xref: /petsc/src/mat/impls/aij/mpi/mumps/mumps.c (revision 53587d9363d5827a6b4fd92b4918af4444814a40)
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 // If the input Mat (sub) is either MATTRANSPOSEVIRTUAL or MATHERMITIANTRANSPOSEVIRTUAL, this function gets the parent Mat until it is not a
1058 // MATTRANSPOSEVIRTUAL or MATHERMITIANTRANSPOSEVIRTUAL itself and returns the appropriate shift, scaling, and whether the parent Mat should be conjugated
1059 // and its rows and columns permuted
1060 // TODO FIXME: this should not be in this file and should instead be refactored where the same logic applies, e.g., MatAXPY_Dense_Nest()
1061 static PetscErrorCode MatGetTranspose_TransposeVirtual(Mat *sub, PetscBool *conjugate, PetscScalar *vshift, PetscScalar *vscale, PetscBool *swap)
1062 {
1063   Mat         A;
1064   PetscScalar s[2];
1065   PetscBool   isTrans, isHTrans, compare;
1066 
1067   PetscFunctionBegin;
1068   do {
1069     PetscCall(PetscObjectTypeCompare((PetscObject)*sub, MATTRANSPOSEVIRTUAL, &isTrans));
1070     if (isTrans) {
1071       PetscCall(MatTransposeGetMat(*sub, &A));
1072       isHTrans = PETSC_FALSE;
1073     } else {
1074       PetscCall(PetscObjectTypeCompare((PetscObject)*sub, MATHERMITIANTRANSPOSEVIRTUAL, &isHTrans));
1075       if (isHTrans) PetscCall(MatHermitianTransposeGetMat(*sub, &A));
1076     }
1077     compare = (PetscBool)(isTrans || isHTrans);
1078     if (compare) {
1079       if (vshift && vscale) {
1080         PetscCall(MatShellGetScalingShifts(*sub, s, s + 1, (Vec *)MAT_SHELL_NOT_ALLOWED, (Vec *)MAT_SHELL_NOT_ALLOWED, (Vec *)MAT_SHELL_NOT_ALLOWED, (Mat *)MAT_SHELL_NOT_ALLOWED, (IS *)MAT_SHELL_NOT_ALLOWED, (IS *)MAT_SHELL_NOT_ALLOWED));
1081         if (!*conjugate) {
1082           *vshift += s[0] * *vscale;
1083           *vscale *= s[1];
1084         } else {
1085           *vshift += PetscConj(s[0]) * *vscale;
1086           *vscale *= PetscConj(s[1]);
1087         }
1088       }
1089       if (swap) *swap = (PetscBool)!*swap;
1090       if (isHTrans && conjugate) *conjugate = (PetscBool)!*conjugate;
1091       *sub = A;
1092     }
1093   } while (compare);
1094   PetscFunctionReturn(PETSC_SUCCESS);
1095 }
1096 
1097 static PetscErrorCode MatConvertToTriples_nest_xaij(Mat A, PetscInt shift, MatReuse reuse, Mat_MUMPS *mumps)
1098 {
1099   Mat     **mats;
1100   PetscInt  nr, nc;
1101   PetscBool chol = mumps->sym ? PETSC_TRUE : PETSC_FALSE;
1102 
1103   PetscFunctionBegin;
1104   PetscCall(MatNestGetSubMats(A, &nr, &nc, &mats));
1105   if (reuse == MAT_INITIAL_MATRIX) {
1106     PetscMUMPSInt *irns, *jcns;
1107     PetscScalar   *vals;
1108     PetscCount     totnnz, cumnnz, maxnnz;
1109     PetscInt      *pjcns_w;
1110     IS            *rows, *cols;
1111     PetscInt     **rows_idx, **cols_idx;
1112 
1113     cumnnz = 0;
1114     maxnnz = 0;
1115     PetscCall(PetscMalloc2(nr * nc + 1, &mumps->nest_vals_start, nr * nc, &mumps->nest_convert_to_triples));
1116     for (PetscInt r = 0; r < nr; r++) {
1117       for (PetscInt c = 0; c < nc; c++) {
1118         Mat sub = mats[r][c];
1119 
1120         mumps->nest_convert_to_triples[r * nc + c] = NULL;
1121         if (chol && c < r) continue; /* skip lower-triangular block for Cholesky */
1122         if (sub) {
1123           PetscErrorCode (*convert_to_triples)(Mat, PetscInt, MatReuse, Mat_MUMPS *) = NULL;
1124           PetscBool isSeqAIJ, isMPIAIJ, isSeqBAIJ, isMPIBAIJ, isSeqSBAIJ, isMPISBAIJ, isDiag, isDense;
1125           MatInfo   info;
1126 
1127           PetscCall(MatGetTranspose_TransposeVirtual(&sub, NULL, NULL, NULL, NULL));
1128           PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATSEQAIJ, &isSeqAIJ));
1129           PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATMPIAIJ, &isMPIAIJ));
1130           PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATSEQBAIJ, &isSeqBAIJ));
1131           PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATMPIBAIJ, &isMPIBAIJ));
1132           PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATSEQSBAIJ, &isSeqSBAIJ));
1133           PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATMPISBAIJ, &isMPISBAIJ));
1134           PetscCall(PetscObjectTypeCompare((PetscObject)sub, MATDIAGONAL, &isDiag));
1135           PetscCall(PetscObjectTypeCompareAny((PetscObject)sub, &isDense, MATSEQDENSE, MATMPIDENSE, NULL));
1136 
1137           if (chol) {
1138             if (r == c) {
1139               if (isSeqAIJ) convert_to_triples = MatConvertToTriples_seqaij_seqsbaij;
1140               else if (isMPIAIJ) convert_to_triples = MatConvertToTriples_mpiaij_mpisbaij;
1141               else if (isSeqSBAIJ) convert_to_triples = MatConvertToTriples_seqsbaij_seqsbaij;
1142               else if (isMPISBAIJ) convert_to_triples = MatConvertToTriples_mpisbaij_mpisbaij;
1143               else if (isDiag) convert_to_triples = MatConvertToTriples_diagonal_xaij;
1144               else if (isDense) convert_to_triples = MatConvertToTriples_dense_xaij;
1145             } else {
1146               if (isSeqAIJ) convert_to_triples = MatConvertToTriples_seqaij_seqaij;
1147               else if (isMPIAIJ) convert_to_triples = MatConvertToTriples_mpiaij_mpiaij;
1148               else if (isSeqBAIJ) convert_to_triples = MatConvertToTriples_seqbaij_seqaij;
1149               else if (isMPIBAIJ) convert_to_triples = MatConvertToTriples_mpibaij_mpiaij;
1150               else if (isDiag) convert_to_triples = MatConvertToTriples_diagonal_xaij;
1151               else if (isDense) convert_to_triples = MatConvertToTriples_dense_xaij;
1152             }
1153           } else {
1154             if (isSeqAIJ) convert_to_triples = MatConvertToTriples_seqaij_seqaij;
1155             else if (isMPIAIJ) convert_to_triples = MatConvertToTriples_mpiaij_mpiaij;
1156             else if (isSeqBAIJ) convert_to_triples = MatConvertToTriples_seqbaij_seqaij;
1157             else if (isMPIBAIJ) convert_to_triples = MatConvertToTriples_mpibaij_mpiaij;
1158             else if (isDiag) convert_to_triples = MatConvertToTriples_diagonal_xaij;
1159             else if (isDense) convert_to_triples = MatConvertToTriples_dense_xaij;
1160           }
1161           PetscCheck(convert_to_triples, PetscObjectComm((PetscObject)sub), PETSC_ERR_SUP, "Not for block of type %s", ((PetscObject)sub)->type_name);
1162           mumps->nest_convert_to_triples[r * nc + c] = convert_to_triples;
1163           PetscCall(MatGetInfo(sub, MAT_LOCAL, &info));
1164           cumnnz += (PetscCount)info.nz_used; /* can be overestimated for Cholesky */
1165           maxnnz = PetscMax(maxnnz, info.nz_used);
1166         }
1167       }
1168     }
1169 
1170     /* Allocate total COO */
1171     totnnz = cumnnz;
1172     PetscCall(PetscMalloc2(totnnz, &irns, totnnz, &jcns));
1173     PetscCall(PetscMalloc1(totnnz, &vals));
1174 
1175     /* Handle rows and column maps
1176        We directly map rows and use an SF for the columns */
1177     PetscCall(PetscMalloc4(nr, &rows, nc, &cols, nr, &rows_idx, nc, &cols_idx));
1178     PetscCall(MatNestGetISs(A, rows, cols));
1179     for (PetscInt r = 0; r < nr; r++) PetscCall(ISGetIndices(rows[r], (const PetscInt **)&rows_idx[r]));
1180     for (PetscInt c = 0; c < nc; c++) PetscCall(ISGetIndices(cols[c], (const PetscInt **)&cols_idx[c]));
1181     if (PetscDefined(USE_64BIT_INDICES)) PetscCall(PetscMalloc1(maxnnz, &pjcns_w));
1182     else (void)maxnnz;
1183 
1184     cumnnz = 0;
1185     for (PetscInt r = 0; r < nr; r++) {
1186       for (PetscInt c = 0; c < nc; c++) {
1187         Mat             sub    = mats[r][c];
1188         const PetscInt *ridx   = rows_idx[r];
1189         const PetscInt *cidx   = cols_idx[c];
1190         PetscScalar     vscale = 1.0, vshift = 0.0;
1191         PetscInt        rst;
1192         PetscSF         csf;
1193         PetscBool       conjugate = PETSC_FALSE, swap = PETSC_FALSE;
1194         PetscLayout     cmap;
1195         PetscInt        innz;
1196 
1197         mumps->nest_vals_start[r * nc + c] = cumnnz;
1198         if (!mumps->nest_convert_to_triples[r * nc + c]) continue;
1199 
1200         /* Extract inner blocks if needed */
1201         PetscCall(MatGetTranspose_TransposeVirtual(&sub, &conjugate, &vshift, &vscale, &swap));
1202         PetscCheck(vshift == 0.0, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Nonzero shift in parent MatShell");
1203 
1204         /* Get column layout to map off-process columns */
1205         PetscCall(MatGetLayouts(sub, NULL, &cmap));
1206 
1207         /* Get row start to map on-process rows */
1208         PetscCall(MatGetOwnershipRange(sub, &rst, NULL));
1209 
1210         /* Directly use the mumps datastructure and use C ordering for now */
1211         PetscCall((*mumps->nest_convert_to_triples[r * nc + c])(sub, 0, MAT_INITIAL_MATRIX, mumps));
1212 
1213         /* Swap the role of rows and columns indices for transposed blocks
1214            since we need values with global final ordering */
1215         if (swap) {
1216           cidx = rows_idx[r];
1217           ridx = cols_idx[c];
1218         }
1219 
1220         /* Communicate column indices
1221            This could have been done with a single SF but it would have complicated the code a lot.
1222            But since we do it only once, we pay the price of setting up an SF for each block */
1223         if (PetscDefined(USE_64BIT_INDICES)) {
1224           for (PetscInt k = 0; k < mumps->nnz; k++) pjcns_w[k] = mumps->jcn[k];
1225         } else pjcns_w = (PetscInt *)mumps->jcn; /* This cast is needed only to silence warnings for 64bit integers builds */
1226         PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &csf));
1227         PetscCall(PetscIntCast(mumps->nnz, &innz));
1228         PetscCall(PetscSFSetGraphLayout(csf, cmap, innz, NULL, PETSC_OWN_POINTER, pjcns_w));
1229         PetscCall(PetscSFBcastBegin(csf, MPIU_INT, cidx, pjcns_w, MPI_REPLACE));
1230         PetscCall(PetscSFBcastEnd(csf, MPIU_INT, cidx, pjcns_w, MPI_REPLACE));
1231         PetscCall(PetscSFDestroy(&csf));
1232 
1233         /* Import indices: use direct map for rows and mapped indices for columns */
1234         if (swap) {
1235           for (PetscInt k = 0; k < mumps->nnz; k++) {
1236             PetscCall(PetscMUMPSIntCast(ridx[mumps->irn[k] - rst] + shift, &jcns[cumnnz + k]));
1237             PetscCall(PetscMUMPSIntCast(pjcns_w[k] + shift, &irns[cumnnz + k]));
1238           }
1239         } else {
1240           for (PetscInt k = 0; k < mumps->nnz; k++) {
1241             PetscCall(PetscMUMPSIntCast(ridx[mumps->irn[k] - rst] + shift, &irns[cumnnz + k]));
1242             PetscCall(PetscMUMPSIntCast(pjcns_w[k] + shift, &jcns[cumnnz + k]));
1243           }
1244         }
1245 
1246         /* Import values to full COO */
1247         if (conjugate) { /* conjugate the entries */
1248           PetscScalar *v = vals + cumnnz;
1249           for (PetscInt k = 0; k < mumps->nnz; k++) v[k] = vscale * PetscConj(mumps->val[k]);
1250         } else if (vscale != 1.0) {
1251           PetscScalar *v = vals + cumnnz;
1252           for (PetscInt k = 0; k < mumps->nnz; k++) v[k] = vscale * mumps->val[k];
1253         } else PetscCall(PetscArraycpy(vals + cumnnz, mumps->val, mumps->nnz));
1254 
1255         /* Shift new starting point and sanity check */
1256         cumnnz += mumps->nnz;
1257         PetscCheck(cumnnz <= totnnz, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unexpected number of nonzeros %" PetscCount_FMT " != %" PetscCount_FMT, cumnnz, totnnz);
1258 
1259         /* Free scratch memory */
1260         PetscCall(PetscFree2(mumps->irn, mumps->jcn));
1261         PetscCall(PetscFree(mumps->val_alloc));
1262         mumps->val = NULL;
1263         mumps->nnz = 0;
1264       }
1265     }
1266     if (PetscDefined(USE_64BIT_INDICES)) PetscCall(PetscFree(pjcns_w));
1267     for (PetscInt r = 0; r < nr; r++) PetscCall(ISRestoreIndices(rows[r], (const PetscInt **)&rows_idx[r]));
1268     for (PetscInt c = 0; c < nc; c++) PetscCall(ISRestoreIndices(cols[c], (const PetscInt **)&cols_idx[c]));
1269     PetscCall(PetscFree4(rows, cols, rows_idx, cols_idx));
1270     if (!chol) PetscCheck(cumnnz == totnnz, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Different number of nonzeros %" PetscCount_FMT " != %" PetscCount_FMT, cumnnz, totnnz);
1271     mumps->nest_vals_start[nr * nc] = cumnnz;
1272 
1273     /* Set pointers for final MUMPS data structure */
1274     mumps->nest_vals = vals;
1275     mumps->val_alloc = NULL; /* do not use val_alloc since it may be reallocated with the OMP callpath */
1276     mumps->val       = vals;
1277     mumps->irn       = irns;
1278     mumps->jcn       = jcns;
1279     mumps->nnz       = cumnnz;
1280   } else {
1281     PetscScalar *oval = mumps->nest_vals;
1282     for (PetscInt r = 0; r < nr; r++) {
1283       for (PetscInt c = 0; c < nc; c++) {
1284         PetscBool   conjugate = PETSC_FALSE;
1285         Mat         sub       = mats[r][c];
1286         PetscScalar vscale = 1.0, vshift = 0.0;
1287         PetscInt    midx = r * nc + c;
1288 
1289         if (!mumps->nest_convert_to_triples[midx]) continue;
1290         PetscCall(MatGetTranspose_TransposeVirtual(&sub, &conjugate, &vshift, &vscale, NULL));
1291         PetscCheck(vshift == 0.0, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Nonzero shift in parent MatShell");
1292         mumps->val = oval + mumps->nest_vals_start[midx];
1293         PetscCall((*mumps->nest_convert_to_triples[midx])(sub, shift, MAT_REUSE_MATRIX, mumps));
1294         if (conjugate) {
1295           PetscCount nnz = mumps->nest_vals_start[midx + 1] - mumps->nest_vals_start[midx];
1296           for (PetscCount k = 0; k < nnz; k++) mumps->val[k] = vscale * PetscConj(mumps->val[k]);
1297         } else if (vscale != 1.0) {
1298           PetscCount nnz = mumps->nest_vals_start[midx + 1] - mumps->nest_vals_start[midx];
1299           for (PetscCount k = 0; k < nnz; k++) mumps->val[k] *= vscale;
1300         }
1301       }
1302     }
1303     mumps->val = oval;
1304   }
1305   PetscFunctionReturn(PETSC_SUCCESS);
1306 }
1307 
1308 static PetscErrorCode MatDestroy_MUMPS(Mat A)
1309 {
1310   Mat_MUMPS *mumps = (Mat_MUMPS *)A->data;
1311 
1312   PetscFunctionBegin;
1313   PetscCall(PetscFree2(mumps->id.sol_loc, mumps->id.isol_loc));
1314   PetscCall(VecScatterDestroy(&mumps->scat_rhs));
1315   PetscCall(VecScatterDestroy(&mumps->scat_sol));
1316   PetscCall(VecDestroy(&mumps->b_seq));
1317   PetscCall(VecDestroy(&mumps->x_seq));
1318   PetscCall(PetscFree(mumps->id.perm_in));
1319   PetscCall(PetscFree2(mumps->irn, mumps->jcn));
1320   PetscCall(PetscFree(mumps->val_alloc));
1321   PetscCall(PetscFree(mumps->info));
1322   PetscCall(PetscFree(mumps->ICNTL_pre));
1323   PetscCall(PetscFree(mumps->CNTL_pre));
1324   PetscCall(MatMumpsResetSchur_Private(mumps));
1325   if (mumps->id.job != JOB_NULL) { /* cannot call PetscMUMPS_c() if JOB_INIT has never been called for this instance */
1326     mumps->id.job = JOB_END;
1327     PetscMUMPS_c(mumps);
1328     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));
1329     if (mumps->mumps_comm != MPI_COMM_NULL) {
1330       if (PetscDefined(HAVE_OPENMP_SUPPORT) && mumps->use_petsc_omp_support) PetscCallMPI(MPI_Comm_free(&mumps->mumps_comm));
1331       else PetscCall(PetscCommRestoreComm(PetscObjectComm((PetscObject)A), &mumps->mumps_comm));
1332     }
1333   }
1334 #if defined(PETSC_HAVE_OPENMP_SUPPORT)
1335   if (mumps->use_petsc_omp_support) {
1336     PetscCall(PetscOmpCtrlDestroy(&mumps->omp_ctrl));
1337     PetscCall(PetscFree2(mumps->rhs_loc, mumps->rhs_recvbuf));
1338     PetscCall(PetscFree3(mumps->rhs_nrow, mumps->rhs_recvcounts, mumps->rhs_disps));
1339   }
1340 #endif
1341   PetscCall(PetscFree(mumps->ia_alloc));
1342   PetscCall(PetscFree(mumps->ja_alloc));
1343   PetscCall(PetscFree(mumps->recvcount));
1344   PetscCall(PetscFree(mumps->reqs));
1345   PetscCall(PetscFree(mumps->irhs_loc));
1346   PetscCall(PetscFree2(mumps->nest_vals_start, mumps->nest_convert_to_triples));
1347   PetscCall(PetscFree(mumps->nest_vals));
1348   PetscCall(PetscFree(A->data));
1349 
1350   /* clear composed functions */
1351   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatFactorGetSolverType_C", NULL));
1352   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatFactorSetSchurIS_C", NULL));
1353   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatFactorCreateSchurComplement_C", NULL));
1354   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsSetIcntl_C", NULL));
1355   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetIcntl_C", NULL));
1356   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsSetCntl_C", NULL));
1357   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetCntl_C", NULL));
1358   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetInfo_C", NULL));
1359   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetInfog_C", NULL));
1360   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetRinfo_C", NULL));
1361   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetRinfog_C", NULL));
1362   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetNullPivots_C", NULL));
1363   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetInverse_C", NULL));
1364   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetInverseTranspose_C", NULL));
1365   PetscFunctionReturn(PETSC_SUCCESS);
1366 }
1367 
1368 /* Set up the distributed RHS info for MUMPS. <nrhs> is the number of RHS. <array> points to start of RHS on the local processor. */
1369 static PetscErrorCode MatMumpsSetUpDistRHSInfo(Mat A, PetscInt nrhs, const PetscScalar *array)
1370 {
1371   Mat_MUMPS        *mumps   = (Mat_MUMPS *)A->data;
1372   const PetscMPIInt ompsize = mumps->omp_comm_size;
1373   PetscInt          i, m, M, rstart;
1374 
1375   PetscFunctionBegin;
1376   PetscCall(MatGetSize(A, &M, NULL));
1377   PetscCall(MatGetLocalSize(A, &m, NULL));
