Actual source code: mumps.c

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

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

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

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

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

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

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

     69: /* Cast PetscInt to PetscMUMPSInt. Usually there is no overflow since <a> is row/col indices or some small integers*/
     70: static inline PetscErrorCode PetscMUMPSIntCast(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: }

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

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

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

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

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

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

    167:   MatStructure   matstruc;
    168:   PetscMPIInt    myid, petsc_size;
    169:   PetscMUMPSInt *irn, *jcn;       /* the (i,j,v) triplets passed to mumps. */
    170:   PetscScalar   *val, *val_alloc; /* For some matrices, we can directly access their data array without a buffer. For others, we need a buffer. So comes val_alloc. */
    171:   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 *);

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

    199:   /* stuff used by petsc/mumps OpenMP support*/
    200:   PetscBool    use_petsc_omp_support;
    201:   PetscOmpCtrl omp_ctrl;             /* an OpenMP controller that blocked processes will release their CPU (MPI_Barrier does not have this guarantee) */
    202:   MPI_Comm     petsc_comm, omp_comm; /* petsc_comm is PETSc matrix's comm */
    203:   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: };

    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 */

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

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

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

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

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

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

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

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

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

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

    368:  */

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

    378:   PetscFunctionBegin;
    379:   PetscCall(MatSeqAIJGetArrayRead(A, &av));
    380:   if (reuse == MAT_INITIAL_MATRIX) {
    381:     nz = aa->nz;
    382:     ai = aa->i;
    383:     aj = aa->j;
    384:     PetscCall(PetscMalloc2(nz, &row, nz, &col));
    385:     for (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: }

    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;

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

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

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

    464: static PetscErrorCode MatConvertToTriples_seqsbaij_seqsbaij(Mat A, PetscInt shift, MatReuse reuse, Mat_MUMPS *mumps)
    465: {
    466:   const PetscInt *ai, *aj, *ajj;
    467:   PetscInt        bs;
    468:   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

    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;

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

    503:   nz = 0;
    504:   if (bs > 1) {
    505:     for (i = 0; i < mbs; i++) {
    506:       rnz = ai[i + 1] - ai[i];
    507:       ajj = aj + ai[i];
    508:       for (j = 0; j < rnz; j++) {
    509:         for (k = 0; k < bs; k++) {
    510:           for (m = 0; m < bs; m++) {
    511:             if (ajj[j] > i || k >= m) {
    512:               if (reuse == MAT_INITIAL_MATRIX) {
    513:                 PetscCall(PetscMUMPSIntCast(i * bs + m + shift, &row[nz]));
    514:                 PetscCall(PetscMUMPSIntCast(ajj[j] * bs + k + shift, &col[nz]));
    515:               }
    516:               val[nz++] = aa->a[(ai[i] + j) * bs2 + m + k * bs];
    517:             }
    518:           }
    519:         }
    520:       }
    521:     }
    522:   } else if (reuse == MAT_INITIAL_MATRIX) {
    523:     for (i = 0; i < mbs; i++) {
    524:       rnz = ai[i + 1] - ai[i];
    525:       ajj = aj + ai[i];
    526:       for (j = 0; j < rnz; j++) {
    527:         PetscCall(PetscMUMPSIntCast(i + shift, &row[nz]));
    528:         PetscCall(PetscMUMPSIntCast(ajj[j] + shift, &col[nz]));
    529:         nz++;
    530:       }
    531:     }
    532:     PetscCheck(nz == aa->nz, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Different numbers of nonzeros %" 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: }

    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

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

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

    649: static PetscErrorCode MatConvertToTriples_mpisbaij_mpisbaij(Mat A, PetscInt shift, MatReuse reuse, Mat_MUMPS *mumps)
    650: {
    651:   const PetscInt    *ai, *aj, *bi, *bj, *garray, *ajj, *bjj;
    652:   PetscInt           bs;
    653:   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

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

    679:   garray = mat->garray;

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

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

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

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

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

    756: static PetscErrorCode MatConvertToTriples_mpiaij_mpiaij(Mat A, PetscInt shift, MatReuse reuse, Mat_MUMPS *mumps)
    757: {
    758:   const PetscInt    *ai, *aj, *bi, *bj, *garray, m = A->rmap->n, *ajj, *bjj;
    759:   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;

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

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

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

    782:   if (reuse == MAT_INITIAL_MATRIX) {
    783:     nz = (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:   }

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

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

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

    828: static PetscErrorCode MatConvertToTriples_mpibaij_mpiaij(Mat A, PetscInt shift, MatReuse reuse, Mat_MUMPS *mumps)
    829: {
    830:   Mat_MPIBAIJ       *mat = (Mat_MPIBAIJ *)A->data;
    831:   Mat_SeqBAIJ       *aa  = (Mat_SeqBAIJ *)mat->A->data;
    832:   Mat_SeqBAIJ       *bb  = (Mat_SeqBAIJ *)mat->B->data;
    833:   const PetscInt    *ai = aa->i, *bi = bb->i, *aj = aa->j, *bj = bb->j, *ajj, *bjj;
    834:   const PetscInt    *garray = mat->garray, mbs = mat->mbs, rstart = A->rmap->rstart, cstart = A->cmap->rstart;
    835:   const PetscInt     bs2 = mat->bs2;
    836:   PetscInt           bs;
    837:   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;

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

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

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

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

    898: static PetscErrorCode MatConvertToTriples_mpiaij_mpisbaij(Mat A, PetscInt shift, MatReuse reuse, Mat_MUMPS *mumps)
    899: {
    900:   const PetscInt    *ai, *aj, *adiag, *bi, *bj, *garray, m = A->rmap->n, *ajj, *bjj;
    901:   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

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

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

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

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

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

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

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

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

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

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

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

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

    1057: // 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;

    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: }

    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;

    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, Mbs = 0;
    1110:     IS            *rows, *cols;
    1111:     PetscInt     **rows_idx, **cols_idx;

    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];

    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;

    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));

    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:     }

    1170:     /* Allocate total COO */
    1171:     totnnz = cumnnz;
    1172:     PetscCall(PetscMalloc2(totnnz, &irns, totnnz, &jcns));
    1173:     PetscCall(PetscMalloc1(totnnz, &vals));

    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;

    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, size, bs;
    1192:         PetscSF         csf;
    1193:         PetscBool       conjugate = PETSC_FALSE, swap = PETSC_FALSE;
    1194:         PetscLayout     cmap;
    1195:         PetscInt        innz;

    1197:         mumps->nest_vals_start[r * nc + c] = cumnnz;
    1198:         if (c == r) {
    1199:           PetscCall(ISGetSize(rows[r], &size));
    1200:           if (!mumps->nest_convert_to_triples[r * nc + c]) {
    1201:             for (PetscInt c = 0; c < nc && !sub; ++c) sub = mats[r][c]; // diagonal Mat is NULL, so start over from the beginning of the current row
    1202:           }
    1203:           PetscCall(MatGetBlockSize(sub, &bs));
    1204:           Mbs += size / bs;
    1205:         }
    1206:         if (!mumps->nest_convert_to_triples[r * nc + c]) continue;

    1208:         /* Extract inner blocks if needed */
    1209:         PetscCall(MatGetTranspose_TransposeVirtual(&sub, &conjugate, &vshift, &vscale, &swap));
    1210:         PetscCheck(vshift == 0.0, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Nonzero shift in parent MatShell");

    1212:         /* Get column layout to map off-process columns */
    1213:         PetscCall(MatGetLayouts(sub, NULL, &cmap));

    1215:         /* Get row start to map on-process rows */
    1216:         PetscCall(MatGetOwnershipRange(sub, &rst, NULL));

    1218:         /* Directly use the mumps datastructure and use C ordering for now */
    1219:         PetscCall((*mumps->nest_convert_to_triples[r * nc + c])(sub, 0, MAT_INITIAL_MATRIX, mumps));

    1221:         /* Swap the role of rows and columns indices for transposed blocks
    1222:            since we need values with global final ordering */
    1223:         if (swap) {
    1224:           cidx = rows_idx[r];
    1225:           ridx = cols_idx[c];
    1226:         }

    1228:         /* Communicate column indices
    1229:            This could have been done with a single SF but it would have complicated the code a lot.
    1230:            But since we do it only once, we pay the price of setting up an SF for each block */
    1231:         if (PetscDefined(USE_64BIT_INDICES)) {
    1232:           for (PetscInt k = 0; k < mumps->nnz; k++) pjcns_w[k] = mumps->jcn[k];
    1233:         } else pjcns_w = (PetscInt *)mumps->jcn; /* This cast is needed only to silence warnings for 64bit integers builds */
    1234:         PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &csf));
    1235:         PetscCall(PetscIntCast(mumps->nnz, &innz));
    1236:         PetscCall(PetscSFSetGraphLayout(csf, cmap, innz, NULL, PETSC_OWN_POINTER, pjcns_w));
    1237:         PetscCall(PetscSFBcastBegin(csf, MPIU_INT, cidx, pjcns_w, MPI_REPLACE));
    1238:         PetscCall(PetscSFBcastEnd(csf, MPIU_INT, cidx, pjcns_w, MPI_REPLACE));
    1239:         PetscCall(PetscSFDestroy(&csf));

    1241:         /* Import indices: use direct map for rows and mapped indices for columns */
    1242:         if (swap) {
    1243:           for (PetscInt k = 0; k < mumps->nnz; k++) {
    1244:             PetscCall(PetscMUMPSIntCast(ridx[mumps->irn[k] - rst] + shift, &jcns[cumnnz + k]));
    1245:             PetscCall(PetscMUMPSIntCast(pjcns_w[k] + shift, &irns[cumnnz + k]));
    1246:           }
    1247:         } else {
    1248:           for (PetscInt k = 0; k < mumps->nnz; k++) {
    1249:             PetscCall(PetscMUMPSIntCast(ridx[mumps->irn[k] - rst] + shift, &irns[cumnnz + k]));
    1250:             PetscCall(PetscMUMPSIntCast(pjcns_w[k] + shift, &jcns[cumnnz + k]));
    1251:           }
    1252:         }

    1254:         /* Import values to full COO */
    1255:         if (conjugate) { /* conjugate the entries */
    1256:           PetscScalar *v = vals + cumnnz;
    1257:           for (PetscInt k = 0; k < mumps->nnz; k++) v[k] = vscale * PetscConj(mumps->val[k]);
    1258:         } else if (vscale != 1.0) {
    1259:           PetscScalar *v = vals + cumnnz;
    1260:           for (PetscInt k = 0; k < mumps->nnz; k++) v[k] = vscale * mumps->val[k];
    1261:         } else PetscCall(PetscArraycpy(vals + cumnnz, mumps->val, mumps->nnz));

    1263:         /* Shift new starting point and sanity check */
    1264:         cumnnz += mumps->nnz;
    1265:         PetscCheck(cumnnz <= totnnz, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unexpected number of nonzeros %" PetscCount_FMT " != %" PetscCount_FMT, cumnnz, totnnz);

    1267:         /* Free scratch memory */
    1268:         PetscCall(PetscFree2(mumps->irn, mumps->jcn));
    1269:         PetscCall(PetscFree(mumps->val_alloc));
    1270:         mumps->val = NULL;
    1271:         mumps->nnz = 0;
    1272:       }
    1273:     }
    1274:     if (mumps->id.ICNTL(15) == 1) {
    1275:       if (Mbs != A->rmap->N) {
    1276:         PetscMPIInt rank, size;

    1278:         PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)A), &rank));
    1279:         PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
    1280:         if (rank == 0) {
    1281:           PetscInt shift = 0;

    1283:           PetscCall(PetscMUMPSIntCast(Mbs, &mumps->id.nblk));
    1284:           PetscCall(PetscFree(mumps->id.blkptr));
    1285:           PetscCall(PetscMalloc1(Mbs + 1, &mumps->id.blkptr));
    1286:           mumps->id.blkptr[0] = 1;
    1287:           for (PetscInt i = 0; i < size; ++i) {
    1288:             for (PetscInt r = 0; r < nr; r++) {
    1289:               Mat             sub = mats[r][r];
    1290:               const PetscInt *ranges;
    1291:               PetscInt        bs;

    1293:               for (PetscInt c = 0; c < nc && !sub; ++c) sub = mats[r][c]; // diagonal Mat is NULL, so start over from the beginning of the current row
    1294:               PetscCall(MatGetOwnershipRanges(sub, &ranges));
    1295:               PetscCall(MatGetBlockSize(sub, &bs));
    1296:               for (PetscInt j = 0, start = mumps->id.blkptr[shift] + bs; j < ranges[i + 1] - ranges[i]; j += bs) PetscCall(PetscMUMPSIntCast(start + j, mumps->id.blkptr + shift + j / bs + 1));
    1297:               shift += (ranges[i + 1] - ranges[i]) / bs;
    1298:             }
    1299:           }
    1300:         }
    1301:       } else mumps->id.ICNTL(15) = 0;
    1302:     }
    1303:     if (PetscDefined(USE_64BIT_INDICES)) PetscCall(PetscFree(pjcns_w));
    1304:     for (PetscInt r = 0; r < nr; r++) PetscCall(ISRestoreIndices(rows[r], (const PetscInt **)&rows_idx[r]));
    1305:     for (PetscInt c = 0; c < nc; c++) PetscCall(ISRestoreIndices(cols[c], (const PetscInt **)&cols_idx[c]));
    1306:     PetscCall(PetscFree4(rows, cols, rows_idx, cols_idx));
    1307:     if (!chol) PetscCheck(cumnnz == totnnz, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Different number of nonzeros %" PetscCount_FMT " != %" PetscCount_FMT, cumnnz, totnnz);
    1308:     mumps->nest_vals_start[nr * nc] = cumnnz;

    1310:     /* Set pointers for final MUMPS data structure */
    1311:     mumps->nest_vals = vals;
    1312:     mumps->val_alloc = NULL; /* do not use val_alloc since it may be reallocated with the OMP callpath */
    1313:     mumps->val       = vals;
    1314:     mumps->irn       = irns;
    1315:     mumps->jcn       = jcns;
    1316:     mumps->nnz       = cumnnz;
    1317:   } else {
    1318:     PetscScalar *oval = mumps->nest_vals;
    1319:     for (PetscInt r = 0; r < nr; r++) {
    1320:       for (PetscInt c = 0; c < nc; c++) {
    1321:         PetscBool   conjugate = PETSC_FALSE;
    1322:         Mat         sub       = mats[r][c];
    1323:         PetscScalar vscale = 1.0, vshift = 0.0;
    1324:         PetscInt    midx = r * nc + c;

    1326:         if (!mumps->nest_convert_to_triples[midx]) continue;
    1327:         PetscCall(MatGetTranspose_TransposeVirtual(&sub, &conjugate, &vshift, &vscale, NULL));
    1328:         PetscCheck(vshift == 0.0, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Nonzero shift in parent MatShell");
    1329:         mumps->val = oval + mumps->nest_vals_start[midx];
    1330:         PetscCall((*mumps->nest_convert_to_triples[midx])(sub, shift, MAT_REUSE_MATRIX, mumps));
    1331:         if (conjugate) {
    1332:           PetscCount nnz = mumps->nest_vals_start[midx + 1] - mumps->nest_vals_start[midx];
    1333:           for (PetscCount k = 0; k < nnz; k++) mumps->val[k] = vscale * PetscConj(mumps->val[k]);
    1334:         } else if (vscale != 1.0) {
    1335:           PetscCount nnz = mumps->nest_vals_start[midx + 1] - mumps->nest_vals_start[midx];
    1336:           for (PetscCount k = 0; k < nnz; k++) mumps->val[k] *= vscale;
    1337:         }
    1338:       }
    1339:     }
    1340:     mumps->val = oval;
    1341:   }
    1342:   PetscFunctionReturn(PETSC_SUCCESS);
    1343: }

    1345: static PetscErrorCode MatDestroy_MUMPS(Mat A)
    1346: {
    1347:   Mat_MUMPS *mumps = (Mat_MUMPS *)A->data;

    1349:   PetscFunctionBegin;
    1350:   PetscCall(PetscFree2(mumps->id.sol_loc, mumps->id.isol_loc));
    1351:   PetscCall(VecScatterDestroy(&mumps->scat_rhs));
    1352:   PetscCall(VecScatterDestroy(&mumps->scat_sol));
    1353:   PetscCall(VecDestroy(&mumps->b_seq));
    1354:   PetscCall(VecDestroy(&mumps->x_seq));
    1355:   PetscCall(PetscFree(mumps->id.perm_in));
    1356:   PetscCall(PetscFree(mumps->id.blkvar));
    1357:   PetscCall(PetscFree(mumps->id.blkptr));
    1358:   PetscCall(PetscFree2(mumps->irn, mumps->jcn));
    1359:   PetscCall(PetscFree(mumps->val_alloc));
    1360:   PetscCall(PetscFree(mumps->info));
    1361:   PetscCall(PetscFree(mumps->ICNTL_pre));
    1362:   PetscCall(PetscFree(mumps->CNTL_pre));
    1363:   PetscCall(MatMumpsResetSchur_Private(mumps));
    1364:   if (mumps->id.job != JOB_NULL) { /* cannot call PetscMUMPS_c() if JOB_INIT has never been called for this instance */
    1365:     mumps->id.job = JOB_END;
    1366:     PetscMUMPS_c(mumps);
    1367:     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));
    1368:     if (mumps->mumps_comm != MPI_COMM_NULL) {
    1369:       if (PetscDefined(HAVE_OPENMP_SUPPORT) && mumps->use_petsc_omp_support) PetscCallMPI(MPI_Comm_free(&mumps->mumps_comm));
    1370:       else PetscCall(PetscCommRestoreComm(PetscObjectComm((PetscObject)A), &mumps->mumps_comm));
    1371:     }
    1372:   }
    1373: #if defined(PETSC_HAVE_OPENMP_SUPPORT)
    1374:   if (mumps->use_petsc_omp_support) {
    1375:     PetscCall(PetscOmpCtrlDestroy(&mumps->omp_ctrl));
    1376:     PetscCall(PetscFree2(mumps->rhs_loc, mumps->rhs_recvbuf));
    1377:     PetscCall(PetscFree3(mumps->rhs_nrow, mumps->rhs_recvcounts, mumps->rhs_disps));
    1378:   }
    1379: #endif
    1380:   PetscCall(PetscFree(mumps->ia_alloc));
    1381:   PetscCall(PetscFree(mumps->ja_alloc));
    1382:   PetscCall(PetscFree(mumps->recvcount));
    1383:   PetscCall(PetscFree(mumps->reqs));
    1384:   PetscCall(PetscFree(mumps->irhs_loc));
    1385:   PetscCall(PetscFree2(mumps->nest_vals_start, mumps->nest_convert_to_triples));
    1386:   PetscCall(PetscFree(mumps->nest_vals));
    1387:   PetscCall(PetscFree(A->data));

    1389:   /* clear composed functions */
    1390:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatFactorGetSolverType_C", NULL));
    1391:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatFactorSetSchurIS_C", NULL));
    1392:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatFactorCreateSchurComplement_C", NULL));
    1393:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsSetIcntl_C", NULL));
    1394:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetIcntl_C", NULL));
    1395:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsSetCntl_C", NULL));
    1396:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetCntl_C", NULL));
    1397:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetInfo_C", NULL));
    1398:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetInfog_C", NULL));
    1399:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetRinfo_C", NULL));
    1400:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetRinfog_C", NULL));
    1401:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetNullPivots_C", NULL));
    1402:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetInverse_C", NULL));
    1403:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsGetInverseTranspose_C", NULL));
    1404:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatMumpsSetBlk_C", NULL));
    1405:   PetscFunctionReturn(PETSC_SUCCESS);
    1406: }

    1408: /* Set up the distributed RHS info for MUMPS. <nrhs> is the number of RHS. <array> points to start of RHS on the local processor. */
    1409: static PetscErrorCode MatMumpsSetUpDistRHSInfo(Mat A, PetscInt nrhs, const PetscScalar *array)
    1410: {
    1411:   Mat_MUMPS        *mumps   = (Mat_MUMPS *)A->data;
    1412:   const PetscMPIInt ompsize = mumps->omp_comm_size;
    1413:   PetscInt          i, m, M, rstart;

    1415:   PetscFunctionBegin;
    1416:   PetscCall(MatGetSize(A, &M, NULL));
    1417:   PetscCall(MatGetLocalSize(A, &m, NULL));
    1418:   PetscCheck(M <= PETSC_MUMPS_INT_MAX, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "PetscInt too long for PetscMUMPSInt");
    1419:   if (ompsize == 1) {
    1420:     if (!mumps->irhs_loc) {
    1421:       mumps->nloc_rhs = (PetscMUMPSInt)m;
    1422:       PetscCall(PetscMalloc1(m, &mumps->irhs_loc));
    1423:       PetscCall(MatGetOwnershipRange(A, &rstart, NULL));
    1424:       for (i = 0; i < m; i++) PetscCall(PetscMUMPSIntCast(rstart + i + 1, &mumps->irhs_loc[i])); /* use 1-based indices */
    1425:     }
    1426:     mumps->id.rhs_loc = (MumpsScalar *)array;
    1427:   } else {
    1428: #if defined(PETSC_HAVE_OPENMP_SUPPORT)
    1429:     const PetscInt *ranges;
    1430:     PetscMPIInt     j, k, sendcount, *petsc_ranks, *omp_ranks;
    1431:     MPI_Group       petsc_group, omp_group;
    1432:     PetscScalar    *recvbuf = NULL;

    1434:     if (mumps->is_omp_master) {
    1435:       /* Lazily initialize the omp stuff for distributed rhs */
    1436:       if (!mumps->irhs_loc) {
    1437:         PetscCall(PetscMalloc2(ompsize, &omp_ranks, ompsize, &petsc_ranks));
    1438:         PetscCall(PetscMalloc3(ompsize, &mumps->rhs_nrow, ompsize, &mumps->rhs_recvcounts, ompsize, &mumps->rhs_disps));
    1439:         PetscCallMPI(MPI_Comm_group(mumps->petsc_comm, &petsc_group));
    1440:         PetscCallMPI(MPI_Comm_group(mumps->omp_comm, &omp_group));
    1441:         for (j = 0; j < ompsize; j++) omp_ranks[j] = j;
    1442:         PetscCallMPI(MPI_Group_translate_ranks(omp_group, ompsize, omp_ranks, petsc_group, petsc_ranks));

