Date: 2013-07-02T14:41:32+00:00

Actual source code: matmatmult.c
petsc-3.4.2 2013-07-02

      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> /*I "petscmat.h" I*/
      8: #include <../src/mat/utils/freespace.h>
      9: #include <../src/mat/utils/petscheap.h>
     10: #include <petscbt.h>
     11: #include <../src/mat/impls/dense/seq/dense.h>

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

     17: PetscErrorCode MatMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
     18: {
     20:   PetscBool      scalable=PETSC_FALSE,scalable_fast=PETSC_FALSE,heap = PETSC_FALSE,btheap = PETSC_FALSE,llcondensed = PETSC_FALSE;

     23:   if (scall == MAT_INITIAL_MATRIX) {
     24:     PetscObjectOptionsBegin((PetscObject)A);
     25:     PetscOptionsBool("-matmatmult_scalable","Use a scalable but slower C=A*B","",scalable,&scalable,NULL);
     26:     PetscOptionsBool("-matmatmult_scalable_fast","Use a scalable but slower C=A*B","",scalable_fast,&scalable_fast,NULL);
     27:     PetscOptionsBool("-matmatmult_heap","Use heap implementation of symbolic factorization C=A*B","",heap,&heap,NULL);
     28:     PetscOptionsBool("-matmatmult_btheap","Use btheap implementation of symbolic factorization C=A*B","",btheap,&btheap,NULL);
     29:     PetscOptionsBool("-matmatmult_llcondensed","Use LLCondensed to for symbolic C=A*B","",llcondensed,&llcondensed,NULL);
     30:     PetscOptionsEnd();
     31:     PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);
     32:     if (scalable_fast) {
     33:       MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(A,B,fill,C);
     34:     } else if (scalable) {
     35:       MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(A,B,fill,C);
     36:     } else if (heap) {
     37:       MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(A,B,fill,C);
     38:     } else if (btheap) {
     39:       MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(A,B,fill,C);
     40:     } else if (llcondensed) {
     41:       MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(A,B,fill,C);
     42:     } else {
     43:       MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);
     44:     }
     45:     PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);
     46:   }

     48:   PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);
     49:   (*(*C)->ops->matmultnumeric)(A,B,*C);
     50:   PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);
     51:   return(0);
     52: }

     56: static PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat A,Mat B,PetscReal fill,Mat *C)
     57: {
     58:   PetscErrorCode     ierr;
     59:   Mat_SeqAIJ         *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
     60:   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
     61:   PetscInt           am =A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
     62:   PetscReal          afill;
     63:   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
     64:   PetscBT            lnkbt;
     65:   PetscFreeSpaceList free_space=NULL,current_space=NULL;

     68:   /* Get ci and cj */
     69:   /*---------------*/
     70:   /* Allocate ci array, arrays for fill computation and */
     71:   /* free space for accumulating nonzero column info */
     72:   PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);
     73:   ci[0] = 0;

     75:   /* create and initialize a linked list */
     76:   nlnk_max = a->rmax*b->rmax;
     77:   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn;
     78:   PetscLLCondensedCreate(nlnk_max,bn,&lnk,&lnkbt);

     80:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
     81:   PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);

     83:   current_space = free_space;

     85:   /* Determine ci and cj */
     86:   for (i=0; i<am; i++) {
     87:     anzi = ai[i+1] - ai[i];
     88:     aj   = a->j + ai[i];
     89:     for (j=0; j<anzi; j++) {
     90:       brow = aj[j];
     91:       bnzj = bi[brow+1] - bi[brow];
     92:       bj   = b->j + bi[brow];
     93:       /* add non-zero cols of B into the sorted linked list lnk */
     94:       PetscLLCondensedAddSorted(bnzj,bj,lnk,lnkbt);
     95:     }
     96:     cnzi = lnk[0];

     98:     /* If free space is not available, make more free space */
     99:     /* Double the amount of total space in the list */
    100:     if (current_space->local_remaining<cnzi) {
    101:       PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);
    102:       ndouble++;
    103:     }

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

    108:     current_space->array           += cnzi;
    109:     current_space->local_used      += cnzi;
    110:     current_space->local_remaining -= cnzi;

    112:     ci[i+1] = ci[i] + cnzi;
    113:   }

    115:   /* Column indices are in the list of free space */
    116:   /* Allocate space for cj, initialize cj, and */
    117:   /* destroy list of free space and other temporary array(s) */
    118:   PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);
    119:   PetscFreeSpaceContiguous(&free_space,cj);
    120:   PetscLLCondensedDestroy(lnk,lnkbt);

    122:   /* put together the new symbolic matrix */
    123:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);

    125:   (*C)->rmap->bs = A->rmap->bs;
    126:   (*C)->cmap->bs = B->cmap->bs;

    128:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    129:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
    130:   c                         = (Mat_SeqAIJ*)((*C)->data);
    131:   c->free_a                 = PETSC_FALSE;
    132:   c->free_ij                = PETSC_TRUE;
    133:   c->nonew                  = 0;
    134:   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ; /* fast, needs non-scalable O(bn) array 'abdense' */

    136:   /* set MatInfo */
    137:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
    138:   if (afill < 1.0) afill = 1.0;
    139:   c->maxnz                     = ci[am];
    140:   c->nz                        = ci[am];
    141:   (*C)->info.mallocs           = ndouble;
    142:   (*C)->info.fill_ratio_given  = fill;
    143:   (*C)->info.fill_ratio_needed = afill;

    145: #if defined(PETSC_USE_INFO)
    146:   if (ci[am]) {
    147:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);
    148:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);
    149:   } else {
    150:     PetscInfo((*C),"Empty matrix product\n");
    151:   }
    152: #endif
    153:   return(0);
    154: }

    158: PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
    159: {
    161:   PetscLogDouble flops=0.0;
    162:   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
    163:   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
    164:   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
    165:   PetscInt       *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
    166:   PetscInt       am   =A->rmap->n,cm=C->rmap->n;
    167:   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
    168:   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca,valtmp;
    169:   PetscScalar    *ab_dense;

    172:   /* printf("MatMatMultNumeric_SeqAIJ_SeqAIJ...ca %p\n",c->a); */
    173:   if (!c->a) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
    174:     PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);
    175:     c->a      = ca;
    176:     c->free_a = PETSC_TRUE;

    178:     PetscMalloc(B->cmap->N*sizeof(PetscScalar),&ab_dense);
    179:     PetscMemzero(ab_dense,B->cmap->N*sizeof(PetscScalar));

    181:     c->matmult_abdense = ab_dense;
    182:   } else {
    183:     ca       = c->a;
    184:     ab_dense = c->matmult_abdense;
    185:   }

    187:   /* clean old values in C */
    188:   PetscMemzero(ca,ci[cm]*sizeof(MatScalar));
    189:   /* Traverse A row-wise. */
    190:   /* Build the ith row in C by summing over nonzero columns in A, */
    191:   /* the rows of B corresponding to nonzeros of A. */
    192:   for (i=0; i<am; i++) {
    193:     anzi = ai[i+1] - ai[i];
    194:     for (j=0; j<anzi; j++) {
    195:       brow = aj[j];
    196:       bnzi = bi[brow+1] - bi[brow];
    197:       bjj  = bj + bi[brow];
    198:       baj  = ba + bi[brow];
    199:       /* perform dense axpy */
    200:       valtmp = aa[j];
    201:       for (k=0; k<bnzi; k++) {
    202:         ab_dense[bjj[k]] += valtmp*baj[k];
    203:       }
    204:       flops += 2*bnzi;
    205:     }
    206:     aj += anzi; aa += anzi;