1378   PetscCheck(M <= PETSC_MUMPS_INT_MAX, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "PetscInt too long for PetscMUMPSInt");
1379   if (ompsize == 1) {
1380     if (!mumps->irhs_loc) {
1381       mumps->nloc_rhs = (PetscMUMPSInt)m;
1382       PetscCall(PetscMalloc1(m, &mumps->irhs_loc));
1383       PetscCall(MatGetOwnershipRange(A, &rstart, NULL));
1384       for (i = 0; i < m; i++) PetscCall(PetscMUMPSIntCast(rstart + i + 1, &mumps->irhs_loc[i])); /* use 1-based indices */
1385     }
1386     mumps->id.rhs_loc = (MumpsScalar *)array;
1387   } else {
1388 #if defined(PETSC_HAVE_OPENMP_SUPPORT)
1389     const PetscInt *ranges;
1390     PetscMPIInt     j, k, sendcount, *petsc_ranks, *omp_ranks;
1391     MPI_Group       petsc_group, omp_group;
1392     PetscScalar    *recvbuf = NULL;
1393 
1394     if (mumps->is_omp_master) {
1395       /* Lazily initialize the omp stuff for distributed rhs */
1396       if (!mumps->irhs_loc) {
1397         PetscCall(PetscMalloc2(ompsize, &omp_ranks, ompsize, &petsc_ranks));
1398         PetscCall(PetscMalloc3(ompsize, &mumps->rhs_nrow, ompsize, &mumps->rhs_recvcounts, ompsize, &mumps->rhs_disps));
1399         PetscCallMPI(MPI_Comm_group(mumps->petsc_comm, &petsc_group));
1400         PetscCallMPI(MPI_Comm_group(mumps->omp_comm, &omp_group));
1401         for (j = 0; j < ompsize; j++) omp_ranks[j] = j;
1402         PetscCallMPI(MPI_Group_translate_ranks(omp_group, ompsize, omp_ranks, petsc_group, petsc_ranks));
1403 
1404         /* Populate mumps->irhs_loc[], rhs_nrow[] */
1405         mumps->nloc_rhs = 0;
1406         PetscCall(MatGetOwnershipRanges(A, &ranges));
1407         for (j = 0; j < ompsize; j++) {
1408           mumps->rhs_nrow[j] = ranges[petsc_ranks[j] + 1] - ranges[petsc_ranks[j]];
1409           mumps->nloc_rhs += mumps->rhs_nrow[j];
1410         }
1411         PetscCall(PetscMalloc1(mumps->nloc_rhs, &mumps->irhs_loc));
1412         for (j = k = 0; j < ompsize; j++) {
1413           for (i = ranges[petsc_ranks[j]]; i < ranges[petsc_ranks[j] + 1]; i++, k++) mumps->irhs_loc[k] = i + 1; /* uses 1-based indices */
1414         }
1415 
1416         PetscCall(PetscFree2(omp_ranks, petsc_ranks));
1417         PetscCallMPI(MPI_Group_free(&petsc_group));
1418         PetscCallMPI(MPI_Group_free(&omp_group));
1419       }
1420 
1421       /* Realloc buffers when current nrhs is bigger than what we have met */
1422       if (nrhs > mumps->max_nrhs) {
1423         PetscCall(PetscFree2(mumps->rhs_loc, mumps->rhs_recvbuf));
1424         PetscCall(PetscMalloc2(mumps->nloc_rhs * nrhs, &mumps->rhs_loc, mumps->nloc_rhs * nrhs, &mumps->rhs_recvbuf));
1425         mumps->max_nrhs = nrhs;
1426       }
1427 
1428       /* Setup recvcounts[], disps[], recvbuf on omp rank 0 for the upcoming MPI_Gatherv */
1429       for (j = 0; j < ompsize; j++) PetscCall(PetscMPIIntCast(mumps->rhs_nrow[j] * nrhs, &mumps->rhs_recvcounts[j]));
1430       mumps->rhs_disps[0] = 0;
1431       for (j = 1; j < ompsize; j++) {
1432         mumps->rhs_disps[j] = mumps->rhs_disps[j - 1] + mumps->rhs_recvcounts[j - 1];
1433         PetscCheck(mumps->rhs_disps[j] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "PetscMPIInt overflow!");
1434       }
1435       recvbuf = (nrhs == 1) ? mumps->rhs_loc : mumps->rhs_recvbuf; /* Directly use rhs_loc[] as recvbuf. Single rhs is common in Ax=b */
1436     }
1437 
1438     PetscCall(PetscMPIIntCast(m * nrhs, &sendcount));
1439     PetscCallMPI(MPI_Gatherv(array, sendcount, MPIU_SCALAR, recvbuf, mumps->rhs_recvcounts, mumps->rhs_disps, MPIU_SCALAR, 0, mumps->omp_comm));
1440 
1441     if (mumps->is_omp_master) {
1442       if (nrhs > 1) { /* Copy & re-arrange data from rhs_recvbuf[] to mumps->rhs_loc[] only when there are multiple rhs */
1443         PetscScalar *dst, *dstbase = mumps->rhs_loc;
1444         for (j = 0; j < ompsize; j++) {
1445           const PetscScalar *src = mumps->rhs_recvbuf + mumps->rhs_disps[j];
1446           dst                    = dstbase;
1447           for (i = 0; i < nrhs; i++) {
1448             PetscCall(PetscArraycpy(dst, src, mumps->rhs_nrow[j]));
1449             src += mumps->rhs_nrow[j];
1450             dst += mumps->nloc_rhs;
1451           }
1452           dstbase += mumps->rhs_nrow[j];
1453         }
1454       }
1455       mumps->id.rhs_loc = (MumpsScalar *)mumps->rhs_loc;
1456     }
1457 #endif /* PETSC_HAVE_OPENMP_SUPPORT */
1458   }
1459   mumps->id.nrhs     = (PetscMUMPSInt)nrhs;
1460   mumps->id.nloc_rhs = (PetscMUMPSInt)mumps->nloc_rhs;
1461   mumps->id.lrhs_loc = mumps->nloc_rhs;
1462   mumps->id.irhs_loc = mumps->irhs_loc;
1463   PetscFunctionReturn(PETSC_SUCCESS);
1464 }
1465 
1466 static PetscErrorCode MatSolve_MUMPS(Mat A, Vec b, Vec x)
1467 {
1468   Mat_MUMPS         *mumps  = (Mat_MUMPS *)A->data;
1469   const PetscScalar *rarray = NULL;
1470   PetscScalar       *array;
1471   IS                 is_iden, is_petsc;
1472   PetscInt           i;
1473   PetscBool          second_solve = PETSC_FALSE;
1474   static PetscBool   cite1 = PETSC_FALSE, cite2 = PETSC_FALSE;
1475 
1476   PetscFunctionBegin;
1477   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 "
1478                                    "Journal on Matrix Analysis and Applications},\n  volume = {23},\n  number = {1},\n  pages = {15--41},\n  year = {2001}\n}\n",
1479                                    &cite1));
1480   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 "
1481                                    "Computing},\n  volume = {32},\n  number = {2},\n  pages = {136--156},\n  year = {2006}\n}\n",
1482                                    &cite2));
1483 
1484   PetscCall(VecFlag(x, A->factorerrortype));
1485   if (A->factorerrortype) {
1486     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)));
1487     PetscFunctionReturn(PETSC_SUCCESS);
1488   }
1489 
1490   mumps->id.nrhs = 1;
1491   if (mumps->petsc_size > 1) {
1492     if (mumps->ICNTL20 == 10) {
1493       mumps->id.ICNTL(20) = 10; /* dense distributed RHS */
1494       PetscCall(VecGetArrayRead(b, &rarray));
1495       PetscCall(MatMumpsSetUpDistRHSInfo(A, 1, rarray));
1496     } else {
1497       mumps->id.ICNTL(20) = 0; /* dense centralized RHS; Scatter b into a sequential rhs vector*/
1498       PetscCall(VecScatterBegin(mumps->scat_rhs, b, mumps->b_seq, INSERT_VALUES, SCATTER_FORWARD));
1499       PetscCall(VecScatterEnd(mumps->scat_rhs, b, mumps->b_seq, INSERT_VALUES, SCATTER_FORWARD));
1500       if (!mumps->myid) {
1501         PetscCall(VecGetArray(mumps->b_seq, &array));
1502         mumps->id.rhs = (MumpsScalar *)array;
1503       }
1504     }
1505   } else {                   /* petsc_size == 1 */
1506     mumps->id.ICNTL(20) = 0; /* dense centralized RHS */
1507     PetscCall(VecCopy(b, x));
1508     PetscCall(VecGetArray(x, &array));
1509     mumps->id.rhs = (MumpsScalar *)array;
1510   }
1511 
1512   /*
1513      handle condensation step of Schur complement (if any)
1514      We set by default ICNTL(26) == -1 when Schur indices have been provided by the user.
1515      According to MUMPS (5.0.0) manual, any value should be harmful during the factorization phase
1516      Unless the user provides a valid value for ICNTL(26), MatSolve and MatMatSolve routines solve the full system.
1517      This requires an extra call to PetscMUMPS_c and the computation of the factors for S
1518   */
1519   if (mumps->id.size_schur > 0) {
1520     PetscCheck(mumps->petsc_size <= 1, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Parallel Schur complements not yet supported from PETSc");
1521     if (mumps->id.ICNTL(26) < 0 || mumps->id.ICNTL(26) > 2) {
1522       second_solve = PETSC_TRUE;
1523       PetscCall(MatMumpsHandleSchur_Private(A, PETSC_FALSE));
1524       mumps->id.ICNTL(26) = 1; /* condensation phase */
1525     } else if (mumps->id.ICNTL(26) == 1) PetscCall(MatMumpsHandleSchur_Private(A, PETSC_FALSE));
1526   }
1527   /* solve phase */
1528   mumps->id.job = JOB_SOLVE;
1529   PetscMUMPS_c(mumps);
1530   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));
1531 
1532   /* handle expansion step of Schur complement (if any) */
1533   if (second_solve) PetscCall(MatMumpsHandleSchur_Private(A, PETSC_TRUE));
1534   else if (mumps->id.ICNTL(26) == 1) {
1535     PetscCall(MatMumpsSolveSchur_Private(A));
1536     for (i = 0; i < mumps->id.size_schur; ++i) {
1537 #if !defined(PETSC_USE_COMPLEX)
1538       PetscScalar val = mumps->id.redrhs[i];
1539 #else
1540       PetscScalar val = mumps->id.redrhs[i].r + PETSC_i * mumps->id.redrhs[i].i;
1541 #endif
1542       array[mumps->id.listvar_schur[i] - 1] = val;
1543     }
1544   }
1545 
1546   if (mumps->petsc_size > 1) { /* convert mumps distributed solution to PETSc mpi x */
1547     if (mumps->scat_sol && mumps->ICNTL9_pre != mumps->id.ICNTL(9)) {
1548       /* when id.ICNTL(9) changes, the contents of lsol_loc may change (not its size, lsol_loc), recreates scat_sol */
1549       PetscCall(VecScatterDestroy(&mumps->scat_sol));
1550     }
1551     if (!mumps->scat_sol) { /* create scatter scat_sol */
1552       PetscInt *isol2_loc = NULL;
1553       PetscCall(ISCreateStride(PETSC_COMM_SELF, mumps->id.lsol_loc, 0, 1, &is_iden)); /* from */
1554       PetscCall(PetscMalloc1(mumps->id.lsol_loc, &isol2_loc));
1555       for (i = 0; i < mumps->id.lsol_loc; i++) isol2_loc[i] = mumps->id.isol_loc[i] - 1;                        /* change Fortran style to C style */
1556       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, mumps->id.lsol_loc, isol2_loc, PETSC_OWN_POINTER, &is_petsc)); /* to */
1557       PetscCall(VecScatterCreate(mumps->x_seq, is_iden, x, is_petsc, &mumps->scat_sol));
1558       PetscCall(ISDestroy(&is_iden));
1559       PetscCall(ISDestroy(&is_petsc));
1560       mumps->ICNTL9_pre = mumps->id.ICNTL(9); /* save current value of id.ICNTL(9) */
1561     }
1562 
1563     PetscCall(VecScatterBegin(mumps->scat_sol, mumps->x_seq, x, INSERT_VALUES, SCATTER_FORWARD));
1564     PetscCall(VecScatterEnd(mumps->scat_sol, mumps->x_seq, x, INSERT_VALUES, SCATTER_FORWARD));
1565   }
1566 
1567   if (mumps->petsc_size > 1) {
1568     if (mumps->ICNTL20 == 10) {
1569       PetscCall(VecRestoreArrayRead(b, &rarray));
1570     } else if (!mumps->myid) {
1571       PetscCall(VecRestoreArray(mumps->b_seq, &array));
1572     }
1573   } else PetscCall(VecRestoreArray(x, &array));
1574 
1575   PetscCall(PetscLogFlops(2.0 * PetscMax(0, (mumps->id.INFO(28) >= 0 ? mumps->id.INFO(28) : -1000000 * mumps->id.INFO(28)) - A->cmap->n)));
1576   PetscFunctionReturn(PETSC_SUCCESS);
1577 }
1578 
1579 static PetscErrorCode MatSolveTranspose_MUMPS(Mat A, Vec b, Vec x)
1580 {
1581   Mat_MUMPS          *mumps = (Mat_MUMPS *)A->data;
1582   const PetscMUMPSInt value = mumps->id.ICNTL(9);
1583 
1584   PetscFunctionBegin;
1585   mumps->id.ICNTL(9) = 0;
1586   PetscCall(MatSolve_MUMPS(A, b, x));
1587   mumps->id.ICNTL(9) = value;
1588   PetscFunctionReturn(PETSC_SUCCESS);
1589 }
1590 
1591 static PetscErrorCode MatMatSolve_MUMPS(Mat A, Mat B, Mat X)
1592 {
1593   Mat                Bt = NULL;
1594   PetscBool          denseX, denseB, flg, flgT;
1595   Mat_MUMPS         *mumps = (Mat_MUMPS *)A->data;
1596   PetscInt           i, nrhs, M, nrhsM;
1597   PetscScalar       *array;
1598   const PetscScalar *rbray;
1599   PetscInt           lsol_loc, nlsol_loc, *idxx, iidx = 0;
1600   PetscMUMPSInt     *isol_loc, *isol_loc_save;
1601   PetscScalar       *bray, *sol_loc, *sol_loc_save;
1602   IS                 is_to, is_from;
1603   PetscInt           k, proc, j, m, myrstart;
1604   const PetscInt    *rstart;
1605   Vec                v_mpi, msol_loc;
1606   VecScatter         scat_sol;
1607   Vec                b_seq;
1608   VecScatter         scat_rhs;
1609   PetscScalar       *aa;
1610   PetscInt           spnr, *ia, *ja;
1611   Mat_MPIAIJ        *b = NULL;
1612 
1613   PetscFunctionBegin;
1614   PetscCall(PetscObjectTypeCompareAny((PetscObject)X, &denseX, MATSEQDENSE, MATMPIDENSE, NULL));
1615   PetscCheck(denseX, PetscObjectComm((PetscObject)X), PETSC_ERR_ARG_WRONG, "Matrix X must be MATDENSE matrix");
1616 
1617   PetscCall(PetscObjectTypeCompareAny((PetscObject)B, &denseB, MATSEQDENSE, MATMPIDENSE, NULL));
1618   if (denseB) {
1619     PetscCheck(B->rmap->n == X->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Matrix B and X must have same row distribution");
1620     mumps->id.ICNTL(20) = 0; /* dense RHS */
1621   } else {                   /* sparse B */
1622     PetscCheck(X != B, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_IDN, "X and B must be different matrices");
1623     PetscCall(PetscObjectTypeCompare((PetscObject)B, MATTRANSPOSEVIRTUAL, &flgT));
1624     PetscCheck(flgT, PetscObjectComm((PetscObject)B), PETSC_ERR_ARG_WRONG, "Matrix B must be MATTRANSPOSEVIRTUAL matrix");
1625     PetscCall(MatShellGetScalingShifts(B, (PetscScalar *)MAT_SHELL_NOT_ALLOWED, (PetscScalar *)MAT_SHELL_NOT_ALLOWED, (Vec *)MAT_SHELL_NOT_ALLOWED, (Vec *)MAT_SHELL_NOT_ALLOWED, (Vec *)MAT_SHELL_NOT_ALLOWED, (Mat *)MAT_SHELL_NOT_ALLOWED, (IS *)MAT_SHELL_NOT_ALLOWED, (IS *)MAT_SHELL_NOT_ALLOWED));
1626     /* input B is transpose of actual RHS matrix,
1627      because mumps requires sparse compressed COLUMN storage! See MatMatTransposeSolve_MUMPS() */
1628     PetscCall(MatTransposeGetMat(B, &Bt));
1629     mumps->id.ICNTL(20) = 1; /* sparse RHS */
1630   }
1631 
1632   PetscCall(MatGetSize(B, &M, &nrhs));
1633   PetscCall(PetscIntMultError(nrhs, M, &nrhsM));
1634   mumps->id.nrhs = (PetscMUMPSInt)nrhs;
1635   mumps->id.lrhs = (PetscMUMPSInt)M;
1636   mumps->id.rhs  = NULL;
1637 
1638   if (mumps->petsc_size == 1) {
1639     PetscScalar *aa;
1640     PetscInt     spnr, *ia, *ja;
1641     PetscBool    second_solve = PETSC_FALSE;
1642 
1643     PetscCall(MatDenseGetArray(X, &array));
1644     mumps->id.rhs = (MumpsScalar *)array;
1645 
1646     if (denseB) {
1647       /* copy B to X */
1648       PetscCall(MatDenseGetArrayRead(B, &rbray));
1649       PetscCall(PetscArraycpy(array, rbray, nrhsM));
1650       PetscCall(MatDenseRestoreArrayRead(B, &rbray));
1651     } else { /* sparse B */
1652       PetscCall(MatSeqAIJGetArray(Bt, &aa));
1653       PetscCall(MatGetRowIJ(Bt, 1, PETSC_FALSE, PETSC_FALSE, &spnr, (const PetscInt **)&ia, (const PetscInt **)&ja, &flg));
1654       PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot get IJ structure");
1655       PetscCall(PetscMUMPSIntCSRCast(mumps, spnr, ia, ja, &mumps->id.irhs_ptr, &mumps->id.irhs_sparse, &mumps->id.nz_rhs));
1656       mumps->id.rhs_sparse = (MumpsScalar *)aa;
1657     }
1658     /* handle condensation step of Schur complement (if any) */
1659     if (mumps->id.size_schur > 0) {
1660       if (mumps->id.ICNTL(26) < 0 || mumps->id.ICNTL(26) > 2) {
1661         second_solve = PETSC_TRUE;
1662         PetscCall(MatMumpsHandleSchur_Private(A, PETSC_FALSE));
1663         mumps->id.ICNTL(26) = 1; /* condensation phase */
1664       } else if (mumps->id.ICNTL(26) == 1) PetscCall(MatMumpsHandleSchur_Private(A, PETSC_FALSE));
1665     }
1666     /* solve phase */
1667     mumps->id.job = JOB_SOLVE;
1668     PetscMUMPS_c(mumps);
1669     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));
1670 
1671     /* handle expansion step of Schur complement (if any) */
1672     if (second_solve) PetscCall(MatMumpsHandleSchur_Private(A, PETSC_TRUE));
1673     else if (mumps->id.ICNTL(26) == 1) {
1674       PetscCall(MatMumpsSolveSchur_Private(A));
1675       for (j = 0; j < nrhs; ++j)
1676         for (i = 0; i < mumps->id.size_schur; ++i) {
1677 #if !defined(PETSC_USE_COMPLEX)
1678           PetscScalar val = mumps->id.redrhs[i + j * mumps->id.lredrhs];
1679 #else
1680           PetscScalar val = mumps->id.redrhs[i + j * mumps->id.lredrhs].r + PETSC_i * mumps->id.redrhs[i + j * mumps->id.lredrhs].i;
1681 #endif
1682           array[mumps->id.listvar_schur[i] - 1 + j * M] = val;
1683         }
1684     }
1685     if (!denseB) { /* sparse B */
1686       PetscCall(MatSeqAIJRestoreArray(Bt, &aa));
1687       PetscCall(MatRestoreRowIJ(Bt, 1, PETSC_FALSE, PETSC_FALSE, &spnr, (const PetscInt **)&ia, (const PetscInt **)&ja, &flg));
1688       PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot restore IJ structure");
1689     }
1690     PetscCall(MatDenseRestoreArray(X, &array));
1691     PetscFunctionReturn(PETSC_SUCCESS);
1692   }
1693 
1694   /* parallel case: MUMPS requires rhs B to be centralized on the host! */
1695   PetscCheck(!mumps->id.ICNTL(19), PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Parallel Schur complements not yet supported from PETSc");
1696 
1697   /* create msol_loc to hold mumps local solution */
1698   isol_loc_save = mumps->id.isol_loc; /* save it for MatSolve() */
1699   sol_loc_save  = (PetscScalar *)mumps->id.sol_loc;
1700 
1701   lsol_loc = mumps->id.lsol_loc;
1702   PetscCall(PetscIntMultError(nrhs, lsol_loc, &nlsol_loc)); /* length of sol_loc */
1703   PetscCall(PetscMalloc2(nlsol_loc, &sol_loc, lsol_loc, &isol_loc));
1704   mumps->id.sol_loc  = (MumpsScalar *)sol_loc;
1705   mumps->id.isol_loc = isol_loc;
1706 
1707   PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, nlsol_loc, (PetscScalar *)sol_loc, &msol_loc));
1708 
1709   if (denseB) {
1710     if (mumps->ICNTL20 == 10) {
1711       mumps->id.ICNTL(20) = 10; /* dense distributed RHS */
1712       PetscCall(MatDenseGetArrayRead(B, &rbray));
1713       PetscCall(MatMumpsSetUpDistRHSInfo(A, nrhs, rbray));
1714       PetscCall(MatDenseRestoreArrayRead(B, &rbray));
1715       PetscCall(MatGetLocalSize(B, &m, NULL));
1716       PetscCall(VecCreateMPIWithArray(PetscObjectComm((PetscObject)B), 1, nrhs * m, nrhsM, NULL, &v_mpi));
1717     } else {
1718       mumps->id.ICNTL(20) = 0; /* dense centralized RHS */
1719       /* TODO: Because of non-contiguous indices, the created vecscatter scat_rhs is not done in MPI_Gather, resulting in
1720         very inefficient communication. An optimization is to use VecScatterCreateToZero to gather B to rank 0. Then on rank
1721         0, re-arrange B into desired order, which is a local operation.
