Actual source code: matmatmult.c
petsc-3.10.5 2019-03-28
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      2: /*
      3:   Defines matrix-matrix product routines for pairs of SeqAIJ matrices
      4:           C = A * B
      5: */

      7:  #include <../src/mat/impls/aij/seq/aij.h>
      8:  #include <../src/mat/utils/freespace.h>
      9:  #include <petscbt.h>
     10:  #include <petsc/private/isimpl.h>
     11:  #include <../src/mat/impls/dense/seq/dense.h>

     13: static PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat,Mat,PetscReal,Mat*);

     15: #if defined(PETSC_HAVE_HYPRE)
     16: PETSC_INTERN PetscErrorCode MatMatMultSymbolic_AIJ_AIJ_wHYPRE(Mat,Mat,PetscReal,Mat*);
     17: #endif

     19: PETSC_INTERN PetscErrorCode MatMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
     20: {
     22: #if !defined(PETSC_HAVE_HYPRE)
     23:   const char     *algTypes[7] = {"sorted","scalable","scalable_fast","heap","btheap","llcondensed","combined"};
     24:   PetscInt       nalg = 7;
     25: #else
     26:   const char     *algTypes[8] = {"sorted","scalable","scalable_fast","heap","btheap","llcondensed","combined","hypre"};
     27:   PetscInt       nalg = 8;
     28: #endif
     29:   PetscInt       alg = 0; /* set default algorithm */
     30:   PetscBool      combined = PETSC_FALSE;  /* Indicates whether the symbolic stage already computed the numerical values. */

     33:   if (scall == MAT_INITIAL_MATRIX) {
     34:     PetscObjectOptionsBegin((PetscObject)A);
     35:     PetscOptionsObject->alreadyprinted = PETSC_FALSE; /* a hack to ensure the option shows in '-help' */
     36:     PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[0],&alg,NULL);
     37:     PetscOptionsEnd();
     38:     PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);
     39:     switch (alg) {
     40:     case 1:
     41:       MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(A,B,fill,C);
     42:       break;
     43:     case 2:
     44:       MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(A,B,fill,C);
     45:       break;
     46:     case 3:
     47:       MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(A,B,fill,C);
     48:       break;
     49:     case 4:
     50:       MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(A,B,fill,C);
     51:       break;
     52:     case 5:
     53:       MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(A,B,fill,C);
     54:       break;
     55:     case 6:
     56:       MatMatMult_SeqAIJ_SeqAIJ_Combined(A,B,fill,C);
     57:       combined = PETSC_TRUE;
     58:       break;
     59: #if defined(PETSC_HAVE_HYPRE)
     60:     case 7:
     61:       MatMatMultSymbolic_AIJ_AIJ_wHYPRE(A,B,fill,C);
     62:       break;
     63: #endif
     64:     default:
     65:       MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);
     66:      break;
     67:     }
     68:     PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);
     69:   }

     71:   PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);
     72:   if (!combined) {
     73:     (*(*C)->ops->matmultnumeric)(A,B,*C);
     74:   }
     75:   PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);
     76:   return(0);
     77: }

     79: static PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat A,Mat B,PetscReal fill,Mat *C)
     80: {
     81:   PetscErrorCode     ierr;
     82:   Mat_SeqAIJ         *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
     83:   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
     84:   PetscInt           am =A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
     85:   PetscReal          afill;
     86:   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax;
     87:   PetscTable         ta;
     88:   PetscBT            lnkbt;
     89:   PetscFreeSpaceList free_space=NULL,current_space=NULL;

     92:   /* Get ci and cj */
     93:   /*---------------*/
     94:   /* Allocate ci array, arrays for fill computation and */
     95:   /* free space for accumulating nonzero column info */
     96:   PetscMalloc1(am+2,&ci);
     97:   ci[0] = 0;

     99:   /* create and initialize a linked list */
    100:   PetscTableCreate(bn,bn,&ta);
    101:   MatRowMergeMax_SeqAIJ(b,bm,ta);
    102:   PetscTableGetCount(ta,&Crmax);
    103:   PetscTableDestroy(&ta);

    105:   PetscLLCondensedCreate(Crmax,bn,&lnk,&lnkbt);

    107:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
    108:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);

    110:   current_space = free_space;

    112:   /* Determine ci and cj */
    113:   for (i=0; i<am; i++) {
    114:     anzi = ai[i+1] - ai[i];
    115:     aj   = a->j + ai[i];
    116:     for (j=0; j<anzi; j++) {
    117:       brow = aj[j];
    118:       bnzj = bi[brow+1] - bi[brow];
    119:       bj   = b->j + bi[brow];
    120:       /* add non-zero cols of B into the sorted linked list lnk */
    121:       PetscLLCondensedAddSorted(bnzj,bj,lnk,lnkbt);
    122:     }
    123:     cnzi = lnk[0];

    125:     /* If free space is not available, make more free space */
    126:     /* Double the amount of total space in the list */
    127:     if (current_space->local_remaining<cnzi) {
    128:       PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);
    129:       ndouble++;
    130:     }

    132:     /* Copy data into free space, then initialize lnk */
    133:     PetscLLCondensedClean(bn,cnzi,current_space->array,lnk,lnkbt);

    135:     current_space->array           += cnzi;
    136:     current_space->local_used      += cnzi;
    137:     current_space->local_remaining -= cnzi;

    139:     ci[i+1] = ci[i] + cnzi;
    140:   }

    142:   /* Column indices are in the list of free space */
    143:   /* Allocate space for cj, initialize cj, and */
    144:   /* destroy list of free space and other temporary array(s) */
    145:   PetscMalloc1(ci[am]+1,&cj);
    146:   PetscFreeSpaceContiguous(&free_space,cj);
    147:   PetscLLCondensedDestroy(lnk,lnkbt);

    149:   /* put together the new symbolic matrix */
    150:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);
    151:   MatSetBlockSizesFromMats(*C,A,B);

    153:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    154:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
    155:   c                         = (Mat_SeqAIJ*)((*C)->data);
    156:   c->free_a                 = PETSC_FALSE;
    157:   c->free_ij                = PETSC_TRUE;
    158:   c->nonew                  = 0;
    159:   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ; /* fast, needs non-scalable O(bn) array 'abdense' */

    161:   /* set MatInfo */
    162:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
    163:   if (afill < 1.0) afill = 1.0;
    164:   c->maxnz                     = ci[am];
    165:   c->nz                        = ci[am];
    166:   (*C)->info.mallocs           = ndouble;
    167:   (*C)->info.fill_ratio_given  = fill;
    168:   (*C)->info.fill_ratio_needed = afill;

    170: #if defined(PETSC_USE_INFO)
    171:   if (ci[am]) {
    172:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);
    173:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
    174:   } else {
    175:     PetscInfo((*C),"Empty matrix product\n");
    176:   }
    177: #endif
    178:   return(0);
    179: }

    181: PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
    182: {
    184:   PetscLogDouble flops=0.0;
    185:   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
    186:   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
    187:   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
    188:   PetscInt       *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
    189:   PetscInt       am   =A->rmap->n,cm=C->rmap->n;
    190:   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
    191:   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca,valtmp;
    192:   PetscScalar    *ab_dense;

    195:   if (!c->a) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
    196:     PetscMalloc1(ci[cm]+1,&ca);
    197:     c->a      = ca;
    198:     c->free_a = PETSC_TRUE;
    199:   } else {
    200:     ca        = c->a;
    201:   }
    202:   if (!c->matmult_abdense) {
    203:     PetscCalloc1(B->cmap->N,&ab_dense);
    204:     c->matmult_abdense = ab_dense;
    205:   } else {
    206:     ab_dense = c->matmult_abdense;
    207:   }

