Date: 2022-08-02T03:13:49+00:00

Actual source code: mumps.c

      2: /*
      3:     Provides an interface to the MUMPS sparse solver
      4: */
      5: #include <petscpkg_version.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: EXTERN_C_BEGIN
     11: #if defined(PETSC_USE_COMPLEX)
     12: #if defined(PETSC_USE_REAL_SINGLE)
     13: #include <cmumps_c.h>
     14: #else
     15: #include <zmumps_c.h>
     16: #endif
     17: #else
     18: #if defined(PETSC_USE_REAL_SINGLE)
     19: #include <smumps_c.h>
     20: #else
     21: #include <dmumps_c.h>
     22: #endif
     23: #endif
     24: EXTERN_C_END
     25: #define JOB_INIT -1
     26: #define JOB_FACTSYMBOLIC 1
     27: #define JOB_FACTNUMERIC 2
     28: #define JOB_SOLVE 3
     29: #define JOB_END -2

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

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

     52: #if PETSC_PKG_MUMPS_VERSION_GE(5,3,0)
     53:   #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 */
     54:     #error "Petsc has not been tested with full 64-bit MUMPS and we choose to error out"
     55:   #endif
     56: #else
     57:   #if defined(INTSIZE64) /* INTSIZE64 is a command line macro one used to build MUMPS in full 64-bit mode */
     58:     #error "Petsc has not been tested with full 64-bit MUMPS and we choose to error out"
     59:   #endif
     60: #endif

     62: #define MPIU_MUMPSINT             MPI_INT
     63: #define PETSC_MUMPS_INT_MAX       2147483647
     64: #define PETSC_MUMPS_INT_MIN       -2147483648

     66: /* Cast PetscInt to PetscMUMPSInt. Usually there is no overflow since <a> is row/col indices or some small integers*/
     67: static inline PetscErrorCode PetscMUMPSIntCast(PetscInt a,PetscMUMPSInt *b)
     68: {
     69: #if PetscDefined(USE_64BIT_INDICES)
     70:   PetscAssert(a <= PETSC_MUMPS_INT_MAX && a >= PETSC_MUMPS_INT_MIN,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"PetscInt too long for PetscMUMPSInt");
     71: #endif
     72:   *b = (PetscMUMPSInt)(a);
     73:   return 0;
     74: }

     76: /* Put these utility routines here since they are only used in this file */
     77: 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)
     78: {
     79:   PetscInt       myval;
     80:   PetscBool      myset;
     81:   /* PetscInt's size should be always >= PetscMUMPSInt's. It is safe to call PetscOptionsInt_Private to read a PetscMUMPSInt */
     82:   PetscOptionsInt_Private(PetscOptionsObject,opt,text,man,(PetscInt)currentvalue,&myval,&myset,lb,ub);
     83:   if (myset) PetscMUMPSIntCast(myval,value);
     84:   if (set) *set = myset;
     85:   return 0;
     86: }
     87: #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)

     89: /* 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 */
     90: #if defined(PETSC_HAVE_OPENMP_SUPPORT)
     91: #define PetscMUMPS_c(mumps) \
     92:   do { \
     93:     if (mumps->use_petsc_omp_support) { \
     94:       if (mumps->is_omp_master) { \
     95:         PetscOmpCtrlOmpRegionOnMasterBegin(mumps->omp_ctrl); \
     96:         MUMPS_c(&mumps->id); \
     97:         PetscOmpCtrlOmpRegionOnMasterEnd(mumps->omp_ctrl); \
     98:       } \
     99:       PetscOmpCtrlBarrier(mumps->omp_ctrl); \
    100:       /* Global info is same on all processes so we Bcast it within omp_comm. Local info is specific      \
    101:          to processes, so we only Bcast info[1], an error code and leave others (since they do not have   \
    102:          an easy translation between omp_comm and petsc_comm). See MUMPS-5.1.2 manual p82.                   \
    103:          omp_comm is a small shared memory communicator, hence doing multiple Bcast as shown below is OK. \
    104:       */ \
    105:       MPI_Bcast(mumps->id.infog, 40,MPIU_MUMPSINT, 0,mumps->omp_comm);\
    106:       MPI_Bcast(mumps->id.rinfog,20,MPIU_REAL,     0,mumps->omp_comm);\
    107:       MPI_Bcast(mumps->id.info,  1, MPIU_MUMPSINT, 0,mumps->omp_comm);\
    108:     } else { \
    109:       MUMPS_c(&mumps->id); \
    110:     } \
    111:   } while (0)
    112: #else
    113: #define PetscMUMPS_c(mumps) \
    114:   do { MUMPS_c(&mumps->id); } while (0)
    115: #endif

    117: /* declare MumpsScalar */
    118: #if defined(PETSC_USE_COMPLEX)
    119: #if defined(PETSC_USE_REAL_SINGLE)
    120: #define MumpsScalar mumps_complex
    121: #else
    122: #define MumpsScalar mumps_double_complex
    123: #endif
    124: #else
    125: #define MumpsScalar PetscScalar
    126: #endif

    128: /* macros s.t. indices match MUMPS documentation */
    129: #define ICNTL(I) icntl[(I)-1]
    130: #define CNTL(I) cntl[(I)-1]
    131: #define INFOG(I) infog[(I)-1]
    132: #define INFO(I) info[(I)-1]
    133: #define RINFOG(I) rinfog[(I)-1]
    134: #define RINFO(I) rinfo[(I)-1]

    136: typedef struct Mat_MUMPS Mat_MUMPS;
    137: struct Mat_MUMPS {
    138: #if defined(PETSC_USE_COMPLEX)
    139: #if defined(PETSC_USE_REAL_SINGLE)
    140:   CMUMPS_STRUC_C id;
    141: #else
    142:   ZMUMPS_STRUC_C id;
    143: #endif
    144: #else
    145: #if defined(PETSC_USE_REAL_SINGLE)
    146:   SMUMPS_STRUC_C id;
    147: #else
    148:   DMUMPS_STRUC_C id;
    149: #endif
    150: #endif

    152:   MatStructure   matstruc;
    153:   PetscMPIInt    myid,petsc_size;
    154:   PetscMUMPSInt  *irn,*jcn;             /* the (i,j,v) triplets passed to mumps. */
    155:   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. */
    156:   PetscInt64     nnz;                   /* number of nonzeros. The type is called selective 64-bit in mumps */
    157:   PetscMUMPSInt  sym;
    158:   MPI_Comm       mumps_comm;
    159:   PetscMUMPSInt  ICNTL9_pre;            /* check if ICNTL(9) is changed from previous MatSolve */
    160:   VecScatter     scat_rhs, scat_sol;    /* used by MatSolve() */
    161:   PetscMUMPSInt  ICNTL20;               /* use centralized (0) or distributed (10) dense RHS */
    162:   PetscMUMPSInt  lrhs_loc,nloc_rhs,*irhs_loc;
    163: #if defined(PETSC_HAVE_OPENMP_SUPPORT)
    164:   PetscInt       *rhs_nrow,max_nrhs;
    165:   PetscMPIInt    *rhs_recvcounts,*rhs_disps;
    166:   PetscScalar    *rhs_loc,*rhs_recvbuf;
    167: #endif
    168:   Vec            b_seq,x_seq;
    169:   PetscInt       ninfo,*info;           /* which INFO to display */
    170:   PetscInt       sizeredrhs;
    171:   PetscScalar    *schur_sol;
    172:   PetscInt       schur_sizesol;
    173:   PetscMUMPSInt  *ia_alloc,*ja_alloc;   /* work arrays used for the CSR struct for sparse rhs */
    174:   PetscInt64     cur_ilen,cur_jlen;     /* current len of ia_alloc[], ja_alloc[] */
    175:   PetscErrorCode (*ConvertToTriples)(Mat,PetscInt,MatReuse,Mat_MUMPS*);

    177:   /* stuff used by petsc/mumps OpenMP support*/
    178:   PetscBool      use_petsc_omp_support;
    179:   PetscOmpCtrl   omp_ctrl;              /* an OpenMP controler that blocked processes will release their CPU (MPI_Barrier does not have this guarantee) */
    180:   MPI_Comm       petsc_comm,omp_comm;   /* petsc_comm is petsc matrix's comm */
    181:   PetscInt64     *recvcount;            /* a collection of nnz on omp_master */
    182:   PetscMPIInt    tag,omp_comm_size;
    183:   PetscBool      is_omp_master;         /* is this rank the master of omp_comm */
    184:   MPI_Request    *reqs;
    185: };

    187: /* Cast a 1-based CSR represented by (nrow, ia, ja) of type PetscInt to a CSR of type PetscMUMPSInt.
    188:    Here, nrow is number of rows, ia[] is row pointer and ja[] is column indices.
    189:  */
    190: static PetscErrorCode PetscMUMPSIntCSRCast(Mat_MUMPS *mumps,PetscInt nrow,PetscInt *ia,PetscInt *ja,PetscMUMPSInt **ia_mumps,PetscMUMPSInt **ja_mumps,PetscMUMPSInt *nnz_mumps)
    191: {
    192:   PetscInt       nnz=ia[nrow]-1; /* mumps uses 1-based indices. Uses PetscInt instead of PetscInt64 since mumps only uses PetscMUMPSInt for rhs */

    194: #if defined(PETSC_USE_64BIT_INDICES)
    195:   {
    196:     PetscInt i;
    197:     if (nrow+1 > mumps->cur_ilen) { /* realloc ia_alloc/ja_alloc to fit ia/ja */
    198:       PetscFree(mumps->ia_alloc);
    199:       PetscMalloc1(nrow+1,&mumps->ia_alloc);
    200:       mumps->cur_ilen = nrow+1;
    201:     }
    202:     if (nnz > mumps->cur_jlen) {
    203:       PetscFree(mumps->ja_alloc);
    204:       PetscMalloc1(nnz,&mumps->ja_alloc);
    205:       mumps->cur_jlen = nnz;
    206:     }
    207:     for (i=0; i<nrow+1; i++) PetscMUMPSIntCast(ia[i],&(mumps->ia_alloc[i]));
    208:     for (i=0; i<nnz; i++)    PetscMUMPSIntCast(ja[i],&(mumps->ja_alloc[i]));
    209:     *ia_mumps = mumps->ia_alloc;
    210:     *ja_mumps = mumps->ja_alloc;
    211:   }
    212: #else
    213:   *ia_mumps = ia;
    214:   *ja_mumps = ja;
    215: #endif
    216:   PetscMUMPSIntCast(nnz,nnz_mumps);
    217:   return 0;
    218: }

    220: static PetscErrorCode MatMumpsResetSchur_Private(Mat_MUMPS* mumps)
    221: {
    222:   PetscFree(mumps->id.listvar_schur);
    223:   PetscFree(mumps->id.redrhs);
    224:   PetscFree(mumps->schur_sol);
    225:   mumps->id.size_schur = 0;
    226:   mumps->id.schur_lld  = 0;
    227:   mumps->id.ICNTL(19)  = 0;
    228:   return 0;
    229: }

    231: /* solve with rhs in mumps->id.redrhs and return in the same location */
    232: static PetscErrorCode MatMumpsSolveSchur_Private(Mat F)
    233: {
    234:   Mat_MUMPS            *mumps=(Mat_MUMPS*)F->data;
    235:   Mat                  S,B,X;
    236:   MatFactorSchurStatus schurstatus;
    237:   PetscInt             sizesol;

    239:   MatFactorFactorizeSchurComplement(F);
    240:   MatFactorGetSchurComplement(F,&S,&schurstatus);
    241:   MatCreateSeqDense(PETSC_COMM_SELF,mumps->id.size_schur,mumps->id.nrhs,(PetscScalar*)mumps->id.redrhs,&B);
    242:   MatSetType(B,((PetscObject)S)->type_name);
    243: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
    244:   MatBindToCPU(B,S->boundtocpu);
    245: #endif
    246:   switch (schurstatus) {
    247:   case MAT_FACTOR_SCHUR_FACTORED:
    248:     MatCreateSeqDense(PETSC_COMM_SELF,mumps->id.size_schur,mumps->id.nrhs,(PetscScalar*)mumps->id.redrhs,&X);
    249:     MatSetType(X,((PetscObject)S)->type_name);
    250: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
    251:     MatBindToCPU(X,S->boundtocpu);
    252: #endif
    253:     if (!mumps->id.ICNTL(9)) { /* transpose solve */
    254:       MatMatSolveTranspose(S,B,X);
    255:     } else {
    256:       MatMatSolve(S,B,X);
    257:     }
    258:     break;
    259:   case MAT_FACTOR_SCHUR_INVERTED:
    260:     sizesol = mumps->id.nrhs*mumps->id.size_schur;
    261:     if (!mumps->schur_sol || sizesol > mumps->schur_sizesol) {
    262:       PetscFree(mumps->schur_sol);
    263:       PetscMalloc1(sizesol,&mumps->schur_sol);
    264:       mumps->schur_sizesol = sizesol;
    265:     }
    266:     MatCreateSeqDense(PETSC_COMM_SELF,mumps->id.size_schur,mumps->id.nrhs,mumps->schur_sol,&X);
    267:     MatSetType(X,((PetscObject)S)->type_name);
    268: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
    269:     MatBindToCPU(X,S->boundtocpu);
    270: #endif
    271:     MatProductCreateWithMat(S,B,NULL,X);
    272:     if (!mumps->id.ICNTL(9)) { /* transpose solve */
    273:       MatProductSetType(X,MATPRODUCT_AtB);
    274:     } else {
    275:       MatProductSetType(X,MATPRODUCT_AB);
    276:     }
    277:     MatProductSetFromOptions(X);
    278:     MatProductSymbolic(X);
    279:     MatProductNumeric(X);

    281:     MatCopy(X,B,SAME_NONZERO_PATTERN);
    282:     break;
    283:   default:
    284:     SETERRQ(PetscObjectComm((PetscObject)F),PETSC_ERR_SUP,"Unhandled MatFactorSchurStatus %d",F->schur_status);
    285:   }
    286:   MatFactorRestoreSchurComplement(F,&S,schurstatus);
    287:   MatDestroy(&B);
    288:   MatDestroy(&X);
    289:   return 0;
    290: }

    292: static PetscErrorCode MatMumpsHandleSchur_Private(Mat F, PetscBool expansion)
    293: {
    294:   Mat_MUMPS     *mumps=(Mat_MUMPS*)F->data;

    296:   if (!mumps->id.ICNTL(19)) { /* do nothing when Schur complement has not been computed */
    297:     return 0;
    298:   }
    299:   if (!expansion) { /* prepare for the condensation step */
    300:     PetscInt sizeredrhs = mumps->id.nrhs*mumps->id.size_schur;
    301:     /* allocate MUMPS internal array to store reduced right-hand sides */
    302:     if (!mumps->id.redrhs || sizeredrhs > mumps->sizeredrhs) {
    303:       PetscFree(mumps->id.redrhs);
    304:       mumps->id.lredrhs = mumps->id.size_schur;
    305:       PetscMalloc1(mumps->id.nrhs*mumps->id.lredrhs,&mumps->id.redrhs);
    306:       mumps->sizeredrhs = mumps->id.nrhs*mumps->id.lredrhs;
    307:     }
    308:     mumps->id.ICNTL(26) = 1; /* condensation phase */
    309:   } else { /* prepare for the expansion step */
    310:     /* solve Schur complement (this has to be done by the MUMPS user, so basically us) */
    311:     MatMumpsSolveSchur_Private(F);
    312:     mumps->id.ICNTL(26) = 2; /* expansion phase */
    313:     PetscMUMPS_c(mumps);
    315:     /* restore defaults */
    316:     mumps->id.ICNTL(26) = -1;
    317:     /* free MUMPS internal array for redrhs if we have solved for multiple rhs in order to save memory space */
    318:     if (mumps->id.nrhs > 1) {
    319:       PetscFree(mumps->id.redrhs);
    320:       mumps->id.lredrhs = 0;
    321:       mumps->sizeredrhs = 0;
    322:     }
    323:   }
    324:   return 0;
    325: }

    327: /*
    328:   MatConvertToTriples_A_B - convert Petsc matrix to triples: row[nz], col[nz], val[nz]

    330:   input:
    331:     A       - matrix in aij,baij or sbaij format
    332:     shift   - 0: C style output triple; 1: Fortran style output triple.
    333:     reuse   - MAT_INITIAL_MATRIX: spaces are allocated and values are set for the triple
    334:               MAT_REUSE_MATRIX:   only the values in v array are updated
    335:   output:
    336:     nnz     - dim of r, c, and v (number of local nonzero entries of A)
    337:     r, c, v - row and col index, matrix values (matrix triples)

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

    343:  */

    345: PetscErrorCode MatConvertToTriples_seqaij_seqaij(Mat A,PetscInt shift,MatReuse reuse,Mat_MUMPS *mumps)
    346: {
    347:   const PetscScalar *av;
    348:   const PetscInt    *ai,*aj,*ajj,M=A->rmap->n;
    349:   PetscInt64        nz,rnz,i,j,k;
    350:   PetscMUMPSInt     *row,*col;
    351:   Mat_SeqAIJ        *aa=(Mat_SeqAIJ*)A->data;

    353:   MatSeqAIJGetArrayRead(A,&av);
    354:   mumps->val = (PetscScalar*)av;
    355:   if (reuse == MAT_INITIAL_MATRIX) {
    356:     nz   = aa->nz;
    357:     ai   = aa->i;
    358:     aj   = aa->j;
    359:     PetscMalloc2(nz,&row,nz,&col);
    360:     for (i=k=0; i<M; i++) {
    361:       rnz = ai[i+1] - ai[i];
    362:       ajj = aj + ai[i];
    363:       for (j=0; j<rnz; j++) {
    364:         PetscMUMPSIntCast(i+shift,&row[k]);
    365:         PetscMUMPSIntCast(ajj[j] + shift,&col[k]);
    366:         k++;
    367:       }
    368:     }
    369:     mumps->irn = row;
    370:     mumps->jcn = col;
    371:     mumps->nnz = nz;
    372:   }
    373:   MatSeqAIJRestoreArrayRead(A,&av);
    374:   return 0;
    375: }

    377: PetscErrorCode MatConvertToTriples_seqsell_seqaij(Mat A,PetscInt shift,MatReuse reuse,Mat_MUMPS *mumps)
    378: {
    379:   PetscInt64     nz,i,j,k,r;
    380:   Mat_SeqSELL    *a=(Mat_SeqSELL*)A->data;
    381:   PetscMUMPSInt  *row,*col;

    383:   mumps->val = a->val;
    384:   if (reuse == MAT_INITIAL_MATRIX) {
    385:     nz   = a->sliidx[a->totalslices];
    386:     PetscMalloc2(nz,&row,nz,&col);
    387:     for (i=k=0; i<a->totalslices; i++) {
    388:       for (j=a->sliidx[i],r=0; j<a->sliidx[i+1]; j++,r=((r+1)&0x07)) {
    389:         PetscMUMPSIntCast(8*i+r+shift,&row[k++]);
    390:       }
    391:     }
    392:     for (i=0;i<nz;i++) PetscMUMPSIntCast(a->colidx[i]+shift,&col[i]);
    393:     mumps->irn = row;
    394:     mumps->jcn = col;
    395:     mumps->nnz = nz;
    396:   }
    397:   return 0;
    398: }

    400: PetscErrorCode MatConvertToTriples_seqbaij_seqaij(Mat A,PetscInt shift,MatReuse reuse,Mat_MUMPS *mumps)
    401: {
    402:   Mat_SeqBAIJ    *aa=(Mat_SeqBAIJ*)A->data;
    403:   const PetscInt *ai,*aj,*ajj,bs2 = aa->bs2;
    404:   PetscInt64     M,nz,idx=0,rnz,i,j,k,m;
    405:   PetscInt       bs;
    406:   PetscMUMPSInt  *row,*col;

    408:   MatGetBlockSize(A,&bs);
    409:   M          = A->rmap->N/bs;
    410:   mumps->val = aa->a;
    411:   if (reuse == MAT_INITIAL_MATRIX) {
    412:     ai   = aa->i; aj = aa->j;
    413:     nz   = bs2*aa->nz;
    414:     PetscMalloc2(nz,&row,nz,&col);
    415:     for (i=0; i<M; i++) {
    416:       ajj = aj + ai[i];
    417:       rnz = ai[i+1] - ai[i];
    418:       for (k=0; k<rnz; k++) {
    419:         for (j=0; j<bs; j++) {
    420:           for (m=0; m<bs; m++) {
    421:             PetscMUMPSIntCast(i*bs + m + shift,&row[idx]);
    422:             PetscMUMPSIntCast(bs*ajj[k] + j + shift,&col[idx]);
    423:             idx++;
    424:           }
    425:         }
    426:       }
    427:     }
    428:     mumps->irn = row;
    429:     mumps->jcn = col;
    430:     mumps->nnz = nz;
    431:   }
    432:   return 0;
    433: }

    435: PetscErrorCode MatConvertToTriples_seqsbaij_seqsbaij(Mat A,PetscInt shift,MatReuse reuse,Mat_MUMPS *mumps)
    436: {
    437:   const PetscInt *ai, *aj,*ajj;
    438:   PetscInt        bs;
    439:   PetscInt64      nz,rnz,i,j,k,m;
    440:   PetscMUMPSInt   *row,*col;
    441:   PetscScalar     *val;
    442:   Mat_SeqSBAIJ    *aa=(Mat_SeqSBAIJ*)A->data;
    443:   const PetscInt  bs2=aa->bs2,mbs=aa->mbs;
    444: #if defined(PETSC_USE_COMPLEX)
    445:   PetscBool       hermitian;
    446: #endif

    448: #if defined(PETSC_USE_COMPLEX)
    449:   MatGetOption(A,MAT_HERMITIAN,&hermitian);
    451: #endif
    452:   ai   = aa->i;
    453:   aj   = aa->j;
    454:   MatGetBlockSize(A,&bs);
    455:   if (reuse == MAT_INITIAL_MATRIX) {
    456:     nz   = aa->nz;
    457:     PetscMalloc2(bs2*nz,&row,bs2*nz,&col);
    458:     if (bs>1) {
    459:       PetscMalloc1(bs2*nz,&mumps->val_alloc);
    460:       mumps->val = mumps->val_alloc;
    461:     } else {
    462:       mumps->val = aa->a;
    463:     }
    464:     mumps->irn = row;
    465:     mumps->jcn = col;
    466:   } else {
    467:     if (bs == 1) mumps->val = aa->a;
    468:     row = mumps->irn;
    469:     col = mumps->jcn;
    470:   }
    471:   val = mumps->val;