    208:     cnzi = ci[i+1] - ci[i];
    209:     for (k=0; k<cnzi; k++) {
    210:       ca[k]          += ab_dense[cj[k]];
    211:       ab_dense[cj[k]] = 0.0; /* zero ab_dense */
    212:     }
    213:     flops += cnzi;
    214:     cj    += cnzi; ca += cnzi;
    215:   }
    216:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    217:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    218:   PetscLogFlops(flops);
    219:   return(0);
    220: }

    224: PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,Mat C)
    225: {
    227:   PetscLogDouble flops=0.0;
    228:   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
    229:   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
    230:   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
    231:   PetscInt       *ai  = a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
    232:   PetscInt       am   = A->rmap->N,cm=C->rmap->N;
    233:   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
    234:   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca=c->a,valtmp;
    235:   PetscInt       nextb;

    238:   /* clean old values in C */
    239:   PetscMemzero(ca,ci[cm]*sizeof(MatScalar));
    240:   /* Traverse A row-wise. */
    241:   /* Build the ith row in C by summing over nonzero columns in A, */
    242:   /* the rows of B corresponding to nonzeros of A. */
    243:   for (i=0; i<am; i++) {
    244:     anzi = ai[i+1] - ai[i];
    245:     cnzi = ci[i+1] - ci[i];
    246:     for (j=0; j<anzi; j++) {
    247:       brow = aj[j];
    248:       bnzi = bi[brow+1] - bi[brow];
    249:       bjj  = bj + bi[brow];
    250:       baj  = ba + bi[brow];
    251:       /* perform sparse axpy */
    252:       valtmp = aa[j];
    253:       nextb  = 0;
    254:       for (k=0; nextb<bnzi; k++) {
    255:         if (cj[k] == bjj[nextb]) { /* ccol == bcol */
    256:           ca[k] += valtmp*baj[nextb++];
    257:         }
    258:       }
    259:       flops += 2*bnzi;
    260:     }
    261:     aj += anzi; aa += anzi;
    262:     cj += cnzi; ca += cnzi;
    263:   }

    265:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    266:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    267:   PetscLogFlops(flops);
    268:   return(0);
    269: }

    273: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat A,Mat B,PetscReal fill,Mat *C)
    274: {
    275:   PetscErrorCode     ierr;
    276:   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
    277:   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
    278:   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
    279:   MatScalar          *ca;
    280:   PetscReal          afill;
    281:   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
    282:   PetscFreeSpaceList free_space=NULL,current_space=NULL;

    285:   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_fast() */
    286:   /*-----------------------------------------------------------------------------------------*/
    287:   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
    288:   PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);
    289:   ci[0] = 0;

    291:   /* create and initialize a linked list */
    292:   nlnk_max = a->rmax*b->rmax;
    293:   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn; /* in case rmax is not defined for A or B */
    294:   PetscLLCondensedCreate_fast(nlnk_max,&lnk);

    296:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
    297:   PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);
    298:   current_space = free_space;

    300:   /* Determine ci and cj */
    301:   for (i=0; i<am; i++) {
    302:     anzi = ai[i+1] - ai[i];
    303:     aj   = a->j + ai[i];
    304:     for (j=0; j<anzi; j++) {
    305:       brow = aj[j];
    306:       bnzj = bi[brow+1] - bi[brow];
    307:       bj   = b->j + bi[brow];
    308:       /* add non-zero cols of B into the sorted linked list lnk */
    309:       PetscLLCondensedAddSorted_fast(bnzj,bj,lnk);
    310:     }
    311:     cnzi = lnk[1];

    313:     /* If free space is not available, make more free space */
    314:     /* Double the amount of total space in the list */
    315:     if (current_space->local_remaining<cnzi) {
    316:       PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);
    317:       ndouble++;
    318:     }

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

    323:     current_space->array           += cnzi;
    324:     current_space->local_used      += cnzi;
    325:     current_space->local_remaining -= cnzi;

    327:     ci[i+1] = ci[i] + cnzi;
    328:   }

    330:   /* Column indices are in the list of free space */
    331:   /* Allocate space for cj, initialize cj, and */
    332:   /* destroy list of free space and other temporary array(s) */
    333:   PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);
    334:   PetscFreeSpaceContiguous(&free_space,cj);
    335:   PetscLLCondensedDestroy_fast(lnk);

    337:   /* Allocate space for ca */
    338:   PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);
    339:   PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));

    341:   /* put together the new symbolic matrix */
    342:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);

    344:   (*C)->rmap->bs = A->rmap->bs;
    345:   (*C)->cmap->bs = B->cmap->bs;

    347:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    348:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
    349:   c          = (Mat_SeqAIJ*)((*C)->data);
    350:   c->free_a  = PETSC_TRUE;
    351:   c->free_ij = PETSC_TRUE;
    352:   c->nonew   = 0;

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

    356:   /* set MatInfo */
    357:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
    358:   if (afill < 1.0) afill = 1.0;
    359:   c->maxnz                     = ci[am];
    360:   c->nz                        = ci[am];
    361:   (*C)->info.mallocs           = ndouble;
    362:   (*C)->info.fill_ratio_given  = fill;
    363:   (*C)->info.fill_ratio_needed = afill;

    365: #if defined(PETSC_USE_INFO)
    366:   if (ci[am]) {
    367:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);
    368:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);
    369:   } else {
    370:     PetscInfo((*C),"Empty matrix product\n");
    371:   }
    372: #endif
    373:   return(0);
    374: }

    379: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,PetscReal fill,Mat *C)
    380: {
    381:   PetscErrorCode     ierr;
    382:   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
    383:   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
    384:   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
    385:   MatScalar          *ca;
    386:   PetscReal          afill;
    387:   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
    388:   PetscFreeSpaceList free_space=NULL,current_space=NULL;

    391:   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
    392:   /*---------------------------------------------------------------------------------------------*/
    393:   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
    394:   PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);
    395:   ci[0] = 0;

    397:   /* create and initialize a linked list */
    398:   nlnk_max = a->rmax*b->rmax;
    399:   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn; /* in case rmax is not defined for A or B */
    400:   PetscLLCondensedCreate_Scalable(nlnk_max,&lnk);

    402:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
    403:   PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);
    404:   current_space = free_space;

    406:   /* Determine ci and cj */
    407:   for (i=0; i<am; i++) {
    408:     anzi = ai[i+1] - ai[i];
    409:     aj   = a->j + ai[i];
    410:     for (j=0; j<anzi; j++) {
    411:       brow = aj[j];
    412:       bnzj = bi[brow+1] - bi[brow];
    413:       bj   = b->j + bi[brow];
    414:       /* add non-zero cols of B into the sorted linked list lnk */
    415:       PetscLLCondensedAddSorted_Scalable(bnzj,bj,lnk);
    416:     }
    417:     cnzi = lnk[0];

    419:     /* If free space is not available, make more free space */
    420:     /* Double the amount of total space in the list */
    421:     if (current_space->local_remaining<cnzi) {
    422:       PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);
    423:       ndouble++;
    424:     }

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

    429:     current_space->array           += cnzi;
    430:     current_space->local_used      += cnzi;
    431:     current_space->local_remaining -= cnzi;

    433:     ci[i+1] = ci[i] + cnzi;
    434:   }

    436:   /* Column indices are in the list of free space */
    437:   /* Allocate space for cj, initialize cj, and */
    438:   /* destroy list of free space and other temporary array(s) */
    439:   PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);
    440:   PetscFreeSpaceContiguous(&free_space,cj);
    441:   PetscLLCondensedDestroy_Scalable(lnk);

    443:   /* Allocate space for ca */
    444:   /*-----------------------*/
    445:   PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);
    446:   PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));

    448:   /* put together the new symbolic matrix */
    449:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);