    209:   /* clean old values in C */
    210:   PetscMemzero(ca,ci[cm]*sizeof(MatScalar));
    211:   /* Traverse A row-wise. */
    212:   /* Build the ith row in C by summing over nonzero columns in A, */
    213:   /* the rows of B corresponding to nonzeros of A. */
    214:   for (i=0; i<am; i++) {
    215:     anzi = ai[i+1] - ai[i];
    216:     for (j=0; j<anzi; j++) {
    217:       brow = aj[j];
    218:       bnzi = bi[brow+1] - bi[brow];
    219:       bjj  = bj + bi[brow];
    220:       baj  = ba + bi[brow];
    221:       /* perform dense axpy */
    222:       valtmp = aa[j];
    223:       for (k=0; k<bnzi; k++) {
    224:         ab_dense[bjj[k]] += valtmp*baj[k];
    225:       }
    226:       flops += 2*bnzi;
    227:     }
    228:     aj += anzi; aa += anzi;

    230:     cnzi = ci[i+1] - ci[i];
    231:     for (k=0; k<cnzi; k++) {
    232:       ca[k]          += ab_dense[cj[k]];
    233:       ab_dense[cj[k]] = 0.0; /* zero ab_dense */
    234:     }
    235:     flops += cnzi;
    236:     cj    += cnzi; ca += cnzi;
    237:   }
    238:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    239:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    240:   PetscLogFlops(flops);
    241:   return(0);
    242: }

    244: PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,Mat C)
    245: {
    247:   PetscLogDouble flops=0.0;
    248:   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
    249:   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
    250:   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
    251:   PetscInt       *ai  = a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
    252:   PetscInt       am   = A->rmap->N,cm=C->rmap->N;
    253:   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
    254:   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca=c->a,valtmp;
    255:   PetscInt       nextb;

    258:   if (!ca) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
    259:     PetscMalloc1(ci[cm]+1,&ca);
    260:     c->a      = ca;
    261:     c->free_a = PETSC_TRUE;
    262:   }

    264:   /* clean old values in C */
    265:   PetscMemzero(ca,ci[cm]*sizeof(MatScalar));
    266:   /* Traverse A row-wise. */
    267:   /* Build the ith row in C by summing over nonzero columns in A, */
    268:   /* the rows of B corresponding to nonzeros of A. */
    269:   for (i=0; i<am; i++) {
    270:     anzi = ai[i+1] - ai[i];
    271:     cnzi = ci[i+1] - ci[i];
    272:     for (j=0; j<anzi; j++) {
    273:       brow = aj[j];
    274:       bnzi = bi[brow+1] - bi[brow];
    275:       bjj  = bj + bi[brow];
    276:       baj  = ba + bi[brow];
    277:       /* perform sparse axpy */
    278:       valtmp = aa[j];
    279:       nextb  = 0;
    280:       for (k=0; nextb<bnzi; k++) {
    281:         if (cj[k] == bjj[nextb]) { /* ccol == bcol */
    282:           ca[k] += valtmp*baj[nextb++];
    283:         }
    284:       }
    285:       flops += 2*bnzi;
    286:     }
    287:     aj += anzi; aa += anzi;
    288:     cj += cnzi; ca += cnzi;
    289:   }

    291:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    292:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    293:   PetscLogFlops(flops);
    294:   return(0);
    295: }

    297: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat A,Mat B,PetscReal fill,Mat *C)
    298: {
    299:   PetscErrorCode     ierr;
    300:   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
    301:   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
    302:   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
    303:   MatScalar          *ca;
    304:   PetscReal          afill;
    305:   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax;
    306:   PetscTable         ta;
    307:   PetscFreeSpaceList free_space=NULL,current_space=NULL;

    310:   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_fast() */
    311:   /*-----------------------------------------------------------------------------------------*/
    312:   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
    313:   PetscMalloc1(am+2,&ci);
    314:   ci[0] = 0;

    316:   /* create and initialize a linked list */
    317:   PetscTableCreate(bn,bn,&ta);
    318:   MatRowMergeMax_SeqAIJ(b,bm,ta);
    319:   PetscTableGetCount(ta,&Crmax);
    320:   PetscTableDestroy(&ta);

    322:   PetscLLCondensedCreate_fast(Crmax,&lnk);

    324:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
    325:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);
    326:   current_space = free_space;

    328:   /* Determine ci and cj */
    329:   for (i=0; i<am; i++) {
    330:     anzi = ai[i+1] - ai[i];
    331:     aj   = a->j + ai[i];
    332:     for (j=0; j<anzi; j++) {
    333:       brow = aj[j];
    334:       bnzj = bi[brow+1] - bi[brow];
    335:       bj   = b->j + bi[brow];
    336:       /* add non-zero cols of B into the sorted linked list lnk */
    337:       PetscLLCondensedAddSorted_fast(bnzj,bj,lnk);
    338:     }
    339:     cnzi = lnk[1];

    341:     /* If free space is not available, make more free space */
    342:     /* Double the amount of total space in the list */
    343:     if (current_space->local_remaining<cnzi) {
    344:       PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);
    345:       ndouble++;
    346:     }

    348:     /* Copy data into free space, then initialize lnk */
    349:     PetscLLCondensedClean_fast(cnzi,current_space->array,lnk);

    351:     current_space->array           += cnzi;
    352:     current_space->local_used      += cnzi;
    353:     current_space->local_remaining -= cnzi;

    355:     ci[i+1] = ci[i] + cnzi;
    356:   }

    358:   /* Column indices are in the list of free space */
    359:   /* Allocate space for cj, initialize cj, and */
    360:   /* destroy list of free space and other temporary array(s) */
    361:   PetscMalloc1(ci[am]+1,&cj);
    362:   PetscFreeSpaceContiguous(&free_space,cj);
    363:   PetscLLCondensedDestroy_fast(lnk);

    365:   /* Allocate space for ca */
    366:   PetscMalloc1(ci[am]+1,&ca);
    367:   PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));

    369:   /* put together the new symbolic matrix */
    370:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);
    371:   MatSetBlockSizesFromMats(*C,A,B);

    373:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    374:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
    375:   c          = (Mat_SeqAIJ*)((*C)->data);
    376:   c->free_a  = PETSC_TRUE;
    377:   c->free_ij = PETSC_TRUE;
    378:   c->nonew   = 0;

    380:   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */

    382:   /* set MatInfo */
    383:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
    384:   if (afill < 1.0) afill = 1.0;
    385:   c->maxnz                     = ci[am];
    386:   c->nz                        = ci[am];
    387:   (*C)->info.mallocs           = ndouble;
    388:   (*C)->info.fill_ratio_given  = fill;
    389:   (*C)->info.fill_ratio_needed = afill;

    391: #if defined(PETSC_USE_INFO)
    392:   if (ci[am]) {
    393:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);
    394:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
    395:   } else {
    396:     PetscInfo((*C),"Empty matrix product\n");
    397:   }
    398: #endif
    399:   return(0);
    400: }

    403: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,PetscReal fill,Mat *C)
    404: {
    405:   PetscErrorCode     ierr;
    406:   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
    407:   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
    408:   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
    409:   MatScalar          *ca;
    410:   PetscReal          afill;
    411:   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax;
    412:   PetscTable         ta;
    413:   PetscFreeSpaceList free_space=NULL,current_space=NULL;

    416:   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
    417:   /*---------------------------------------------------------------------------------------------*/
    418:   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
    419:   PetscMalloc1(am+2,&ci);
    420:   ci[0] = 0;

    422:   /* create and initialize a linked list */
    423:   PetscTableCreate(bn,bn,&ta);
    424:   MatRowMergeMax_SeqAIJ(b,bm,ta);
    425:   PetscTableGetCount(ta,&Crmax);
    426:   PetscTableDestroy(&ta);
    427:   PetscLLCondensedCreate_Scalable(Crmax,&lnk);

    429:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
    430:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);
    431:   current_space = free_space;

    433:   /* Determine ci and cj */
    434:   for (i=0; i<am; i++) {
    435:     anzi = ai[i+1] - ai[i];
    436:     aj   = a->j + ai[i];
    437:     for (j=0; j<anzi; j++) {
    438:       brow = aj[j];
    439:       bnzj = bi[brow+1] - bi[brow];
    440:       bj   = b->j + bi[brow];
    441:       /* add non-zero cols of B into the sorted linked list lnk */
    442:       PetscLLCondensedAddSorted_Scalable(bnzj,bj,lnk);
    443:     }
    444:     cnzi = lnk[0];

