaij;
3562     else mumps->ConvertToTriples = MatConvertToTriples_mpibaij_mpiaij;
3563     mumps->sym = 0;
3564     PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&B->preferredordering[MAT_FACTOR_LU]));
3565   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot use PETSc BAIJ matrices with MUMPS Cholesky, use SBAIJ or AIJ matrix instead");
3566 
3567   B->ops->view    = MatView_MUMPS;
3568   B->ops->getinfo = MatGetInfo_MUMPS;
3569 
3570   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorGetSolverType_C", MatFactorGetSolverType_mumps));
3571   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorSetSchurIS_C", MatFactorSetSchurIS_MUMPS));
3572   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorCreateSchurComplement_C", MatFactorCreateSchurComplement_MUMPS));
3573   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetIcntl_C", MatMumpsSetIcntl_MUMPS));
3574   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetIcntl_C", MatMumpsGetIcntl_MUMPS));
3575   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetCntl_C", MatMumpsSetCntl_MUMPS));
3576   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetCntl_C", MatMumpsGetCntl_MUMPS));
3577   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfo_C", MatMumpsGetInfo_MUMPS));
3578   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfog_C", MatMumpsGetInfog_MUMPS));
3579   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfo_C", MatMumpsGetRinfo_MUMPS));
3580   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfog_C", MatMumpsGetRinfog_MUMPS));
3581   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetNullPivots_C", MatMumpsGetNullPivots_MUMPS));
3582   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverse_C", MatMumpsGetInverse_MUMPS));
3583   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverseTranspose_C", MatMumpsGetInverseTranspose_MUMPS));
3584 
3585   /* set solvertype */
3586   PetscCall(PetscFree(B->solvertype));
3587   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &B->solvertype));
3588   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
3589   if (size == 1) {
3590     /* MUMPS option -mat_mumps_icntl_7 1 is automatically set if PETSc ordering is passed into symbolic factorization */
3591     B->canuseordering = PETSC_TRUE;
3592   }
3593   B->ops->destroy = MatDestroy_MUMPS;
3594   B->data         = (void *)mumps;
3595 
3596   *F               = B;
3597   mumps->id.job    = JOB_NULL;
3598   mumps->ICNTL_pre = NULL;
3599   mumps->CNTL_pre  = NULL;
3600   mumps->matstruc  = DIFFERENT_NONZERO_PATTERN;
3601   PetscFunctionReturn(PETSC_SUCCESS);
3602 }
3603 
3604 /* MatGetFactor for Seq and MPI SELL matrices */
3605 static PetscErrorCode MatGetFactor_sell_mumps(Mat A, MatFactorType ftype, Mat *F)
3606 {
3607   Mat         B;
3608   Mat_MUMPS  *mumps;
3609   PetscBool   isSeqSELL;
3610   PetscMPIInt size;
3611 
3612   PetscFunctionBegin;
3613   /* Create the factorization matrix */
3614   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQSELL, &isSeqSELL));
3615   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
3616   PetscCall(MatSetSizes(B, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
3617   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &((PetscObject)B)->type_name));
3618   PetscCall(MatSetUp(B));
3619 
3620   PetscCall(PetscNew(&mumps));
3621 
3622   B->ops->view    = MatView_MUMPS;
3623   B->ops->getinfo = MatGetInfo_MUMPS;
3624 
3625   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorGetSolverType_C", MatFactorGetSolverType_mumps));
3626   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorSetSchurIS_C", MatFactorSetSchurIS_MUMPS));
3627   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorCreateSchurComplement_C", MatFactorCreateSchurComplement_MUMPS));
3628   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetIcntl_C", MatMumpsSetIcntl_MUMPS));
3629   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetIcntl_C", MatMumpsGetIcntl_MUMPS));
3630   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetCntl_C", MatMumpsSetCntl_MUMPS));