    451:   (*C)->rmap->bs = A->rmap->bs;
    452:   (*C)->cmap->bs = B->cmap->bs;

    454:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    455:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
    456:   c          = (Mat_SeqAIJ*)((*C)->data);
    457:   c->free_a  = PETSC_TRUE;
    458:   c->free_ij = PETSC_TRUE;
    459:   c->nonew   = 0;

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

    463:   /* set MatInfo */
    464:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
    465:   if (afill < 1.0) afill = 1.0;
    466:   c->maxnz                     = ci[am];
    467:   c->nz                        = ci[am];
    468:   (*C)->info.mallocs           = ndouble;
    469:   (*C)->info.fill_ratio_given  = fill;
    470:   (*C)->info.fill_ratio_needed = afill;

    472: #if defined(PETSC_USE_INFO)
    473:   if (ci[am]) {
    474:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);
    475:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);
    476:   } else {
    477:     PetscInfo((*C),"Empty matrix product\n");
    478:   }
    479: #endif
    480:   return(0);
    481: }

    485: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat A,Mat B,PetscReal fill,Mat *C)
    486: {
    487:   PetscErrorCode     ierr;
    488:   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
    489:   const PetscInt     *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j;
    490:   PetscInt           *ci,*cj,*bb;
    491:   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
    492:   PetscReal          afill;
    493:   PetscInt           i,j,col,ndouble = 0;
    494:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
    495:   PetscHeap          h;

    498:   /* Get ci and cj - by merging sorted rows using a heap */
    499:   /*---------------------------------------------------------------------------------------------*/
    500:   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
    501:   PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);
    502:   ci[0] = 0;

    504:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
    505:   PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);
    506:   current_space = free_space;

    508:   PetscHeapCreate(a->rmax,&h);
    509:   PetscMalloc(a->rmax*sizeof(PetscInt),&bb);

    511:   /* Determine ci and cj */
    512:   for (i=0; i<am; i++) {
    513:     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 */
    514:     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
    515:     ci[i+1] = ci[i];
    516:     /* Populate the min heap */
    517:     for (j=0; j<anzi; j++) {
    518:       bb[j] = bi[acol[j]];         /* bb points at the start of the row */
    519:       if (bb[j] < bi[acol[j]+1]) { /* Add if row is nonempty */
    520:         PetscHeapAdd(h,j,bj[bb[j]++]);
    521:       }
    522:     }
    523:     /* Pick off the min element, adding it to free space */
    524:     PetscHeapPop(h,&j,&col);
    525:     while (j >= 0) {
    526:       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
    527:         PetscFreeSpaceGet(PetscMin(2*current_space->total_array_size,16 << 20),&current_space);
    528:         ndouble++;
    529:       }
    530:       *(current_space->array++) = col;
    531:       current_space->local_used++;
    532:       current_space->local_remaining--;
    533:       ci[i+1]++;

    535:       /* stash if anything else remains in this row of B */
    536:       if (bb[j] < bi[acol[j]+1]) {PetscHeapStash(h,j,bj[bb[j]++]);}
    537:       while (1) {               /* pop and stash any other rows of B that also had an entry in this column */
    538:         PetscInt j2,col2;
    539:         PetscHeapPeek(h,&j2,&col2);
    540:         if (col2 != col) break;
    541:         PetscHeapPop(h,&j2,&col2);
    542:         if (bb[j2] < bi[acol[j2]+1]) {PetscHeapStash(h,j2,bj[bb[j2]++]);}
    543:       }
    544:       /* Put any stashed elements back into the min heap */
    545:       PetscHeapUnstash(h);
    546:       PetscHeapPop(h,&j,&col);
    547:     }
    548:   }
    549:   PetscFree(bb);
    550:   PetscHeapDestroy(&h);

    552:   /* Column indices are in the list of free space */
    553:   /* Allocate space for cj, initialize cj, and */
    554:   /* destroy list of free space and other temporary array(s) */
    555:   PetscMalloc(ci[am]*sizeof(PetscInt),&cj);
    556:   PetscFreeSpaceContiguous(&free_space,cj);

    558:   /* put together the new symbolic matrix */
    559:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);

    561:   (*C)->rmap->bs = A->rmap->bs;
    562:   (*C)->cmap->bs = B->cmap->bs;

    564:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    565:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
    566:   c          = (Mat_SeqAIJ*)((*C)->data);
    567:   c->free_a  = PETSC_TRUE;
    568:   c->free_ij = PETSC_TRUE;
    569:   c->nonew   = 0;

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

    573:   /* set MatInfo */
    574:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
    575:   if (afill < 1.0) afill = 1.0;
    576:   c->maxnz                     = ci[am];
    577:   c->nz                        = ci[am];
    578:   (*C)->info.mallocs           = ndouble;
    579:   (*C)->info.fill_ratio_given  = fill;
    580:   (*C)->info.fill_ratio_needed = afill;

    582: #if defined(PETSC_USE_INFO)
    583:   if (ci[am]) {
    584:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);
    585:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);
    586:   } else {
    587:     PetscInfo((*C),"Empty matrix product\n");
    588:   }
    589: #endif
    590:   return(0);
    591: }

    595: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(Mat A,Mat B,PetscReal fill,Mat *C)
    596: {
    597:   PetscErrorCode     ierr;
    598:   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
    599:   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
    600:   PetscInt           *ci,*cj,*bb;
    601:   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
    602:   PetscReal          afill;
    603:   PetscInt           i,j,col,ndouble = 0;
    604:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
    605:   PetscHeap          h;
    606:   PetscBT            bt;

    609:   /* Get ci and cj - using a heap for the sorted rows, but use BT so that each index is only added once */
    610:   /*---------------------------------------------------------------------------------------------*/
    611:   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
    612:   PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);
    613:   ci[0] = 0;

    615:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
    616:   PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);

    618:   current_space = free_space;

    620:   PetscHeapCreate(a->rmax,&h);
    621:   PetscMalloc(a->rmax*sizeof(PetscInt),&bb);
    622:   PetscBTCreate(bn,&bt);

    624:   /* Determine ci and cj */
    625:   for (i=0; i<am; i++) {
    626:     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 */
    627:     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
    628:     const PetscInt *fptr = current_space->array; /* Save beginning of the row so we can clear the BT later */
    629:     ci[i+1] = ci[i];
    630:     /* Populate the min heap */
    631:     for (j=0; j<anzi; j++) {
    632:       PetscInt brow = acol[j];
    633:       for (bb[j] = bi[brow]; bb[j] < bi[brow+1]; bb[j]++) {
    634:         PetscInt bcol = bj[bb[j]];
    635:         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
    636:           PetscHeapAdd(h,j,bcol);
    637:           bb[j]++;
    638:           break;
    639:         }
    640:       }
    641:     }
    642:     /* Pick off the min element, adding it to free space */
    643:     PetscHeapPop(h,&j,&col);
    644:     while (j >= 0) {
    645:       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
    646:         fptr = NULL;                      /* need PetscBTMemzero */
    647:         PetscFreeSpaceGet(PetscMin(2*current_space->total_array_size,16 << 20),&current_space);
    648:         ndouble++;
    649:       }
    650:       *(current_space->array++) = col;
    651:       current_space->local_used++;
    652:       current_space->local_remaining--;
    653:       ci[i+1]++;

    655:       /* stash if anything else remains in this row of B */
    656:       for (; bb[j] < bi[acol[j]+1]; bb[j]++) {
    657:         PetscInt bcol = bj[bb[j]];
    658:         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
    659:           PetscHeapAdd(h,j,bcol);
    660:           bb[j]++;
    661:           break;
    662:         }
    663:       }
    664:       PetscHeapPop(h,&j,&col);
    665:     }
    666:     if (fptr) {                 /* Clear the bits for this row */
    667:       for (; fptr<current_space->array; fptr++) {PetscBTClear(bt,*fptr);}
    668:     } else {                    /* We reallocated so we don't remember (easily) how to clear only the bits we changed */
    669:       PetscBTMemzero(bn,bt);
    670:     }
    671:   }
    672:   PetscFree(bb);
    673:   PetscHeapDestroy(&h);
    674:   PetscBTDestroy(&bt);