    446:     /* If free space is not available, make more free space */
    447:     /* Double the amount of total space in the list */
    448:     if (current_space->local_remaining<cnzi) {
    449:       PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);
    450:       ndouble++;
    451:     }

    453:     /* Copy data into free space, then initialize lnk */
    454:     PetscLLCondensedClean_Scalable(cnzi,current_space->array,lnk);

    456:     current_space->array           += cnzi;
    457:     current_space->local_used      += cnzi;
    458:     current_space->local_remaining -= cnzi;

    460:     ci[i+1] = ci[i] + cnzi;
    461:   }

    463:   /* Column indices are in the list of free space */
    464:   /* Allocate space for cj, initialize cj, and */
    465:   /* destroy list of free space and other temporary array(s) */
    466:   PetscMalloc1(ci[am]+1,&cj);
    467:   PetscFreeSpaceContiguous(&free_space,cj);
    468:   PetscLLCondensedDestroy_Scalable(lnk);

    470:   /* Allocate space for ca */
    471:   /*-----------------------*/
    472:   PetscMalloc1(ci[am]+1,&ca);
    473:   PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));

    475:   /* put together the new symbolic matrix */
    476:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);
    477:   MatSetBlockSizesFromMats(*C,A,B);

    479:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    480:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
    481:   c          = (Mat_SeqAIJ*)((*C)->data);
    482:   c->free_a  = PETSC_TRUE;
    483:   c->free_ij = PETSC_TRUE;
    484:   c->nonew   = 0;

    486:   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */

    488:   /* set MatInfo */
    489:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
    490:   if (afill < 1.0) afill = 1.0;
    491:   c->maxnz                     = ci[am];
    492:   c->nz                        = ci[am];
    493:   (*C)->info.mallocs           = ndouble;
    494:   (*C)->info.fill_ratio_given  = fill;
    495:   (*C)->info.fill_ratio_needed = afill;

    497: #if defined(PETSC_USE_INFO)
    498:   if (ci[am]) {
    499:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);
    500:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
    501:   } else {
    502:     PetscInfo((*C),"Empty matrix product\n");
    503:   }
    504: #endif
    505:   return(0);
    506: }

    508: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat A,Mat B,PetscReal fill,Mat *C)
    509: {
    510:   PetscErrorCode     ierr;
    511:   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
    512:   const PetscInt     *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j;
    513:   PetscInt           *ci,*cj,*bb;
    514:   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
    515:   PetscReal          afill;
    516:   PetscInt           i,j,col,ndouble = 0;
    517:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
    518:   PetscHeap          h;

    521:   /* Get ci and cj - by merging sorted rows using a heap */
    522:   /*---------------------------------------------------------------------------------------------*/
    523:   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
    524:   PetscMalloc1(am+2,&ci);
    525:   ci[0] = 0;

    527:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
    528:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);
    529:   current_space = free_space;

    531:   PetscHeapCreate(a->rmax,&h);
    532:   PetscMalloc1(a->rmax,&bb);

    534:   /* Determine ci and cj */
    535:   for (i=0; i<am; i++) {
    536:     const PetscInt anzi  = ai[i+1] - ai[i]; /* number of nonzeros in this row of A, this is the number of rows of B that we merge */
    537:     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
    538:     ci[i+1] = ci[i];
    539:     /* Populate the min heap */
    540:     for (j=0; j<anzi; j++) {
    541:       bb[j] = bi[acol[j]];         /* bb points at the start of the row */
    542:       if (bb[j] < bi[acol[j]+1]) { /* Add if row is nonempty */
    543:         PetscHeapAdd(h,j,bj[bb[j]++]);
    544:       }
    545:     }
    546:     /* Pick off the min element, adding it to free space */
    547:     PetscHeapPop(h,&j,&col);
    548:     while (j >= 0) {
    549:       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
    550:         PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2,current_space->total_array_size),16 << 20),&current_space);
    551:         ndouble++;
    552:       }
    553:       *(current_space->array++) = col;
    554:       current_space->local_used++;
    555:       current_space->local_remaining--;
    556:       ci[i+1]++;

    558:       /* stash if anything else remains in this row of B */
    559:       if (bb[j] < bi[acol[j]+1]) {PetscHeapStash(h,j,bj[bb[j]++]);}
    560:       while (1) {               /* pop and stash any other rows of B that also had an entry in this column */
    561:         PetscInt j2,col2;
    562:         PetscHeapPeek(h,&j2,&col2);
    563:         if (col2 != col) break;
    564:         PetscHeapPop(h,&j2,&col2);
    565:         if (bb[j2] < bi[acol[j2]+1]) {PetscHeapStash(h,j2,bj[bb[j2]++]);}
    566:       }
    567:       /* Put any stashed elements back into the min heap */
    568:       PetscHeapUnstash(h);
    569:       PetscHeapPop(h,&j,&col);
    570:     }
    571:   }
    572:   PetscFree(bb);
    573:   PetscHeapDestroy(&h);

    575:   /* Column indices are in the list of free space */
    576:   /* Allocate space for cj, initialize cj, and */
    577:   /* destroy list of free space and other temporary array(s) */
    578:   PetscMalloc1(ci[am],&cj);
    579:   PetscFreeSpaceContiguous(&free_space,cj);

    581:   /* put together the new symbolic matrix */
    582:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);
    583:   MatSetBlockSizesFromMats(*C,A,B);

    585:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    586:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
    587:   c          = (Mat_SeqAIJ*)((*C)->data);
    588:   c->free_a  = PETSC_TRUE;
    589:   c->free_ij = PETSC_TRUE;
    590:   c->nonew   = 0;

    592:   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;

    594:   /* set MatInfo */
    595:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
    596:   if (afill < 1.0) afill = 1.0;
    597:   c->maxnz                     = ci[am];
    598:   c->nz                        = ci[am];
    599:   (*C)->info.mallocs           = ndouble;
    600:   (*C)->info.fill_ratio_given  = fill;
    601:   (*C)->info.fill_ratio_needed = afill;

    603: #if defined(PETSC_USE_INFO)
    604:   if (ci[am]) {
    605:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);
    606:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
    607:   } else {
    608:     PetscInfo((*C),"Empty matrix product\n");
    609:   }
    610: #endif
    611:   return(0);
    612: }

    614: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(Mat A,Mat B,PetscReal fill,Mat *C)
    615: {
    616:   PetscErrorCode     ierr;
    617:   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
    618:   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
    619:   PetscInt           *ci,*cj,*bb;
    620:   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
    621:   PetscReal          afill;
    622:   PetscInt           i,j,col,ndouble = 0;
    623:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
    624:   PetscHeap          h;
    625:   PetscBT            bt;

    628:   /* Get ci and cj - using a heap for the sorted rows, but use BT so that each index is only added once */
    629:   /*---------------------------------------------------------------------------------------------*/
    630:   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
    631:   PetscMalloc1(am+2,&ci);
    632:   ci[0] = 0;

    634:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
    635:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);

    637:   current_space = free_space;

    639:   PetscHeapCreate(a->rmax,&h);
    640:   PetscMalloc1(a->rmax,&bb);
    641:   PetscBTCreate(bn,&bt);

    643:   /* Determine ci and cj */
    644:   for (i=0; i<am; i++) {
    645:     const PetscInt anzi  = ai[i+1] - ai[i]; /* number of nonzeros in this row of A, this is the number of rows of B that we merge */
    646:     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
    647:     const PetscInt *fptr = current_space->array; /* Save beginning of the row so we can clear the BT later */
    648:     ci[i+1] = ci[i];
    649:     /* Populate the min heap */
    650:     for (j=0; j<anzi; j++) {
    651:       PetscInt brow = acol[j];
    652:       for (bb[j] = bi[brow]; bb[j] < bi[brow+1]; bb[j]++) {
    653:         PetscInt bcol = bj[bb[j]];
    654:         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
    655:           PetscHeapAdd(h,j,bcol);
    656:           bb[j]++;
    657:           break;
    658:         }
    659:       }
    660:     }
    661:     /* Pick off the min element, adding it to free space */
    662:     PetscHeapPop(h,&j,&col);
    663:     while (j >= 0) {
    664:       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
    665:         fptr = NULL;                      /* need PetscBTMemzero */
    666:         PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2,current_space->total_array_size),16 << 20),&current_space);
    667:         ndouble++;
    668:       }
    669:       *(current_space->array++) = col;
    670:       current_space->local_used++;
    671:       current_space->local_remaining--;
    672:       ci[i+1]++;

