Date: 2022-08-02T03:13:53+00:00

Actual source code: sbaijcholmod.c

      2: /*
      3:    Provides an interface to the CHOLMOD sparse solver available through SuiteSparse version 4.2.1

      5:    When built with PETSC_USE_64BIT_INDICES this will use Suitesparse_long as the
      6:    integer type in UMFPACK, otherwise it will use int. This means
      7:    all integers in this file as simply declared as PetscInt. Also it means
      8:    that one cannot use 64BIT_INDICES on 32bit machines [as Suitesparse_long is 32bit only]

     10: */

     12: #include <../src/mat/impls/sbaij/seq/sbaij.h>
     13: #include <../src/mat/impls/sbaij/seq/cholmod/cholmodimpl.h>

     15: /*
     16:    This is a terrible hack, but it allows the error handler to retain a context.
     17:    Note that this hack really cannot be made both reentrant and concurrent.
     18: */
     19: static Mat static_F;

     21: static void CholmodErrorHandler(int status,const char *file,int line,const char *message)
     22: {
     23:   if (status > CHOLMOD_OK) {
     24:     PetscInfo(static_F,"CHOLMOD warning %d at %s:%d: %s\n",status,file,line,message);
     25:   } else if (status == CHOLMOD_OK) { /* Documentation says this can happen, but why? */
     26:     PetscInfo(static_F,"CHOLMOD OK at %s:%d: %s\n",file,line,message);
     27:   } else {
     28:     PetscErrorPrintf("CHOLMOD error %d at %s:%d: %s\n",status,file,line,message);
     29:   }
     30:   return;
     31: }

     33: PetscErrorCode  CholmodStart(Mat F)
     34: {
     36:   Mat_CHOLMOD    *chol=(Mat_CHOLMOD*)F->data;
     37:   cholmod_common *c;
     38:   PetscBool      flg;

     40:   if (chol->common) return 0;
     41:   PetscMalloc1(1,&chol->common);
     42:   !cholmod_X_start(chol->common);

     44:   c                = chol->common;
     45:   c->error_handler = CholmodErrorHandler;

     47: #define CHOLMOD_OPTION_DOUBLE(name,help) do {                            \
     48:     PetscReal tmp = (PetscReal)c->name;                                  \
     49:     PetscOptionsReal("-mat_cholmod_" #name,help,"None",tmp,&tmp,NULL); \
     50:     c->name = (double)tmp;                                               \
     51: } while (0)

     53: #define CHOLMOD_OPTION_INT(name,help) do {                               \
     54:     PetscInt tmp = (PetscInt)c->name;                                    \
     55:     PetscOptionsInt("-mat_cholmod_" #name,help,"None",tmp,&tmp,NULL); \
     56:     c->name = (int)tmp;                                                  \
     57: } while (0)

     59: #define CHOLMOD_OPTION_SIZE_T(name,help) do {                            \
     60:     PetscReal tmp = (PetscInt)c->name;                                   \
     61:     PetscOptionsReal("-mat_cholmod_" #name,help,"None",tmp,&tmp,NULL); \
     63:     c->name = (size_t)tmp;                                               \
     64: } while (0)

     66: #define CHOLMOD_OPTION_BOOL(name,help) do {                             \
     67:     PetscBool tmp = (PetscBool) !!c->name;                              \
     68:     PetscOptionsBool("-mat_cholmod_" #name,help,"None",tmp,&tmp,NULL); \
     69:     c->name = (int)tmp;                                                  \
     70: } while (0)

     72:   PetscOptionsBegin(PetscObjectComm((PetscObject)F),((PetscObject)F)->prefix,"CHOLMOD Options","Mat");
     73:   CHOLMOD_OPTION_INT(nmethods,"Number of different ordering methods to try");

     75: #if defined(PETSC_USE_SUITESPARSE_GPU)
     76:   c->useGPU = 1;
     77:   CHOLMOD_OPTION_INT(useGPU,"Use GPU for BLAS 1, otherwise 0");
     78:   CHOLMOD_OPTION_SIZE_T(maxGpuMemBytes,"Maximum memory to allocate on the GPU");
     79:   CHOLMOD_OPTION_DOUBLE(maxGpuMemFraction,"Fraction of available GPU memory to allocate");
     80: #endif