    676:   /* Column indices are in the list of free space */
    677:   /* Allocate space for cj, initialize cj, and */
    678:   /* destroy list of free space and other temporary array(s) */
    679:   PetscMalloc(ci[am]*sizeof(PetscInt),&cj);
    680:   PetscFreeSpaceContiguous(&free_space,cj);

    682:   /* put together the new symbolic matrix */
    683:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);

    685:   (*C)->rmap->bs = A->rmap->bs;
    686:   (*C)->cmap->bs = B->cmap->bs;

    688:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    689:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
    690:   c          = (Mat_SeqAIJ*)((*C)->data);
    691:   c->free_a  = PETSC_TRUE;
    692:   c->free_ij = PETSC_TRUE;
    693:   c->nonew   = 0;

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

    697:   /* set MatInfo */
    698:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
    699:   if (afill < 1.0) afill = 1.0;
    700:   c->maxnz                     = ci[am];
    701:   c->nz                        = ci[am];
    702:   (*C)->info.mallocs           = ndouble;
    703:   (*C)->info.fill_ratio_given  = fill;
    704:   (*C)->info.fill_ratio_needed = afill;

    706: #if defined(PETSC_USE_INFO)
    707:   if (ci[am]) {
    708:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);
    709:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);
    710:   } else {
    711:     PetscInfo((*C),"Empty matrix product\n");
    712:   }
    713: #endif
    714:   return(0);
    715: }

    719: /* concatenate unique entries and then sort */
    720: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
    721: {
    722:   PetscErrorCode     ierr;
    723:   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
    724:   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
    725:   PetscInt           *ci,*cj;
    726:   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
    727:   PetscReal          afill;
    728:   PetscInt           i,j,ndouble = 0;
    729:   PetscSegBuffer     seg,segrow;
    730:   char               *seen;

    733:   PetscMalloc((am+1)*sizeof(PetscInt),&ci);
    734:   ci[0] = 0;

    736:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
    737:   PetscSegBufferCreate(sizeof(PetscInt),(PetscInt)(fill*(ai[am]+bi[bm])),&seg);
    738:   PetscSegBufferCreate(sizeof(PetscInt),100,&segrow);
    739:   PetscMalloc(bn*sizeof(char),&seen);
    740:   PetscMemzero(seen,bn*sizeof(char));

    742:   /* Determine ci and cj */
    743:   for (i=0; i<am; i++) {
    744:     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 */
    745:     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
    746:     PetscInt packlen = 0,*PETSC_RESTRICT crow;
    747:     /* Pack segrow */
    748:     for (j=0; j<anzi; j++) {
    749:       PetscInt brow = acol[j],bjstart = bi[brow],bjend = bi[brow+1],k;
    750:       for (k=bjstart; k<bjend; k++) {
    751:         PetscInt bcol = bj[k];
    752:         if (!seen[bcol]) { /* new entry */
    753:           PetscInt *PETSC_RESTRICT slot;
    754:           PetscSegBufferGetInts(segrow,1,&slot);
    755:           *slot = bcol;
    756:           seen[bcol] = 1;
    757:           packlen++;
    758:         }
    759:       }
    760:     }
    761:     PetscSegBufferGetInts(seg,packlen,&crow);
    762:     PetscSegBufferExtractTo(segrow,crow);
    763:     PetscSortInt(packlen,crow);
    764:     ci[i+1] = ci[i] + packlen;
    765:     for (j=0; j<packlen; j++) seen[crow[j]] = 0;
    766:   }
    767:   PetscSegBufferDestroy(&segrow);
    768:   PetscFree(seen);

    770:   /* Column indices are in the segmented buffer */
    771:   PetscSegBufferExtractAlloc(seg,&cj);
    772:   PetscSegBufferDestroy(&seg);

    774:   /* put together the new symbolic matrix */
    775:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);

    777:   (*C)->rmap->bs = A->rmap->bs;
    778:   (*C)->cmap->bs = B->cmap->bs;

    780:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    781:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
    782:   c          = (Mat_SeqAIJ*)((*C)->data);
    783:   c->free_a  = PETSC_TRUE;
    784:   c->free_ij = PETSC_TRUE;
    785:   c->nonew   = 0;

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

    789:   /* set MatInfo */
    790:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
    791:   if (afill < 1.0) afill = 1.0;
    792:   c->maxnz                     = ci[am];
    793:   c->nz                        = ci[am];
    794:   (*C)->info.mallocs           = ndouble;
    795:   (*C)->info.fill_ratio_given  = fill;
    796:   (*C)->info.fill_ratio_needed = afill;

    798: #if defined(PETSC_USE_INFO)
    799:   if (ci[am]) {
    800:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);
    801:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);
    802:   } else {
    803:     PetscInfo((*C),"Empty matrix product\n");
    804:   }
    805: #endif
    806:   return(0);
    807: }

    809: /* This routine is not used. Should be removed! */
    812: PetscErrorCode MatMatTransposeMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
    813: {

    817:   if (scall == MAT_INITIAL_MATRIX) {
    818:     PetscLogEventBegin(MAT_MatTransposeMultSymbolic,A,B,0,0);
    819:     MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);
    820:     PetscLogEventEnd(MAT_MatTransposeMultSymbolic,A,B,0,0);
    821:   }
    822:   PetscLogEventBegin(MAT_MatTransposeMultNumeric,A,B,0,0);
    823:   MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);
    824:   PetscLogEventEnd(MAT_MatTransposeMultNumeric,A,B,0,0);
    825:   return(0);
    826: }

    830: PetscErrorCode PetscContainerDestroy_Mat_MatMatTransMult(void *ptr)
    831: {
    832:   PetscErrorCode      ierr;
    833:   Mat_MatMatTransMult *multtrans=(Mat_MatMatTransMult*)ptr;

    836:   MatTransposeColoringDestroy(&multtrans->matcoloring);
    837:   MatDestroy(&multtrans->Bt_den);
    838:   MatDestroy(&multtrans->ABt_den);
    839:   PetscFree(multtrans);
    840:   return(0);
    841: }

    845: PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(Mat A)
    846: {
    847:   PetscErrorCode      ierr;
    848:   PetscContainer      container;
    849:   Mat_MatMatTransMult *multtrans=NULL;

    852:   PetscObjectQuery((PetscObject)A,"Mat_MatMatTransMult",(PetscObject*)&container);
    853:   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
    854:   PetscContainerGetPointer(container,(void**)&multtrans);

    856:   A->ops->destroy = multtrans->destroy;
    857:   if (A->ops->destroy) {
    858:     (*A->ops->destroy)(A);
    859:   }
    860:   PetscObjectCompose((PetscObject)A,"Mat_MatMatTransMult",0);
    861:   return(0);
    862: }

    866: PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
    867: {
    868:   PetscErrorCode      ierr;
    869:   Mat                 Bt;
    870:   PetscInt            *bti,*btj;
    871:   Mat_MatMatTransMult *multtrans;
    872:   PetscContainer      container;

    875:   /* create symbolic Bt */
    876:   MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);
    877:   MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,NULL,&Bt);

    879:   Bt->rmap->bs = A->cmap->bs;
    880:   Bt->cmap->bs = B->cmap->bs;

    882:   /* get symbolic C=A*Bt */
    883:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);