    473:   nz = 0;
    474:   if (bs>1) {
    475:     for (i=0; i<mbs; i++) {
    476:       rnz = ai[i+1] - ai[i];
    477:       ajj = aj + ai[i];
    478:       for (j=0; j<rnz; j++) {
    479:         for (k=0; k<bs; k++) {
    480:           for (m=0; m<bs; m++) {
    481:             if (ajj[j]>i || k>=m) {
    482:               if (reuse == MAT_INITIAL_MATRIX) {
    483:                 PetscMUMPSIntCast(i*bs + m + shift,&row[nz]);
    484:                 PetscMUMPSIntCast(ajj[j]*bs + k + shift,&col[nz]);
    485:               }
    486:               val[nz++] = aa->a[(ai[i]+j)*bs2 + m + k*bs];
    487:             }
    488:           }
    489:         }
    490:       }
    491:     }
    492:   } else if (reuse == MAT_INITIAL_MATRIX) {
    493:     for (i=0; i<mbs; i++) {
    494:       rnz = ai[i+1] - ai[i];
    495:       ajj = aj + ai[i];
    496:       for (j=0; j<rnz; j++) {
    497:         PetscMUMPSIntCast(i+shift,&row[nz]);
    498:         PetscMUMPSIntCast(ajj[j] + shift,&col[nz]);
    499:         nz++;
    500:       }
    501:     }
    503:   }
    504:   if (reuse == MAT_INITIAL_MATRIX) mumps->nnz = nz;
    505:   return 0;
    506: }

    508: PetscErrorCode MatConvertToTriples_seqaij_seqsbaij(Mat A,PetscInt shift,MatReuse reuse,Mat_MUMPS *mumps)
    509: {
    510:   const PetscInt    *ai,*aj,*ajj,*adiag,M=A->rmap->n;
    511:   PetscInt64        nz,rnz,i,j;
    512:   const PetscScalar *av,*v1;
    513:   PetscScalar       *val;
    514:   PetscMUMPSInt     *row,*col;
    515:   Mat_SeqAIJ        *aa=(Mat_SeqAIJ*)A->data;
    516:   PetscBool         missing;
    517: #if defined(PETSC_USE_COMPLEX)
    518:   PetscBool         hermitian;
    519: #endif

    521: #if defined(PETSC_USE_COMPLEX)
    522:   MatGetOption(A,MAT_HERMITIAN,&hermitian);
    524: #endif
    525:   MatSeqAIJGetArrayRead(A,&av);
    526:   ai    = aa->i; aj = aa->j;
    527:   adiag = aa->diag;
    528:   MatMissingDiagonal_SeqAIJ(A,&missing,NULL);
    529:   if (reuse == MAT_INITIAL_MATRIX) {
    530:     /* count nz in the upper triangular part of A */
    531:     nz = 0;
    532:     if (missing) {
    533:       for (i=0; i<M; i++) {
    534:         if (PetscUnlikely(adiag[i] >= ai[i+1])) {
    535:           for (j=ai[i];j<ai[i+1];j++) {
    536:             if (aj[j] < i) continue;
    537:             nz++;
    538:           }
    539:         } else {
    540:           nz += ai[i+1] - adiag[i];
    541:         }
    542:       }
    543:     } else {
    544:       for (i=0; i<M; i++) nz += ai[i+1] - adiag[i];
    545:     }
    546:     PetscMalloc2(nz,&row,nz,&col);
    547:     PetscMalloc1(nz,&val);
    548:     mumps->nnz = nz;
    549:     mumps->irn = row;
    550:     mumps->jcn = col;
    551:     mumps->val = mumps->val_alloc = val;

    553:     nz = 0;
    554:     if (missing) {
    555:       for (i=0; i<M; i++) {
    556:         if (PetscUnlikely(adiag[i] >= ai[i+1])) {
    557:           for (j=ai[i];j<ai[i+1];j++) {
    558:             if (aj[j] < i) continue;
    559:             PetscMUMPSIntCast(i+shift,&row[nz]);
    560:             PetscMUMPSIntCast(aj[j]+shift,&col[nz]);
    561:             val[nz] = av[j];
    562:             nz++;
    563:           }
    564:         } else {
    565:           rnz = ai[i+1] - adiag[i];
    566:           ajj = aj + adiag[i];
    567:           v1  = av + adiag[i];
    568:           for (j=0; j<rnz; j++) {
    569:             PetscMUMPSIntCast(i+shift,&row[nz]);
    570:             PetscMUMPSIntCast(ajj[j] + shift,&col[nz]);
    571:             val[nz++] = v1[j];
    572:           }
    573:         }
    574:       }
    575:     } else {
    576:       for (i=0; i<M; i++) {
    577:         rnz = ai[i+1] - adiag[i];
    578:         ajj = aj + adiag[i];
    579:         v1  = av + adiag[i];
    580:         for (j=0; j<rnz; j++) {
    581:           PetscMUMPSIntCast(i+shift,&row[nz]);
    582:           PetscMUMPSIntCast(ajj[j] + shift,&col[nz]);
    583:           val[nz++] = v1[j];
    584:         }
    585:       }
    586:     }
    587:   } else {
    588:     nz = 0;
    589:     val = mumps->val;
    590:     if (missing) {
    591:       for (i=0; i <M; i++) {
    592:         if (PetscUnlikely(adiag[i] >= ai[i+1])) {
    593:           for (j=ai[i];j<ai[i+1];j++) {
    594:             if (aj[j] < i) continue;
    595:             val[nz++] = av[j];
    596:           }
    597:         } else {
    598:           rnz = ai[i+1] - adiag[i];
    599:           v1  = av + adiag[i];
    600:           for (j=0; j<rnz; j++) {
    601:             val[nz++] = v1[j];
    602:           }
    603:         }
    604:       }
    605:     } else {
    606:       for (i=0; i <M; i++) {
    607:         rnz = ai[i+1] - adiag[i];
    608:         v1  = av + adiag[i];
    609:         for (j=0; j<rnz; j++) {
    610:           val[nz++] = v1[j];
    611:         }
    612:       }
    613:     }
    614:   }
    615:   MatSeqAIJRestoreArrayRead(A,&av);
    616:   return 0;
    617: }

    619: PetscErrorCode MatConvertToTriples_mpisbaij_mpisbaij(Mat A,PetscInt shift,MatReuse reuse,Mat_MUMPS *mumps)
    620: {
    621:   const PetscInt    *ai,*aj,*bi,*bj,*garray,*ajj,*bjj;
    622:   PetscInt          bs;
    623:   PetscInt64        rstart,nz,i,j,k,m,jj,irow,countA,countB;
    624:   PetscMUMPSInt     *row,*col;
    625:   const PetscScalar *av,*bv,*v1,*v2;
    626:   PetscScalar       *val;
    627:   Mat_MPISBAIJ      *mat = (Mat_MPISBAIJ*)A->data;
    628:   Mat_SeqSBAIJ      *aa  = (Mat_SeqSBAIJ*)(mat->A)->data;
    629:   Mat_SeqBAIJ       *bb  = (Mat_SeqBAIJ*)(mat->B)->data;
    630:   const PetscInt    bs2=aa->bs2,mbs=aa->mbs;
    631: #if defined(PETSC_USE_COMPLEX)
    632:   PetscBool         hermitian;
    633: #endif

    635: #if defined(PETSC_USE_COMPLEX)
    636:   MatGetOption(A,MAT_HERMITIAN,&hermitian);
    638: #endif
    639:   MatGetBlockSize(A,&bs);
    640:   rstart = A->rmap->rstart;
    641:   ai = aa->i;
    642:   aj = aa->j;
    643:   bi = bb->i;
    644:   bj = bb->j;
    645:   av = aa->a;
    646:   bv = bb->a;

    648:   garray = mat->garray;

    650:   if (reuse == MAT_INITIAL_MATRIX) {
    651:     nz   = (aa->nz+bb->nz)*bs2; /* just a conservative estimate */
    652:     PetscMalloc2(nz,&row,nz,&col);
    653:     PetscMalloc1(nz,&val);
    654:     /* can not decide the exact mumps->nnz now because of the SBAIJ */
    655:     mumps->irn = row;
    656:     mumps->jcn = col;
    657:     mumps->val = mumps->val_alloc = val;
    658:   } else {
    659:     val = mumps->val;
    660:   }

    662:   jj = 0; irow = rstart;
    663:   for (i=0; i<mbs; i++) {
    664:     ajj    = aj + ai[i];                 /* ptr to the beginning of this row */
    665:     countA = ai[i+1] - ai[i];
    666:     countB = bi[i+1] - bi[i];
    667:     bjj    = bj + bi[i];
    668:     v1     = av + ai[i]*bs2;
    669:     v2     = bv + bi[i]*bs2;

    671:     if (bs>1) {
    672:       /* A-part */
    673:       for (j=0; j<countA; j++) {
    674:         for (k=0; k<bs; k++) {
    675:           for (m=0; m<bs; m++) {
    676:             if (rstart + ajj[j]*bs>irow || k>=m) {
    677:               if (reuse == MAT_INITIAL_MATRIX) {
    678:                 PetscMUMPSIntCast(irow + m + shift,&row[jj]);
    679:                 PetscMUMPSIntCast(rstart + ajj[j]*bs + k + shift,&col[jj]);
    680:               }
    681:               val[jj++] = v1[j*bs2 + m + k*bs];
    682:             }
    683:           }
    684:         }
    685:       }

    687:       /* B-part */
    688:       for (j=0; j < countB; j++) {
    689:         for (k=0; k<bs; k++) {
    690:           for (m=0; m<bs; m++) {
    691:             if (reuse == MAT_INITIAL_MATRIX) {
    692:               PetscMUMPSIntCast(irow + m + shift,&row[jj]);
    693:               PetscMUMPSIntCast(garray[bjj[j]]*bs + k + shift,&col[jj]);
    694:             }
    695:             val[jj++] = v2[j*bs2 + m + k*bs];
    696:           }
    697:         }
    698:       }
    699:     } else {
    700:       /* A-part */
    701:       for (j=0; j<countA; j++) {
    702:         if (reuse == MAT_INITIAL_MATRIX) {
    703:           PetscMUMPSIntCast(irow + shift,&row[jj]);
    704:           PetscMUMPSIntCast(rstart + ajj[j] + shift,&col[jj]);
    705:         }
    706:         val[jj++] = v1[j];
    707:       }

    709:       /* B-part */
    710:       for (j=0; j < countB; j++) {
    711:         if (reuse == MAT_INITIAL_MATRIX) {
    712:           PetscMUMPSIntCast(irow + shift,&row[jj]);
    713:           PetscMUMPSIntCast(garray[bjj[j]] + shift,&col[jj]);
    714:         }
    715:         val[jj++] = v2[j];
    716:       }
    717:     }
    718:     irow+=bs;
    719:   }
    720:   mumps->nnz = jj;
    721:   return 0;
    722: }

    724: PetscErrorCode MatConvertToTriples_mpiaij_mpiaij(Mat A,PetscInt shift,MatReuse reuse,Mat_MUMPS *mumps)
    725: {
    726:   const PetscInt    *ai, *aj, *bi, *bj,*garray,m=A->rmap->n,*ajj,*bjj;
    727:   PetscInt64        rstart,nz,i,j,jj,irow,countA,countB;
    728:   PetscMUMPSInt     *row,*col;
    729:   const PetscScalar *av, *bv,*v1,*v2;
    730:   PetscScalar       *val;
    731:   Mat               Ad,Ao;
    732:   Mat_SeqAIJ        *aa;
    733:   Mat_SeqAIJ        *bb;

    735:   MatMPIAIJGetSeqAIJ(A,&Ad,&Ao,&garray);
    736:   MatSeqAIJGetArrayRead(Ad,&av);
    737:   MatSeqAIJGetArrayRead(Ao,&bv);

    739:   aa = (Mat_SeqAIJ*)(Ad)->data;
    740:   bb = (Mat_SeqAIJ*)(Ao)->data;
    741:   ai = aa->i;
    742:   aj = aa->j;
    743:   bi = bb->i;
    744:   bj = bb->j;

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

    748:   if (reuse == MAT_INITIAL_MATRIX) {
    749:     nz   = (PetscInt64)aa->nz + bb->nz; /* make sure the sum won't overflow PetscInt */
    750:     PetscMalloc2(nz,&row,nz,&col);
    751:     PetscMalloc1(nz,&val);
    752:     mumps->nnz = nz;
    753:     mumps->irn = row;
    754:     mumps->jcn = col;
    755:     mumps->val = mumps->val_alloc = val;
    756:   } else {
    757:     val = mumps->val;
    758:   }

    760:   jj = 0; irow = rstart;
    761:   for (i=0; i<m; i++) {
    762:     ajj    = aj + ai[i];                 /* ptr to the beginning of this row */
    763:     countA = ai[i+1] - ai[i];
    764:     countB = bi[i+1] - bi[i];
    765:     bjj    = bj + bi[i];
    766:     v1     = av + ai[i];
    767:     v2     = bv + bi[i];

    769:     /* A-part */
    770:     for (j=0; j<countA; j++) {
    771:       if (reuse == MAT_INITIAL_MATRIX) {
    772:         PetscMUMPSIntCast(irow + shift,&row[jj]);
    773:         PetscMUMPSIntCast(rstart + ajj[j] + shift,&col[jj]);
    774:       }
    775:       val[jj++] = v1[j];
    776:     }

    778:     /* B-part */
    779:     for (j=0; j < countB; j++) {
    780:       if (reuse == MAT_INITIAL_MATRIX) {
    781:         PetscMUMPSIntCast(irow + shift,&row[jj]);
    782:         PetscMUMPSIntCast(garray[bjj[j]] + shift,&col[jj]);
    783:       }
    784:       val[jj++] = v2[j];
    785:     }
    786:     irow++;
    787:   }
    788:   MatSeqAIJRestoreArrayRead(Ad,&av);
    789:   MatSeqAIJRestoreArrayRead(Ao,&bv);
    790:   return 0;
    791: }

    793: PetscErrorCode MatConvertToTriples_mpibaij_mpiaij(Mat A,PetscInt shift,MatReuse reuse,Mat_MUMPS *mumps)
    794: {
    795:   Mat_MPIBAIJ       *mat    = (Mat_MPIBAIJ*)A->data;
    796:   Mat_SeqBAIJ       *aa     = (Mat_SeqBAIJ*)(mat->A)->data;
    797:   Mat_SeqBAIJ       *bb     = (Mat_SeqBAIJ*)(mat->B)->data;
    798:   const PetscInt    *ai     = aa->i, *bi = bb->i, *aj = aa->j, *bj = bb->j,*ajj, *bjj;
    799:   const PetscInt    *garray = mat->garray,mbs=mat->mbs,rstart=A->rmap->rstart;
    800:   const PetscInt    bs2=mat->bs2;
    801:   PetscInt          bs;
    802:   PetscInt64        nz,i,j,k,n,jj,irow,countA,countB,idx;
    803:   PetscMUMPSInt     *row,*col;
    804:   const PetscScalar *av=aa->a, *bv=bb->a,*v1,*v2;
    805:   PetscScalar       *val;

    807:   MatGetBlockSize(A,&bs);
    808:   if (reuse == MAT_INITIAL_MATRIX) {
    809:     nz   = bs2*(aa->nz + bb->nz);
    810:     PetscMalloc2(nz,&row,nz,&col);
    811:     PetscMalloc1(nz,&val);
    812:     mumps->nnz = nz;
    813:     mumps->irn = row;
    814:     mumps->jcn = col;
    815:     mumps->val = mumps->val_alloc = val;
    816:   } else {
    817:     val = mumps->val;
    818:   }

    820:   jj = 0; irow = rstart;
    821:   for (i=0; i<mbs; i++) {
    822:     countA = ai[i+1] - ai[i];
    823:     countB = bi[i+1] - bi[i];
    824:     ajj    = aj + ai[i];
    825:     bjj    = bj + bi[i];
    826:     v1     = av + bs2*ai[i];
    827:     v2     = bv + bs2*bi[i];

    829:     idx = 0;
    830:     /* A-part */
    831:     for (k=0; k<countA; k++) {
    832:       for (j=0; j<bs; j++) {
    833:         for (n=0; n<bs; n++) {
    834:           if (reuse == MAT_INITIAL_MATRIX) {
    835:             PetscMUMPSIntCast(irow + n + shift,&row[jj]);
    836:             PetscMUMPSIntCast(rstart + bs*ajj[k] + j + shift,&col[jj]);
    837:           }
    838:           val[jj++] = v1[idx++];
    839:         }
    840:       }
    841:     }

    843:     idx = 0;
    844:     /* B-part */
    845:     for (k=0; k<countB; k++) {
    846:       for (j=0; j<bs; j++) {
    847:         for (n=0; n<bs; n++) {
    848:           if (reuse == MAT_INITIAL_MATRIX) {
    849:             PetscMUMPSIntCast(irow + n + shift,&row[jj]);
    850:             PetscMUMPSIntCast(bs*garray[bjj[k]] + j + shift,&col[jj]);
    851:           }
    852:           val[jj++] = v2[idx++];
    853:         }
    854:       }
    855:     }
    856:     irow += bs;
    857:   }
    858:   return 0;
    859: }

    861: PetscErrorCode MatConvertToTriples_mpiaij_mpisbaij(Mat A,PetscInt shift,MatReuse reuse,Mat_MUMPS *mumps)
    862: {
    863:   const PetscInt    *ai, *aj,*adiag, *bi, *bj,*garray,m=A->rmap->n,*ajj,*bjj;
    864:   PetscInt64        rstart,nz,nza,nzb,i,j,jj,irow,countA,countB;
    865:   PetscMUMPSInt     *row,*col;
    866:   const PetscScalar *av, *bv,*v1,*v2;
    867:   PetscScalar       *val;
    868:   Mat               Ad,Ao;
    869:   Mat_SeqAIJ        *aa;
    870:   Mat_SeqAIJ        *bb;
    871: #if defined(PETSC_USE_COMPLEX)
    872:   PetscBool         hermitian;
    873: #endif

    875: #if defined(PETSC_USE_COMPLEX)
    876:   MatGetOption(A,MAT_HERMITIAN,&hermitian);
    878: #endif
    879:   MatMPIAIJGetSeqAIJ(A,&Ad,&Ao,&garray);
    880:   MatSeqAIJGetArrayRead(Ad,&av);
    881:   MatSeqAIJGetArrayRead(Ao,&bv);

    883:   aa    = (Mat_SeqAIJ*)(Ad)->data;
    884:   bb    = (Mat_SeqAIJ*)(Ao)->data;
    885:   ai    = aa->i;
    886:   aj    = aa->j;
    887:   adiag = aa->diag;
    888:   bi    = bb->i;
    889:   bj    = bb->j;

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

    893:   if (reuse == MAT_INITIAL_MATRIX) {
    894:     nza = 0;    /* num of upper triangular entries in mat->A, including diagonals */
    895:     nzb = 0;    /* num of upper triangular entries in mat->B */
    896:     for (i=0; i<m; i++) {
    897:       nza   += (ai[i+1] - adiag[i]);
    898:       countB = bi[i+1] - bi[i];
    899:       bjj    = bj + bi[i];
    900:       for (j=0; j<countB; j++) {
    901:         if (garray[bjj[j]] > rstart) nzb++;
    902:       }
    903:     }

    905:     nz   = nza + nzb; /* total nz of upper triangular part of mat */
    906:     PetscMalloc2(nz,&row,nz,&col);
    907:     PetscMalloc1(nz,&val);
    908:     mumps->nnz = nz;
    909:     mumps->irn = row;
    910:     mumps->jcn = col;
    911:     mumps->val = mumps->val_alloc = val;
    912:   } else {
    913:     val = mumps->val;
    914:   }

    916:   jj = 0; irow = rstart;
    917:   for (i=0; i<m; i++) {
    918:     ajj    = aj + adiag[i];                 /* ptr to the beginning of the diagonal of this row */
    919:     v1     = av + adiag[i];
    920:     countA = ai[i+1] - adiag[i];
    921:     countB = bi[i+1] - bi[i];
    922:     bjj    = bj + bi[i];
    923:     v2     = bv + bi[i];

    925:     /* A-part */
    926:     for (j=0; j<countA; j++) {
    927:       if (reuse == MAT_INITIAL_MATRIX) {
    928:         PetscMUMPSIntCast(irow + shift,&row[jj]);
    929:         PetscMUMPSIntCast(rstart + ajj[j] + shift,&col[jj]);
    930:       }
    931:       val[jj++] = v1[j];
    932:     }

    934:     /* B-part */
    935:     for (j=0; j < countB; j++) {
    936:       if (garray[bjj[j]] > rstart) {
    937:         if (reuse == MAT_INITIAL_MATRIX) {
    938:           PetscMUMPSIntCast(irow + shift,&row[jj]);
    939:           PetscMUMPSIntCast(garray[bjj[j]] + shift,&col[jj]);
    940:         }
    941:         val[jj++] = v2[j];
    942:       }
    943:     }
    944:     irow++;
    945:   }
    946:   MatSeqAIJRestoreArrayRead(Ad,&av);
    947:   MatSeqAIJRestoreArrayRead(Ao,&bv);
    948:   return 0;
    949: }

    951: PetscErrorCode MatDestroy_MUMPS(Mat A)
    952: {
    953:   Mat_MUMPS      *mumps=(Mat_MUMPS*)A->data;

    955:   PetscFree2(mumps->id.sol_loc,mumps->id.isol_loc);
    956:   VecScatterDestroy(&mumps->scat_rhs);
    957:   VecScatterDestroy(&mumps->scat_sol);
    958:   VecDestroy(&mumps->b_seq);
    959:   VecDestroy(&mumps->x_seq);
    960:   PetscFree(mumps->id.perm_in);
    961:   PetscFree2(mumps->irn,mumps->jcn);
    962:   PetscFree(mumps->val_alloc);
    963:   PetscFree(mumps->info);
    964:   MatMumpsResetSchur_Private(mumps);
    965:   mumps->id.job = JOB_END;
    966:   PetscMUMPS_c(mumps);
    968: #if defined(PETSC_HAVE_OPENMP_SUPPORT)
    969:   if (mumps->use_petsc_omp_support) {
    970:     PetscOmpCtrlDestroy(&mumps->omp_ctrl);
    971:     PetscFree2(mumps->rhs_loc,mumps->rhs_recvbuf);
    972:     PetscFree3(mumps->rhs_nrow,mumps->rhs_recvcounts,mumps->rhs_disps);
    973:   }
    974: #endif
    975:   PetscFree(mumps->ia_alloc);
    976:   PetscFree(mumps->ja_alloc);
    977:   PetscFree(mumps->recvcount);
    978:   PetscFree(mumps->reqs);
    979:   PetscFree(mumps->irhs_loc);
    980:   if (mumps->mumps_comm != MPI_COMM_NULL) PetscCommRestoreComm(PetscObjectComm((PetscObject)A),&mumps->mumps_comm);
    981:   PetscFree(A->data);