     82:   /* CHOLMOD handles first-time packing and refactor-packing separately, but we usually want them to be the same. */
     83:   chol->pack = (PetscBool)c->final_pack;
     84:   PetscOptionsBool("-mat_cholmod_pack","Pack factors after factorization [disable for frequent repeat factorization]","None",chol->pack,&chol->pack,NULL);
     85:   c->final_pack = (int)chol->pack;

     87:   CHOLMOD_OPTION_DOUBLE(dbound,"Minimum absolute value of diagonal entries of D");
     88:   CHOLMOD_OPTION_DOUBLE(grow0,"Global growth ratio when factors are modified");
     89:   CHOLMOD_OPTION_DOUBLE(grow1,"Column growth ratio when factors are modified");
     90:   CHOLMOD_OPTION_SIZE_T(grow2,"Affine column growth constant when factors are modified");
     91:   CHOLMOD_OPTION_SIZE_T(maxrank,"Max rank of update, larger values are faster but use more memory [2,4,8]");
     92:   {
     93:     static const char *const list[] = {"SIMPLICIAL","AUTO","SUPERNODAL","MatCholmodFactorType","MAT_CHOLMOD_FACTOR_",0};
     94:     PetscOptionsEnum("-mat_cholmod_factor","Factorization method","None",list,(PetscEnum)c->supernodal,(PetscEnum*)&c->supernodal,NULL);
     95:   }
     96:   if (c->supernodal) CHOLMOD_OPTION_DOUBLE(supernodal_switch,"flop/nnz_L threshold for switching to supernodal factorization");
     97:   CHOLMOD_OPTION_BOOL(final_asis,"Leave factors \"as is\"");
     98:   CHOLMOD_OPTION_BOOL(final_pack,"Pack the columns when finished (use FALSE if the factors will be updated later)");
     99:   if (!c->final_asis) {
    100:     CHOLMOD_OPTION_BOOL(final_super,"Leave supernodal factors instead of converting to simplicial");
    101:     CHOLMOD_OPTION_BOOL(final_ll,"Turn LDL' factorization into LL'");
    102:     CHOLMOD_OPTION_BOOL(final_monotonic,"Ensure columns are monotonic when done");
    103:     CHOLMOD_OPTION_BOOL(final_resymbol,"Remove numerically zero values resulting from relaxed supernodal amalgamation");
    104:   }
    105:   {
    106:     PetscReal tmp[] = {(PetscReal)c->zrelax[0],(PetscReal)c->zrelax[1],(PetscReal)c->zrelax[2]};
    107:     PetscInt  n     = 3;
    108:     PetscOptionsRealArray("-mat_cholmod_zrelax","3 real supernodal relaxed amalgamation parameters","None",tmp,&n,&flg);
    110:     if (flg) while (n--) c->zrelax[n] = (double)tmp[n];
    111:   }
    112:   {
    113:     PetscInt n,tmp[] = {(PetscInt)c->nrelax[0],(PetscInt)c->nrelax[1],(PetscInt)c->nrelax[2]};
    114:     PetscOptionsIntArray("-mat_cholmod_nrelax","3 size_t supernodal relaxed amalgamation parameters","None",tmp,&n,&flg);
    116:     if (flg) while (n--) c->nrelax[n] = (size_t)tmp[n];
    117:   }
    118:   CHOLMOD_OPTION_BOOL(prefer_upper,"Work with upper triangular form [faster when using fill-reducing ordering, slower in natural ordering]");
    119:   CHOLMOD_OPTION_BOOL(default_nesdis,"Use NESDIS instead of METIS for nested dissection");
    120:   CHOLMOD_OPTION_INT(print,"Verbosity level");
    121:   PetscOptionsEnd();
    122:   return 0;
    123: }