    885:   /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */
    886:   PetscNew(Mat_MatMatTransMult,&multtrans);

    888:   /* attach the supporting struct to C */
    889:   PetscContainerCreate(PETSC_COMM_SELF,&container);
    890:   PetscContainerSetPointer(container,multtrans);
    891:   PetscContainerSetUserDestroy(container,PetscContainerDestroy_Mat_MatMatTransMult);
    892:   PetscObjectCompose((PetscObject)(*C),"Mat_MatMatTransMult",(PetscObject)container);
    893:   PetscContainerDestroy(&container);

    895:   multtrans->usecoloring = PETSC_FALSE;
    896:   multtrans->destroy     = (*C)->ops->destroy;
    897:   (*C)->ops->destroy     = MatDestroy_SeqAIJ_MatMatMultTrans;

    899:   PetscOptionsGetBool(NULL,"-matmattransmult_color",&multtrans->usecoloring,NULL);
    900:   if (multtrans->usecoloring) {
    901:     /* Create MatTransposeColoring from symbolic C=A*B^T */
    902:     MatTransposeColoring matcoloring;
    903:     ISColoring           iscoloring;
    904:     Mat                  Bt_dense,C_dense;

    906:     MatGetColoring(*C,MATCOLORINGLF,&iscoloring);
    907:     MatTransposeColoringCreate(*C,iscoloring,&matcoloring);

    909:     multtrans->matcoloring = matcoloring;

    911:     ISColoringDestroy(&iscoloring);

    913:     /* Create Bt_dense and C_dense = A*Bt_dense */
    914:     MatCreate(PETSC_COMM_SELF,&Bt_dense);
    915:     MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);
    916:     MatSetType(Bt_dense,MATSEQDENSE);
    917:     MatSeqDenseSetPreallocation(Bt_dense,NULL);

    919:     Bt_dense->assembled = PETSC_TRUE;
    920:     multtrans->Bt_den   = Bt_dense;

    922:     MatCreate(PETSC_COMM_SELF,&C_dense);
    923:     MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);
    924:     MatSetType(C_dense,MATSEQDENSE);
    925:     MatSeqDenseSetPreallocation(C_dense,NULL);

    927:     Bt_dense->assembled = PETSC_TRUE;
    928:     multtrans->ABt_den  = C_dense;

    930: #if defined(PETSC_USE_INFO)
    931:     {
    932:       Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*C)->data;
    933:       PetscInfo5(*C,"Bt_dense: %D,%D; Cnz %D / (cm*ncolors %D) = %g\n",A->cmap->n,matcoloring->ncolors,c->nz,A->rmap->n*matcoloring->ncolors,(PetscReal)(c->nz)/(A->rmap->n*matcoloring->ncolors));
    934:     }
    935: #endif
    936:   }
    937:   /* clean up */
    938:   MatDestroy(&Bt);
    939:   MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);

    943: #if defined(INEFFICIENT_ALGORITHM)
    944:   /* The algorithm below computes am*bm sparse inner-product - inefficient! It will be deleted later. */
    945:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
    946:   Mat_SeqAIJ         *a        =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
    947:   PetscInt           *ai       =a->i,*aj=a->j,*bi=b->i,*bj=b->j,*ci,*cj,*acol,*bcol;
    948:   PetscInt           am        =A->rmap->N,bm=B->rmap->N;
    949:   PetscInt           i,j,anzi,bnzj,cnzi,nlnk,*lnk,nspacedouble=0,ka,kb,index[1];
    950:   MatScalar          *ca;
    951:   PetscBT            lnkbt;
    952:   PetscReal          afill;

    954:   /* Allocate row pointer array ci  */
    955:   PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);
    956:   ci[0] = 0;

    958:   /* Create and initialize a linked list for C columns */
    959:   nlnk = bm+1;
    960:   PetscLLCreate(bm,bm,nlnk,lnk,lnkbt);

    962:   /* Initial FreeSpace with size fill*(nnz(A)+nnz(B)) */
    963:   PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);
    964:   current_space = free_space;

    966:   /* Determine symbolic info for each row of the product A*B^T: */
    967:   for (i=0; i<am; i++) {
    968:     anzi = ai[i+1] - ai[i];
    969:     cnzi = 0;
    970:     acol = aj + ai[i];
    971:     for (j=0; j<bm; j++) {
    972:       bnzj = bi[j+1] - bi[j];
    973:       bcol = bj + bi[j];
    974:       /* sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
    975:       ka = 0; kb = 0;
    976:       while (ka < anzi && kb < bnzj) {
    977:         while (acol[ka] < bcol[kb] && ka < anzi) ka++;
    978:         if (ka == anzi) break;
    979:         while (acol[ka] > bcol[kb] && kb < bnzj) kb++;
    980:         if (kb == bnzj) break;
    981:         if (acol[ka] == bcol[kb]) { /* add nonzero c(i,j) to lnk */
    982:           index[0] = j;
    983:           PetscLLAdd(1,index,bm,nlnk,lnk,lnkbt);
    984:           cnzi++;
    985:           break;
    986:         }
    987:       }
    988:     }

    990:     /* If free space is not available, make more free space */
    991:     /* Double the amount of total space in the list */
    992:     if (current_space->local_remaining<cnzi) {
    993:       PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);
    994:       nspacedouble++;
    995:     }

    997:     /* Copy data into free space, then initialize lnk */
    998:     PetscLLClean(bm,bm,cnzi,lnk,current_space->array,lnkbt);

    1000:     current_space->array           += cnzi;
    1001:     current_space->local_used      += cnzi;
    1002:     current_space->local_remaining -= cnzi;

    1004:     ci[i+1] = ci[i] + cnzi;
    1005:   }

    1008:   /* Column indices are in the list of free space.
    1009:      Allocate array cj, copy column indices to cj, and destroy list of free space */
    1010:   PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);
    1011:   PetscFreeSpaceContiguous(&free_space,cj);
    1012:   PetscLLDestroy(lnk,lnkbt);

    1014:   /* Allocate space for ca */
    1015:   PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);
    1016:   PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));

    1018:   /* put together the new symbolic matrix */
    1019:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bm,ci,cj,ca,C);

    1021:   (*C)->rmap->bs = A->cmap->bs;
    1022:   (*C)->cmap->bs = B->cmap->bs;

    1024:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    1025:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
    1026:   c          = (Mat_SeqAIJ*)((*C)->data);
    1027:   c->free_a  = PETSC_TRUE;
    1028:   c->free_ij = PETSC_TRUE;
    1029:   c->nonew   = 0;

    1031:   /* set MatInfo */
    1032:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
    1033:   if (afill < 1.0) afill = 1.0;
    1034:   c->maxnz                     = ci[am];
    1035:   c->nz                        = ci[am];
    1036:   (*C)->info.mallocs           = nspacedouble;
    1037:   (*C)->info.fill_ratio_given  = fill;
    1038:   (*C)->info.fill_ratio_needed = afill;

    1040: #if defined(PETSC_USE_INFO)
    1041:   if (ci[am]) {
    1042:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);
    1043:     PetscInfo1((*C),"Use MatMatTransposeMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);
    1044:   } else {
    1045:     PetscInfo((*C),"Empty matrix product\n");
    1046:   }
    1047: #endif
    1048: #endif
    1049:   return(0);
    1050: }

    1052: /* #define USE_ARRAY - for sparse dot product. Slower than !USE_ARRAY */
    1055: PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
    1056: {
    1057:   PetscErrorCode      ierr;
    1058:   Mat_SeqAIJ          *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
    1059:   PetscInt            *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
    1060:   PetscInt            cm   =C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
    1061:   PetscLogDouble      flops=0.0;
    1062:   MatScalar           *aa  =a->a,*aval,*ba=b->a,*bval,*ca,*cval;
    1063:   Mat_MatMatTransMult *multtrans;
    1064:   PetscContainer      container;
    1065: #if defined(USE_ARRAY)
    1066:   MatScalar *spdot;
    1067: #endif