    983:   /* clear composed functions */
    984:   PetscObjectComposeFunction((PetscObject)A,"MatFactorGetSolverType_C",NULL);
    985:   PetscObjectComposeFunction((PetscObject)A,"MatFactorSetSchurIS_C",NULL);
    986:   PetscObjectComposeFunction((PetscObject)A,"MatFactorCreateSchurComplement_C",NULL);
    987:   PetscObjectComposeFunction((PetscObject)A,"MatMumpsSetIcntl_C",NULL);
    988:   PetscObjectComposeFunction((PetscObject)A,"MatMumpsGetIcntl_C",NULL);
    989:   PetscObjectComposeFunction((PetscObject)A,"MatMumpsSetCntl_C",NULL);
    990:   PetscObjectComposeFunction((PetscObject)A,"MatMumpsGetCntl_C",NULL);
    991:   PetscObjectComposeFunction((PetscObject)A,"MatMumpsGetInfo_C",NULL);
    992:   PetscObjectComposeFunction((PetscObject)A,"MatMumpsGetInfog_C",NULL);
    993:   PetscObjectComposeFunction((PetscObject)A,"MatMumpsGetRinfo_C",NULL);
    994:   PetscObjectComposeFunction((PetscObject)A,"MatMumpsGetRinfog_C",NULL);
    995:   PetscObjectComposeFunction((PetscObject)A,"MatMumpsGetInverse_C",NULL);
    996:   PetscObjectComposeFunction((PetscObject)A,"MatMumpsGetInverseTranspose_C",NULL);
    997:   return 0;
    998: }

    1000: /* Set up the distributed RHS info for MUMPS. <nrhs> is the number of RHS. <array> points to start of RHS on the local processor. */
    1001: static PetscErrorCode MatMumpsSetUpDistRHSInfo(Mat A,PetscInt nrhs,const PetscScalar *array)
    1002: {
    1003:   Mat_MUMPS          *mumps=(Mat_MUMPS*)A->data;
    1004:   const PetscMPIInt  ompsize=mumps->omp_comm_size;
    1005:   PetscInt           i,m,M,rstart;

    1007:   MatGetSize(A,&M,NULL);
    1008:   MatGetLocalSize(A,&m,NULL);
    1010:   if (ompsize == 1) {
    1011:     if (!mumps->irhs_loc) {
    1012:       mumps->nloc_rhs = m;
    1013:       PetscMalloc1(m,&mumps->irhs_loc);
    1014:       MatGetOwnershipRange(A,&rstart,NULL);
    1015:       for (i=0; i<m; i++) mumps->irhs_loc[i] = rstart+i+1; /* use 1-based indices */
    1016:     }
    1017:     mumps->id.rhs_loc = (MumpsScalar*)array;
    1018:   } else {
    1019:   #if defined(PETSC_HAVE_OPENMP_SUPPORT)
    1020:     const PetscInt  *ranges;
    1021:     PetscMPIInt     j,k,sendcount,*petsc_ranks,*omp_ranks;
    1022:     MPI_Group       petsc_group,omp_group;
    1023:     PetscScalar     *recvbuf=NULL;

    1025:     if (mumps->is_omp_master) {
    1026:       /* Lazily initialize the omp stuff for distributed rhs */
    1027:       if (!mumps->irhs_loc) {
    1028:         PetscMalloc2(ompsize,&omp_ranks,ompsize,&petsc_ranks);
    1029:         PetscMalloc3(ompsize,&mumps->rhs_nrow,ompsize,&mumps->rhs_recvcounts,ompsize,&mumps->rhs_disps);
    1030:         MPI_Comm_group(mumps->petsc_comm,&petsc_group);
    1031:         MPI_Comm_group(mumps->omp_comm,&omp_group);
    1032:         for (j=0; j<ompsize; j++) omp_ranks[j] = j;
    1033:         MPI_Group_translate_ranks(omp_group,ompsize,omp_ranks,petsc_group,petsc_ranks);

    1035:         /* Populate mumps->irhs_loc[], rhs_nrow[] */
    1036:         mumps->nloc_rhs = 0;
    1037:         MatGetOwnershipRanges(A,&ranges);
    1038:         for (j=0; j<ompsize; j++) {
    1039:           mumps->rhs_nrow[j] = ranges[petsc_ranks[j]+1] - ranges[petsc_ranks[j]];
    1040:           mumps->nloc_rhs   += mumps->rhs_nrow[j];
    1041:         }
    1042:         PetscMalloc1(mumps->nloc_rhs,&mumps->irhs_loc);
    1043:         for (j=k=0; j<ompsize; j++) {
    1044:           for (i=ranges[petsc_ranks[j]]; i<ranges[petsc_ranks[j]+1]; i++,k++) mumps->irhs_loc[k] = i+1; /* uses 1-based indices */
    1045:         }

    1047:         PetscFree2(omp_ranks,petsc_ranks);
    1048:         MPI_Group_free(&petsc_group);
    1049:         MPI_Group_free(&omp_group);
    1050:       }

    1052:       /* Realloc buffers when current nrhs is bigger than what we have met */
    1053:       if (nrhs > mumps->max_nrhs) {
    1054:         PetscFree2(mumps->rhs_loc,mumps->rhs_recvbuf);
    1055:         PetscMalloc2(mumps->nloc_rhs*nrhs,&mumps->rhs_loc,mumps->nloc_rhs*nrhs,&mumps->rhs_recvbuf);
    1056:         mumps->max_nrhs = nrhs;
    1057:       }

    1059:       /* Setup recvcounts[], disps[], recvbuf on omp rank 0 for the upcoming MPI_Gatherv */
    1060:       for (j=0; j<ompsize; j++) PetscMPIIntCast(mumps->rhs_nrow[j]*nrhs,&mumps->rhs_recvcounts[j]);
    1061:       mumps->rhs_disps[0] = 0;
    1062:       for (j=1; j<ompsize; j++) {
    1063:         mumps->rhs_disps[j] = mumps->rhs_disps[j-1] + mumps->rhs_recvcounts[j-1];
    1065:       }
    1066:       recvbuf = (nrhs == 1) ? mumps->rhs_loc : mumps->rhs_recvbuf; /* Directly use rhs_loc[] as recvbuf. Single rhs is common in Ax=b */
    1067:     }

    1069:     PetscMPIIntCast(m*nrhs,&sendcount);
    1070:     MPI_Gatherv(array,sendcount,MPIU_SCALAR,recvbuf,mumps->rhs_recvcounts,mumps->rhs_disps,MPIU_SCALAR,0,mumps->omp_comm);

    1072:     if (mumps->is_omp_master) {
    1073:       if (nrhs > 1) { /* Copy & re-arrange data from rhs_recvbuf[] to mumps->rhs_loc[] only when there are multiple rhs */
    1074:         PetscScalar *dst,*dstbase = mumps->rhs_loc;
    1075:         for (j=0; j<ompsize; j++) {
    1076:           const PetscScalar *src = mumps->rhs_recvbuf + mumps->rhs_disps[j];
    1077:           dst = dstbase;
    1078:           for (i=0; i<nrhs; i++) {
    1079:             PetscArraycpy(dst,src,mumps->rhs_nrow[j]);
    1080:             src += mumps->rhs_nrow[j];
    1081:             dst += mumps->nloc_rhs;
    1082:           }
    1083:           dstbase += mumps->rhs_nrow[j];
    1084:         }
    1085:       }
    1086:       mumps->id.rhs_loc = (MumpsScalar*)mumps->rhs_loc;
    1087:     }
    1088:   #endif /* PETSC_HAVE_OPENMP_SUPPORT */
    1089:   }
    1090:   mumps->id.nrhs     = nrhs;
    1091:   mumps->id.nloc_rhs = mumps->nloc_rhs;
    1092:   mumps->id.lrhs_loc = mumps->nloc_rhs;
    1093:   mumps->id.irhs_loc = mumps->irhs_loc;
    1094:   return 0;
    1095: }

    1097: PetscErrorCode MatSolve_MUMPS(Mat A,Vec b,Vec x)
    1098: {
    1099:   Mat_MUMPS          *mumps=(Mat_MUMPS*)A->data;
    1100:   const PetscScalar  *rarray = NULL;
    1101:   PetscScalar        *array;
    1102:   IS                 is_iden,is_petsc;
    1103:   PetscInt           i;
    1104:   PetscBool          second_solve = PETSC_FALSE;
    1105:   static PetscBool   cite1 = PETSC_FALSE,cite2 = PETSC_FALSE;

    1107:   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 Journal on Matrix Analysis and Applications},\n  volume = {23},\n  number = {1},\n  pages = {15--41},\n  year = {2001}\n}\n",&cite1);
    1108:   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 Computing},\n  volume = {32},\n  number = {2},\n  pages = {136--156},\n  year = {2006}\n}\n",&cite2);

    1110:   if (A->factorerrortype) {
    1111:     PetscInfo(A,"MatSolve is called with singular matrix factor, INFOG(1)=%d, INFO(2)=%d\n",mumps->id.INFOG(1),mumps->id.INFO(2));
    1112:     VecSetInf(x);
    1113:     return 0;
    1114:   }

    1116:   mumps->id.nrhs = 1;
    1117:   if (mumps->petsc_size > 1) {
    1118:     if (mumps->ICNTL20 == 10) {
    1119:       mumps->id.ICNTL(20) = 10; /* dense distributed RHS */
    1120:       VecGetArrayRead(b,&rarray);
    1121:       MatMumpsSetUpDistRHSInfo(A,1,rarray);
    1122:     } else {
    1123:       mumps->id.ICNTL(20) = 0; /* dense centralized RHS; Scatter b into a sequential rhs vector*/
    1124:       VecScatterBegin(mumps->scat_rhs,b,mumps->b_seq,INSERT_VALUES,SCATTER_FORWARD);
    1125:       VecScatterEnd(mumps->scat_rhs,b,mumps->b_seq,INSERT_VALUES,SCATTER_FORWARD);
    1126:       if (!mumps->myid) {
    1127:         VecGetArray(mumps->b_seq,&array);
    1128:         mumps->id.rhs = (MumpsScalar*)array;
    1129:       }
    1130:     }
    1131:   } else {  /* petsc_size == 1 */
    1132:     mumps->id.ICNTL(20) = 0; /* dense centralized RHS */
    1133:     VecCopy(b,x);
    1134:     VecGetArray(x,&array);
    1135:     mumps->id.rhs = (MumpsScalar*)array;
    1136:   }

    1138:   /*
    1139:      handle condensation step of Schur complement (if any)
    1140:      We set by default ICNTL(26) == -1 when Schur indices have been provided by the user.
    1141:      According to MUMPS (5.0.0) manual, any value should be harmful during the factorization phase
    1142:      Unless the user provides a valid value for ICNTL(26), MatSolve and MatMatSolve routines solve the full system.
    1143:      This requires an extra call to PetscMUMPS_c and the computation of the factors for S
    1144:   */
    1145:   if (mumps->id.size_schur > 0 && (mumps->id.ICNTL(26) < 0 || mumps->id.ICNTL(26) > 2)) {
    1147:     second_solve = PETSC_TRUE;
    1148:     MatMumpsHandleSchur_Private(A,PETSC_FALSE);
    1149:   }
    1150:   /* solve phase */
    1151:   /*-------------*/
    1152:   mumps->id.job = JOB_SOLVE;
    1153:   PetscMUMPS_c(mumps);

    1156:   /* handle expansion step of Schur complement (if any) */
    1157:   if (second_solve) {
    1158:     MatMumpsHandleSchur_Private(A,PETSC_TRUE);
    1159:   }

    1161:   if (mumps->petsc_size > 1) { /* convert mumps distributed solution to petsc mpi x */
    1162:     if (mumps->scat_sol && mumps->ICNTL9_pre != mumps->id.ICNTL(9)) {
    1163:       /* when id.ICNTL(9) changes, the contents of lsol_loc may change (not its size, lsol_loc), recreates scat_sol */
    1164:       VecScatterDestroy(&mumps->scat_sol);
    1165:     }
    1166:     if (!mumps->scat_sol) { /* create scatter scat_sol */
    1167:       PetscInt *isol2_loc=NULL;
    1168:       ISCreateStride(PETSC_COMM_SELF,mumps->id.lsol_loc,0,1,&is_iden); /* from */
    1169:       PetscMalloc1(mumps->id.lsol_loc,&isol2_loc);
    1170:       for (i=0; i<mumps->id.lsol_loc; i++) isol2_loc[i] = mumps->id.isol_loc[i]-1; /* change Fortran style to C style */
    1171:       ISCreateGeneral(PETSC_COMM_SELF,mumps->id.lsol_loc,isol2_loc,PETSC_OWN_POINTER,&is_petsc);  /* to */
    1172:       VecScatterCreate(mumps->x_seq,is_iden,x,is_petsc,&mumps->scat_sol);
    1173:       ISDestroy(&is_iden);
    1174:       ISDestroy(&is_petsc);
    1175:       mumps->ICNTL9_pre = mumps->id.ICNTL(9); /* save current value of id.ICNTL(9) */
    1176:     }

    1178:     VecScatterBegin(mumps->scat_sol,mumps->x_seq,x,INSERT_VALUES,SCATTER_FORWARD);
    1179:     VecScatterEnd(mumps->scat_sol,mumps->x_seq,x,INSERT_VALUES,SCATTER_FORWARD);
    1180:   }

    1182:   if (mumps->petsc_size > 1) {
    1183:     if (mumps->ICNTL20 == 10) {
    1184:       VecRestoreArrayRead(b,&rarray);
    1185:     } else if (!mumps->myid) {
    1186:       VecRestoreArray(mumps->b_seq,&array);
    1187:     }
    1188:   } else VecRestoreArray(x,&array);

    1190:   PetscLogFlops(2.0*mumps->id.RINFO(3));
    1191:   return 0;
    1192: }

    1194: PetscErrorCode MatSolveTranspose_MUMPS(Mat A,Vec b,Vec x)
    1195: {
    1196:   Mat_MUMPS      *mumps=(Mat_MUMPS*)A->data;

    1198:   mumps->id.ICNTL(9) = 0;
    1199:   MatSolve_MUMPS(A,b,x);
    1200:   mumps->id.ICNTL(9) = 1;
    1201:   return 0;
    1202: }

    1204: PetscErrorCode MatMatSolve_MUMPS(Mat A,Mat B,Mat X)
    1205: {
    1206:   Mat               Bt = NULL;
    1207:   PetscBool         denseX,denseB,flg,flgT;
    1208:   Mat_MUMPS         *mumps=(Mat_MUMPS*)A->data;
    1209:   PetscInt          i,nrhs,M;
    1210:   PetscScalar       *array;
    1211:   const PetscScalar *rbray;
    1212:   PetscInt          lsol_loc,nlsol_loc,*idxx,iidx = 0;
    1213:   PetscMUMPSInt     *isol_loc,*isol_loc_save;
    1214:   PetscScalar       *bray,*sol_loc,*sol_loc_save;
    1215:   IS                is_to,is_from;
    1216:   PetscInt          k,proc,j,m,myrstart;
    1217:   const PetscInt    *rstart;
    1218:   Vec               v_mpi,msol_loc;
    1219:   VecScatter        scat_sol;
    1220:   Vec               b_seq;
    1221:   VecScatter        scat_rhs;
    1222:   PetscScalar       *aa;
    1223:   PetscInt          spnr,*ia,*ja;
    1224:   Mat_MPIAIJ        *b = NULL;

    1226:   PetscObjectTypeCompareAny((PetscObject)X,&denseX,MATSEQDENSE,MATMPIDENSE,NULL);

    1229:   PetscObjectTypeCompareAny((PetscObject)B,&denseB,MATSEQDENSE,MATMPIDENSE,NULL);
    1230:   if (denseB) {
    1232:     mumps->id.ICNTL(20)= 0; /* dense RHS */
    1233:   } else { /* sparse B */
    1235:     PetscObjectTypeCompare((PetscObject)B,MATTRANSPOSEMAT,&flgT);
    1236:     if (flgT) { /* input B is transpose of actural RHS matrix,
    1237:                  because mumps requires sparse compressed COLUMN storage! See MatMatTransposeSolve_MUMPS() */
    1238:       MatTransposeGetMat(B,&Bt);
    1239:     } else SETERRQ(PetscObjectComm((PetscObject)B),PETSC_ERR_ARG_WRONG,"Matrix B must be MATTRANSPOSEMAT matrix");
    1240:     mumps->id.ICNTL(20)= 1; /* sparse RHS */
    1241:   }

    1243:   MatGetSize(B,&M,&nrhs);
    1244:   mumps->id.nrhs = nrhs;
    1245:   mumps->id.lrhs = M;
    1246:   mumps->id.rhs  = NULL;

    1248:   if (mumps->petsc_size == 1) {
    1249:     PetscScalar *aa;
    1250:     PetscInt    spnr,*ia,*ja;
    1251:     PetscBool   second_solve = PETSC_FALSE;

    1253:     MatDenseGetArray(X,&array);
    1254:     mumps->id.rhs = (MumpsScalar*)array;

    1256:     if (denseB) {
    1257:       /* copy B to X */
    1258:       MatDenseGetArrayRead(B,&rbray);
    1259:       PetscArraycpy(array,rbray,M*nrhs);
    1260:       MatDenseRestoreArrayRead(B,&rbray);
    1261:     } else { /* sparse B */
    1262:       MatSeqAIJGetArray(Bt,&aa);
    1263:       MatGetRowIJ(Bt,1,PETSC_FALSE,PETSC_FALSE,&spnr,(const PetscInt**)&ia,(const PetscInt**)&ja,&flg);
    1265:       PetscMUMPSIntCSRCast(mumps,spnr,ia,ja,&mumps->id.irhs_ptr,&mumps->id.irhs_sparse,&mumps->id.nz_rhs);
    1266:       mumps->id.rhs_sparse  = (MumpsScalar*)aa;
    1267:     }
    1268:     /* handle condensation step of Schur complement (if any) */
    1269:     if (mumps->id.size_schur > 0 && (mumps->id.ICNTL(26) < 0 || mumps->id.ICNTL(26) > 2)) {
    1270:       second_solve = PETSC_TRUE;
    1271:       MatMumpsHandleSchur_Private(A,PETSC_FALSE);
    1272:     }
    1273:     /* solve phase */
    1274:     /*-------------*/
    1275:     mumps->id.job = JOB_SOLVE;
    1276:     PetscMUMPS_c(mumps);

    1279:     /* handle expansion step of Schur complement (if any) */
    1280:     if (second_solve) {
    1281:       MatMumpsHandleSchur_Private(A,PETSC_TRUE);
    1282:     }
    1283:     if (!denseB) { /* sparse B */
    1284:       MatSeqAIJRestoreArray(Bt,&aa);
    1285:       MatRestoreRowIJ(Bt,1,PETSC_FALSE,PETSC_FALSE,&spnr,(const PetscInt**)&ia,(const PetscInt**)&ja,&flg);
    1287:     }
    1288:     MatDenseRestoreArray(X,&array);
    1289:     return 0;
    1290:   }

    1292:   /*--------- parallel case: MUMPS requires rhs B to be centralized on the host! --------*/

    1295:   /* create msol_loc to hold mumps local solution */
    1296:   isol_loc_save = mumps->id.isol_loc; /* save it for MatSolve() */
    1297:   sol_loc_save  = (PetscScalar*)mumps->id.sol_loc;

    1299:   lsol_loc  = mumps->id.lsol_loc;
    1300:   nlsol_loc = nrhs*lsol_loc;     /* length of sol_loc */
    1301:   PetscMalloc2(nlsol_loc,&sol_loc,lsol_loc,&isol_loc);
    1302:   mumps->id.sol_loc  = (MumpsScalar*)sol_loc;
    1303:   mumps->id.isol_loc = isol_loc;

    1305:   VecCreateSeqWithArray(PETSC_COMM_SELF,1,nlsol_loc,(PetscScalar*)sol_loc,&msol_loc);

    1307:   if (denseB) {
    1308:     if (mumps->ICNTL20 == 10) {
    1309:       mumps->id.ICNTL(20) = 10; /* dense distributed RHS */
    1310:       MatDenseGetArrayRead(B,&rbray);
    1311:       MatMumpsSetUpDistRHSInfo(A,nrhs,rbray);
    1312:       MatDenseRestoreArrayRead(B,&rbray);
    1313:       MatGetLocalSize(B,&m,NULL);
    1314:       VecCreateMPIWithArray(PetscObjectComm((PetscObject)B),1,nrhs*m,nrhs*M,NULL,&v_mpi);
    1315:     } else {
    1316:       mumps->id.ICNTL(20) = 0; /* dense centralized RHS */
    1317:       /* TODO: Because of non-contiguous indices, the created vecscatter scat_rhs is not done in MPI_Gather, resulting in
    1318:         very inefficient communication. An optimization is to use VecScatterCreateToZero to gather B to rank 0. Then on rank
    1319:         0, re-arrange B into desired order, which is a local operation.
    1320:       */

    1322:       /* scatter v_mpi to b_seq because MUMPS before 5.3.0 only supports centralized rhs */
    1323:       /* wrap dense rhs matrix B into a vector v_mpi */
    1324:       MatGetLocalSize(B,&m,NULL);
    1325:       MatDenseGetArray(B,&bray);
    1326:       VecCreateMPIWithArray(PetscObjectComm((PetscObject)B),1,nrhs*m,nrhs*M,(const PetscScalar*)bray,&v_mpi);
    1327:       MatDenseRestoreArray(B,&bray);

    1329:       /* scatter v_mpi to b_seq in proc[0]. MUMPS requires rhs to be centralized on the host! */
    1330:       if (!mumps->myid) {
    1331:         PetscInt *idx;
    1332:         /* idx: maps from k-th index of v_mpi to (i,j)-th global entry of B */
    1333:         PetscMalloc1(nrhs*M,&idx);
    1334:         MatGetOwnershipRanges(B,&rstart);
    1335:         k = 0;
    1336:         for (proc=0; proc<mumps->petsc_size; proc++) {
    1337:           for (j=0; j<nrhs; j++) {
    1338:             for (i=rstart[proc]; i<rstart[proc+1]; i++) idx[k++] = j*M + i;
    1339:           }
    1340:         }