3631   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetCntl_C", MatMumpsGetCntl_MUMPS));
3632   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfo_C", MatMumpsGetInfo_MUMPS));
3633   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfog_C", MatMumpsGetInfog_MUMPS));
3634   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfo_C", MatMumpsGetRinfo_MUMPS));
3635   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfog_C", MatMumpsGetRinfog_MUMPS));
3636   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetNullPivots_C", MatMumpsGetNullPivots_MUMPS));
3637 
3638   if (ftype == MAT_FACTOR_LU) {
3639     B->ops->lufactorsymbolic = MatLUFactorSymbolic_AIJMUMPS;
3640     B->factortype            = MAT_FACTOR_LU;
3641     if (isSeqSELL) mumps->ConvertToTriples = MatConvertToTriples_seqsell_seqaij;
3642     else SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "To be implemented");
3643     mumps->sym = 0;
3644     PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&B->preferredordering[MAT_FACTOR_LU]));
3645   } else SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "To be implemented");
3646 
3647   /* set solvertype */
3648   PetscCall(PetscFree(B->solvertype));
3649   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &B->solvertype));
3650   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
3651   if (size == 1) {
3652     /* MUMPS option -mat_mumps_icntl_7 1 is automatically set if PETSc ordering is passed into symbolic factorization  */
3653     B->canuseordering = PETSC_TRUE;
3654   }
3655   B->ops->destroy = MatDestroy_MUMPS;
3656   B->data         = (void *)mumps;
3657 
3658   *F               = B;
3659   mumps->id.job    = JOB_NULL;
3660   mumps->ICNTL_pre = NULL;
3661   mumps->CNTL_pre  = NULL;
3662   mumps->matstruc  = DIFFERENT_NONZERO_PATTERN;
3663   PetscFunctionReturn(PETSC_SUCCESS);
3664 }
3665 
3666 /* MatGetFactor for MATNEST matrices */
3667 static PetscErrorCode MatGetFactor_nest_mumps(Mat A, MatFactorType ftype, Mat *F)
3668 {
3669   Mat         B, **mats;
3670   Mat_MUMPS  *mumps;
3671   PetscInt    nr, nc;
3672   PetscMPIInt size;
3673   PetscBool   flg = PETSC_TRUE;
3674 
3675   PetscFunctionBegin;
3676 #if defined(PETSC_USE_COMPLEX)
3677   if (ftype == MAT_FACTOR_CHOLESKY && A->hermitian == PETSC_BOOL3_TRUE && A->symmetric != PETSC_BOOL3_TRUE) {
3678     PetscCall(PetscInfo(A, "Hermitian MAT_FACTOR_CHOLESKY is not supported. Use MAT_FACTOR_LU instead.\n"));
3679     *F = NULL;
3680     PetscFunctionReturn(PETSC_SUCCESS);
3681   }
3682 #endif
3683 
3684   /* Return if some condition is not satisfied */
3685   *F = NULL;
3686   PetscCall(MatNestGetSubMats(A, &nr, &nc, &mats));
3687   if (ftype == MAT_FACTOR_CHOLESKY) {
3688     IS       *rows, *cols;
3689     PetscInt *m, *M;
3690 
3691     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);
3692     PetscCall(PetscMalloc2(nr, &rows, nc, &cols));
3693     PetscCall(MatNestGetISs(A, rows, cols));
3694     for (PetscInt r = 0; flg && r < nr; r++) PetscCall(ISEqualUnsorted(rows[r], cols[r], &flg));
3695     if (!flg) {
3696       PetscCall(PetscFree2(rows, cols));
3697       PetscCall(PetscInfo(A, "MAT_FACTOR_CHOLESKY not supported for unequal row and column maps. Use MAT_FACTOR_LU.\n"));
3698       PetscFunctionReturn(PETSC_SUCCESS);
3699     }
3700     PetscCall(PetscMalloc2(nr, &m, nr, &M));
3701     for (PetscInt r = 0; r < nr; r++) PetscCall(ISGetMinMax(rows[r], &m[r], &M[r]));
3702     for (PetscInt r = 0; flg && r < nr; r++)
3703       for (PetscInt k = r + 1; flg && k < nr; k++)
3704         if ((m[k] <= m[r] && m[r] <= M[k]) || (m[k] <= M[r] && M[r] <= M[k])) flg = PETSC_FALSE;
3705     PetscCall(PetscFree2(m, M));
3706     PetscCall(PetscFree2(rows, cols));
3707     if (!flg) {
3708       PetscCall(PetscInfo(A, "MAT_FACTOR_CHOLESKY not supported for intersecting row maps. Use MAT_FACTOR_LU.\n"));
3709       PetscFunctionReturn(PETSC_SUCCESS);
3710     }
3711   }
3712 
3713   for (PetscInt r = 0; r < nr; r++) {