    1444:         /* Populate mumps->irhs_loc[], rhs_nrow[] */
    1445:         mumps->nloc_rhs = 0;
    1446:         PetscCall(MatGetOwnershipRanges(A, &ranges));
    1447:         for (j = 0; j < ompsize; j++) {
    1448:           mumps->rhs_nrow[j] = ranges[petsc_ranks[j] + 1] - ranges[petsc_ranks[j]];
    1449:           mumps->nloc_rhs += mumps->rhs_nrow[j];
    1450:         }
    1451:         PetscCall(PetscMalloc1(mumps->nloc_rhs, &mumps->irhs_loc));
    1452:         for (j = k = 0; j < ompsize; j++) {
    1453:           for (i = ranges[petsc_ranks[j]]; i < ranges[petsc_ranks[j] + 1]; i++, k++) PetscCall(PetscMUMPSIntCast(i + 1, &mumps->irhs_loc[k])); /* uses 1-based indices */
    1454:         }

    1456:         PetscCall(PetscFree2(omp_ranks, petsc_ranks));
    1457:         PetscCallMPI(MPI_Group_free(&petsc_group));
    1458:         PetscCallMPI(MPI_Group_free(&omp_group));
    1459:       }

    1461:       /* Realloc buffers when current nrhs is bigger than what we have met */
    1462:       if (nrhs > mumps->max_nrhs) {
    1463:         PetscCall(PetscFree2(mumps->rhs_loc, mumps->rhs_recvbuf));
    1464:         PetscCall(PetscMalloc2(mumps->nloc_rhs * nrhs, &mumps->rhs_loc, mumps->nloc_rhs * nrhs, &mumps->rhs_recvbuf));
    1465:         mumps->max_nrhs = nrhs;
    1466:       }

    1468:       /* Setup recvcounts[], disps[], recvbuf on omp rank 0 for the upcoming MPI_Gatherv */
    1469:       for (j = 0; j < ompsize; j++) PetscCall(PetscMPIIntCast(mumps->rhs_nrow[j] * nrhs, &mumps->rhs_recvcounts[j]));
    1470:       mumps->rhs_disps[0] = 0;
    1471:       for (j = 1; j < ompsize; j++) {
    1472:         mumps->rhs_disps[j] = mumps->rhs_disps[j - 1] + mumps->rhs_recvcounts[j - 1];
    1473:         PetscCheck(mumps->rhs_disps[j] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "PetscMPIInt overflow!");
    1474:       }
    1475:       recvbuf = (nrhs == 1) ? mumps->rhs_loc : mumps->rhs_recvbuf; /* Directly use rhs_loc[] as recvbuf. Single rhs is common in Ax=b */
    1476:     }

    1478:     PetscCall(PetscMPIIntCast(m * nrhs, &sendcount));
    1479:     PetscCallMPI(MPI_Gatherv(array, sendcount, MPIU_SCALAR, recvbuf, mumps->rhs_recvcounts, mumps->rhs_disps, MPIU_SCALAR, 0, mumps->omp_comm));

    1481:     if (mumps->is_omp_master) {
    1482:       if (nrhs > 1) { /* Copy & re-arrange data from rhs_recvbuf[] to mumps->rhs_loc[] only when there are multiple rhs */
    1483:         PetscScalar *dst, *dstbase = mumps->rhs_loc;
    1484:         for (j = 0; j < ompsize; j++) {
    1485:           const PetscScalar *src = mumps->rhs_recvbuf + mumps->rhs_disps[j];
    1486:           dst                    = dstbase;
    1487:           for (i = 0; i < nrhs; i++) {
    1488:             PetscCall(PetscArraycpy(dst, src, mumps->rhs_nrow[j]));
    1489:             src += mumps->rhs_nrow[j];
    1490:             dst += mumps->nloc_rhs;
    1491:           }
    1492:           dstbase += mumps->rhs_nrow[j];
    1493:         }
    1494:       }
    1495:       mumps->id.rhs_loc = (MumpsScalar *)mumps->rhs_loc;
    1496:     }
    1497: #endif /* PETSC_HAVE_OPENMP_SUPPORT */
    1498:   }
    1499:   mumps->id.nrhs     = (PetscMUMPSInt)nrhs;
    1500:   mumps->id.nloc_rhs = (PetscMUMPSInt)mumps->nloc_rhs;
    1501:   mumps->id.lrhs_loc = mumps->nloc_rhs;
    1502:   mumps->id.irhs_loc = mumps->irhs_loc;
    1503:   PetscFunctionReturn(PETSC_SUCCESS);
    1504: }

    1506: static PetscErrorCode MatSolve_MUMPS(Mat A, Vec b, Vec x)
    1507: {
    1508:   Mat_MUMPS         *mumps  = (Mat_MUMPS *)A->data;
    1509:   const PetscScalar *rarray = NULL;
    1510:   PetscScalar       *array;
    1511:   IS                 is_iden, is_petsc;
    1512:   PetscInt           i;
    1513:   PetscBool          second_solve = PETSC_FALSE;
    1514:   static PetscBool   cite1 = PETSC_FALSE, cite2 = PETSC_FALSE;

    1516:   PetscFunctionBegin;
    1517:   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 "
    1518:                                    "Journal on Matrix Analysis and Applications},\n  volume = {23},\n  number = {1},\n  pages = {15--41},\n  year = {2001}\n}\n",
    1519:                                    &cite1));
    1520:   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 "
    1521:                                    "Computing},\n  volume = {32},\n  number = {2},\n  pages = {136--156},\n  year = {2006}\n}\n",
    1522:                                    &cite2));

    1524:   PetscCall(VecFlag(x, A->factorerrortype));
    1525:   if (A->factorerrortype) {
    1526:     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)));
    1527:     PetscFunctionReturn(PETSC_SUCCESS);
    1528:   }

    1530:   mumps->id.nrhs = 1;
    1531:   if (mumps->petsc_size > 1) {
    1532:     if (mumps->ICNTL20 == 10) {
    1533:       mumps->id.ICNTL(20) = 10; /* dense distributed RHS */
    1534:       PetscCall(VecGetArrayRead(b, &rarray));
    1535:       PetscCall(MatMumpsSetUpDistRHSInfo(A, 1, rarray));
    1536:     } else {
    1537:       mumps->id.ICNTL(20) = 0; /* dense centralized RHS; Scatter b into a sequential rhs vector*/
    1538:       PetscCall(VecScatterBegin(mumps->scat_rhs, b, mumps->b_seq, INSERT_VALUES, SCATTER_FORWARD));
    1539:       PetscCall(VecScatterEnd(mumps->scat_rhs, b, mumps->b_seq, INSERT_VALUES, SCATTER_FORWARD));
    1540:       if (!mumps->myid) {
    1541:         PetscCall(VecGetArray(mumps->b_seq, &array));
    1542:         mumps->id.rhs = (MumpsScalar *)array;
    1543:       }
    1544:     }
    1545:   } else {                   /* petsc_size == 1 */
    1546:     mumps->id.ICNTL(20) = 0; /* dense centralized RHS */
    1547:     PetscCall(VecCopy(b, x));
    1548:     PetscCall(VecGetArray(x, &array));
    1549:     mumps->id.rhs = (MumpsScalar *)array;
    1550:   }

    1552:   /*
    1553:      handle condensation step of Schur complement (if any)
    1554:      We set by default ICNTL(26) == -1 when Schur indices have been provided by the user.
    1555:      According to MUMPS (5.0.0) manual, any value should be harmful during the factorization phase
    1556:      Unless the user provides a valid value for ICNTL(26), MatSolve and MatMatSolve routines solve the full system.
    1557:      This requires an extra call to PetscMUMPS_c and the computation of the factors for S
    1558:   */
    1559:   if (mumps->id.size_schur > 0) {
    1560:     PetscCheck(mumps->petsc_size <= 1, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Parallel Schur complements not yet supported from PETSc");
    1561:     if (mumps->id.ICNTL(26) < 0 || mumps->id.ICNTL(26) > 2) {
    1562:       second_solve = PETSC_TRUE;
    1563:       PetscCall(MatMumpsHandleSchur_Private(A, PETSC_FALSE));
    1564:       mumps->id.ICNTL(26) = 1; /* condensation phase */
    1565:     } else if (mumps->id.ICNTL(26) == 1) PetscCall(MatMumpsHandleSchur_Private(A, PETSC_FALSE));
    1566:   }
    1567:   /* solve phase */
    1568:   mumps->id.job = JOB_SOLVE;
    1569:   PetscMUMPS_c(mumps);
    1570:   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));

    1572:   /* handle expansion step of Schur complement (if any) */
    1573:   if (second_solve) PetscCall(MatMumpsHandleSchur_Private(A, PETSC_TRUE));
    1574:   else if (mumps->id.ICNTL(26) == 1) {
    1575:     PetscCall(MatMumpsSolveSchur_Private(A));
    1576:     for (i = 0; i < mumps->id.size_schur; ++i) {
    1577: #if !defined(PETSC_USE_COMPLEX)
    1578:       PetscScalar val = mumps->id.redrhs[i];
    1579: #else
    1580:       PetscScalar val = mumps->id.redrhs[i].r + PETSC_i * mumps->id.redrhs[i].i;
    1581: #endif
    1582:       array[mumps->id.listvar_schur[i] - 1] = val;
    1583:     }
    1584:   }

    1586:   if (mumps->petsc_size > 1) { /* convert mumps distributed solution to PETSc mpi x */
    1587:     if (mumps->scat_sol && mumps->ICNTL9_pre != mumps->id.ICNTL(9)) {
    1588:       /* when id.ICNTL(9) changes, the contents of lsol_loc may change (not its size, lsol_loc), recreates scat_sol */
    1589:       PetscCall(VecScatterDestroy(&mumps->scat_sol));
    1590:     }
    1591:     if (!mumps->scat_sol) { /* create scatter scat_sol */
    1592:       PetscInt *isol2_loc = NULL;
    1593:       PetscCall(ISCreateStride(PETSC_COMM_SELF, mumps->id.lsol_loc, 0, 1, &is_iden)); /* from */
    1594:       PetscCall(PetscMalloc1(mumps->id.lsol_loc, &isol2_loc));
    1595:       for (i = 0; i < mumps->id.lsol_loc; i++) isol2_loc[i] = mumps->id.isol_loc[i] - 1;                        /* change Fortran style to C style */
    1596:       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, mumps->id.lsol_loc, isol2_loc, PETSC_OWN_POINTER, &is_petsc)); /* to */
    1597:       PetscCall(VecScatterCreate(mumps->x_seq, is_iden, x, is_petsc, &mumps->scat_sol));
    1598:       PetscCall(ISDestroy(&is_iden));
    1599:       PetscCall(ISDestroy(&is_petsc));
    1600:       mumps->ICNTL9_pre = mumps->id.ICNTL(9); /* save current value of id.ICNTL(9) */
    1601:     }

    1603:     PetscCall(VecScatterBegin(mumps->scat_sol, mumps->x_seq, x, INSERT_VALUES, SCATTER_FORWARD));
    1604:     PetscCall(VecScatterEnd(mumps->scat_sol, mumps->x_seq, x, INSERT_VALUES, SCATTER_FORWARD));
    1605:   }

    1607:   if (mumps->petsc_size > 1) {
    1608:     if (mumps->ICNTL20 == 10) {
    1609:       PetscCall(VecRestoreArrayRead(b, &rarray));
    1610:     } else if (!mumps->myid) {
    1611:       PetscCall(VecRestoreArray(mumps->b_seq, &array));
    1612:     }
    1613:   } else PetscCall(VecRestoreArray(x, &array));

    1615:   PetscCall(PetscLogFlops(2.0 * PetscMax(0, (mumps->id.INFO(28) >= 0 ? mumps->id.INFO(28) : -1000000 * mumps->id.INFO(28)) - A->cmap->n)));
    1616:   PetscFunctionReturn(PETSC_SUCCESS);
    1617: }

    1619: static PetscErrorCode MatSolveTranspose_MUMPS(Mat A, Vec b, Vec x)
    1620: {
    1621:   Mat_MUMPS          *mumps = (Mat_MUMPS *)A->data;
    1622:   const PetscMUMPSInt value = mumps->id.ICNTL(9);

    1624:   PetscFunctionBegin;
    1625:   mumps->id.ICNTL(9) = 0;
    1626:   PetscCall(MatSolve_MUMPS(A, b, x));
    1627:   mumps->id.ICNTL(9) = value;
    1628:   PetscFunctionReturn(PETSC_SUCCESS);
    1629: }

    1631: static PetscErrorCode MatMatSolve_MUMPS(Mat A, Mat B, Mat X)
    1632: {
    1633:   Mat                Bt = NULL;
    1634:   PetscBool          denseX, denseB, flg, flgT;
    1635:   Mat_MUMPS         *mumps = (Mat_MUMPS *)A->data;
    1636:   PetscInt           i, nrhs, M, nrhsM;
    1637:   PetscScalar       *array;
    1638:   const PetscScalar *rbray;
    1639:   PetscInt           lsol_loc, nlsol_loc, *idxx, iidx = 0;
    1640:   PetscMUMPSInt     *isol_loc, *isol_loc_save;
    1641:   PetscScalar       *bray, *sol_loc, *sol_loc_save;
    1642:   IS                 is_to, is_from;
    1643:   PetscInt           k, proc, j, m, myrstart;
    1644:   const PetscInt    *rstart;
    1645:   Vec                v_mpi, msol_loc;
    1646:   VecScatter         scat_sol;
    1647:   Vec                b_seq;
    1648:   VecScatter         scat_rhs;
    1649:   PetscScalar       *aa;
    1650:   PetscInt           spnr, *ia, *ja;
    1651:   Mat_MPIAIJ        *b = NULL;

    1653:   PetscFunctionBegin;
    1654:   PetscCall(PetscObjectTypeCompareAny((PetscObject)X, &denseX, MATSEQDENSE, MATMPIDENSE, NULL));
    1655:   PetscCheck(denseX, PetscObjectComm((PetscObject)X), PETSC_ERR_ARG_WRONG, "Matrix X must be MATDENSE matrix");

    1657:   PetscCall(PetscObjectTypeCompareAny((PetscObject)B, &denseB, MATSEQDENSE, MATMPIDENSE, NULL));
    1658:   if (denseB) {
    1659:     PetscCheck(B->rmap->n == X->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Matrix B and X must have same row distribution");
    1660:     mumps->id.ICNTL(20) = 0; /* dense RHS */
    1661:   } else {                   /* sparse B */
    1662:     PetscCheck(X != B, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_IDN, "X and B must be different matrices");
    1663:     PetscCall(PetscObjectTypeCompare((PetscObject)B, MATTRANSPOSEVIRTUAL, &flgT));
    1664:     PetscCheck(flgT, PetscObjectComm((PetscObject)B), PETSC_ERR_ARG_WRONG, "Matrix B must be MATTRANSPOSEVIRTUAL matrix");
    1665:     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));
    1666:     /* input B is transpose of actual RHS matrix,
    1667:      because mumps requires sparse compressed COLUMN storage! See MatMatTransposeSolve_MUMPS() */
    1668:     PetscCall(MatTransposeGetMat(B, &Bt));
    1669:     mumps->id.ICNTL(20) = 1; /* sparse RHS */
    1670:   }

    1672:   PetscCall(MatGetSize(B, &M, &nrhs));
    1673:   PetscCall(PetscIntMultError(nrhs, M, &nrhsM));
    1674:   mumps->id.nrhs = (PetscMUMPSInt)nrhs;
    1675:   mumps->id.lrhs = (PetscMUMPSInt)M;
    1676:   mumps->id.rhs  = NULL;

    1678:   if (mumps->petsc_size == 1) {
    1679:     PetscScalar *aa;
    1680:     PetscInt     spnr, *ia, *ja;
    1681:     PetscBool    second_solve = PETSC_FALSE;

    1683:     PetscCall(MatDenseGetArray(X, &array));
    1684:     mumps->id.rhs = (MumpsScalar *)array;

    1686:     if (denseB) {
    1687:       /* copy B to X */
    1688:       PetscCall(MatDenseGetArrayRead(B, &rbray));
    1689:       PetscCall(PetscArraycpy(array, rbray, nrhsM));
    1690:       PetscCall(MatDenseRestoreArrayRead(B, &rbray));
    1691:     } else { /* sparse B */
    1692:       PetscCall(MatSeqAIJGetArray(Bt, &aa));
    1693:       PetscCall(MatGetRowIJ(Bt, 1, PETSC_FALSE, PETSC_FALSE, &spnr, (const PetscInt **)&ia, (const PetscInt **)&ja, &flg));
    1694:       PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot get IJ structure");
    1695:       PetscCall(PetscMUMPSIntCSRCast(mumps, spnr, ia, ja, &mumps->id.irhs_ptr, &mumps->id.irhs_sparse, &mumps->id.nz_rhs));
    1696:       mumps->id.rhs_sparse = (MumpsScalar *)aa;
    1697:     }
    1698:     /* handle condensation step of Schur complement (if any) */
    1699:     if (mumps->id.size_schur > 0) {
    1700:       if (mumps->id.ICNTL(26) < 0 || mumps->id.ICNTL(26) > 2) {
    1701:         second_solve = PETSC_TRUE;
    1702:         PetscCall(MatMumpsHandleSchur_Private(A, PETSC_FALSE));
    1703:         mumps->id.ICNTL(26) = 1; /* condensation phase */
    1704:       } else if (mumps->id.ICNTL(26) == 1) PetscCall(MatMumpsHandleSchur_Private(A, PETSC_FALSE));
    1705:     }
    1706:     /* solve phase */
    1707:     mumps->id.job = JOB_SOLVE;
    1708:     PetscMUMPS_c(mumps);
    1709:     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));

    1711:     /* handle expansion step of Schur complement (if any) */
    1712:     if (second_solve) PetscCall(MatMumpsHandleSchur_Private(A, PETSC_TRUE));
    1713:     else if (mumps->id.ICNTL(26) == 1) {
    1714:       PetscCall(MatMumpsSolveSchur_Private(A));
    1715:       for (j = 0; j < nrhs; ++j)
    1716:         for (i = 0; i < mumps->id.size_schur; ++i) {
    1717: #if !defined(PETSC_USE_COMPLEX)
    1718:           PetscScalar val = mumps->id.redrhs[i + j * mumps->id.lredrhs];
    1719: #else
    1720:           PetscScalar val = mumps->id.redrhs[i + j * mumps->id.lredrhs].r + PETSC_i * mumps->id.redrhs[i + j * mumps->id.lredrhs].i;
    1721: #endif
    1722:           array[mumps->id.listvar_schur[i] - 1 + j * M] = val;
    1723:         }
    1724:     }
    1725:     if (!denseB) { /* sparse B */
    1726:       PetscCall(MatSeqAIJRestoreArray(Bt, &aa));
    1727:       PetscCall(MatRestoreRowIJ(Bt, 1, PETSC_FALSE, PETSC_FALSE, &spnr, (const PetscInt **)&ia, (const PetscInt **)&ja, &flg));
    1728:       PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot restore IJ structure");
    1729:     }
    1730:     PetscCall(MatDenseRestoreArray(X, &array));
    1731:     PetscFunctionReturn(PETSC_SUCCESS);
    1732:   }

    1734:   /* parallel case: MUMPS requires rhs B to be centralized on the host! */
    1735:   PetscCheck(!mumps->id.ICNTL(19), PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Parallel Schur complements not yet supported from PETSc");

    1737:   /* create msol_loc to hold mumps local solution */
    1738:   isol_loc_save = mumps->id.isol_loc; /* save it for MatSolve() */
    1739:   sol_loc_save  = (PetscScalar *)mumps->id.sol_loc;

    1741:   lsol_loc = mumps->id.lsol_loc;
    1742:   PetscCall(PetscIntMultError(nrhs, lsol_loc, &nlsol_loc)); /* length of sol_loc */
    1743:   PetscCall(PetscMalloc2(nlsol_loc, &sol_loc, lsol_loc, &isol_loc));
    1744:   mumps->id.sol_loc  = (MumpsScalar *)sol_loc;
    1745:   mumps->id.isol_loc = isol_loc;

    1747:   PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, nlsol_loc, (PetscScalar *)sol_loc, &msol_loc));

    1749:   if (denseB) {
    1750:     if (mumps->ICNTL20 == 10) {
    1751:       mumps->id.ICNTL(20) = 10; /* dense distributed RHS */
    1752:       PetscCall(MatDenseGetArrayRead(B, &rbray));
    1753:       PetscCall(MatMumpsSetUpDistRHSInfo(A, nrhs, rbray));
    1754:       PetscCall(MatDenseRestoreArrayRead(B, &rbray));
    1755:       PetscCall(MatGetLocalSize(B, &m, NULL));
    1756:       PetscCall(VecCreateMPIWithArray(PetscObjectComm((PetscObject)B), 1, nrhs * m, nrhsM, NULL, &v_mpi));
    1757:     } else {
    1758:       mumps->id.ICNTL(20) = 0; /* dense centralized RHS */
    1759:       /* TODO: Because of non-contiguous indices, the created vecscatter scat_rhs is not done in MPI_Gather, resulting in
    1760:         very inefficient communication. An optimization is to use VecScatterCreateToZero to gather B to rank 0. Then on rank
    1761:         0, re-arrange B into desired order, which is a local operation.
    1762:       */

    1764:       /* scatter v_mpi to b_seq because MUMPS before 5.3.0 only supports centralized rhs */
    1765:       /* wrap dense rhs matrix B into a vector v_mpi */
    1766:       PetscCall(MatGetLocalSize(B, &m, NULL));
    1767:       PetscCall(MatDenseGetArray(B, &bray));
    1768:       PetscCall(VecCreateMPIWithArray(PetscObjectComm((PetscObject)B), 1, nrhs * m, nrhsM, (const PetscScalar *)bray, &v_mpi));
    1769:       PetscCall(MatDenseRestoreArray(B, &bray));

    1771:       /* scatter v_mpi to b_seq in proc[0]. MUMPS requires rhs to be centralized on the host! */
    1772:       if (!mumps->myid) {
    1773:         PetscInt *idx;
    1774:         /* idx: maps from k-th index of v_mpi to (i,j)-th global entry of B */
    1775:         PetscCall(PetscMalloc1(nrhsM, &idx));
    1776:         PetscCall(MatGetOwnershipRanges(B, &rstart));
    1777:         for (proc = 0, k = 0; proc < mumps->petsc_size; proc++) {
    1778:           for (j = 0; j < nrhs; j++) {
    1779:             for (i = rstart[proc]; i < rstart[proc + 1]; i++) idx[k++] = j * M + i;
    1780:           }
    1781:         }

