Date: 2022-03-04T17:37:43+00:00

Actual source code: matptap.c

      2: /*
      3:   Defines projective product routines where A is a SeqAIJ matrix
      4:           C = P^T * A * P
      5: */

      7: #include <../src/mat/impls/aij/seq/aij.h>
      8: #include <../src/mat/utils/freespace.h>
      9: #include <petscbt.h>
     10: #include <petsctime.h>

     12: #if defined(PETSC_HAVE_HYPRE)
     13: PETSC_INTERN PetscErrorCode MatPtAPSymbolic_AIJ_AIJ_wHYPRE(Mat,Mat,PetscReal,Mat);
     14: #endif

     16: PetscErrorCode MatProductSymbolic_PtAP_SeqAIJ_SeqAIJ(Mat C)
     17: {
     18:   PetscErrorCode      ierr;
     19:   Mat_Product         *product = C->product;
     20:   Mat                 A=product->A,P=product->B;
     21:   MatProductAlgorithm alg=product->alg;
     22:   PetscReal           fill=product->fill;
     23:   PetscBool           flg;
     24:   Mat                 Pt;

     27:   /* "scalable" */
     28:   PetscStrcmp(alg,"scalable",&flg);
     29:   if (flg) {
     30:     MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(A,P,fill,C);
     31:     C->ops->productnumeric = MatProductNumeric_PtAP;
     32:     return(0);
     33:   }

     35:   /* "rap" */
     36:   PetscStrcmp(alg,"rap",&flg);
     37:   if (flg) {
     38:     Mat_MatTransMatMult *atb;

     40:     PetscNew(&atb);
     41:     MatTranspose_SeqAIJ(P,MAT_INITIAL_MATRIX,&Pt);
     42:     MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ(Pt,A,P,fill,C);

     44:     atb->At                = Pt;
     45:     atb->data              = C->product->data;
     46:     atb->destroy           = C->product->destroy;
     47:     C->product->data       = atb;
     48:     C->product->destroy    = MatDestroy_SeqAIJ_MatTransMatMult;
     49:     C->ops->ptapnumeric    = MatPtAPNumeric_SeqAIJ_SeqAIJ;
     50:     C->ops->productnumeric = MatProductNumeric_PtAP;
     51:     return(0);
     52:   }

     54:   /* hypre */
     55: #if defined(PETSC_HAVE_HYPRE)
     56:   PetscStrcmp(alg,"hypre",&flg);
     57:   if (flg) {
     58:     MatPtAPSymbolic_AIJ_AIJ_wHYPRE(A,P,fill,C);
     59:     return(0);
     60:   }
     61: #endif

     63:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatProductType is not supported");
     64: }

     66: PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,PetscReal fill,Mat C)
     67: {
     68:   PetscErrorCode     ierr;
     69:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
     70:   Mat_SeqAIJ         *a        = (Mat_SeqAIJ*)A->data,*p = (Mat_SeqAIJ*)P->data,*c;
     71:   PetscInt           *pti,*ptj,*ptJ,*ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj;
     72:   PetscInt           *ci,*cj,*ptadenserow,*ptasparserow,*ptaj,nspacedouble=0;
     73:   PetscInt           an=A->cmap->N,am=A->rmap->N,pn=P->cmap->N,pm=P->rmap->N;
     74:   PetscInt           i,j,k,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi,nlnk,*lnk;
     75:   MatScalar          *ca;
     76:   PetscBT            lnkbt;
     77:   PetscReal          afill;

     80:   /* Get ij structure of P^T */
     81:   MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);
     82:   ptJ  = ptj;

     84:   /* Allocate ci array, arrays for fill computation and */
     85:   /* free space for accumulating nonzero column info */
     86:   PetscMalloc1(pn+1,&ci);
     87:   ci[0] = 0;

     89:   PetscCalloc1(2*an+1,&ptadenserow);
     90:   ptasparserow = ptadenserow  + an;

     92:   /* create and initialize a linked list */
     93:   nlnk = pn+1;
     94:   PetscLLCreate(pn,pn,nlnk,lnk,lnkbt);

     96:   /* Set initial free space to be fill*(nnz(A)+ nnz(P)) */
     97:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],pi[pm])),&free_space);
     98:   current_space = free_space;