    1342:         VecCreateSeq(PETSC_COMM_SELF,nrhs*M,&b_seq);
    1343:         ISCreateGeneral(PETSC_COMM_SELF,nrhs*M,idx,PETSC_OWN_POINTER,&is_to);
    1344:         ISCreateStride(PETSC_COMM_SELF,nrhs*M,0,1,&is_from);
    1345:       } else {
    1346:         VecCreateSeq(PETSC_COMM_SELF,0,&b_seq);
    1347:         ISCreateStride(PETSC_COMM_SELF,0,0,1,&is_to);
    1348:         ISCreateStride(PETSC_COMM_SELF,0,0,1,&is_from);
    1349:       }
    1350:       VecScatterCreate(v_mpi,is_from,b_seq,is_to,&scat_rhs);
    1351:       VecScatterBegin(scat_rhs,v_mpi,b_seq,INSERT_VALUES,SCATTER_FORWARD);
    1352:       ISDestroy(&is_to);
    1353:       ISDestroy(&is_from);
    1354:       VecScatterEnd(scat_rhs,v_mpi,b_seq,INSERT_VALUES,SCATTER_FORWARD);

    1356:       if (!mumps->myid) { /* define rhs on the host */
    1357:         VecGetArray(b_seq,&bray);
    1358:         mumps->id.rhs = (MumpsScalar*)bray;
    1359:         VecRestoreArray(b_seq,&bray);
    1360:       }
    1361:     }
    1362:   } else { /* sparse B */
    1363:     b = (Mat_MPIAIJ*)Bt->data;

    1365:     /* wrap dense X into a vector v_mpi */
    1366:     MatGetLocalSize(X,&m,NULL);
    1367:     MatDenseGetArray(X,&bray);
    1368:     VecCreateMPIWithArray(PetscObjectComm((PetscObject)X),1,nrhs*m,nrhs*M,(const PetscScalar*)bray,&v_mpi);
    1369:     MatDenseRestoreArray(X,&bray);

    1371:     if (!mumps->myid) {
    1372:       MatSeqAIJGetArray(b->A,&aa);
    1373:       MatGetRowIJ(b->A,1,PETSC_FALSE,PETSC_FALSE,&spnr,(const PetscInt**)&ia,(const PetscInt**)&ja,&flg);
    1375:       PetscMUMPSIntCSRCast(mumps,spnr,ia,ja,&mumps->id.irhs_ptr,&mumps->id.irhs_sparse,&mumps->id.nz_rhs);
    1376:       mumps->id.rhs_sparse  = (MumpsScalar*)aa;
    1377:     } else {
    1378:       mumps->id.irhs_ptr    = NULL;
    1379:       mumps->id.irhs_sparse = NULL;
    1380:       mumps->id.nz_rhs      = 0;
    1381:       mumps->id.rhs_sparse  = NULL;
    1382:     }
    1383:   }

    1385:   /* solve phase */
    1386:   /*-------------*/
    1387:   mumps->id.job = JOB_SOLVE;
    1388:   PetscMUMPS_c(mumps);

    1391:   /* scatter mumps distributed solution to petsc vector v_mpi, which shares local arrays with solution matrix X */
    1392:   MatDenseGetArray(X,&array);
    1393:   VecPlaceArray(v_mpi,array);

    1395:   /* create scatter scat_sol */
    1396:   MatGetOwnershipRanges(X,&rstart);
    1397:   /* iidx: index for scatter mumps solution to petsc X */

    1399:   ISCreateStride(PETSC_COMM_SELF,nlsol_loc,0,1,&is_from);
    1400:   PetscMalloc1(nlsol_loc,&idxx);
    1401:   for (i=0; i<lsol_loc; i++) {
    1402:     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 */

    1404:     for (proc=0; proc<mumps->petsc_size; proc++) {
    1405:       if (isol_loc[i] >= rstart[proc] && isol_loc[i] < rstart[proc+1]) {
    1406:         myrstart = rstart[proc];
    1407:         k        = isol_loc[i] - myrstart;        /* local index on 1st column of petsc vector X */
    1408:         iidx     = k + myrstart*nrhs;             /* maps mumps isol_loc[i] to petsc index in X */
    1409:         m        = rstart[proc+1] - rstart[proc]; /* rows of X for this proc */
    1410:         break;
    1411:       }
    1412:     }

    1414:     for (j=0; j<nrhs; j++) idxx[i+j*lsol_loc] = iidx + j*m;
    1415:   }
    1416:   ISCreateGeneral(PETSC_COMM_SELF,nlsol_loc,idxx,PETSC_COPY_VALUES,&is_to);
    1417:   VecScatterCreate(msol_loc,is_from,v_mpi,is_to,&scat_sol);
    1418:   VecScatterBegin(scat_sol,msol_loc,v_mpi,INSERT_VALUES,SCATTER_FORWARD);
    1419:   ISDestroy(&is_from);
    1420:   ISDestroy(&is_to);
    1421:   VecScatterEnd(scat_sol,msol_loc,v_mpi,INSERT_VALUES,SCATTER_FORWARD);
    1422:   MatDenseRestoreArray(X,&array);

    1424:   /* free spaces */
    1425:   mumps->id.sol_loc  = (MumpsScalar*)sol_loc_save;
    1426:   mumps->id.isol_loc = isol_loc_save;

    1428:   PetscFree2(sol_loc,isol_loc);
    1429:   PetscFree(idxx);
    1430:   VecDestroy(&msol_loc);
    1431:   VecDestroy(&v_mpi);
    1432:   if (!denseB) {
    1433:     if (!mumps->myid) {
    1434:       b = (Mat_MPIAIJ*)Bt->data;
    1435:       MatSeqAIJRestoreArray(b->A,&aa);
    1436:       MatRestoreRowIJ(b->A,1,PETSC_FALSE,PETSC_FALSE,&spnr,(const PetscInt**)&ia,(const PetscInt**)&ja,&flg);
    1438:     }
    1439:   } else {
    1440:     if (mumps->ICNTL20 == 0) {
    1441:       VecDestroy(&b_seq);
    1442:       VecScatterDestroy(&scat_rhs);
    1443:     }
    1444:   }
    1445:   VecScatterDestroy(&scat_sol);
    1446:   PetscLogFlops(2.0*nrhs*mumps->id.RINFO(3));
    1447:   return 0;
    1448: }

    1450: PetscErrorCode MatMatTransposeSolve_MUMPS(Mat A,Mat Bt,Mat X)
    1451: {
    1452:   PetscBool      flg;
    1453:   Mat            B;

    1455:   PetscObjectTypeCompareAny((PetscObject)Bt,&flg,MATSEQAIJ,MATMPIAIJ,NULL);

    1458:   /* Create B=Bt^T that uses Bt's data structure */
    1459:   MatCreateTranspose(Bt,&B);

    1461:   MatMatSolve_MUMPS(A,B,X);
    1462:   MatDestroy(&B);
    1463:   return 0;
    1464: }

    1466: #if !defined(PETSC_USE_COMPLEX)
    1467: /*
    1468:   input:
    1469:    F:        numeric factor
    1470:   output:
    1471:    nneg:     total number of negative pivots
    1472:    nzero:    total number of zero pivots
    1473:    npos:     (global dimension of F) - nneg - nzero
    1474: */
    1475: PetscErrorCode MatGetInertia_SBAIJMUMPS(Mat F,PetscInt *nneg,PetscInt *nzero,PetscInt *npos)
    1476: {
    1477:   Mat_MUMPS      *mumps =(Mat_MUMPS*)F->data;
    1478:   PetscMPIInt    size;

    1480:   MPI_Comm_size(PetscObjectComm((PetscObject)F),&size);
    1481:   /* 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 */

    1484:   if (nneg) *nneg = mumps->id.INFOG(12);
    1485:   if (nzero || npos) {
    1487:     if (nzero) *nzero = mumps->id.INFOG(28);
    1488:     if (npos) *npos   = F->rmap->N - (mumps->id.INFOG(12) + mumps->id.INFOG(28));
    1489:   }
    1490:   return 0;
    1491: }
    1492: #endif

    1494: PetscErrorCode MatMumpsGatherNonzerosOnMaster(MatReuse reuse,Mat_MUMPS *mumps)
    1495: {
    1496:   PetscInt       i,nreqs;
    1497:   PetscMUMPSInt  *irn,*jcn;
    1498:   PetscMPIInt    count;
    1499:   PetscInt64     totnnz,remain;
    1500:   const PetscInt osize=mumps->omp_comm_size;
    1501:   PetscScalar    *val;

    1503:   if (osize > 1) {
    1504:     if (reuse == MAT_INITIAL_MATRIX) {
    1505:       /* master first gathers counts of nonzeros to receive */
    1506:       if (mumps->is_omp_master) PetscMalloc1(osize,&mumps->recvcount);
    1507:       MPI_Gather(&mumps->nnz,1,MPIU_INT64,mumps->recvcount,1,MPIU_INT64,0/*master*/,mumps->omp_comm);

    1509:       /* Then each computes number of send/recvs */
    1510:       if (mumps->is_omp_master) {
    1511:         /* Start from 1 since self communication is not done in MPI */
    1512:         nreqs = 0;
    1513:         for (i=1; i<osize; i++) nreqs += (mumps->recvcount[i]+PETSC_MPI_INT_MAX-1)/PETSC_MPI_INT_MAX;
    1514:       } else {
    1515:         nreqs = (mumps->nnz+PETSC_MPI_INT_MAX-1)/PETSC_MPI_INT_MAX;
    1516:       }
    1517:       PetscMalloc1(nreqs*3,&mumps->reqs); /* Triple the requests since we send irn, jcn and val seperately */

    1519:       /* The following code is doing a very simple thing: omp_master rank gathers irn/jcn/val from others.
    1520:          MPI_Gatherv would be enough if it supports big counts > 2^31-1. Since it does not, and mumps->nnz
    1521:          might be a prime number > 2^31-1, we have to slice the message. Note omp_comm_size
    1522:          is very small, the current approach should have no extra overhead compared to MPI_Gatherv.
    1523:        */
    1524:       nreqs = 0; /* counter for actual send/recvs */
    1525:       if (mumps->is_omp_master) {
    1526:         for (i=0,totnnz=0; i<osize; i++) totnnz += mumps->recvcount[i]; /* totnnz = sum of nnz over omp_comm */
    1527:         PetscMalloc2(totnnz,&irn,totnnz,&jcn);
    1528:         PetscMalloc1(totnnz,&val);

    1530:         /* Self communication */
    1531:         PetscArraycpy(irn,mumps->irn,mumps->nnz);
    1532:         PetscArraycpy(jcn,mumps->jcn,mumps->nnz);
    1533:         PetscArraycpy(val,mumps->val,mumps->nnz);

    1535:         /* Replace mumps->irn/jcn etc on master with the newly allocated bigger arrays */
    1536:         PetscFree2(mumps->irn,mumps->jcn);
    1537:         PetscFree(mumps->val_alloc);
    1538:         mumps->nnz = totnnz;
    1539:         mumps->irn = irn;
    1540:         mumps->jcn = jcn;
    1541:         mumps->val = mumps->val_alloc = val;

    1543:         irn += mumps->recvcount[0]; /* recvcount[0] is old mumps->nnz on omp rank 0 */
    1544:         jcn += mumps->recvcount[0];
    1545:         val += mumps->recvcount[0];

    1547:         /* Remote communication */
    1548:         for (i=1; i<osize; i++) {
    1549:           count  = PetscMin(mumps->recvcount[i],PETSC_MPI_INT_MAX);
    1550:           remain = mumps->recvcount[i] - count;
    1551:           while (count>0) {
    1552:             MPI_Irecv(irn,count,MPIU_MUMPSINT,i,mumps->tag,mumps->omp_comm,&mumps->reqs[nreqs++]);
    1553:             MPI_Irecv(jcn,count,MPIU_MUMPSINT,i,mumps->tag,mumps->omp_comm,&mumps->reqs[nreqs++]);
    1554:             MPI_Irecv(val,count,MPIU_SCALAR,  i,mumps->tag,mumps->omp_comm,&mumps->reqs[nreqs++]);
    1555:             irn    += count;
    1556:             jcn    += count;
    1557:             val    += count;
    1558:             count   = PetscMin(remain,PETSC_MPI_INT_MAX);
    1559:             remain -= count;
    1560:           }
    1561:         }
    1562:       } else {
    1563:         irn    = mumps->irn;
    1564:         jcn    = mumps->jcn;
    1565:         val    = mumps->val;
    1566:         count  = PetscMin(mumps->nnz,PETSC_MPI_INT_MAX);
    1567:         remain = mumps->nnz - count;
    1568:         while (count>0) {
    1569:           MPI_Isend(irn,count,MPIU_MUMPSINT,0,mumps->tag,mumps->omp_comm,&mumps->reqs[nreqs++]);
    1570:           MPI_Isend(jcn,count,MPIU_MUMPSINT,0,mumps->tag,mumps->omp_comm,&mumps->reqs[nreqs++]);
    1571:           MPI_Isend(val,count,MPIU_SCALAR,  0,mumps->tag,mumps->omp_comm,&mumps->reqs[nreqs++]);
    1572:           irn    += count;
    1573:           jcn    += count;
    1574:           val    += count;
    1575:           count   = PetscMin(remain,PETSC_MPI_INT_MAX);
    1576:           remain -= count;
    1577:         }
    1578:       }
    1579:     } else {
    1580:       nreqs = 0;
    1581:       if (mumps->is_omp_master) {
    1582:         val = mumps->val + mumps->recvcount[0];
    1583:         for (i=1; i<osize; i++) { /* Remote communication only since self data is already in place */
    1584:           count  = PetscMin(mumps->recvcount[i],PETSC_MPI_INT_MAX);
    1585:           remain = mumps->recvcount[i] - count;
    1586:           while (count>0) {
    1587:             MPI_Irecv(val,count,MPIU_SCALAR,i,mumps->tag,mumps->omp_comm,&mumps->reqs[nreqs++]);
    1588:             val    += count;
    1589:             count   = PetscMin(remain,PETSC_MPI_INT_MAX);
    1590:             remain -= count;
    1591:           }
    1592:         }
    1593:       } else {
    1594:         val    = mumps->val;
    1595:         count  = PetscMin(mumps->nnz,PETSC_MPI_INT_MAX);
    1596:         remain = mumps->nnz - count;
    1597:         while (count>0) {
    1598:           MPI_Isend(val,count,MPIU_SCALAR,0,mumps->tag,mumps->omp_comm,&mumps->reqs[nreqs++]);
    1599:           val    += count;
    1600:           count   = PetscMin(remain,PETSC_MPI_INT_MAX);
    1601:           remain -= count;
    1602:         }
    1603:       }
    1604:     }
    1605:     MPI_Waitall(nreqs,mumps->reqs,MPI_STATUSES_IGNORE);
    1606:     mumps->tag++; /* It is totally fine for above send/recvs to share one mpi tag */
    1607:   }
    1608:   return 0;
    1609: }

    1611: PetscErrorCode MatFactorNumeric_MUMPS(Mat F,Mat A,const MatFactorInfo *info)
    1612: {
    1613:   Mat_MUMPS      *mumps =(Mat_MUMPS*)(F)->data;
    1614:   PetscBool      isMPIAIJ;

    1616:   if (mumps->id.INFOG(1) < 0 && !(mumps->id.INFOG(1) == -16 && mumps->id.INFOG(1) == 0)) {
    1617:     if (mumps->id.INFOG(1) == -6) {
    1618:       PetscInfo(A,"MatFactorNumeric is called with singular matrix structure, INFOG(1)=%d, INFO(2)=%d\n",mumps->id.INFOG(1),mumps->id.INFO(2));
    1619:     }
    1620:     PetscInfo(A,"MatFactorNumeric is called after analysis phase fails, INFOG(1)=%d, INFO(2)=%d\n",mumps->id.INFOG(1),mumps->id.INFO(2));
    1621:     return 0;
    1622:   }

    1624:   (*mumps->ConvertToTriples)(A, 1, MAT_REUSE_MATRIX, mumps);
    1625:   MatMumpsGatherNonzerosOnMaster(MAT_REUSE_MATRIX,mumps);

    1627:   /* numerical factorization phase */
    1628:   /*-------------------------------*/
    1629:   mumps->id.job = JOB_FACTNUMERIC;
    1630:   if (!mumps->id.ICNTL(18)) { /* A is centralized */
    1631:     if (!mumps->myid) {
    1632:       mumps->id.a = (MumpsScalar*)mumps->val;
    1633:     }
    1634:   } else {
    1635:     mumps->id.a_loc = (MumpsScalar*)mumps->val;
    1636:   }
    1637:   PetscMUMPS_c(mumps);
    1638:   if (mumps->id.INFOG(1) < 0) {
    1639:     if (A->erroriffailure) {
    1640:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error reported by MUMPS in numerical factorization phase: INFOG(1)=%d, INFO(2)=%d",mumps->id.INFOG(1),mumps->id.INFO(2));
    1641:     } else {
    1642:       if (mumps->id.INFOG(1) == -10) { /* numerically singular matrix */
    1643:         PetscInfo(F,"matrix is numerically singular, INFOG(1)=%d, INFO(2)=%d\n",mumps->id.INFOG(1),mumps->id.INFO(2));
    1644:         F->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    1645:       } else if (mumps->id.INFOG(1) == -13) {
    1646:         PetscInfo(F,"MUMPS in numerical factorization phase: INFOG(1)=%d, cannot allocate required memory %d megabytes\n",mumps->id.INFOG(1),mumps->id.INFO(2));
    1647:         F->factorerrortype = MAT_FACTOR_OUTMEMORY;
    1648:       } else if (mumps->id.INFOG(1) == -8 || mumps->id.INFOG(1) == -9 || (-16 < mumps->id.INFOG(1) && mumps->id.INFOG(1) < -10)) {
    1649:         PetscInfo(F,"MUMPS in numerical factorization phase: INFOG(1)=%d, INFO(2)=%d, problem with workarray \n",mumps->id.INFOG(1),mumps->id.INFO(2));
    1650:         F->factorerrortype = MAT_FACTOR_OUTMEMORY;
    1651:       } else {
    1652:         PetscInfo(F,"MUMPS in numerical factorization phase: INFOG(1)=%d, INFO(2)=%d\n",mumps->id.INFOG(1),mumps->id.INFO(2));
    1653:         F->factorerrortype = MAT_FACTOR_OTHER;
    1654:       }
    1655:     }
    1656:   }

    1659:   F->assembled    = PETSC_TRUE;

    1661:   if (F->schur) { /* reset Schur status to unfactored */
    1662: #if defined(PETSC_HAVE_CUDA)
    1663:     F->schur->offloadmask = PETSC_OFFLOAD_CPU;
    1664: #endif
    1665:     if (mumps->id.ICNTL(19) == 1) { /* stored by rows */
    1666:       mumps->id.ICNTL(19) = 2;
    1667:       MatTranspose(F->schur,MAT_INPLACE_MATRIX,&F->schur);
    1668:     }
    1669:     MatFactorRestoreSchurComplement(F,NULL,MAT_FACTOR_SCHUR_UNFACTORED);
    1670:   }

    1672:   /* just to be sure that ICNTL(19) value returned by a call from MatMumpsGetIcntl is always consistent */
    1673:   if (!mumps->sym && mumps->id.ICNTL(19) && mumps->id.ICNTL(19) != 1) mumps->id.ICNTL(19) = 3;

    1675:   if (!mumps->is_omp_master) mumps->id.INFO(23) = 0;
    1676:   if (mumps->petsc_size > 1) {
    1677:     PetscInt    lsol_loc;
    1678:     PetscScalar *sol_loc;

    1680:     PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&isMPIAIJ);

    1682:     /* distributed solution; Create x_seq=sol_loc for repeated use */
    1683:     if (mumps->x_seq) {
    1684:       VecScatterDestroy(&mumps->scat_sol);
    1685:       PetscFree2(mumps->id.sol_loc,mumps->id.isol_loc);
    1686:       VecDestroy(&mumps->x_seq);
    1687:     }
    1688:     lsol_loc = mumps->id.INFO(23); /* length of sol_loc */
    1689:     PetscMalloc2(lsol_loc,&sol_loc,lsol_loc,&mumps->id.isol_loc);
    1690:     mumps->id.lsol_loc = lsol_loc;
    1691:     mumps->id.sol_loc = (MumpsScalar*)sol_loc;
    1692:     VecCreateSeqWithArray(PETSC_COMM_SELF,1,lsol_loc,sol_loc,&mumps->x_seq);
    1693:   }
    1694:   PetscLogFlops(mumps->id.RINFO(2));
    1695:   return 0;
    1696: }

    1698: /* Sets MUMPS options from the options database */
    1699: PetscErrorCode PetscSetMUMPSFromOptions(Mat F, Mat A)
    1700: {
    1701:   Mat_MUMPS      *mumps = (Mat_MUMPS*)F->data;
    1703:   PetscMUMPSInt  icntl=0;
    1704:   PetscInt       info[80],i,ninfo=80;
    1705:   PetscBool      flg=PETSC_FALSE;

    1707:   PetscOptionsBegin(PetscObjectComm((PetscObject)A),((PetscObject)A)->prefix,"MUMPS Options","Mat");
    1708:   PetscOptionsMUMPSInt("-mat_mumps_icntl_1","ICNTL(1): output stream for error messages","None",mumps->id.ICNTL(1),&icntl,&flg);
    1709:   if (flg) mumps->id.ICNTL(1) = icntl;
    1710:   PetscOptionsMUMPSInt("-mat_mumps_icntl_2","ICNTL(2): output stream for diagnostic printing, statistics, and warning","None",mumps->id.ICNTL(2),&icntl,&flg);
    1711:   if (flg) mumps->id.ICNTL(2) = icntl;
    1712:   PetscOptionsMUMPSInt("-mat_mumps_icntl_3","ICNTL(3): output stream for global information, collected on the host","None",mumps->id.ICNTL(3),&icntl,&flg);
    1713:   if (flg) mumps->id.ICNTL(3) = icntl;

    1715:   PetscOptionsMUMPSInt("-mat_mumps_icntl_4","ICNTL(4): level of printing (0 to 4)","None",mumps->id.ICNTL(4),&icntl,&flg);
    1716:   if (flg) mumps->id.ICNTL(4) = icntl;
    1717:   if (mumps->id.ICNTL(4) || PetscLogPrintInfo) mumps->id.ICNTL(3) = 6; /* resume MUMPS default id.ICNTL(3) = 6 */