1722       */
1723 
1724       /* scatter v_mpi to b_seq because MUMPS before 5.3.0 only supports centralized rhs */
1725       /* wrap dense rhs matrix B into a vector v_mpi */
1726       PetscCall(MatGetLocalSize(B, &m, NULL));
1727       PetscCall(MatDenseGetArray(B, &bray));
1728       PetscCall(VecCreateMPIWithArray(PetscObjectComm((PetscObject)B), 1, nrhs * m, nrhsM, (const PetscScalar *)bray, &v_mpi));
1729       PetscCall(MatDenseRestoreArray(B, &bray));
1730 
1731       /* scatter v_mpi to b_seq in proc[0]. MUMPS requires rhs to be centralized on the host! */
1732       if (!mumps->myid) {
1733         PetscInt *idx;
1734         /* idx: maps from k-th index of v_mpi to (i,j)-th global entry of B */
1735         PetscCall(PetscMalloc1(nrhsM, &idx));
1736         PetscCall(MatGetOwnershipRanges(B, &rstart));
1737         for (proc = 0, k = 0; proc < mumps->petsc_size; proc++) {
1738           for (j = 0; j < nrhs; j++) {
1739             for (i = rstart[proc]; i < rstart[proc + 1]; i++) idx[k++] = j * M + i;
1740           }
1741         }
1742 
1743         PetscCall(VecCreateSeq(PETSC_COMM_SELF, nrhsM, &b_seq));
1744         PetscCall(ISCreateGeneral(PETSC_COMM_SELF, nrhsM, idx, PETSC_OWN_POINTER, &is_to));
1745         PetscCall(ISCreateStride(PETSC_COMM_SELF, nrhsM, 0, 1, &is_from));
1746       } else {
1747         PetscCall(VecCreateSeq(PETSC_COMM_SELF, 0, &b_seq));
1748         PetscCall(ISCreateStride(PETSC_COMM_SELF, 0, 0, 1, &is_to));
1749         PetscCall(ISCreateStride(PETSC_COMM_SELF, 0, 0, 1, &is_from));
1750       }
1751       PetscCall(VecScatterCreate(v_mpi, is_from, b_seq, is_to, &scat_rhs));
1752       PetscCall(VecScatterBegin(scat_rhs, v_mpi, b_seq, INSERT_VALUES, SCATTER_FORWARD));
1753       PetscCall(ISDestroy(&is_to));
1754       PetscCall(ISDestroy(&is_from));
1755       PetscCall(VecScatterEnd(scat_rhs, v_mpi, b_seq, INSERT_VALUES, SCATTER_FORWARD));
1756 
1757       if (!mumps->myid) { /* define rhs on the host */
1758         PetscCall(VecGetArray(b_seq, &bray));
1759         mumps->id.rhs = (MumpsScalar *)bray;
1760         PetscCall(VecRestoreArray(b_seq, &bray));
1761       }
1762     }
1763   } else { /* sparse B */
1764     b = (Mat_MPIAIJ *)Bt->data;
1765 
1766     /* wrap dense X into a vector v_mpi */
1767     PetscCall(MatGetLocalSize(X, &m, NULL));
1768     PetscCall(MatDenseGetArray(X, &bray));
1769     PetscCall(VecCreateMPIWithArray(PetscObjectComm((PetscObject)X), 1, nrhs * m, nrhsM, (const PetscScalar *)bray, &v_mpi));
1770     PetscCall(MatDenseRestoreArray(X, &bray));
1771 
1772     if (!mumps->myid) {
1773       PetscCall(MatSeqAIJGetArray(b->A, &aa));
1774       PetscCall(MatGetRowIJ(b->A, 1, PETSC_FALSE, PETSC_FALSE, &spnr, (const PetscInt **)&ia, (const PetscInt **)&ja, &flg));
1775       PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot get IJ structure");
1776       PetscCall(PetscMUMPSIntCSRCast(mumps, spnr, ia, ja, &mumps->id.irhs_ptr, &mumps->id.irhs_sparse, &mumps->id.nz_rhs));
1777       mumps->id.rhs_sparse = (MumpsScalar *)aa;
1778     } else {
1779       mumps->id.irhs_ptr    = NULL;
1780       mumps->id.irhs_sparse = NULL;
1781       mumps->id.nz_rhs      = 0;
1782       mumps->id.rhs_sparse  = NULL;
1783     }
1784   }
1785 
1786   /* solve phase */
1787   mumps->id.job = JOB_SOLVE;
1788   PetscMUMPS_c(mumps);
1789   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));
1790 
1791   /* scatter mumps distributed solution to PETSc vector v_mpi, which shares local arrays with solution matrix X */
1792   PetscCall(MatDenseGetArray(X, &array));
1793   PetscCall(VecPlaceArray(v_mpi, array));
1794 
1795   /* create scatter scat_sol */
1796   PetscCall(MatGetOwnershipRanges(X, &rstart));
1797   /* iidx: index for scatter mumps solution to PETSc X */
1798 
1799   PetscCall(ISCreateStride(PETSC_COMM_SELF, nlsol_loc, 0, 1, &is_from));
1800   PetscCall(PetscMalloc1(nlsol_loc, &idxx));
1801   for (i = 0; i < lsol_loc; i++) {
1802     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 */
1803 
1804     for (proc = 0; proc < mumps->petsc_size; proc++) {
1805       if (isol_loc[i] >= rstart[proc] && isol_loc[i] < rstart[proc + 1]) {
1806         myrstart = rstart[proc];
1807         k        = isol_loc[i] - myrstart;          /* local index on 1st column of PETSc vector X */
1808         iidx     = k + myrstart * nrhs;             /* maps mumps isol_loc[i] to PETSc index in X */
1809         m        = rstart[proc + 1] - rstart[proc]; /* rows of X for this proc */
1810         break;
1811       }
1812     }
1813 
1814     for (j = 0; j < nrhs; j++) idxx[i + j * lsol_loc] = iidx + j * m;
1815   }
1816   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, nlsol_loc, idxx, PETSC_COPY_VALUES, &is_to));
1817   PetscCall(VecScatterCreate(msol_loc, is_from, v_mpi, is_to, &scat_sol));
1818   PetscCall(VecScatterBegin(scat_sol, msol_loc, v_mpi, INSERT_VALUES, SCATTER_FORWARD));
1819   PetscCall(ISDestroy(&is_from));
1820   PetscCall(ISDestroy(&is_to));
1821   PetscCall(VecScatterEnd(scat_sol, msol_loc, v_mpi, INSERT_VALUES, SCATTER_FORWARD));
1822   PetscCall(MatDenseRestoreArray(X, &array));
1823 
1824   /* free spaces */
1825   mumps->id.sol_loc  = (MumpsScalar *)sol_loc_save;
1826   mumps->id.isol_loc = isol_loc_save;
1827 
1828   PetscCall(PetscFree2(sol_loc, isol_loc));
1829   PetscCall(PetscFree(idxx));
1830   PetscCall(VecDestroy(&msol_loc));
1831   PetscCall(VecDestroy(&v_mpi));
1832   if (!denseB) {
1833     if (!mumps->myid) {
1834       b = (Mat_MPIAIJ *)Bt->data;
1835       PetscCall(MatSeqAIJRestoreArray(b->A, &aa));
1836       PetscCall(MatRestoreRowIJ(b->A, 1, PETSC_FALSE, PETSC_FALSE, &spnr, (const PetscInt **)&ia, (const PetscInt **)&ja, &flg));
1837       PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot restore IJ structure");
1838     }
1839   } else {
1840     if (mumps->ICNTL20 == 0) {
1841       PetscCall(VecDestroy(&b_seq));
1842       PetscCall(VecScatterDestroy(&scat_rhs));
1843     }
1844   }
1845   PetscCall(VecScatterDestroy(&scat_sol));
1846   PetscCall(PetscLogFlops(nrhs * PetscMax(0, 2.0 * (mumps->id.INFO(28) >= 0 ? mumps->id.INFO(28) : -1000000 * mumps->id.INFO(28)) - A->cmap->n)));
1847   PetscFunctionReturn(PETSC_SUCCESS);
1848 }
1849 
1850 static PetscErrorCode MatMatSolveTranspose_MUMPS(Mat A, Mat B, Mat X)
1851 {
1852   Mat_MUMPS          *mumps = (Mat_MUMPS *)A->data;
1853   const PetscMUMPSInt value = mumps->id.ICNTL(9);
1854 
1855   PetscFunctionBegin;
1856   mumps->id.ICNTL(9) = 0;
1857   PetscCall(MatMatSolve_MUMPS(A, B, X));
1858   mumps->id.ICNTL(9) = value;
1859   PetscFunctionReturn(PETSC_SUCCESS);
1860 }
1861 
1862 static PetscErrorCode MatMatTransposeSolve_MUMPS(Mat A, Mat Bt, Mat X)
1863 {
1864   PetscBool flg;
1865   Mat       B;
1866 
1867   PetscFunctionBegin;
1868   PetscCall(PetscObjectTypeCompareAny((PetscObject)Bt, &flg, MATSEQAIJ, MATMPIAIJ, NULL));
1869   PetscCheck(flg, PetscObjectComm((PetscObject)Bt), PETSC_ERR_ARG_WRONG, "Matrix Bt must be MATAIJ matrix");
1870 
1871   /* Create B=Bt^T that uses Bt's data structure */
1872   PetscCall(MatCreateTranspose(Bt, &B));
1873 
1874   PetscCall(MatMatSolve_MUMPS(A, B, X));
1875   PetscCall(MatDestroy(&B));
1876   PetscFunctionReturn(PETSC_SUCCESS);
1877 }
1878 
1879 #if !defined(PETSC_USE_COMPLEX)
1880 /*
1881   input:
1882    F:        numeric factor
1883   output:
1884    nneg:     total number of negative pivots
1885    nzero:    total number of zero pivots
1886    npos:     (global dimension of F) - nneg - nzero
1887 */
1888 static PetscErrorCode MatGetInertia_SBAIJMUMPS(Mat F, PetscInt *nneg, PetscInt *nzero, PetscInt *npos)
1889 {
1890   Mat_MUMPS  *mumps = (Mat_MUMPS *)F->data;
1891   PetscMPIInt size;
1892 
1893   PetscFunctionBegin;
1894   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)F), &size));
1895   /* 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 */
1896   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));
1897 
1898   if (nneg) *nneg = mumps->id.INFOG(12);
1899   if (nzero || npos) {
1900     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");
1901     if (nzero) *nzero = mumps->id.INFOG(28);
1902     if (npos) *npos = F->rmap->N - (mumps->id.INFOG(12) + mumps->id.INFOG(28));
1903   }
1904   PetscFunctionReturn(PETSC_SUCCESS);
1905 }
1906 #endif
1907 
1908 static PetscErrorCode MatMumpsGatherNonzerosOnMaster(MatReuse reuse, Mat_MUMPS *mumps)
1909 {
1910   PetscMPIInt    nreqs;
1911   PetscMUMPSInt *irn, *jcn;
1912   PetscMPIInt    count;
1913   PetscCount     totnnz, remain;
1914   const PetscInt osize = mumps->omp_comm_size;
1915   PetscScalar   *val;
1916 
1917   PetscFunctionBegin;
1918   if (osize > 1) {
1919     if (reuse == MAT_INITIAL_MATRIX) {
1920       /* master first gathers counts of nonzeros to receive */
1921       if (mumps->is_omp_master) PetscCall(PetscMalloc1(osize, &mumps->recvcount));
1922       PetscCallMPI(MPI_Gather(&mumps->nnz, 1, MPIU_INT64, mumps->recvcount, 1, MPIU_INT64, 0 /*master*/, mumps->omp_comm));
1923 
1924       /* Then each computes number of send/recvs */
1925       if (mumps->is_omp_master) {
1926         /* Start from 1 since self communication is not done in MPI */
1927         nreqs = 0;
1928         for (PetscMPIInt i = 1; i < osize; i++) nreqs += (mumps->recvcount[i] + PETSC_MPI_INT_MAX - 1) / PETSC_MPI_INT_MAX;
1929       } else {
1930         nreqs = (PetscMPIInt)(((mumps->nnz + PETSC_MPI_INT_MAX - 1) / PETSC_MPI_INT_MAX));
1931       }
1932       PetscCall(PetscMalloc1(nreqs * 3, &mumps->reqs)); /* Triple the requests since we send irn, jcn and val separately */
1933 
1934       /* The following code is doing a very simple thing: omp_master rank gathers irn/jcn/val from others.
1935          MPI_Gatherv would be enough if it supports big counts > 2^31-1. Since it does not, and mumps->nnz
1936          might be a prime number > 2^31-1, we have to slice the message. Note omp_comm_size
1937          is very small, the current approach should have no extra overhead compared to MPI_Gatherv.
1938        */
1939       nreqs = 0; /* counter for actual send/recvs */
1940       if (mumps->is_omp_master) {
1941         totnnz = 0;
1942 
1943         for (PetscMPIInt i = 0; i < osize; i++) totnnz += mumps->recvcount[i]; /* totnnz = sum of nnz over omp_comm */
1944         PetscCall(PetscMalloc2(totnnz, &irn, totnnz, &jcn));
1945         PetscCall(PetscMalloc1(totnnz, &val));
1946 
1947         /* Self communication */
1948         PetscCall(PetscArraycpy(irn, mumps->irn, mumps->nnz));
1949         PetscCall(PetscArraycpy(jcn, mumps->jcn, mumps->nnz));
1950         PetscCall(PetscArraycpy(val, mumps->val, mumps->nnz));
1951 
1952         /* Replace mumps->irn/jcn etc on master with the newly allocated bigger arrays */
1953         PetscCall(PetscFree2(mumps->irn, mumps->jcn));
1954         PetscCall(PetscFree(mumps->val_alloc));
1955         mumps->nnz = totnnz;
1956         mumps->irn = irn;
1957         mumps->jcn = jcn;
1958         mumps->val = mumps->val_alloc = val;
1959 
1960         irn += mumps->recvcount[0]; /* recvcount[0] is old mumps->nnz on omp rank 0 */
1961         jcn += mumps->recvcount[0];
1962         val += mumps->recvcount[0];
1963 
1964         /* Remote communication */
1965         for (PetscMPIInt i = 1; i < osize; i++) {
1966           count  = (PetscMPIInt)PetscMin(mumps->recvcount[i], (PetscMPIInt)PETSC_MPI_INT_MAX);
1967           remain = mumps->recvcount[i] - count;
1968           while (count > 0) {
1969             PetscCallMPI(MPIU_Irecv(irn, count, MPIU_MUMPSINT, i, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
1970             PetscCallMPI(MPIU_Irecv(jcn, count, MPIU_MUMPSINT, i, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
1971             PetscCallMPI(MPIU_Irecv(val, count, MPIU_SCALAR, i, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
1972             irn += count;
1973             jcn += count;
1974             val += count;
1975             count = (PetscMPIInt)PetscMin(remain, (PetscMPIInt)PETSC_MPI_INT_MAX);
1976             remain -= count;
1977           }
1978         }
1979       } else {
1980         irn    = mumps->irn;
1981         jcn    = mumps->jcn;
1982         val    = mumps->val;
1983         count  = (PetscMPIInt)PetscMin(mumps->nnz, (PetscMPIInt)PETSC_MPI_INT_MAX);
1984         remain = mumps->nnz - count;
1985         while (count > 0) {
1986           PetscCallMPI(MPIU_Isend(irn, count, MPIU_MUMPSINT, 0, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
1987           PetscCallMPI(MPIU_Isend(jcn, count, MPIU_MUMPSINT, 0, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
1988           PetscCallMPI(MPIU_Isend(val, count, MPIU_SCALAR, 0, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
1989           irn += count;
1990           jcn += count;
1991           val += count;
1992           count = (PetscMPIInt)PetscMin(remain, (PetscMPIInt)PETSC_MPI_INT_MAX);
1993           remain -= count;
1994         }
1995       }
1996     } else {
1997       nreqs = 0;
1998       if (mumps->is_omp_master) {
1999         val = mumps->val + mumps->recvcount[0];
2000         for (PetscMPIInt i = 1; i < osize; i++) { /* Remote communication only since self data is already in place */
2001           count  = (PetscMPIInt)PetscMin(mumps->recvcount[i], (PetscMPIInt)PETSC_MPI_INT_MAX);
2002           remain = mumps->recvcount[i] - count;
2003           while (count > 0) {
2004             PetscCallMPI(MPIU_Irecv(val, count, MPIU_SCALAR, i, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
2005             val += count;
2006             count = (PetscMPIInt)PetscMin(remain, (PetscMPIInt)PETSC_MPI_INT_MAX);
2007             remain -= count;
2008           }
2009         }
2010       } else {
2011         val    = mumps->val;
2012         count  = (PetscMPIInt)PetscMin(mumps->nnz, (PetscMPIInt)PETSC_MPI_INT_MAX);
2013         remain = mumps->nnz - count;
2014         while (count > 0) {
2015           PetscCallMPI(MPIU_Isend(val, count, MPIU_SCALAR, 0, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
2016           val += count;
2017           count = (PetscMPIInt)PetscMin(remain, (PetscMPIInt)PETSC_MPI_INT_MAX);
2018           remain -= count;
2019         }
2020       }
2021     }
2022     PetscCallMPI(MPI_Waitall(nreqs, mumps->reqs, MPI_STATUSES_IGNORE));
2023     mumps->tag++; /* It is totally fine for above send/recvs to share one mpi tag */
2024   }
2025   PetscFunctionReturn(PETSC_SUCCESS);
2026 }
2027 
2028 static PetscErrorCode MatFactorNumeric_MUMPS(Mat F, Mat A, PETSC_UNUSED const MatFactorInfo *info)
2029 {
2030   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;
2031   PetscBool  isMPIAIJ;
2032 
2033   PetscFunctionBegin;
2034   if (mumps->id.INFOG(1) < 0 && !(mumps->id.INFOG(1) == -16 && mumps->id.INFOG(1) == 0)) {
2035     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)));
2036     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)));
2037     PetscFunctionReturn(PETSC_SUCCESS);
2038   }
2039 
2040   PetscCall((*mumps->ConvertToTriples)(A, 1, MAT_REUSE_MATRIX, mumps));
2041   PetscCall(MatMumpsGatherNonzerosOnMaster(MAT_REUSE_MATRIX, mumps));
2042 
2043   /* numerical factorization phase */
2044   mumps->id.job = JOB_FACTNUMERIC;
2045   if (!mumps->id.ICNTL(18)) { /* A is centralized */
2046     if (!mumps->myid) mumps->id.a = (MumpsScalar *)mumps->val;
2047   } else {
2048     mumps->id.a_loc = (MumpsScalar *)mumps->val;
2049   }
2050   PetscMUMPS_c(mumps);
2051   if (mumps->id.INFOG(1) < 0) {
2052     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));
2053     if (mumps->id.INFOG(1) == -10) {
2054       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)));
2055       F->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
2056     } else if (mumps->id.INFOG(1) == -13) {
2057       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)));
2058       F->factorerrortype = MAT_FACTOR_OUTMEMORY;
2059     } else if (mumps->id.INFOG(1) == -8 || mumps->id.INFOG(1) == -9 || (-16 < mumps->id.INFOG(1) && mumps->id.INFOG(1) < -10)) {
2060       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)));
2061       F->factorerrortype = MAT_FACTOR_OUTMEMORY;
2062     } else {
2063       PetscCall(PetscInfo(F, "MUMPS error in numerical factorization: INFOG(1)=%d, INFO(2)=%d\n", mumps->id.INFOG(1), mumps->id.INFO(2)));
2064       F->factorerrortype = MAT_FACTOR_OTHER;
2065     }
2066   }
2067   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));
2068 
2069   F->assembled = PETSC_TRUE;
2070 
2071   if (F->schur) { /* reset Schur status to unfactored */
2072 #if defined(PETSC_HAVE_CUDA)
2073     F->schur->offloadmask = PETSC_OFFLOAD_CPU;
2074 #endif
2075     if (mumps->id.ICNTL(19) == 1) { /* stored by rows */
2076       mumps->id.ICNTL(19) = 2;
2077       PetscCall(MatTranspose(F->schur, MAT_INPLACE_MATRIX, &F->schur));
2078     }
2079     PetscCall(MatFactorRestoreSchurComplement(F, NULL, MAT_FACTOR_SCHUR_UNFACTORED));
2080   }
2081 
2082   /* just to be sure that ICNTL(19) value returned by a call from MatMumpsGetIcntl is always consistent */
2083   if (!mumps->sym && mumps->id.ICNTL(19) && mumps->id.ICNTL(19) != 1) mumps->id.ICNTL(19) = 3;
2084 
2085   if (!mumps->is_omp_master) mumps->id.INFO(23) = 0;
2086   if (mumps->petsc_size > 1) {
2087     PetscInt     lsol_loc;
2088     PetscScalar *sol_loc;
2089 
2090     PetscCall(PetscObjectTypeCompare((PetscObject)A, MATMPIAIJ, &isMPIAIJ));
2091 
2092     /* distributed solution; Create x_seq=sol_loc for repeated use */
2093     if (mumps->x_seq) {
2094       PetscCall(VecScatterDestroy(&mumps->scat_sol));
2095       PetscCall(PetscFree2(mumps->id.sol_loc, mumps->id.isol_loc));
2096       PetscCall(VecDestroy(&mumps->x_seq));
2097     }
2098     lsol_loc = mumps->id.INFO(23); /* length of sol_loc */