    125: static PetscErrorCode MatWrapCholmod_seqsbaij(Mat A,PetscBool values,cholmod_sparse *C,PetscBool *aijalloc,PetscBool *valloc)
    126: {
    127:   Mat_SeqSBAIJ   *sbaij = (Mat_SeqSBAIJ*)A->data;
    128:   PetscBool      vallocin = PETSC_FALSE;

    130:   PetscMemzero(C,sizeof(*C));
    131:   /* CHOLMOD uses column alignment, SBAIJ stores the upper factor, so we pass it on as a lower factor, swapping the meaning of row and column */
    132:   C->nrow   = (size_t)A->cmap->n;
    133:   C->ncol   = (size_t)A->rmap->n;
    134:   C->nzmax  = (size_t)sbaij->maxnz;
    135:   C->p      = sbaij->i;
    136:   C->i      = sbaij->j;
    137:   if (values) {
    138: #if defined(PETSC_USE_COMPLEX)
    139:     /* we need to pass CHOLMOD the conjugate matrix */
    140:     PetscScalar *v;
    141:     PetscInt    i;

    143:     PetscMalloc1(sbaij->maxnz,&v);
    144:     for (i = 0; i < sbaij->maxnz; i++) v[i] = PetscConj(sbaij->a[i]);
    145:     C->x = v;
    146:     vallocin = PETSC_TRUE;
    147: #else
    148:     C->x = sbaij->a;
    149: #endif
    150:   }
    151:   C->stype  = -1;
    152:   C->itype  = CHOLMOD_INT_TYPE;
    153:   C->xtype  = values ? CHOLMOD_SCALAR_TYPE : CHOLMOD_PATTERN;
    154:   C->dtype  = CHOLMOD_DOUBLE;
    155:   C->sorted = 1;
    156:   C->packed = 1;
    157:   *aijalloc = PETSC_FALSE;
    158:   *valloc   = vallocin;
    159:   return 0;
    160: }

    162: #define GET_ARRAY_READ 0
    163: #define GET_ARRAY_WRITE 1

    165: PetscErrorCode VecWrapCholmod(Vec X,PetscInt rw,cholmod_dense *Y)
    166: {
    167:   PetscScalar    *x;
    168:   PetscInt       n;

    170:   PetscMemzero(Y,sizeof(*Y));
    171:   switch (rw) {
    172:   case GET_ARRAY_READ:
    173:     VecGetArrayRead(X,(const PetscScalar**)&x);
    174:     break;
    175:   case GET_ARRAY_WRITE:
    176:     VecGetArrayWrite(X,&x);
    177:     break;
    178:   default:
    179:     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Case %" PetscInt_FMT " not handled",rw);
    180:     break;
    181:   }
    182:   VecGetSize(X,&n);

    184:   Y->x     = x;
    185:   Y->nrow  = n;
    186:   Y->ncol  = 1;
    187:   Y->nzmax = n;
    188:   Y->d     = n;
    189:   Y->xtype = CHOLMOD_SCALAR_TYPE;
    190:   Y->dtype = CHOLMOD_DOUBLE;
    191:   return 0;
    192: }

    194: PetscErrorCode VecUnWrapCholmod(Vec X,PetscInt rw,cholmod_dense *Y)
    195: {
    196:   switch (rw) {
    197:   case GET_ARRAY_READ:
    198:     VecRestoreArrayRead(X,(const PetscScalar**)&Y->x);
    199:     break;
    200:   case GET_ARRAY_WRITE:
    201:     VecRestoreArrayWrite(X,(PetscScalar**)&Y->x);
    202:     break;
    203:   default:
    204:     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Case %" PetscInt_FMT " not handled",rw);
    205:     break;
    206:   }
    207:   return 0;
    208: }

    210: PetscErrorCode MatDenseWrapCholmod(Mat X,PetscInt rw,cholmod_dense *Y)
    211: {
    212:   PetscScalar    *x;
    213:   PetscInt       m,n,lda;