    1719:   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);
    1720:   if (flg) mumps->id.ICNTL(6) = icntl;

    1722:   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);
    1723:   if (flg) {
    1725:     mumps->id.ICNTL(7) = icntl;
    1726:   }

    1728:   PetscOptionsMUMPSInt("-mat_mumps_icntl_8","ICNTL(8): scaling strategy (-2 to 8 or 77)","None",mumps->id.ICNTL(8),&mumps->id.ICNTL(8),NULL);
    1729:   /* 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() */
    1730:   PetscOptionsMUMPSInt("-mat_mumps_icntl_10","ICNTL(10): max num of refinements","None",mumps->id.ICNTL(10),&mumps->id.ICNTL(10),NULL);
    1731:   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);
    1732:   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);
    1733:   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);
    1734:   PetscOptionsMUMPSInt("-mat_mumps_icntl_14","ICNTL(14): percentage increase in the estimated working space","None",mumps->id.ICNTL(14),&mumps->id.ICNTL(14),NULL);
    1735:   PetscOptionsMUMPSInt("-mat_mumps_icntl_19","ICNTL(19): computes the Schur complement","None",mumps->id.ICNTL(19),&mumps->id.ICNTL(19),NULL);
    1736:   if (mumps->id.ICNTL(19) <= 0 || mumps->id.ICNTL(19) > 3) { /* reset any schur data (if any) */
    1737:     MatDestroy(&F->schur);
    1738:     MatMumpsResetSchur_Private(mumps);
    1739:   }

    1741:   /* Two MPICH Fortran MPI_IN_PLACE binding bugs prevented the use of 'mpich + mumps'. One happened with "mpi4py + mpich + mumps",
    1742:      and was reported by Firedrake. See https://bitbucket.org/mpi4py/mpi4py/issues/162/mpi4py-initialization-breaks-fortran
    1743:      and a petsc-maint mailing list thread with subject 'MUMPS segfaults in parallel because of ...'
    1744:      This bug was fixed by https://github.com/pmodels/mpich/pull/4149. But the fix brought a new bug,
    1745:      see https://github.com/pmodels/mpich/issues/5589. This bug was fixed by https://github.com/pmodels/mpich/pull/5590.
    1746:      In short, we could not use distributed RHS with MPICH until v4.0b1.
    1747:    */
    1748: #if PETSC_PKG_MUMPS_VERSION_LT(5,3,0) || (defined(PETSC_HAVE_MPICH_NUMVERSION) && (PETSC_HAVE_MPICH_NUMVERSION < 40000101))
    1749:   mumps->ICNTL20 = 0;  /* Centralized dense RHS*/
    1750: #else
    1751:   mumps->ICNTL20 = 10; /* Distributed dense RHS*/
    1752: #endif
    1753:   PetscOptionsMUMPSInt("-mat_mumps_icntl_20","ICNTL(20): give mumps centralized (0) or distributed (10) dense right-hand sides","None",mumps->ICNTL20,&mumps->ICNTL20,&flg);
    1755: #if PETSC_PKG_MUMPS_VERSION_LT(5,3,0)
    1757: #endif
    1758:   /* 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 */

    1760:   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);
    1761:   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);
    1762:   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);
    1763:   if (mumps->id.ICNTL(24)) {
    1764:     mumps->id.ICNTL(13) = 1; /* turn-off ScaLAPACK to help with the correct detection of null pivots */
    1765:   }

    1767:   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);
    1768:   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);
    1769:   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);
    1770:   PetscOptionsMUMPSInt("-mat_mumps_icntl_28","ICNTL(28): use 1 for sequential analysis and ictnl(7) ordering, or 2 for parallel analysis and ictnl(29) ordering","None",mumps->id.ICNTL(28),&mumps->id.ICNTL(28),NULL);
    1771:   PetscOptionsMUMPSInt("-mat_mumps_icntl_29","ICNTL(29): parallel ordering 1 = ptscotch, 2 = parmetis","None",mumps->id.ICNTL(29),&mumps->id.ICNTL(29),NULL);
    1772:   /* 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 */
    1773:   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);
    1774:   /* PetscOptionsMUMPSInt("-mat_mumps_icntl_32","ICNTL(32): performs the forward elemination of the right-hand sides during factorization","None",mumps->id.ICNTL(32),&mumps->id.ICNTL(32),NULL);  -- not supported by PETSc API */
    1775:   PetscOptionsMUMPSInt("-mat_mumps_icntl_33","ICNTL(33): compute determinant","None",mumps->id.ICNTL(33),&mumps->id.ICNTL(33),NULL);
    1776:   PetscOptionsMUMPSInt("-mat_mumps_icntl_35","ICNTL(35): activates Block Low Rank (BLR) based factorization","None",mumps->id.ICNTL(35),&mumps->id.ICNTL(35),NULL);
    1777:   PetscOptionsMUMPSInt("-mat_mumps_icntl_36","ICNTL(36): choice of BLR factorization variant","None",mumps->id.ICNTL(36),&mumps->id.ICNTL(36),NULL);
    1778:   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);

    1780:   PetscOptionsReal("-mat_mumps_cntl_1","CNTL(1): relative pivoting threshold","None",mumps->id.CNTL(1),&mumps->id.CNTL(1),NULL);
    1781:   PetscOptionsReal("-mat_mumps_cntl_2","CNTL(2): stopping criterion of refinement","None",mumps->id.CNTL(2),&mumps->id.CNTL(2),NULL);
    1782:   PetscOptionsReal("-mat_mumps_cntl_3","CNTL(3): absolute pivoting threshold","None",mumps->id.CNTL(3),&mumps->id.CNTL(3),NULL);
    1783:   PetscOptionsReal("-mat_mumps_cntl_4","CNTL(4): value for static pivoting","None",mumps->id.CNTL(4),&mumps->id.CNTL(4),NULL);
    1784:   PetscOptionsReal("-mat_mumps_cntl_5","CNTL(5): fixation for null pivots","None",mumps->id.CNTL(5),&mumps->id.CNTL(5),NULL);
    1785:   PetscOptionsReal("-mat_mumps_cntl_7","CNTL(7): dropping parameter used during BLR","None",mumps->id.CNTL(7),&mumps->id.CNTL(7),NULL);

    1787:   PetscOptionsString("-mat_mumps_ooc_tmpdir", "out of core directory", "None", mumps->id.ooc_tmpdir, mumps->id.ooc_tmpdir, sizeof(mumps->id.ooc_tmpdir), NULL);

    1789:   PetscOptionsIntArray("-mat_mumps_view_info","request INFO local to each processor","",info,&ninfo,NULL);
    1790:   if (ninfo) {
    1792:     PetscMalloc1(ninfo,&mumps->info);
    1793:     mumps->ninfo = ninfo;
    1794:     for (i=0; i<ninfo; i++) {
    1796:       else  mumps->info[i] = info[i];
    1797:     }
    1798:   }

    1800:   PetscOptionsEnd();
    1801:   return 0;
    1802: }

    1804: PetscErrorCode PetscInitializeMUMPS(Mat A,Mat_MUMPS *mumps)
    1805: {
    1806:   PetscInt       nthreads=0;

    1808:   mumps->petsc_comm = PetscObjectComm((PetscObject)A);
    1809:   MPI_Comm_size(mumps->petsc_comm,&mumps->petsc_size);
    1810:   MPI_Comm_rank(mumps->petsc_comm,&mumps->myid);/* "if (!myid)" still works even if mumps_comm is different */

    1812:   PetscOptionsHasName(NULL,((PetscObject)A)->prefix,"-mat_mumps_use_omp_threads",&mumps->use_petsc_omp_support);
    1813:   if (mumps->use_petsc_omp_support) nthreads = -1; /* -1 will let PetscOmpCtrlCreate() guess a proper value when user did not supply one */
    1814:   PetscOptionsGetInt(NULL,((PetscObject)A)->prefix,"-mat_mumps_use_omp_threads",&nthreads,NULL);
    1815:   if (mumps->use_petsc_omp_support) {
    1816: #if defined(PETSC_HAVE_OPENMP_SUPPORT)
    1817:     PetscOmpCtrlCreate(mumps->petsc_comm,nthreads,&mumps->omp_ctrl);
    1818:     PetscOmpCtrlGetOmpComms(mumps->omp_ctrl,&mumps->omp_comm,&mumps->mumps_comm,&mumps->is_omp_master);
    1819: #else
    1820:     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",((PetscObject)A)->prefix?((PetscObject)A)->prefix:"");
    1821: #endif
    1822:   } else {
    1823:     mumps->omp_comm      = PETSC_COMM_SELF;
    1824:     mumps->mumps_comm    = mumps->petsc_comm;
    1825:     mumps->is_omp_master = PETSC_TRUE;
    1826:   }
    1827:   MPI_Comm_size(mumps->omp_comm,&mumps->omp_comm_size);
    1828:   mumps->reqs = NULL;
    1829:   mumps->tag  = 0;

    1831:   /* It looks like MUMPS does not dup the input comm. Dup a new comm for MUMPS to avoid any tag mismatches. */
    1832:   if (mumps->mumps_comm != MPI_COMM_NULL) {
    1833:     PetscCommGetComm(PetscObjectComm((PetscObject)A),&mumps->mumps_comm);
    1834:   }

    1836:   mumps->id.comm_fortran = MPI_Comm_c2f(mumps->mumps_comm);
    1837:   mumps->id.job = JOB_INIT;
    1838:   mumps->id.par = 1;  /* host participates factorizaton and solve */
    1839:   mumps->id.sym = mumps->sym;

    1841:   PetscMUMPS_c(mumps);

    1844:   /* copy MUMPS default control values from master to slaves. Although slaves do not call MUMPS, they may access these values in code.
    1845:      For example, ICNTL(9) is initialized to 1 by MUMPS and slaves check ICNTL(9) in MatSolve_MUMPS.
    1846:    */
    1847:   MPI_Bcast(mumps->id.icntl,40,MPI_INT,  0,mumps->omp_comm);
    1848:   MPI_Bcast(mumps->id.cntl, 15,MPIU_REAL,0,mumps->omp_comm);

    1850:   mumps->scat_rhs = NULL;
    1851:   mumps->scat_sol = NULL;

    1853:   /* set PETSc-MUMPS default options - override MUMPS default */
    1854:   mumps->id.ICNTL(3) = 0;
    1855:   mumps->id.ICNTL(4) = 0;
    1856:   if (mumps->petsc_size == 1) {
    1857:     mumps->id.ICNTL(18) = 0;   /* centralized assembled matrix input */
    1858:     mumps->id.ICNTL(7)  = 7;   /* automatic choice of ordering done by the package */
    1859:   } else {
    1860:     mumps->id.ICNTL(18) = 3;   /* distributed assembled matrix input */
    1861:     mumps->id.ICNTL(21) = 1;   /* distributed solution */
    1862:   }

    1864:   /* schur */
    1865:   mumps->id.size_schur    = 0;
    1866:   mumps->id.listvar_schur = NULL;
    1867:   mumps->id.schur         = NULL;
    1868:   mumps->sizeredrhs       = 0;
    1869:   mumps->schur_sol        = NULL;
    1870:   mumps->schur_sizesol    = 0;
    1871:   return 0;
    1872: }

    1874: PetscErrorCode MatFactorSymbolic_MUMPS_ReportIfError(Mat F,Mat A,const MatFactorInfo *info,Mat_MUMPS *mumps)
    1875: {
    1876:   if (mumps->id.INFOG(1) < 0) {
    1877:     if (A->erroriffailure) {
    1878:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error reported by MUMPS in analysis phase: INFOG(1)=%d",mumps->id.INFOG(1));
    1879:     } else {
    1880:       if (mumps->id.INFOG(1) == -6) {
    1881:         PetscInfo(F,"matrix is singular in structure, INFOG(1)=%d, INFO(2)=%d\n",mumps->id.INFOG(1),mumps->id.INFO(2));
    1882:         F->factorerrortype = MAT_FACTOR_STRUCT_ZEROPIVOT;
    1883:       } else if (mumps->id.INFOG(1) == -5 || mumps->id.INFOG(1) == -7) {
    1884:         PetscInfo(F,"problem of workspace, INFOG(1)=%d, INFO(2)=%d\n",mumps->id.INFOG(1),mumps->id.INFO(2));
    1885:         F->factorerrortype = MAT_FACTOR_OUTMEMORY;
    1886:       } else if (mumps->id.INFOG(1) == -16 && mumps->id.INFOG(1) == 0) {
    1887:         PetscInfo(F,"Empty matrix\n");
    1888:       } else {
    1889:         PetscInfo(F,"Error reported by MUMPS in analysis phase: INFOG(1)=%d, INFO(2)=%d\n",mumps->id.INFOG(1),mumps->id.INFO(2));
    1890:         F->factorerrortype = MAT_FACTOR_OTHER;
    1891:       }
    1892:     }
    1893:   }
    1894:   return 0;
    1895: }

    1897: PetscErrorCode MatLUFactorSymbolic_AIJMUMPS(Mat F,Mat A,IS r,IS c,const MatFactorInfo *info)
    1898: {
    1899:   Mat_MUMPS      *mumps = (Mat_MUMPS*)F->data;
    1900:   Vec            b;
    1901:   const PetscInt M = A->rmap->N;

    1903:   if (mumps->matstruc == SAME_NONZERO_PATTERN) {
    1904:     /* F is assembled by a previous call of MatLUFactorSymbolic_AIJMUMPS() */
    1905:     return 0;
    1906:   }

    1908:   /* Set MUMPS options from the options database */
    1909:   PetscSetMUMPSFromOptions(F,A);

    1911:   (*mumps->ConvertToTriples)(A, 1, MAT_INITIAL_MATRIX, mumps);
    1912:   MatMumpsGatherNonzerosOnMaster(MAT_INITIAL_MATRIX,mumps);

    1914:   /* analysis phase */
    1915:   /*----------------*/
    1916:   mumps->id.job = JOB_FACTSYMBOLIC;
    1917:   mumps->id.n   = M;
    1918:   switch (mumps->id.ICNTL(18)) {
    1919:   case 0:  /* centralized assembled matrix input */
    1920:     if (!mumps->myid) {
    1921:       mumps->id.nnz = mumps->nnz;
    1922:       mumps->id.irn = mumps->irn;
    1923:       mumps->id.jcn = mumps->jcn;
    1924:       if (mumps->id.ICNTL(6)>1) mumps->id.a = (MumpsScalar*)mumps->val;
    1925:       if (r) {
    1926:         mumps->id.ICNTL(7) = 1;
    1927:         if (!mumps->myid) {
    1928:           const PetscInt *idx;
    1929:           PetscInt       i;

    1931:           PetscMalloc1(M,&mumps->id.perm_in);
    1932:           ISGetIndices(r,&idx);
    1933:           for (i=0; i<M; i++) PetscMUMPSIntCast(idx[i]+1,&(mumps->id.perm_in[i])); /* perm_in[]: start from 1, not 0! */
    1934:           ISRestoreIndices(r,&idx);
    1935:         }
    1936:       }
    1937:     }
    1938:     break;
    1939:   case 3:  /* distributed assembled matrix input (size>1) */
    1940:     mumps->id.nnz_loc = mumps->nnz;
    1941:     mumps->id.irn_loc = mumps->irn;
    1942:     mumps->id.jcn_loc = mumps->jcn;
    1943:     if (mumps->id.ICNTL(6)>1) mumps->id.a_loc = (MumpsScalar*)mumps->val;
    1944:     if (mumps->ICNTL20 == 0) { /* Centralized rhs. Create scatter scat_rhs for repeated use in MatSolve() */
    1945:       MatCreateVecs(A,NULL,&b);
    1946:       VecScatterCreateToZero(b,&mumps->scat_rhs,&mumps->b_seq);
    1947:       VecDestroy(&b);
    1948:     }
    1949:     break;
    1950:   }
    1951:   PetscMUMPS_c(mumps);
    1952:   MatFactorSymbolic_MUMPS_ReportIfError(F,A,info,mumps);

    1954:   F->ops->lufactornumeric = MatFactorNumeric_MUMPS;
    1955:   F->ops->solve           = MatSolve_MUMPS;
    1956:   F->ops->solvetranspose  = MatSolveTranspose_MUMPS;
    1957:   F->ops->matsolve        = MatMatSolve_MUMPS;
    1958:   F->ops->mattransposesolve = MatMatTransposeSolve_MUMPS;

    1960:   mumps->matstruc = SAME_NONZERO_PATTERN;
    1961:   return 0;
    1962: }

    1964: /* Note the Petsc r and c permutations are ignored */
    1965: PetscErrorCode MatLUFactorSymbolic_BAIJMUMPS(Mat F,Mat A,IS r,IS c,const MatFactorInfo *info)
    1966: {
    1967:   Mat_MUMPS      *mumps = (Mat_MUMPS*)F->data;
    1968:   Vec            b;
    1969:   const PetscInt M = A->rmap->N;

    1971:   if (mumps->matstruc == SAME_NONZERO_PATTERN) {
    1972:     /* F is assembled by a previous call of MatLUFactorSymbolic_AIJMUMPS() */
    1973:     return 0;
    1974:   }

    1976:   /* Set MUMPS options from the options database */
    1977:   PetscSetMUMPSFromOptions(F,A);

    1979:   (*mumps->ConvertToTriples)(A, 1, MAT_INITIAL_MATRIX, mumps);
    1980:   MatMumpsGatherNonzerosOnMaster(MAT_INITIAL_MATRIX,mumps);

    1982:   /* analysis phase */
    1983:   /*----------------*/
    1984:   mumps->id.job = JOB_FACTSYMBOLIC;
    1985:   mumps->id.n   = M;
    1986:   switch (mumps->id.ICNTL(18)) {
    1987:   case 0:  /* centralized assembled matrix input */
    1988:     if (!mumps->myid) {
    1989:       mumps->id.nnz = mumps->nnz;
    1990:       mumps->id.irn = mumps->irn;
    1991:       mumps->id.jcn = mumps->jcn;
    1992:       if (mumps->id.ICNTL(6)>1) {
    1993:         mumps->id.a = (MumpsScalar*)mumps->val;
    1994:       }
    1995:     }
    1996:     break;
    1997:   case 3:  /* distributed assembled matrix input (size>1) */
    1998:     mumps->id.nnz_loc = mumps->nnz;
    1999:     mumps->id.irn_loc = mumps->irn;
    2000:     mumps->id.jcn_loc = mumps->jcn;
    2001:     if (mumps->id.ICNTL(6)>1) {
    2002:       mumps->id.a_loc = (MumpsScalar*)mumps->val;
    2003:     }
    2004:     if (mumps->ICNTL20 == 0) { /* Centralized rhs. Create scatter scat_rhs for repeated use in MatSolve() */
    2005:       MatCreateVecs(A,NULL,&b);
    2006:       VecScatterCreateToZero(b,&mumps->scat_rhs,&mumps->b_seq);
    2007:       VecDestroy(&b);
    2008:     }
    2009:     break;
    2010:   }
    2011:   PetscMUMPS_c(mumps);
    2012:   MatFactorSymbolic_MUMPS_ReportIfError(F,A,info,mumps);

    2014:   F->ops->lufactornumeric = MatFactorNumeric_MUMPS;
    2015:   F->ops->solve           = MatSolve_MUMPS;
    2016:   F->ops->solvetranspose  = MatSolveTranspose_MUMPS;

    2018:   mumps->matstruc = SAME_NONZERO_PATTERN;
    2019:   return 0;
    2020: }

    2022: /* Note the Petsc r permutation and factor info are ignored */
    2023: PetscErrorCode MatCholeskyFactorSymbolic_MUMPS(Mat F,Mat A,IS r,const MatFactorInfo *info)
    2024: {
    2025:   Mat_MUMPS      *mumps = (Mat_MUMPS*)F->data;
    2026:   Vec            b;
    2027:   const PetscInt M = A->rmap->N;

    2029:   if (mumps->matstruc == SAME_NONZERO_PATTERN) {
    2030:     /* F is assembled by a previous call of MatLUFactorSymbolic_AIJMUMPS() */
    2031:     return 0;
    2032:   }

    2034:   /* Set MUMPS options from the options database */
    2035:   PetscSetMUMPSFromOptions(F,A);

    2037:   (*mumps->ConvertToTriples)(A, 1, MAT_INITIAL_MATRIX, mumps);
    2038:   MatMumpsGatherNonzerosOnMaster(MAT_INITIAL_MATRIX,mumps);

    2040:   /* analysis phase */
    2041:   /*----------------*/
    2042:   mumps->id.job = JOB_FACTSYMBOLIC;
    2043:   mumps->id.n   = M;
    2044:   switch (mumps->id.ICNTL(18)) {
    2045:   case 0:  /* centralized assembled matrix input */
    2046:     if (!mumps->myid) {
    2047:       mumps->id.nnz = mumps->nnz;
    2048:       mumps->id.irn = mumps->irn;
    2049:       mumps->id.jcn = mumps->jcn;
    2050:       if (mumps->id.ICNTL(6)>1) {
    2051:         mumps->id.a = (MumpsScalar*)mumps->val;
    2052:       }
    2053:     }
    2054:     break;
    2055:   case 3:  /* distributed assembled matrix input (size>1) */
    2056:     mumps->id.nnz_loc = mumps->nnz;
    2057:     mumps->id.irn_loc = mumps->irn;
    2058:     mumps->id.jcn_loc = mumps->jcn;
    2059:     if (mumps->id.ICNTL(6)>1) {
    2060:       mumps->id.a_loc = (MumpsScalar*)mumps->val;
    2061:     }
    2062:     if (mumps->ICNTL20 == 0) { /* Centralized rhs. Create scatter scat_rhs for repeated use in MatSolve() */
    2063:       MatCreateVecs(A,NULL,&b);
    2064:       VecScatterCreateToZero(b,&mumps->scat_rhs,&mumps->b_seq);
    2065:       VecDestroy(&b);
    2066:     }
    2067:     break;
    2068:   }
    2069:   PetscMUMPS_c(mumps);
    2070:   MatFactorSymbolic_MUMPS_ReportIfError(F,A,info,mumps);

    2072:   F->ops->choleskyfactornumeric = MatFactorNumeric_MUMPS;
    2073:   F->ops->solve                 = MatSolve_MUMPS;
    2074:   F->ops->solvetranspose        = MatSolve_MUMPS;
    2075:   F->ops->matsolve              = MatMatSolve_MUMPS;
    2076:   F->ops->mattransposesolve     = MatMatTransposeSolve_MUMPS;
    2077: #if defined(PETSC_USE_COMPLEX)
    2078:   F->ops->getinertia = NULL;
    2079: #else
    2080:   F->ops->getinertia = MatGetInertia_SBAIJMUMPS;
    2081: #endif