2099     PetscCall(PetscMalloc2(lsol_loc, &sol_loc, lsol_loc, &mumps->id.isol_loc));
2100     mumps->id.lsol_loc = (PetscMUMPSInt)lsol_loc;
2101     mumps->id.sol_loc  = (MumpsScalar *)sol_loc;
2102     PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, lsol_loc, sol_loc, &mumps->x_seq));
2103   }
2104   PetscCall(PetscLogFlops((double)mumps->id.RINFO(2)));
2105   PetscFunctionReturn(PETSC_SUCCESS);
2106 }
2107 
2108 /* Sets MUMPS options from the options database */
2109 static PetscErrorCode MatSetFromOptions_MUMPS(Mat F, Mat A)
2110 {
2111   Mat_MUMPS    *mumps = (Mat_MUMPS *)F->data;
2112   PetscMUMPSInt icntl = 0, size, *listvar_schur;
2113   PetscInt      info[80], i, ninfo = 80, rbs, cbs;
2114   PetscBool     flg = PETSC_FALSE, schur = (PetscBool)(mumps->id.ICNTL(26) == -1);
2115   MumpsScalar  *arr;
2116 
2117   PetscFunctionBegin;
2118   PetscOptionsBegin(PetscObjectComm((PetscObject)F), ((PetscObject)F)->prefix, "MUMPS Options", "Mat");
2119   if (mumps->id.job == JOB_NULL) { /* MatSetFromOptions_MUMPS() has never been called before */
2120     PetscInt nthreads   = 0;
2121     PetscInt nCNTL_pre  = mumps->CNTL_pre ? mumps->CNTL_pre[0] : 0;
2122     PetscInt nICNTL_pre = mumps->ICNTL_pre ? mumps->ICNTL_pre[0] : 0;
2123 
2124     mumps->petsc_comm = PetscObjectComm((PetscObject)A);
2125     PetscCallMPI(MPI_Comm_size(mumps->petsc_comm, &mumps->petsc_size));
2126     PetscCallMPI(MPI_Comm_rank(mumps->petsc_comm, &mumps->myid)); /* "if (!myid)" still works even if mumps_comm is different */
2127 
2128     PetscCall(PetscOptionsName("-mat_mumps_use_omp_threads", "Convert MPI processes into OpenMP threads", "None", &mumps->use_petsc_omp_support));
2129     if (mumps->use_petsc_omp_support) nthreads = -1; /* -1 will let PetscOmpCtrlCreate() guess a proper value when user did not supply one */
2130     /* do not use PetscOptionsInt() so that the option -mat_mumps_use_omp_threads is not displayed twice in the help */
2131     PetscCall(PetscOptionsGetInt(NULL, ((PetscObject)F)->prefix, "-mat_mumps_use_omp_threads", &nthreads, NULL));
2132     if (mumps->use_petsc_omp_support) {
2133       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 : "");
2134 #if defined(PETSC_HAVE_OPENMP_SUPPORT)
2135       PetscCall(PetscOmpCtrlCreate(mumps->petsc_comm, nthreads, &mumps->omp_ctrl));
2136       PetscCall(PetscOmpCtrlGetOmpComms(mumps->omp_ctrl, &mumps->omp_comm, &mumps->mumps_comm, &mumps->is_omp_master));
2137 #else
2138       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",
2139               ((PetscObject)F)->prefix ? ((PetscObject)F)->prefix : "");
2140 #endif
2141     } else {
2142       mumps->omp_comm      = PETSC_COMM_SELF;
2143       mumps->mumps_comm    = mumps->petsc_comm;
2144       mumps->is_omp_master = PETSC_TRUE;
2145     }
2146     PetscCallMPI(MPI_Comm_size(mumps->omp_comm, &mumps->omp_comm_size));
2147     mumps->reqs = NULL;
2148     mumps->tag  = 0;
2149 
2150     if (mumps->mumps_comm != MPI_COMM_NULL) {
2151       if (PetscDefined(HAVE_OPENMP_SUPPORT) && mumps->use_petsc_omp_support) {
2152         /* It looks like MUMPS does not dup the input comm. Dup a new comm for MUMPS to avoid any tag mismatches. */
2153         MPI_Comm comm;
2154         PetscCallMPI(MPI_Comm_dup(mumps->mumps_comm, &comm));
2155         mumps->mumps_comm = comm;
2156       } else PetscCall(PetscCommGetComm(mumps->petsc_comm, &mumps->mumps_comm));
2157     }
2158 
2159     mumps->id.comm_fortran = MPI_Comm_c2f(mumps->mumps_comm);
2160     mumps->id.job          = JOB_INIT;
2161     mumps->id.par          = 1; /* host participates factorizaton and solve */
2162     mumps->id.sym          = mumps->sym;
2163 
2164     size          = mumps->id.size_schur;
2165     arr           = mumps->id.schur;
2166     listvar_schur = mumps->id.listvar_schur;
2167     PetscMUMPS_c(mumps);
2168     PetscCheck(mumps->id.INFOG(1) >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "MUMPS error: INFOG(1)=%d " MUMPS_MANUALS, mumps->id.INFOG(1));
2169 
2170     /* set PETSc-MUMPS default options - override MUMPS default */
2171     mumps->id.ICNTL(3) = 0;
2172     mumps->id.ICNTL(4) = 0;
2173     if (mumps->petsc_size == 1) {
2174       mumps->id.ICNTL(18) = 0; /* centralized assembled matrix input */
2175       mumps->id.ICNTL(7)  = 7; /* automatic choice of ordering done by the package */
2176     } else {
2177       mumps->id.ICNTL(18) = 3; /* distributed assembled matrix input */
2178       mumps->id.ICNTL(21) = 1; /* distributed solution */
2179     }
2180 
2181     /* restore cached ICNTL and CNTL values */
2182     for (icntl = 0; icntl < nICNTL_pre; ++icntl) mumps->id.ICNTL(mumps->ICNTL_pre[1 + 2 * icntl]) = mumps->ICNTL_pre[2 + 2 * icntl];
2183     for (icntl = 0; icntl < nCNTL_pre; ++icntl) mumps->id.CNTL((PetscInt)mumps->CNTL_pre[1 + 2 * icntl]) = mumps->CNTL_pre[2 + 2 * icntl];
2184     PetscCall(PetscFree(mumps->ICNTL_pre));
2185     PetscCall(PetscFree(mumps->CNTL_pre));
2186 
2187     if (schur) {
2188       mumps->id.size_schur    = size;
2189       mumps->id.schur_lld     = size;
2190       mumps->id.schur         = arr;
2191       mumps->id.listvar_schur = listvar_schur;
2192       if (mumps->petsc_size > 1) {
2193         PetscBool gs; /* gs is false if any rank other than root has non-empty IS */
2194 
2195         mumps->id.ICNTL(19) = 1;                                                                            /* MUMPS returns Schur centralized on the host */
2196         gs                  = mumps->myid ? (mumps->id.size_schur ? PETSC_FALSE : PETSC_TRUE) : PETSC_TRUE; /* always true on root; false on others if their size != 0 */
2197         PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &gs, 1, MPIU_BOOL, MPI_LAND, mumps->petsc_comm));
2198         PetscCheck(gs, PETSC_COMM_SELF, PETSC_ERR_SUP, "MUMPS distributed parallel Schur complements not yet supported from PETSc");
2199       } else {
2200         if (F->factortype == MAT_FACTOR_LU) {
2201           mumps->id.ICNTL(19) = 3; /* MUMPS returns full matrix */
2202         } else {
2203           mumps->id.ICNTL(19) = 2; /* MUMPS returns lower triangular part */
2204         }
2205       }
2206       mumps->id.ICNTL(26) = -1;
2207     }
2208 
2209     /* copy MUMPS default control values from master to slaves. Although slaves do not call MUMPS, they may access these values in code.
2210        For example, ICNTL(9) is initialized to 1 by MUMPS and slaves check ICNTL(9) in MatSolve_MUMPS.
2211      */
2212     PetscCallMPI(MPI_Bcast(mumps->id.icntl, 40, MPI_INT, 0, mumps->omp_comm));
2213     PetscCallMPI(MPI_Bcast(mumps->id.cntl, 15, MPIU_REAL, 0, mumps->omp_comm));
2214 
2215     mumps->scat_rhs = NULL;
2216     mumps->scat_sol = NULL;
2217   }
2218   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_1", "ICNTL(1): output stream for error messages", "None", mumps->id.ICNTL(1), &icntl, &flg));
2219   if (flg) mumps->id.ICNTL(1) = icntl;
2220   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_2", "ICNTL(2): output stream for diagnostic printing, statistics, and warning", "None", mumps->id.ICNTL(2), &icntl, &flg));
2221   if (flg) mumps->id.ICNTL(2) = icntl;
2222   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_3", "ICNTL(3): output stream for global information, collected on the host", "None", mumps->id.ICNTL(3), &icntl, &flg));
2223   if (flg) mumps->id.ICNTL(3) = icntl;
2224 
2225   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_4", "ICNTL(4): level of printing (0 to 4)", "None", mumps->id.ICNTL(4), &icntl, &flg));
2226   if (flg) mumps->id.ICNTL(4) = icntl;
2227   if (mumps->id.ICNTL(4) || PetscLogPrintInfo) mumps->id.ICNTL(3) = 6; /* resume MUMPS default id.ICNTL(3) = 6 */
2228 
2229   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));
2230   if (flg) mumps->id.ICNTL(6) = icntl;
2231 
2232   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));
2233   if (flg) {
2234     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");
2235     mumps->id.ICNTL(7) = icntl;
2236   }
2237 
2238   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));
2239   /* 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() */
2240   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_10", "ICNTL(10): max num of refinements", "None", mumps->id.ICNTL(10), &mumps->id.ICNTL(10), NULL));
2241   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));
2242   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));
2243   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));
2244   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));
2245   PetscCall(MatGetBlockSizes(A, &rbs, &cbs));
2246   if (rbs == cbs && rbs > 1) mumps->id.ICNTL(15) = (PetscMUMPSInt)-rbs;
2247   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));
2248   if (flg) {
2249     PetscCheck(mumps->id.ICNTL(15) <= 0, PETSC_COMM_SELF, PETSC_ERR_SUP, "Positive -mat_mumps_icntl_15 not handled");
2250     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");
2251   }
2252   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_19", "ICNTL(19): computes the Schur complement", "None", mumps->id.ICNTL(19), &mumps->id.ICNTL(19), NULL));
2253   if (mumps->id.ICNTL(19) <= 0 || mumps->id.ICNTL(19) > 3) { /* reset any schur data (if any) */
2254     PetscCall(MatDestroy(&F->schur));
2255     PetscCall(MatMumpsResetSchur_Private(mumps));
2256   }
2257 
2258   /* Two MPICH Fortran MPI_IN_PLACE binding bugs prevented the use of 'mpich + mumps'. One happened with "mpi4py + mpich + mumps",
2259      and was reported by Firedrake. See https://bitbucket.org/mpi4py/mpi4py/issues/162/mpi4py-initialization-breaks-fortran
2260      and a petsc-maint mailing list thread with subject 'MUMPS segfaults in parallel because of ...'
2261      This bug was fixed by https://github.com/pmodels/mpich/pull/4149. But the fix brought a new bug,
2262      see https://github.com/pmodels/mpich/issues/5589. This bug was fixed by https://github.com/pmodels/mpich/pull/5590.
2263      In short, we could not use distributed RHS until with MPICH v4.0b1 or we enabled a workaround in mumps-5.6.2+
2264    */
2265   mumps->ICNTL20 = 10; /* Distributed dense RHS, by default */
2266 #if PETSC_PKG_MUMPS_VERSION_LT(5, 3, 0) || (PetscDefined(HAVE_MPICH) && MPICH_NUMVERSION < 40000101) || PetscDefined(HAVE_MSMPI)
2267   mumps->ICNTL20 = 0; /* Centralized dense RHS, if need be */
2268 #endif
2269   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));
2270   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);
2271 #if PETSC_PKG_MUMPS_VERSION_LT(5, 3, 0)
2272   PetscCheck(!flg || mumps->ICNTL20 != 10, PETSC_COMM_SELF, PETSC_ERR_SUP, "ICNTL(20)=10 is not supported before MUMPS-5.3.0");
2273 #endif
2274   /* 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 */
2275 
2276   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));
2277   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));
2278   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));
2279   if (mumps->id.ICNTL(24)) { mumps->id.ICNTL(13) = 1; /* turn-off ScaLAPACK to help with the correct detection of null pivots */ }
2280 
2281   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));
2282   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));
2283   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));
2284   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));
2285   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_29", "ICNTL(29): parallel ordering 1 = ptscotch, 2 = parmetis", "None", mumps->id.ICNTL(29), &mumps->id.ICNTL(29), NULL));
2286   /* 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 */
2287   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));
2288   /* 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 */
2289   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_33", "ICNTL(33): compute determinant", "None", mumps->id.ICNTL(33), &mumps->id.ICNTL(33), NULL));
2290   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));
2291   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_36", "ICNTL(36): choice of BLR factorization variant", "None", mumps->id.ICNTL(36), &mumps->id.ICNTL(36), NULL));
2292   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_37", "ICNTL(37): compression of the contribution blocks (CB)", "None", mumps->id.ICNTL(37), &mumps->id.ICNTL(37), NULL));
2293   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));
2294   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_48", "ICNTL(48): multithreading with tree parallelism", "None", mumps->id.ICNTL(48), &mumps->id.ICNTL(48), NULL));
2295   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_58", "ICNTL(58): defines options for symbolic factorization", "None", mumps->id.ICNTL(58), &mumps->id.ICNTL(58), NULL));
2296 
2297   PetscCall(PetscOptionsReal("-mat_mumps_cntl_1", "CNTL(1): relative pivoting threshold", "None", mumps->id.CNTL(1), &mumps->id.CNTL(1), NULL));
2298   PetscCall(PetscOptionsReal("-mat_mumps_cntl_2", "CNTL(2): stopping criterion of refinement", "None", mumps->id.CNTL(2), &mumps->id.CNTL(2), NULL));
2299   PetscCall(PetscOptionsReal("-mat_mumps_cntl_3", "CNTL(3): absolute pivoting threshold", "None", mumps->id.CNTL(3), &mumps->id.CNTL(3), NULL));
2300   PetscCall(PetscOptionsReal("-mat_mumps_cntl_4", "CNTL(4): value for static pivoting", "None", mumps->id.CNTL(4), &mumps->id.CNTL(4), NULL));
2301   PetscCall(PetscOptionsReal("-mat_mumps_cntl_5", "CNTL(5): fixation for null pivots", "None", mumps->id.CNTL(5), &mumps->id.CNTL(5), NULL));
2302   PetscCall(PetscOptionsReal("-mat_mumps_cntl_7", "CNTL(7): dropping parameter used during BLR", "None", mumps->id.CNTL(7), &mumps->id.CNTL(7), NULL));
2303 
2304   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));
2305 
2306   PetscCall(PetscOptionsIntArray("-mat_mumps_view_info", "request INFO local to each processor", "", info, &ninfo, NULL));
2307   if (ninfo) {
2308     PetscCheck(ninfo <= 80, PETSC_COMM_SELF, PETSC_ERR_USER, "number of INFO %" PetscInt_FMT " must <= 80", ninfo);
2309     PetscCall(PetscMalloc1(ninfo, &mumps->info));
2310     mumps->ninfo = ninfo;
2311     for (i = 0; i < ninfo; i++) {
2312       PetscCheck(info[i] >= 0 && info[i] <= 80, PETSC_COMM_SELF, PETSC_ERR_USER, "index of INFO %" PetscInt_FMT " must between 1 and 80", ninfo);
2313       mumps->info[i] = info[i];
2314     }
2315   }
2316   PetscOptionsEnd();
2317   PetscFunctionReturn(PETSC_SUCCESS);
2318 }
2319 
2320 static PetscErrorCode MatFactorSymbolic_MUMPS_ReportIfError(Mat F, Mat A, PETSC_UNUSED const MatFactorInfo *info, Mat_MUMPS *mumps)
2321 {
2322   PetscFunctionBegin;
2323   if (mumps->id.INFOG(1) < 0) {
2324     PetscCheck(!A->erroriffailure, PETSC_COMM_SELF, PETSC_ERR_LIB, "MUMPS error in analysis: INFOG(1)=%d " MUMPS_MANUALS, mumps->id.INFOG(1));
2325     if (mumps->id.INFOG(1) == -6) {
2326       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)));
2327       F->factorerrortype = MAT_FACTOR_STRUCT_ZEROPIVOT;
2328     } else if (mumps->id.INFOG(1) == -5 || mumps->id.INFOG(1) == -7) {
2329       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)));
2330       F->factorerrortype = MAT_FACTOR_OUTMEMORY;
2331     } else if (mumps->id.INFOG(1) == -16 && mumps->id.INFOG(1) == 0) {
2332       PetscCall(PetscInfo(F, "MUMPS error in analysis: empty matrix\n"));
2333     } else {
2334       PetscCall(PetscInfo(F, "MUMPS error in analysis: INFOG(1)=%d, INFO(2)=%d " MUMPS_MANUALS "\n", mumps->id.INFOG(1), mumps->id.INFO(2)));
2335       F->factorerrortype = MAT_FACTOR_OTHER;
2336     }
2337   }
2338   if (!mumps->id.n) F->factorerrortype = MAT_FACTOR_NOERROR;
2339   PetscFunctionReturn(PETSC_SUCCESS);
2340 }
2341 
2342 static PetscErrorCode MatLUFactorSymbolic_AIJMUMPS(Mat F, Mat A, IS r, PETSC_UNUSED IS c, const MatFactorInfo *info)
2343 {
2344   Mat_MUMPS     *mumps = (Mat_MUMPS *)F->data;
2345   Vec            b;
2346   const PetscInt M = A->rmap->N;
2347 
2348   PetscFunctionBegin;
2349   if (mumps->matstruc == SAME_NONZERO_PATTERN) {
2350     /* F is assembled by a previous call of MatLUFactorSymbolic_AIJMUMPS() */
2351     PetscFunctionReturn(PETSC_SUCCESS);
2352   }
2353 
2354   /* Set MUMPS options from the options database */
2355   PetscCall(MatSetFromOptions_MUMPS(F, A));
2356 
2357   PetscCall((*mumps->ConvertToTriples)(A, 1, MAT_INITIAL_MATRIX, mumps));
2358   PetscCall(MatMumpsGatherNonzerosOnMaster(MAT_INITIAL_MATRIX, mumps));
2359 
2360   /* analysis phase */
2361   mumps->id.job = JOB_FACTSYMBOLIC;
2362   PetscCall(PetscMUMPSIntCast(M, &mumps->id.n));
2363   switch (mumps->id.ICNTL(18)) {
2364   case 0: /* centralized assembled matrix input */
2365     if (!mumps->myid) {
2366       mumps->id.nnz = mumps->nnz;
2367       mumps->id.irn = mumps->irn;
2368       mumps->id.jcn = mumps->jcn;
2369       if (mumps->id.ICNTL(6) > 1) mumps->id.a = (MumpsScalar *)mumps->val;
2370       if (r && mumps->id.ICNTL(7) == 7) {
2371         mumps->id.ICNTL(7) = 1;
2372         if (!mumps->myid) {
2373           const PetscInt *idx;
2374           PetscInt        i;
2375 
2376           PetscCall(PetscMalloc1(M, &mumps->id.perm_in));
2377           PetscCall(ISGetIndices(r, &idx));
2378           for (i = 0; i < M; i++) PetscCall(PetscMUMPSIntCast(idx[i] + 1, &mumps->id.perm_in[i])); /* perm_in[]: start from 1, not 0! */
2379           PetscCall(ISRestoreIndices(r, &idx));
2380         }
2381       }
2382     }
2383     break;
2384   case 3: /* distributed assembled matrix input (size>1) */
2385     mumps->id.nnz_loc = mumps->nnz;
2386     mumps->id.irn_loc = mumps->irn;
2387     mumps->id.jcn_loc = mumps->jcn;
2388     if (mumps->id.ICNTL(6) > 1) mumps->id.a_loc = (MumpsScalar *)mumps->val;
2389     if (mumps->ICNTL20 == 0) { /* Centralized rhs. Create scatter scat_rhs for repeated use in MatSolve() */
2390       PetscCall(MatCreateVecs(A, NULL, &b));