    215:   PetscMemzero(Y,sizeof(*Y));
    216:   switch (rw) {
    217:   case GET_ARRAY_READ:
    218:     MatDenseGetArrayRead(X,(const PetscScalar**)&x);
    219:     break;
    220:   case GET_ARRAY_WRITE:
    221:     MatDenseGetArrayWrite(X,&x);
    222:     break;
    223:   default:
    224:     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Case %" PetscInt_FMT " not handled",rw);
    225:     break;
    226:   }
    227:   MatDenseGetLDA(X,&lda);
    228:   MatGetLocalSize(X,&m,&n);

    230:   Y->x     = x;
    231:   Y->nrow  = m;
    232:   Y->ncol  = n;
    233:   Y->nzmax = lda*n;
    234:   Y->d     = lda;
    235:   Y->xtype = CHOLMOD_SCALAR_TYPE;
    236:   Y->dtype = CHOLMOD_DOUBLE;
    237:   return 0;
    238: }

    240: PetscErrorCode MatDenseUnWrapCholmod(Mat X,PetscInt rw,cholmod_dense *Y)
    241: {
    242:   switch (rw) {
    243:   case GET_ARRAY_READ:
    244:     MatDenseRestoreArrayRead(X,(const PetscScalar**)&Y->x);
    245:     break;
    246:   case GET_ARRAY_WRITE:
    247:     /* we don't have MatDenseRestoreArrayWrite */
    248:     MatDenseRestoreArray(X,(PetscScalar**)&Y->x);
    249:     break;
    250:   default:
    251:     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Case %" PetscInt_FMT " not handled",rw);
    252:     break;
    253:   }
    254:   return 0;
    255: }

    257: PETSC_INTERN PetscErrorCode  MatDestroy_CHOLMOD(Mat F)
    258: {
    259:   Mat_CHOLMOD    *chol=(Mat_CHOLMOD*)F->data;

    261:   if (chol->spqrfact) {
    262:     !SuiteSparseQR_C_free(&chol->spqrfact, chol->common);
    263:   }
    264:   if (chol->factor) {
    265:     !cholmod_X_free_factor(&chol->factor,chol->common);
    266:   }
    267:   if (chol->common->itype == CHOLMOD_INT) {
    268:     !cholmod_finish(chol->common);
    269:   } else {
    270:     !cholmod_l_finish(chol->common);
    271:   }
    272:   PetscFree(chol->common);
    273:   PetscFree(chol->matrix);
    274:   PetscObjectComposeFunction((PetscObject)F,"MatFactorGetSolverType_C",NULL);
    275:   PetscFree(F->data);
    276:   return 0;
    277: }

    279: static PetscErrorCode MatSolve_CHOLMOD(Mat,Vec,Vec);
    280: static PetscErrorCode MatMatSolve_CHOLMOD(Mat,Mat,Mat);

    282: /*static const char *const CholmodOrderingMethods[] = {"User","AMD","METIS","NESDIS(default)","Natural","NESDIS(small=20000)","NESDIS(small=4,no constrained)","NESDIS()"};*/

    284: static PetscErrorCode MatView_Info_CHOLMOD(Mat F,PetscViewer viewer)
    285: {
    286:   Mat_CHOLMOD          *chol = (Mat_CHOLMOD*)F->data;
    287:   const cholmod_common *c    = chol->common;
    288:   PetscErrorCode       ierr;
    289:   PetscInt             i;