    1783:         PetscCall(VecCreateSeq(PETSC_COMM_SELF, nrhsM, &b_seq));
    1784:         PetscCall(ISCreateGeneral(PETSC_COMM_SELF, nrhsM, idx, PETSC_OWN_POINTER, &is_to));
    1785:         PetscCall(ISCreateStride(PETSC_COMM_SELF, nrhsM, 0, 1, &is_from));
    1786:       } else {
    1787:         PetscCall(VecCreateSeq(PETSC_COMM_SELF, 0, &b_seq));
    1788:         PetscCall(ISCreateStride(PETSC_COMM_SELF, 0, 0, 1, &is_to));
    1789:         PetscCall(ISCreateStride(PETSC_COMM_SELF, 0, 0, 1, &is_from));
    1790:       }
    1791:       PetscCall(VecScatterCreate(v_mpi, is_from, b_seq, is_to, &scat_rhs));
    1792:       PetscCall(VecScatterBegin(scat_rhs, v_mpi, b_seq, INSERT_VALUES, SCATTER_FORWARD));
    1793:       PetscCall(ISDestroy(&is_to));
    1794:       PetscCall(ISDestroy(&is_from));
    1795:       PetscCall(VecScatterEnd(scat_rhs, v_mpi, b_seq, INSERT_VALUES, SCATTER_FORWARD));

    1797:       if (!mumps->myid) { /* define rhs on the host */
    1798:         PetscCall(VecGetArray(b_seq, &bray));
    1799:         mumps->id.rhs = (MumpsScalar *)bray;
    1800:         PetscCall(VecRestoreArray(b_seq, &bray));
    1801:       }
    1802:     }
    1803:   } else { /* sparse B */
    1804:     b = (Mat_MPIAIJ *)Bt->data;

    1806:     /* wrap dense X into a vector v_mpi */
    1807:     PetscCall(MatGetLocalSize(X, &m, NULL));
    1808:     PetscCall(MatDenseGetArray(X, &bray));
    1809:     PetscCall(VecCreateMPIWithArray(PetscObjectComm((PetscObject)X), 1, nrhs * m, nrhsM, (const PetscScalar *)bray, &v_mpi));
    1810:     PetscCall(MatDenseRestoreArray(X, &bray));

    1812:     if (!mumps->myid) {
    1813:       PetscCall(MatSeqAIJGetArray(b->A, &aa));
    1814:       PetscCall(MatGetRowIJ(b->A, 1, PETSC_FALSE, PETSC_FALSE, &spnr, (const PetscInt **)&ia, (const PetscInt **)&ja, &flg));
    1815:       PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot get IJ structure");
    1816:       PetscCall(PetscMUMPSIntCSRCast(mumps, spnr, ia, ja, &mumps->id.irhs_ptr, &mumps->id.irhs_sparse, &mumps->id.nz_rhs));
    1817:       mumps->id.rhs_sparse = (MumpsScalar *)aa;
    1818:     } else {
    1819:       mumps->id.irhs_ptr    = NULL;
    1820:       mumps->id.irhs_sparse = NULL;
    1821:       mumps->id.nz_rhs      = 0;
    1822:       mumps->id.rhs_sparse  = NULL;
    1823:     }
    1824:   }

    1826:   /* solve phase */
    1827:   mumps->id.job = JOB_SOLVE;
    1828:   PetscMUMPS_c(mumps);
    1829:   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));

    1831:   /* scatter mumps distributed solution to PETSc vector v_mpi, which shares local arrays with solution matrix X */
    1832:   PetscCall(MatDenseGetArray(X, &array));
    1833:   PetscCall(VecPlaceArray(v_mpi, array));

    1835:   /* create scatter scat_sol */
    1836:   PetscCall(MatGetOwnershipRanges(X, &rstart));
    1837:   /* iidx: index for scatter mumps solution to PETSc X */

    1839:   PetscCall(ISCreateStride(PETSC_COMM_SELF, nlsol_loc, 0, 1, &is_from));
    1840:   PetscCall(PetscMalloc1(nlsol_loc, &idxx));
    1841:   for (i = 0; i < lsol_loc; i++) {
    1842:     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 */

    1844:     for (proc = 0; proc < mumps->petsc_size; proc++) {
    1845:       if (isol_loc[i] >= rstart[proc] && isol_loc[i] < rstart[proc + 1]) {
    1846:         myrstart = rstart[proc];
    1847:         k        = isol_loc[i] - myrstart;          /* local index on 1st column of PETSc vector X */
    1848:         iidx     = k + myrstart * nrhs;             /* maps mumps isol_loc[i] to PETSc index in X */
    1849:         m        = rstart[proc + 1] - rstart[proc]; /* rows of X for this proc */
    1850:         break;
    1851:       }
    1852:     }

    1854:     for (j = 0; j < nrhs; j++) idxx[i + j * lsol_loc] = iidx + j * m;
    1855:   }
    1856:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, nlsol_loc, idxx, PETSC_COPY_VALUES, &is_to));
    1857:   PetscCall(VecScatterCreate(msol_loc, is_from, v_mpi, is_to, &scat_sol));
    1858:   PetscCall(VecScatterBegin(scat_sol, msol_loc, v_mpi, INSERT_VALUES, SCATTER_FORWARD));
    1859:   PetscCall(ISDestroy(&is_from));
    1860:   PetscCall(ISDestroy(&is_to));
    1861:   PetscCall(VecScatterEnd(scat_sol, msol_loc, v_mpi, INSERT_VALUES, SCATTER_FORWARD));
    1862:   PetscCall(MatDenseRestoreArray(X, &array));

    1864:   /* free spaces */
    1865:   mumps->id.sol_loc  = (MumpsScalar *)sol_loc_save;
    1866:   mumps->id.isol_loc = isol_loc_save;

    1868:   PetscCall(PetscFree2(sol_loc, isol_loc));
    1869:   PetscCall(PetscFree(idxx));
    1870:   PetscCall(VecDestroy(&msol_loc));
    1871:   PetscCall(VecDestroy(&v_mpi));
    1872:   if (!denseB) {
    1873:     if (!mumps->myid) {
    1874:       b = (Mat_MPIAIJ *)Bt->data;
    1875:       PetscCall(MatSeqAIJRestoreArray(b->A, &aa));
    1876:       PetscCall(MatRestoreRowIJ(b->A, 1, PETSC_FALSE, PETSC_FALSE, &spnr, (const PetscInt **)&ia, (const PetscInt **)&ja, &flg));
    1877:       PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot restore IJ structure");
    1878:     }
    1879:   } else {
    1880:     if (mumps->ICNTL20 == 0) {
    1881:       PetscCall(VecDestroy(&b_seq));
    1882:       PetscCall(VecScatterDestroy(&scat_rhs));
    1883:     }
    1884:   }
    1885:   PetscCall(VecScatterDestroy(&scat_sol));
    1886:   PetscCall(PetscLogFlops(nrhs * PetscMax(0, 2.0 * (mumps->id.INFO(28) >= 0 ? mumps->id.INFO(28) : -1000000 * mumps->id.INFO(28)) - A->cmap->n)));
    1887:   PetscFunctionReturn(PETSC_SUCCESS);
    1888: }

    1890: static PetscErrorCode MatMatSolveTranspose_MUMPS(Mat A, Mat B, Mat X)
    1891: {
    1892:   Mat_MUMPS          *mumps = (Mat_MUMPS *)A->data;
    1893:   const PetscMUMPSInt value = mumps->id.ICNTL(9);

    1895:   PetscFunctionBegin;
    1896:   mumps->id.ICNTL(9) = 0;
    1897:   PetscCall(MatMatSolve_MUMPS(A, B, X));
    1898:   mumps->id.ICNTL(9) = value;
    1899:   PetscFunctionReturn(PETSC_SUCCESS);
    1900: }

    1902: static PetscErrorCode MatMatTransposeSolve_MUMPS(Mat A, Mat Bt, Mat X)
    1903: {
    1904:   PetscBool flg;
    1905:   Mat       B;

    1907:   PetscFunctionBegin;
    1908:   PetscCall(PetscObjectTypeCompareAny((PetscObject)Bt, &flg, MATSEQAIJ, MATMPIAIJ, NULL));
    1909:   PetscCheck(flg, PetscObjectComm((PetscObject)Bt), PETSC_ERR_ARG_WRONG, "Matrix Bt must be MATAIJ matrix");

    1911:   /* Create B=Bt^T that uses Bt's data structure */
    1912:   PetscCall(MatCreateTranspose(Bt, &B));

    1914:   PetscCall(MatMatSolve_MUMPS(A, B, X));
    1915:   PetscCall(MatDestroy(&B));
    1916:   PetscFunctionReturn(PETSC_SUCCESS);
    1917: }

    1919: #if !defined(PETSC_USE_COMPLEX)
    1920: /*
    1921:   input:
    1922:    F:        numeric factor
    1923:   output:
    1924:    nneg:     total number of negative pivots
    1925:    nzero:    total number of zero pivots
    1926:    npos:     (global dimension of F) - nneg - nzero
    1927: */
    1928: static PetscErrorCode MatGetInertia_SBAIJMUMPS(Mat F, PetscInt *nneg, PetscInt *nzero, PetscInt *npos)
    1929: {
    1930:   Mat_MUMPS  *mumps = (Mat_MUMPS *)F->data;
    1931:   PetscMPIInt size;

    1933:   PetscFunctionBegin;
    1934:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)F), &size));
    1935:   /* 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 */
    1936:   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));

    1938:   if (nneg) *nneg = mumps->id.INFOG(12);
    1939:   if (nzero || npos) {
    1940:     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");
    1941:     if (nzero) *nzero = mumps->id.INFOG(28);
    1942:     if (npos) *npos = F->rmap->N - (mumps->id.INFOG(12) + mumps->id.INFOG(28));
    1943:   }
    1944:   PetscFunctionReturn(PETSC_SUCCESS);
    1945: }
    1946: #endif

    1948: static PetscErrorCode MatMumpsGatherNonzerosOnMaster(MatReuse reuse, Mat_MUMPS *mumps)
    1949: {
    1950:   PetscMPIInt    nreqs;
    1951:   PetscMUMPSInt *irn, *jcn;
    1952:   PetscMPIInt    count;
    1953:   PetscCount     totnnz, remain;
    1954:   const PetscInt osize = mumps->omp_comm_size;
    1955:   PetscScalar   *val;

    1957:   PetscFunctionBegin;
    1958:   if (osize > 1) {
    1959:     if (reuse == MAT_INITIAL_MATRIX) {
    1960:       /* master first gathers counts of nonzeros to receive */
    1961:       if (mumps->is_omp_master) PetscCall(PetscMalloc1(osize, &mumps->recvcount));
    1962:       PetscCallMPI(MPI_Gather(&mumps->nnz, 1, MPIU_INT64, mumps->recvcount, 1, MPIU_INT64, 0 /*master*/, mumps->omp_comm));

    1964:       /* Then each computes number of send/recvs */
    1965:       if (mumps->is_omp_master) {
    1966:         /* Start from 1 since self communication is not done in MPI */
    1967:         nreqs = 0;
    1968:         for (PetscMPIInt i = 1; i < osize; i++) nreqs += (mumps->recvcount[i] + PETSC_MPI_INT_MAX - 1) / PETSC_MPI_INT_MAX;
    1969:       } else {
    1970:         nreqs = (PetscMPIInt)(((mumps->nnz + PETSC_MPI_INT_MAX - 1) / PETSC_MPI_INT_MAX));
    1971:       }
    1972:       PetscCall(PetscMalloc1(nreqs * 3, &mumps->reqs)); /* Triple the requests since we send irn, jcn and val separately */

    1974:       /* The following code is doing a very simple thing: omp_master rank gathers irn/jcn/val from others.
    1975:          MPI_Gatherv would be enough if it supports big counts > 2^31-1. Since it does not, and mumps->nnz
    1976:          might be a prime number > 2^31-1, we have to slice the message. Note omp_comm_size
    1977:          is very small, the current approach should have no extra overhead compared to MPI_Gatherv.
    1978:        */
    1979:       nreqs = 0; /* counter for actual send/recvs */
    1980:       if (mumps->is_omp_master) {
    1981:         totnnz = 0;

    1983:         for (PetscMPIInt i = 0; i < osize; i++) totnnz += mumps->recvcount[i]; /* totnnz = sum of nnz over omp_comm */
    1984:         PetscCall(PetscMalloc2(totnnz, &irn, totnnz, &jcn));
    1985:         PetscCall(PetscMalloc1(totnnz, &val));

    1987:         /* Self communication */
    1988:         PetscCall(PetscArraycpy(irn, mumps->irn, mumps->nnz));
    1989:         PetscCall(PetscArraycpy(jcn, mumps->jcn, mumps->nnz));
    1990:         PetscCall(PetscArraycpy(val, mumps->val, mumps->nnz));

    1992:         /* Replace mumps->irn/jcn etc on master with the newly allocated bigger arrays */
    1993:         PetscCall(PetscFree2(mumps->irn, mumps->jcn));
    1994:         PetscCall(PetscFree(mumps->val_alloc));
    1995:         mumps->nnz = totnnz;
    1996:         mumps->irn = irn;
    1997:         mumps->jcn = jcn;
    1998:         mumps->val = mumps->val_alloc = val;

    2000:         irn += mumps->recvcount[0]; /* recvcount[0] is old mumps->nnz on omp rank 0 */
    2001:         jcn += mumps->recvcount[0];
    2002:         val += mumps->recvcount[0];

    2004:         /* Remote communication */
    2005:         for (PetscMPIInt i = 1; i < osize; i++) {
    2006:           count  = (PetscMPIInt)PetscMin(mumps->recvcount[i], (PetscMPIInt)PETSC_MPI_INT_MAX);
    2007:           remain = mumps->recvcount[i] - count;
    2008:           while (count > 0) {
    2009:             PetscCallMPI(MPIU_Irecv(irn, count, MPIU_MUMPSINT, i, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
    2010:             PetscCallMPI(MPIU_Irecv(jcn, count, MPIU_MUMPSINT, i, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
    2011:             PetscCallMPI(MPIU_Irecv(val, count, MPIU_SCALAR, i, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
    2012:             irn += count;
    2013:             jcn += count;
    2014:             val += count;
    2015:             count = (PetscMPIInt)PetscMin(remain, (PetscMPIInt)PETSC_MPI_INT_MAX);
    2016:             remain -= count;
    2017:           }
    2018:         }
    2019:       } else {
    2020:         irn    = mumps->irn;
    2021:         jcn    = mumps->jcn;
    2022:         val    = mumps->val;
    2023:         count  = (PetscMPIInt)PetscMin(mumps->nnz, (PetscMPIInt)PETSC_MPI_INT_MAX);
    2024:         remain = mumps->nnz - count;
    2025:         while (count > 0) {
    2026:           PetscCallMPI(MPIU_Isend(irn, count, MPIU_MUMPSINT, 0, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
    2027:           PetscCallMPI(MPIU_Isend(jcn, count, MPIU_MUMPSINT, 0, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
    2028:           PetscCallMPI(MPIU_Isend(val, count, MPIU_SCALAR, 0, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
    2029:           irn += count;
    2030:           jcn += count;
    2031:           val += count;
    2032:           count = (PetscMPIInt)PetscMin(remain, (PetscMPIInt)PETSC_MPI_INT_MAX);
    2033:           remain -= count;
    2034:         }
    2035:       }
    2036:     } else {
    2037:       nreqs = 0;
    2038:       if (mumps->is_omp_master) {
    2039:         val = mumps->val + mumps->recvcount[0];
    2040:         for (PetscMPIInt i = 1; i < osize; i++) { /* Remote communication only since self data is already in place */
    2041:           count  = (PetscMPIInt)PetscMin(mumps->recvcount[i], (PetscMPIInt)PETSC_MPI_INT_MAX);
    2042:           remain = mumps->recvcount[i] - count;
    2043:           while (count > 0) {
    2044:             PetscCallMPI(MPIU_Irecv(val, count, MPIU_SCALAR, i, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
    2045:             val += count;
    2046:             count = (PetscMPIInt)PetscMin(remain, (PetscMPIInt)PETSC_MPI_INT_MAX);
    2047:             remain -= count;
    2048:           }
    2049:         }
    2050:       } else {
    2051:         val    = mumps->val;
    2052:         count  = (PetscMPIInt)PetscMin(mumps->nnz, (PetscMPIInt)PETSC_MPI_INT_MAX);
    2053:         remain = mumps->nnz - count;
    2054:         while (count > 0) {
    2055:           PetscCallMPI(MPIU_Isend(val, count, MPIU_SCALAR, 0, mumps->tag, mumps->omp_comm, &mumps->reqs[nreqs++]));
    2056:           val += count;
    2057:           count = (PetscMPIInt)PetscMin(remain, (PetscMPIInt)PETSC_MPI_INT_MAX);
    2058:           remain -= count;
    2059:         }
    2060:       }
    2061:     }
    2062:     PetscCallMPI(MPI_Waitall(nreqs, mumps->reqs, MPI_STATUSES_IGNORE));
    2063:     mumps->tag++; /* It is totally fine for above send/recvs to share one mpi tag */
    2064:   }
    2065:   PetscFunctionReturn(PETSC_SUCCESS);
    2066: }

    2068: static PetscErrorCode MatFactorNumeric_MUMPS(Mat F, Mat A, PETSC_UNUSED const MatFactorInfo *info)
    2069: {
    2070:   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;
    2071:   PetscBool  isMPIAIJ;

    2073:   PetscFunctionBegin;
    2074:   if (mumps->id.INFOG(1) < 0 && !(mumps->id.INFOG(1) == -16 && mumps->id.INFOG(1) == 0)) {
    2075:     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)));
    2076:     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)));
    2077:     PetscFunctionReturn(PETSC_SUCCESS);
    2078:   }

    2080:   PetscCall((*mumps->ConvertToTriples)(A, 1, MAT_REUSE_MATRIX, mumps));
    2081:   PetscCall(MatMumpsGatherNonzerosOnMaster(MAT_REUSE_MATRIX, mumps));

    2083:   /* numerical factorization phase */
    2084:   mumps->id.job = JOB_FACTNUMERIC;
    2085:   if (!mumps->id.ICNTL(18)) { /* A is centralized */
    2086:     if (!mumps->myid) mumps->id.a = (MumpsScalar *)mumps->val;
    2087:   } else {
    2088:     mumps->id.a_loc = (MumpsScalar *)mumps->val;
    2089:   }
    2090:   PetscMUMPS_c(mumps);
    2091:   if (mumps->id.INFOG(1) < 0) {
    2092:     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));
    2093:     if (mumps->id.INFOG(1) == -10) {
    2094:       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)));
    2095:       F->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    2096:     } else if (mumps->id.INFOG(1) == -13) {
    2097:       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)));
    2098:       F->factorerrortype = MAT_FACTOR_OUTMEMORY;
    2099:     } else if (mumps->id.INFOG(1) == -8 || mumps->id.INFOG(1) == -9 || (-16 < mumps->id.INFOG(1) && mumps->id.INFOG(1) < -10)) {
    2100:       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)));
    2101:       F->factorerrortype = MAT_FACTOR_OUTMEMORY;
    2102:     } else {
    2103:       PetscCall(PetscInfo(F, "MUMPS error in numerical factorization: INFOG(1)=%d, INFO(2)=%d\n", mumps->id.INFOG(1), mumps->id.INFO(2)));
    2104:       F->factorerrortype = MAT_FACTOR_OTHER;
    2105:     }
    2106:   }
    2107:   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));

    2109:   F->assembled = PETSC_TRUE;

    2111:   if (F->schur) { /* reset Schur status to unfactored */
    2112: #if defined(PETSC_HAVE_CUDA)
    2113:     F->schur->offloadmask = PETSC_OFFLOAD_CPU;
    2114: #endif
    2115:     if (mumps->id.ICNTL(19) == 1) { /* stored by rows */
    2116:       mumps->id.ICNTL(19) = 2;
    2117:       PetscCall(MatTranspose(F->schur, MAT_INPLACE_MATRIX, &F->schur));
    2118:     }
    2119:     PetscCall(MatFactorRestoreSchurComplement(F, NULL, MAT_FACTOR_SCHUR_UNFACTORED));
    2120:   }

    2122:   /* just to be sure that ICNTL(19) value returned by a call from MatMumpsGetIcntl is always consistent */
    2123:   if (!mumps->sym && mumps->id.ICNTL(19) && mumps->id.ICNTL(19) != 1) mumps->id.ICNTL(19) = 3;

    2125:   if (!mumps->is_omp_master) mumps->id.INFO(23) = 0;
    2126:   if (mumps->petsc_size > 1) {
    2127:     PetscInt     lsol_loc;
    2128:     PetscScalar *sol_loc;

    2130:     PetscCall(PetscObjectTypeCompare((PetscObject)A, MATMPIAIJ, &isMPIAIJ));

    2132:     /* distributed solution; Create x_seq=sol_loc for repeated use */
    2133:     if (mumps->x_seq) {
    2134:       PetscCall(VecScatterDestroy(&mumps->scat_sol));
    2135:       PetscCall(PetscFree2(mumps->id.sol_loc, mumps->id.isol_loc));
    2136:       PetscCall(VecDestroy(&mumps->x_seq));
    2137:     }
    2138:     lsol_loc = mumps->id.INFO(23); /* length of sol_loc */
    2139:     PetscCall(PetscMalloc2(lsol_loc, &sol_loc, lsol_loc, &mumps->id.isol_loc));
    2140:     mumps->id.lsol_loc = (PetscMUMPSInt)lsol_loc;
    2141:     mumps->id.sol_loc  = (MumpsScalar *)sol_loc;
    2142:     PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, lsol_loc, sol_loc, &mumps->x_seq));
    2143:   }
    2144:   PetscCall(PetscLogFlops((double)mumps->id.RINFO(2)));
    2145:   PetscFunctionReturn(PETSC_SUCCESS);
    2146: }

    2148: /* Sets MUMPS options from the options database */
    2149: static PetscErrorCode MatSetFromOptions_MUMPS(Mat F, Mat A)
    2150: {
    2151:   Mat_MUMPS    *mumps = (Mat_MUMPS *)F->data;
    2152:   PetscMUMPSInt icntl = 0, size, *listvar_schur;
    2153:   PetscInt      info[80], i, ninfo = 80, rbs, cbs;
    2154:   PetscBool     flg = PETSC_FALSE, schur = (PetscBool)(mumps->id.ICNTL(26) == -1);
    2155:   MumpsScalar  *arr;

    2157:   PetscFunctionBegin;
    2158:   PetscOptionsBegin(PetscObjectComm((PetscObject)F), ((PetscObject)F)->prefix, "MUMPS Options", "Mat");
    2159:   if (mumps->id.job == JOB_NULL) { /* MatSetFromOptions_MUMPS() has never been called before */
    2160:     PetscInt      nthreads   = 0;
    2161:     PetscInt      nCNTL_pre  = mumps->CNTL_pre ? mumps->CNTL_pre[0] : 0;
    2162:     PetscInt      nICNTL_pre = mumps->ICNTL_pre ? mumps->ICNTL_pre[0] : 0;
    2163:     PetscMUMPSInt nblk, *blkvar, *blkptr;