2391       PetscCall(VecScatterCreateToZero(b, &mumps->scat_rhs, &mumps->b_seq));
2392       PetscCall(VecDestroy(&b));
2393     }
2394     break;
2395   }
2396   PetscMUMPS_c(mumps);
2397   PetscCall(MatFactorSymbolic_MUMPS_ReportIfError(F, A, info, mumps));
2398 
2399   F->ops->lufactornumeric   = MatFactorNumeric_MUMPS;
2400   F->ops->solve             = MatSolve_MUMPS;
2401   F->ops->solvetranspose    = MatSolveTranspose_MUMPS;
2402   F->ops->matsolve          = MatMatSolve_MUMPS;
2403   F->ops->mattransposesolve = MatMatTransposeSolve_MUMPS;
2404   F->ops->matsolvetranspose = MatMatSolveTranspose_MUMPS;
2405 
2406   mumps->matstruc = SAME_NONZERO_PATTERN;
2407   PetscFunctionReturn(PETSC_SUCCESS);
2408 }
2409 
2410 /* Note the PETSc r and c permutations are ignored */
2411 static PetscErrorCode MatLUFactorSymbolic_BAIJMUMPS(Mat F, Mat A, PETSC_UNUSED IS r, PETSC_UNUSED IS c, const MatFactorInfo *info)
2412 {
2413   Mat_MUMPS     *mumps = (Mat_MUMPS *)F->data;
2414   Vec            b;
2415   const PetscInt M = A->rmap->N;
2416 
2417   PetscFunctionBegin;
2418   if (mumps->matstruc == SAME_NONZERO_PATTERN) {
2419     /* F is assembled by a previous call of MatLUFactorSymbolic_BAIJMUMPS() */
2420     PetscFunctionReturn(PETSC_SUCCESS);
2421   }
2422 
2423   /* Set MUMPS options from the options database */
2424   PetscCall(MatSetFromOptions_MUMPS(F, A));
2425 
2426   PetscCall((*mumps->ConvertToTriples)(A, 1, MAT_INITIAL_MATRIX, mumps));
2427   PetscCall(MatMumpsGatherNonzerosOnMaster(MAT_INITIAL_MATRIX, mumps));
2428 
2429   /* analysis phase */
2430   mumps->id.job = JOB_FACTSYMBOLIC;
2431   PetscCall(PetscMUMPSIntCast(M, &mumps->id.n));
2432   switch (mumps->id.ICNTL(18)) {
2433   case 0: /* centralized assembled matrix input */
2434     if (!mumps->myid) {
2435       mumps->id.nnz = mumps->nnz;
2436       mumps->id.irn = mumps->irn;
2437       mumps->id.jcn = mumps->jcn;
2438       if (mumps->id.ICNTL(6) > 1) mumps->id.a = (MumpsScalar *)mumps->val;
2439     }
2440     break;
2441   case 3: /* distributed assembled matrix input (size>1) */
2442     mumps->id.nnz_loc = mumps->nnz;
2443     mumps->id.irn_loc = mumps->irn;
2444     mumps->id.jcn_loc = mumps->jcn;
2445     if (mumps->id.ICNTL(6) > 1) mumps->id.a_loc = (MumpsScalar *)mumps->val;
2446     if (mumps->ICNTL20 == 0) { /* Centralized rhs. Create scatter scat_rhs for repeated use in MatSolve() */
2447       PetscCall(MatCreateVecs(A, NULL, &b));
2448       PetscCall(VecScatterCreateToZero(b, &mumps->scat_rhs, &mumps->b_seq));
2449       PetscCall(VecDestroy(&b));
2450     }
2451     break;
2452   }
2453   PetscMUMPS_c(mumps);
2454   PetscCall(MatFactorSymbolic_MUMPS_ReportIfError(F, A, info, mumps));
2455 
2456   F->ops->lufactornumeric   = MatFactorNumeric_MUMPS;
2457   F->ops->solve             = MatSolve_MUMPS;
2458   F->ops->solvetranspose    = MatSolveTranspose_MUMPS;
2459   F->ops->matsolvetranspose = MatMatSolveTranspose_MUMPS;
2460 
2461   mumps->matstruc = SAME_NONZERO_PATTERN;
2462   PetscFunctionReturn(PETSC_SUCCESS);
2463 }
2464 
2465 /* Note the PETSc r permutation and factor info are ignored */
2466 static PetscErrorCode MatCholeskyFactorSymbolic_MUMPS(Mat F, Mat A, PETSC_UNUSED IS r, const MatFactorInfo *info)
2467 {
2468   Mat_MUMPS     *mumps = (Mat_MUMPS *)F->data;
2469   Vec            b;
2470   const PetscInt M = A->rmap->N;
2471 
2472   PetscFunctionBegin;
2473   if (mumps->matstruc == SAME_NONZERO_PATTERN) {
2474     /* F is assembled by a previous call of MatCholeskyFactorSymbolic_MUMPS() */
2475     PetscFunctionReturn(PETSC_SUCCESS);
2476   }
2477 
2478   /* Set MUMPS options from the options database */
2479   PetscCall(MatSetFromOptions_MUMPS(F, A));
2480 
2481   PetscCall((*mumps->ConvertToTriples)(A, 1, MAT_INITIAL_MATRIX, mumps));
2482   PetscCall(MatMumpsGatherNonzerosOnMaster(MAT_INITIAL_MATRIX, mumps));
2483 
2484   /* analysis phase */
2485   mumps->id.job = JOB_FACTSYMBOLIC;
2486   PetscCall(PetscMUMPSIntCast(M, &mumps->id.n));
2487   switch (mumps->id.ICNTL(18)) {
2488   case 0: /* centralized assembled matrix input */
2489     if (!mumps->myid) {
2490       mumps->id.nnz = mumps->nnz;
2491       mumps->id.irn = mumps->irn;
2492       mumps->id.jcn = mumps->jcn;
2493       if (mumps->id.ICNTL(6) > 1) mumps->id.a = (MumpsScalar *)mumps->val;
2494     }
2495     break;
2496   case 3: /* distributed assembled matrix input (size>1) */
2497     mumps->id.nnz_loc = mumps->nnz;
2498     mumps->id.irn_loc = mumps->irn;
2499     mumps->id.jcn_loc = mumps->jcn;
2500     if (mumps->id.ICNTL(6) > 1) mumps->id.a_loc = (MumpsScalar *)mumps->val;
2501     if (mumps->ICNTL20 == 0) { /* Centralized rhs. Create scatter scat_rhs for repeated use in MatSolve() */
2502       PetscCall(MatCreateVecs(A, NULL, &b));
2503       PetscCall(VecScatterCreateToZero(b, &mumps->scat_rhs, &mumps->b_seq));
2504       PetscCall(VecDestroy(&b));
2505     }
2506     break;
2507   }
2508   PetscMUMPS_c(mumps);
2509   PetscCall(MatFactorSymbolic_MUMPS_ReportIfError(F, A, info, mumps));
2510 
2511   F->ops->choleskyfactornumeric = MatFactorNumeric_MUMPS;
2512   F->ops->solve                 = MatSolve_MUMPS;
2513   F->ops->solvetranspose        = MatSolve_MUMPS;
2514   F->ops->matsolve              = MatMatSolve_MUMPS;
2515   F->ops->mattransposesolve     = MatMatTransposeSolve_MUMPS;
2516   F->ops->matsolvetranspose     = MatMatSolveTranspose_MUMPS;
2517 #if defined(PETSC_USE_COMPLEX)
2518   F->ops->getinertia = NULL;
2519 #else
2520   F->ops->getinertia = MatGetInertia_SBAIJMUMPS;
2521 #endif
2522 
2523   mumps->matstruc = SAME_NONZERO_PATTERN;
2524   PetscFunctionReturn(PETSC_SUCCESS);
2525 }
2526 
2527 static PetscErrorCode MatView_MUMPS(Mat A, PetscViewer viewer)
2528 {
2529   PetscBool         iascii;
2530   PetscViewerFormat format;
2531   Mat_MUMPS        *mumps = (Mat_MUMPS *)A->data;
2532 
2533   PetscFunctionBegin;
2534   /* check if matrix is mumps type */
2535   if (A->ops->solve != MatSolve_MUMPS) PetscFunctionReturn(PETSC_SUCCESS);
2536 
2537   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
2538   if (iascii) {
2539     PetscCall(PetscViewerGetFormat(viewer, &format));
2540     if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
2541       PetscCall(PetscViewerASCIIPrintf(viewer, "MUMPS run parameters:\n"));
2542       if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
2543         PetscCall(PetscViewerASCIIPrintf(viewer, "  SYM (matrix type):                   %d\n", mumps->id.sym));
2544         PetscCall(PetscViewerASCIIPrintf(viewer, "  PAR (host participation):            %d\n", mumps->id.par));
2545         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(1) (output for error):         %d\n", mumps->id.ICNTL(1)));
2546         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(2) (output of diagnostic msg): %d\n", mumps->id.ICNTL(2)));
2547         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(3) (output for global info):   %d\n", mumps->id.ICNTL(3)));
2548         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(4) (level of printing):        %d\n", mumps->id.ICNTL(4)));
2549         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(5) (input mat struct):         %d\n", mumps->id.ICNTL(5)));
2550         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(6) (matrix prescaling):        %d\n", mumps->id.ICNTL(6)));
2551         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(7) (sequential matrix ordering):%d\n", mumps->id.ICNTL(7)));
2552         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(8) (scaling strategy):         %d\n", mumps->id.ICNTL(8)));
2553         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(10) (max num of refinements):  %d\n", mumps->id.ICNTL(10)));
2554         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(11) (error analysis):          %d\n", mumps->id.ICNTL(11)));
2555         if (mumps->id.ICNTL(11) > 0) {
2556           PetscCall(PetscViewerASCIIPrintf(viewer, "    RINFOG(4) (inf norm of input mat):        %g\n", (double)mumps->id.RINFOG(4)));
2557           PetscCall(PetscViewerASCIIPrintf(viewer, "    RINFOG(5) (inf norm of solution):         %g\n", (double)mumps->id.RINFOG(5)));
2558           PetscCall(PetscViewerASCIIPrintf(viewer, "    RINFOG(6) (inf norm of residual):         %g\n", (double)mumps->id.RINFOG(6)));
2559           PetscCall(PetscViewerASCIIPrintf(viewer, "    RINFOG(7),RINFOG(8) (backward error est): %g, %g\n", (double)mumps->id.RINFOG(7), (double)mumps->id.RINFOG(8)));
2560           PetscCall(PetscViewerASCIIPrintf(viewer, "    RINFOG(9) (error estimate):               %g\n", (double)mumps->id.RINFOG(9)));
2561           PetscCall(PetscViewerASCIIPrintf(viewer, "    RINFOG(10),RINFOG(11)(condition numbers): %g, %g\n", (double)mumps->id.RINFOG(10), (double)mumps->id.RINFOG(11)));
2562         }
2563         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(12) (efficiency control):                         %d\n", mumps->id.ICNTL(12)));
2564         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(13) (sequential factorization of the root node):  %d\n", mumps->id.ICNTL(13)));
2565         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(14) (percentage of estimated workspace increase): %d\n", mumps->id.ICNTL(14)));
2566         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(15) (compression of the input matrix):            %d\n", mumps->id.ICNTL(15)));
2567         /* ICNTL(15-17) not used */
2568         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(18) (input mat struct):                           %d\n", mumps->id.ICNTL(18)));
2569         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(19) (Schur complement info):                      %d\n", mumps->id.ICNTL(19)));
2570         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(20) (RHS sparse pattern):                         %d\n", mumps->id.ICNTL(20)));
2571         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(21) (solution struct):                            %d\n", mumps->id.ICNTL(21)));
2572         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(22) (in-core/out-of-core facility):               %d\n", mumps->id.ICNTL(22)));
2573         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(23) (max size of memory can be allocated locally):%d\n", mumps->id.ICNTL(23)));
2574 
2575         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(24) (detection of null pivot rows):               %d\n", mumps->id.ICNTL(24)));
2576         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(25) (computation of a null space basis):          %d\n", mumps->id.ICNTL(25)));
2577         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(26) (Schur options for RHS or solution):          %d\n", mumps->id.ICNTL(26)));
2578         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(27) (blocking size for multiple RHS):             %d\n", mumps->id.ICNTL(27)));
2579         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(28) (use parallel or sequential ordering):        %d\n", mumps->id.ICNTL(28)));
2580         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(29) (parallel ordering):                          %d\n", mumps->id.ICNTL(29)));
2581 
2582         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(30) (user-specified set of entries in inv(A)):    %d\n", mumps->id.ICNTL(30)));
2583         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(31) (factors is discarded in the solve phase):    %d\n", mumps->id.ICNTL(31)));
2584         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(33) (compute determinant):                        %d\n", mumps->id.ICNTL(33)));
2585         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(35) (activate BLR based factorization):           %d\n", mumps->id.ICNTL(35)));
2586         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(36) (choice of BLR factorization variant):        %d\n", mumps->id.ICNTL(36)));
2587         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(37) (compression of the contribution blocks):     %d\n", mumps->id.ICNTL(37)));
2588         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(38) (estimated compression rate of LU factors):   %d\n", mumps->id.ICNTL(38)));
2589         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(48) (multithreading with tree parallelism):       %d\n", mumps->id.ICNTL(48)));
2590         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(58) (options for symbolic factorization):         %d\n", mumps->id.ICNTL(58)));
2591 
2592         PetscCall(PetscViewerASCIIPrintf(viewer, "  CNTL(1) (relative pivoting threshold):      %g\n", (double)mumps->id.CNTL(1)));
2593         PetscCall(PetscViewerASCIIPrintf(viewer, "  CNTL(2) (stopping criterion of refinement): %g\n", (double)mumps->id.CNTL(2)));
2594         PetscCall(PetscViewerASCIIPrintf(viewer, "  CNTL(3) (absolute pivoting threshold):      %g\n", (double)mumps->id.CNTL(3)));
2595         PetscCall(PetscViewerASCIIPrintf(viewer, "  CNTL(4) (value of static pivoting):         %g\n", (double)mumps->id.CNTL(4)));
2596         PetscCall(PetscViewerASCIIPrintf(viewer, "  CNTL(5) (fixation for null pivots):         %g\n", (double)mumps->id.CNTL(5)));
2597         PetscCall(PetscViewerASCIIPrintf(viewer, "  CNTL(7) (dropping parameter for BLR):       %g\n", (double)mumps->id.CNTL(7)));
2598 
2599         /* information local to each processor */
2600         PetscCall(PetscViewerASCIIPrintf(viewer, "  RINFO(1) (local estimated flops for the elimination after analysis):\n"));
2601         PetscCall(PetscViewerASCIIPushSynchronized(viewer));
2602         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %g\n", mumps->myid, (double)mumps->id.RINFO(1)));
2603         PetscCall(PetscViewerFlush(viewer));
2604         PetscCall(PetscViewerASCIIPrintf(viewer, "  RINFO(2) (local estimated flops for the assembly after factorization):\n"));
2605         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %g\n", mumps->myid, (double)mumps->id.RINFO(2)));
2606         PetscCall(PetscViewerFlush(viewer));
2607         PetscCall(PetscViewerASCIIPrintf(viewer, "  RINFO(3) (local estimated flops for the elimination after factorization):\n"));
2608         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %g\n", mumps->myid, (double)mumps->id.RINFO(3)));
2609         PetscCall(PetscViewerFlush(viewer));
2610 
2611         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFO(15) (estimated size of (in MB) MUMPS internal data for running numerical factorization):\n"));
2612         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %d\n", mumps->myid, mumps->id.INFO(15)));
2613         PetscCall(PetscViewerFlush(viewer));
2614 
2615         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFO(16) (size of (in MB) MUMPS internal data used during numerical factorization):\n"));
2616         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %d\n", mumps->myid, mumps->id.INFO(16)));
2617         PetscCall(PetscViewerFlush(viewer));
2618 
2619         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFO(23) (num of pivots eliminated on this processor after factorization):\n"));
2620         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %d\n", mumps->myid, mumps->id.INFO(23)));
2621         PetscCall(PetscViewerFlush(viewer));
2622 
2623         if (mumps->ninfo && mumps->ninfo <= 80) {
2624           PetscInt i;
2625           for (i = 0; i < mumps->ninfo; i++) {
2626             PetscCall(PetscViewerASCIIPrintf(viewer, "  INFO(%" PetscInt_FMT "):\n", mumps->info[i]));
2627             PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %d\n", mumps->myid, mumps->id.INFO(mumps->info[i])));
2628             PetscCall(PetscViewerFlush(viewer));
2629           }
2630         }
2631         PetscCall(PetscViewerASCIIPopSynchronized(viewer));
2632       } else PetscCall(PetscViewerASCIIPrintf(viewer, "  Use -%sksp_view ::ascii_info_detail to display information for all processes\n", ((PetscObject)A)->prefix ? ((PetscObject)A)->prefix : ""));
2633 
2634       if (mumps->myid == 0) { /* information from the host */
2635         PetscCall(PetscViewerASCIIPrintf(viewer, "  RINFOG(1) (global estimated flops for the elimination after analysis): %g\n", (double)mumps->id.RINFOG(1)));
2636         PetscCall(PetscViewerASCIIPrintf(viewer, "  RINFOG(2) (global estimated flops for the assembly after factorization): %g\n", (double)mumps->id.RINFOG(2)));
2637         PetscCall(PetscViewerASCIIPrintf(viewer, "  RINFOG(3) (global estimated flops for the elimination after factorization): %g\n", (double)mumps->id.RINFOG(3)));
2638         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)));
2639 
2640         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(3) (estimated real workspace for factors on all processors after analysis): %d\n", mumps->id.INFOG(3)));
2641         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(4) (estimated integer workspace for factors on all processors after analysis): %d\n", mumps->id.INFOG(4)));
2642         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(5) (estimated maximum front size in the complete tree): %d\n", mumps->id.INFOG(5)));
2643         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(6) (number of nodes in the complete tree): %d\n", mumps->id.INFOG(6)));
2644         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(7) (ordering option effectively used after analysis): %d\n", mumps->id.INFOG(7)));
2645         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(8) (structural symmetry in percent of the permuted matrix after analysis): %d\n", mumps->id.INFOG(8)));
2646         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(9) (total real/complex workspace to store the matrix factors after factorization): %d\n", mumps->id.INFOG(9)));