    291:   if (F->ops->solve != MatSolve_CHOLMOD) return 0;
    292:   PetscViewerASCIIPrintf(viewer,"CHOLMOD run parameters:\n");
    293:   PetscViewerASCIIPushTab(viewer);
    294:   PetscViewerASCIIPrintf(viewer,"Pack factors after symbolic factorization: %s\n",chol->pack ? "TRUE" : "FALSE");
    295:   PetscViewerASCIIPrintf(viewer,"Common.dbound            %g  (Smallest absolute value of diagonal entries of D)\n",c->dbound);
    296:   PetscViewerASCIIPrintf(viewer,"Common.grow0             %g\n",c->grow0);
    297:   PetscViewerASCIIPrintf(viewer,"Common.grow1             %g\n",c->grow1);
    298:   PetscViewerASCIIPrintf(viewer,"Common.grow2             %u\n",(unsigned)c->grow2);
    299:   PetscViewerASCIIPrintf(viewer,"Common.maxrank           %u\n",(unsigned)c->maxrank);
    300:   PetscViewerASCIIPrintf(viewer,"Common.supernodal_switch %g\n",c->supernodal_switch);
    301:   PetscViewerASCIIPrintf(viewer,"Common.supernodal        %d\n",c->supernodal);
    302:   PetscViewerASCIIPrintf(viewer,"Common.final_asis        %d\n",c->final_asis);
    303:   PetscViewerASCIIPrintf(viewer,"Common.final_super       %d\n",c->final_super);
    304:   PetscViewerASCIIPrintf(viewer,"Common.final_ll          %d\n",c->final_ll);
    305:   PetscViewerASCIIPrintf(viewer,"Common.final_pack        %d\n",c->final_pack);
    306:   PetscViewerASCIIPrintf(viewer,"Common.final_monotonic   %d\n",c->final_monotonic);
    307:   PetscViewerASCIIPrintf(viewer,"Common.final_resymbol    %d\n",c->final_resymbol);
    308:   PetscViewerASCIIPrintf(viewer,"Common.zrelax            [%g,%g,%g]\n",c->zrelax[0],c->zrelax[1],c->zrelax[2]);
    309:   PetscViewerASCIIPrintf(viewer,"Common.nrelax            [%u,%u,%u]\n",(unsigned)c->nrelax[0],(unsigned)c->nrelax[1],(unsigned)c->nrelax[2]);
    310:   PetscViewerASCIIPrintf(viewer,"Common.prefer_upper      %d\n",c->prefer_upper);
    311:   PetscViewerASCIIPrintf(viewer,"Common.print             %d\n",c->print);
    312:   for (i=0; i<c->nmethods; i++) {
    313:     PetscViewerASCIIPrintf(viewer,"Ordering method %" PetscInt_FMT "%s:\n",i,i==c->selected ? " [SELECTED]" : "");
    314:     PetscViewerASCIIPrintf(viewer,"  lnz %g, fl %g, prune_dense %g, prune_dense2 %g\n",
    315:                                   c->method[i].lnz,c->method[i].fl,c->method[i].prune_dense,c->method[i].prune_dense2);
    316:   }
    317:   PetscViewerASCIIPrintf(viewer,"Common.postorder         %d\n",c->postorder);
    318:   PetscViewerASCIIPrintf(viewer,"Common.default_nesdis    %d (use NESDIS instead of METIS for nested dissection)\n",c->default_nesdis);
    319:   /* Statistics */
    320:   PetscViewerASCIIPrintf(viewer,"Common.fl                %g (flop count from most recent analysis)\n",c->fl);
    321:   PetscViewerASCIIPrintf(viewer,"Common.lnz               %g (fundamental nz in L)\n",c->lnz);
    322:   PetscViewerASCIIPrintf(viewer,"Common.anz               %g\n",c->anz);
    323:   PetscViewerASCIIPrintf(viewer,"Common.modfl             %g (flop count from most recent update)\n",c->modfl);
    324:   PetscViewerASCIIPrintf(viewer,"Common.malloc_count      %g (number of live objects)\n",(double)c->malloc_count);
    325:   PetscViewerASCIIPrintf(viewer,"Common.memory_usage      %g (peak memory usage in bytes)\n",(double)c->memory_usage);
    326:   PetscViewerASCIIPrintf(viewer,"Common.memory_inuse      %g (current memory usage in bytes)\n",(double)c->memory_inuse);
    327:   PetscViewerASCIIPrintf(viewer,"Common.nrealloc_col      %g (number of column reallocations)\n",c->nrealloc_col);
    328:   PetscViewerASCIIPrintf(viewer,"Common.nrealloc_factor   %g (number of factor reallocations due to column reallocations)\n",c->nrealloc_factor);
    329:   PetscViewerASCIIPrintf(viewer,"Common.ndbounds_hit      %g (number of times diagonal was modified by dbound)\n",c->ndbounds_hit);
    330:   PetscViewerASCIIPrintf(viewer,"Common.rowfacfl          %g (number of flops in last call to cholmod_rowfac)\n",c->rowfacfl);
    331:   PetscViewerASCIIPrintf(viewer,"Common.aatfl             %g (number of flops to compute A(:,f)*A(:,f)')\n",c->aatfl);
    332: #if defined(PETSC_USE_SUITESPARSE_GPU)
    333:   PetscViewerASCIIPrintf(viewer,"Common.useGPU            %d\n",c->useGPU);
    334: #endif
    335:   PetscViewerASCIIPopTab(viewer);
    336:   return 0;
    337: }