    2165:     mumps->petsc_comm = PetscObjectComm((PetscObject)A);
    2166:     PetscCallMPI(MPI_Comm_size(mumps->petsc_comm, &mumps->petsc_size));
    2167:     PetscCallMPI(MPI_Comm_rank(mumps->petsc_comm, &mumps->myid)); /* "if (!myid)" still works even if mumps_comm is different */

    2169:     PetscCall(PetscOptionsName("-mat_mumps_use_omp_threads", "Convert MPI processes into OpenMP threads", "None", &mumps->use_petsc_omp_support));
    2170:     if (mumps->use_petsc_omp_support) nthreads = -1; /* -1 will let PetscOmpCtrlCreate() guess a proper value when user did not supply one */
    2171:     /* do not use PetscOptionsInt() so that the option -mat_mumps_use_omp_threads is not displayed twice in the help */
    2172:     PetscCall(PetscOptionsGetInt(NULL, ((PetscObject)F)->prefix, "-mat_mumps_use_omp_threads", &nthreads, NULL));
    2173:     if (mumps->use_petsc_omp_support) {
    2174:       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 : "");
    2175: #if defined(PETSC_HAVE_OPENMP_SUPPORT)
    2176:       PetscCall(PetscOmpCtrlCreate(mumps->petsc_comm, nthreads, &mumps->omp_ctrl));
    2177:       PetscCall(PetscOmpCtrlGetOmpComms(mumps->omp_ctrl, &mumps->omp_comm, &mumps->mumps_comm, &mumps->is_omp_master));
    2178: #else
    2179:       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",
    2180:               ((PetscObject)F)->prefix ? ((PetscObject)F)->prefix : "");
    2181: #endif
    2182:     } else {
    2183:       mumps->omp_comm      = PETSC_COMM_SELF;
    2184:       mumps->mumps_comm    = mumps->petsc_comm;
    2185:       mumps->is_omp_master = PETSC_TRUE;
    2186:     }
    2187:     PetscCallMPI(MPI_Comm_size(mumps->omp_comm, &mumps->omp_comm_size));
    2188:     mumps->reqs = NULL;
    2189:     mumps->tag  = 0;

    2191:     if (mumps->mumps_comm != MPI_COMM_NULL) {
    2192:       if (PetscDefined(HAVE_OPENMP_SUPPORT) && mumps->use_petsc_omp_support) {
    2193:         /* It looks like MUMPS does not dup the input comm. Dup a new comm for MUMPS to avoid any tag mismatches. */
    2194:         MPI_Comm comm;
    2195:         PetscCallMPI(MPI_Comm_dup(mumps->mumps_comm, &comm));
    2196:         mumps->mumps_comm = comm;
    2197:       } else PetscCall(PetscCommGetComm(mumps->petsc_comm, &mumps->mumps_comm));
    2198:     }

    2200:     mumps->id.comm_fortran = MPI_Comm_c2f(mumps->mumps_comm);
    2201:     mumps->id.job          = JOB_INIT;
    2202:     mumps->id.par          = 1; /* host participates factorizaton and solve */
    2203:     mumps->id.sym          = mumps->sym;

    2205:     size          = mumps->id.size_schur;
    2206:     arr           = mumps->id.schur;
    2207:     listvar_schur = mumps->id.listvar_schur;
    2208:     nblk          = mumps->id.nblk;
    2209:     blkvar        = mumps->id.blkvar;
    2210:     blkptr        = mumps->id.blkptr;
    2211:     if (PetscDefined(USE_DEBUG)) {
    2212:       for (PetscInt i = 0; i < size; i++)
    2213:         PetscCheck(listvar_schur[i] - 1 >= 0 && listvar_schur[i] - 1 < A->rmap->N, PETSC_COMM_SELF, PETSC_ERR_USER, "Invalid Schur index at position %" PetscInt_FMT "! %" PetscInt_FMT " must be in [0, %" PetscInt_FMT ")", i, (PetscInt)listvar_schur[i] - 1,
    2214:                    A->rmap->N);
    2215:     }

    2217:     PetscMUMPS_c(mumps);
    2218:     PetscCheck(mumps->id.INFOG(1) >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "MUMPS error: INFOG(1)=%d " MUMPS_MANUALS, mumps->id.INFOG(1));

    2220:     /* set PETSc-MUMPS default options - override MUMPS default */
    2221:     mumps->id.ICNTL(3) = 0;
    2222:     mumps->id.ICNTL(4) = 0;
    2223:     if (mumps->petsc_size == 1) {
    2224:       mumps->id.ICNTL(18) = 0; /* centralized assembled matrix input */
    2225:       mumps->id.ICNTL(7)  = 7; /* automatic choice of ordering done by the package */
    2226:     } else {
    2227:       mumps->id.ICNTL(18) = 3; /* distributed assembled matrix input */
    2228:       mumps->id.ICNTL(21) = 1; /* distributed solution */
    2229:     }
    2230:     if (nblk && blkptr) {
    2231:       mumps->id.ICNTL(15) = 1;
    2232:       mumps->id.nblk      = nblk;
    2233:       mumps->id.blkvar    = blkvar;
    2234:       mumps->id.blkptr    = blkptr;
    2235:     }

    2237:     /* restore cached ICNTL and CNTL values */
    2238:     for (icntl = 0; icntl < nICNTL_pre; ++icntl) mumps->id.ICNTL(mumps->ICNTL_pre[1 + 2 * icntl]) = mumps->ICNTL_pre[2 + 2 * icntl];
    2239:     for (icntl = 0; icntl < nCNTL_pre; ++icntl) mumps->id.CNTL((PetscInt)mumps->CNTL_pre[1 + 2 * icntl]) = mumps->CNTL_pre[2 + 2 * icntl];
    2240:     PetscCall(PetscFree(mumps->ICNTL_pre));
    2241:     PetscCall(PetscFree(mumps->CNTL_pre));

    2243:     if (schur) {
    2244:       mumps->id.size_schur    = size;
    2245:       mumps->id.schur_lld     = size;
    2246:       mumps->id.schur         = arr;
    2247:       mumps->id.listvar_schur = listvar_schur;
    2248:       if (mumps->petsc_size > 1) {
    2249:         PetscBool gs; /* gs is false if any rank other than root has non-empty IS */

    2251:         mumps->id.ICNTL(19) = 1;                                                                            /* MUMPS returns Schur centralized on the host */
    2252:         gs                  = mumps->myid ? (mumps->id.size_schur ? PETSC_FALSE : PETSC_TRUE) : PETSC_TRUE; /* always true on root; false on others if their size != 0 */
    2253:         PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &gs, 1, MPI_C_BOOL, MPI_LAND, mumps->petsc_comm));
    2254:         PetscCheck(gs, PETSC_COMM_SELF, PETSC_ERR_SUP, "MUMPS distributed parallel Schur complements not yet supported from PETSc");
    2255:       } else {
    2256:         if (F->factortype == MAT_FACTOR_LU) {
    2257:           mumps->id.ICNTL(19) = 3; /* MUMPS returns full matrix */
    2258:         } else {
    2259:           mumps->id.ICNTL(19) = 2; /* MUMPS returns lower triangular part */
    2260:         }
    2261:       }
    2262:       mumps->id.ICNTL(26) = -1;
    2263:     }

    2265:     /* copy MUMPS default control values from master to slaves. Although slaves do not call MUMPS, they may access these values in code.
    2266:        For example, ICNTL(9) is initialized to 1 by MUMPS and slaves check ICNTL(9) in MatSolve_MUMPS.
    2267:      */
    2268:     PetscCallMPI(MPI_Bcast(mumps->id.icntl, 40, MPI_INT, 0, mumps->omp_comm));
    2269:     PetscCallMPI(MPI_Bcast(mumps->id.cntl, 15, MPIU_REAL, 0, mumps->omp_comm));

    2271:     mumps->scat_rhs = NULL;
    2272:     mumps->scat_sol = NULL;
    2273:   }
    2274:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_1", "ICNTL(1): output stream for error messages", "None", mumps->id.ICNTL(1), &icntl, &flg));
    2275:   if (flg) mumps->id.ICNTL(1) = icntl;
    2276:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_2", "ICNTL(2): output stream for diagnostic printing, statistics, and warning", "None", mumps->id.ICNTL(2), &icntl, &flg));
    2277:   if (flg) mumps->id.ICNTL(2) = icntl;
    2278:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_3", "ICNTL(3): output stream for global information, collected on the host", "None", mumps->id.ICNTL(3), &icntl, &flg));
    2279:   if (flg) mumps->id.ICNTL(3) = icntl;

    2281:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_4", "ICNTL(4): level of printing (0 to 4)", "None", mumps->id.ICNTL(4), &icntl, &flg));
    2282:   if (flg) mumps->id.ICNTL(4) = icntl;
    2283:   if (mumps->id.ICNTL(4) || PetscLogPrintInfo) mumps->id.ICNTL(3) = 6; /* resume MUMPS default id.ICNTL(3) = 6 */

    2285:   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));
    2286:   if (flg) mumps->id.ICNTL(6) = icntl;

    2288:   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));
    2289:   if (flg) {
    2290:     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");
    2291:     mumps->id.ICNTL(7) = icntl;
    2292:   }

    2294:   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));
    2295:   /* 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() */
    2296:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_10", "ICNTL(10): max num of refinements", "None", mumps->id.ICNTL(10), &mumps->id.ICNTL(10), NULL));
    2297:   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));
    2298:   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));
    2299:   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));
    2300:   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));
    2301:   PetscCall(MatGetBlockSizes(A, &rbs, &cbs));
    2302:   if (rbs == cbs && rbs > 1) mumps->id.ICNTL(15) = (PetscMUMPSInt)-rbs;
    2303:   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));
    2304:   if (flg) {
    2305:     if (mumps->id.ICNTL(15) < 0) 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");
    2306:     else if (mumps->id.ICNTL(15) > 0) {
    2307:       const PetscInt *bsizes;
    2308:       PetscInt        nblocks, p, *blkptr = NULL;
    2309:       PetscMPIInt    *recvcounts, *displs, n;
    2310:       PetscMPIInt     rank, size = 0;

    2312:       PetscCall(MatGetVariableBlockSizes(A, &nblocks, &bsizes));
    2313:       flg = PETSC_TRUE;
    2314:       for (p = 0; p < nblocks; ++p) {
    2315:         if (bsizes[p] > 1) break;
    2316:       }
    2317:       if (p == nblocks) flg = PETSC_FALSE;
    2318:       PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &flg, 1, MPI_C_BOOL, MPI_LOR, PetscObjectComm((PetscObject)A)));
    2319:       if (flg) { // if at least one process supplies variable block sizes and they are not all set to 1
    2320:         PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)A), &rank));
    2321:         if (rank == 0) PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
    2322:         PetscCall(PetscCalloc2(size, &recvcounts, size + 1, &displs));
    2323:         PetscCall(PetscMPIIntCast(nblocks, &n));
    2324:         PetscCallMPI(MPI_Gather(&n, 1, MPI_INT, recvcounts, 1, MPI_INT, 0, PetscObjectComm((PetscObject)A)));
    2325:         for (PetscInt p = 0; p < size; ++p) displs[p + 1] = displs[p] + recvcounts[p];
    2326:         PetscCall(PetscMalloc1(displs[size] + 1, &blkptr));
    2327:         PetscCallMPI(MPI_Bcast(displs + size, 1, MPIU_INT, 0, PetscObjectComm((PetscObject)A)));
    2328:         PetscCallMPI(MPI_Gatherv(bsizes, n, MPIU_INT, blkptr + 1, recvcounts, displs, MPIU_INT, 0, PetscObjectComm((PetscObject)A)));
    2329:         if (rank == 0) {
    2330:           blkptr[0] = 1;
    2331:           for (PetscInt p = 0; p < n; ++p) blkptr[p + 1] += blkptr[p];
    2332:           PetscCall(MatMumpsSetBlk(F, displs[size], NULL, blkptr));
    2333:         }
    2334:         PetscCall(PetscFree2(recvcounts, displs));
    2335:         PetscCall(PetscFree(blkptr));
    2336:       }
    2337:     }
    2338:   }
    2339:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_19", "ICNTL(19): computes the Schur complement", "None", mumps->id.ICNTL(19), &mumps->id.ICNTL(19), NULL));
    2340:   if (mumps->id.ICNTL(19) <= 0 || mumps->id.ICNTL(19) > 3) { /* reset any schur data (if any) */
    2341:     PetscCall(MatDestroy(&F->schur));
    2342:     PetscCall(MatMumpsResetSchur_Private(mumps));
    2343:   }

    2345:   /* Two MPICH Fortran MPI_IN_PLACE binding bugs prevented the use of 'mpich + mumps'. One happened with "mpi4py + mpich + mumps",
    2346:      and was reported by Firedrake. See https://bitbucket.org/mpi4py/mpi4py/issues/162/mpi4py-initialization-breaks-fortran
    2347:      and a petsc-maint mailing list thread with subject 'MUMPS segfaults in parallel because of ...'
    2348:      This bug was fixed by https://github.com/pmodels/mpich/pull/4149. But the fix brought a new bug,
    2349:      see https://github.com/pmodels/mpich/issues/5589. This bug was fixed by https://github.com/pmodels/mpich/pull/5590.
    2350:      In short, we could not use distributed RHS until with MPICH v4.0b1 or we enabled a workaround in mumps-5.6.2+
    2351:    */
    2352:   mumps->ICNTL20 = 10; /* Distributed dense RHS, by default */
    2353: #if PETSC_PKG_MUMPS_VERSION_LT(5, 3, 0) || (PetscDefined(HAVE_MPICH) && MPICH_NUMVERSION < 40000101) || PetscDefined(HAVE_MSMPI)
    2354:   mumps->ICNTL20 = 0; /* Centralized dense RHS, if need be */
    2355: #endif
    2356:   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));
    2357:   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);
    2358: #if PETSC_PKG_MUMPS_VERSION_LT(5, 3, 0)
    2359:   PetscCheck(!flg || mumps->ICNTL20 != 10, PETSC_COMM_SELF, PETSC_ERR_SUP, "ICNTL(20)=10 is not supported before MUMPS-5.3.0");
    2360: #endif
    2361:   /* 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 */

    2363:   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));
    2364:   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));
    2365:   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));
    2366:   if (mumps->id.ICNTL(24)) mumps->id.ICNTL(13) = 1; /* turn-off ScaLAPACK to help with the correct detection of null pivots */

    2368:   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));
    2369:   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));
    2370:   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));
    2371:   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));
    2372:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_29", "ICNTL(29): parallel ordering 1 = ptscotch, 2 = parmetis", "None", mumps->id.ICNTL(29), &mumps->id.ICNTL(29), NULL));
    2373:   /* 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 */
    2374:   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));
    2375:   /* 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 */
    2376:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_33", "ICNTL(33): compute determinant", "None", mumps->id.ICNTL(33), &mumps->id.ICNTL(33), NULL));
    2377:   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));
    2378:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_36", "ICNTL(36): choice of BLR factorization variant", "None", mumps->id.ICNTL(36), &mumps->id.ICNTL(36), NULL));
    2379:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_37", "ICNTL(37): compression of the contribution blocks (CB)", "None", mumps->id.ICNTL(37), &mumps->id.ICNTL(37), NULL));
    2380:   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));
    2381:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_48", "ICNTL(48): multithreading with tree parallelism", "None", mumps->id.ICNTL(48), &mumps->id.ICNTL(48), NULL));
    2382:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_56", "ICNTL(56): postponing and rank-revealing factorization", "None", mumps->id.ICNTL(56), &mumps->id.ICNTL(56), NULL));
    2383:   PetscCall(PetscOptionsMUMPSInt("-mat_mumps_icntl_58", "ICNTL(58): defines options for symbolic factorization", "None", mumps->id.ICNTL(58), &mumps->id.ICNTL(58), NULL));

    2385:   PetscCall(PetscOptionsReal("-mat_mumps_cntl_1", "CNTL(1): relative pivoting threshold", "None", mumps->id.CNTL(1), &mumps->id.CNTL(1), NULL));
    2386:   PetscCall(PetscOptionsReal("-mat_mumps_cntl_2", "CNTL(2): stopping criterion of refinement", "None", mumps->id.CNTL(2), &mumps->id.CNTL(2), NULL));
    2387:   PetscCall(PetscOptionsReal("-mat_mumps_cntl_3", "CNTL(3): absolute pivoting threshold", "None", mumps->id.CNTL(3), &mumps->id.CNTL(3), NULL));
    2388:   PetscCall(PetscOptionsReal("-mat_mumps_cntl_4", "CNTL(4): value for static pivoting", "None", mumps->id.CNTL(4), &mumps->id.CNTL(4), NULL));
    2389:   PetscCall(PetscOptionsReal("-mat_mumps_cntl_5", "CNTL(5): fixation for null pivots", "None", mumps->id.CNTL(5), &mumps->id.CNTL(5), NULL));
    2390:   PetscCall(PetscOptionsReal("-mat_mumps_cntl_7", "CNTL(7): dropping parameter used during BLR", "None", mumps->id.CNTL(7), &mumps->id.CNTL(7), NULL));

    2392:   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));

    2394:   PetscCall(PetscOptionsIntArray("-mat_mumps_view_info", "request INFO local to each processor", "", info, &ninfo, NULL));
    2395:   if (ninfo) {
    2396:     PetscCheck(ninfo <= 80, PETSC_COMM_SELF, PETSC_ERR_USER, "number of INFO %" PetscInt_FMT " must <= 80", ninfo);
    2397:     PetscCall(PetscMalloc1(ninfo, &mumps->info));
    2398:     mumps->ninfo = ninfo;
    2399:     for (i = 0; i < ninfo; i++) {
    2400:       PetscCheck(info[i] >= 0 && info[i] <= 80, PETSC_COMM_SELF, PETSC_ERR_USER, "index of INFO %" PetscInt_FMT " must between 1 and 80", ninfo);
    2401:       mumps->info[i] = info[i];
    2402:     }
    2403:   }
    2404:   PetscOptionsEnd();
    2405:   PetscFunctionReturn(PETSC_SUCCESS);
    2406: }

    2408: static PetscErrorCode MatFactorSymbolic_MUMPS_ReportIfError(Mat F, Mat A, PETSC_UNUSED const MatFactorInfo *info, Mat_MUMPS *mumps)
    2409: {
    2410:   PetscFunctionBegin;
    2411:   if (mumps->id.INFOG(1) < 0) {
    2412:     PetscCheck(!A->erroriffailure, PETSC_COMM_SELF, PETSC_ERR_LIB, "MUMPS error in analysis: INFOG(1)=%d " MUMPS_MANUALS, mumps->id.INFOG(1));
    2413:     if (mumps->id.INFOG(1) == -6) {
    2414:       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)));
    2415:       F->factorerrortype = MAT_FACTOR_STRUCT_ZEROPIVOT;
    2416:     } else if (mumps->id.INFOG(1) == -5 || mumps->id.INFOG(1) == -7) {
    2417:       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)));
    2418:       F->factorerrortype = MAT_FACTOR_OUTMEMORY;
    2419:     } else if (mumps->id.INFOG(1) == -16 && mumps->id.INFOG(1) == 0) {
    2420:       PetscCall(PetscInfo(F, "MUMPS error in analysis: empty matrix\n"));
    2421:     } else {
    2422:       PetscCall(PetscInfo(F, "MUMPS error in analysis: INFOG(1)=%d, INFO(2)=%d " MUMPS_MANUALS "\n", mumps->id.INFOG(1), mumps->id.INFO(2)));
    2423:       F->factorerrortype = MAT_FACTOR_OTHER;
    2424:     }
    2425:   }
    2426:   if (!mumps->id.n) F->factorerrortype = MAT_FACTOR_NOERROR;
    2427:   PetscFunctionReturn(PETSC_SUCCESS);
    2428: }

    2430: static PetscErrorCode MatLUFactorSymbolic_AIJMUMPS(Mat F, Mat A, IS r, PETSC_UNUSED IS c, const MatFactorInfo *info)
    2431: {
    2432:   Mat_MUMPS     *mumps = (Mat_MUMPS *)F->data;
    2433:   Vec            b;
    2434:   const PetscInt M = A->rmap->N;

    2436:   PetscFunctionBegin;
    2437:   if (mumps->matstruc == SAME_NONZERO_PATTERN) {
    2438:     /* F is assembled by a previous call of MatLUFactorSymbolic_AIJMUMPS() */
    2439:     PetscFunctionReturn(PETSC_SUCCESS);
    2440:   }

    2442:   /* Set MUMPS options from the options database */
    2443:   PetscCall(MatSetFromOptions_MUMPS(F, A));

    2445:   PetscCall((*mumps->ConvertToTriples)(A, 1, MAT_INITIAL_MATRIX, mumps));
    2446:   PetscCall(MatMumpsGatherNonzerosOnMaster(MAT_INITIAL_MATRIX, mumps));

    2448:   /* analysis phase */
    2449:   mumps->id.job = JOB_FACTSYMBOLIC;
    2450:   PetscCall(PetscMUMPSIntCast(M, &mumps->id.n));
    2451:   switch (mumps->id.ICNTL(18)) {
    2452:   case 0: /* centralized assembled matrix input */
    2453:     if (!mumps->myid) {
    2454:       mumps->id.nnz = mumps->nnz;
    2455:       mumps->id.irn = mumps->irn;
    2456:       mumps->id.jcn = mumps->jcn;
    2457:       if (mumps->id.ICNTL(6) > 1) mumps->id.a = (MumpsScalar *)mumps->val;
    2458:       if (r && mumps->id.ICNTL(7) == 7) {
    2459:         mumps->id.ICNTL(7) = 1;
    2460:         if (!mumps->myid) {
    2461:           const PetscInt *idx;
    2462:           PetscInt        i;

    2464:           PetscCall(PetscMalloc1(M, &mumps->id.perm_in));
    2465:           PetscCall(ISGetIndices(r, &idx));
    2466:           for (i = 0; i < M; i++) PetscCall(PetscMUMPSIntCast(idx[i] + 1, &mumps->id.perm_in[i])); /* perm_in[]: start from 1, not 0! */
    2467:           PetscCall(ISRestoreIndices(r, &idx));
    2468:         }
    2469:       }
    2470:     }
    2471:     break;
    2472:   case 3: /* distributed assembled matrix input (size>1) */
    2473:     mumps->id.nnz_loc = mumps->nnz;
    2474:     mumps->id.irn_loc = mumps->irn;
    2475:     mumps->id.jcn_loc = mumps->jcn;
    2476:     if (mumps->id.ICNTL(6) > 1) mumps->id.a_loc = (MumpsScalar *)mumps->val;
    2477:     if (mumps->ICNTL20 == 0) { /* Centralized rhs. Create scatter scat_rhs for repeated use in MatSolve() */
    2478:       PetscCall(MatCreateVecs(A, NULL, &b));
    2479:       PetscCall(VecScatterCreateToZero(b, &mumps->scat_rhs, &mumps->b_seq));
    2480:       PetscCall(VecDestroy(&b));
    2481:     }
    2482:     break;
    2483:   }
    2484:   PetscMUMPS_c(mumps);
    2485:   PetscCall(MatFactorSymbolic_MUMPS_ReportIfError(F, A, info, mumps));