    1070:   /* clear old values in C */
    1071:   if (!c->a) {
    1072:     PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);
    1073:     c->a      = ca;
    1074:     c->free_a = PETSC_TRUE;
    1075:   } else {
    1076:     ca =  c->a;
    1077:   }
    1078:   PetscMemzero(ca,ci[cm]*sizeof(MatScalar));

    1080:   PetscObjectQuery((PetscObject)C,"Mat_MatMatTransMult",(PetscObject*)&container);
    1081:   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
    1082:   PetscContainerGetPointer(container,(void**)&multtrans);
    1083:   if (multtrans->usecoloring) {
    1084:     MatTransposeColoring matcoloring = multtrans->matcoloring;
    1085:     Mat                  Bt_dense;
    1086:     PetscInt             m,n;
    1087:     Mat                  C_dense = multtrans->ABt_den;

    1089:     Bt_dense = multtrans->Bt_den;
    1090:     MatGetLocalSize(Bt_dense,&m,&n);

    1092:     /* Get Bt_dense by Apply MatTransposeColoring to B */
    1093:     MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);

    1095:     /* C_dense = A*Bt_dense */
    1096:     MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);

    1098:     /* Recover C from C_dense */
    1099:     MatTransColoringApplyDenToSp(matcoloring,C_dense,C);
    1100:     return(0);
    1101:   }

    1103: #if defined(USE_ARRAY)
    1104:   /* allocate an array for implementing sparse inner-product */
    1105:   PetscMalloc((A->cmap->n+1)*sizeof(MatScalar),&spdot);
    1106:   PetscMemzero(spdot,(A->cmap->n+1)*sizeof(MatScalar));
    1107: #endif

    1109:   for (i=0; i<cm; i++) {
    1110:     anzi = ai[i+1] - ai[i];
    1111:     acol = aj + ai[i];
    1112:     aval = aa + ai[i];
    1113:     cnzi = ci[i+1] - ci[i];
    1114:     ccol = cj + ci[i];
    1115:     cval = ca + ci[i];
    1116:     for (j=0; j<cnzi; j++) {
    1117:       brow = ccol[j];
    1118:       bnzj = bi[brow+1] - bi[brow];
    1119:       bcol = bj + bi[brow];
    1120:       bval = ba + bi[brow];

    1122:       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
    1123: #if defined(USE_ARRAY)
    1124:       /* put ba to spdot array */
    1125:       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = bval[nextb];
    1126:       /* c(i,j)=A[i,:]*B[j,:]^T */
    1127:       for (nexta=0; nexta<anzi; nexta++) {
    1128:         cval[j] += spdot[acol[nexta]]*aval[nexta];
    1129:       }
    1130:       /* zero spdot array */
    1131:       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = 0.0;
    1132: #else
    1133:       nexta = 0; nextb = 0;
    1134:       while (nexta<anzi && nextb<bnzj) {
    1135:         while (nexta < anzi && acol[nexta] < bcol[nextb]) nexta++;
    1136:         if (nexta == anzi) break;
    1137:         while (nextb < bnzj && acol[nexta] > bcol[nextb]) nextb++;
    1138:         if (nextb == bnzj) break;
    1139:         if (acol[nexta] == bcol[nextb]) {
    1140:           cval[j] += aval[nexta]*bval[nextb];
    1141:           nexta++; nextb++;
    1142:           flops += 2;
    1143:         }
    1144:       }
    1145: #endif
    1146:     }
    1147:   }
    1148:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1149:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    1150:   PetscLogFlops(flops);
    1151: #if defined(USE_ARRAY)
    1152:   PetscFree(spdot);
    1153: #endif
    1154:   return(0);
    1155: }

    1159: PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
    1160: {

    1164:   if (scall == MAT_INITIAL_MATRIX) {
    1165:     MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);
    1166:   }
    1167:   MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);
    1168:   return(0);
    1169: }

    1173: PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
    1174: {
    1176:   Mat            At;
    1177:   PetscInt       *ati,*atj;

    1180:   /* create symbolic At */
    1181:   MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);
    1182:   MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,NULL,&At);

    1184:   At->rmap->bs = A->cmap->bs;
    1185:   At->cmap->bs = B->cmap->bs;

    1187:   /* get symbolic C=At*B */
    1188:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);

    1190:   /* clean up */
    1191:   MatDestroy(&At);
    1192:   MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);
    1193:   return(0);
    1194: }

    1198: PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
    1199: {
    1201:   Mat_SeqAIJ     *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
    1202:   PetscInt       am   =A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
    1203:   PetscInt       cm   =C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
    1204:   PetscLogDouble flops=0.0;
    1205:   MatScalar      *aa  =a->a,*ba,*ca,*caj;

    1208:   if (!c->a) {
    1209:     PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);

    1211:     c->a      = ca;
    1212:     c->free_a = PETSC_TRUE;
    1213:   } else {
    1214:     ca = c->a;
    1215:   }
    1216:   /* clear old values in C */
    1217:   PetscMemzero(ca,ci[cm]*sizeof(MatScalar));

    1219:   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
    1220:   for (i=0; i<am; i++) {
    1221:     bj   = b->j + bi[i];
    1222:     ba   = b->a + bi[i];
    1223:     bnzi = bi[i+1] - bi[i];
    1224:     anzi = ai[i+1] - ai[i];
    1225:     for (j=0; j<anzi; j++) {
    1226:       nextb = 0;
    1227:       crow  = *aj++;
    1228:       cjj   = cj + ci[crow];
    1229:       caj   = ca + ci[crow];
    1230:       /* perform sparse axpy operation.  Note cjj includes bj. */
    1231:       for (k=0; nextb<bnzi; k++) {
    1232:         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
    1233:           caj[k] += (*aa)*(*(ba+nextb));
    1234:           nextb++;
    1235:         }
    1236:       }
    1237:       flops += 2*bnzi;
    1238:       aa++;
    1239:     }
    1240:   }

    1242:   /* Assemble the final matrix and clean up */
    1243:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1244:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    1245:   PetscLogFlops(flops);
    1246:   return(0);
    1247: }

    1251: PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
    1252: {

    1256:   if (scall == MAT_INITIAL_MATRIX) {
    1257:     PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);
    1258:     MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);
    1259:     PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);
    1260:   }
    1261:   PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);
    1262:   MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);
    1263:   PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);
    1264:   return(0);
    1265: }

    1269: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
    1270: {

    1274:   MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);

    1276:   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqDense;
    1277:   return(0);
    1278: }

    1282: PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
    1283: {
    1284:   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
    1286:   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
    1287:   MatScalar      *aa;
    1288:   PetscInt       cm  = C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n;
    1289:   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam;