    339: PETSC_INTERN PetscErrorCode  MatView_CHOLMOD(Mat F,PetscViewer viewer)
    340: {
    341:   PetscBool         iascii;
    342:   PetscViewerFormat format;

    344:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    345:   if (iascii) {
    346:     PetscViewerGetFormat(viewer,&format);
    347:     if (format == PETSC_VIEWER_ASCII_INFO) {
    348:       MatView_Info_CHOLMOD(F,viewer);
    349:     }
    350:   }
    351:   return 0;
    352: }

    354: static PetscErrorCode MatSolve_CHOLMOD(Mat F,Vec B,Vec X)
    355: {
    356:   Mat_CHOLMOD    *chol = (Mat_CHOLMOD*)F->data;
    357:   cholmod_dense  cholB,cholX,*X_handle,*Y_handle = NULL,*E_handle = NULL;

    359:   static_F = F;
    360:   VecWrapCholmod(B,GET_ARRAY_READ,&cholB);
    361:   VecWrapCholmod(X,GET_ARRAY_WRITE,&cholX);
    362:   X_handle = &cholX;
    363:   !cholmod_X_solve2(CHOLMOD_A,chol->factor,&cholB,NULL,&X_handle,NULL,&Y_handle,&E_handle,chol->common);
    364:   !cholmod_X_free_dense(&Y_handle,chol->common);
    365:   !cholmod_X_free_dense(&E_handle,chol->common);
    366:   VecUnWrapCholmod(B,GET_ARRAY_READ,&cholB);
    367:   VecUnWrapCholmod(X,GET_ARRAY_WRITE,&cholX);
    368:   PetscLogFlops(4.0*chol->common->lnz);
    369:   return 0;
    370: }

    372: static PetscErrorCode MatMatSolve_CHOLMOD(Mat F,Mat B,Mat X)
    373: {
    374:   Mat_CHOLMOD    *chol = (Mat_CHOLMOD*)F->data;
    375:   cholmod_dense  cholB,cholX,*X_handle,*Y_handle = NULL,*E_handle = NULL;

    377:   static_F = F;
    378:   MatDenseWrapCholmod(B,GET_ARRAY_READ,&cholB);
    379:   MatDenseWrapCholmod(X,GET_ARRAY_WRITE,&cholX);
    380:   X_handle = &cholX;
    381:   !cholmod_X_solve2(CHOLMOD_A,chol->factor,&cholB,NULL,&X_handle,NULL,&Y_handle,&E_handle,chol->common);
    382:   !cholmod_X_free_dense(&Y_handle,chol->common);
    383:   !cholmod_X_free_dense(&E_handle,chol->common);
    384:   MatDenseUnWrapCholmod(B,GET_ARRAY_READ,&cholB);
    385:   MatDenseUnWrapCholmod(X,GET_ARRAY_WRITE,&cholX);
    386:   PetscLogFlops(4.0*B->cmap->n*chol->common->lnz);
    387:   return 0;
    388: }

    390: static PetscErrorCode MatCholeskyFactorNumeric_CHOLMOD(Mat F,Mat A,const MatFactorInfo *info)
    391: {
    392:   Mat_CHOLMOD    *chol = (Mat_CHOLMOD*)F->data;
    393:   cholmod_sparse cholA;
    394:   PetscBool      aijalloc,valloc;