2647         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(10) (total integer space store the matrix factors after factorization): %d\n", mumps->id.INFOG(10)));
2648         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(11) (order of largest frontal matrix after factorization): %d\n", mumps->id.INFOG(11)));
2649         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(12) (number of off-diagonal pivots): %d\n", mumps->id.INFOG(12)));
2650         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(13) (number of delayed pivots after factorization): %d\n", mumps->id.INFOG(13)));
2651         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(14) (number of memory compress after factorization): %d\n", mumps->id.INFOG(14)));
2652         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(15) (number of steps of iterative refinement after solution): %d\n", mumps->id.INFOG(15)));
2653         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)));
2654         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)));
2655         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)));
2656         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(19) (size of all MUMPS internal data allocated during factorization: sum over all processors): %d\n", mumps->id.INFOG(19)));
2657         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(20) (estimated number of entries in the factors): %d\n", mumps->id.INFOG(20)));
2658         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)));
2659         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(22) (size in MB of memory effectively used during factorization - sum over all processors): %d\n", mumps->id.INFOG(22)));
2660         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(23) (after analysis: value of ICNTL(6) effectively used): %d\n", mumps->id.INFOG(23)));
2661         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(24) (after analysis: value of ICNTL(12) effectively used): %d\n", mumps->id.INFOG(24)));
2662         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(25) (after factorization: number of pivots modified by static pivoting): %d\n", mumps->id.INFOG(25)));
2663         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(28) (after factorization: number of null pivots encountered): %d\n", mumps->id.INFOG(28)));
2664         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(29) (after factorization: effective number of entries in the factors (sum over all processors)): %d\n", mumps->id.INFOG(29)));
2665         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)));
2666         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(32) (after analysis: type of analysis done): %d\n", mumps->id.INFOG(32)));
2667         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(33) (value used for ICNTL(8)): %d\n", mumps->id.INFOG(33)));
2668         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(34) (exponent of the determinant if determinant is requested): %d\n", mumps->id.INFOG(34)));
2669         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)));
2670         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)));
2671         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)));
2672         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)));
2673         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)));
2674       }
2675     }
2676   }
2677   PetscFunctionReturn(PETSC_SUCCESS);
2678 }
2679 
2680 static PetscErrorCode MatGetInfo_MUMPS(Mat A, PETSC_UNUSED MatInfoType flag, MatInfo *info)
2681 {
2682   Mat_MUMPS *mumps = (Mat_MUMPS *)A->data;
2683 
2684   PetscFunctionBegin;
2685   info->block_size        = 1.0;
2686   info->nz_allocated      = mumps->id.INFOG(20) >= 0 ? mumps->id.INFOG(20) : -1000000 * mumps->id.INFOG(20);
2687   info->nz_used           = mumps->id.INFOG(20) >= 0 ? mumps->id.INFOG(20) : -1000000 * mumps->id.INFOG(20);
2688   info->nz_unneeded       = 0.0;
2689   info->assemblies        = 0.0;
2690   info->mallocs           = 0.0;
2691   info->memory            = 0.0;
2692   info->fill_ratio_given  = 0;
2693   info->fill_ratio_needed = 0;
2694   info->factor_mallocs    = 0;
2695   PetscFunctionReturn(PETSC_SUCCESS);
2696 }
2697 
2698 static PetscErrorCode MatFactorSetSchurIS_MUMPS(Mat F, IS is)
2699 {
2700   Mat_MUMPS         *mumps = (Mat_MUMPS *)F->data;
2701   const PetscScalar *arr;
2702   const PetscInt    *idxs;
2703   PetscInt           size, i;
2704 
2705   PetscFunctionBegin;
2706   PetscCall(ISGetLocalSize(is, &size));
2707   /* Schur complement matrix */
2708   PetscCall(MatDestroy(&F->schur));
2709   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, size, size, NULL, &F->schur));
2710   PetscCall(MatDenseGetArrayRead(F->schur, &arr));
2711   mumps->id.schur = (MumpsScalar *)arr;
2712   PetscCall(PetscMUMPSIntCast(size, &mumps->id.size_schur));
2713   PetscCall(PetscMUMPSIntCast(size, &mumps->id.schur_lld));
2714   PetscCall(MatDenseRestoreArrayRead(F->schur, &arr));
2715   if (mumps->sym == 1) PetscCall(MatSetOption(F->schur, MAT_SPD, PETSC_TRUE));
2716 
2717   /* MUMPS expects Fortran style indices */
2718   PetscCall(PetscFree(mumps->id.listvar_schur));
2719   PetscCall(PetscMalloc1(size, &mumps->id.listvar_schur));
2720   PetscCall(ISGetIndices(is, &idxs));
2721   for (i = 0; i < size; i++) PetscCall(PetscMUMPSIntCast(idxs[i] + 1, &mumps->id.listvar_schur[i]));
2722   PetscCall(ISRestoreIndices(is, &idxs));
2723   /* set a special value of ICNTL (not handled my MUMPS) to be used in the solve phase by PETSc */
2724   mumps->id.ICNTL(26) = -1;
2725   PetscFunctionReturn(PETSC_SUCCESS);
2726 }
2727 
2728 static PetscErrorCode MatFactorCreateSchurComplement_MUMPS(Mat F, Mat *S)
2729 {
2730   Mat          St;
2731   Mat_MUMPS   *mumps = (Mat_MUMPS *)F->data;
2732   PetscScalar *array;
2733 
2734   PetscFunctionBegin;
2735   PetscCheck(mumps->id.ICNTL(19), PetscObjectComm((PetscObject)F), PETSC_ERR_ORDER, "Schur complement mode not selected! Call MatFactorSetSchurIS() to enable it");
2736   PetscCall(MatCreate(PETSC_COMM_SELF, &St));
2737   PetscCall(MatSetSizes(St, PETSC_DECIDE, PETSC_DECIDE, mumps->id.size_schur, mumps->id.size_schur));
2738   PetscCall(MatSetType(St, MATDENSE));
2739   PetscCall(MatSetUp(St));
2740   PetscCall(MatDenseGetArray(St, &array));
2741   if (!mumps->sym) {                /* MUMPS always return a full matrix */
2742     if (mumps->id.ICNTL(19) == 1) { /* stored by rows */
2743       PetscInt i, j, N = mumps->id.size_schur;
2744       for (i = 0; i < N; i++) {
2745         for (j = 0; j < N; j++) {
2746 #if !defined(PETSC_USE_COMPLEX)
2747           PetscScalar val = mumps->id.schur[i * N + j];
2748 #else
2749           PetscScalar val = mumps->id.schur[i * N + j].r + PETSC_i * mumps->id.schur[i * N + j].i;
2750 #endif
2751           array[j * N + i] = val;
2752         }
2753       }
2754     } else { /* stored by columns */
2755       PetscCall(PetscArraycpy(array, mumps->id.schur, mumps->id.size_schur * mumps->id.size_schur));
2756     }
2757   } else {                          /* either full or lower-triangular (not packed) */
2758     if (mumps->id.ICNTL(19) == 2) { /* lower triangular stored by columns */
2759       PetscInt i, j, N = mumps->id.size_schur;
2760       for (i = 0; i < N; i++) {
2761         for (j = i; j < N; j++) {
2762 #if !defined(PETSC_USE_COMPLEX)
2763           PetscScalar val = mumps->id.schur[i * N + j];
2764 #else
2765           PetscScalar val = mumps->id.schur[i * N + j].r + PETSC_i * mumps->id.schur[i * N + j].i;
2766 #endif
2767           array[i * N + j] = array[j * N + i] = val;
2768         }
2769       }
2770     } else if (mumps->id.ICNTL(19) == 3) { /* full matrix */
2771       PetscCall(PetscArraycpy(array, mumps->id.schur, mumps->id.size_schur * mumps->id.size_schur));
2772     } else { /* ICNTL(19) == 1 lower triangular stored by rows */
2773       PetscInt i, j, N = mumps->id.size_schur;
2774       for (i = 0; i < N; i++) {
2775         for (j = 0; j < i + 1; j++) {
2776 #if !defined(PETSC_USE_COMPLEX)
2777           PetscScalar val = mumps->id.schur[i * N + j];
2778 #else
2779           PetscScalar val = mumps->id.schur[i * N + j].r + PETSC_i * mumps->id.schur[i * N + j].i;
2780 #endif
2781           array[i * N + j] = array[j * N + i] = val;
2782         }
2783       }
2784     }
2785   }
2786   PetscCall(MatDenseRestoreArray(St, &array));
2787   *S = St;
2788   PetscFunctionReturn(PETSC_SUCCESS);
2789 }
2790 
2791 static PetscErrorCode MatMumpsSetIcntl_MUMPS(Mat F, PetscInt icntl, PetscInt ival)
2792 {
2793   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;
2794 
2795   PetscFunctionBegin;
2796   if (mumps->id.job == JOB_NULL) {                                            /* need to cache icntl and ival since PetscMUMPS_c() has never been called */
2797     PetscMUMPSInt i, nICNTL_pre = mumps->ICNTL_pre ? mumps->ICNTL_pre[0] : 0; /* number of already cached ICNTL */
2798     for (i = 0; i < nICNTL_pre; ++i)
2799       if (mumps->ICNTL_pre[1 + 2 * i] == icntl) break; /* is this ICNTL already cached? */
2800     if (i == nICNTL_pre) {                             /* not already cached */
2801       if (i > 0) PetscCall(PetscRealloc(sizeof(PetscMUMPSInt) * (2 * nICNTL_pre + 3), &mumps->ICNTL_pre));
2802       else PetscCall(PetscCalloc(sizeof(PetscMUMPSInt) * 3, &mumps->ICNTL_pre));
2803       mumps->ICNTL_pre[0]++;
2804     }
2805     mumps->ICNTL_pre[1 + 2 * i] = (PetscMUMPSInt)icntl;
2806     PetscCall(PetscMUMPSIntCast(ival, mumps->ICNTL_pre + 2 + 2 * i));
2807   } else PetscCall(PetscMUMPSIntCast(ival, &mumps->id.ICNTL(icntl)));
2808   PetscFunctionReturn(PETSC_SUCCESS);
2809 }
2810 
2811 static PetscErrorCode MatMumpsGetIcntl_MUMPS(Mat F, PetscInt icntl, PetscInt *ival)
2812 {
2813   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;
2814 
2815   PetscFunctionBegin;
2816   if (mumps->id.job == JOB_NULL) {
2817     PetscInt i, nICNTL_pre = mumps->ICNTL_pre ? mumps->ICNTL_pre[0] : 0;
2818     *ival = 0;
2819     for (i = 0; i < nICNTL_pre; ++i) {
2820       if (mumps->ICNTL_pre[1 + 2 * i] == icntl) *ival = mumps->ICNTL_pre[2 + 2 * i];
2821     }
2822   } else *ival = mumps->id.ICNTL(icntl);
2823   PetscFunctionReturn(PETSC_SUCCESS);
2824 }
2825 
2826 /*@
2827   MatMumpsSetIcntl - Set MUMPS parameter ICNTL() <https://mumps-solver.org/index.php?page=doc>
2828 
2829   Logically Collective
2830 
2831   Input Parameters:
2832 + F     - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
2833 . icntl - index of MUMPS parameter array `ICNTL()`
2834 - ival  - value of MUMPS `ICNTL(icntl)`
2835 
2836   Options Database Key:
2837 . -mat_mumps_icntl_<icntl> <ival> - change the option numbered `icntl` to `ival`
2838 
2839   Level: beginner
2840 
2841   Note:
2842   Ignored if MUMPS is not installed or `F` is not a MUMPS matrix
2843 
2844 .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`
2845 @*/
2846 PetscErrorCode MatMumpsSetIcntl(Mat F, PetscInt icntl, PetscInt ival)
2847 {
2848   PetscFunctionBegin;
2849   PetscValidType(F, 1);
2850   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
2851   PetscValidLogicalCollectiveInt(F, icntl, 2);
2852   PetscValidLogicalCollectiveInt(F, ival, 3);
2853   PetscCheck((icntl >= 1 && icntl <= 38) || icntl == 48 || icntl == 58, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONG, "Unsupported ICNTL value %" PetscInt_FMT, icntl);
2854   PetscTryMethod(F, "MatMumpsSetIcntl_C", (Mat, PetscInt, PetscInt), (F, icntl, ival));
2855   PetscFunctionReturn(PETSC_SUCCESS);
2856 }
2857 
2858 /*@
2859   MatMumpsGetIcntl - Get MUMPS parameter ICNTL() <https://mumps-solver.org/index.php?page=doc>
2860 
2861   Logically Collective
2862 
2863   Input Parameters:
2864 + F     - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
2865 - icntl - index of MUMPS parameter array ICNTL()
2866 
2867   Output Parameter:
2868 . ival - value of MUMPS ICNTL(icntl)
2869 
2870   Level: beginner
2871 
2872 .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`
2873 @*/
2874 PetscErrorCode MatMumpsGetIcntl(Mat F, PetscInt icntl, PetscInt *ival)
2875 {
2876   PetscFunctionBegin;
2877   PetscValidType(F, 1);
2878   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
2879   PetscValidLogicalCollectiveInt(F, icntl, 2);
2880   PetscAssertPointer(ival, 3);
2881   PetscCheck((icntl >= 1 && icntl <= 38) || icntl == 48 || icntl == 58, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONG, "Unsupported ICNTL value %" PetscInt_FMT, icntl);
2882   PetscUseMethod(F, "MatMumpsGetIcntl_C", (Mat, PetscInt, PetscInt *), (F, icntl, ival));
2883   PetscFunctionReturn(PETSC_SUCCESS);
2884 }
2885 
2886 static PetscErrorCode MatMumpsSetCntl_MUMPS(Mat F, PetscInt icntl, PetscReal val)
2887 {
2888   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;
2889 
2890   PetscFunctionBegin;
2891   if (mumps->id.job == JOB_NULL) {
2892     PetscInt i, nCNTL_pre = mumps->CNTL_pre ? mumps->CNTL_pre[0] : 0;
2893     for (i = 0; i < nCNTL_pre; ++i)
2894       if (mumps->CNTL_pre[1 + 2 * i] == icntl) break;
2895     if (i == nCNTL_pre) {
2896       if (i > 0) PetscCall(PetscRealloc(sizeof(PetscReal) * (2 * nCNTL_pre + 3), &mumps->CNTL_pre));
2897       else PetscCall(PetscCalloc(sizeof(PetscReal) * 3, &mumps->CNTL_pre));
2898       mumps->CNTL_pre[0]++;
2899     }
2900     mumps->CNTL_pre[1 + 2 * i] = icntl;
2901     mumps->CNTL_pre[2 + 2 * i] = val;
2902   } else mumps->id.CNTL(icntl) = val;
2903   PetscFunctionReturn(PETSC_SUCCESS);
2904 }
2905 
2906 static PetscErrorCode MatMumpsGetCntl_MUMPS(Mat F, PetscInt icntl, PetscReal *val)
2907 {
2908   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;
2909 
2910   PetscFunctionBegin;
2911   if (mumps->id.job == JOB_NULL) {
2912     PetscInt i, nCNTL_pre = mumps->CNTL_pre ? mumps->CNTL_pre[0] : 0;
2913     *val = 0.0;
2914     for (i = 0; i < nCNTL_pre; ++i) {
2915       if (mumps->CNTL_pre[1 + 2 * i] == icntl) *val = mumps->CNTL_pre[2 + 2 * i];
2916     }
2917   } else *val = mumps->id.CNTL(icntl);
2918   PetscFunctionReturn(PETSC_SUCCESS);
2919 }
2920 
2921 /*@
2922   MatMumpsSetCntl - Set MUMPS parameter CNTL() <https://mumps-solver.org/index.php?page=doc>
2923 
2924   Logically Collective
2925 
2926   Input Parameters:
2927 + F     - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
2928 . icntl - index of MUMPS parameter array `CNTL()`
2929 - val   - value of MUMPS `CNTL(icntl)`
2930 
2931   Options Database Key:
2932 . -mat_mumps_cntl_<icntl> <val> - change the option numbered icntl to ival
2933 
2934   Level: beginner
2935 
2936   Note:
2937   Ignored if MUMPS is not installed or `F` is not a MUMPS matrix
2938 
2939 .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`
2940 @*/
2941 PetscErrorCode MatMumpsSetCntl(Mat F, PetscInt icntl, PetscReal val)
2942 {
2943   PetscFunctionBegin;
2944   PetscValidType(F, 1);
2945   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
2946   PetscValidLogicalCollectiveInt(F, icntl, 2);
2947   PetscValidLogicalCollectiveReal(F, val, 3);
2948   PetscCheck(icntl >= 1 && icntl <= 7, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONG, "Unsupported CNTL value %" PetscInt_FMT, icntl);
2949   PetscTryMethod(F, "MatMumpsSetCntl_C", (Mat, PetscInt, PetscReal), (F, icntl, val));
2950   PetscFunctionReturn(PETSC_SUCCESS);
2951 }
2952 
2953 /*@
2954   MatMumpsGetCntl - Get MUMPS parameter CNTL() <https://mumps-solver.org/index.php?page=doc>
2955 
2956   Logically Collective
2957 
2958   Input Parameters:
2959 + F     - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
2960 - icntl - index of MUMPS parameter array CNTL()
2961 
2962   Output Parameter:
2963 . val - value of MUMPS CNTL(icntl)
2964 
2965   Level: beginner
2966 
2967 .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`
2968 @*/
2969 PetscErrorCode MatMumpsGetCntl(Mat F, PetscInt icntl, PetscReal *val)
2970 {
2971   PetscFunctionBegin;
2972   PetscValidType(F, 1);
2973   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
2974   PetscValidLogicalCollectiveInt(F, icntl, 2);
2975   PetscAssertPointer(val, 3);
2976   PetscCheck(icntl >= 1 && icntl <= 7, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONG, "Unsupported CNTL value %" PetscInt_FMT, icntl);
2977   PetscUseMethod(F, "MatMumpsGetCntl_C", (Mat, PetscInt, PetscReal *), (F, icntl, val));
2978   PetscFunctionReturn(PETSC_SUCCESS);
2979 }
2980 
2981 static PetscErrorCode MatMumpsGetInfo_MUMPS(Mat F, PetscInt icntl, PetscInt *info)
2982 {
2983   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;
2984 
2985   PetscFunctionBegin;
2986   *info = mumps->id.INFO(icntl);
2987   PetscFunctionReturn(PETSC_SUCCESS);
2988 }
2989 
2990 static PetscErrorCode MatMumpsGetInfog_MUMPS(Mat F, PetscInt icntl, PetscInt *infog)
2991 {
2992   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;
2993 
2994   PetscFunctionBegin;
2995   *infog = mumps->id.INFOG(icntl);
2996   PetscFunctionReturn(PETSC_SUCCESS);
2997 }
2998 
2999 static PetscErrorCode MatMumpsGetRinfo_MUMPS(Mat F, PetscInt icntl, PetscReal *rinfo)
3000 {
3001   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;
3002 
3003   PetscFunctionBegin;
3004   *rinfo = mumps->id.RINFO(icntl);
3005   PetscFunctionReturn(PETSC_SUCCESS);
3006 }
3007 
3008 static PetscErrorCode MatMumpsGetRinfog_MUMPS(Mat F, PetscInt icntl, PetscReal *rinfog)
3009 {
3010   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;
3011 
3012   PetscFunctionBegin;
3013   *rinfog = mumps->id.RINFOG(icntl);
3014   PetscFunctionReturn(PETSC_SUCCESS);
3015 }
3016 
3017 static PetscErrorCode MatMumpsGetNullPivots_MUMPS(Mat F, PetscInt *size, PetscInt **array)
3018 {
3019   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;
3020 
3021   PetscFunctionBegin;