    2083:   mumps->matstruc = SAME_NONZERO_PATTERN;
    2084:   return 0;
    2085: }

    2087: PetscErrorCode MatView_MUMPS(Mat A,PetscViewer viewer)
    2088: {
    2089:   PetscBool         iascii;
    2090:   PetscViewerFormat format;
    2091:   Mat_MUMPS         *mumps=(Mat_MUMPS*)A->data;

    2093:   /* check if matrix is mumps type */
    2094:   if (A->ops->solve != MatSolve_MUMPS) return 0;

    2096:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    2097:   if (iascii) {
    2098:     PetscViewerGetFormat(viewer,&format);
    2099:     if (format == PETSC_VIEWER_ASCII_INFO) {
    2100:       PetscViewerASCIIPrintf(viewer,"MUMPS run parameters:\n");
    2101:       PetscViewerASCIIPrintf(viewer,"  SYM (matrix type):                   %d\n",mumps->id.sym);
    2102:       PetscViewerASCIIPrintf(viewer,"  PAR (host participation):            %d\n",mumps->id.par);
    2103:       PetscViewerASCIIPrintf(viewer,"  ICNTL(1) (output for error):         %d\n",mumps->id.ICNTL(1));
    2104:       PetscViewerASCIIPrintf(viewer,"  ICNTL(2) (output of diagnostic msg): %d\n",mumps->id.ICNTL(2));
    2105:       PetscViewerASCIIPrintf(viewer,"  ICNTL(3) (output for global info):   %d\n",mumps->id.ICNTL(3));
    2106:       PetscViewerASCIIPrintf(viewer,"  ICNTL(4) (level of printing):        %d\n",mumps->id.ICNTL(4));
    2107:       PetscViewerASCIIPrintf(viewer,"  ICNTL(5) (input mat struct):         %d\n",mumps->id.ICNTL(5));
    2108:       PetscViewerASCIIPrintf(viewer,"  ICNTL(6) (matrix prescaling):        %d\n",mumps->id.ICNTL(6));
    2109:       PetscViewerASCIIPrintf(viewer,"  ICNTL(7) (sequential matrix ordering):%d\n",mumps->id.ICNTL(7));
    2110:       PetscViewerASCIIPrintf(viewer,"  ICNTL(8) (scaling strategy):        %d\n",mumps->id.ICNTL(8));
    2111:       PetscViewerASCIIPrintf(viewer,"  ICNTL(10) (max num of refinements):  %d\n",mumps->id.ICNTL(10));
    2112:       PetscViewerASCIIPrintf(viewer,"  ICNTL(11) (error analysis):          %d\n",mumps->id.ICNTL(11));
    2113:       if (mumps->id.ICNTL(11)>0) {
    2114:         PetscViewerASCIIPrintf(viewer,"    RINFOG(4) (inf norm of input mat):        %g\n",mumps->id.RINFOG(4));
    2115:         PetscViewerASCIIPrintf(viewer,"    RINFOG(5) (inf norm of solution):         %g\n",mumps->id.RINFOG(5));
    2116:         PetscViewerASCIIPrintf(viewer,"    RINFOG(6) (inf norm of residual):         %g\n",mumps->id.RINFOG(6));
    2117:         PetscViewerASCIIPrintf(viewer,"    RINFOG(7),RINFOG(8) (backward error est): %g, %g\n",mumps->id.RINFOG(7),mumps->id.RINFOG(8));
    2118:         PetscViewerASCIIPrintf(viewer,"    RINFOG(9) (error estimate):               %g \n",mumps->id.RINFOG(9));
    2119:         PetscViewerASCIIPrintf(viewer,"    RINFOG(10),RINFOG(11)(condition numbers): %g, %g\n",mumps->id.RINFOG(10),mumps->id.RINFOG(11));
    2120:       }
    2121:       PetscViewerASCIIPrintf(viewer,"  ICNTL(12) (efficiency control):                         %d\n",mumps->id.ICNTL(12));
    2122:       PetscViewerASCIIPrintf(viewer,"  ICNTL(13) (sequential factorization of the root node):  %d\n",mumps->id.ICNTL(13));
    2123:       PetscViewerASCIIPrintf(viewer,"  ICNTL(14) (percentage of estimated workspace increase): %d\n",mumps->id.ICNTL(14));
    2124:       /* ICNTL(15-17) not used */
    2125:       PetscViewerASCIIPrintf(viewer,"  ICNTL(18) (input mat struct):                           %d\n",mumps->id.ICNTL(18));
    2126:       PetscViewerASCIIPrintf(viewer,"  ICNTL(19) (Schur complement info):                      %d\n",mumps->id.ICNTL(19));
    2127:       PetscViewerASCIIPrintf(viewer,"  ICNTL(20) (RHS sparse pattern):                         %d\n",mumps->id.ICNTL(20));
    2128:       PetscViewerASCIIPrintf(viewer,"  ICNTL(21) (solution struct):                            %d\n",mumps->id.ICNTL(21));
    2129:       PetscViewerASCIIPrintf(viewer,"  ICNTL(22) (in-core/out-of-core facility):               %d\n",mumps->id.ICNTL(22));
    2130:       PetscViewerASCIIPrintf(viewer,"  ICNTL(23) (max size of memory can be allocated locally):%d\n",mumps->id.ICNTL(23));

    2132:       PetscViewerASCIIPrintf(viewer,"  ICNTL(24) (detection of null pivot rows):               %d\n",mumps->id.ICNTL(24));
    2133:       PetscViewerASCIIPrintf(viewer,"  ICNTL(25) (computation of a null space basis):          %d\n",mumps->id.ICNTL(25));
    2134:       PetscViewerASCIIPrintf(viewer,"  ICNTL(26) (Schur options for RHS or solution):          %d\n",mumps->id.ICNTL(26));
    2135:       PetscViewerASCIIPrintf(viewer,"  ICNTL(27) (blocking size for multiple RHS):             %d\n",mumps->id.ICNTL(27));
    2136:       PetscViewerASCIIPrintf(viewer,"  ICNTL(28) (use parallel or sequential ordering):        %d\n",mumps->id.ICNTL(28));
    2137:       PetscViewerASCIIPrintf(viewer,"  ICNTL(29) (parallel ordering):                          %d\n",mumps->id.ICNTL(29));

    2139:       PetscViewerASCIIPrintf(viewer,"  ICNTL(30) (user-specified set of entries in inv(A)):    %d\n",mumps->id.ICNTL(30));
    2140:       PetscViewerASCIIPrintf(viewer,"  ICNTL(31) (factors is discarded in the solve phase):    %d\n",mumps->id.ICNTL(31));
    2141:       PetscViewerASCIIPrintf(viewer,"  ICNTL(33) (compute determinant):                        %d\n",mumps->id.ICNTL(33));
    2142:       PetscViewerASCIIPrintf(viewer,"  ICNTL(35) (activate BLR based factorization):           %d\n",mumps->id.ICNTL(35));
    2143:       PetscViewerASCIIPrintf(viewer,"  ICNTL(36) (choice of BLR factorization variant):        %d\n",mumps->id.ICNTL(36));
    2144:       PetscViewerASCIIPrintf(viewer,"  ICNTL(38) (estimated compression rate of LU factors):   %d\n",mumps->id.ICNTL(38));

    2146:       PetscViewerASCIIPrintf(viewer,"  CNTL(1) (relative pivoting threshold):      %g \n",mumps->id.CNTL(1));
    2147:       PetscViewerASCIIPrintf(viewer,"  CNTL(2) (stopping criterion of refinement): %g \n",mumps->id.CNTL(2));
    2148:       PetscViewerASCIIPrintf(viewer,"  CNTL(3) (absolute pivoting threshold):      %g \n",mumps->id.CNTL(3));
    2149:       PetscViewerASCIIPrintf(viewer,"  CNTL(4) (value of static pivoting):         %g \n",mumps->id.CNTL(4));
    2150:       PetscViewerASCIIPrintf(viewer,"  CNTL(5) (fixation for null pivots):         %g \n",mumps->id.CNTL(5));
    2151:       PetscViewerASCIIPrintf(viewer,"  CNTL(7) (dropping parameter for BLR):       %g \n",mumps->id.CNTL(7));

    2153:       /* information local to each processor */
    2154:       PetscViewerASCIIPrintf(viewer, "  RINFO(1) (local estimated flops for the elimination after analysis): \n");
    2155:       PetscViewerASCIIPushSynchronized(viewer);
    2156:       PetscViewerASCIISynchronizedPrintf(viewer,"    [%d] %g \n",mumps->myid,mumps->id.RINFO(1));
    2157:       PetscViewerFlush(viewer);
    2158:       PetscViewerASCIIPrintf(viewer, "  RINFO(2) (local estimated flops for the assembly after factorization): \n");
    2159:       PetscViewerASCIISynchronizedPrintf(viewer,"    [%d]  %g \n",mumps->myid,mumps->id.RINFO(2));
    2160:       PetscViewerFlush(viewer);
    2161:       PetscViewerASCIIPrintf(viewer, "  RINFO(3) (local estimated flops for the elimination after factorization): \n");
    2162:       PetscViewerASCIISynchronizedPrintf(viewer,"    [%d]  %g \n",mumps->myid,mumps->id.RINFO(3));
    2163:       PetscViewerFlush(viewer);

    2165:       PetscViewerASCIIPrintf(viewer, "  INFO(15) (estimated size of (in MB) MUMPS internal data for running numerical factorization): \n");
    2166:       PetscViewerASCIISynchronizedPrintf(viewer,"  [%d] %d\n",mumps->myid,mumps->id.INFO(15));
    2167:       PetscViewerFlush(viewer);

    2169:       PetscViewerASCIIPrintf(viewer, "  INFO(16) (size of (in MB) MUMPS internal data used during numerical factorization): \n");
    2170:       PetscViewerASCIISynchronizedPrintf(viewer,"    [%d] %d\n",mumps->myid,mumps->id.INFO(16));
    2171:       PetscViewerFlush(viewer);

    2173:       PetscViewerASCIIPrintf(viewer, "  INFO(23) (num of pivots eliminated on this processor after factorization): \n");
    2174:       PetscViewerASCIISynchronizedPrintf(viewer,"    [%d] %d\n",mumps->myid,mumps->id.INFO(23));
    2175:       PetscViewerFlush(viewer);

    2177:       if (mumps->ninfo && mumps->ninfo <= 80) {
    2178:         PetscInt i;
    2179:         for (i=0; i<mumps->ninfo; i++) {
    2180:           PetscViewerASCIIPrintf(viewer, "  INFO(%" PetscInt_FMT "): \n",mumps->info[i]);
    2181:           PetscViewerASCIISynchronizedPrintf(viewer,"    [%d] %d\n",mumps->myid,mumps->id.INFO(mumps->info[i]));
    2182:           PetscViewerFlush(viewer);
    2183:         }
    2184:       }
    2185:       PetscViewerASCIIPopSynchronized(viewer);

    2187:       if (!mumps->myid) { /* information from the host */
    2188:         PetscViewerASCIIPrintf(viewer,"  RINFOG(1) (global estimated flops for the elimination after analysis): %g \n",mumps->id.RINFOG(1));
    2189:         PetscViewerASCIIPrintf(viewer,"  RINFOG(2) (global estimated flops for the assembly after factorization): %g \n",mumps->id.RINFOG(2));
    2190:         PetscViewerASCIIPrintf(viewer,"  RINFOG(3) (global estimated flops for the elimination after factorization): %g \n",mumps->id.RINFOG(3));
    2191:         PetscViewerASCIIPrintf(viewer,"  (RINFOG(12) RINFOG(13))*2^INFOG(34) (determinant): (%g,%g)*(2^%d)\n",mumps->id.RINFOG(12),mumps->id.RINFOG(13),mumps->id.INFOG(34));

    2193:         PetscViewerASCIIPrintf(viewer,"  INFOG(3) (estimated real workspace for factors on all processors after analysis): %d\n",mumps->id.INFOG(3));
    2194:         PetscViewerASCIIPrintf(viewer,"  INFOG(4) (estimated integer workspace for factors on all processors after analysis): %d\n",mumps->id.INFOG(4));
    2195:         PetscViewerASCIIPrintf(viewer,"  INFOG(5) (estimated maximum front size in the complete tree): %d\n",mumps->id.INFOG(5));
    2196:         PetscViewerASCIIPrintf(viewer,"  INFOG(6) (number of nodes in the complete tree): %d\n",mumps->id.INFOG(6));
    2197:         PetscViewerASCIIPrintf(viewer,"  INFOG(7) (ordering option effectively used after analysis): %d\n",mumps->id.INFOG(7));
    2198:         PetscViewerASCIIPrintf(viewer,"  INFOG(8) (structural symmetry in percent of the permuted matrix after analysis): %d\n",mumps->id.INFOG(8));
    2199:         PetscViewerASCIIPrintf(viewer,"  INFOG(9) (total real/complex workspace to store the matrix factors after factorization): %d\n",mumps->id.INFOG(9));
    2200:         PetscViewerASCIIPrintf(viewer,"  INFOG(10) (total integer space store the matrix factors after factorization): %d\n",mumps->id.INFOG(10));
    2201:         PetscViewerASCIIPrintf(viewer,"  INFOG(11) (order of largest frontal matrix after factorization): %d\n",mumps->id.INFOG(11));
    2202:         PetscViewerASCIIPrintf(viewer,"  INFOG(12) (number of off-diagonal pivots): %d\n",mumps->id.INFOG(12));
    2203:         PetscViewerASCIIPrintf(viewer,"  INFOG(13) (number of delayed pivots after factorization): %d\n",mumps->id.INFOG(13));
    2204:         PetscViewerASCIIPrintf(viewer,"  INFOG(14) (number of memory compress after factorization): %d\n",mumps->id.INFOG(14));
    2205:         PetscViewerASCIIPrintf(viewer,"  INFOG(15) (number of steps of iterative refinement after solution): %d\n",mumps->id.INFOG(15));
    2206:         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));
    2207:         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));
    2208:         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));
    2209:         PetscViewerASCIIPrintf(viewer,"  INFOG(19) (size of all MUMPS internal data allocated during factorization: sum over all processors): %d\n",mumps->id.INFOG(19));
    2210:         PetscViewerASCIIPrintf(viewer,"  INFOG(20) (estimated number of entries in the factors): %d\n",mumps->id.INFOG(20));
    2211:         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));
    2212:         PetscViewerASCIIPrintf(viewer,"  INFOG(22) (size in MB of memory effectively used during factorization - sum over all processors): %d\n",mumps->id.INFOG(22));
    2213:         PetscViewerASCIIPrintf(viewer,"  INFOG(23) (after analysis: value of ICNTL(6) effectively used): %d\n",mumps->id.INFOG(23));
    2214:         PetscViewerASCIIPrintf(viewer,"  INFOG(24) (after analysis: value of ICNTL(12) effectively used): %d\n",mumps->id.INFOG(24));
    2215:         PetscViewerASCIIPrintf(viewer,"  INFOG(25) (after factorization: number of pivots modified by static pivoting): %d\n",mumps->id.INFOG(25));
    2216:         PetscViewerASCIIPrintf(viewer,"  INFOG(28) (after factorization: number of null pivots encountered): %d\n",mumps->id.INFOG(28));
    2217:         PetscViewerASCIIPrintf(viewer,"  INFOG(29) (after factorization: effective number of entries in the factors (sum over all processors)): %d\n",mumps->id.INFOG(29));
    2218:         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));
    2219:         PetscViewerASCIIPrintf(viewer,"  INFOG(32) (after analysis: type of analysis done): %d\n",mumps->id.INFOG(32));
    2220:         PetscViewerASCIIPrintf(viewer,"  INFOG(33) (value used for ICNTL(8)): %d\n",mumps->id.INFOG(33));
    2221:         PetscViewerASCIIPrintf(viewer,"  INFOG(34) (exponent of the determinant if determinant is requested): %d\n",mumps->id.INFOG(34));
    2222:         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));
    2223:         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));
    2224:         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));
    2225:         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));
    2226:         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));
    2227:       }
    2228:     }
    2229:   }
    2230:   return 0;
    2231: }

    2233: PetscErrorCode MatGetInfo_MUMPS(Mat A,MatInfoType flag,MatInfo *info)
    2234: {
    2235:   Mat_MUMPS *mumps =(Mat_MUMPS*)A->data;

    2237:   info->block_size        = 1.0;
    2238:   info->nz_allocated      = mumps->id.INFOG(20);
    2239:   info->nz_used           = mumps->id.INFOG(20);
    2240:   info->nz_unneeded       = 0.0;
    2241:   info->assemblies        = 0.0;
    2242:   info->mallocs           = 0.0;
    2243:   info->memory            = 0.0;
    2244:   info->fill_ratio_given  = 0;
    2245:   info->fill_ratio_needed = 0;
    2246:   info->factor_mallocs    = 0;
    2247:   return 0;
    2248: }

    2250: /* -------------------------------------------------------------------------------------------*/
    2251: PetscErrorCode MatFactorSetSchurIS_MUMPS(Mat F, IS is)
    2252: {
    2253:   Mat_MUMPS         *mumps =(Mat_MUMPS*)F->data;
    2254:   const PetscScalar *arr;
    2255:   const PetscInt    *idxs;
    2256:   PetscInt          size,i;

    2258:   ISGetLocalSize(is,&size);
    2259:   if (mumps->petsc_size > 1) {
    2260:     PetscBool ls,gs; /* gs is false if any rank other than root has non-empty IS */

    2262:     ls   = mumps->myid ? (size ? PETSC_FALSE : PETSC_TRUE) : PETSC_TRUE; /* always true on root; false on others if their size != 0 */
    2263:     MPI_Allreduce(&ls,&gs,1,MPIU_BOOL,MPI_LAND,mumps->petsc_comm);
    2265:   }

    2267:   /* Schur complement matrix */
    2268:   MatDestroy(&F->schur);
    2269:   MatCreateSeqDense(PETSC_COMM_SELF,size,size,NULL,&F->schur);
    2270:   MatDenseGetArrayRead(F->schur,&arr);
    2271:   mumps->id.schur      = (MumpsScalar*)arr;
    2272:   mumps->id.size_schur = size;
    2273:   mumps->id.schur_lld  = size;
    2274:   MatDenseRestoreArrayRead(F->schur,&arr);
    2275:   if (mumps->sym == 1) {
    2276:     MatSetOption(F->schur,MAT_SPD,PETSC_TRUE);
    2277:   }

    2279:   /* MUMPS expects Fortran style indices */
    2280:   PetscFree(mumps->id.listvar_schur);
    2281:   PetscMalloc1(size,&mumps->id.listvar_schur);
    2282:   ISGetIndices(is,&idxs);
    2283:   for (i=0; i<size; i++) PetscMUMPSIntCast(idxs[i]+1,&(mumps->id.listvar_schur[i]));
    2284:   ISRestoreIndices(is,&idxs);
    2285:   if (mumps->petsc_size > 1) {
    2286:     mumps->id.ICNTL(19) = 1; /* MUMPS returns Schur centralized on the host */
    2287:   } else {
    2288:     if (F->factortype == MAT_FACTOR_LU) {
    2289:       mumps->id.ICNTL(19) = 3; /* MUMPS returns full matrix */
    2290:     } else {
    2291:       mumps->id.ICNTL(19) = 2; /* MUMPS returns lower triangular part */
    2292:     }
    2293:   }
    2294:   /* set a special value of ICNTL (not handled my MUMPS) to be used in the solve phase by PETSc */
    2295:   mumps->id.ICNTL(26) = -1;
    2296:   return 0;
    2297: }

    2299: /* -------------------------------------------------------------------------------------------*/
    2300: PetscErrorCode MatFactorCreateSchurComplement_MUMPS(Mat F,Mat* S)
    2301: {
    2302:   Mat            St;
    2303:   Mat_MUMPS      *mumps =(Mat_MUMPS*)F->data;
    2304:   PetscScalar    *array;
    2305: #if defined(PETSC_USE_COMPLEX)
    2306:   PetscScalar    im = PetscSqrtScalar((PetscScalar)-1.0);
    2307: #endif

    2310:   MatCreate(PETSC_COMM_SELF,&St);
    2311:   MatSetSizes(St,PETSC_DECIDE,PETSC_DECIDE,mumps->id.size_schur,mumps->id.size_schur);
    2312:   MatSetType(St,MATDENSE);
    2313:   MatSetUp(St);
    2314:   MatDenseGetArray(St,&array);
    2315:   if (!mumps->sym) { /* MUMPS always return a full matrix */
    2316:     if (mumps->id.ICNTL(19) == 1) { /* stored by rows */
    2317:       PetscInt i,j,N=mumps->id.size_schur;
    2318:       for (i=0;i<N;i++) {
    2319:         for (j=0;j<N;j++) {
    2320: #if !defined(PETSC_USE_COMPLEX)
    2321:           PetscScalar val = mumps->id.schur[i*N+j];
    2322: #else
    2323:           PetscScalar val = mumps->id.schur[i*N+j].r + im*mumps->id.schur[i*N+j].i;
    2324: #endif
    2325:           array[j*N+i] = val;
    2326:         }
    2327:       }
    2328:     } else { /* stored by columns */
    2329:       PetscArraycpy(array,mumps->id.schur,mumps->id.size_schur*mumps->id.size_schur);
    2330:     }
    2331:   } else { /* either full or lower-triangular (not packed) */
    2332:     if (mumps->id.ICNTL(19) == 2) { /* lower triangular stored by columns */
    2333:       PetscInt i,j,N=mumps->id.size_schur;
    2334:       for (i=0;i<N;i++) {
    2335:         for (j=i;j<N;j++) {
    2336: #if !defined(PETSC_USE_COMPLEX)
    2337:           PetscScalar val = mumps->id.schur[i*N+j];
    2338: #else
    2339:           PetscScalar val = mumps->id.schur[i*N+j].r + im*mumps->id.schur[i*N+j].i;
    2340: #endif
    2341:           array[i*N+j] = val;
    2342:           array[j*N+i] = val;
    2343:         }
    2344:       }
    2345:     } else if (mumps->id.ICNTL(19) == 3) { /* full matrix */
    2346:       PetscArraycpy(array,mumps->id.schur,mumps->id.size_schur*mumps->id.size_schur);
    2347:     } else { /* ICNTL(19) == 1 lower triangular stored by rows */
    2348:       PetscInt i,j,N=mumps->id.size_schur;
    2349:       for (i=0;i<N;i++) {
    2350:         for (j=0;j<i+1;j++) {
    2351: #if !defined(PETSC_USE_COMPLEX)
    2352:           PetscScalar val = mumps->id.schur[i*N+j];
    2353: #else
    2354:           PetscScalar val = mumps->id.schur[i*N+j].r + im*mumps->id.schur[i*N+j].i;
    2355: #endif
    2356:           array[i*N+j] = val;
    2357:           array[j*N+i] = val;
    2358:         }
    2359:       }
    2360:     }
    2361:   }
    2362:   MatDenseRestoreArray(St,&array);
    2363:   *S   = St;
    2364:   return 0;
    2365: }