    397:   (*chol->Wrap)(A,PETSC_TRUE,&cholA,&aijalloc,&valloc);
    398:   static_F = F;
    399:   !cholmod_X_factorize(&cholA,chol->factor,chol->common);

    403:   PetscLogFlops(chol->common->fl);
    404:   if (aijalloc) PetscFree2(cholA.p,cholA.i);
    405:   if (valloc) PetscFree(cholA.x);
    406: #if defined(PETSC_USE_SUITESPARSE_GPU)
    407:   PetscLogGpuTimeAdd(chol->common->CHOLMOD_GPU_GEMM_TIME + chol->common->CHOLMOD_GPU_SYRK_TIME + chol->common->CHOLMOD_GPU_TRSM_TIME + chol->common->CHOLMOD_GPU_POTRF_TIME);
    408: #endif

    410:   F->ops->solve             = MatSolve_CHOLMOD;
    411:   F->ops->solvetranspose    = MatSolve_CHOLMOD;
    412:   F->ops->matsolve          = MatMatSolve_CHOLMOD;
    413:   F->ops->matsolvetranspose = MatMatSolve_CHOLMOD;
    414:   return 0;
    415: }

    417: PETSC_INTERN PetscErrorCode  MatCholeskyFactorSymbolic_CHOLMOD(Mat F,Mat A,IS perm,const MatFactorInfo *info)
    418: {
    419:   Mat_CHOLMOD    *chol = (Mat_CHOLMOD*)F->data;
    421:   cholmod_sparse cholA;
    422:   PetscBool      aijalloc,valloc;
    423:   PetscInt       *fset = 0;
    424:   size_t         fsize = 0;

    426:   (*chol->Wrap)(A,PETSC_FALSE,&cholA,&aijalloc,&valloc);
    427:   static_F = F;
    428:   if (chol->factor) {
    429:     !cholmod_X_resymbol(&cholA,fset,fsize,(int)chol->pack,chol->factor,chol->common);
    431:   } else if (perm) {
    432:     const PetscInt *ip;
    433:     ISGetIndices(perm,&ip);
    434:     chol->factor = cholmod_X_analyze_p(&cholA,(PetscInt*)ip,fset,fsize,chol->common);
    436:     ISRestoreIndices(perm,&ip);
    437:   } else {
    438:     chol->factor = cholmod_X_analyze(&cholA,chol->common);
    440:   }

    442:   if (aijalloc) PetscFree2(cholA.p,cholA.i);
    443:   if (valloc) PetscFree(cholA.x);

    445:   F->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_CHOLMOD;
    446:   return 0;
    447: }

    449: static PetscErrorCode MatFactorGetSolverType_seqsbaij_cholmod(Mat A,MatSolverType *type)
    450: {
    451:   *type = MATSOLVERCHOLMOD;
    452:   return 0;
    453: }

    455: PETSC_INTERN PetscErrorCode MatGetInfo_CHOLMOD(Mat F,MatInfoType flag,MatInfo *info)
    456: {
    457:   Mat_CHOLMOD *chol = (Mat_CHOLMOD*)F->data;

    459:   info->block_size        = 1.0;
    460:   info->nz_allocated      = chol->common->lnz;
    461:   info->nz_used           = chol->common->lnz;
    462:   info->nz_unneeded       = 0.0;
    463:   info->assemblies        = 0.0;
    464:   info->mallocs           = 0.0;
    465:   info->memory            = chol->common->memory_inuse;
    466:   info->fill_ratio_given  = 0;
    467:   info->fill_ratio_needed = 0;
    468:   info->factor_mallocs    = chol->common->malloc_count;
    469:   return 0;
    470: }

    472: /*MC
    473:   MATSOLVERCHOLMOD

    475:   A matrix type providing direct solvers (Cholesky) for sequential matrices
    476:   via the external package CHOLMOD.

    478:   Use ./configure --download-suitesparse to install PETSc to use CHOLMOD

    480:   Use -pc_type cholesky -pc_factor_mat_solver_type cholmod to use this direct solver

    482:   Consult CHOLMOD documentation for more information about the Common parameters
    483:   which correspond to the options database keys below.