    674:       /* stash if anything else remains in this row of B */
    675:       for (; bb[j] < bi[acol[j]+1]; bb[j]++) {
    676:         PetscInt bcol = bj[bb[j]];
    677:         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
    678:           PetscHeapAdd(h,j,bcol);
    679:           bb[j]++;
    680:           break;
    681:         }
    682:       }
    683:       PetscHeapPop(h,&j,&col);
    684:     }
    685:     if (fptr) {                 /* Clear the bits for this row */
    686:       for (; fptr<current_space->array; fptr++) {PetscBTClear(bt,*fptr);}
    687:     } else {                    /* We reallocated so we don't remember (easily) how to clear only the bits we changed */
    688:       PetscBTMemzero(bn,bt);
    689:     }
    690:   }
    691:   PetscFree(bb);
    692:   PetscHeapDestroy(&h);
    693:   PetscBTDestroy(&bt);

    695:   /* Column indices are in the list of free space */
    696:   /* Allocate space for cj, initialize cj, and */
    697:   /* destroy list of free space and other temporary array(s) */
    698:   PetscMalloc1(ci[am],&cj);
    699:   PetscFreeSpaceContiguous(&free_space,cj);

    701:   /* put together the new symbolic matrix */
    702:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);
    703:   MatSetBlockSizesFromMats(*C,A,B);

    705:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    706:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
    707:   c          = (Mat_SeqAIJ*)((*C)->data);
    708:   c->free_a  = PETSC_TRUE;
    709:   c->free_ij = PETSC_TRUE;
    710:   c->nonew   = 0;

    712:   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;

    714:   /* set MatInfo */
    715:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
    716:   if (afill < 1.0) afill = 1.0;
    717:   c->maxnz                     = ci[am];
    718:   c->nz                        = ci[am];
    719:   (*C)->info.mallocs           = ndouble;
    720:   (*C)->info.fill_ratio_given  = fill;
    721:   (*C)->info.fill_ratio_needed = afill;

    723: #if defined(PETSC_USE_INFO)
    724:   if (ci[am]) {
    725:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);
    726:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
    727:   } else {
    728:     PetscInfo((*C),"Empty matrix product\n");
    729:   }
    730: #endif
    731:   return(0);
    732: }

    734: /* concatenate unique entries and then sort */
    735: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
    736: {
    737:   PetscErrorCode     ierr;
    738:   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
    739:   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
    740:   PetscInt           *ci,*cj;
    741:   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
    742:   PetscReal          afill;
    743:   PetscInt           i,j,ndouble = 0;
    744:   PetscSegBuffer     seg,segrow;
    745:   char               *seen;

    748:   PetscMalloc1(am+1,&ci);
    749:   ci[0] = 0;

    751:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
    752:   PetscSegBufferCreate(sizeof(PetscInt),(PetscInt)(fill*(ai[am]+bi[bm])),&seg);
    753:   PetscSegBufferCreate(sizeof(PetscInt),100,&segrow);
    754:   PetscMalloc1(bn,&seen);
    755:   PetscMemzero(seen,bn*sizeof(char));

    757:   /* Determine ci and cj */
    758:   for (i=0; i<am; i++) {
    759:     const PetscInt anzi  = ai[i+1] - ai[i]; /* number of nonzeros in this row of A, this is the number of rows of B that we merge */
    760:     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
    761:     PetscInt packlen = 0,*PETSC_RESTRICT crow;
    762:     /* Pack segrow */
    763:     for (j=0; j<anzi; j++) {
    764:       PetscInt brow = acol[j],bjstart = bi[brow],bjend = bi[brow+1],k;
    765:       for (k=bjstart; k<bjend; k++) {
    766:         PetscInt bcol = bj[k];
    767:         if (!seen[bcol]) { /* new entry */
    768:           PetscInt *PETSC_RESTRICT slot;
    769:           PetscSegBufferGetInts(segrow,1,&slot);
    770:           *slot = bcol;
    771:           seen[bcol] = 1;
    772:           packlen++;
    773:         }
    774:       }
    775:     }
    776:     PetscSegBufferGetInts(seg,packlen,&crow);
    777:     PetscSegBufferExtractTo(segrow,crow);
    778:     PetscSortInt(packlen,crow);
    779:     ci[i+1] = ci[i] + packlen;
    780:     for (j=0; j<packlen; j++) seen[crow[j]] = 0;
    781:   }
    782:   PetscSegBufferDestroy(&segrow);
    783:   PetscFree(seen);

    785:   /* Column indices are in the segmented buffer */
    786:   PetscSegBufferExtractAlloc(seg,&cj);
    787:   PetscSegBufferDestroy(&seg);

    789:   /* put together the new symbolic matrix */
    790:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);
    791:   MatSetBlockSizesFromMats(*C,A,B);

    793:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    794:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
    795:   c          = (Mat_SeqAIJ*)((*C)->data);
    796:   c->free_a  = PETSC_TRUE;
    797:   c->free_ij = PETSC_TRUE;
    798:   c->nonew   = 0;

    800:   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;

    802:   /* set MatInfo */
    803:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
    804:   if (afill < 1.0) afill = 1.0;
    805:   c->maxnz                     = ci[am];
    806:   c->nz                        = ci[am];
    807:   (*C)->info.mallocs           = ndouble;
    808:   (*C)->info.fill_ratio_given  = fill;
    809:   (*C)->info.fill_ratio_needed = afill;

    811: #if defined(PETSC_USE_INFO)
    812:   if (ci[am]) {
    813:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);
    814:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
    815:   } else {
    816:     PetscInfo((*C),"Empty matrix product\n");
    817:   }
    818: #endif
    819:   return(0);
    820: }

    822: /* This routine is not used. Should be removed! */
    823: PetscErrorCode MatMatTransposeMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
    824: {

    828:   if (scall == MAT_INITIAL_MATRIX) {
    829:     PetscLogEventBegin(MAT_MatTransposeMultSymbolic,A,B,0,0);
    830:     MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);
    831:     PetscLogEventEnd(MAT_MatTransposeMultSymbolic,A,B,0,0);
    832:   }
    833:   PetscLogEventBegin(MAT_MatTransposeMultNumeric,A,B,0,0);
    834:   MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);
    835:   PetscLogEventEnd(MAT_MatTransposeMultNumeric,A,B,0,0);
    836:   return(0);
    837: }

    839: PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(Mat A)
    840: {
    841:   PetscErrorCode      ierr;
    842:   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)A->data;
    843:   Mat_MatMatTransMult *abt=a->abt;

    846:   (abt->destroy)(A);
    847:   MatTransposeColoringDestroy(&abt->matcoloring);
    848:   MatDestroy(&abt->Bt_den);
    849:   MatDestroy(&abt->ABt_den);
    850:   PetscFree(abt);
    851:   return(0);
    852: }

    854: PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
    855: {
    856:   PetscErrorCode      ierr;
    857:   Mat                 Bt;
    858:   PetscInt            *bti,*btj;
    859:   Mat_MatMatTransMult *abt;
    860:   Mat_SeqAIJ          *c;

    863:   /* create symbolic Bt */
    864:   MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);
    865:   MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,NULL,&Bt);
    866:   MatSetBlockSizes(Bt,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));

    868:   /* get symbolic C=A*Bt */
    869:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);

    871:   /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */
    872:   PetscNew(&abt);
    873:   c      = (Mat_SeqAIJ*)(*C)->data;
    874:   c->abt = abt;

    876:   abt->usecoloring = PETSC_FALSE;
    877:   abt->destroy     = (*C)->ops->destroy;
    878:   (*C)->ops->destroy     = MatDestroy_SeqAIJ_MatMatMultTrans;