    2367: /* -------------------------------------------------------------------------------------------*/
    2368: PetscErrorCode MatMumpsSetIcntl_MUMPS(Mat F,PetscInt icntl,PetscInt ival)
    2369: {
    2370:   Mat_MUMPS *mumps =(Mat_MUMPS*)F->data;

    2372:   PetscMUMPSIntCast(ival,&mumps->id.ICNTL(icntl));
    2373:   return 0;
    2374: }

    2376: PetscErrorCode MatMumpsGetIcntl_MUMPS(Mat F,PetscInt icntl,PetscInt *ival)
    2377: {
    2378:   Mat_MUMPS *mumps =(Mat_MUMPS*)F->data;

    2380:   *ival = mumps->id.ICNTL(icntl);
    2381:   return 0;
    2382: }

    2384: /*@
    2385:   MatMumpsSetIcntl - Set MUMPS parameter ICNTL()

    2387:    Logically Collective on Mat

    2389:    Input Parameters:
    2390: +  F - the factored matrix obtained by calling MatGetFactor() from PETSc-MUMPS interface
    2391: .  icntl - index of MUMPS parameter array ICNTL()
    2392: -  ival - value of MUMPS ICNTL(icntl)

    2394:   Options Database:
    2395: .   -mat_mumps_icntl_<icntl> <ival> - change the option numbered icntl to ival

    2397:    Level: beginner

    2399:    References:
    2400: .  * - MUMPS Users' Guide

    2402: .seealso: MatGetFactor(), MatMumpsGetIcntl(), MatMumpsSetCntl(), MatMumpsGetCntl(), MatMumpsGetInfo(), MatMumpsGetInfog(), MatMumpsGetRinfo(), MatMumpsGetRinfog()
    2403: @*/
    2404: PetscErrorCode MatMumpsSetIcntl(Mat F,PetscInt icntl,PetscInt ival)
    2405: {
    2410:   PetscTryMethod(F,"MatMumpsSetIcntl_C",(Mat,PetscInt,PetscInt),(F,icntl,ival));
    2411:   return 0;
    2412: }

    2414: /*@
    2415:   MatMumpsGetIcntl - Get MUMPS parameter ICNTL()

    2417:    Logically Collective on Mat

    2419:    Input Parameters:
    2420: +  F - the factored matrix obtained by calling MatGetFactor() from PETSc-MUMPS interface
    2421: -  icntl - index of MUMPS parameter array ICNTL()

    2423:   Output Parameter:
    2424: .  ival - value of MUMPS ICNTL(icntl)

    2426:    Level: beginner

    2428:    References:
    2429: .  * - MUMPS Users' Guide

    2431: .seealso: MatGetFactor(), MatMumpsSetIcntl(), MatMumpsSetCntl(), MatMumpsGetCntl(), MatMumpsGetInfo(), MatMumpsGetInfog(), MatMumpsGetRinfo(), MatMumpsGetRinfog()
    2432: @*/
    2433: PetscErrorCode MatMumpsGetIcntl(Mat F,PetscInt icntl,PetscInt *ival)
    2434: {
    2439:   PetscUseMethod(F,"MatMumpsGetIcntl_C",(Mat,PetscInt,PetscInt*),(F,icntl,ival));
    2440:   return 0;
    2441: }

    2443: /* -------------------------------------------------------------------------------------------*/
    2444: PetscErrorCode MatMumpsSetCntl_MUMPS(Mat F,PetscInt icntl,PetscReal val)
    2445: {
    2446:   Mat_MUMPS *mumps =(Mat_MUMPS*)F->data;

    2448:   mumps->id.CNTL(icntl) = val;
    2449:   return 0;
    2450: }

    2452: PetscErrorCode MatMumpsGetCntl_MUMPS(Mat F,PetscInt icntl,PetscReal *val)
    2453: {
    2454:   Mat_MUMPS *mumps =(Mat_MUMPS*)F->data;

    2456:   *val = mumps->id.CNTL(icntl);
    2457:   return 0;
    2458: }

    2460: /*@
    2461:   MatMumpsSetCntl - Set MUMPS parameter CNTL()

    2463:    Logically Collective on Mat

    2465:    Input Parameters:
    2466: +  F - the factored matrix obtained by calling MatGetFactor() from PETSc-MUMPS interface
    2467: .  icntl - index of MUMPS parameter array CNTL()
    2468: -  val - value of MUMPS CNTL(icntl)

    2470:   Options Database:
    2471: .   -mat_mumps_cntl_<icntl> <val>  - change the option numbered icntl to ival

    2473:    Level: beginner

    2475:    References:
    2476: .  * - MUMPS Users' Guide

    2478: .seealso: MatGetFactor(), MatMumpsSetIcntl(), MatMumpsGetIcntl(), MatMumpsGetCntl(), MatMumpsGetInfo(), MatMumpsGetInfog(), MatMumpsGetRinfo(), MatMumpsGetRinfog()
    2479: @*/
    2480: PetscErrorCode MatMumpsSetCntl(Mat F,PetscInt icntl,PetscReal val)
    2481: {
    2486:   PetscTryMethod(F,"MatMumpsSetCntl_C",(Mat,PetscInt,PetscReal),(F,icntl,val));
    2487:   return 0;
    2488: }

    2490: /*@
    2491:   MatMumpsGetCntl - Get MUMPS parameter CNTL()

    2493:    Logically Collective on Mat

    2495:    Input Parameters:
    2496: +  F - the factored matrix obtained by calling MatGetFactor() from PETSc-MUMPS interface
    2497: -  icntl - index of MUMPS parameter array CNTL()

    2499:   Output Parameter:
    2500: .  val - value of MUMPS CNTL(icntl)

    2502:    Level: beginner

    2504:    References:
    2505: .  * - MUMPS Users' Guide

    2507: .seealso: MatGetFactor(), MatMumpsSetIcntl(), MatMumpsGetIcntl(), MatMumpsSetCntl(), MatMumpsGetInfo(), MatMumpsGetInfog(), MatMumpsGetRinfo(), MatMumpsGetRinfog()
    2508: @*/
    2509: PetscErrorCode MatMumpsGetCntl(Mat F,PetscInt icntl,PetscReal *val)
    2510: {
    2515:   PetscUseMethod(F,"MatMumpsGetCntl_C",(Mat,PetscInt,PetscReal*),(F,icntl,val));
    2516:   return 0;
    2517: }

    2519: PetscErrorCode MatMumpsGetInfo_MUMPS(Mat F,PetscInt icntl,PetscInt *info)
    2520: {
    2521:   Mat_MUMPS *mumps =(Mat_MUMPS*)F->data;

    2523:   *info = mumps->id.INFO(icntl);
    2524:   return 0;
    2525: }

    2527: PetscErrorCode MatMumpsGetInfog_MUMPS(Mat F,PetscInt icntl,PetscInt *infog)
    2528: {
    2529:   Mat_MUMPS *mumps =(Mat_MUMPS*)F->data;

    2531:   *infog = mumps->id.INFOG(icntl);
    2532:   return 0;
    2533: }

    2535: PetscErrorCode MatMumpsGetRinfo_MUMPS(Mat F,PetscInt icntl,PetscReal *rinfo)
    2536: {
    2537:   Mat_MUMPS *mumps =(Mat_MUMPS*)F->data;

    2539:   *rinfo = mumps->id.RINFO(icntl);
    2540:   return 0;
    2541: }

    2543: PetscErrorCode MatMumpsGetRinfog_MUMPS(Mat F,PetscInt icntl,PetscReal *rinfog)
    2544: {
    2545:   Mat_MUMPS *mumps =(Mat_MUMPS*)F->data;

    2547:   *rinfog = mumps->id.RINFOG(icntl);
    2548:   return 0;
    2549: }

    2551: PetscErrorCode MatMumpsGetInverse_MUMPS(Mat F,Mat spRHS)
    2552: {
    2553:   Mat            Bt = NULL,Btseq = NULL;
    2554:   PetscBool      flg;
    2555:   Mat_MUMPS      *mumps =(Mat_MUMPS*)F->data;
    2556:   PetscScalar    *aa;
    2557:   PetscInt       spnr,*ia,*ja,M,nrhs;

    2560:   PetscObjectTypeCompare((PetscObject)spRHS,MATTRANSPOSEMAT,&flg);
    2561:   if (flg) {
    2562:     MatTransposeGetMat(spRHS,&Bt);
    2563:   } else SETERRQ(PetscObjectComm((PetscObject)spRHS),PETSC_ERR_ARG_WRONG,"Matrix spRHS must be type MATTRANSPOSEMAT matrix");

    2565:   MatMumpsSetIcntl(F,30,1);

    2567:   if (mumps->petsc_size > 1) {
    2568:     Mat_MPIAIJ *b = (Mat_MPIAIJ*)Bt->data;
    2569:     Btseq = b->A;
    2570:   } else {
    2571:     Btseq = Bt;
    2572:   }

    2574:   MatGetSize(spRHS,&M,&nrhs);
    2575:   mumps->id.nrhs = nrhs;
    2576:   mumps->id.lrhs = M;
    2577:   mumps->id.rhs  = NULL;

    2579:   if (!mumps->myid) {
    2580:     MatSeqAIJGetArray(Btseq,&aa);
    2581:     MatGetRowIJ(Btseq,1,PETSC_FALSE,PETSC_FALSE,&spnr,(const PetscInt**)&ia,(const PetscInt**)&ja,&flg);
    2583:     PetscMUMPSIntCSRCast(mumps,spnr,ia,ja,&mumps->id.irhs_ptr,&mumps->id.irhs_sparse,&mumps->id.nz_rhs);
    2584:     mumps->id.rhs_sparse  = (MumpsScalar*)aa;
    2585:   } else {
    2586:     mumps->id.irhs_ptr    = NULL;
    2587:     mumps->id.irhs_sparse = NULL;
    2588:     mumps->id.nz_rhs      = 0;
    2589:     mumps->id.rhs_sparse  = NULL;
    2590:   }
    2591:   mumps->id.ICNTL(20)   = 1; /* rhs is sparse */
    2592:   mumps->id.ICNTL(21)   = 0; /* solution is in assembled centralized format */

    2594:   /* solve phase */
    2595:   /*-------------*/
    2596:   mumps->id.job = JOB_SOLVE;
    2597:   PetscMUMPS_c(mumps);
    2598:   if (mumps->id.INFOG(1) < 0)
    2599:     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error reported by MUMPS in solve phase: INFOG(1)=%d INFO(2)=%d",mumps->id.INFOG(1),mumps->id.INFO(2));

    2601:   if (!mumps->myid) {
    2602:     MatSeqAIJRestoreArray(Btseq,&aa);
    2603:     MatRestoreRowIJ(Btseq,1,PETSC_FALSE,PETSC_FALSE,&spnr,(const PetscInt**)&ia,(const PetscInt**)&ja,&flg);
    2605:   }
    2606:   return 0;
    2607: }

    2609: /*@
    2610:   MatMumpsGetInverse - Get user-specified set of entries in inverse of A

    2612:    Logically Collective on Mat

    2614:    Input Parameters:
    2615: +  F - the factored matrix obtained by calling MatGetFactor() from PETSc-MUMPS interface
    2616: -  spRHS - sequential sparse matrix in MATTRANSPOSEMAT format holding specified indices in processor[0]

    2618:   Output Parameter:
    2619: . spRHS - requested entries of inverse of A

    2621:    Level: beginner

    2623:    References:
    2624: .  * - MUMPS Users' Guide

    2626: .seealso: MatGetFactor(), MatCreateTranspose()
    2627: @*/
    2628: PetscErrorCode MatMumpsGetInverse(Mat F,Mat spRHS)
    2629: {
    2632:   PetscUseMethod(F,"MatMumpsGetInverse_C",(Mat,Mat),(F,spRHS));
    2633:   return 0;
    2634: }

    2636: PetscErrorCode MatMumpsGetInverseTranspose_MUMPS(Mat F,Mat spRHST)
    2637: {
    2638:   Mat            spRHS;

    2640:   MatCreateTranspose(spRHST,&spRHS);
    2641:   MatMumpsGetInverse_MUMPS(F,spRHS);
    2642:   MatDestroy(&spRHS);
    2643:   return 0;
    2644: }

    2646: /*@
    2647:   MatMumpsGetInverseTranspose - Get user-specified set of entries in inverse of matrix A^T

    2649:    Logically Collective on Mat

    2651:    Input Parameters:
    2652: +  F - the factored matrix of A obtained by calling MatGetFactor() from PETSc-MUMPS interface
    2653: -  spRHST - sequential sparse matrix in MATAIJ format holding specified indices of A^T in processor[0]

    2655:   Output Parameter:
    2656: . spRHST - requested entries of inverse of A^T

    2658:    Level: beginner

    2660:    References:
    2661: .  * - MUMPS Users' Guide

    2663: .seealso: MatGetFactor(), MatCreateTranspose(), MatMumpsGetInverse()
    2664: @*/
    2665: PetscErrorCode MatMumpsGetInverseTranspose(Mat F,Mat spRHST)
    2666: {
    2667:   PetscBool      flg;

    2671:   PetscObjectTypeCompareAny((PetscObject)spRHST,&flg,MATSEQAIJ,MATMPIAIJ,NULL);

    2674:   PetscUseMethod(F,"MatMumpsGetInverseTranspose_C",(Mat,Mat),(F,spRHST));
    2675:   return 0;
    2676: }

    2678: /*@
    2679:   MatMumpsGetInfo - Get MUMPS parameter INFO()

    2681:    Logically Collective on Mat

    2683:    Input Parameters:
    2684: +  F - the factored matrix obtained by calling MatGetFactor() from PETSc-MUMPS interface
    2685: -  icntl - index of MUMPS parameter array INFO()

    2687:   Output Parameter:
    2688: .  ival - value of MUMPS INFO(icntl)

    2690:    Level: beginner

    2692:    References:
    2693: .  * - MUMPS Users' Guide

    2695: .seealso: MatGetFactor(), MatMumpsSetIcntl(), MatMumpsGetIcntl(), MatMumpsSetCntl(), MatMumpsGetCntl(), MatMumpsGetInfog(), MatMumpsGetRinfo(), MatMumpsGetRinfog()
    2696: @*/
    2697: PetscErrorCode MatMumpsGetInfo(Mat F,PetscInt icntl,PetscInt *ival)
    2698: {
    2702:   PetscUseMethod(F,"MatMumpsGetInfo_C",(Mat,PetscInt,PetscInt*),(F,icntl,ival));
    2703:   return 0;
    2704: }

    2706: /*@
    2707:   MatMumpsGetInfog - Get MUMPS parameter INFOG()

    2709:    Logically Collective on Mat

    2711:    Input Parameters:
    2712: +  F - the factored matrix obtained by calling MatGetFactor() from PETSc-MUMPS interface
    2713: -  icntl - index of MUMPS parameter array INFOG()

    2715:   Output Parameter:
    2716: .  ival - value of MUMPS INFOG(icntl)

    2718:    Level: beginner

    2720:    References:
    2721: .  * - MUMPS Users' Guide

    2723: .seealso: MatGetFactor(), MatMumpsSetIcntl(), MatMumpsGetIcntl(), MatMumpsSetCntl(), MatMumpsGetCntl(), MatMumpsGetInfo(), MatMumpsGetRinfo(), MatMumpsGetRinfog()
    2724: @*/
    2725: PetscErrorCode MatMumpsGetInfog(Mat F,PetscInt icntl,PetscInt *ival)
    2726: {
    2730:   PetscUseMethod(F,"MatMumpsGetInfog_C",(Mat,PetscInt,PetscInt*),(F,icntl,ival));
    2731:   return 0;
    2732: }

    2734: /*@
    2735:   MatMumpsGetRinfo - Get MUMPS parameter RINFO()

    2737:    Logically Collective on Mat

    2739:    Input Parameters:
    2740: +  F - the factored matrix obtained by calling MatGetFactor() from PETSc-MUMPS interface
    2741: -  icntl - index of MUMPS parameter array RINFO()

    2743:   Output Parameter:
    2744: .  val - value of MUMPS RINFO(icntl)

    2746:    Level: beginner

    2748:    References:
    2749: .  * - MUMPS Users' Guide

    2751: .seealso: MatGetFactor(), MatMumpsSetIcntl(), MatMumpsGetIcntl(), MatMumpsSetCntl(), MatMumpsGetCntl(), MatMumpsGetInfo(), MatMumpsGetInfog(), MatMumpsGetRinfog()
    2752: @*/
    2753: PetscErrorCode MatMumpsGetRinfo(Mat F,PetscInt icntl,PetscReal *val)
    2754: {
    2758:   PetscUseMethod(F,"MatMumpsGetRinfo_C",(Mat,PetscInt,PetscReal*),(F,icntl,val));
    2759:   return 0;
    2760: }

    2762: /*@
    2763:   MatMumpsGetRinfog - Get MUMPS parameter RINFOG()

    2765:    Logically Collective on Mat

    2767:    Input Parameters:
    2768: +  F - the factored matrix obtained by calling MatGetFactor() from PETSc-MUMPS interface
    2769: -  icntl - index of MUMPS parameter array RINFOG()

    2771:   Output Parameter:
    2772: .  val - value of MUMPS RINFOG(icntl)

    2774:    Level: beginner

    2776:    References:
    2777: .  * - MUMPS Users' Guide

    2779: .seealso: MatGetFactor(), MatMumpsSetIcntl(), MatMumpsGetIcntl(), MatMumpsSetCntl(), MatMumpsGetCntl(), MatMumpsGetInfo(), MatMumpsGetInfog(), MatMumpsGetRinfo()
    2780: @*/
    2781: PetscErrorCode MatMumpsGetRinfog(Mat F,PetscInt icntl,PetscReal *val)
    2782: {
    2786:   PetscUseMethod(F,"MatMumpsGetRinfog_C",(Mat,PetscInt,PetscReal*),(F,icntl,val));
    2787:   return 0;
    2788: }

    2790: /*MC
    2791:   MATSOLVERMUMPS -  A matrix type providing direct solvers (LU and Cholesky) for
    2792:   distributed and sequential matrices via the external package MUMPS.

    2794:   Works with MATAIJ and MATSBAIJ matrices

    2796:   Use ./configure --download-mumps --download-scalapack --download-parmetis --download-metis --download-ptscotch to have PETSc installed with MUMPS

    2798:   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. See details below.

    2800:   Use -pc_type cholesky or lu -pc_factor_mat_solver_type mumps to use this direct solver

    2802:   Options Database Keys:
    2803: +  -mat_mumps_icntl_1 - ICNTL(1): output stream for error messages
    2804: .  -mat_mumps_icntl_2 - ICNTL(2): output stream for diagnostic printing, statistics, and warning
    2805: .  -mat_mumps_icntl_3 -  ICNTL(3): output stream for global information, collected on the host
    2806: .  -mat_mumps_icntl_4 -  ICNTL(4): level of printing (0 to 4)
    2807: .  -mat_mumps_icntl_6 - ICNTL(6): permutes to a zero-free diagonal and/or scale the matrix (0 to 7)
    2808: .  -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
    2809:                         Use -pc_factor_mat_ordering_type <type> to have PETSc perform the ordering (sequential only)
    2810: .  -mat_mumps_icntl_8  - ICNTL(8): scaling strategy (-2 to 8 or 77)
    2811: .  -mat_mumps_icntl_10  - ICNTL(10): max num of refinements
    2812: .  -mat_mumps_icntl_11  - ICNTL(11): statistics related to an error analysis (via -ksp_view)
    2813: .  -mat_mumps_icntl_12  - ICNTL(12): an ordering strategy for symmetric matrices (0 to 3)
    2814: .  -mat_mumps_icntl_13  - ICNTL(13): parallelism of the root node (enable ScaLAPACK) and its splitting
    2815: .  -mat_mumps_icntl_14  - ICNTL(14): percentage increase in the estimated working space
    2816: .  -mat_mumps_icntl_19  - ICNTL(19): computes the Schur complement
    2817: .  -mat_mumps_icntl_20  - ICNTL(20): give MUMPS centralized (0) or distributed (10) dense RHS
    2818: .  -mat_mumps_icntl_22  - ICNTL(22): in-core/out-of-core factorization and solve (0 or 1)
    2819: .  -mat_mumps_icntl_23  - ICNTL(23): max size of the working memory (MB) that can allocate per processor
    2820: .  -mat_mumps_icntl_24  - ICNTL(24): detection of null pivot rows (0 or 1)
    2821: .  -mat_mumps_icntl_25  - ICNTL(25): compute a solution of a deficient matrix and a null space basis
    2822: .  -mat_mumps_icntl_26  - ICNTL(26): drives the solution phase if a Schur complement matrix
    2823: .  -mat_mumps_icntl_28  - ICNTL(28): use 1 for sequential analysis and ictnl(7) ordering, or 2 for parallel analysis and ictnl(29) ordering
    2824: .  -mat_mumps_icntl_29 - ICNTL(29): parallel ordering 1 = ptscotch, 2 = parmetis
    2825: .  -mat_mumps_icntl_30 - ICNTL(30): compute user-specified set of entries in inv(A)
    2826: .  -mat_mumps_icntl_31 - ICNTL(31): indicates which factors may be discarded during factorization
    2827: .  -mat_mumps_icntl_33 - ICNTL(33): compute determinant
    2828: .  -mat_mumps_icntl_35 - ICNTL(35): level of activation of BLR (Block Low-Rank) feature
    2829: .  -mat_mumps_icntl_36 - ICNTL(36): controls the choice of BLR factorization variant
    2830: .  -mat_mumps_icntl_38 - ICNTL(38): sets the estimated compression rate of LU factors with BLR
    2831: .  -mat_mumps_cntl_1  - CNTL(1): relative pivoting threshold
    2832: .  -mat_mumps_cntl_2  -  CNTL(2): stopping criterion of refinement
    2833: .  -mat_mumps_cntl_3 - CNTL(3): absolute pivoting threshold
    2834: .  -mat_mumps_cntl_4 - CNTL(4): value for static pivoting
    2835: .  -mat_mumps_cntl_5 - CNTL(5): fixation for null pivots
    2836: .  -mat_mumps_cntl_7 - CNTL(7): precision of the dropping parameter used during BLR factorization
    2837: -  -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.
    2838:                                    Default might be the number of cores per CPU package (socket) as reported by hwloc and suggested by the MUMPS manual.