    100:   /* Determine symbolic info for each row of C: */
    101:   for (i=0; i<pn; i++) {
    102:     ptnzi  = pti[i+1] - pti[i];
    103:     ptanzi = 0;
    104:     /* Determine symbolic row of PtA: */
    105:     for (j=0; j<ptnzi; j++) {
    106:       arow = *ptJ++;
    107:       anzj = ai[arow+1] - ai[arow];
    108:       ajj  = aj + ai[arow];
    109:       for (k=0; k<anzj; k++) {
    110:         if (!ptadenserow[ajj[k]]) {
    111:           ptadenserow[ajj[k]]    = -1;
    112:           ptasparserow[ptanzi++] = ajj[k];
    113:         }
    114:       }
    115:     }
    116:     /* Using symbolic info for row of PtA, determine symbolic info for row of C: */
    117:     ptaj = ptasparserow;
    118:     cnzi = 0;
    119:     for (j=0; j<ptanzi; j++) {
    120:       prow = *ptaj++;
    121:       pnzj = pi[prow+1] - pi[prow];
    122:       pjj  = pj + pi[prow];
    123:       /* add non-zero cols of P into the sorted linked list lnk */
    124:       PetscLLAddSorted(pnzj,pjj,pn,nlnk,lnk,lnkbt);
    125:       cnzi += nlnk;
    126:     }

    128:     /* If free space is not available, make more free space */
    129:     /* Double the amount of total space in the list */
    130:     if (current_space->local_remaining<cnzi) {
    131:       PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);
    132:       nspacedouble++;
    133:     }

    135:     /* Copy data into free space, and zero out denserows */
    136:     PetscLLClean(pn,pn,cnzi,lnk,current_space->array,lnkbt);

    138:     current_space->array           += cnzi;
    139:     current_space->local_used      += cnzi;
    140:     current_space->local_remaining -= cnzi;

    142:     for (j=0; j<ptanzi; j++) ptadenserow[ptasparserow[j]] = 0;

    144:     /* Aside: Perhaps we should save the pta info for the numerical factorization. */
    145:     /*        For now, we will recompute what is needed. */
    146:     ci[i+1] = ci[i] + cnzi;
    147:   }
    148:   /* nnz is now stored in ci[ptm], column indices are in the list of free space */
    149:   /* Allocate space for cj, initialize cj, and */
    150:   /* destroy list of free space and other temporary array(s) */
    151:   PetscMalloc1(ci[pn]+1,&cj);
    152:   PetscFreeSpaceContiguous(&free_space,cj);
    153:   PetscFree(ptadenserow);
    154:   PetscLLDestroy(lnk,lnkbt);

    156:   PetscCalloc1(ci[pn]+1,&ca);

    158:   /* put together the new matrix */
    159:   MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A),pn,pn,ci,cj,ca,((PetscObject)A)->type_name,C);
    160:   MatSetBlockSizes(C,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));

    162:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    163:   /* Since these are PETSc arrays, change flags to free them as necessary. */
    164:   c          = (Mat_SeqAIJ*)((C)->data);
    165:   c->free_a  = PETSC_TRUE;
    166:   c->free_ij = PETSC_TRUE;
    167:   c->nonew   = 0;

    169:   C->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy;

    171:   /* set MatInfo */
    172:   afill = (PetscReal)ci[pn]/(ai[am]+pi[pm] + 1.e-5);
    173:   if (afill < 1.0) afill = 1.0;
    174:   c->maxnz                     = ci[pn];
    175:   c->nz                        = ci[pn];
    176:   C->info.mallocs           = nspacedouble;
    177:   C->info.fill_ratio_given  = fill;
    178:   C->info.fill_ratio_needed = afill;

    180:   /* Clean up. */
    181:   MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);
    182: #if defined(PETSC_USE_INFO)
    183:   if (ci[pn] != 0) {
    184:     PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    185:     PetscInfo1(C,"Use MatPtAP(A,P,MatReuse,%g,&C) for best performance.\n",(double)afill);
    186:   } else {
    187:     PetscInfo(C,"Empty matrix product\n");
    188:   }
    189: #endif
    190:   return(0);
    191: }

    193: PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,Mat C)
    194: {
    196:   Mat_SeqAIJ     *a = (Mat_SeqAIJ*) A->data;
    197:   Mat_SeqAIJ     *p = (Mat_SeqAIJ*) P->data;
    198:   Mat_SeqAIJ     *c = (Mat_SeqAIJ*) C->data;
    199:   PetscInt       *ai=a->i,*aj=a->j,*apj,*apjdense,*pi=p->i,*pj=p->j,*pJ=p->j,*pjj;
    200:   PetscInt       *ci=c->i,*cj=c->j,*cjj;
    201:   PetscInt       am =A->rmap->N,cn=C->cmap->N,cm=C->rmap->N;
    202:   PetscInt       i,j,k,anzi,pnzi,apnzj,nextap,pnzj,prow,crow;
    203:   MatScalar      *aa,*apa,*pa,*pA,*paj,*ca,*caj;