    1292:   if (!cm || !cn) return(0);
    1293:   if (bm != 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,bm);
    1294:   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);
    1295:   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);
    1296:   MatDenseGetArray(B,&b);
    1297:   MatDenseGetArray(C,&c);
    1298:   b1   = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
    1299:   for (col=0; col<cn-4; col += 4) {  /* over columns of C */
    1300:     colam = col*am;
    1301:     for (i=0; i<am; i++) {        /* over rows of C in those columns */
    1302:       r1 = r2 = r3 = r4 = 0.0;
    1303:       n  = a->i[i+1] - a->i[i];
    1304:       aj = a->j + a->i[i];
    1305:       aa = a->a + a->i[i];
    1306:       for (j=0; j<n; j++) {
    1307:         r1 += (*aa)*b1[*aj];
    1308:         r2 += (*aa)*b2[*aj];
    1309:         r3 += (*aa)*b3[*aj];
    1310:         r4 += (*aa++)*b4[*aj++];
    1311:       }
    1312:       c[colam + i]       = r1;
    1313:       c[colam + am + i]  = r2;
    1314:       c[colam + am2 + i] = r3;
    1315:       c[colam + am3 + i] = r4;
    1316:     }
    1317:     b1 += bm4;
    1318:     b2 += bm4;
    1319:     b3 += bm4;
    1320:     b4 += bm4;
    1321:   }
    1322:   for (; col<cn; col++) {     /* over extra columns of C */
    1323:     for (i=0; i<am; i++) {  /* over rows of C in those columns */
    1324:       r1 = 0.0;
    1325:       n  = a->i[i+1] - a->i[i];
    1326:       aj = a->j + a->i[i];
    1327:       aa = a->a + a->i[i];

    1329:       for (j=0; j<n; j++) {
    1330:         r1 += (*aa++)*b1[*aj++];
    1331:       }
    1332:       c[col*am + i] = r1;
    1333:     }
    1334:     b1 += bm;
    1335:   }
    1336:   PetscLogFlops(cn*(2.0*a->nz));
    1337:   MatDenseRestoreArray(B,&b);
    1338:   MatDenseRestoreArray(C,&c);
    1339:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1340:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    1341:   return(0);
    1342: }

    1344: /*
    1345:    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
    1346: */
    1349: PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
    1350: {
    1351:   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
    1353:   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
    1354:   MatScalar      *aa;
    1355:   PetscInt       cm  = C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
    1356:   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;

    1359:   if (!cm || !cn) return(0);
    1360:   MatDenseGetArray(B,&b);
    1361:   MatDenseGetArray(C,&c);
    1362:   b1   = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;

    1364:   if (a->compressedrow.use) { /* use compressed row format */
    1365:     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
    1366:       colam = col*am;
    1367:       arm   = a->compressedrow.nrows;
    1368:       ii    = a->compressedrow.i;
    1369:       ridx  = a->compressedrow.rindex;
    1370:       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
    1371:         r1 = r2 = r3 = r4 = 0.0;
    1372:         n  = ii[i+1] - ii[i];
    1373:         aj = a->j + ii[i];
    1374:         aa = a->a + ii[i];
    1375:         for (j=0; j<n; j++) {
    1376:           r1 += (*aa)*b1[*aj];
    1377:           r2 += (*aa)*b2[*aj];
    1378:           r3 += (*aa)*b3[*aj];
    1379:           r4 += (*aa++)*b4[*aj++];
    1380:         }
    1381:         c[colam       + ridx[i]] += r1;
    1382:         c[colam + am  + ridx[i]] += r2;
    1383:         c[colam + am2 + ridx[i]] += r3;
    1384:         c[colam + am3 + ridx[i]] += r4;
    1385:       }
    1386:       b1 += bm4;
    1387:       b2 += bm4;
    1388:       b3 += bm4;
    1389:       b4 += bm4;
    1390:     }
    1391:     for (; col<cn; col++) {     /* over extra columns of C */
    1392:       colam = col*am;
    1393:       arm   = a->compressedrow.nrows;
    1394:       ii    = a->compressedrow.i;
    1395:       ridx  = a->compressedrow.rindex;
    1396:       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
    1397:         r1 = 0.0;
    1398:         n  = ii[i+1] - ii[i];
    1399:         aj = a->j + ii[i];
    1400:         aa = a->a + ii[i];

    1402:         for (j=0; j<n; j++) {
    1403:           r1 += (*aa++)*b1[*aj++];
    1404:         }
    1405:         c[colam + ridx[i]] += r1;
    1406:       }
    1407:       b1 += bm;
    1408:     }
    1409:   } else {
    1410:     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
    1411:       colam = col*am;
    1412:       for (i=0; i<am; i++) {        /* over rows of C in those columns */
    1413:         r1 = r2 = r3 = r4 = 0.0;
    1414:         n  = a->i[i+1] - a->i[i];
    1415:         aj = a->j + a->i[i];
    1416:         aa = a->a + a->i[i];
    1417:         for (j=0; j<n; j++) {
    1418:           r1 += (*aa)*b1[*aj];
    1419:           r2 += (*aa)*b2[*aj];
    1420:           r3 += (*aa)*b3[*aj];
    1421:           r4 += (*aa++)*b4[*aj++];
    1422:         }
    1423:         c[colam + i]       += r1;
    1424:         c[colam + am + i]  += r2;
    1425:         c[colam + am2 + i] += r3;
    1426:         c[colam + am3 + i] += r4;
    1427:       }
    1428:       b1 += bm4;
    1429:       b2 += bm4;
    1430:       b3 += bm4;
    1431:       b4 += bm4;
    1432:     }
    1433:     for (; col<cn; col++) {     /* over extra columns of C */
    1434:       colam = col*am;
    1435:       for (i=0; i<am; i++) {  /* over rows of C in those columns */
    1436:         r1 = 0.0;
    1437:         n  = a->i[i+1] - a->i[i];
    1438:         aj = a->j + a->i[i];
    1439:         aa = a->a + a->i[i];

    1441:         for (j=0; j<n; j++) {
    1442:           r1 += (*aa++)*b1[*aj++];
    1443:         }
    1444:         c[colam + i] += r1;
    1445:       }
    1446:       b1 += bm;
    1447:     }
    1448:   }
    1449:   PetscLogFlops(cn*2.0*a->nz);
    1450:   MatDenseRestoreArray(B,&b);
    1451:   MatDenseRestoreArray(C,&c);
    1452:   return(0);
    1453: }

    1457: PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
    1458: {
    1460:   Mat_SeqAIJ     *b       = (Mat_SeqAIJ*)B->data;
    1461:   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
    1462:   PetscInt       *bi      = b->i,*bj=b->j;
    1463:   PetscInt       m        = Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
    1464:   MatScalar      *btval,*btval_den,*ba=b->a;
    1465:   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;

    1468:   btval_den=btdense->v;
    1469:   PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));
    1470:   for (k=0; k<ncolors; k++) {
    1471:     ncolumns = coloring->ncolumns[k];
    1472:     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
    1473:       col   = *(columns + colorforcol[k] + l);
    1474:       btcol = bj + bi[col];
    1475:       btval = ba + bi[col];
    1476:       anz   = bi[col+1] - bi[col];
    1477:       for (j=0; j<anz; j++) {
    1478:         brow            = btcol[j];
    1479:         btval_den[brow] = btval[j];
    1480:       }
    1481:     }
    1482:     btval_den += m;
    1483:   }
    1484:   return(0);
    1485: }

    1489: PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
    1490: {
    1492:   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)Csp->data;
    1493:   PetscInt       k,l,*row,*idx,m,ncolors=matcoloring->ncolors,nrows;
    1494:   PetscScalar    *ca_den,*cp_den,*ca=csp->a;
    1495:   PetscInt       *rows=matcoloring->rows,*spidx=matcoloring->columnsforspidx,*colorforrow=matcoloring->colorforrow;

    1498:   MatGetLocalSize(Csp,&m,NULL);
    1499:   MatDenseGetArray(Cden,&ca_den);
    1500:   cp_den = ca_den;
    1501:   for (k=0; k<ncolors; k++) {
    1502:     nrows = matcoloring->nrows[k];
    1503:     row   = rows  + colorforrow[k];
    1504:     idx   = spidx + colorforrow[k];
    1505:     for (l=0; l<nrows; l++) {
    1506:       ca[idx[l]] = cp_den[row[l]];
    1507:     }
    1508:     cp_den += m;
    1509:   }
    1510:   MatDenseRestoreArray(Cden,&ca_den);
    1511:   return(0);
    1512: }