    2487:   F->ops->lufactornumeric   = MatFactorNumeric_MUMPS;
    2488:   F->ops->solve             = MatSolve_MUMPS;
    2489:   F->ops->solvetranspose    = MatSolveTranspose_MUMPS;
    2490:   F->ops->matsolve          = MatMatSolve_MUMPS;
    2491:   F->ops->mattransposesolve = MatMatTransposeSolve_MUMPS;
    2492:   F->ops->matsolvetranspose = MatMatSolveTranspose_MUMPS;

    2494:   mumps->matstruc = SAME_NONZERO_PATTERN;
    2495:   PetscFunctionReturn(PETSC_SUCCESS);
    2496: }

    2498: /* Note the PETSc r and c permutations are ignored */
    2499: static PetscErrorCode MatLUFactorSymbolic_BAIJMUMPS(Mat F, Mat A, PETSC_UNUSED IS r, PETSC_UNUSED IS c, const MatFactorInfo *info)
    2500: {
    2501:   Mat_MUMPS     *mumps = (Mat_MUMPS *)F->data;
    2502:   Vec            b;
    2503:   const PetscInt M = A->rmap->N;

    2505:   PetscFunctionBegin;
    2506:   if (mumps->matstruc == SAME_NONZERO_PATTERN) {
    2507:     /* F is assembled by a previous call of MatLUFactorSymbolic_BAIJMUMPS() */
    2508:     PetscFunctionReturn(PETSC_SUCCESS);
    2509:   }

    2511:   /* Set MUMPS options from the options database */
    2512:   PetscCall(MatSetFromOptions_MUMPS(F, A));

    2514:   PetscCall((*mumps->ConvertToTriples)(A, 1, MAT_INITIAL_MATRIX, mumps));
    2515:   PetscCall(MatMumpsGatherNonzerosOnMaster(MAT_INITIAL_MATRIX, mumps));

    2517:   /* analysis phase */
    2518:   mumps->id.job = JOB_FACTSYMBOLIC;
    2519:   PetscCall(PetscMUMPSIntCast(M, &mumps->id.n));
    2520:   switch (mumps->id.ICNTL(18)) {
    2521:   case 0: /* centralized assembled matrix input */
    2522:     if (!mumps->myid) {
    2523:       mumps->id.nnz = mumps->nnz;
    2524:       mumps->id.irn = mumps->irn;
    2525:       mumps->id.jcn = mumps->jcn;
    2526:       if (mumps->id.ICNTL(6) > 1) mumps->id.a = (MumpsScalar *)mumps->val;
    2527:     }
    2528:     break;
    2529:   case 3: /* distributed assembled matrix input (size>1) */
    2530:     mumps->id.nnz_loc = mumps->nnz;
    2531:     mumps->id.irn_loc = mumps->irn;
    2532:     mumps->id.jcn_loc = mumps->jcn;
    2533:     if (mumps->id.ICNTL(6) > 1) mumps->id.a_loc = (MumpsScalar *)mumps->val;
    2534:     if (mumps->ICNTL20 == 0) { /* Centralized rhs. Create scatter scat_rhs for repeated use in MatSolve() */
    2535:       PetscCall(MatCreateVecs(A, NULL, &b));
    2536:       PetscCall(VecScatterCreateToZero(b, &mumps->scat_rhs, &mumps->b_seq));
    2537:       PetscCall(VecDestroy(&b));
    2538:     }
    2539:     break;
    2540:   }
    2541:   PetscMUMPS_c(mumps);
    2542:   PetscCall(MatFactorSymbolic_MUMPS_ReportIfError(F, A, info, mumps));

    2544:   F->ops->lufactornumeric   = MatFactorNumeric_MUMPS;
    2545:   F->ops->solve             = MatSolve_MUMPS;
    2546:   F->ops->solvetranspose    = MatSolveTranspose_MUMPS;
    2547:   F->ops->matsolvetranspose = MatMatSolveTranspose_MUMPS;

    2549:   mumps->matstruc = SAME_NONZERO_PATTERN;
    2550:   PetscFunctionReturn(PETSC_SUCCESS);
    2551: }

    2553: /* Note the PETSc r permutation and factor info are ignored */
    2554: static PetscErrorCode MatCholeskyFactorSymbolic_MUMPS(Mat F, Mat A, PETSC_UNUSED IS r, const MatFactorInfo *info)
    2555: {
    2556:   Mat_MUMPS     *mumps = (Mat_MUMPS *)F->data;
    2557:   Vec            b;
    2558:   const PetscInt M = A->rmap->N;

    2560:   PetscFunctionBegin;
    2561:   if (mumps->matstruc == SAME_NONZERO_PATTERN) {
    2562:     /* F is assembled by a previous call of MatCholeskyFactorSymbolic_MUMPS() */
    2563:     PetscFunctionReturn(PETSC_SUCCESS);
    2564:   }

    2566:   /* Set MUMPS options from the options database */
    2567:   PetscCall(MatSetFromOptions_MUMPS(F, A));

    2569:   PetscCall((*mumps->ConvertToTriples)(A, 1, MAT_INITIAL_MATRIX, mumps));
    2570:   PetscCall(MatMumpsGatherNonzerosOnMaster(MAT_INITIAL_MATRIX, mumps));

    2572:   /* analysis phase */
    2573:   mumps->id.job = JOB_FACTSYMBOLIC;
    2574:   PetscCall(PetscMUMPSIntCast(M, &mumps->id.n));
    2575:   switch (mumps->id.ICNTL(18)) {
    2576:   case 0: /* centralized assembled matrix input */
    2577:     if (!mumps->myid) {
    2578:       mumps->id.nnz = mumps->nnz;
    2579:       mumps->id.irn = mumps->irn;
    2580:       mumps->id.jcn = mumps->jcn;
    2581:       if (mumps->id.ICNTL(6) > 1) mumps->id.a = (MumpsScalar *)mumps->val;
    2582:     }
    2583:     break;
    2584:   case 3: /* distributed assembled matrix input (size>1) */
    2585:     mumps->id.nnz_loc = mumps->nnz;
    2586:     mumps->id.irn_loc = mumps->irn;
    2587:     mumps->id.jcn_loc = mumps->jcn;
    2588:     if (mumps->id.ICNTL(6) > 1) mumps->id.a_loc = (MumpsScalar *)mumps->val;
    2589:     if (mumps->ICNTL20 == 0) { /* Centralized rhs. Create scatter scat_rhs for repeated use in MatSolve() */
    2590:       PetscCall(MatCreateVecs(A, NULL, &b));
    2591:       PetscCall(VecScatterCreateToZero(b, &mumps->scat_rhs, &mumps->b_seq));
    2592:       PetscCall(VecDestroy(&b));
    2593:     }
    2594:     break;
    2595:   }
    2596:   PetscMUMPS_c(mumps);
    2597:   PetscCall(MatFactorSymbolic_MUMPS_ReportIfError(F, A, info, mumps));

    2599:   F->ops->choleskyfactornumeric = MatFactorNumeric_MUMPS;
    2600:   F->ops->solve                 = MatSolve_MUMPS;
    2601:   F->ops->solvetranspose        = MatSolve_MUMPS;
    2602:   F->ops->matsolve              = MatMatSolve_MUMPS;
    2603:   F->ops->mattransposesolve     = MatMatTransposeSolve_MUMPS;
    2604:   F->ops->matsolvetranspose     = MatMatSolveTranspose_MUMPS;
    2605: #if defined(PETSC_USE_COMPLEX)
    2606:   F->ops->getinertia = NULL;
    2607: #else
    2608:   F->ops->getinertia = MatGetInertia_SBAIJMUMPS;
    2609: #endif

    2611:   mumps->matstruc = SAME_NONZERO_PATTERN;
    2612:   PetscFunctionReturn(PETSC_SUCCESS);
    2613: }

    2615: static PetscErrorCode MatView_MUMPS(Mat A, PetscViewer viewer)
    2616: {
    2617:   PetscBool         isascii;
    2618:   PetscViewerFormat format;
    2619:   Mat_MUMPS        *mumps = (Mat_MUMPS *)A->data;

    2621:   PetscFunctionBegin;
    2622:   /* check if matrix is mumps type */
    2623:   if (A->ops->solve != MatSolve_MUMPS) PetscFunctionReturn(PETSC_SUCCESS);

    2625:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
    2626:   if (isascii) {
    2627:     PetscCall(PetscViewerGetFormat(viewer, &format));
    2628:     if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
    2629:       PetscCall(PetscViewerASCIIPrintf(viewer, "MUMPS run parameters:\n"));
    2630:       if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
    2631:         PetscCall(PetscViewerASCIIPrintf(viewer, "  SYM (matrix type):                   %d\n", mumps->id.sym));
    2632:         PetscCall(PetscViewerASCIIPrintf(viewer, "  PAR (host participation):            %d\n", mumps->id.par));
    2633:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(1) (output for error):         %d\n", mumps->id.ICNTL(1)));
    2634:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(2) (output of diagnostic msg): %d\n", mumps->id.ICNTL(2)));
    2635:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(3) (output for global info):   %d\n", mumps->id.ICNTL(3)));
    2636:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(4) (level of printing):        %d\n", mumps->id.ICNTL(4)));
    2637:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(5) (input mat struct):         %d\n", mumps->id.ICNTL(5)));
    2638:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(6) (matrix prescaling):        %d\n", mumps->id.ICNTL(6)));
    2639:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(7) (sequential matrix ordering):%d\n", mumps->id.ICNTL(7)));
    2640:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(8) (scaling strategy):         %d\n", mumps->id.ICNTL(8)));
    2641:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(10) (max num of refinements):  %d\n", mumps->id.ICNTL(10)));
    2642:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(11) (error analysis):          %d\n", mumps->id.ICNTL(11)));
    2643:         if (mumps->id.ICNTL(11) > 0) {
    2644:           PetscCall(PetscViewerASCIIPrintf(viewer, "    RINFOG(4) (inf norm of input mat):        %g\n", (double)mumps->id.RINFOG(4)));
    2645:           PetscCall(PetscViewerASCIIPrintf(viewer, "    RINFOG(5) (inf norm of solution):         %g\n", (double)mumps->id.RINFOG(5)));
    2646:           PetscCall(PetscViewerASCIIPrintf(viewer, "    RINFOG(6) (inf norm of residual):         %g\n", (double)mumps->id.RINFOG(6)));
    2647:           PetscCall(PetscViewerASCIIPrintf(viewer, "    RINFOG(7),RINFOG(8) (backward error est): %g, %g\n", (double)mumps->id.RINFOG(7), (double)mumps->id.RINFOG(8)));
    2648:           PetscCall(PetscViewerASCIIPrintf(viewer, "    RINFOG(9) (error estimate):               %g\n", (double)mumps->id.RINFOG(9)));
    2649:           PetscCall(PetscViewerASCIIPrintf(viewer, "    RINFOG(10),RINFOG(11)(condition numbers): %g, %g\n", (double)mumps->id.RINFOG(10), (double)mumps->id.RINFOG(11)));
    2650:         }
    2651:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(12) (efficiency control):                         %d\n", mumps->id.ICNTL(12)));
    2652:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(13) (sequential factorization of the root node):  %d\n", mumps->id.ICNTL(13)));
    2653:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(14) (percentage of estimated workspace increase): %d\n", mumps->id.ICNTL(14)));
    2654:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(15) (compression of the input matrix):            %d\n", mumps->id.ICNTL(15)));
    2655:         /* ICNTL(15-17) not used */
    2656:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(18) (input mat struct):                           %d\n", mumps->id.ICNTL(18)));
    2657:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(19) (Schur complement info):                      %d\n", mumps->id.ICNTL(19)));
    2658:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(20) (RHS sparse pattern):                         %d\n", mumps->id.ICNTL(20)));
    2659:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(21) (solution struct):                            %d\n", mumps->id.ICNTL(21)));
    2660:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(22) (in-core/out-of-core facility):               %d\n", mumps->id.ICNTL(22)));
    2661:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(23) (max size of memory can be allocated locally):%d\n", mumps->id.ICNTL(23)));

    2663:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(24) (detection of null pivot rows):               %d\n", mumps->id.ICNTL(24)));
    2664:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(25) (computation of a null space basis):          %d\n", mumps->id.ICNTL(25)));
    2665:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(26) (Schur options for RHS or solution):          %d\n", mumps->id.ICNTL(26)));
    2666:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(27) (blocking size for multiple RHS):             %d\n", mumps->id.ICNTL(27)));
    2667:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(28) (use parallel or sequential ordering):        %d\n", mumps->id.ICNTL(28)));
    2668:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(29) (parallel ordering):                          %d\n", mumps->id.ICNTL(29)));

    2670:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(30) (user-specified set of entries in inv(A)):    %d\n", mumps->id.ICNTL(30)));
    2671:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(31) (factors is discarded in the solve phase):    %d\n", mumps->id.ICNTL(31)));
    2672:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(33) (compute determinant):                        %d\n", mumps->id.ICNTL(33)));
    2673:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(35) (activate BLR based factorization):           %d\n", mumps->id.ICNTL(35)));
    2674:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(36) (choice of BLR factorization variant):        %d\n", mumps->id.ICNTL(36)));
    2675:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(37) (compression of the contribution blocks):     %d\n", mumps->id.ICNTL(37)));
    2676:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(38) (estimated compression rate of LU factors):   %d\n", mumps->id.ICNTL(38)));
    2677:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(48) (multithreading with tree parallelism):       %d\n", mumps->id.ICNTL(48)));
    2678:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(56) (postponing and rank-revealing factorization):%d\n", mumps->id.ICNTL(56)));
    2679:         PetscCall(PetscViewerASCIIPrintf(viewer, "  ICNTL(58) (options for symbolic factorization):         %d\n", mumps->id.ICNTL(58)));

    2681:         PetscCall(PetscViewerASCIIPrintf(viewer, "  CNTL(1) (relative pivoting threshold):      %g\n", (double)mumps->id.CNTL(1)));
    2682:         PetscCall(PetscViewerASCIIPrintf(viewer, "  CNTL(2) (stopping criterion of refinement): %g\n", (double)mumps->id.CNTL(2)));
    2683:         PetscCall(PetscViewerASCIIPrintf(viewer, "  CNTL(3) (absolute pivoting threshold):      %g\n", (double)mumps->id.CNTL(3)));
    2684:         PetscCall(PetscViewerASCIIPrintf(viewer, "  CNTL(4) (value of static pivoting):         %g\n", (double)mumps->id.CNTL(4)));
    2685:         PetscCall(PetscViewerASCIIPrintf(viewer, "  CNTL(5) (fixation for null pivots):         %g\n", (double)mumps->id.CNTL(5)));
    2686:         PetscCall(PetscViewerASCIIPrintf(viewer, "  CNTL(7) (dropping parameter for BLR):       %g\n", (double)mumps->id.CNTL(7)));

    2688:         /* information local to each processor */
    2689:         PetscCall(PetscViewerASCIIPrintf(viewer, "  RINFO(1) (local estimated flops for the elimination after analysis):\n"));
    2690:         PetscCall(PetscViewerASCIIPushSynchronized(viewer));
    2691:         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %g\n", mumps->myid, (double)mumps->id.RINFO(1)));
    2692:         PetscCall(PetscViewerFlush(viewer));
    2693:         PetscCall(PetscViewerASCIIPrintf(viewer, "  RINFO(2) (local estimated flops for the assembly after factorization):\n"));
    2694:         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %g\n", mumps->myid, (double)mumps->id.RINFO(2)));
    2695:         PetscCall(PetscViewerFlush(viewer));
    2696:         PetscCall(PetscViewerASCIIPrintf(viewer, "  RINFO(3) (local estimated flops for the elimination after factorization):\n"));
    2697:         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %g\n", mumps->myid, (double)mumps->id.RINFO(3)));
    2698:         PetscCall(PetscViewerFlush(viewer));

    2700:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFO(15) (estimated size of (in MB) MUMPS internal data for running numerical factorization):\n"));
    2701:         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %d\n", mumps->myid, mumps->id.INFO(15)));
    2702:         PetscCall(PetscViewerFlush(viewer));

    2704:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFO(16) (size of (in MB) MUMPS internal data used during numerical factorization):\n"));
    2705:         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %d\n", mumps->myid, mumps->id.INFO(16)));
    2706:         PetscCall(PetscViewerFlush(viewer));

    2708:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFO(23) (num of pivots eliminated on this processor after factorization):\n"));
    2709:         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %d\n", mumps->myid, mumps->id.INFO(23)));
    2710:         PetscCall(PetscViewerFlush(viewer));

    2712:         if (mumps->ninfo && mumps->ninfo <= 80) {
    2713:           PetscInt i;
    2714:           for (i = 0; i < mumps->ninfo; i++) {
    2715:             PetscCall(PetscViewerASCIIPrintf(viewer, "  INFO(%" PetscInt_FMT "):\n", mumps->info[i]));
    2716:             PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "    [%d] %d\n", mumps->myid, mumps->id.INFO(mumps->info[i])));
    2717:             PetscCall(PetscViewerFlush(viewer));
    2718:           }
    2719:         }
    2720:         PetscCall(PetscViewerASCIIPopSynchronized(viewer));
    2721:       } else PetscCall(PetscViewerASCIIPrintf(viewer, "  Use -%sksp_view ::ascii_info_detail to display information for all processes\n", ((PetscObject)A)->prefix ? ((PetscObject)A)->prefix : ""));

    2723:       if (mumps->myid == 0) { /* information from the host */
    2724:         PetscCall(PetscViewerASCIIPrintf(viewer, "  RINFOG(1) (global estimated flops for the elimination after analysis): %g\n", (double)mumps->id.RINFOG(1)));
    2725:         PetscCall(PetscViewerASCIIPrintf(viewer, "  RINFOG(2) (global estimated flops for the assembly after factorization): %g\n", (double)mumps->id.RINFOG(2)));
    2726:         PetscCall(PetscViewerASCIIPrintf(viewer, "  RINFOG(3) (global estimated flops for the elimination after factorization): %g\n", (double)mumps->id.RINFOG(3)));
    2727:         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)));

    2729:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(3) (estimated real workspace for factors on all processors after analysis): %d\n", mumps->id.INFOG(3)));
    2730:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(4) (estimated integer workspace for factors on all processors after analysis): %d\n", mumps->id.INFOG(4)));
    2731:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(5) (estimated maximum front size in the complete tree): %d\n", mumps->id.INFOG(5)));
    2732:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(6) (number of nodes in the complete tree): %d\n", mumps->id.INFOG(6)));
    2733:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(7) (ordering option effectively used after analysis): %d\n", mumps->id.INFOG(7)));
    2734:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(8) (structural symmetry in percent of the permuted matrix after analysis): %d\n", mumps->id.INFOG(8)));
    2735:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(9) (total real/complex workspace to store the matrix factors after factorization): %d\n", mumps->id.INFOG(9)));
    2736:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(10) (total integer space store the matrix factors after factorization): %d\n", mumps->id.INFOG(10)));
    2737:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(11) (order of largest frontal matrix after factorization): %d\n", mumps->id.INFOG(11)));
    2738:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(12) (number of off-diagonal pivots): %d\n", mumps->id.INFOG(12)));
    2739:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(13) (number of delayed pivots after factorization): %d\n", mumps->id.INFOG(13)));
    2740:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(14) (number of memory compress after factorization): %d\n", mumps->id.INFOG(14)));
    2741:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(15) (number of steps of iterative refinement after solution): %d\n", mumps->id.INFOG(15)));
    2742:         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)));
    2743:         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)));
    2744:         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)));
    2745:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(19) (size of all MUMPS internal data allocated during factorization: sum over all processors): %d\n", mumps->id.INFOG(19)));
    2746:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(20) (estimated number of entries in the factors): %d\n", mumps->id.INFOG(20)));
    2747:         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)));
    2748:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(22) (size in MB of memory effectively used during factorization - sum over all processors): %d\n", mumps->id.INFOG(22)));
    2749:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(23) (after analysis: value of ICNTL(6) effectively used): %d\n", mumps->id.INFOG(23)));
    2750:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(24) (after analysis: value of ICNTL(12) effectively used): %d\n", mumps->id.INFOG(24)));
    2751:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(25) (after factorization: number of pivots modified by static pivoting): %d\n", mumps->id.INFOG(25)));
    2752:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(28) (after factorization: number of null pivots encountered): %d\n", mumps->id.INFOG(28)));
    2753:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(29) (after factorization: effective number of entries in the factors (sum over all processors)): %d\n", mumps->id.INFOG(29)));
    2754:         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)));
    2755:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(32) (after analysis: type of analysis done): %d\n", mumps->id.INFOG(32)));
    2756:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(33) (value used for ICNTL(8)): %d\n", mumps->id.INFOG(33)));
    2757:         PetscCall(PetscViewerASCIIPrintf(viewer, "  INFOG(34) (exponent of the determinant if determinant is requested): %d\n", mumps->id.INFOG(34)));
    2758:         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)));
    2759:         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)));
    2760:         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)));
    2761:         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)));
    2762:         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)));
    2763:       }
    2764:     }
    2765:   }
    2766:   PetscFunctionReturn(PETSC_SUCCESS);
    2767: }

    2769: static PetscErrorCode MatGetInfo_MUMPS(Mat A, PETSC_UNUSED MatInfoType flag, MatInfo *info)
    2770: {
    2771:   Mat_MUMPS *mumps = (Mat_MUMPS *)A->data;

    2773:   PetscFunctionBegin;
    2774:   info->block_size        = 1.0;
    2775:   info->nz_allocated      = mumps->id.INFOG(20) >= 0 ? mumps->id.INFOG(20) : -1000000 * mumps->id.INFOG(20);
    2776:   info->nz_used           = mumps->id.INFOG(20) >= 0 ? mumps->id.INFOG(20) : -1000000 * mumps->id.INFOG(20);
    2777:   info->nz_unneeded       = 0.0;
    2778:   info->assemblies        = 0.0;
    2779:   info->mallocs           = 0.0;
    2780:   info->memory            = 0.0;
    2781:   info->fill_ratio_given  = 0;
    2782:   info->fill_ratio_needed = 0;
    2783:   info->factor_mallocs    = 0;
    2784:   PetscFunctionReturn(PETSC_SUCCESS);
    2785: }