    2840:   Level: beginner

    2842:     Notes:
    2843:     MUMPS Cholesky does not handle (complex) Hermitian matrices http://mumps.enseeiht.fr/doc/userguide_5.2.1.pdf so using it will error if the matrix is Hermitian.

    2845:     When a MUMPS factorization fails inside a KSP solve, for example with a KSP_DIVERGED_PC_FAILED, one can find the MUMPS information about the failure by calling
    2846: $          KSPGetPC(ksp,&pc);
    2847: $          PCFactorGetMatrix(pc,&mat);
    2848: $          MatMumpsGetInfo(mat,....);
    2849: $          MatMumpsGetInfog(mat,....); etc.
    2850:            Or you can run with -ksp_error_if_not_converged and the program will be stopped and the information printed in the error message.

    2852:   Using MUMPS with 64-bit integers
    2853:     MUMPS provides 64-bit integer support in two build modes:
    2854:       full 64-bit: here MUMPS is built with C preprocessing flag -DINTSIZE64 and Fortran compiler option -i8, -fdefault-integer-8 or equivalent, and
    2855:       requires all dependent libraries MPI, ScaLAPACK, LAPACK and BLAS built the same way with 64-bit integers (for example ILP64 Intel MKL and MPI).

    2857:       selective 64-bit: with the default MUMPS build, 64-bit integers have been introduced where needed. In compressed sparse row (CSR) storage of matrices,
    2858:       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
    2859:       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
    2860:       integer) build of all dependent libraries MPI, ScaLAPACK, LAPACK and BLAS.

    2862:     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.

    2864:   Two modes to run MUMPS/PETSc with OpenMP
    2865: $     Set OMP_NUM_THREADS and run with fewer MPI ranks than cores. For example, if you want to have 16 OpenMP
    2866: $     threads per rank, then you may use "export OMP_NUM_THREADS=16 && mpirun -n 4 ./test".

    2868: $     -mat_mumps_use_omp_threads [m] and run your code with as many MPI ranks as the number of cores. For example,
    2869: $     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"

    2871:    To run MUMPS in MPI+OpenMP hybrid mode (i.e., enable multithreading in MUMPS), but still run the non-MUMPS part
    2872:    (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
    2873:    (or --with-hwloc), and have an MPI that supports MPI-3.0's process shared memory (which is usually available). Since MUMPS calls BLAS
    2874:    libraries, to really get performance, you should have multithreaded BLAS libraries such as Intel MKL, AMD ACML, Cray libSci or OpenBLAS
    2875:    (PETSc will automatically try to utilized a threaded BLAS if --with-openmp is provided).

    2877:    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
    2878:    processes on each compute node. Listing the processes in rank ascending order, we split processes on a node into consecutive groups of
    2879:    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
    2880:    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
    2881:    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.
    2882:    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,
    2883:    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
    2884:    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
    2885:    cores in socket 1, that definitely hurts locality. On the other hand, if you map MPI ranks consecutively on the two sockets, then the
    2886:    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.
    2887:    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
    2888:    examine the mapping result.

    2890:    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,
    2891:    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
    2892:    calls omp_set_num_threads(m) internally before calling MUMPS.

    2894:    References:
    2895: +  * - Heroux, Michael A., R. Brightwell, and Michael M. Wolf. "Bi-modal MPI and MPI+ threads computing on scalable multicore systems." IJHPCA (Submitted) (2011).
    2896: -  * - Gutierrez, Samuel K., et al. "Accommodating Thread-Level Heterogeneity in Coupled Parallel Applications." Parallel and Distributed Processing Symposium (IPDPS), 2017 IEEE International. IEEE, 2017.

    2898: .seealso: PCFactorSetMatSolverType(), MatSolverType, MatMumpsSetIcntl(), MatMumpsGetIcntl(), MatMumpsSetCntl(), MatMumpsGetCntl(), MatMumpsGetInfo(), MatMumpsGetInfog(), MatMumpsGetRinfo(), MatMumpsGetRinfog(), KSPGetPC(), PCFactorGetMatrix()

    2900: M*/

    2902: static PetscErrorCode MatFactorGetSolverType_mumps(Mat A,MatSolverType *type)
    2903: {
    2904:   *type = MATSOLVERMUMPS;
    2905:   return 0;
    2906: }

    2908: /* MatGetFactor for Seq and MPI AIJ matrices */
    2909: static PetscErrorCode MatGetFactor_aij_mumps(Mat A,MatFactorType ftype,Mat *F)
    2910: {
    2911:   Mat            B;
    2912:   Mat_MUMPS      *mumps;
    2913:   PetscBool      isSeqAIJ;
    2914:   PetscMPIInt    size;

    2916:  #if defined(PETSC_USE_COMPLEX)
    2918:  #endif
    2919:   /* Create the factorization matrix */
    2920:   PetscObjectBaseTypeCompare((PetscObject)A,MATSEQAIJ,&isSeqAIJ);
    2921:   MatCreate(PetscObjectComm((PetscObject)A),&B);
    2922:   MatSetSizes(B,A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N);
    2923:   PetscStrallocpy("mumps",&((PetscObject)B)->type_name);
    2924:   MatSetUp(B);

    2926:   PetscNewLog(B,&mumps);

    2928:   B->ops->view    = MatView_MUMPS;
    2929:   B->ops->getinfo = MatGetInfo_MUMPS;

    2931:   PetscObjectComposeFunction((PetscObject)B,"MatFactorGetSolverType_C",MatFactorGetSolverType_mumps);
    2932:   PetscObjectComposeFunction((PetscObject)B,"MatFactorSetSchurIS_C",MatFactorSetSchurIS_MUMPS);
    2933:   PetscObjectComposeFunction((PetscObject)B,"MatFactorCreateSchurComplement_C",MatFactorCreateSchurComplement_MUMPS);
    2934:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsSetIcntl_C",MatMumpsSetIcntl_MUMPS);
    2935:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetIcntl_C",MatMumpsGetIcntl_MUMPS);
    2936:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsSetCntl_C",MatMumpsSetCntl_MUMPS);
    2937:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetCntl_C",MatMumpsGetCntl_MUMPS);
    2938:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetInfo_C",MatMumpsGetInfo_MUMPS);
    2939:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetInfog_C",MatMumpsGetInfog_MUMPS);
    2940:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetRinfo_C",MatMumpsGetRinfo_MUMPS);
    2941:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetRinfog_C",MatMumpsGetRinfog_MUMPS);
    2942:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetInverse_C",MatMumpsGetInverse_MUMPS);
    2943:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetInverseTranspose_C",MatMumpsGetInverseTranspose_MUMPS);

    2945:   if (ftype == MAT_FACTOR_LU) {
    2946:     B->ops->lufactorsymbolic = MatLUFactorSymbolic_AIJMUMPS;
    2947:     B->factortype            = MAT_FACTOR_LU;
    2948:     if (isSeqAIJ) mumps->ConvertToTriples = MatConvertToTriples_seqaij_seqaij;
    2949:     else mumps->ConvertToTriples = MatConvertToTriples_mpiaij_mpiaij;
    2950:     PetscStrallocpy(MATORDERINGEXTERNAL,(char**)&B->preferredordering[MAT_FACTOR_LU]);
    2951:     mumps->sym = 0;
    2952:   } else {
    2953:     B->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_MUMPS;
    2954:     B->factortype                  = MAT_FACTOR_CHOLESKY;
    2955:     if (isSeqAIJ) mumps->ConvertToTriples = MatConvertToTriples_seqaij_seqsbaij;
    2956:     else mumps->ConvertToTriples = MatConvertToTriples_mpiaij_mpisbaij;
    2957:     PetscStrallocpy(MATORDERINGEXTERNAL,(char**)&B->preferredordering[MAT_FACTOR_CHOLESKY]);
    2958: #if defined(PETSC_USE_COMPLEX)
    2959:     mumps->sym = 2;
    2960: #else
    2961:     if (A->spd_set && A->spd) mumps->sym = 1;
    2962:     else                      mumps->sym = 2;
    2963: #endif
    2964:   }

    2966:   /* set solvertype */
    2967:   PetscFree(B->solvertype);
    2968:   PetscStrallocpy(MATSOLVERMUMPS,&B->solvertype);
    2969:   MPI_Comm_size(PetscObjectComm((PetscObject)A),&size);
    2970:   if (size == 1) {
    2971:     /* MUMPS option -mat_mumps_icntl_7 1 is automatically set if PETSc ordering is passed into symbolic factorization */
    2972:     B->canuseordering = PETSC_TRUE;
    2973:   }
    2974:   B->ops->destroy = MatDestroy_MUMPS;
    2975:   B->data         = (void*)mumps;

    2977:   PetscInitializeMUMPS(A,mumps);

    2979:   *F = B;
    2980:   mumps->matstruc = DIFFERENT_NONZERO_PATTERN;
    2981:   return 0;
    2982: }

    2984: /* MatGetFactor for Seq and MPI SBAIJ matrices */
    2985: static PetscErrorCode MatGetFactor_sbaij_mumps(Mat A,MatFactorType ftype,Mat *F)
    2986: {
    2987:   Mat            B;
    2988:   Mat_MUMPS      *mumps;
    2989:   PetscBool      isSeqSBAIJ;
    2990:   PetscMPIInt    size;

    2992:  #if defined(PETSC_USE_COMPLEX)
    2994:  #endif
    2995:   MatCreate(PetscObjectComm((PetscObject)A),&B);
    2996:   MatSetSizes(B,A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N);
    2997:   PetscStrallocpy("mumps",&((PetscObject)B)->type_name);
    2998:   MatSetUp(B);

    3000:   PetscNewLog(B,&mumps);
    3001:   PetscObjectTypeCompare((PetscObject)A,MATSEQSBAIJ,&isSeqSBAIJ);
    3002:   if (isSeqSBAIJ) {
    3003:     mumps->ConvertToTriples = MatConvertToTriples_seqsbaij_seqsbaij;
    3004:   } else {
    3005:     mumps->ConvertToTriples = MatConvertToTriples_mpisbaij_mpisbaij;
    3006:   }

    3008:   B->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_MUMPS;
    3009:   B->ops->view                   = MatView_MUMPS;
    3010:   B->ops->getinfo                = MatGetInfo_MUMPS;

    3012:   PetscObjectComposeFunction((PetscObject)B,"MatFactorGetSolverType_C",MatFactorGetSolverType_mumps);
    3013:   PetscObjectComposeFunction((PetscObject)B,"MatFactorSetSchurIS_C",MatFactorSetSchurIS_MUMPS);
    3014:   PetscObjectComposeFunction((PetscObject)B,"MatFactorCreateSchurComplement_C",MatFactorCreateSchurComplement_MUMPS);
    3015:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsSetIcntl_C",MatMumpsSetIcntl_MUMPS);
    3016:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetIcntl_C",MatMumpsGetIcntl_MUMPS);
    3017:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsSetCntl_C",MatMumpsSetCntl_MUMPS);
    3018:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetCntl_C",MatMumpsGetCntl_MUMPS);
    3019:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetInfo_C",MatMumpsGetInfo_MUMPS);
    3020:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetInfog_C",MatMumpsGetInfog_MUMPS);
    3021:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetRinfo_C",MatMumpsGetRinfo_MUMPS);
    3022:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetRinfog_C",MatMumpsGetRinfog_MUMPS);
    3023:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetInverse_C",MatMumpsGetInverse_MUMPS);
    3024:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetInverseTranspose_C",MatMumpsGetInverseTranspose_MUMPS);

    3026:   B->factortype = MAT_FACTOR_CHOLESKY;
    3027: #if defined(PETSC_USE_COMPLEX)
    3028:   mumps->sym = 2;
    3029: #else
    3030:   if (A->spd_set && A->spd) mumps->sym = 1;
    3031:   else                      mumps->sym = 2;
    3032: #endif

    3034:   /* set solvertype */
    3035:   PetscFree(B->solvertype);
    3036:   PetscStrallocpy(MATSOLVERMUMPS,&B->solvertype);
    3037:   MPI_Comm_size(PetscObjectComm((PetscObject)A),&size);
    3038:   if (size == 1) {
    3039:     /* MUMPS option -mat_mumps_icntl_7 1 is automatically set if PETSc ordering is passed into symbolic factorization */
    3040:     B->canuseordering = PETSC_TRUE;
    3041:   }
    3042:   PetscStrallocpy(MATORDERINGEXTERNAL,(char**)&B->preferredordering[MAT_FACTOR_CHOLESKY]);
    3043:   B->ops->destroy = MatDestroy_MUMPS;
    3044:   B->data         = (void*)mumps;

    3046:   PetscInitializeMUMPS(A,mumps);

    3048:   *F = B;
    3049:   mumps->matstruc = DIFFERENT_NONZERO_PATTERN;
    3050:   return 0;
    3051: }

    3053: static PetscErrorCode MatGetFactor_baij_mumps(Mat A,MatFactorType ftype,Mat *F)
    3054: {
    3055:   Mat            B;
    3056:   Mat_MUMPS      *mumps;
    3057:   PetscBool      isSeqBAIJ;
    3058:   PetscMPIInt    size;

    3060:   /* Create the factorization matrix */
    3061:   PetscObjectTypeCompare((PetscObject)A,MATSEQBAIJ,&isSeqBAIJ);
    3062:   MatCreate(PetscObjectComm((PetscObject)A),&B);
    3063:   MatSetSizes(B,A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N);
    3064:   PetscStrallocpy("mumps",&((PetscObject)B)->type_name);
    3065:   MatSetUp(B);

    3067:   PetscNewLog(B,&mumps);
    3068:   if (ftype == MAT_FACTOR_LU) {
    3069:     B->ops->lufactorsymbolic = MatLUFactorSymbolic_BAIJMUMPS;
    3070:     B->factortype            = MAT_FACTOR_LU;
    3071:     if (isSeqBAIJ) mumps->ConvertToTriples = MatConvertToTriples_seqbaij_seqaij;
    3072:     else mumps->ConvertToTriples = MatConvertToTriples_mpibaij_mpiaij;
    3073:     mumps->sym = 0;
    3074:     PetscStrallocpy(MATORDERINGEXTERNAL,(char**)&B->preferredordering[MAT_FACTOR_LU]);
    3075:   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Cannot use PETSc BAIJ matrices with MUMPS Cholesky, use SBAIJ or AIJ matrix instead");

    3077:   B->ops->view        = MatView_MUMPS;
    3078:   B->ops->getinfo     = MatGetInfo_MUMPS;

    3080:   PetscObjectComposeFunction((PetscObject)B,"MatFactorGetSolverType_C",MatFactorGetSolverType_mumps);
    3081:   PetscObjectComposeFunction((PetscObject)B,"MatFactorSetSchurIS_C",MatFactorSetSchurIS_MUMPS);
    3082:   PetscObjectComposeFunction((PetscObject)B,"MatFactorCreateSchurComplement_C",MatFactorCreateSchurComplement_MUMPS);
    3083:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsSetIcntl_C",MatMumpsSetIcntl_MUMPS);
    3084:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetIcntl_C",MatMumpsGetIcntl_MUMPS);
    3085:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsSetCntl_C",MatMumpsSetCntl_MUMPS);
    3086:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetCntl_C",MatMumpsGetCntl_MUMPS);
    3087:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetInfo_C",MatMumpsGetInfo_MUMPS);
    3088:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetInfog_C",MatMumpsGetInfog_MUMPS);
    3089:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetRinfo_C",MatMumpsGetRinfo_MUMPS);
    3090:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetRinfog_C",MatMumpsGetRinfog_MUMPS);
    3091:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetInverse_C",MatMumpsGetInverse_MUMPS);
    3092:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetInverseTranspose_C",MatMumpsGetInverseTranspose_MUMPS);

    3094:   /* set solvertype */
    3095:   PetscFree(B->solvertype);
    3096:   PetscStrallocpy(MATSOLVERMUMPS,&B->solvertype);
    3097:   MPI_Comm_size(PetscObjectComm((PetscObject)A),&size);
    3098:   if (size == 1) {
    3099:     /* MUMPS option -mat_mumps_icntl_7 1 is automatically set if PETSc ordering is passed into symbolic factorization */
    3100:     B->canuseordering = PETSC_TRUE;
    3101:   }
    3102:   B->ops->destroy = MatDestroy_MUMPS;
    3103:   B->data         = (void*)mumps;

    3105:   PetscInitializeMUMPS(A,mumps);

    3107:   *F = B;
    3108:   mumps->matstruc = DIFFERENT_NONZERO_PATTERN;
    3109:   return 0;
    3110: }

    3112: /* MatGetFactor for Seq and MPI SELL matrices */
    3113: static PetscErrorCode MatGetFactor_sell_mumps(Mat A,MatFactorType ftype,Mat *F)
    3114: {
    3115:   Mat            B;
    3116:   Mat_MUMPS      *mumps;
    3117:   PetscBool      isSeqSELL;
    3118:   PetscMPIInt    size;

    3120:   /* Create the factorization matrix */
    3121:   PetscObjectTypeCompare((PetscObject)A,MATSEQSELL,&isSeqSELL);
    3122:   MatCreate(PetscObjectComm((PetscObject)A),&B);
    3123:   MatSetSizes(B,A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N);
    3124:   PetscStrallocpy("mumps",&((PetscObject)B)->type_name);
    3125:   MatSetUp(B);

    3127:   PetscNewLog(B,&mumps);

    3129:   B->ops->view        = MatView_MUMPS;
    3130:   B->ops->getinfo     = MatGetInfo_MUMPS;

    3132:   PetscObjectComposeFunction((PetscObject)B,"MatFactorGetSolverType_C",MatFactorGetSolverType_mumps);
    3133:   PetscObjectComposeFunction((PetscObject)B,"MatFactorSetSchurIS_C",MatFactorSetSchurIS_MUMPS);
    3134:   PetscObjectComposeFunction((PetscObject)B,"MatFactorCreateSchurComplement_C",MatFactorCreateSchurComplement_MUMPS);
    3135:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsSetIcntl_C",MatMumpsSetIcntl_MUMPS);
    3136:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetIcntl_C",MatMumpsGetIcntl_MUMPS);
    3137:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsSetCntl_C",MatMumpsSetCntl_MUMPS);
    3138:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetCntl_C",MatMumpsGetCntl_MUMPS);
    3139:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetInfo_C",MatMumpsGetInfo_MUMPS);
    3140:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetInfog_C",MatMumpsGetInfog_MUMPS);
    3141:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetRinfo_C",MatMumpsGetRinfo_MUMPS);
    3142:   PetscObjectComposeFunction((PetscObject)B,"MatMumpsGetRinfog_C",MatMumpsGetRinfog_MUMPS);

    3144:   if (ftype == MAT_FACTOR_LU) {
    3145:     B->ops->lufactorsymbolic = MatLUFactorSymbolic_AIJMUMPS;
    3146:     B->factortype            = MAT_FACTOR_LU;
    3147:     if (isSeqSELL) mumps->ConvertToTriples = MatConvertToTriples_seqsell_seqaij;
    3148:     else SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"To be implemented");
    3149:     mumps->sym = 0;
    3150:     PetscStrallocpy(MATORDERINGEXTERNAL,(char**)&B->preferredordering[MAT_FACTOR_LU]);
    3151:   } else SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"To be implemented");

    3153:   /* set solvertype */
    3154:   PetscFree(B->solvertype);
    3155:   PetscStrallocpy(MATSOLVERMUMPS,&B->solvertype);
    3156:   MPI_Comm_size(PetscObjectComm((PetscObject)A),&size);
    3157:   if (size == 1) {
    3158:     /* MUMPS option -mat_mumps_icntl_7 1 is automatically set if PETSc ordering is passed into symbolic factorization  */
    3159:     B->canuseordering = PETSC_TRUE;
    3160:   }
    3161:   B->ops->destroy = MatDestroy_MUMPS;
    3162:   B->data         = (void*)mumps;

    3164:   PetscInitializeMUMPS(A,mumps);

    3166:   *F = B;
    3167:   mumps->matstruc = DIFFERENT_NONZERO_PATTERN;
    3168:   return 0;
    3169: }

    3171: PETSC_EXTERN PetscErrorCode MatSolverTypeRegister_MUMPS(void)
    3172: {
    3173:   MatSolverTypeRegister(MATSOLVERMUMPS,MATMPIAIJ,MAT_FACTOR_LU,MatGetFactor_aij_mumps);
    3174:   MatSolverTypeRegister(MATSOLVERMUMPS,MATMPIAIJ,MAT_FACTOR_CHOLESKY,MatGetFactor_aij_mumps);
    3175:   MatSolverTypeRegister(MATSOLVERMUMPS,MATMPIBAIJ,MAT_FACTOR_LU,MatGetFactor_baij_mumps);
    3176:   MatSolverTypeRegister(MATSOLVERMUMPS,MATMPIBAIJ,MAT_FACTOR_CHOLESKY,MatGetFactor_baij_mumps);
    3177:   MatSolverTypeRegister(MATSOLVERMUMPS,MATMPISBAIJ,MAT_FACTOR_CHOLESKY,MatGetFactor_sbaij_mumps);
    3178:   MatSolverTypeRegister(MATSOLVERMUMPS,MATSEQAIJ,MAT_FACTOR_LU,MatGetFactor_aij_mumps);
    3179:   MatSolverTypeRegister(MATSOLVERMUMPS,MATSEQAIJ,MAT_FACTOR_CHOLESKY,MatGetFactor_aij_mumps);
    3180:   MatSolverTypeRegister(MATSOLVERMUMPS,MATSEQBAIJ,MAT_FACTOR_LU,MatGetFactor_baij_mumps);
    3181:   MatSolverTypeRegister(MATSOLVERMUMPS,MATSEQBAIJ,MAT_FACTOR_CHOLESKY,MatGetFactor_baij_mumps);
    3182:   MatSolverTypeRegister(MATSOLVERMUMPS,MATSEQSBAIJ,MAT_FACTOR_CHOLESKY,MatGetFactor_sbaij_mumps);
    3183:   MatSolverTypeRegister(MATSOLVERMUMPS,MATSEQSELL,MAT_FACTOR_LU,MatGetFactor_sell_mumps);
    3184:   return 0;
    3185: }