    1514: /*
    1515:  MatGetColumnIJ_SeqAIJ_Color() and MatRestoreColumnIJ_SeqAIJ_Color() are customized from
    1516:  MatGetColumnIJ_SeqAIJ() and MatRestoreColumnIJ_SeqAIJ() by adding an output
    1517:  spidx[], index of a->j, to be used for setting 'columnsforspidx' in MatTransposeColoringCreate_SeqAIJ().
    1518:  */
    1521: PetscErrorCode MatGetColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *nn,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
    1522: {
    1523:   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
    1525:   PetscInt       i,*collengths,*cia,*cja,n = A->cmap->n,m = A->rmap->n;
    1526:   PetscInt       nz = a->i[m],row,*jj,mr,col;
    1527:   PetscInt       *cspidx;

    1530:   *nn = n;
    1531:   if (!ia) return(0);
    1532:   if (symmetric) {
    1533:     SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"MatGetColumnIJ_SeqAIJ_Color() not supported for the case symmetric");
    1534:     MatToSymmetricIJ_SeqAIJ(A->rmap->n,a->i,a->j,0,oshift,(PetscInt**)ia,(PetscInt**)ja);
    1535:   } else {
    1536:     PetscMalloc((n+1)*sizeof(PetscInt),&collengths);
    1537:     PetscMemzero(collengths,n*sizeof(PetscInt));
    1538:     PetscMalloc((n+1)*sizeof(PetscInt),&cia);
    1539:     PetscMalloc((nz+1)*sizeof(PetscInt),&cja);
    1540:     PetscMalloc((nz+1)*sizeof(PetscInt),&cspidx);
    1541:     jj   = a->j;
    1542:     for (i=0; i<nz; i++) {
    1543:       collengths[jj[i]]++;
    1544:     }
    1545:     cia[0] = oshift;
    1546:     for (i=0; i<n; i++) {
    1547:       cia[i+1] = cia[i] + collengths[i];
    1548:     }
    1549:     PetscMemzero(collengths,n*sizeof(PetscInt));
    1550:     jj   = a->j;
    1551:     for (row=0; row<m; row++) {
    1552:       mr = a->i[row+1] - a->i[row];
    1553:       for (i=0; i<mr; i++) {
    1554:         col = *jj++;

    1556:         cspidx[cia[col] + collengths[col] - oshift] = a->i[row] + i; /* index of a->j */
    1557:         cja[cia[col] + collengths[col]++ - oshift]  = row + oshift;
    1558:       }
    1559:     }
    1560:     PetscFree(collengths);
    1561:     *ia    = cia; *ja = cja;
    1562:     *spidx = cspidx;
    1563:   }
    1564:   return(0);
    1565: }

    1569: PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
    1570: {

    1574:   if (!ia) return(0);

    1576:   PetscFree(*ia);
    1577:   PetscFree(*ja);
    1578:   PetscFree(*spidx);
    1579:   return(0);
    1580: }

    1584: PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
    1585: {
    1587:   PetscInt       i,n,nrows,N,j,k,m,ncols,col,cm;
    1588:   const PetscInt *is,*ci,*cj,*row_idx;
    1589:   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
    1590:   IS             *isa;
    1591:   PetscBool      flg1,flg2;
    1592:   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
    1593:   PetscInt       *colorforrow,*rows,*rows_i,*columnsforspidx,*columnsforspidx_i,*idxhit,*spidx;
    1594:   PetscInt       *colorforcol,*columns,*columns_i;

    1597:   ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);

    1599:   /* this is ugly way to get blocksize but cannot call MatGetBlockSize() because AIJ can have bs > 1 */
    1600:   PetscObjectTypeCompare((PetscObject)mat,MATSEQBAIJ,&flg1);
    1601:   PetscObjectTypeCompare((PetscObject)mat,MATMPIBAIJ,&flg2);
    1602:   if (flg1 || flg2) {
    1603:     MatGetBlockSize(mat,&bs);
    1604:   }

    1606:   N         = mat->cmap->N/bs;
    1607:   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
    1608:   c->N      = mat->cmap->N/bs;
    1609:   c->m      = mat->rmap->N/bs;
    1610:   c->rstart = 0;

    1612:   c->ncolors = nis;
    1613:   PetscMalloc(nis*sizeof(PetscInt),&c->ncolumns);
    1614:   PetscMalloc(nis*sizeof(PetscInt),&c->nrows);
    1615:   PetscMalloc2(csp->nz+1,PetscInt,&rows,csp->nz+1,PetscInt,&columnsforspidx);
    1616:   PetscMalloc((nis+1)*sizeof(PetscInt),&colorforrow);

    1618:   colorforrow[0]    = 0;
    1619:   rows_i            = rows;
    1620:   columnsforspidx_i = columnsforspidx;

    1622:   PetscMalloc((nis+1)*sizeof(PetscInt),&colorforcol);
    1623:   PetscMalloc((N+1)*sizeof(PetscInt),&columns);

    1625:   colorforcol[0] = 0;
    1626:   columns_i      = columns;

    1628:   MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL); /* column-wise storage of mat */

    1630:   cm   = c->m;
    1631:   PetscMalloc((cm+1)*sizeof(PetscInt),&rowhit);
    1632:   PetscMalloc((cm+1)*sizeof(PetscInt),&idxhit);
    1633:   for (i=0; i<nis; i++) {
    1634:     ISGetLocalSize(isa[i],&n);
    1635:     ISGetIndices(isa[i],&is);

    1637:     c->ncolumns[i] = n;
    1638:     if (n) {
    1639:       PetscMemcpy(columns_i,is,n*sizeof(PetscInt));
    1640:     }
    1641:     colorforcol[i+1] = colorforcol[i] + n;
    1642:     columns_i       += n;

    1644:     /* fast, crude version requires O(N*N) work */
    1645:     PetscMemzero(rowhit,cm*sizeof(PetscInt));

    1647:     /* loop over columns*/
    1648:     for (j=0; j<n; j++) {
    1649:       col     = is[j];
    1650:       row_idx = cj + ci[col];
    1651:       m       = ci[col+1] - ci[col];
    1652:       /* loop over columns marking them in rowhit */
    1653:       for (k=0; k<m; k++) {
    1654:         idxhit[*row_idx]   = spidx[ci[col] + k];
    1655:         rowhit[*row_idx++] = col + 1;
    1656:       }
    1657:     }
    1658:     /* count the number of hits */
    1659:     nrows = 0;
    1660:     for (j=0; j<cm; j++) {
    1661:       if (rowhit[j]) nrows++;
    1662:     }
    1663:     c->nrows[i]      = nrows;
    1664:     colorforrow[i+1] = colorforrow[i] + nrows;

    1666:     nrows = 0;
    1667:     for (j=0; j<cm; j++) {
    1668:       if (rowhit[j]) {
    1669:         rows_i[nrows]            = j;
    1670:         columnsforspidx_i[nrows] = idxhit[j];
    1671:         nrows++;
    1672:       }
    1673:     }
    1674:     ISRestoreIndices(isa[i],&is);
    1675:     rows_i += nrows; columnsforspidx_i += nrows;
    1676:   }
    1677:   MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);
    1678:   PetscFree(rowhit);
    1679:   ISColoringRestoreIS(iscoloring,&isa);
    1680: #if defined(PETSC_USE_DEBUG)
    1681:   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);
    1682: #endif

    1684:   c->colorforrow     = colorforrow;
    1685:   c->rows            = rows;
    1686:   c->columnsforspidx = columnsforspidx;
    1687:   c->colorforcol     = colorforcol;
    1688:   c->columns         = columns;

    1690:   PetscFree(idxhit);
    1691:   return(0);
    1692: }