3022   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");
3023   *size  = 0;
3024   *array = NULL;
3025   if (!mumps->myid) {
3026     *size = mumps->id.INFOG(28);
3027     PetscCall(PetscMalloc1(*size, array));
3028     for (int i = 0; i < *size; i++) (*array)[i] = mumps->id.pivnul_list[i] - 1;
3029   }
3030   PetscFunctionReturn(PETSC_SUCCESS);
3031 }
3032 
3033 static PetscErrorCode MatMumpsGetInverse_MUMPS(Mat F, Mat spRHS)
3034 {
3035   Mat          Bt = NULL, Btseq = NULL;
3036   PetscBool    flg;
3037   Mat_MUMPS   *mumps = (Mat_MUMPS *)F->data;
3038   PetscScalar *aa;
3039   PetscInt     spnr, *ia, *ja, M, nrhs;
3040 
3041   PetscFunctionBegin;
3042   PetscAssertPointer(spRHS, 2);
3043   PetscCall(PetscObjectTypeCompare((PetscObject)spRHS, MATTRANSPOSEVIRTUAL, &flg));
3044   PetscCheck(flg, PetscObjectComm((PetscObject)spRHS), PETSC_ERR_ARG_WRONG, "Matrix spRHS must be type MATTRANSPOSEVIRTUAL matrix");
3045   PetscCall(MatShellGetScalingShifts(spRHS, (PetscScalar *)MAT_SHELL_NOT_ALLOWED, (PetscScalar *)MAT_SHELL_NOT_ALLOWED, (Vec *)MAT_SHELL_NOT_ALLOWED, (Vec *)MAT_SHELL_NOT_ALLOWED, (Vec *)MAT_SHELL_NOT_ALLOWED, (Mat *)MAT_SHELL_NOT_ALLOWED, (IS *)MAT_SHELL_NOT_ALLOWED, (IS *)MAT_SHELL_NOT_ALLOWED));
3046   PetscCall(MatTransposeGetMat(spRHS, &Bt));
3047 
3048   PetscCall(MatMumpsSetIcntl(F, 30, 1));
3049 
3050   if (mumps->petsc_size > 1) {
3051     Mat_MPIAIJ *b = (Mat_MPIAIJ *)Bt->data;
3052     Btseq         = b->A;
3053   } else {
3054     Btseq = Bt;
3055   }
3056 
3057   PetscCall(MatGetSize(spRHS, &M, &nrhs));
3058   mumps->id.nrhs = (PetscMUMPSInt)nrhs;
3059   PetscCall(PetscMUMPSIntCast(M, &mumps->id.lrhs));
3060   mumps->id.rhs = NULL;
3061 
3062   if (!mumps->myid) {
3063     PetscCall(MatSeqAIJGetArray(Btseq, &aa));
3064     PetscCall(MatGetRowIJ(Btseq, 1, PETSC_FALSE, PETSC_FALSE, &spnr, (const PetscInt **)&ia, (const PetscInt **)&ja, &flg));
3065     PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot get IJ structure");
3066     PetscCall(PetscMUMPSIntCSRCast(mumps, spnr, ia, ja, &mumps->id.irhs_ptr, &mumps->id.irhs_sparse, &mumps->id.nz_rhs));
3067     mumps->id.rhs_sparse = (MumpsScalar *)aa;
3068   } else {
3069     mumps->id.irhs_ptr    = NULL;
3070     mumps->id.irhs_sparse = NULL;
3071     mumps->id.nz_rhs      = 0;
3072     mumps->id.rhs_sparse  = NULL;
3073   }
3074   mumps->id.ICNTL(20) = 1; /* rhs is sparse */
3075   mumps->id.ICNTL(21) = 0; /* solution is in assembled centralized format */
3076 
3077   /* solve phase */
3078   mumps->id.job = JOB_SOLVE;
3079   PetscMUMPS_c(mumps);
3080   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));
3081 
3082   if (!mumps->myid) {
3083     PetscCall(MatSeqAIJRestoreArray(Btseq, &aa));
3084     PetscCall(MatRestoreRowIJ(Btseq, 1, PETSC_FALSE, PETSC_FALSE, &spnr, (const PetscInt **)&ia, (const PetscInt **)&ja, &flg));
3085     PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot get IJ structure");
3086   }
3087   PetscFunctionReturn(PETSC_SUCCESS);
3088 }
3089 
3090 /*@
3091   MatMumpsGetInverse - Get user-specified set of entries in inverse of `A` <https://mumps-solver.org/index.php?page=doc>
3092 
3093   Logically Collective
3094 
3095   Input Parameter:
3096 . F - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
3097 
3098   Output Parameter:
3099 . spRHS - sequential sparse matrix in `MATTRANSPOSEVIRTUAL` format with requested entries of inverse of `A`
3100 
3101   Level: beginner
3102 
3103 .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatCreateTranspose()`
3104 @*/
3105 PetscErrorCode MatMumpsGetInverse(Mat F, Mat spRHS)
3106 {
3107   PetscFunctionBegin;
3108   PetscValidType(F, 1);
3109   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
3110   PetscUseMethod(F, "MatMumpsGetInverse_C", (Mat, Mat), (F, spRHS));
3111   PetscFunctionReturn(PETSC_SUCCESS);
3112 }
3113 
3114 static PetscErrorCode MatMumpsGetInverseTranspose_MUMPS(Mat F, Mat spRHST)
3115 {
3116   Mat spRHS;
3117 
3118   PetscFunctionBegin;
3119   PetscCall(MatCreateTranspose(spRHST, &spRHS));
3120   PetscCall(MatMumpsGetInverse_MUMPS(F, spRHS));
3121   PetscCall(MatDestroy(&spRHS));
3122   PetscFunctionReturn(PETSC_SUCCESS);
3123 }
3124 
3125 /*@
3126   MatMumpsGetInverseTranspose - Get user-specified set of entries in inverse of matrix $A^T $ <https://mumps-solver.org/index.php?page=doc>
3127 
3128   Logically Collective
3129 
3130   Input Parameter:
3131 . 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`
3132 
3133   Output Parameter:
3134 . spRHST - sequential sparse matrix in `MATAIJ` format containing the requested entries of inverse of `A`^T
3135 
3136   Level: beginner
3137 
3138 .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatCreateTranspose()`, `MatMumpsGetInverse()`
3139 @*/
3140 PetscErrorCode MatMumpsGetInverseTranspose(Mat F, Mat spRHST)
3141 {
3142   PetscBool flg;
3143 
3144   PetscFunctionBegin;
3145   PetscValidType(F, 1);
3146   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
3147   PetscCall(PetscObjectTypeCompareAny((PetscObject)spRHST, &flg, MATSEQAIJ, MATMPIAIJ, NULL));
3148   PetscCheck(flg, PetscObjectComm((PetscObject)spRHST), PETSC_ERR_ARG_WRONG, "Matrix spRHST must be MATAIJ matrix");
3149   PetscUseMethod(F, "MatMumpsGetInverseTranspose_C", (Mat, Mat), (F, spRHST));
3150   PetscFunctionReturn(PETSC_SUCCESS);
3151 }
3152 
3153 /*@
3154   MatMumpsGetInfo - Get MUMPS parameter INFO() <https://mumps-solver.org/index.php?page=doc>
3155 
3156   Logically Collective
3157 
3158   Input Parameters:
3159 + F     - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
3160 - icntl - index of MUMPS parameter array INFO()
3161 
3162   Output Parameter:
3163 . ival - value of MUMPS INFO(icntl)
3164 
3165   Level: beginner
3166 
3167 .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`
3168 @*/
3169 PetscErrorCode MatMumpsGetInfo(Mat F, PetscInt icntl, PetscInt *ival)
3170 {
3171   PetscFunctionBegin;
3172   PetscValidType(F, 1);
3173   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
3174   PetscAssertPointer(ival, 3);
3175   PetscUseMethod(F, "MatMumpsGetInfo_C", (Mat, PetscInt, PetscInt *), (F, icntl, ival));
3176   PetscFunctionReturn(PETSC_SUCCESS);
3177 }
3178 
3179 /*@
3180   MatMumpsGetInfog - Get MUMPS parameter INFOG() <https://mumps-solver.org/index.php?page=doc>
3181 
3182   Logically Collective
3183 
3184   Input Parameters:
3185 + F     - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
3186 - icntl - index of MUMPS parameter array INFOG()
3187 
3188   Output Parameter:
3189 . ival - value of MUMPS INFOG(icntl)
3190 
3191   Level: beginner
3192 
3193 .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`
3194 @*/
3195 PetscErrorCode MatMumpsGetInfog(Mat F, PetscInt icntl, PetscInt *ival)
3196 {
3197   PetscFunctionBegin;
3198   PetscValidType(F, 1);
3199   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
3200   PetscAssertPointer(ival, 3);
3201   PetscUseMethod(F, "MatMumpsGetInfog_C", (Mat, PetscInt, PetscInt *), (F, icntl, ival));
3202   PetscFunctionReturn(PETSC_SUCCESS);
3203 }
3204 
3205 /*@
3206   MatMumpsGetRinfo - Get MUMPS parameter RINFO() <https://mumps-solver.org/index.php?page=doc>
3207 
3208   Logically Collective
3209 
3210   Input Parameters:
3211 + F     - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
3212 - icntl - index of MUMPS parameter array RINFO()
3213 
3214   Output Parameter:
3215 . val - value of MUMPS RINFO(icntl)
3216 
3217   Level: beginner
3218 
3219 .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfog()`
3220 @*/
3221 PetscErrorCode MatMumpsGetRinfo(Mat F, PetscInt icntl, PetscReal *val)
3222 {
3223   PetscFunctionBegin;
3224   PetscValidType(F, 1);
3225   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
3226   PetscAssertPointer(val, 3);
3227   PetscUseMethod(F, "MatMumpsGetRinfo_C", (Mat, PetscInt, PetscReal *), (F, icntl, val));
3228   PetscFunctionReturn(PETSC_SUCCESS);
3229 }
3230 
3231 /*@
3232   MatMumpsGetRinfog - Get MUMPS parameter RINFOG() <https://mumps-solver.org/index.php?page=doc>
3233 
3234   Logically Collective
3235 
3236   Input Parameters:
3237 + F     - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
3238 - icntl - index of MUMPS parameter array RINFOG()
3239 
3240   Output Parameter:
3241 . val - value of MUMPS RINFOG(icntl)
3242 
3243   Level: beginner
3244 
3245 .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`
3246 @*/
3247 PetscErrorCode MatMumpsGetRinfog(Mat F, PetscInt icntl, PetscReal *val)
3248 {
3249   PetscFunctionBegin;
3250   PetscValidType(F, 1);
3251   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
3252   PetscAssertPointer(val, 3);
3253   PetscUseMethod(F, "MatMumpsGetRinfog_C", (Mat, PetscInt, PetscReal *), (F, icntl, val));
3254   PetscFunctionReturn(PETSC_SUCCESS);
3255 }
3256 
3257 /*@
3258   MatMumpsGetNullPivots - Get MUMPS parameter PIVNUL_LIST() <https://mumps-solver.org/index.php?page=doc>
3259 
3260   Logically Collective
3261 
3262   Input Parameter:
3263 . F - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
3264 
3265   Output Parameters:
3266 + size  - local size of the array. The size of the array is non-zero only on MPI rank 0
3267 - 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
3268           for freeing this array.
3269 
3270   Level: beginner
3271 
3272 .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`
3273 @*/
3274 PetscErrorCode MatMumpsGetNullPivots(Mat F, PetscInt *size, PetscInt **array)
3275 {
3276   PetscFunctionBegin;
3277   PetscValidType(F, 1);
3278   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
3279   PetscAssertPointer(size, 2);
3280   PetscAssertPointer(array, 3);
3281   PetscUseMethod(F, "MatMumpsGetNullPivots_C", (Mat, PetscInt *, PetscInt **), (F, size, array));
3282   PetscFunctionReturn(PETSC_SUCCESS);
3283 }
3284 
3285 /*MC
3286   MATSOLVERMUMPS -  A matrix type providing direct solvers (LU and Cholesky) for
3287   MPI distributed and sequential matrices via the external package MUMPS <https://mumps-solver.org/index.php?page=doc>
3288 
3289   Works with `MATAIJ` and `MATSBAIJ` matrices
3290 
3291   Use ./configure --download-mumps --download-scalapack --download-parmetis --download-metis --download-ptscotch to have PETSc installed with MUMPS
3292 
3293   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.
3294   See details below.
3295 
3296   Use `-pc_type cholesky` or `lu` `-pc_factor_mat_solver_type mumps` to use this direct solver
3297 
3298   Options Database Keys:
3299 +  -mat_mumps_icntl_1  - ICNTL(1): output stream for error messages
3300 .  -mat_mumps_icntl_2  - ICNTL(2): output stream for diagnostic printing, statistics, and warning
3301 .  -mat_mumps_icntl_3  - ICNTL(3): output stream for global information, collected on the host
3302 .  -mat_mumps_icntl_4  - ICNTL(4): level of printing (0 to 4)
3303 .  -mat_mumps_icntl_6  - ICNTL(6): permutes to a zero-free diagonal and/or scale the matrix (0 to 7)
3304 .  -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
3305                           Use -pc_factor_mat_ordering_type <type> to have PETSc perform the ordering (sequential only)
3306 .  -mat_mumps_icntl_8  - ICNTL(8): scaling strategy (-2 to 8 or 77)
3307 .  -mat_mumps_icntl_10 - ICNTL(10): max num of refinements
3308 .  -mat_mumps_icntl_11 - ICNTL(11): statistics related to an error analysis (via -ksp_view)
3309 .  -mat_mumps_icntl_12 - ICNTL(12): an ordering strategy for symmetric matrices (0 to 3)
3310 .  -mat_mumps_icntl_13 - ICNTL(13): parallelism of the root node (enable ScaLAPACK) and its splitting
3311 .  -mat_mumps_icntl_14 - ICNTL(14): percentage increase in the estimated working space
3312 .  -mat_mumps_icntl_15 - ICNTL(15): compression of the input matrix resulting from a block format
3313 .  -mat_mumps_icntl_19 - ICNTL(19): computes the Schur complement
3314 .  -mat_mumps_icntl_20 - ICNTL(20): give MUMPS centralized (0) or distributed (10) dense RHS
3315 .  -mat_mumps_icntl_22 - ICNTL(22): in-core/out-of-core factorization and solve (0 or 1)
3316 .  -mat_mumps_icntl_23 - ICNTL(23): max size of the working memory (MB) that can allocate per processor
3317 .  -mat_mumps_icntl_24 - ICNTL(24): detection of null pivot rows (0 or 1)
3318 .  -mat_mumps_icntl_25 - ICNTL(25): compute a solution of a deficient matrix and a null space basis
3319 .  -mat_mumps_icntl_26 - ICNTL(26): drives the solution phase if a Schur complement matrix
3320 .  -mat_mumps_icntl_28 - ICNTL(28): use 1 for sequential analysis and ICNTL(7) ordering, or 2 for parallel analysis and ICNTL(29) ordering
3321 .  -mat_mumps_icntl_29 - ICNTL(29): parallel ordering 1 = ptscotch, 2 = parmetis
3322 .  -mat_mumps_icntl_30 - ICNTL(30): compute user-specified set of entries in inv(A)
3323 .  -mat_mumps_icntl_31 - ICNTL(31): indicates which factors may be discarded during factorization
3324 .  -mat_mumps_icntl_33 - ICNTL(33): compute determinant
3325 .  -mat_mumps_icntl_35 - ICNTL(35): level of activation of BLR (Block Low-Rank) feature
3326 .  -mat_mumps_icntl_36 - ICNTL(36): controls the choice of BLR factorization variant
3327 .  -mat_mumps_icntl_37 - ICNTL(37): compression of the contribution blocks (CB)
3328 .  -mat_mumps_icntl_38 - ICNTL(38): sets the estimated compression rate of LU factors with BLR
3329 .  -mat_mumps_icntl_48 - ICNTL(48): multithreading with tree parallelism
3330 .  -mat_mumps_icntl_58 - ICNTL(58): options for symbolic factorization
3331 .  -mat_mumps_cntl_1   - CNTL(1): relative pivoting threshold
3332 .  -mat_mumps_cntl_2   - CNTL(2): stopping criterion of refinement
3333 .  -mat_mumps_cntl_3   - CNTL(3): absolute pivoting threshold
3334 .  -mat_mumps_cntl_4   - CNTL(4): value for static pivoting
3335 .  -mat_mumps_cntl_5   - CNTL(5): fixation for null pivots
3336 .  -mat_mumps_cntl_7   - CNTL(7): precision of the dropping parameter used during BLR factorization
3337 -  -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.
3338                                     Default might be the number of cores per CPU package (socket) as reported by hwloc and suggested by the MUMPS manual.
3339 
3340   Level: beginner
3341 
3342   Notes:
3343   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
3344   error if the matrix is Hermitian.
3345 
3346   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
3347   `MatSetOptionsPrefixFactor()` on the matrix from which the factor was obtained or `MatSetOptionsPrefix()` on the factor matrix.
3348 
3349   When a MUMPS factorization fails inside a KSP solve, for example with a `KSP_DIVERGED_PC_FAILED`, one can find the MUMPS information about
3350   the failure with
3351 .vb
3352           KSPGetPC(ksp,&pc);
3353           PCFactorGetMatrix(pc,&mat);
3354           MatMumpsGetInfo(mat,....);
3355           MatMumpsGetInfog(mat,....); etc.
3356 .ve
3357   Or run with `-ksp_error_if_not_converged` and the program will be stopped and the information printed in the error message.
3358 
3359   MUMPS provides 64-bit integer support in two build modes:
3360   full 64-bit: here MUMPS is built with C preprocessing flag -DINTSIZE64 and Fortran compiler option -i8, -fdefault-integer-8 or equivalent, and
3361   requires all dependent libraries MPI, ScaLAPACK, LAPACK and BLAS built the same way with 64-bit integers (for example ILP64 Intel MKL and MPI).
3362 
3363   selective 64-bit: with the default MUMPS build, 64-bit integers have been introduced where needed. In compressed sparse row (CSR) storage of matrices,
3364   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
3365   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
3366   integer) build of all dependent libraries MPI, ScaLAPACK, LAPACK and BLAS.
3367 
3368   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.
3369 
3370   Two modes to run MUMPS/PETSc with OpenMP
3371 .vb
3372    Set `OMP_NUM_THREADS` and run with fewer MPI ranks than cores. For example, if you want to have 16 OpenMP
3373    threads per rank, then you may use "export `OMP_NUM_THREADS` = 16 && mpirun -n 4 ./test".
3374 .ve
3375 
3376 .vb
3377    `-mat_mumps_use_omp_threads` [m] and run your code with as many MPI ranks as the number of cores. For example,
3378    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"
3379 .ve
3380 
3381    To run MUMPS in MPI+OpenMP hybrid mode (i.e., enable multithreading in MUMPS), but still run the non-MUMPS part
3382    (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`
3383    (or `--with-hwloc`), and have an MPI that supports MPI-3.0's process shared memory (which is usually available). Since MUMPS calls BLAS
3384    libraries, to really get performance, you should have multithreaded BLAS libraries such as Intel MKL, AMD ACML, Cray libSci or OpenBLAS
3385    (PETSc will automatically try to utilized a threaded BLAS if `--with-openmp` is provided).
3386 
3387    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
3388    processes on each compute node. Listing the processes in rank ascending order, we split processes on a node into consecutive groups of
3389    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
3390    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
3391    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.
3392    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,
3393    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
3394    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
3395    cores in socket 1, that definitely hurts locality. On the other hand, if you map MPI ranks consecutively on the two sockets, then the
3396    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.
3397    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
3398    examine the mapping result.
3399 
3400    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,
3401    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
3402    calls `omp_set_num_threads`(m) internally before calling MUMPS.