    206:   /* Allocate temporary array for storage of one row of A*P (cn: non-scalable) */
    207:   PetscCalloc2(cn,&apa,cn,&apjdense);
    208:   PetscMalloc1(cn,&apj);
    209:   /* trigger CPU copies if needed and flag CPU mask for C */
    210: #if defined(PETSC_HAVE_DEVICE)
    211:   {
    212:     const PetscScalar *dummy;
    213:     MatSeqAIJGetArrayRead(A,&dummy);
    214:     MatSeqAIJRestoreArrayRead(A,&dummy);
    215:     MatSeqAIJGetArrayRead(P,&dummy);
    216:     MatSeqAIJRestoreArrayRead(P,&dummy);
    217:     if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
    218:   }
    219: #endif
    220:   aa = a->a;
    221:   pa = p->a;
    222:   pA = p->a;
    223:   ca = c->a;

    225:   /* Clear old values in C */
    226:   PetscArrayzero(ca,ci[cm]);

    228:   for (i=0; i<am; i++) {
    229:     /* Form sparse row of A*P */
    230:     anzi  = ai[i+1] - ai[i];
    231:     apnzj = 0;
    232:     for (j=0; j<anzi; j++) {
    233:       prow = *aj++;
    234:       pnzj = pi[prow+1] - pi[prow];
    235:       pjj  = pj + pi[prow];
    236:       paj  = pa + pi[prow];
    237:       for (k=0; k<pnzj; k++) {
    238:         if (!apjdense[pjj[k]]) {
    239:           apjdense[pjj[k]] = -1;
    240:           apj[apnzj++]     = pjj[k];
    241:         }
    242:         apa[pjj[k]] += (*aa)*paj[k];
    243:       }
    244:       PetscLogFlops(2.0*pnzj);
    245:       aa++;
    246:     }

    248:     /* Sort the j index array for quick sparse axpy. */
    249:     /* Note: a array does not need sorting as it is in dense storage locations. */
    250:     PetscSortInt(apnzj,apj);

    252:     /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */
    253:     pnzi = pi[i+1] - pi[i];
    254:     for (j=0; j<pnzi; j++) {
    255:       nextap = 0;
    256:       crow   = *pJ++;
    257:       cjj    = cj + ci[crow];
    258:       caj    = ca + ci[crow];
    259:       /* Perform sparse axpy operation.  Note cjj includes apj. */
    260:       for (k=0; nextap<apnzj; k++) {
    261:         if (PetscUnlikelyDebug(k >= ci[crow+1] - ci[crow])) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"k too large k %d, crow %d",k,crow);
    262:         if (cjj[k]==apj[nextap]) {
    263:           caj[k] += (*pA)*apa[apj[nextap++]];
    264:         }
    265:       }
    266:       PetscLogFlops(2.0*apnzj);
    267:       pA++;
    268:     }

    270:     /* Zero the current row info for A*P */
    271:     for (j=0; j<apnzj; j++) {
    272:       apa[apj[j]]      = 0.;
    273:       apjdense[apj[j]] = 0;
    274:     }
    275:   }

    277:   /* Assemble the final matrix and clean up */
    278:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    279:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

    281:   PetscFree2(apa,apjdense);
    282:   PetscFree(apj);
    283:   return(0);
    284: }

    286: PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat C)
    287: {
    288:   PetscErrorCode      ierr;
    289:   Mat_MatTransMatMult *atb;

    292:   MatCheckProduct(C,3);
    293:   atb  = (Mat_MatTransMatMult*)C->product->data;
    294:   if (!atb) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Missing data structure");
    295:   MatTranspose_SeqAIJ(P,MAT_REUSE_MATRIX,&atb->At);
    296:   if (!C->ops->matmultnumeric) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Missing numeric operation");
    297:   /* when using rap, MatMatMatMultSymbolic used a different data */
    298:   if (atb->data) C->product->data = atb->data;
    299:   (*C->ops->matmatmultnumeric)(atb->At,A,P,C);
    300:   C->product->data = atb;
    301:   return(0);
    302: }