    880:   PetscOptionsGetBool(((PetscObject)A)->options,NULL,"-matmattransmult_color",&abt->usecoloring,NULL);
    881:   if (abt->usecoloring) {
    882:     /* Create MatTransposeColoring from symbolic C=A*B^T */
    883:     MatTransposeColoring matcoloring;
    884:     MatColoring          coloring;
    885:     ISColoring           iscoloring;
    886:     Mat                  Bt_dense,C_dense;
    887:     Mat_SeqAIJ           *c=(Mat_SeqAIJ*)(*C)->data;
    888:     /* inode causes memory problem, don't know why */
    889:     if (c->inode.use) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MAT_USE_INODES is not supported. Use '-mat_no_inode'");

    891:     MatColoringCreate(*C,&coloring);
    892:     MatColoringSetDistance(coloring,2);
    893:     MatColoringSetType(coloring,MATCOLORINGSL);
    894:     MatColoringSetFromOptions(coloring);
    895:     MatColoringApply(coloring,&iscoloring);
    896:     MatColoringDestroy(&coloring);
    897:     MatTransposeColoringCreate(*C,iscoloring,&matcoloring);

    899:     abt->matcoloring = matcoloring;

    901:     ISColoringDestroy(&iscoloring);

    903:     /* Create Bt_dense and C_dense = A*Bt_dense */
    904:     MatCreate(PETSC_COMM_SELF,&Bt_dense);
    905:     MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);
    906:     MatSetType(Bt_dense,MATSEQDENSE);
    907:     MatSeqDenseSetPreallocation(Bt_dense,NULL);

    909:     Bt_dense->assembled = PETSC_TRUE;
    910:     abt->Bt_den   = Bt_dense;

    912:     MatCreate(PETSC_COMM_SELF,&C_dense);
    913:     MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);
    914:     MatSetType(C_dense,MATSEQDENSE);
    915:     MatSeqDenseSetPreallocation(C_dense,NULL);

    917:     Bt_dense->assembled = PETSC_TRUE;
    918:     abt->ABt_den  = C_dense;

    920: #if defined(PETSC_USE_INFO)
    921:     {
    922:       Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*C)->data;
    923:       PetscInfo7(*C,"Use coloring of C=A*B^T; B^T: %D %D, Bt_dense: %D,%D; Cnz %D / (cm*ncolors %D) = %g\n",B->cmap->n,B->rmap->n,Bt_dense->rmap->n,Bt_dense->cmap->n,c->nz,A->rmap->n*matcoloring->ncolors,(PetscReal)(c->nz)/(A->rmap->n*matcoloring->ncolors));
    924:     }
    925: #endif
    926:   }
    927:   /* clean up */
    928:   MatDestroy(&Bt);
    929:   MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);
    930:   return(0);
    931: }

    933: PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
    934: {
    935:   PetscErrorCode      ierr;
    936:   Mat_SeqAIJ          *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
    937:   PetscInt            *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
    938:   PetscInt            cm   =C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
    939:   PetscLogDouble      flops=0.0;
    940:   MatScalar           *aa  =a->a,*aval,*ba=b->a,*bval,*ca,*cval;
    941:   Mat_MatMatTransMult *abt = c->abt;

    944:   /* clear old values in C */
    945:   if (!c->a) {
    946:     PetscMalloc1(ci[cm]+1,&ca);
    947:     c->a      = ca;
    948:     c->free_a = PETSC_TRUE;
    949:   } else {
    950:     ca =  c->a;
    951:   }
    952:   PetscMemzero(ca,ci[cm]*sizeof(MatScalar));

    954:   if (abt->usecoloring) {
    955:     MatTransposeColoring matcoloring = abt->matcoloring;
    956:     Mat                  Bt_dense,C_dense = abt->ABt_den;

    958:     /* Get Bt_dense by Apply MatTransposeColoring to B */
    959:     Bt_dense = abt->Bt_den;
    960:     MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);

    962:     /* C_dense = A*Bt_dense */
    963:     MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);

    965:     /* Recover C from C_dense */
    966:     MatTransColoringApplyDenToSp(matcoloring,C_dense,C);
    967:     return(0);
    968:   }

    970:   for (i=0; i<cm; i++) {
    971:     anzi = ai[i+1] - ai[i];
    972:     acol = aj + ai[i];
    973:     aval = aa + ai[i];
    974:     cnzi = ci[i+1] - ci[i];
    975:     ccol = cj + ci[i];
    976:     cval = ca + ci[i];
    977:     for (j=0; j<cnzi; j++) {
    978:       brow = ccol[j];
    979:       bnzj = bi[brow+1] - bi[brow];
    980:       bcol = bj + bi[brow];
    981:       bval = ba + bi[brow];

    983:       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
    984:       nexta = 0; nextb = 0;
    985:       while (nexta<anzi && nextb<bnzj) {
    986:         while (nexta < anzi && acol[nexta] < bcol[nextb]) nexta++;
    987:         if (nexta == anzi) break;
    988:         while (nextb < bnzj && acol[nexta] > bcol[nextb]) nextb++;
    989:         if (nextb == bnzj) break;
    990:         if (acol[nexta] == bcol[nextb]) {
    991:           cval[j] += aval[nexta]*bval[nextb];
    992:           nexta++; nextb++;
    993:           flops += 2;
    994:         }
    995:       }
    996:     }
    997:   }
    998:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    999:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    1000:   PetscLogFlops(flops);
    1001:   return(0);
    1002: }

    1004: PetscErrorCode MatDestroy_SeqAIJ_MatTransMatMult(Mat A)
    1005: {
    1006:   PetscErrorCode      ierr;
    1007:   Mat_SeqAIJ          *a = (Mat_SeqAIJ*)A->data;
    1008:   Mat_MatTransMatMult *atb = a->atb;

    1011:   MatDestroy(&atb->At);
    1012:   (atb->destroy)(A);
    1013:   PetscFree(atb);
    1014:   return(0);
    1015: }

    1017: PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
    1018: {
    1019:   PetscErrorCode      ierr;
    1020:   const char          *algTypes[2] = {"matmatmult","outerproduct"};
    1021:   PetscInt            alg=0; /* set default algorithm */
    1022:   Mat                 At;
    1023:   Mat_MatTransMatMult *atb;
    1024:   Mat_SeqAIJ          *c;

    1027:   if (scall == MAT_INITIAL_MATRIX) {
    1028:     PetscObjectOptionsBegin((PetscObject)A);
    1029:     PetscOptionsObject->alreadyprinted = PETSC_FALSE; /* a hack to ensure the option shows in '-help' */
    1030:     PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,2,algTypes[0],&alg,NULL);
    1031:     PetscOptionsEnd();

    1033:     switch (alg) {
    1034:     case 1:
    1035:       MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);
    1036:       break;
    1037:     default:
    1038:       PetscNew(&atb);
    1039:       MatTranspose_SeqAIJ(A,MAT_INITIAL_MATRIX,&At);
    1040:       MatMatMult_SeqAIJ_SeqAIJ(At,B,MAT_INITIAL_MATRIX,fill,C);

    1042:       c                  = (Mat_SeqAIJ*)(*C)->data;
    1043:       c->atb             = atb;
    1044:       atb->At            = At;
    1045:       atb->destroy       = (*C)->ops->destroy;
    1046:       (*C)->ops->destroy = MatDestroy_SeqAIJ_MatTransMatMult;

    1048:       break;
    1049:     }
    1050:   }
    1051:   if (alg) {
    1052:     (*(*C)->ops->mattransposemultnumeric)(A,B,*C);
    1053:   } else if (!alg && scall == MAT_REUSE_MATRIX) {
    1054:     c   = (Mat_SeqAIJ*)(*C)->data;
    1055:     atb = c->atb;
    1056:     At  = atb->At;
    1057:     MatTranspose_SeqAIJ(A,MAT_REUSE_MATRIX,&At);
    1058:     MatMatMult_SeqAIJ_SeqAIJ(At,B,MAT_REUSE_MATRIX,fill,C);
    1059:   }
    1060:   return(0);
    1061: }

    1063: PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
    1064: {
    1066:   Mat            At;
    1067:   PetscInt       *ati,*atj;

    1070:   /* create symbolic At */
    1071:   MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);
    1072:   MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,NULL,&At);
    1073:   MatSetBlockSizes(At,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));

    1075:   /* get symbolic C=At*B */
    1076:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);