    2787: static PetscErrorCode MatFactorSetSchurIS_MUMPS(Mat F, IS is)
    2788: {
    2789:   Mat_MUMPS         *mumps = (Mat_MUMPS *)F->data;
    2790:   const PetscScalar *arr;
    2791:   const PetscInt    *idxs;
    2792:   PetscInt           size, i;

    2794:   PetscFunctionBegin;
    2795:   PetscCall(ISGetLocalSize(is, &size));
    2796:   /* Schur complement matrix */
    2797:   PetscCall(MatDestroy(&F->schur));
    2798:   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, size, size, NULL, &F->schur));
    2799:   PetscCall(MatDenseGetArrayRead(F->schur, &arr));
    2800:   mumps->id.schur = (MumpsScalar *)arr;
    2801:   PetscCall(PetscMUMPSIntCast(size, &mumps->id.size_schur));
    2802:   PetscCall(PetscMUMPSIntCast(size, &mumps->id.schur_lld));
    2803:   PetscCall(MatDenseRestoreArrayRead(F->schur, &arr));
    2804:   if (mumps->sym == 1) PetscCall(MatSetOption(F->schur, MAT_SPD, PETSC_TRUE));

    2806:   /* MUMPS expects Fortran style indices */
    2807:   PetscCall(PetscFree(mumps->id.listvar_schur));
    2808:   PetscCall(PetscMalloc1(size, &mumps->id.listvar_schur));
    2809:   PetscCall(ISGetIndices(is, &idxs));
    2810:   for (i = 0; i < size; i++) PetscCall(PetscMUMPSIntCast(idxs[i] + 1, &mumps->id.listvar_schur[i]));
    2811:   PetscCall(ISRestoreIndices(is, &idxs));
    2812:   /* set a special value of ICNTL (not handled my MUMPS) to be used in the solve phase by PETSc */
    2813:   mumps->id.ICNTL(26) = -1;
    2814:   PetscFunctionReturn(PETSC_SUCCESS);
    2815: }

    2817: static PetscErrorCode MatFactorCreateSchurComplement_MUMPS(Mat F, Mat *S)
    2818: {
    2819:   Mat          St;
    2820:   Mat_MUMPS   *mumps = (Mat_MUMPS *)F->data;
    2821:   PetscScalar *array;

    2823:   PetscFunctionBegin;
    2824:   PetscCheck(mumps->id.ICNTL(19), PetscObjectComm((PetscObject)F), PETSC_ERR_ORDER, "Schur complement mode not selected! Call MatFactorSetSchurIS() to enable it");
    2825:   PetscCall(MatCreate(PETSC_COMM_SELF, &St));
    2826:   PetscCall(MatSetSizes(St, PETSC_DECIDE, PETSC_DECIDE, mumps->id.size_schur, mumps->id.size_schur));
    2827:   PetscCall(MatSetType(St, MATDENSE));
    2828:   PetscCall(MatSetUp(St));
    2829:   PetscCall(MatDenseGetArray(St, &array));
    2830:   if (!mumps->sym) {                /* MUMPS always return a full matrix */
    2831:     if (mumps->id.ICNTL(19) == 1) { /* stored by rows */
    2832:       PetscInt i, j, N = mumps->id.size_schur;
    2833:       for (i = 0; i < N; i++) {
    2834:         for (j = 0; j < N; j++) {
    2835: #if !defined(PETSC_USE_COMPLEX)
    2836:           PetscScalar val = mumps->id.schur[i * N + j];
    2837: #else
    2838:           PetscScalar val = mumps->id.schur[i * N + j].r + PETSC_i * mumps->id.schur[i * N + j].i;
    2839: #endif
    2840:           array[j * N + i] = val;
    2841:         }
    2842:       }
    2843:     } else { /* stored by columns */
    2844:       PetscCall(PetscArraycpy(array, mumps->id.schur, mumps->id.size_schur * mumps->id.size_schur));
    2845:     }
    2846:   } else {                          /* either full or lower-triangular (not packed) */
    2847:     if (mumps->id.ICNTL(19) == 2) { /* lower triangular stored by columns */
    2848:       PetscInt i, j, N = mumps->id.size_schur;
    2849:       for (i = 0; i < N; i++) {
    2850:         for (j = i; j < N; j++) {
    2851: #if !defined(PETSC_USE_COMPLEX)
    2852:           PetscScalar val = mumps->id.schur[i * N + j];
    2853: #else
    2854:           PetscScalar val = mumps->id.schur[i * N + j].r + PETSC_i * mumps->id.schur[i * N + j].i;
    2855: #endif
    2856:           array[i * N + j] = array[j * N + i] = val;
    2857:         }
    2858:       }
    2859:     } else if (mumps->id.ICNTL(19) == 3) { /* full matrix */
    2860:       PetscCall(PetscArraycpy(array, mumps->id.schur, mumps->id.size_schur * mumps->id.size_schur));
    2861:     } else { /* ICNTL(19) == 1 lower triangular stored by rows */
    2862:       PetscInt i, j, N = mumps->id.size_schur;
    2863:       for (i = 0; i < N; i++) {
    2864:         for (j = 0; j < i + 1; j++) {
    2865: #if !defined(PETSC_USE_COMPLEX)
    2866:           PetscScalar val = mumps->id.schur[i * N + j];
    2867: #else
    2868:           PetscScalar val = mumps->id.schur[i * N + j].r + PETSC_i * mumps->id.schur[i * N + j].i;
    2869: #endif
    2870:           array[i * N + j] = array[j * N + i] = val;
    2871:         }
    2872:       }
    2873:     }
    2874:   }
    2875:   PetscCall(MatDenseRestoreArray(St, &array));
    2876:   *S = St;
    2877:   PetscFunctionReturn(PETSC_SUCCESS);
    2878: }

    2880: static PetscErrorCode MatMumpsSetIcntl_MUMPS(Mat F, PetscInt icntl, PetscInt ival)
    2881: {
    2882:   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;

    2884:   PetscFunctionBegin;
    2885:   if (mumps->id.job == JOB_NULL) {                                            /* need to cache icntl and ival since PetscMUMPS_c() has never been called */
    2886:     PetscMUMPSInt i, nICNTL_pre = mumps->ICNTL_pre ? mumps->ICNTL_pre[0] : 0; /* number of already cached ICNTL */
    2887:     for (i = 0; i < nICNTL_pre; ++i)
    2888:       if (mumps->ICNTL_pre[1 + 2 * i] == icntl) break; /* is this ICNTL already cached? */
    2889:     if (i == nICNTL_pre) {                             /* not already cached */
    2890:       if (i > 0) PetscCall(PetscRealloc(sizeof(PetscMUMPSInt) * (2 * nICNTL_pre + 3), &mumps->ICNTL_pre));
    2891:       else PetscCall(PetscCalloc(sizeof(PetscMUMPSInt) * 3, &mumps->ICNTL_pre));
    2892:       mumps->ICNTL_pre[0]++;
    2893:     }
    2894:     mumps->ICNTL_pre[1 + 2 * i] = (PetscMUMPSInt)icntl;
    2895:     PetscCall(PetscMUMPSIntCast(ival, mumps->ICNTL_pre + 2 + 2 * i));
    2896:   } else PetscCall(PetscMUMPSIntCast(ival, &mumps->id.ICNTL(icntl)));
    2897:   PetscFunctionReturn(PETSC_SUCCESS);
    2898: }

    2900: static PetscErrorCode MatMumpsGetIcntl_MUMPS(Mat F, PetscInt icntl, PetscInt *ival)
    2901: {
    2902:   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;

    2904:   PetscFunctionBegin;
    2905:   if (mumps->id.job == JOB_NULL) {
    2906:     PetscInt i, nICNTL_pre = mumps->ICNTL_pre ? mumps->ICNTL_pre[0] : 0;
    2907:     *ival = 0;
    2908:     for (i = 0; i < nICNTL_pre; ++i) {
    2909:       if (mumps->ICNTL_pre[1 + 2 * i] == icntl) *ival = mumps->ICNTL_pre[2 + 2 * i];
    2910:     }
    2911:   } else *ival = mumps->id.ICNTL(icntl);
    2912:   PetscFunctionReturn(PETSC_SUCCESS);
    2913: }

    2915: /*@
    2916:   MatMumpsSetIcntl - Set MUMPS parameter ICNTL() <https://mumps-solver.org/index.php?page=doc>

    2918:   Logically Collective

    2920:   Input Parameters:
    2921: + F     - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
    2922: . icntl - index of MUMPS parameter array `ICNTL()`
    2923: - ival  - value of MUMPS `ICNTL(icntl)`

    2925:   Options Database Key:
    2926: . -mat_mumps_icntl_<icntl> <ival> - change the option numbered `icntl` to `ival`

    2928:   Level: beginner

    2930:   Note:
    2931:   Ignored if MUMPS is not installed or `F` is not a MUMPS matrix

    2933: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`
    2934: @*/
    2935: PetscErrorCode MatMumpsSetIcntl(Mat F, PetscInt icntl, PetscInt ival)
    2936: {
    2937:   PetscFunctionBegin;
    2939:   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
    2942:   PetscCheck((icntl >= 1 && icntl <= 38) || icntl == 48 || icntl == 56 || icntl == 58, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONG, "Unsupported ICNTL value %" PetscInt_FMT, icntl);
    2943:   PetscTryMethod(F, "MatMumpsSetIcntl_C", (Mat, PetscInt, PetscInt), (F, icntl, ival));
    2944:   PetscFunctionReturn(PETSC_SUCCESS);
    2945: }

    2947: /*@
    2948:   MatMumpsGetIcntl - Get MUMPS parameter ICNTL() <https://mumps-solver.org/index.php?page=doc>

    2950:   Logically Collective

    2952:   Input Parameters:
    2953: + F     - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
    2954: - icntl - index of MUMPS parameter array ICNTL()

    2956:   Output Parameter:
    2957: . ival - value of MUMPS ICNTL(icntl)

    2959:   Level: beginner

    2961: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`
    2962: @*/
    2963: PetscErrorCode MatMumpsGetIcntl(Mat F, PetscInt icntl, PetscInt *ival)
    2964: {
    2965:   PetscFunctionBegin;
    2967:   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
    2969:   PetscAssertPointer(ival, 3);
    2970:   PetscCheck((icntl >= 1 && icntl <= 38) || icntl == 48 || icntl == 58, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONG, "Unsupported ICNTL value %" PetscInt_FMT, icntl);
    2971:   PetscUseMethod(F, "MatMumpsGetIcntl_C", (Mat, PetscInt, PetscInt *), (F, icntl, ival));
    2972:   PetscFunctionReturn(PETSC_SUCCESS);
    2973: }

    2975: static PetscErrorCode MatMumpsSetCntl_MUMPS(Mat F, PetscInt icntl, PetscReal val)
    2976: {
    2977:   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;

    2979:   PetscFunctionBegin;
    2980:   if (mumps->id.job == JOB_NULL) {
    2981:     PetscInt i, nCNTL_pre = mumps->CNTL_pre ? mumps->CNTL_pre[0] : 0;
    2982:     for (i = 0; i < nCNTL_pre; ++i)
    2983:       if (mumps->CNTL_pre[1 + 2 * i] == icntl) break;
    2984:     if (i == nCNTL_pre) {
    2985:       if (i > 0) PetscCall(PetscRealloc(sizeof(PetscReal) * (2 * nCNTL_pre + 3), &mumps->CNTL_pre));
    2986:       else PetscCall(PetscCalloc(sizeof(PetscReal) * 3, &mumps->CNTL_pre));
    2987:       mumps->CNTL_pre[0]++;
    2988:     }
    2989:     mumps->CNTL_pre[1 + 2 * i] = icntl;
    2990:     mumps->CNTL_pre[2 + 2 * i] = val;
    2991:   } else mumps->id.CNTL(icntl) = val;
    2992:   PetscFunctionReturn(PETSC_SUCCESS);
    2993: }

    2995: static PetscErrorCode MatMumpsGetCntl_MUMPS(Mat F, PetscInt icntl, PetscReal *val)
    2996: {
    2997:   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;

    2999:   PetscFunctionBegin;
    3000:   if (mumps->id.job == JOB_NULL) {
    3001:     PetscInt i, nCNTL_pre = mumps->CNTL_pre ? mumps->CNTL_pre[0] : 0;
    3002:     *val = 0.0;
    3003:     for (i = 0; i < nCNTL_pre; ++i) {
    3004:       if (mumps->CNTL_pre[1 + 2 * i] == icntl) *val = mumps->CNTL_pre[2 + 2 * i];
    3005:     }
    3006:   } else *val = mumps->id.CNTL(icntl);
    3007:   PetscFunctionReturn(PETSC_SUCCESS);
    3008: }

    3010: /*@
    3011:   MatMumpsSetCntl - Set MUMPS parameter CNTL() <https://mumps-solver.org/index.php?page=doc>

    3013:   Logically Collective

    3015:   Input Parameters:
    3016: + F     - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
    3017: . icntl - index of MUMPS parameter array `CNTL()`
    3018: - val   - value of MUMPS `CNTL(icntl)`

    3020:   Options Database Key:
    3021: . -mat_mumps_cntl_<icntl> <val> - change the option numbered icntl to ival

    3023:   Level: beginner

    3025:   Note:
    3026:   Ignored if MUMPS is not installed or `F` is not a MUMPS matrix

    3028: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`
    3029: @*/
    3030: PetscErrorCode MatMumpsSetCntl(Mat F, PetscInt icntl, PetscReal val)
    3031: {
    3032:   PetscFunctionBegin;
    3034:   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
    3037:   PetscCheck(icntl >= 1 && icntl <= 7, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONG, "Unsupported CNTL value %" PetscInt_FMT, icntl);
    3038:   PetscTryMethod(F, "MatMumpsSetCntl_C", (Mat, PetscInt, PetscReal), (F, icntl, val));
    3039:   PetscFunctionReturn(PETSC_SUCCESS);
    3040: }

    3042: /*@
    3043:   MatMumpsGetCntl - Get MUMPS parameter CNTL() <https://mumps-solver.org/index.php?page=doc>

    3045:   Logically Collective

    3047:   Input Parameters:
    3048: + F     - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
    3049: - icntl - index of MUMPS parameter array CNTL()

    3051:   Output Parameter:
    3052: . val - value of MUMPS CNTL(icntl)

    3054:   Level: beginner

    3056: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`
    3057: @*/
    3058: PetscErrorCode MatMumpsGetCntl(Mat F, PetscInt icntl, PetscReal *val)
    3059: {
    3060:   PetscFunctionBegin;
    3062:   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
    3064:   PetscAssertPointer(val, 3);
    3065:   PetscCheck(icntl >= 1 && icntl <= 7, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONG, "Unsupported CNTL value %" PetscInt_FMT, icntl);
    3066:   PetscUseMethod(F, "MatMumpsGetCntl_C", (Mat, PetscInt, PetscReal *), (F, icntl, val));
    3067:   PetscFunctionReturn(PETSC_SUCCESS);
    3068: }

    3070: static PetscErrorCode MatMumpsGetInfo_MUMPS(Mat F, PetscInt icntl, PetscInt *info)
    3071: {
    3072:   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;

    3074:   PetscFunctionBegin;
    3075:   *info = mumps->id.INFO(icntl);
    3076:   PetscFunctionReturn(PETSC_SUCCESS);
    3077: }

    3079: static PetscErrorCode MatMumpsGetInfog_MUMPS(Mat F, PetscInt icntl, PetscInt *infog)
    3080: {
    3081:   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;

    3083:   PetscFunctionBegin;
    3084:   *infog = mumps->id.INFOG(icntl);
    3085:   PetscFunctionReturn(PETSC_SUCCESS);
    3086: }

    3088: static PetscErrorCode MatMumpsGetRinfo_MUMPS(Mat F, PetscInt icntl, PetscReal *rinfo)
    3089: {
    3090:   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;

    3092:   PetscFunctionBegin;
    3093:   *rinfo = mumps->id.RINFO(icntl);
    3094:   PetscFunctionReturn(PETSC_SUCCESS);
    3095: }

    3097: static PetscErrorCode MatMumpsGetRinfog_MUMPS(Mat F, PetscInt icntl, PetscReal *rinfog)
    3098: {
    3099:   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;

    3101:   PetscFunctionBegin;
    3102:   *rinfog = mumps->id.RINFOG(icntl);
    3103:   PetscFunctionReturn(PETSC_SUCCESS);
    3104: }

    3106: static PetscErrorCode MatMumpsGetNullPivots_MUMPS(Mat F, PetscInt *size, PetscInt **array)
    3107: {
    3108:   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;

    3110:   PetscFunctionBegin;
    3111:   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");
    3112:   *size  = 0;
    3113:   *array = NULL;
    3114:   if (!mumps->myid) {
    3115:     *size = mumps->id.INFOG(28);
    3116:     PetscCall(PetscMalloc1(*size, array));
    3117:     for (int i = 0; i < *size; i++) (*array)[i] = mumps->id.pivnul_list[i] - 1;
    3118:   }
    3119:   PetscFunctionReturn(PETSC_SUCCESS);
    3120: }

    3122: static PetscErrorCode MatMumpsGetInverse_MUMPS(Mat F, Mat spRHS)
    3123: {
    3124:   Mat          Bt = NULL, Btseq = NULL;
    3125:   PetscBool    flg;
    3126:   Mat_MUMPS   *mumps = (Mat_MUMPS *)F->data;
    3127:   PetscScalar *aa;
    3128:   PetscInt     spnr, *ia, *ja, M, nrhs;

    3130:   PetscFunctionBegin;
    3131:   PetscAssertPointer(spRHS, 2);
    3132:   PetscCall(PetscObjectTypeCompare((PetscObject)spRHS, MATTRANSPOSEVIRTUAL, &flg));
    3133:   PetscCheck(flg, PetscObjectComm((PetscObject)spRHS), PETSC_ERR_ARG_WRONG, "Matrix spRHS must be type MATTRANSPOSEVIRTUAL matrix");
    3134:   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));
    3135:   PetscCall(MatTransposeGetMat(spRHS, &Bt));

    3137:   PetscCall(MatMumpsSetIcntl(F, 30, 1));

    3139:   if (mumps->petsc_size > 1) {
    3140:     Mat_MPIAIJ *b = (Mat_MPIAIJ *)Bt->data;
    3141:     Btseq         = b->A;
    3142:   } else {
    3143:     Btseq = Bt;
    3144:   }

    3146:   PetscCall(MatGetSize(spRHS, &M, &nrhs));
    3147:   mumps->id.nrhs = (PetscMUMPSInt)nrhs;
    3148:   PetscCall(PetscMUMPSIntCast(M, &mumps->id.lrhs));
    3149:   mumps->id.rhs = NULL;

    3151:   if (!mumps->myid) {
    3152:     PetscCall(MatSeqAIJGetArray(Btseq, &aa));
    3153:     PetscCall(MatGetRowIJ(Btseq, 1, PETSC_FALSE, PETSC_FALSE, &spnr, (const PetscInt **)&ia, (const PetscInt **)&ja, &flg));
    3154:     PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot get IJ structure");
    3155:     PetscCall(PetscMUMPSIntCSRCast(mumps, spnr, ia, ja, &mumps->id.irhs_ptr, &mumps->id.irhs_sparse, &mumps->id.nz_rhs));
    3156:     mumps->id.rhs_sparse = (MumpsScalar *)aa;
    3157:   } else {
    3158:     mumps->id.irhs_ptr    = NULL;
    3159:     mumps->id.irhs_sparse = NULL;
    3160:     mumps->id.nz_rhs      = 0;
    3161:     mumps->id.rhs_sparse  = NULL;
    3162:   }
    3163:   mumps->id.ICNTL(20) = 1; /* rhs is sparse */
    3164:   mumps->id.ICNTL(21) = 0; /* solution is in assembled centralized format */

    3166:   /* solve phase */
    3167:   mumps->id.job = JOB_SOLVE;
    3168:   PetscMUMPS_c(mumps);
    3169:   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));

    3171:   if (!mumps->myid) {
    3172:     PetscCall(MatSeqAIJRestoreArray(Btseq, &aa));
    3173:     PetscCall(MatRestoreRowIJ(Btseq, 1, PETSC_FALSE, PETSC_FALSE, &spnr, (const PetscInt **)&ia, (const PetscInt **)&ja, &flg));
    3174:     PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot get IJ structure");
    3175:   }
    3176:   PetscFunctionReturn(PETSC_SUCCESS);
    3177: }

    3179: /*@
    3180:   MatMumpsGetInverse - Get user-specified set of entries in inverse of `A` <https://mumps-solver.org/index.php?page=doc>

    3182:   Logically Collective

    3184:   Input Parameter:
    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`

    3187:   Output Parameter:
    3188: . spRHS - sequential sparse matrix in `MATTRANSPOSEVIRTUAL` format with requested entries of inverse of `A`

    3190:   Level: beginner

    3192: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatCreateTranspose()`
    3193: @*/
    3194: PetscErrorCode MatMumpsGetInverse(Mat F, Mat spRHS)
    3195: {
    3196:   PetscFunctionBegin;
    3198:   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
    3199:   PetscUseMethod(F, "MatMumpsGetInverse_C", (Mat, Mat), (F, spRHS));
    3200:   PetscFunctionReturn(PETSC_SUCCESS);
    3201: }

    3203: static PetscErrorCode MatMumpsGetInverseTranspose_MUMPS(Mat F, Mat spRHST)
    3204: {
    3205:   Mat spRHS;

    3207:   PetscFunctionBegin;
    3208:   PetscCall(MatCreateTranspose(spRHST, &spRHS));
    3209:   PetscCall(MatMumpsGetInverse_MUMPS(F, spRHS));
    3210:   PetscCall(MatDestroy(&spRHS));
    3211:   PetscFunctionReturn(PETSC_SUCCESS);
    3212: }

    3214: /*@
    3215:   MatMumpsGetInverseTranspose - Get user-specified set of entries in inverse of matrix $A^T $ <https://mumps-solver.org/index.php?page=doc>

    3217:   Logically Collective

    3219:   Input Parameter:
    3220: . 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`

    3222:   Output Parameter:
    3223: . spRHST - sequential sparse matrix in `MATAIJ` format containing the requested entries of inverse of `A`^T

    3225:   Level: beginner

    3227: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatCreateTranspose()`, `MatMumpsGetInverse()`
    3228: @*/
    3229: PetscErrorCode MatMumpsGetInverseTranspose(Mat F, Mat spRHST)
    3230: {
    3231:   PetscBool flg;