3714     for (PetscInt c = 0; c < nc; c++) {
3715       Mat       sub = mats[r][c];
3716       PetscBool isSeqAIJ, isMPIAIJ, isSeqBAIJ, isMPIBAIJ, isSeqSBAIJ, isMPISBAIJ, isTrans, isDiag, isDense;
3717 
3718       if (!sub || (ftype == MAT_FACTOR_CHOLESKY && c < r)) continue;
3719       PetscCall(PetscObjectTypeCompare((PetscObject)sub, MATTRANSPOSEVIRTUAL, &isTrans));
3720       if (isTrans) PetscCall(MatTransposeGetMat(sub, &sub));
3721       else {
3722         PetscCall(PetscObjectTypeCompare((PetscObject)sub, MATHERMITIANTRANSPOSEVIRTUAL, &isTrans));
3723         if (isTrans) PetscCall(MatHermitianTransposeGetMat(sub, &sub));
3724       }
3725       PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATSEQAIJ, &isSeqAIJ));
3726       PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATMPIAIJ, &isMPIAIJ));
3727       PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATSEQBAIJ, &isSeqBAIJ));
3728       PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATMPIBAIJ, &isMPIBAIJ));
3729       PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATSEQSBAIJ, &isSeqSBAIJ));
3730       PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATMPISBAIJ, &isMPISBAIJ));
3731       PetscCall(PetscObjectTypeCompare((PetscObject)sub, MATDIAGONAL, &isDiag));
3732       PetscCall(PetscObjectTypeCompareAny((PetscObject)sub, &isDense, MATSEQDENSE, MATMPIDENSE, NULL));
3733       if (ftype == MAT_FACTOR_CHOLESKY) {
3734         if (r == c) {
3735           if (!isSeqAIJ && !isMPIAIJ && !isSeqBAIJ && !isMPIBAIJ && !isSeqSBAIJ && !isMPISBAIJ && !isDiag && !isDense) {
3736             PetscCall(PetscInfo(sub, "MAT_FACTOR_CHOLESKY not supported for diagonal block of type %s.\n", ((PetscObject)sub)->type_name));
3737             flg = PETSC_FALSE;
3738           }
3739         } else if (!isSeqAIJ && !isMPIAIJ && !isSeqBAIJ && !isMPIBAIJ && !isDiag && !isDense) {
3740           PetscCall(PetscInfo(sub, "MAT_FACTOR_CHOLESKY not supported for off-diagonal block of type %s.\n", ((PetscObject)sub)->type_name));
3741           flg = PETSC_FALSE;
3742         }
3743       } else if (!isSeqAIJ && !isMPIAIJ && !isSeqBAIJ && !isMPIBAIJ && !isDiag && !isDense) {
3744         PetscCall(PetscInfo(sub, "MAT_FACTOR_LU not supported for block of type %s.\n", ((PetscObject)sub)->type_name));
3745         flg = PETSC_FALSE;
3746       }
3747     }
3748   }
3749   if (!flg) PetscFunctionReturn(PETSC_SUCCESS);
3750 
3751   /* Create the factorization matrix */
3752   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
3753   PetscCall(MatSetSizes(B, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
3754   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &((PetscObject)B)->type_name));
3755   PetscCall(MatSetUp(B));
3756 
3757   PetscCall(PetscNew(&mumps));
3758 
3759   B->ops->view    = MatView_MUMPS;
3760   B->ops->getinfo = MatGetInfo_MUMPS;
3761 
3762   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorGetSolverType_C", MatFactorGetSolverType_mumps));
3763   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorSetSchurIS_C", MatFactorSetSchurIS_MUMPS));
3764   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorCreateSchurComplement_C", MatFactorCreateSchurComplement_MUMPS));
3765   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetIcntl_C", MatMumpsSetIcntl_MUMPS));
3766   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetIcntl_C", MatMumpsGetIcntl_MUMPS));
3767   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetCntl_C", MatMumpsSetCntl_MUMPS));
3768   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetCntl_C", MatMumpsGetCntl_MUMPS));
3769   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfo_C", MatMumpsGetInfo_MUMPS));
3770   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfog_C", MatMumpsGetInfog_MUMPS));
3771   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfo_C", MatMumpsGetRinfo_MUMPS));
3772   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfog_C", MatMumpsGetRinfog_MUMPS));