    1078:   /* clean up */
    1079:   MatDestroy(&At);
    1080:   MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);

    1082:   (*C)->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ;
    1083:   return(0);
    1084: }

    1086: PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
    1087: {
    1089:   Mat_SeqAIJ     *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
    1090:   PetscInt       am   =A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
    1091:   PetscInt       cm   =C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
    1092:   PetscLogDouble flops=0.0;
    1093:   MatScalar      *aa  =a->a,*ba,*ca,*caj;

    1096:   if (!c->a) {
    1097:     PetscMalloc1(ci[cm]+1,&ca);

    1099:     c->a      = ca;
    1100:     c->free_a = PETSC_TRUE;
    1101:   } else {
    1102:     ca = c->a;
    1103:   }
    1104:   /* clear old values in C */
    1105:   PetscMemzero(ca,ci[cm]*sizeof(MatScalar));

    1107:   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
    1108:   for (i=0; i<am; i++) {
    1109:     bj   = b->j + bi[i];
    1110:     ba   = b->a + bi[i];
    1111:     bnzi = bi[i+1] - bi[i];
    1112:     anzi = ai[i+1] - ai[i];
    1113:     for (j=0; j<anzi; j++) {
    1114:       nextb = 0;
    1115:       crow  = *aj++;
    1116:       cjj   = cj + ci[crow];
    1117:       caj   = ca + ci[crow];
    1118:       /* perform sparse axpy operation.  Note cjj includes bj. */
    1119:       for (k=0; nextb<bnzi; k++) {
    1120:         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
    1121:           caj[k] += (*aa)*(*(ba+nextb));
    1122:           nextb++;
    1123:         }
    1124:       }
    1125:       flops += 2*bnzi;
    1126:       aa++;
    1127:     }
    1128:   }

    1130:   /* Assemble the final matrix and clean up */
    1131:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1132:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    1133:   PetscLogFlops(flops);
    1134:   return(0);
    1135: }

    1137: PETSC_INTERN PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
    1138: {

    1142:   if (scall == MAT_INITIAL_MATRIX) {
    1143:     PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);
    1144:     MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);
    1145:     PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);
    1146:   }
    1147:   PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);
    1148:   MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);
    1149:   PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);
    1150:   return(0);
    1151: }

    1153: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
    1154: {

    1158:   MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);

    1160:   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqDense;
    1161:   return(0);
    1162: }

    1164: PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
    1165: {
    1166:   Mat_SeqAIJ        *a=(Mat_SeqAIJ*)A->data;
    1167:   Mat_SeqDense      *bd = (Mat_SeqDense*)B->data;
    1168:   PetscErrorCode    ierr;
    1169:   PetscScalar       *c,*b,r1,r2,r3,r4,*c1,*c2,*c3,*c4,aatmp;
    1170:   const PetscScalar *aa,*b1,*b2,*b3,*b4;
    1171:   const PetscInt    *aj;
    1172:   PetscInt          cm=C->rmap->n,cn=B->cmap->n,bm=bd->lda,am=A->rmap->n;
    1173:   PetscInt          am4=4*am,bm4=4*bm,col,i,j,n,ajtmp;

    1176:   if (!cm || !cn) return(0);
    1177:   if (B->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number columns in A %D not equal rows in B %D\n",A->cmap->n,B->rmap->n);
    1178:   if (A->rmap->n != C->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number rows in C %D not equal rows in A %D\n",C->rmap->n,A->rmap->n);
    1179:   if (B->cmap->n != C->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number columns in B %D not equal columns in C %D\n",B->cmap->n,C->cmap->n);
    1180:   b = bd->v;
    1181:   MatDenseGetArray(C,&c);
    1182:   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
    1183:   c1 = c; c2 = c1 + am; c3 = c2 + am; c4 = c3 + am;
    1184:   for (col=0; col<cn-4; col += 4) {  /* over columns of C */
    1185:     for (i=0; i<am; i++) {        /* over rows of C in those columns */
    1186:       r1 = r2 = r3 = r4 = 0.0;
    1187:       n  = a->i[i+1] - a->i[i];
    1188:       aj = a->j + a->i[i];
    1189:       aa = a->a + a->i[i];
    1190:       for (j=0; j<n; j++) {
    1191:         aatmp = aa[j]; ajtmp = aj[j];
    1192:         r1 += aatmp*b1[ajtmp];
    1193:         r2 += aatmp*b2[ajtmp];
    1194:         r3 += aatmp*b3[ajtmp];
    1195:         r4 += aatmp*b4[ajtmp];
    1196:       }
    1197:       c1[i] = r1;
    1198:       c2[i] = r2;
    1199:       c3[i] = r3;
    1200:       c4[i] = r4;
    1201:     }
    1202:     b1 += bm4; b2 += bm4; b3 += bm4; b4 += bm4;
    1203:     c1 += am4; c2 += am4; c3 += am4; c4 += am4;
    1204:   }
    1205:   for (; col<cn; col++) {   /* over extra columns of C */
    1206:     for (i=0; i<am; i++) {  /* over rows of C in those columns */
    1207:       r1 = 0.0;
    1208:       n  = a->i[i+1] - a->i[i];
    1209:       aj = a->j + a->i[i];
    1210:       aa = a->a + a->i[i];
    1211:       for (j=0; j<n; j++) {
    1212:         r1 += aa[j]*b1[aj[j]];
    1213:       }
    1214:       c1[i] = r1;
    1215:     }
    1216:     b1 += bm;
    1217:     c1 += am;
    1218:   }
    1219:   PetscLogFlops(cn*(2.0*a->nz));
    1220:   MatDenseRestoreArray(C,&c);
    1221:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1222:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    1223:   return(0);
    1224: }

    1226: /*
    1227:    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
    1228: */
    1229: PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
    1230: {
    1231:   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
    1232:   Mat_SeqDense   *bd = (Mat_SeqDense*)B->data;
    1234:   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
    1235:   MatScalar      *aa;
    1236:   PetscInt       cm  = C->rmap->n, cn=B->cmap->n, bm=bd->lda, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
    1237:   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;

    1240:   if (!cm || !cn) return(0);
    1241:   b = bd->v;
    1242:   MatDenseGetArray(C,&c);
    1243:   b1   = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;

    1245:   if (a->compressedrow.use) { /* use compressed row format */
    1246:     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
    1247:       colam = col*am;
    1248:       arm   = a->compressedrow.nrows;
    1249:       ii    = a->compressedrow.i;
    1250:       ridx  = a->compressedrow.rindex;
    1251:       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
    1252:         r1 = r2 = r3 = r4 = 0.0;
    1253:         n  = ii[i+1] - ii[i];
    1254:         aj = a->j + ii[i];
    1255:         aa = a->a + ii[i];
    1256:         for (j=0; j<n; j++) {
    1257:           r1 += (*aa)*b1[*aj];
    1258:           r2 += (*aa)*b2[*aj];
    1259:           r3 += (*aa)*b3[*aj];
    1260:           r4 += (*aa++)*b4[*aj++];
    1261:         }
    1262:         c[colam       + ridx[i]] += r1;
    1263:         c[colam + am  + ridx[i]] += r2;
    1264:         c[colam + am2 + ridx[i]] += r3;
    1265:         c[colam + am3 + ridx[i]] += r4;
    1266:       }
    1267:       b1 += bm4;
    1268:       b2 += bm4;
    1269:       b3 += bm4;
    1270:       b4 += bm4;
    1271:     }
    1272:     for (; col<cn; col++) {     /* over extra columns of C */
    1273:       colam = col*am;
    1274:       arm   = a->compressedrow.nrows;
    1275:       ii    = a->compressedrow.i;
    1276:       ridx  = a->compressedrow.rindex;
    1277:       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
    1278:         r1 = 0.0;
    1279:         n  = ii[i+1] - ii[i];
    1280:         aj = a->j + ii[i];
    1281:         aa = a->a + ii[i];