    3233:   PetscFunctionBegin;
    3235:   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
    3236:   PetscCall(PetscObjectTypeCompareAny((PetscObject)spRHST, &flg, MATSEQAIJ, MATMPIAIJ, NULL));
    3237:   PetscCheck(flg, PetscObjectComm((PetscObject)spRHST), PETSC_ERR_ARG_WRONG, "Matrix spRHST must be MATAIJ matrix");
    3238:   PetscUseMethod(F, "MatMumpsGetInverseTranspose_C", (Mat, Mat), (F, spRHST));
    3239:   PetscFunctionReturn(PETSC_SUCCESS);
    3240: }

    3242: static PetscErrorCode MatMumpsSetBlk_MUMPS(Mat F, PetscInt nblk, const PetscInt blkvar[], const PetscInt blkptr[])
    3243: {
    3244:   Mat_MUMPS *mumps = (Mat_MUMPS *)F->data;

    3246:   PetscFunctionBegin;
    3247:   if (nblk) {
    3248:     PetscAssertPointer(blkptr, 4);
    3249:     PetscCall(PetscMUMPSIntCast(nblk, &mumps->id.nblk));
    3250:     PetscCall(PetscFree(mumps->id.blkptr));
    3251:     PetscCall(PetscMalloc1(nblk + 1, &mumps->id.blkptr));
    3252:     for (PetscInt i = 0; i < nblk + 1; ++i) PetscCall(PetscMUMPSIntCast(blkptr[i], mumps->id.blkptr + i));
    3253:     mumps->id.ICNTL(15) = 1;
    3254:     if (blkvar) {
    3255:       PetscCall(PetscFree(mumps->id.blkvar));
    3256:       PetscCall(PetscMalloc1(F->rmap->N, &mumps->id.blkvar));
    3257:       for (PetscInt i = 0; i < F->rmap->N; ++i) PetscCall(PetscMUMPSIntCast(blkvar[i], mumps->id.blkvar + i));
    3258:     }
    3259:   } else {
    3260:     PetscCall(PetscFree(mumps->id.blkptr));
    3261:     PetscCall(PetscFree(mumps->id.blkvar));
    3262:     mumps->id.ICNTL(15) = 0;
    3263:   }
    3264:   PetscFunctionReturn(PETSC_SUCCESS);
    3265: }

    3267: /*@
    3268:   MatMumpsSetBlk - Set user-specified variable block sizes to be used with `-mat_mumps_icntl_15 1`

    3270:   Not collective, only relevant on the first process of the MPI communicator

    3272:   Input Parameters:
    3273: + 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`
    3274: . nblk   - the number of blocks
    3275: . blkvar - see MUMPS documentation, `blkvar(blkptr(iblk):blkptr(iblk+1)-1)`, (`iblk=1, nblk`) holds the variables associated to block `iblk`
    3276: - blkptr - array starting at 1 and of size `nblk + 1` storing the prefix sum of all blocks

    3278:   Level: advanced

    3280: .seealso: [](ch_matrices), `MATSOLVERMUMPS`, `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatSetVariableBlockSizes()`
    3281: @*/
    3282: PetscErrorCode MatMumpsSetBlk(Mat F, PetscInt nblk, const PetscInt blkvar[], const PetscInt blkptr[])
    3283: {
    3284:   PetscFunctionBegin;
    3286:   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
    3287:   PetscUseMethod(F, "MatMumpsSetBlk_C", (Mat, PetscInt, const PetscInt[], const PetscInt[]), (F, nblk, blkvar, blkptr));
    3288:   PetscFunctionReturn(PETSC_SUCCESS);
    3289: }

    3291: /*@
    3292:   MatMumpsGetInfo - Get MUMPS parameter INFO() <https://mumps-solver.org/index.php?page=doc>

    3294:   Logically Collective

    3296:   Input Parameters:
    3297: + F     - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
    3298: - icntl - index of MUMPS parameter array INFO()

    3300:   Output Parameter:
    3301: . ival - value of MUMPS INFO(icntl)

    3303:   Level: beginner

    3305: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`
    3306: @*/
    3307: PetscErrorCode MatMumpsGetInfo(Mat F, PetscInt icntl, PetscInt *ival)
    3308: {
    3309:   PetscFunctionBegin;
    3311:   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
    3312:   PetscAssertPointer(ival, 3);
    3313:   PetscUseMethod(F, "MatMumpsGetInfo_C", (Mat, PetscInt, PetscInt *), (F, icntl, ival));
    3314:   PetscFunctionReturn(PETSC_SUCCESS);
    3315: }

    3317: /*@
    3318:   MatMumpsGetInfog - Get MUMPS parameter INFOG() <https://mumps-solver.org/index.php?page=doc>

    3320:   Logically Collective

    3322:   Input Parameters:
    3323: + F     - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
    3324: - icntl - index of MUMPS parameter array INFOG()

    3326:   Output Parameter:
    3327: . ival - value of MUMPS INFOG(icntl)

    3329:   Level: beginner

    3331: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`
    3332: @*/
    3333: PetscErrorCode MatMumpsGetInfog(Mat F, PetscInt icntl, PetscInt *ival)
    3334: {
    3335:   PetscFunctionBegin;
    3337:   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
    3338:   PetscAssertPointer(ival, 3);
    3339:   PetscUseMethod(F, "MatMumpsGetInfog_C", (Mat, PetscInt, PetscInt *), (F, icntl, ival));
    3340:   PetscFunctionReturn(PETSC_SUCCESS);
    3341: }

    3343: /*@
    3344:   MatMumpsGetRinfo - Get MUMPS parameter RINFO() <https://mumps-solver.org/index.php?page=doc>

    3346:   Logically Collective

    3348:   Input Parameters:
    3349: + F     - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
    3350: - icntl - index of MUMPS parameter array RINFO()

    3352:   Output Parameter:
    3353: . val - value of MUMPS RINFO(icntl)

    3355:   Level: beginner

    3357: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfog()`
    3358: @*/
    3359: PetscErrorCode MatMumpsGetRinfo(Mat F, PetscInt icntl, PetscReal *val)
    3360: {
    3361:   PetscFunctionBegin;
    3363:   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
    3364:   PetscAssertPointer(val, 3);
    3365:   PetscUseMethod(F, "MatMumpsGetRinfo_C", (Mat, PetscInt, PetscReal *), (F, icntl, val));
    3366:   PetscFunctionReturn(PETSC_SUCCESS);
    3367: }

    3369: /*@
    3370:   MatMumpsGetRinfog - Get MUMPS parameter RINFOG() <https://mumps-solver.org/index.php?page=doc>

    3372:   Logically Collective

    3374:   Input Parameters:
    3375: + F     - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`
    3376: - icntl - index of MUMPS parameter array RINFOG()

    3378:   Output Parameter:
    3379: . val - value of MUMPS RINFOG(icntl)

    3381:   Level: beginner

    3383: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`
    3384: @*/
    3385: PetscErrorCode MatMumpsGetRinfog(Mat F, PetscInt icntl, PetscReal *val)
    3386: {
    3387:   PetscFunctionBegin;
    3389:   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
    3390:   PetscAssertPointer(val, 3);
    3391:   PetscUseMethod(F, "MatMumpsGetRinfog_C", (Mat, PetscInt, PetscReal *), (F, icntl, val));
    3392:   PetscFunctionReturn(PETSC_SUCCESS);
    3393: }

    3395: /*@
    3396:   MatMumpsGetNullPivots - Get MUMPS parameter PIVNUL_LIST() <https://mumps-solver.org/index.php?page=doc>

    3398:   Logically Collective

    3400:   Input Parameter:
    3401: . F - the factored matrix obtained by calling `MatGetFactor()` with a `MatSolverType` of `MATSOLVERMUMPS` and a `MatFactorType` of `MAT_FACTOR_LU` or `MAT_FACTOR_CHOLESKY`

    3403:   Output Parameters:
    3404: + size  - local size of the array. The size of the array is non-zero only on MPI rank 0
    3405: - 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
    3406:           for freeing this array.

    3408:   Level: beginner

    3410: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`
    3411: @*/
    3412: PetscErrorCode MatMumpsGetNullPivots(Mat F, PetscInt *size, PetscInt **array)
    3413: {
    3414:   PetscFunctionBegin;
    3416:   PetscCheck(F->factortype, PetscObjectComm((PetscObject)F), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
    3417:   PetscAssertPointer(size, 2);
    3418:   PetscAssertPointer(array, 3);
    3419:   PetscUseMethod(F, "MatMumpsGetNullPivots_C", (Mat, PetscInt *, PetscInt **), (F, size, array));
    3420:   PetscFunctionReturn(PETSC_SUCCESS);
    3421: }

    3423: /*MC
    3424:   MATSOLVERMUMPS -  A matrix type providing direct solvers (LU and Cholesky) for
    3425:   MPI distributed and sequential matrices via the external package MUMPS <https://mumps-solver.org/index.php?page=doc>

    3427:   Works with `MATAIJ` and `MATSBAIJ` matrices

    3429:   Use ./configure --download-mumps --download-scalapack --download-parmetis --download-metis --download-ptscotch to have PETSc installed with MUMPS

    3431:   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.
    3432:   See details below.

    3434:   Use `-pc_type cholesky` or `lu` `-pc_factor_mat_solver_type mumps` to use this direct solver

    3436:   Options Database Keys:
    3437: +  -mat_mumps_icntl_1  - ICNTL(1): output stream for error messages
    3438: .  -mat_mumps_icntl_2  - ICNTL(2): output stream for diagnostic printing, statistics, and warning
    3439: .  -mat_mumps_icntl_3  - ICNTL(3): output stream for global information, collected on the host
    3440: .  -mat_mumps_icntl_4  - ICNTL(4): level of printing (0 to 4)
    3441: .  -mat_mumps_icntl_6  - ICNTL(6): permutes to a zero-free diagonal and/or scale the matrix (0 to 7)
    3442: .  -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
    3443:                           Use -pc_factor_mat_ordering_type <type> to have PETSc perform the ordering (sequential only)
    3444: .  -mat_mumps_icntl_8  - ICNTL(8): scaling strategy (-2 to 8 or 77)
    3445: .  -mat_mumps_icntl_10 - ICNTL(10): max num of refinements
    3446: .  -mat_mumps_icntl_11 - ICNTL(11): statistics related to an error analysis (via -ksp_view)
    3447: .  -mat_mumps_icntl_12 - ICNTL(12): an ordering strategy for symmetric matrices (0 to 3)
    3448: .  -mat_mumps_icntl_13 - ICNTL(13): parallelism of the root node (enable ScaLAPACK) and its splitting
    3449: .  -mat_mumps_icntl_14 - ICNTL(14): percentage increase in the estimated working space
    3450: .  -mat_mumps_icntl_15 - ICNTL(15): compression of the input matrix resulting from a block format
    3451: .  -mat_mumps_icntl_19 - ICNTL(19): computes the Schur complement
    3452: .  -mat_mumps_icntl_20 - ICNTL(20): give MUMPS centralized (0) or distributed (10) dense RHS
    3453: .  -mat_mumps_icntl_22 - ICNTL(22): in-core/out-of-core factorization and solve (0 or 1)
    3454: .  -mat_mumps_icntl_23 - ICNTL(23): max size of the working memory (MB) that can allocate per processor
    3455: .  -mat_mumps_icntl_24 - ICNTL(24): detection of null pivot rows (0 or 1)
    3456: .  -mat_mumps_icntl_25 - ICNTL(25): compute a solution of a deficient matrix and a null space basis
    3457: .  -mat_mumps_icntl_26 - ICNTL(26): drives the solution phase if a Schur complement matrix
    3458: .  -mat_mumps_icntl_28 - ICNTL(28): use 1 for sequential analysis and ICNTL(7) ordering, or 2 for parallel analysis and ICNTL(29) ordering
    3459: .  -mat_mumps_icntl_29 - ICNTL(29): parallel ordering 1 = ptscotch, 2 = parmetis
    3460: .  -mat_mumps_icntl_30 - ICNTL(30): compute user-specified set of entries in inv(A)
    3461: .  -mat_mumps_icntl_31 - ICNTL(31): indicates which factors may be discarded during factorization
    3462: .  -mat_mumps_icntl_33 - ICNTL(33): compute determinant
    3463: .  -mat_mumps_icntl_35 - ICNTL(35): level of activation of BLR (Block Low-Rank) feature
    3464: .  -mat_mumps_icntl_36 - ICNTL(36): controls the choice of BLR factorization variant
    3465: .  -mat_mumps_icntl_37 - ICNTL(37): compression of the contribution blocks (CB)
    3466: .  -mat_mumps_icntl_38 - ICNTL(38): sets the estimated compression rate of LU factors with BLR
    3467: .  -mat_mumps_icntl_48 - ICNTL(48): multithreading with tree parallelism
    3468: .  -mat_mumps_icntl_58 - ICNTL(58): options for symbolic factorization
    3469: .  -mat_mumps_cntl_1   - CNTL(1): relative pivoting threshold
    3470: .  -mat_mumps_cntl_2   - CNTL(2): stopping criterion of refinement
    3471: .  -mat_mumps_cntl_3   - CNTL(3): absolute pivoting threshold
    3472: .  -mat_mumps_cntl_4   - CNTL(4): value for static pivoting
    3473: .  -mat_mumps_cntl_5   - CNTL(5): fixation for null pivots
    3474: .  -mat_mumps_cntl_7   - CNTL(7): precision of the dropping parameter used during BLR factorization
    3475: -  -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.
    3476:                                     Default might be the number of cores per CPU package (socket) as reported by hwloc and suggested by the MUMPS manual.

    3478:   Level: beginner

    3480:   Notes:
    3481:   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
    3482:   error if the matrix is Hermitian.

    3484:   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
    3485:   `MatSetOptionsPrefixFactor()` on the matrix from which the factor was obtained or `MatSetOptionsPrefix()` on the factor matrix.

    3487:   When a MUMPS factorization fails inside a KSP solve, for example with a `KSP_DIVERGED_PC_FAILED`, one can find the MUMPS information about
    3488:   the failure with
    3489: .vb
    3490:           KSPGetPC(ksp,&pc);
    3491:           PCFactorGetMatrix(pc,&mat);
    3492:           MatMumpsGetInfo(mat,....);
    3493:           MatMumpsGetInfog(mat,....); etc.
    3494: .ve
    3495:   Or run with `-ksp_error_if_not_converged` and the program will be stopped and the information printed in the error message.

    3497:   MUMPS provides 64-bit integer support in two build modes:
    3498:   full 64-bit: here MUMPS is built with C preprocessing flag -DINTSIZE64 and Fortran compiler option -i8, -fdefault-integer-8 or equivalent, and
    3499:   requires all dependent libraries MPI, ScaLAPACK, LAPACK and BLAS built the same way with 64-bit integers (for example ILP64 Intel MKL and MPI).

    3501:   selective 64-bit: with the default MUMPS build, 64-bit integers have been introduced where needed. In compressed sparse row (CSR) storage of matrices,
    3502:   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
    3503:   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
    3504:   integer) build of all dependent libraries MPI, ScaLAPACK, LAPACK and BLAS.

    3506:   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.

    3508:   Two modes to run MUMPS/PETSc with OpenMP
    3509: .vb
    3510:    Set `OMP_NUM_THREADS` and run with fewer MPI ranks than cores. For example, if you want to have 16 OpenMP
    3511:    threads per rank, then you may use "export `OMP_NUM_THREADS` = 16 && mpirun -n 4 ./test".
    3512: .ve

    3514: .vb
    3515:    `-mat_mumps_use_omp_threads` [m] and run your code with as many MPI ranks as the number of cores. For example,
    3516:    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"
    3517: .ve

    3519:    To run MUMPS in MPI+OpenMP hybrid mode (i.e., enable multithreading in MUMPS), but still run the non-MUMPS part
    3520:    (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`
    3521:    (or `--with-hwloc`), and have an MPI that supports MPI-3.0's process shared memory (which is usually available). Since MUMPS calls BLAS
    3522:    libraries, to really get performance, you should have multithreaded BLAS libraries such as Intel MKL, AMD ACML, Cray libSci or OpenBLAS
    3523:    (PETSc will automatically try to utilized a threaded BLAS if `--with-openmp` is provided).

    3525:    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
    3526:    processes on each compute node. Listing the processes in rank ascending order, we split processes on a node into consecutive groups of
    3527:    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
    3528:    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
    3529:    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.
    3530:    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,
    3531:    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
    3532:    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
    3533:    cores in socket 1, that definitely hurts locality. On the other hand, if you map MPI ranks consecutively on the two sockets, then the
    3534:    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.
    3535:    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
    3536:    examine the mapping result.

    3538:    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,
    3539:    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
    3540:    calls `omp_set_num_threads`(m) internally before calling MUMPS.

    3542:    See {cite}`heroux2011bi` and {cite}`gutierrez2017accommodating`

    3544: .seealso: [](ch_matrices), `Mat`, `PCFactorSetMatSolverType()`, `MatSolverType`, `MatMumpsSetIcntl()`, `MatMumpsGetIcntl()`, `MatMumpsSetCntl()`, `MatMumpsGetCntl()`, `MatMumpsGetInfo()`, `MatMumpsGetInfog()`, `MatMumpsGetRinfo()`, `MatMumpsGetRinfog()`, `MatMumpsSetBlk()`, `KSPGetPC()`, `PCFactorGetMatrix()`
    3545: M*/

    3547: static PetscErrorCode MatFactorGetSolverType_mumps(PETSC_UNUSED Mat A, MatSolverType *type)
    3548: {
    3549:   PetscFunctionBegin;
    3550:   *type = MATSOLVERMUMPS;
    3551:   PetscFunctionReturn(PETSC_SUCCESS);
    3552: }

    3554: /* MatGetFactor for Seq and MPI AIJ matrices */
    3555: static PetscErrorCode MatGetFactor_aij_mumps(Mat A, MatFactorType ftype, Mat *F)
    3556: {
    3557:   Mat         B;
    3558:   Mat_MUMPS  *mumps;
    3559:   PetscBool   isSeqAIJ, isDiag, isDense;
    3560:   PetscMPIInt size;

    3562:   PetscFunctionBegin;
    3563: #if defined(PETSC_USE_COMPLEX)
    3564:   if (ftype == MAT_FACTOR_CHOLESKY && A->hermitian == PETSC_BOOL3_TRUE && A->symmetric != PETSC_BOOL3_TRUE) {
    3565:     PetscCall(PetscInfo(A, "Hermitian MAT_FACTOR_CHOLESKY is not supported. Use MAT_FACTOR_LU instead.\n"));
    3566:     *F = NULL;
    3567:     PetscFunctionReturn(PETSC_SUCCESS);
    3568:   }
    3569: #endif
    3570:   /* Create the factorization matrix */
    3571:   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATSEQAIJ, &isSeqAIJ));
    3572:   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATDIAGONAL, &isDiag));
    3573:   PetscCall(PetscObjectTypeCompareAny((PetscObject)A, &isDense, MATSEQDENSE, MATMPIDENSE, NULL));
    3574:   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
    3575:   PetscCall(MatSetSizes(B, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
    3576:   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &((PetscObject)B)->type_name));
    3577:   PetscCall(MatSetUp(B));

    3579:   PetscCall(PetscNew(&mumps));

    3581:   B->ops->view    = MatView_MUMPS;
    3582:   B->ops->getinfo = MatGetInfo_MUMPS;

    3584:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorGetSolverType_C", MatFactorGetSolverType_mumps));
    3585:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorSetSchurIS_C", MatFactorSetSchurIS_MUMPS));
    3586:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorCreateSchurComplement_C", MatFactorCreateSchurComplement_MUMPS));
    3587:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetIcntl_C", MatMumpsSetIcntl_MUMPS));
    3588:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetIcntl_C", MatMumpsGetIcntl_MUMPS));
    3589:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetCntl_C", MatMumpsSetCntl_MUMPS));
    3590:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetCntl_C", MatMumpsGetCntl_MUMPS));
    3591:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfo_C", MatMumpsGetInfo_MUMPS));
    3592:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfog_C", MatMumpsGetInfog_MUMPS));
    3593:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfo_C", MatMumpsGetRinfo_MUMPS));
    3594:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfog_C", MatMumpsGetRinfog_MUMPS));
    3595:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetNullPivots_C", MatMumpsGetNullPivots_MUMPS));
    3596:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverse_C", MatMumpsGetInverse_MUMPS));
    3597:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverseTranspose_C", MatMumpsGetInverseTranspose_MUMPS));
    3598:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetBlk_C", MatMumpsSetBlk_MUMPS));

    3600:   if (ftype == MAT_FACTOR_LU) {
    3601:     B->ops->lufactorsymbolic = MatLUFactorSymbolic_AIJMUMPS;
    3602:     B->factortype            = MAT_FACTOR_LU;
    3603:     if (isSeqAIJ) mumps->ConvertToTriples = MatConvertToTriples_seqaij_seqaij;
    3604:     else if (isDiag) mumps->ConvertToTriples = MatConvertToTriples_diagonal_xaij;
    3605:     else if (isDense) mumps->ConvertToTriples = MatConvertToTriples_dense_xaij;
    3606:     else mumps->ConvertToTriples = MatConvertToTriples_mpiaij_mpiaij;
    3607:     PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&B->preferredordering[MAT_FACTOR_LU]));
    3608:     mumps->sym = 0;
    3609:   } else {
    3610:     B->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_MUMPS;
    3611:     B->factortype                  = MAT_FACTOR_CHOLESKY;
    3612:     if (isSeqAIJ) mumps->ConvertToTriples = MatConvertToTriples_seqaij_seqsbaij;
    3613:     else if (isDiag) mumps->ConvertToTriples = MatConvertToTriples_diagonal_xaij;
    3614:     else if (isDense) mumps->ConvertToTriples = MatConvertToTriples_dense_xaij;
    3615:     else mumps->ConvertToTriples = MatConvertToTriples_mpiaij_mpisbaij;
    3616:     PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&B->preferredordering[MAT_FACTOR_CHOLESKY]));
    3617: #if defined(PETSC_USE_COMPLEX)
    3618:     mumps->sym = 2;
    3619: #else
    3620:     if (A->spd == PETSC_BOOL3_TRUE) mumps->sym = 1;
    3621:     else mumps->sym = 2;
    3622: #endif
    3623:   }

    3625:   /* set solvertype */
    3626:   PetscCall(PetscFree(B->solvertype));
    3627:   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &B->solvertype));
    3628:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
    3629:   if (size == 1) {
    3630:     /* MUMPS option -mat_mumps_icntl_7 1 is automatically set if PETSc ordering is passed into symbolic factorization */
    3631:     B->canuseordering = PETSC_TRUE;
    3632:   }
    3633:   B->ops->destroy = MatDestroy_MUMPS;
    3634:   B->data         = (void *)mumps;