3403 
3404    See {cite}`heroux2011bi` and {cite}`gutierrez2017accommodating`
3405 
3406 .seealso: [](ch_matrices), `Mat`, `PCFactorSetMatSolverType()`, `MatSolverType`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`, `KSPGetPC()`, `PCFactorGetMatrix()`
3407 M*/
3408 
3409 static PetscErrorCode MatFactorGetSolverType_mumps(PETSC_UNUSED Mat A, MatSolverType *type)
3410 {
3411   PetscFunctionBegin;
3412   *type = MATSOLVERMUMPS;
3413   PetscFunctionReturn(PETSC_SUCCESS);
3414 }
3415 
3416 /* MatGetFactor for Seq and MPI AIJ matrices */
3417 static PetscErrorCode MatGetFactor_aij_mumps(Mat A, MatFactorType ftype, Mat *F)
3418 {
3419   Mat         B;
3420   Mat_MUMPS  *mumps;
3421   PetscBool   isSeqAIJ, isDiag, isDense;
3422   PetscMPIInt size;
3423 
3424   PetscFunctionBegin;
3425 #if defined(PETSC_USE_COMPLEX)
3426   if (ftype == MAT_FACTOR_CHOLESKY && A->hermitian == PETSC_BOOL3_TRUE && A->symmetric != PETSC_BOOL3_TRUE) {
3427     PetscCall(PetscInfo(A, "Hermitian MAT_FACTOR_CHOLESKY is not supported. Use MAT_FACTOR_LU instead.\n"));
3428     *F = NULL;
3429     PetscFunctionReturn(PETSC_SUCCESS);
3430   }
3431 #endif
3432   /* Create the factorization matrix */
3433   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATSEQAIJ, &isSeqAIJ));
3434   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATDIAGONAL, &isDiag));
3435   PetscCall(PetscObjectTypeCompareAny((PetscObject)A, &isDense, MATSEQDENSE, MATMPIDENSE, NULL));
3436   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
3437   PetscCall(MatSetSizes(B, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
3438   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &((PetscObject)B)->type_name));
3439   PetscCall(MatSetUp(B));
3440 
3441   PetscCall(PetscNew(&mumps));
3442 
3443   B->ops->view    = MatView_MUMPS;
3444   B->ops->getinfo = MatGetInfo_MUMPS;
3445 
3446   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorGetSolverType_C", MatFactorGetSolverType_mumps));
3447   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorSetSchurIS_C", MatFactorSetSchurIS_MUMPS));
3448   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorCreateSchurComplement_C", MatFactorCreateSchurComplement_MUMPS));
3449   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetIcntl_C", MatMumpsSetIcntl_MUMPS));
3450   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetIcntl_C", MatMumpsGetIcntl_MUMPS));
3451   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetCntl_C", MatMumpsSetCntl_MUMPS));
3452   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetCntl_C", MatMumpsGetCntl_MUMPS));
3453   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfo_C", MatMumpsGetInfo_MUMPS));
3454   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfog_C", MatMumpsGetInfog_MUMPS));
3455   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfo_C", MatMumpsGetRinfo_MUMPS));
3456   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfog_C", MatMumpsGetRinfog_MUMPS));
3457   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetNullPivots_C", MatMumpsGetNullPivots_MUMPS));
3458   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverse_C", MatMumpsGetInverse_MUMPS));
3459   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverseTranspose_C", MatMumpsGetInverseTranspose_MUMPS));
3460 
3461   if (ftype == MAT_FACTOR_LU) {
3462     B->ops->lufactorsymbolic = MatLUFactorSymbolic_AIJMUMPS;
3463     B->factortype            = MAT_FACTOR_LU;
3464     if (isSeqAIJ) mumps->ConvertToTriples = MatConvertToTriples_seqaij_seqaij;
3465     else if (isDiag) mumps->ConvertToTriples = MatConvertToTriples_diagonal_xaij;
3466     else if (isDense) mumps->ConvertToTriples = MatConvertToTriples_dense_xaij;
3467     else mumps->ConvertToTriples = MatConvertToTriples_mpiaij_mpiaij;
3468     PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&B->preferredordering[MAT_FACTOR_LU]));
3469     mumps->sym = 0;
3470   } else {
3471     B->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_MUMPS;
3472     B->factortype                  = MAT_FACTOR_CHOLESKY;
3473     if (isSeqAIJ) mumps->ConvertToTriples = MatConvertToTriples_seqaij_seqsbaij;
3474     else if (isDiag) mumps->ConvertToTriples = MatConvertToTriples_diagonal_xaij;
3475     else if (isDense) mumps->ConvertToTriples = MatConvertToTriples_dense_xaij;
3476     else mumps->ConvertToTriples = MatConvertToTriples_mpiaij_mpisbaij;
3477     PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&B->preferredordering[MAT_FACTOR_CHOLESKY]));
3478 #if defined(PETSC_USE_COMPLEX)
3479     mumps->sym = 2;
3480 #else
3481     if (A->spd == PETSC_BOOL3_TRUE) mumps->sym = 1;
3482     else mumps->sym = 2;
3483 #endif
3484   }
3485 
3486   /* set solvertype */
3487   PetscCall(PetscFree(B->solvertype));
3488   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &B->solvertype));
3489   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
3490   if (size == 1) {
3491     /* MUMPS option -mat_mumps_icntl_7 1 is automatically set if PETSc ordering is passed into symbolic factorization */
3492     B->canuseordering = PETSC_TRUE;
3493   }
3494   B->ops->destroy = MatDestroy_MUMPS;
3495   B->data         = (void *)mumps;
3496 
3497   *F               = B;
3498   mumps->id.job    = JOB_NULL;
3499   mumps->ICNTL_pre = NULL;
3500   mumps->CNTL_pre  = NULL;
3501   mumps->matstruc  = DIFFERENT_NONZERO_PATTERN;
3502   PetscFunctionReturn(PETSC_SUCCESS);
3503 }
3504 
3505 /* MatGetFactor for Seq and MPI SBAIJ matrices */
3506 static PetscErrorCode MatGetFactor_sbaij_mumps(Mat A, PETSC_UNUSED MatFactorType ftype, Mat *F)
3507 {
3508   Mat         B;
3509   Mat_MUMPS  *mumps;
3510   PetscBool   isSeqSBAIJ;
3511   PetscMPIInt size;
3512 
3513   PetscFunctionBegin;
3514 #if defined(PETSC_USE_COMPLEX)
3515   if (ftype == MAT_FACTOR_CHOLESKY && A->hermitian == PETSC_BOOL3_TRUE && A->symmetric != PETSC_BOOL3_TRUE) {
3516     PetscCall(PetscInfo(A, "Hermitian MAT_FACTOR_CHOLESKY is not supported. Use MAT_FACTOR_LU instead.\n"));
3517     *F = NULL;
3518     PetscFunctionReturn(PETSC_SUCCESS);
3519   }
3520 #endif
3521   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
3522   PetscCall(MatSetSizes(B, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
3523   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &((PetscObject)B)->type_name));
3524   PetscCall(MatSetUp(B));
3525 
3526   PetscCall(PetscNew(&mumps));
3527   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQSBAIJ, &isSeqSBAIJ));
3528   if (isSeqSBAIJ) {
3529     mumps->ConvertToTriples = MatConvertToTriples_seqsbaij_seqsbaij;
3530   } else {
3531     mumps->ConvertToTriples = MatConvertToTriples_mpisbaij_mpisbaij;
3532   }
3533 
3534   B->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_MUMPS;
3535   B->ops->view                   = MatView_MUMPS;
3536   B->ops->getinfo                = MatGetInfo_MUMPS;
3537 
3538   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorGetSolverType_C", MatFactorGetSolverType_mumps));
3539   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorSetSchurIS_C", MatFactorSetSchurIS_MUMPS));
3540   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorCreateSchurComplement_C", MatFactorCreateSchurComplement_MUMPS));
3541   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetIcntl_C", MatMumpsSetIcntl_MUMPS));
3542   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetIcntl_C", MatMumpsGetIcntl_MUMPS));
3543   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetCntl_C", MatMumpsSetCntl_MUMPS));
3544   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetCntl_C", MatMumpsGetCntl_MUMPS));
3545   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfo_C", MatMumpsGetInfo_MUMPS));
3546   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfog_C", MatMumpsGetInfog_MUMPS));
3547   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfo_C", MatMumpsGetRinfo_MUMPS));
3548   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfog_C", MatMumpsGetRinfog_MUMPS));
3549   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetNullPivots_C", MatMumpsGetNullPivots_MUMPS));
3550   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverse_C", MatMumpsGetInverse_MUMPS));
3551   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverseTranspose_C", MatMumpsGetInverseTranspose_MUMPS));
3552 
3553   B->factortype = MAT_FACTOR_CHOLESKY;
3554 #if defined(PETSC_USE_COMPLEX)
3555   mumps->sym = 2;
3556 #else
3557   if (A->spd == PETSC_BOOL3_TRUE) mumps->sym = 1;
3558   else mumps->sym = 2;
3559 #endif
3560 
3561   /* set solvertype */
3562   PetscCall(PetscFree(B->solvertype));
3563   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &B->solvertype));
3564   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
3565   if (size == 1) {
3566     /* MUMPS option -mat_mumps_icntl_7 1 is automatically set if PETSc ordering is passed into symbolic factorization */
3567     B->canuseordering = PETSC_TRUE;
3568   }
3569   PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&B->preferredordering[MAT_FACTOR_CHOLESKY]));
3570   B->ops->destroy = MatDestroy_MUMPS;
3571   B->data         = (void *)mumps;
3572 
3573   *F               = B;
3574   mumps->id.job    = JOB_NULL;
3575   mumps->ICNTL_pre = NULL;
3576   mumps->CNTL_pre  = NULL;
3577   mumps->matstruc  = DIFFERENT_NONZERO_PATTERN;
3578   PetscFunctionReturn(PETSC_SUCCESS);
3579 }
3580 
3581 static PetscErrorCode MatGetFactor_baij_mumps(Mat A, MatFactorType ftype, Mat *F)
3582 {
3583   Mat         B;
3584   Mat_MUMPS  *mumps;
3585   PetscBool   isSeqBAIJ;
3586   PetscMPIInt size;
3587 
3588   PetscFunctionBegin;
3589   /* Create the factorization matrix */
3590   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQBAIJ, &isSeqBAIJ));
3591   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
3592   PetscCall(MatSetSizes(B, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
3593   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &((PetscObject)B)->type_name));
3594   PetscCall(MatSetUp(B));
3595 
3596   PetscCall(PetscNew(&mumps));
3597   if (ftype == MAT_FACTOR_LU) {
3598     B->ops->lufactorsymbolic = MatLUFactorSymbolic_BAIJMUMPS;
3599     B->factortype            = MAT_FACTOR_LU;
3600     if (isSeqBAIJ) mumps->ConvertToTriples = MatConvertToTriples_seqbaij_seqaij;
3601     else mumps->ConvertToTriples = MatConvertToTriples_mpibaij_mpiaij;
3602     mumps->sym = 0;
3603     PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&B->preferredordering[MAT_FACTOR_LU]));
3604   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot use PETSc BAIJ matrices with MUMPS Cholesky, use SBAIJ or AIJ matrix instead");
3605 
3606   B->ops->view    = MatView_MUMPS;
3607   B->ops->getinfo = MatGetInfo_MUMPS;
3608 
3609   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorGetSolverType_C", MatFactorGetSolverType_mumps));
3610   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorSetSchurIS_C", MatFactorSetSchurIS_MUMPS));
3611   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorCreateSchurComplement_C", MatFactorCreateSchurComplement_MUMPS));
3612   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetIcntl_C", MatMumpsSetIcntl_MUMPS));
3613   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetIcntl_C", MatMumpsGetIcntl_MUMPS));
3614   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetCntl_C", MatMumpsSetCntl_MUMPS));
3615   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetCntl_C", MatMumpsGetCntl_MUMPS));
3616   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfo_C", MatMumpsGetInfo_MUMPS));
3617   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfog_C", MatMumpsGetInfog_MUMPS));
3618   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfo_C", MatMumpsGetRinfo_MUMPS));
3619   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfog_C", MatMumpsGetRinfog_MUMPS));
3620   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetNullPivots_C", MatMumpsGetNullPivots_MUMPS));
3621   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverse_C", MatMumpsGetInverse_MUMPS));
3622   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverseTranspose_C", MatMumpsGetInverseTranspose_MUMPS));
3623 
3624   /* set solvertype */
3625   PetscCall(PetscFree(B->solvertype));
3626   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &B->solvertype));
3627   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
3628   if (size == 1) {
3629     /* MUMPS option -mat_mumps_icntl_7 1 is automatically set if PETSc ordering is passed into symbolic factorization */
3630     B->canuseordering = PETSC_TRUE;
3631   }
3632   B->ops->destroy = MatDestroy_MUMPS;
3633   B->data         = (void *)mumps;
3634 
3635   *F               = B;
3636   mumps->id.job    = JOB_NULL;
3637   mumps->ICNTL_pre = NULL;
3638   mumps->CNTL_pre  = NULL;
3639   mumps->matstruc  = DIFFERENT_NONZERO_PATTERN;
3640   PetscFunctionReturn(PETSC_SUCCESS);
3641 }
3642 
3643 /* MatGetFactor for Seq and MPI SELL matrices */
3644 static PetscErrorCode MatGetFactor_sell_mumps(Mat A, MatFactorType ftype, Mat *F)
3645 {
3646   Mat         B;
3647   Mat_MUMPS  *mumps;
3648   PetscBool   isSeqSELL;
3649   PetscMPIInt size;
3650 
3651   PetscFunctionBegin;
3652   /* Create the factorization matrix */
3653   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQSELL, &isSeqSELL));
3654   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
3655   PetscCall(MatSetSizes(B, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
3656   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &((PetscObject)B)->type_name));
3657   PetscCall(MatSetUp(B));
3658 
3659   PetscCall(PetscNew(&mumps));
3660 
3661   B->ops->view    = MatView_MUMPS;
3662   B->ops->getinfo = MatGetInfo_MUMPS;
3663 
3664   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorGetSolverType_C", MatFactorGetSolverType_mumps));
3665   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorSetSchurIS_C", MatFactorSetSchurIS_MUMPS));
3666   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorCreateSchurComplement_C", MatFactorCreateSchurComplement_MUMPS));
3667   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetIcntl_C", MatMumpsSetIcntl_MUMPS));
3668   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetIcntl_C", MatMumpsGetIcntl_MUMPS));
3669   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetCntl_C", MatMumpsSetCntl_MUMPS));
3670   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetCntl_C", MatMumpsGetCntl_MUMPS));
3671   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfo_C", MatMumpsGetInfo_MUMPS));
3672   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfog_C", MatMumpsGetInfog_MUMPS));
3673   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfo_C", MatMumpsGetRinfo_MUMPS));
3674   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfog_C", MatMumpsGetRinfog_MUMPS));
3675   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetNullPivots_C", MatMumpsGetNullPivots_MUMPS));
3676 
3677   if (ftype == MAT_FACTOR_LU) {
3678     B->ops->lufactorsymbolic = MatLUFactorSymbolic_AIJMUMPS;
3679     B->factortype            = MAT_FACTOR_LU;
3680     if (isSeqSELL) mumps->ConvertToTriples = MatConvertToTriples_seqsell_seqaij;
3681     else SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "To be implemented");
3682     mumps->sym = 0;
3683     PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&B->preferredordering[MAT_FACTOR_LU]));
3684   } else SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "To be implemented");
3685 
3686   /* set solvertype */
3687   PetscCall(PetscFree(B->solvertype));
3688   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &B->solvertype));
3689   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
3690   if (size == 1) {
3691     /* MUMPS option -mat_mumps_icntl_7 1 is automatically set if PETSc ordering is passed into symbolic factorization  */
3692     B->canuseordering = PETSC_TRUE;
3693   }
3694   B->ops->destroy = MatDestroy_MUMPS;
3695   B->data         = (void *)mumps;
3696 
3697   *F               = B;
3698   mumps->id.job    = JOB_NULL;
3699   mumps->ICNTL_pre = NULL;
3700   mumps->CNTL_pre  = NULL;
3701   mumps->matstruc  = DIFFERENT_NONZERO_PATTERN;
3702   PetscFunctionReturn(PETSC_SUCCESS);
3703 }
3704 
3705 /* MatGetFactor for MATNEST matrices */
3706 static PetscErrorCode MatGetFactor_nest_mumps(Mat A, MatFactorType ftype, Mat *F)
3707 {
3708   Mat         B, **mats;
3709   Mat_MUMPS  *mumps;
3710   PetscInt    nr, nc;
3711   PetscMPIInt size;
3712   PetscBool   flg = PETSC_TRUE;
3713 
3714   PetscFunctionBegin;
3715 #if defined(PETSC_USE_COMPLEX)
3716   if (ftype == MAT_FACTOR_CHOLESKY && A->hermitian == PETSC_BOOL3_TRUE && A->symmetric != PETSC_BOOL3_TRUE) {
3717     PetscCall(PetscInfo(A, "Hermitian MAT_FACTOR_CHOLESKY is not supported. Use MAT_FACTOR_LU instead.\n"));
3718     *F = NULL;
3719     PetscFunctionReturn(PETSC_SUCCESS);
3720   }
3721 #endif
3722 
3723   /* Return if some condition is not satisfied */
3724   *F = NULL;
3725   PetscCall(MatNestGetSubMats(A, &nr, &nc, &mats));
3726   if (ftype == MAT_FACTOR_CHOLESKY) {
3727     IS       *rows, *cols;
3728     PetscInt *m, *M;
3729 
3730     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);
3731     PetscCall(PetscMalloc2(nr, &rows, nc, &cols));
3732     PetscCall(MatNestGetISs(A, rows, cols));
3733     for (PetscInt r = 0; flg && r < nr; r++) PetscCall(ISEqualUnsorted(rows[r], cols[r], &flg));
3734     if (!flg) {
3735       PetscCall(PetscFree2(rows, cols));
3736       PetscCall(PetscInfo(A, "MAT_FACTOR_CHOLESKY not supported for unequal row and column maps. Use MAT_FACTOR_LU.\n"));
3737       PetscFunctionReturn(PETSC_SUCCESS);
3738     }
3739     PetscCall(PetscMalloc2(nr, &m, nr, &M));
3740     for (PetscInt r = 0; r < nr; r++) PetscCall(ISGetMinMax(rows[r], &m[r], &M[r]));
3741     for (PetscInt r = 0; flg && r < nr; r++)
3742       for (PetscInt k = r + 1; flg && k < nr; k++)
3743         if ((m[k] <= m[r] && m[r] <= M[k]) || (m[k] <= M[r] && M[r] <= M[k])) flg = PETSC_FALSE;
3744     PetscCall(PetscFree2(m, M));
3745     PetscCall(PetscFree2(rows, cols));
3746     if (!flg) {
3747       PetscCall(PetscInfo(A, "MAT_FACTOR_CHOLESKY not supported for intersecting row maps. Use MAT_FACTOR_LU.\n"));
3748       PetscFunctionReturn(PETSC_SUCCESS);
3749     }
3750   }
3751 
3752   for (PetscInt r = 0; r < nr; r++) {
3753     for (PetscInt c = 0; c < nc; c++) {
3754       Mat       sub = mats[r][c];
3755       PetscBool isSeqAIJ, isMPIAIJ, isSeqBAIJ, isMPIBAIJ, isSeqSBAIJ, isMPISBAIJ, isDiag, isDense;
3756 
3757       if (!sub || (ftype == MAT_FACTOR_CHOLESKY && c < r)) continue;
3758       PetscCall(MatGetTranspose_TransposeVirtual(&sub, NULL, NULL, NULL, NULL));
3759       PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATSEQAIJ, &isSeqAIJ));
3760       PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATMPIAIJ, &isMPIAIJ));
3761       PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATSEQBAIJ, &isSeqBAIJ));
3762       PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATMPIBAIJ, &isMPIBAIJ));
3763       PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATSEQSBAIJ, &isSeqSBAIJ));
3764       PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATMPISBAIJ, &isMPISBAIJ));
3765       PetscCall(PetscObjectTypeCompare((PetscObject)sub, MATDIAGONAL, &isDiag));
3766       PetscCall(PetscObjectTypeCompareAny((PetscObject)sub, &isDense, MATSEQDENSE, MATMPIDENSE, NULL));
3767       if (ftype == MAT_FACTOR_CHOLESKY) {
3768         if (r == c) {
3769           if (!isSeqAIJ && !isMPIAIJ && !isSeqBAIJ && !isMPIBAIJ && !isSeqSBAIJ && !isMPISBAIJ && !isDiag && !isDense) {
3770             PetscCall(PetscInfo(sub, "MAT_FACTOR_CHOLESKY not supported for diagonal block of type %s.\n", ((PetscObject)sub)->type_name));
3771             flg = PETSC_FALSE;
3772           }
3773         } else if (!isSeqAIJ && !isMPIAIJ && !isSeqBAIJ && !isMPIBAIJ && !isDiag && !isDense) {
3774           PetscCall(PetscInfo(sub, "MAT_FACTOR_CHOLESKY not supported for off-diagonal block of type %s.\n", ((PetscObject)sub)->type_name));
3775           flg = PETSC_FALSE;
3776         }
3777       } else if (!isSeqAIJ && !isMPIAIJ && !isSeqBAIJ && !isMPIBAIJ && !isDiag && !isDense) {
3778         PetscCall(PetscInfo(sub, "MAT_FACTOR_LU not supported for block of type %s.\n", ((PetscObject)sub)->type_name));
3779         flg = PETSC_FALSE;
3780       }
3781     }
3782   }
3783   if (!flg) PetscFunctionReturn(PETSC_SUCCESS);
3784 
3785   /* Create the factorization matrix */
3786   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
3787   PetscCall(MatSetSizes(B, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
3788   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &((PetscObject)B)->type_name));
3789   PetscCall(MatSetUp(B));
3790 
3791   PetscCall(PetscNew(&mumps));
3792 
3793   B->ops->view    = MatView_MUMPS;
3794   B->ops->getinfo = MatGetInfo_MUMPS;
3795 
3796   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorGetSolverType_C", MatFactorGetSolverType_mumps));
3797   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorSetSchurIS_C", MatFactorSetSchurIS_MUMPS));
3798   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorCreateSchurComplement_C", MatFactorCreateSchurComplement_MUMPS));
3799   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetIcntl_C", MatMumpsSetIcntl_MUMPS));
3800   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetIcntl_C", MatMumpsGetIcntl_MUMPS));
3801   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetCntl_C", MatMumpsSetCntl_MUMPS));
3802   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetCntl_C", MatMumpsGetCntl_MUMPS));
3803   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfo_C", MatMumpsGetInfo_MUMPS));
3804   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfog_C", MatMumpsGetInfog_MUMPS));
3805   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfo_C", MatMumpsGetRinfo_MUMPS));
3806   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfog_C", MatMumpsGetRinfog_MUMPS));
3807   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetNullPivots_C", MatMumpsGetNullPivots_MUMPS));
3808   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverse_C", MatMumpsGetInverse_MUMPS));
3809   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverseTranspose_C", MatMumpsGetInverseTranspose_MUMPS));
3810 
3811   if (ftype == MAT_FACTOR_LU) {
3812     B->ops->lufactorsymbolic = MatLUFactorSymbolic_AIJMUMPS;
3813     B->factortype            = MAT_FACTOR_LU;
3814     mumps->sym               = 0;
3815   } else {
3816     B->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_MUMPS;
3817     B->factortype                  = MAT_FACTOR_CHOLESKY;
3818 #if defined(PETSC_USE_COMPLEX)
3819     mumps->sym = 2;
3820 #else
3821     if (A->spd == PETSC_BOOL3_TRUE) mumps->sym = 1;
3822     else mumps->sym = 2;
3823 #endif
3824   }
3825   mumps->ConvertToTriples = MatConvertToTriples_nest_xaij;
3826   PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&B->preferredordering[ftype]));
3827 
3828   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
3829   if (size == 1) {
3830     /* MUMPS option -mat_mumps_icntl_7 1 is automatically set if PETSc ordering is passed into symbolic factorization */
3831     B->canuseordering = PETSC_TRUE;
3832   }
3833 
3834   /* set solvertype */
3835   PetscCall(PetscFree(B->solvertype));
3836   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &B->solvertype));
3837   B->ops->destroy = MatDestroy_MUMPS;
3838   B->data         = (void *)mumps;
3839 
3840   *F               = B;
3841   mumps->id.job    = JOB_NULL;
3842   mumps->ICNTL_pre = NULL;
3843   mumps->CNTL_pre  = NULL;
3844   mumps->matstruc  = DIFFERENT_NONZERO_PATTERN;
3845   PetscFunctionReturn(PETSC_SUCCESS);
3846 }
3847 
3848 PETSC_INTERN PetscErrorCode MatSolverTypeRegister_MUMPS(void)
3849 {
3850   PetscFunctionBegin;
3851   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPIAIJ, MAT_FACTOR_LU, MatGetFactor_aij_mumps));
3852   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPIAIJ, MAT_FACTOR_CHOLESKY, MatGetFactor_aij_mumps));
3853   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPIBAIJ, MAT_FACTOR_LU, MatGetFactor_baij_mumps));
3854   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPIBAIJ, MAT_FACTOR_CHOLESKY, MatGetFactor_baij_mumps));
3855   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPISBAIJ, MAT_FACTOR_CHOLESKY, MatGetFactor_sbaij_mumps));
3856   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQAIJ, MAT_FACTOR_LU, MatGetFactor_aij_mumps));
3857   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQAIJ, MAT_FACTOR_CHOLESKY, MatGetFactor_aij_mumps));
3858   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQBAIJ, MAT_FACTOR_LU, MatGetFactor_baij_mumps));
3859   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQBAIJ, MAT_FACTOR_CHOLESKY, MatGetFactor_baij_mumps));
3860   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQSBAIJ, MAT_FACTOR_CHOLESKY, MatGetFactor_sbaij_mumps));
3861   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQSELL, MAT_FACTOR_LU, MatGetFactor_sell_mumps));
3862   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATDIAGONAL, MAT_FACTOR_LU, MatGetFactor_aij_mumps));
3863   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATDIAGONAL, MAT_FACTOR_CHOLESKY, MatGetFactor_aij_mumps));
3864   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQDENSE, MAT_FACTOR_LU, MatGetFactor_aij_mumps));
3865   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQDENSE, MAT_FACTOR_CHOLESKY, MatGetFactor_aij_mumps));
3866   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPIDENSE, MAT_FACTOR_LU, MatGetFactor_aij_mumps));
3867   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPIDENSE, MAT_FACTOR_CHOLESKY, MatGetFactor_aij_mumps));
3868   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATNEST, MAT_FACTOR_LU, MatGetFactor_nest_mumps));
3869   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATNEST, MAT_FACTOR_CHOLESKY, MatGetFactor_nest_mumps));
3870   PetscFunctionReturn(PETSC_SUCCESS);
3871 }
3872