    1283:         for (j=0; j<n; j++) {
    1284:           r1 += (*aa++)*b1[*aj++];
    1285:         }
    1286:         c[colam + ridx[i]] += r1;
    1287:       }
    1288:       b1 += bm;
    1289:     }
    1290:   } else {
    1291:     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
    1292:       colam = col*am;
    1293:       for (i=0; i<am; i++) {        /* over rows of C in those columns */
    1294:         r1 = r2 = r3 = r4 = 0.0;
    1295:         n  = a->i[i+1] - a->i[i];
    1296:         aj = a->j + a->i[i];
    1297:         aa = a->a + a->i[i];
    1298:         for (j=0; j<n; j++) {
    1299:           r1 += (*aa)*b1[*aj];
    1300:           r2 += (*aa)*b2[*aj];
    1301:           r3 += (*aa)*b3[*aj];
    1302:           r4 += (*aa++)*b4[*aj++];
    1303:         }
    1304:         c[colam + i]       += r1;
    1305:         c[colam + am + i]  += r2;
    1306:         c[colam + am2 + i] += r3;
    1307:         c[colam + am3 + i] += r4;
    1308:       }
    1309:       b1 += bm4;
    1310:       b2 += bm4;
    1311:       b3 += bm4;
    1312:       b4 += bm4;
    1313:     }
    1314:     for (; col<cn; col++) {     /* over extra columns of C */
    1315:       colam = col*am;
    1316:       for (i=0; i<am; i++) {  /* over rows of C in those columns */
    1317:         r1 = 0.0;
    1318:         n  = a->i[i+1] - a->i[i];
    1319:         aj = a->j + a->i[i];
    1320:         aa = a->a + a->i[i];

    1322:         for (j=0; j<n; j++) {
    1323:           r1 += (*aa++)*b1[*aj++];
    1324:         }
    1325:         c[colam + i] += r1;
    1326:       }
    1327:       b1 += bm;
    1328:     }
    1329:   }
    1330:   PetscLogFlops(cn*2.0*a->nz);
    1331:   MatDenseRestoreArray(C,&c);
    1332:   return(0);
    1333: }

    1335: PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
    1336: {
    1338:   Mat_SeqAIJ     *b       = (Mat_SeqAIJ*)B->data;
    1339:   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
    1340:   PetscInt       *bi      = b->i,*bj=b->j;
    1341:   PetscInt       m        = Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
    1342:   MatScalar      *btval,*btval_den,*ba=b->a;
    1343:   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;

    1346:   btval_den=btdense->v;
    1347:   PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));
    1348:   for (k=0; k<ncolors; k++) {
    1349:     ncolumns = coloring->ncolumns[k];
    1350:     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
    1351:       col   = *(columns + colorforcol[k] + l);
    1352:       btcol = bj + bi[col];
    1353:       btval = ba + bi[col];
    1354:       anz   = bi[col+1] - bi[col];
    1355:       for (j=0; j<anz; j++) {
    1356:         brow            = btcol[j];
    1357:         btval_den[brow] = btval[j];
    1358:       }
    1359:     }
    1360:     btval_den += m;
    1361:   }
    1362:   return(0);
    1363: }

    1365: PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
    1366: {
    1368:   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)Csp->data;
    1369:   PetscScalar    *ca_den,*ca_den_ptr,*ca=csp->a;
    1370:   PetscInt       k,l,m=Cden->rmap->n,ncolors=matcoloring->ncolors;
    1371:   PetscInt       brows=matcoloring->brows,*den2sp=matcoloring->den2sp;
    1372:   PetscInt       nrows,*row,*idx;
    1373:   PetscInt       *rows=matcoloring->rows,*colorforrow=matcoloring->colorforrow;

    1376:   MatDenseGetArray(Cden,&ca_den);

    1378:   if (brows > 0) {
    1379:     PetscInt *lstart,row_end,row_start;
    1380:     lstart = matcoloring->lstart;
    1381:     PetscMemzero(lstart,ncolors*sizeof(PetscInt));

    1383:     row_end = brows;
    1384:     if (row_end > m) row_end = m;
    1385:     for (row_start=0; row_start<m; row_start+=brows) { /* loop over row blocks of Csp */
    1386:       ca_den_ptr = ca_den;
    1387:       for (k=0; k<ncolors; k++) { /* loop over colors (columns of Cden) */
    1388:         nrows = matcoloring->nrows[k];
    1389:         row   = rows  + colorforrow[k];
    1390:         idx   = den2sp + colorforrow[k];
    1391:         for (l=lstart[k]; l<nrows; l++) {
    1392:           if (row[l] >= row_end) {
    1393:             lstart[k] = l;
    1394:             break;
    1395:           } else {
    1396:             ca[idx[l]] = ca_den_ptr[row[l]];
    1397:           }
    1398:         }
    1399:         ca_den_ptr += m;
    1400:       }
    1401:       row_end += brows;
    1402:       if (row_end > m) row_end = m;
    1403:     }
    1404:   } else { /* non-blocked impl: loop over columns of Csp - slow if Csp is large */
    1405:     ca_den_ptr = ca_den;
    1406:     for (k=0; k<ncolors; k++) {
    1407:       nrows = matcoloring->nrows[k];
    1408:       row   = rows  + colorforrow[k];
    1409:       idx   = den2sp + colorforrow[k];
    1410:       for (l=0; l<nrows; l++) {
    1411:         ca[idx[l]] = ca_den_ptr[row[l]];
    1412:       }
    1413:       ca_den_ptr += m;
    1414:     }
    1415:   }

    1417:   MatDenseRestoreArray(Cden,&ca_den);
    1418: #if defined(PETSC_USE_INFO)
    1419:   if (matcoloring->brows > 0) {
    1420:     PetscInfo1(Csp,"Loop over %D row blocks for den2sp\n",brows);
    1421:   } else {
    1422:     PetscInfo(Csp,"Loop over colors/columns of Cden, inefficient for large sparse matrix product \n");
    1423:   }
    1424: #endif
    1425:   return(0);
    1426: }

    1428: PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
    1429: {
    1431:   PetscInt       i,n,nrows,Nbs,j,k,m,ncols,col,cm;
    1432:   const PetscInt *is,*ci,*cj,*row_idx;
    1433:   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
    1434:   IS             *isa;
    1435:   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
    1436:   PetscInt       *colorforrow,*rows,*rows_i,*idxhit,*spidx,*den2sp,*den2sp_i;
    1437:   PetscInt       *colorforcol,*columns,*columns_i,brows;
    1438:   PetscBool      flg;

    1441:   ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);

    1443:   /* bs >1 is not being tested yet! */
    1444:   Nbs       = mat->cmap->N/bs;
    1445:   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
    1446:   c->N      = Nbs;
    1447:   c->m      = c->M;
    1448:   c->rstart = 0;
    1449:   c->brows  = 100;

    1451:   c->ncolors = nis;
    1452:   PetscMalloc3(nis,&c->ncolumns,nis,&c->nrows,nis+1,&colorforrow);
    1453:   PetscMalloc1(csp->nz+1,&rows);
    1454:   PetscMalloc1(csp->nz+1,&den2sp);

    1456:   brows = c->brows;
    1457:   PetscOptionsGetInt(NULL,NULL,"-matden2sp_brows",&brows,&flg);
    1458:   if (flg) c->brows = brows;
    1459:   if (brows > 0) {
    1460:     PetscMalloc1(nis+1,&c->lstart);
    1461:   }

    1463:   colorforrow[0] = 0;
    1464:   rows_i         = rows;
    1465:   den2sp_i       = den2sp;

    1467:   PetscMalloc1(nis+1,&colorforcol);
    1468:   PetscMalloc1(Nbs+1,&columns);

    1470:   colorforcol[0] = 0;
    1471:   columns_i      = columns;

    1473:   /* get column-wise storage of mat */
    1474:   MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);

    1476:   cm   = c->m;
    1477:   PetscMalloc1(cm+1,&rowhit);
    1478:   PetscMalloc1(cm+1,&idxhit);
    1479:   for (i=0; i<nis; i++) { /* loop over color */
    1480:     ISGetLocalSize(isa[i],&n);
    1481:     ISGetIndices(isa[i],&is);

    1483:     c->ncolumns[i] = n;
    1484:     if (n) {
    1485:       PetscMemcpy(columns_i,is,n*sizeof(PetscInt));
    1486:     }
    1487:     colorforcol[i+1] = colorforcol[i] + n;
    1488:     columns_i       += n;