    3636:   *F               = B;
    3637:   mumps->id.job    = JOB_NULL;
    3638:   mumps->ICNTL_pre = NULL;
    3639:   mumps->CNTL_pre  = NULL;
    3640:   mumps->matstruc  = DIFFERENT_NONZERO_PATTERN;
    3641:   PetscFunctionReturn(PETSC_SUCCESS);
    3642: }

    3644: /* MatGetFactor for Seq and MPI SBAIJ matrices */
    3645: static PetscErrorCode MatGetFactor_sbaij_mumps(Mat A, PETSC_UNUSED MatFactorType ftype, Mat *F)
    3646: {
    3647:   Mat         B;
    3648:   Mat_MUMPS  *mumps;
    3649:   PetscBool   isSeqSBAIJ;
    3650:   PetscMPIInt size;

    3652:   PetscFunctionBegin;
    3653: #if defined(PETSC_USE_COMPLEX)
    3654:   if (ftype == MAT_FACTOR_CHOLESKY && A->hermitian == PETSC_BOOL3_TRUE && A->symmetric != PETSC_BOOL3_TRUE) {
    3655:     PetscCall(PetscInfo(A, "Hermitian MAT_FACTOR_CHOLESKY is not supported. Use MAT_FACTOR_LU instead.\n"));
    3656:     *F = NULL;
    3657:     PetscFunctionReturn(PETSC_SUCCESS);
    3658:   }
    3659: #endif
    3660:   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
    3661:   PetscCall(MatSetSizes(B, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
    3662:   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &((PetscObject)B)->type_name));
    3663:   PetscCall(MatSetUp(B));

    3665:   PetscCall(PetscNew(&mumps));
    3666:   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQSBAIJ, &isSeqSBAIJ));
    3667:   if (isSeqSBAIJ) {
    3668:     mumps->ConvertToTriples = MatConvertToTriples_seqsbaij_seqsbaij;
    3669:   } else {
    3670:     mumps->ConvertToTriples = MatConvertToTriples_mpisbaij_mpisbaij;
    3671:   }

    3673:   B->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_MUMPS;
    3674:   B->ops->view                   = MatView_MUMPS;
    3675:   B->ops->getinfo                = MatGetInfo_MUMPS;

    3677:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorGetSolverType_C", MatFactorGetSolverType_mumps));
    3678:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorSetSchurIS_C", MatFactorSetSchurIS_MUMPS));
    3679:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorCreateSchurComplement_C", MatFactorCreateSchurComplement_MUMPS));
    3680:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetIcntl_C", MatMumpsSetIcntl_MUMPS));
    3681:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetIcntl_C", MatMumpsGetIcntl_MUMPS));
    3682:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetCntl_C", MatMumpsSetCntl_MUMPS));
    3683:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetCntl_C", MatMumpsGetCntl_MUMPS));
    3684:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfo_C", MatMumpsGetInfo_MUMPS));
    3685:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfog_C", MatMumpsGetInfog_MUMPS));
    3686:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfo_C", MatMumpsGetRinfo_MUMPS));
    3687:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfog_C", MatMumpsGetRinfog_MUMPS));
    3688:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetNullPivots_C", MatMumpsGetNullPivots_MUMPS));
    3689:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverse_C", MatMumpsGetInverse_MUMPS));
    3690:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverseTranspose_C", MatMumpsGetInverseTranspose_MUMPS));
    3691:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetBlk_C", MatMumpsSetBlk_MUMPS));

    3693:   B->factortype = MAT_FACTOR_CHOLESKY;
    3694: #if defined(PETSC_USE_COMPLEX)
    3695:   mumps->sym = 2;
    3696: #else
    3697:   if (A->spd == PETSC_BOOL3_TRUE) mumps->sym = 1;
    3698:   else mumps->sym = 2;
    3699: #endif

    3701:   /* set solvertype */
    3702:   PetscCall(PetscFree(B->solvertype));
    3703:   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &B->solvertype));
    3704:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
    3705:   if (size == 1) {
    3706:     /* MUMPS option -mat_mumps_icntl_7 1 is automatically set if PETSc ordering is passed into symbolic factorization */
    3707:     B->canuseordering = PETSC_TRUE;
    3708:   }
    3709:   PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&B->preferredordering[MAT_FACTOR_CHOLESKY]));
    3710:   B->ops->destroy = MatDestroy_MUMPS;
    3711:   B->data         = (void *)mumps;

    3713:   *F               = B;
    3714:   mumps->id.job    = JOB_NULL;
    3715:   mumps->ICNTL_pre = NULL;
    3716:   mumps->CNTL_pre  = NULL;
    3717:   mumps->matstruc  = DIFFERENT_NONZERO_PATTERN;
    3718:   PetscFunctionReturn(PETSC_SUCCESS);
    3719: }

    3721: static PetscErrorCode MatGetFactor_baij_mumps(Mat A, MatFactorType ftype, Mat *F)
    3722: {
    3723:   Mat         B;
    3724:   Mat_MUMPS  *mumps;
    3725:   PetscBool   isSeqBAIJ;
    3726:   PetscMPIInt size;

    3728:   PetscFunctionBegin;
    3729:   /* Create the factorization matrix */
    3730:   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQBAIJ, &isSeqBAIJ));
    3731:   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
    3732:   PetscCall(MatSetSizes(B, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
    3733:   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &((PetscObject)B)->type_name));
    3734:   PetscCall(MatSetUp(B));

    3736:   PetscCall(PetscNew(&mumps));
    3737:   PetscCheck(ftype == MAT_FACTOR_LU, PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot use PETSc BAIJ matrices with MUMPS Cholesky, use SBAIJ or AIJ matrix instead");
    3738:   B->ops->lufactorsymbolic = MatLUFactorSymbolic_BAIJMUMPS;
    3739:   B->factortype            = MAT_FACTOR_LU;
    3740:   if (isSeqBAIJ) mumps->ConvertToTriples = MatConvertToTriples_seqbaij_seqaij;
    3741:   else mumps->ConvertToTriples = MatConvertToTriples_mpibaij_mpiaij;
    3742:   mumps->sym = 0;
    3743:   PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&B->preferredordering[MAT_FACTOR_LU]));

    3745:   B->ops->view    = MatView_MUMPS;
    3746:   B->ops->getinfo = MatGetInfo_MUMPS;

    3748:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorGetSolverType_C", MatFactorGetSolverType_mumps));
    3749:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorSetSchurIS_C", MatFactorSetSchurIS_MUMPS));
    3750:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorCreateSchurComplement_C", MatFactorCreateSchurComplement_MUMPS));
    3751:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetIcntl_C", MatMumpsSetIcntl_MUMPS));
    3752:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetIcntl_C", MatMumpsGetIcntl_MUMPS));
    3753:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetCntl_C", MatMumpsSetCntl_MUMPS));
    3754:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetCntl_C", MatMumpsGetCntl_MUMPS));
    3755:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfo_C", MatMumpsGetInfo_MUMPS));
    3756:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfog_C", MatMumpsGetInfog_MUMPS));
    3757:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfo_C", MatMumpsGetRinfo_MUMPS));
    3758:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfog_C", MatMumpsGetRinfog_MUMPS));
    3759:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetNullPivots_C", MatMumpsGetNullPivots_MUMPS));
    3760:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverse_C", MatMumpsGetInverse_MUMPS));
    3761:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverseTranspose_C", MatMumpsGetInverseTranspose_MUMPS));
    3762:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetBlk_C", MatMumpsSetBlk_MUMPS));

    3764:   /* set solvertype */
    3765:   PetscCall(PetscFree(B->solvertype));
    3766:   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &B->solvertype));
    3767:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
    3768:   if (size == 1) {
    3769:     /* MUMPS option -mat_mumps_icntl_7 1 is automatically set if PETSc ordering is passed into symbolic factorization */
    3770:     B->canuseordering = PETSC_TRUE;
    3771:   }
    3772:   B->ops->destroy = MatDestroy_MUMPS;
    3773:   B->data         = (void *)mumps;

    3775:   *F               = B;
    3776:   mumps->id.job    = JOB_NULL;
    3777:   mumps->ICNTL_pre = NULL;
    3778:   mumps->CNTL_pre  = NULL;
    3779:   mumps->matstruc  = DIFFERENT_NONZERO_PATTERN;
    3780:   PetscFunctionReturn(PETSC_SUCCESS);
    3781: }

    3783: /* MatGetFactor for Seq and MPI SELL matrices */
    3784: static PetscErrorCode MatGetFactor_sell_mumps(Mat A, MatFactorType ftype, Mat *F)
    3785: {
    3786:   Mat         B;
    3787:   Mat_MUMPS  *mumps;
    3788:   PetscBool   isSeqSELL;
    3789:   PetscMPIInt size;

    3791:   PetscFunctionBegin;
    3792:   /* Create the factorization matrix */
    3793:   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQSELL, &isSeqSELL));
    3794:   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
    3795:   PetscCall(MatSetSizes(B, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
    3796:   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &((PetscObject)B)->type_name));
    3797:   PetscCall(MatSetUp(B));

    3799:   PetscCall(PetscNew(&mumps));

    3801:   B->ops->view    = MatView_MUMPS;
    3802:   B->ops->getinfo = MatGetInfo_MUMPS;

    3804:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorGetSolverType_C", MatFactorGetSolverType_mumps));
    3805:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorSetSchurIS_C", MatFactorSetSchurIS_MUMPS));
    3806:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorCreateSchurComplement_C", MatFactorCreateSchurComplement_MUMPS));
    3807:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetIcntl_C", MatMumpsSetIcntl_MUMPS));
    3808:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetIcntl_C", MatMumpsGetIcntl_MUMPS));
    3809:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetCntl_C", MatMumpsSetCntl_MUMPS));
    3810:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetCntl_C", MatMumpsGetCntl_MUMPS));
    3811:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfo_C", MatMumpsGetInfo_MUMPS));
    3812:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfog_C", MatMumpsGetInfog_MUMPS));
    3813:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfo_C", MatMumpsGetRinfo_MUMPS));
    3814:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfog_C", MatMumpsGetRinfog_MUMPS));
    3815:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetNullPivots_C", MatMumpsGetNullPivots_MUMPS));

    3817:   PetscCheck(ftype == MAT_FACTOR_LU, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "To be implemented");
    3818:   B->ops->lufactorsymbolic = MatLUFactorSymbolic_AIJMUMPS;
    3819:   B->factortype            = MAT_FACTOR_LU;
    3820:   PetscCheck(isSeqSELL, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "To be implemented");
    3821:   mumps->ConvertToTriples = MatConvertToTriples_seqsell_seqaij;
    3822:   mumps->sym              = 0;
    3823:   PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&B->preferredordering[MAT_FACTOR_LU]));

    3825:   /* set solvertype */
    3826:   PetscCall(PetscFree(B->solvertype));
    3827:   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &B->solvertype));
    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:   B->ops->destroy = MatDestroy_MUMPS;
    3834:   B->data         = (void *)mumps;

    3836:   *F               = B;
    3837:   mumps->id.job    = JOB_NULL;
    3838:   mumps->ICNTL_pre = NULL;
    3839:   mumps->CNTL_pre  = NULL;
    3840:   mumps->matstruc  = DIFFERENT_NONZERO_PATTERN;
    3841:   PetscFunctionReturn(PETSC_SUCCESS);
    3842: }

    3844: /* MatGetFactor for MATNEST matrices */
    3845: static PetscErrorCode MatGetFactor_nest_mumps(Mat A, MatFactorType ftype, Mat *F)
    3846: {
    3847:   Mat         B, **mats;
    3848:   Mat_MUMPS  *mumps;
    3849:   PetscInt    nr, nc;
    3850:   PetscMPIInt size;
    3851:   PetscBool   flg = PETSC_TRUE;

    3853:   PetscFunctionBegin;
    3854: #if defined(PETSC_USE_COMPLEX)
    3855:   if (ftype == MAT_FACTOR_CHOLESKY && A->hermitian == PETSC_BOOL3_TRUE && A->symmetric != PETSC_BOOL3_TRUE) {
    3856:     PetscCall(PetscInfo(A, "Hermitian MAT_FACTOR_CHOLESKY is not supported. Use MAT_FACTOR_LU instead.\n"));
    3857:     *F = NULL;
    3858:     PetscFunctionReturn(PETSC_SUCCESS);
    3859:   }
    3860: #endif

    3862:   /* Return if some condition is not satisfied */
    3863:   *F = NULL;
    3864:   PetscCall(MatNestGetSubMats(A, &nr, &nc, &mats));
    3865:   if (ftype == MAT_FACTOR_CHOLESKY) {
    3866:     IS       *rows, *cols;
    3867:     PetscInt *m, *M;

    3869:     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);
    3870:     PetscCall(PetscMalloc2(nr, &rows, nc, &cols));
    3871:     PetscCall(MatNestGetISs(A, rows, cols));
    3872:     for (PetscInt r = 0; flg && r < nr; r++) PetscCall(ISEqualUnsorted(rows[r], cols[r], &flg));
    3873:     if (!flg) {
    3874:       PetscCall(PetscFree2(rows, cols));
    3875:       PetscCall(PetscInfo(A, "MAT_FACTOR_CHOLESKY not supported for unequal row and column maps. Use MAT_FACTOR_LU.\n"));
    3876:       PetscFunctionReturn(PETSC_SUCCESS);
    3877:     }
    3878:     PetscCall(PetscMalloc2(nr, &m, nr, &M));
    3879:     for (PetscInt r = 0; r < nr; r++) PetscCall(ISGetMinMax(rows[r], &m[r], &M[r]));
    3880:     for (PetscInt r = 0; flg && r < nr; r++)
    3881:       for (PetscInt k = r + 1; flg && k < nr; k++)
    3882:         if ((m[k] <= m[r] && m[r] <= M[k]) || (m[k] <= M[r] && M[r] <= M[k])) flg = PETSC_FALSE;
    3883:     PetscCall(PetscFree2(m, M));
    3884:     PetscCall(PetscFree2(rows, cols));
    3885:     if (!flg) {
    3886:       PetscCall(PetscInfo(A, "MAT_FACTOR_CHOLESKY not supported for intersecting row maps. Use MAT_FACTOR_LU.\n"));
    3887:       PetscFunctionReturn(PETSC_SUCCESS);
    3888:     }
    3889:   }

    3891:   for (PetscInt r = 0; r < nr; r++) {
    3892:     for (PetscInt c = 0; c < nc; c++) {
    3893:       Mat       sub = mats[r][c];
    3894:       PetscBool isSeqAIJ, isMPIAIJ, isSeqBAIJ, isMPIBAIJ, isSeqSBAIJ, isMPISBAIJ, isDiag, isDense;

    3896:       if (!sub || (ftype == MAT_FACTOR_CHOLESKY && c < r)) continue;
    3897:       PetscCall(MatGetTranspose_TransposeVirtual(&sub, NULL, NULL, NULL, NULL));
    3898:       PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATSEQAIJ, &isSeqAIJ));
    3899:       PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATMPIAIJ, &isMPIAIJ));
    3900:       PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATSEQBAIJ, &isSeqBAIJ));
    3901:       PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATMPIBAIJ, &isMPIBAIJ));
    3902:       PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATSEQSBAIJ, &isSeqSBAIJ));
    3903:       PetscCall(PetscObjectBaseTypeCompare((PetscObject)sub, MATMPISBAIJ, &isMPISBAIJ));
    3904:       PetscCall(PetscObjectTypeCompare((PetscObject)sub, MATDIAGONAL, &isDiag));
    3905:       PetscCall(PetscObjectTypeCompareAny((PetscObject)sub, &isDense, MATSEQDENSE, MATMPIDENSE, NULL));
    3906:       if (ftype == MAT_FACTOR_CHOLESKY) {
    3907:         if (r == c) {
    3908:           if (!isSeqAIJ && !isMPIAIJ && !isSeqBAIJ && !isMPIBAIJ && !isSeqSBAIJ && !isMPISBAIJ && !isDiag && !isDense) {
    3909:             PetscCall(PetscInfo(sub, "MAT_FACTOR_CHOLESKY not supported for diagonal block of type %s.\n", ((PetscObject)sub)->type_name));
    3910:             flg = PETSC_FALSE;
    3911:           }
    3912:         } else if (!isSeqAIJ && !isMPIAIJ && !isSeqBAIJ && !isMPIBAIJ && !isDiag && !isDense) {
    3913:           PetscCall(PetscInfo(sub, "MAT_FACTOR_CHOLESKY not supported for off-diagonal block of type %s.\n", ((PetscObject)sub)->type_name));
    3914:           flg = PETSC_FALSE;
    3915:         }
    3916:       } else if (!isSeqAIJ && !isMPIAIJ && !isSeqBAIJ && !isMPIBAIJ && !isDiag && !isDense) {
    3917:         PetscCall(PetscInfo(sub, "MAT_FACTOR_LU not supported for block of type %s.\n", ((PetscObject)sub)->type_name));
    3918:         flg = PETSC_FALSE;
    3919:       }
    3920:     }
    3921:   }
    3922:   if (!flg) PetscFunctionReturn(PETSC_SUCCESS);

    3924:   /* Create the factorization matrix */
    3925:   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
    3926:   PetscCall(MatSetSizes(B, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
    3927:   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &((PetscObject)B)->type_name));
    3928:   PetscCall(MatSetUp(B));

    3930:   PetscCall(PetscNew(&mumps));

    3932:   B->ops->view    = MatView_MUMPS;
    3933:   B->ops->getinfo = MatGetInfo_MUMPS;

    3935:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorGetSolverType_C", MatFactorGetSolverType_mumps));
    3936:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorSetSchurIS_C", MatFactorSetSchurIS_MUMPS));
    3937:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorCreateSchurComplement_C", MatFactorCreateSchurComplement_MUMPS));
    3938:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetIcntl_C", MatMumpsSetIcntl_MUMPS));
    3939:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetIcntl_C", MatMumpsGetIcntl_MUMPS));
    3940:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetCntl_C", MatMumpsSetCntl_MUMPS));
    3941:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetCntl_C", MatMumpsGetCntl_MUMPS));
    3942:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfo_C", MatMumpsGetInfo_MUMPS));
    3943:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInfog_C", MatMumpsGetInfog_MUMPS));
    3944:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfo_C", MatMumpsGetRinfo_MUMPS));
    3945:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetRinfog_C", MatMumpsGetRinfog_MUMPS));
    3946:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetNullPivots_C", MatMumpsGetNullPivots_MUMPS));
    3947:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverse_C", MatMumpsGetInverse_MUMPS));
    3948:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsGetInverseTranspose_C", MatMumpsGetInverseTranspose_MUMPS));
    3949:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMumpsSetBlk_C", MatMumpsSetBlk_MUMPS));

    3951:   if (ftype == MAT_FACTOR_LU) {
    3952:     B->ops->lufactorsymbolic = MatLUFactorSymbolic_AIJMUMPS;
    3953:     B->factortype            = MAT_FACTOR_LU;
    3954:     mumps->sym               = 0;
    3955:   } else {
    3956:     B->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_MUMPS;
    3957:     B->factortype                  = MAT_FACTOR_CHOLESKY;
    3958: #if defined(PETSC_USE_COMPLEX)
    3959:     mumps->sym = 2;
    3960: #else
    3961:     if (A->spd == PETSC_BOOL3_TRUE) mumps->sym = 1;
    3962:     else mumps->sym = 2;
    3963: #endif
    3964:   }
    3965:   mumps->ConvertToTriples = MatConvertToTriples_nest_xaij;
    3966:   PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&B->preferredordering[ftype]));

    3968:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
    3969:   if (size == 1) {
    3970:     /* MUMPS option -mat_mumps_icntl_7 1 is automatically set if PETSc ordering is passed into symbolic factorization */
    3971:     B->canuseordering = PETSC_TRUE;
    3972:   }

    3974:   /* set solvertype */
    3975:   PetscCall(PetscFree(B->solvertype));
    3976:   PetscCall(PetscStrallocpy(MATSOLVERMUMPS, &B->solvertype));
    3977:   B->ops->destroy = MatDestroy_MUMPS;
    3978:   B->data         = (void *)mumps;

    3980:   *F               = B;
    3981:   mumps->id.job    = JOB_NULL;
    3982:   mumps->ICNTL_pre = NULL;
    3983:   mumps->CNTL_pre  = NULL;
    3984:   mumps->matstruc  = DIFFERENT_NONZERO_PATTERN;
    3985:   PetscFunctionReturn(PETSC_SUCCESS);
    3986: }

    3988: PETSC_INTERN PetscErrorCode MatSolverTypeRegister_MUMPS(void)
    3989: {
    3990:   PetscFunctionBegin;
    3991:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPIAIJ, MAT_FACTOR_LU, MatGetFactor_aij_mumps));
    3992:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPIAIJ, MAT_FACTOR_CHOLESKY, MatGetFactor_aij_mumps));
    3993:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPIBAIJ, MAT_FACTOR_LU, MatGetFactor_baij_mumps));
    3994:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPIBAIJ, MAT_FACTOR_CHOLESKY, MatGetFactor_baij_mumps));
    3995:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPISBAIJ, MAT_FACTOR_CHOLESKY, MatGetFactor_sbaij_mumps));
    3996:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQAIJ, MAT_FACTOR_LU, MatGetFactor_aij_mumps));
    3997:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQAIJ, MAT_FACTOR_CHOLESKY, MatGetFactor_aij_mumps));
    3998:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQBAIJ, MAT_FACTOR_LU, MatGetFactor_baij_mumps));
    3999:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQBAIJ, MAT_FACTOR_CHOLESKY, MatGetFactor_baij_mumps));
    4000:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQSBAIJ, MAT_FACTOR_CHOLESKY, MatGetFactor_sbaij_mumps));
    4001:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQSELL, MAT_FACTOR_LU, MatGetFactor_sell_mumps));
    4002:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATDIAGONAL, MAT_FACTOR_LU, MatGetFactor_aij_mumps));
    4003:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATDIAGONAL, MAT_FACTOR_CHOLESKY, MatGetFactor_aij_mumps));
    4004:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQDENSE, MAT_FACTOR_LU, MatGetFactor_aij_mumps));
    4005:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATSEQDENSE, MAT_FACTOR_CHOLESKY, MatGetFactor_aij_mumps));
    4006:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPIDENSE, MAT_FACTOR_LU, MatGetFactor_aij_mumps));
    4007:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATMPIDENSE, MAT_FACTOR_CHOLESKY, MatGetFactor_aij_mumps));
    4008:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATNEST, MAT_FACTOR_LU, MatGetFactor_nest_mumps));
    4009:   PetscCall(MatSolverTypeRegister(MATSOLVERMUMPS, MATNEST, MAT_FACTOR_CHOLESKY, MatGetFactor_nest_mumps));
    4010:   PetscFunctionReturn(PETSC_SUCCESS);
    4011: }