    485:   Options Database Keys:
    486: + -mat_cholmod_dbound <0>          - Minimum absolute value of diagonal entries of D (None)
    487: . -mat_cholmod_grow0 <1.2>         - Global growth ratio when factors are modified (None)
    488: . -mat_cholmod_grow1 <1.2>         - Column growth ratio when factors are modified (None)
    489: . -mat_cholmod_grow2 <5>           - Affine column growth constant when factors are modified (None)
    490: . -mat_cholmod_maxrank <8>         - Max rank of update, larger values are faster but use more memory [2,4,8] (None)
    491: . -mat_cholmod_factor <AUTO>       - (choose one of) SIMPLICIAL AUTO SUPERNODAL
    492: . -mat_cholmod_supernodal_switch <40> - flop/nnz_L threshold for switching to supernodal factorization (None)
    493: . -mat_cholmod_final_asis <TRUE>   - Leave factors "as is" (None)
    494: . -mat_cholmod_final_pack <TRUE>   - Pack the columns when finished (use FALSE if the factors will be updated later) (None)
    495: . -mat_cholmod_zrelax <0.8>        - 3 real supernodal relaxed amalgamation parameters (None)
    496: . -mat_cholmod_nrelax <4>          - 3 size_t supernodal relaxed amalgamation parameters (None)
    497: . -mat_cholmod_prefer_upper <TRUE> - Work with upper triangular form (faster when using fill-reducing ordering, slower in natural ordering) (None)
    498: . -mat_cholmod_print <3>           - Verbosity level (None)
    499: - -mat_ordering_type internal      - Use the ordering provided by Cholmod

    501:    Level: beginner

    503:    Note: CHOLMOD is part of SuiteSparse http://faculty.cse.tamu.edu/davis/suitesparse.html

    505: .seealso: PCCHOLESKY, PCFactorSetMatSolverType(), MatSolverType
    506: M*/

    508: PETSC_INTERN PetscErrorCode MatGetFactor_seqsbaij_cholmod(Mat A,MatFactorType ftype,Mat *F)
    509: {
    510:   Mat            B;
    511:   Mat_CHOLMOD    *chol;
    512:   PetscInt       m=A->rmap->n,n=A->cmap->n,bs;
    513:   const char     *prefix;

    515:   MatGetBlockSize(A,&bs);
    517: #if defined(PETSC_USE_COMPLEX)
    519: #endif
    520:   /* Create the factorization matrix F */
    521:   MatCreate(PetscObjectComm((PetscObject)A),&B);
    522:   MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,m,n);
    523:   PetscStrallocpy("cholmod",&((PetscObject)B)->type_name);
    524:   MatGetOptionsPrefix(A,&prefix);
    525:   MatSetOptionsPrefix(B,prefix);
    526:   MatSetUp(B);
    527:   PetscNewLog(B,&chol);

    529:   chol->Wrap    = MatWrapCholmod_seqsbaij;
    530:   B->data       = chol;

    532:   B->ops->getinfo                = MatGetInfo_CHOLMOD;
    533:   B->ops->view                   = MatView_CHOLMOD;
    534:   B->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_CHOLMOD;
    535:   B->ops->destroy                = MatDestroy_CHOLMOD;
    536:   PetscObjectComposeFunction((PetscObject)B,"MatFactorGetSolverType_C",MatFactorGetSolverType_seqsbaij_cholmod);
    537:   B->factortype                  = MAT_FACTOR_CHOLESKY;
    538:   B->assembled                   = PETSC_TRUE;
    539:   B->preallocated                = PETSC_TRUE;

    541:   CholmodStart(B);

    543:   PetscFree(B->solvertype);
    544:   PetscStrallocpy(MATSOLVERCHOLMOD,&B->solvertype);
    545:   B->canuseordering = PETSC_TRUE;
    546:   PetscStrallocpy(MATORDERINGEXTERNAL,(char**)&B->preferredordering[MAT_FACTOR_CHOLESKY]);
    547:   *F   = B;
    548:   return 0;
    549: }