3773   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetNullPivots_C", MatMumpsGetNullPivots_MUMPS));
3774   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverse_C", MatMumpsGetInverse_MUMPS));
3775   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverseTranspose_C", MatMumpsGetInverseTranspose_MUMPS));
3776 
3777   if (ftype == MAT_FACTOR_LU) {
3778     B->ops->lufactorsymbolic = MatLUFactorSymbolic_AIJMUMPS;
3779     B->factortype            = MAT_FACTOR_LU;
3780     mumps->sym               = 0;
3781   } else {
3782     B->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_MUMPS;
3783     B->factortype                  = MAT_FACTOR_CHOLESKY;
3784 #if defined(PETSC_USE_COMPLEX)
3785     mumps->sym = 2;
3786 #else
3787     if (A->spd == PETSC_BOOL3_TRUE) mumps->sym = 1;
3788     else mumps->sym = 2;
3789 #endif
3790   }
3791   mumps->ConvertToTriples = MatConvertToTriples_nest_xaij;
3792   PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&B->preferredordering[ftype]));
3793 
3794   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
3795   if (size == 1) {
3796     /* MUMPS option -mat_mumps_icntl_7 1 is automatically set if PETSc ordering is passed into symbolic factorization */
3797     B->canuseordering = PETSC_TRUE;
3798   }
3799 
3800   /* set solvertype */
3801   PetscCall(PetscFree(B->solvertype));
3802   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &B->solvertype));
3803   B->ops->destroy = MatDestroy_MUMPS;
3804   B->data         = (void *)mumps;
3805 
3806   *F               = B;
3807   mumps->id.job    = JOB_NULL;
3808   mumps->ICNTL_pre = NULL;
3809   mumps->CNTL_pre  = NULL;
3810   mumps->matstruc  = DIFFERENT_NONZERO_PATTERN;
3811   PetscFunctionReturn(PETSC_SUCCESS);
3812 }
3813 
3814 PETSC_INTERN PetscErrorCode MatSolverTypeRegister_MUMPS(void)
3815 {
3816   PetscFunctionBegin;
3817   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPIAIJ, MAT_FACTOR_LU, MatGetFactor_aij_mumps));
3818   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPIAIJ, MAT_FACTOR_CHOLESKY, MatGetFactor_aij_mumps));
3819   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPIBAIJ, MAT_FACTOR_LU, MatGetFactor_baij_mumps));
3820   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPIBAIJ, MAT_FACTOR_CHOLESKY, MatGetFactor_baij_mumps));
3821   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPISBAIJ, MAT_FACTOR_CHOLESKY, MatGetFactor_sbaij_mumps));
3822   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQAIJ, MAT_FACTOR_LU, MatGetFactor_aij_mumps));
3823   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQAIJ, MAT_FACTOR_CHOLESKY, MatGetFactor_aij_mumps));
3824   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQBAIJ, MAT_FACTOR_LU, MatGetFactor_baij_mumps));
3825   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQBAIJ, MAT_FACTOR_CHOLESKY, MatGetFactor_baij_mumps));
3826   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQSBAIJ, MAT_FACTOR_CHOLESKY, MatGetFactor_sbaij_mumps));
3827   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQSELL, MAT_FACTOR_LU, MatGetFactor_sell_mumps));
3828   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATDIAGONAL, MAT_FACTOR_LU, MatGetFactor_aij_mumps));
3829   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATDIAGONAL, MAT_FACTOR_CHOLESKY, MatGetFactor_aij_mumps));
3830   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQDENSE, MAT_FACTOR_LU, MatGetFactor_aij_mumps));
3831   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQDENSE, MAT_FACTOR_CHOLESKY, MatGetFactor_aij_mumps));
3832   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPIDENSE, MAT_FACTOR_LU, MatGetFactor_aij_mumps));
3833   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPIDENSE, MAT_FACTOR_CHOLESKY, MatGetFactor_aij_mumps));
3834   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATNEST, MAT_FACTOR_LU, MatGetFactor_nest_mumps));
3835   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATNEST, MAT_FACTOR_CHOLESKY, MatGetFactor_nest_mumps));
3836   PetscFunctionReturn(PETSC_SUCCESS);
3837 }
3838