    1490:     /* fast, crude version requires O(N*N) work */
    1491:     PetscMemzero(rowhit,cm*sizeof(PetscInt));

    1493:     for (j=0; j<n; j++) { /* loop over columns*/
    1494:       col     = is[j];
    1495:       row_idx = cj + ci[col];
    1496:       m       = ci[col+1] - ci[col];
    1497:       for (k=0; k<m; k++) { /* loop over columns marking them in rowhit */
    1498:         idxhit[*row_idx]   = spidx[ci[col] + k];
    1499:         rowhit[*row_idx++] = col + 1;
    1500:       }
    1501:     }
    1502:     /* count the number of hits */
    1503:     nrows = 0;
    1504:     for (j=0; j<cm; j++) {
    1505:       if (rowhit[j]) nrows++;
    1506:     }
    1507:     c->nrows[i]      = nrows;
    1508:     colorforrow[i+1] = colorforrow[i] + nrows;

    1510:     nrows = 0;
    1511:     for (j=0; j<cm; j++) { /* loop over rows */
    1512:       if (rowhit[j]) {
    1513:         rows_i[nrows]   = j;
    1514:         den2sp_i[nrows] = idxhit[j];
    1515:         nrows++;
    1516:       }
    1517:     }
    1518:     den2sp_i += nrows;

    1520:     ISRestoreIndices(isa[i],&is);
    1521:     rows_i += nrows;
    1522:   }
    1523:   MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);
    1524:   PetscFree(rowhit);
    1525:   ISColoringRestoreIS(iscoloring,&isa);
    1526:   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);

    1528:   c->colorforrow = colorforrow;
    1529:   c->rows        = rows;
    1530:   c->den2sp      = den2sp;
    1531:   c->colorforcol = colorforcol;
    1532:   c->columns     = columns;

    1534:   PetscFree(idxhit);
    1535:   return(0);
    1536: }

    1538: /* Needed for MatMatMult_SeqAIJ_SeqAIJ_Combined() */
    1539: /* Append value to an array if the value is not present yet. A bitarray */
    1540: /* was used to determine if there is already an entry at this position. */
    1541: void appendToArray(PetscInt val, PetscInt *array, PetscInt *cnzi)
    1542: {
    1543:   array[(*cnzi)++] = val;
    1544: }

    1546: /* This algorithm combines the symbolic and numeric phase of matrix-matrix multiplication. */
    1547: PetscErrorCode MatMatMult_SeqAIJ_SeqAIJ_Combined(Mat A,Mat B,PetscReal fill,Mat *C)
    1548: {
    1549:   PetscErrorCode     ierr;
    1550:   PetscLogDouble     flops=0.0;
    1551:   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data, *b = (Mat_SeqAIJ*)B->data, *c;
    1552:   const PetscInt     *ai = a->i,*bi = b->i, *aj = a->j;
    1553:   PetscInt           *ci,*cj,*cj_i;
    1554:   PetscScalar        *ca, *ca_i;
    1555:   PetscInt           c_maxmem = 0, a_maxrownnz = 0, a_rownnz, a_col;
    1556:   PetscInt           am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
    1557:   PetscInt           i, k, ndouble = 0;
    1558:   PetscReal          afill;
    1559:   PetscScalar        *c_row_val_dense;
    1560:   PetscBool          *c_row_idx_flags;
    1561:   PetscInt           *aj_i = a->j;
    1562:   PetscScalar        *aa_i = a->a;

    1565:   /* Step 1: Determine upper bounds on memory for C */
    1566:   for (i=0; i<am; i++) { /* iterate over all rows of A */
    1567:     const PetscInt anzi  = ai[i+1] - ai[i]; /* number of nonzeros in this row of A, this is the number of rows of B that we merge */
    1568:     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
    1569:     a_rownnz = 0;
    1570:     for (k=0;k<anzi;++k) a_rownnz += bi[acol[k]+1] - bi[acol[k]];
    1571:     a_maxrownnz = PetscMax(a_maxrownnz, a_rownnz);
    1572:     c_maxmem += a_rownnz;
    1573:   }
    1574:   PetscMalloc1(am+1, &ci);
    1575:   PetscMalloc1(bn, &c_row_val_dense);
    1576:   PetscMalloc1(bn, &c_row_idx_flags);
    1577:   PetscMalloc1(c_maxmem,&cj);
    1578:   PetscMalloc1(c_maxmem,&ca);
    1579:   ca_i = ca;
    1580:   cj_i = cj;
    1581:   ci[0] = 0;
    1582:   PetscMemzero(c_row_val_dense, bn * sizeof(PetscScalar));
    1583:   PetscMemzero(c_row_idx_flags, bn * sizeof(PetscBool));
    1584:   for (i=0; i<am; i++) {
    1585:     /* Step 2: Initialize the dense row vector for C  */
    1586:     const PetscInt anzi     = ai[i+1] - ai[i]; /* number of nonzeros in this row of A, this is the number of rows of B that we merge */
    1587:     PetscInt cnzi           = 0;
    1588:     PetscInt *bj_i;
    1589:     PetscScalar *ba_i;

    1591:     /* Step 3: Do the numerical calculations */
    1592:     for (a_col=0; a_col<anzi; a_col++) {          /* iterate over all non zero values in a row of A */
    1593:       PetscInt a_col_index = aj_i[a_col];
    1594:       const PetscInt bnzi = bi[a_col_index+1] - bi[a_col_index];
    1595:       flops += 2*bnzi;
    1596:       bj_i = b->j + bi[a_col_index];   /* points to the current row in bj */
    1597:       ba_i = b->a + bi[a_col_index];   /* points to the current row in ba */
    1598:       for (k=0; k<bnzi; ++k) { /* iterate over all non zeros of this row in B */
    1599:         if (c_row_idx_flags[ bj_i[k] ] == PETSC_FALSE) {
    1600:           appendToArray(bj_i[k], cj_i, &cnzi);
    1601:           c_row_idx_flags[ bj_i[k] ] = PETSC_TRUE;
    1602:         }
    1603:         c_row_val_dense[ bj_i[k] ] += aa_i[a_col] * ba_i[k];
    1604:       }
    1605:     }

    1607:     /* Sort array */
    1608:     PetscSortInt(cnzi, cj_i);
    1609:     /* Step 4 */
    1610:     for (k=0; k < cnzi; k++) {
    1611:       ca_i[k] = c_row_val_dense[cj_i[k]];
    1612:       c_row_val_dense[cj_i[k]] = 0.;
    1613:       c_row_idx_flags[cj_i[k]] = PETSC_FALSE;
    1614:     }
    1615:     /* terminate current row */
    1616:     aa_i += anzi;
    1617:     aj_i += anzi;
    1618:     ca_i += cnzi;
    1619:     cj_i += cnzi;
    1620:     ci[i+1] = ci[i] + cnzi;
    1621:     flops += cnzi;
    1622:   }

    1624:   /* Step 5 */
    1625:   /* Create the new matrix */
    1626:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);
    1627:   MatSetBlockSizesFromMats(*C,A,B);

    1629:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    1630:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
    1631:   c          = (Mat_SeqAIJ*)((*C)->data);
    1632:   c->a       = ca;
    1633:   c->free_a  = PETSC_TRUE;
    1634:   c->free_ij = PETSC_TRUE;
    1635:   c->nonew   = 0;

    1637:   /* set MatInfo */
    1638:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
    1639:   if (afill < 1.0) afill = 1.0;
    1640:   c->maxnz                     = ci[am];
    1641:   c->nz                        = ci[am];
    1642:   (*C)->info.mallocs           = ndouble;
    1643:   (*C)->info.fill_ratio_given  = fill;
    1644:   (*C)->info.fill_ratio_needed = afill;

    1646:   PetscFree(c_row_val_dense);
    1647:   PetscFree(c_row_idx_flags);

    1649:   MatAssemblyBegin(*C,MAT_FINAL_ASSEMBLY);
    1650:   MatAssemblyEnd(*C,MAT_FINAL_ASSEMBLY);
    1651:   PetscLogFlops(flops);
    1652:   return(0);
    1653: }