Date: 2022-03-31T04:46:45+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:   Mat_Product         *product = C->product;
     19:   Mat                 A=product->A,P=product->B;
     20:   MatProductAlgorithm alg=product->alg;
     21:   PetscReal           fill=product->fill;
     22:   PetscBool           flg;
     23:   Mat                 Pt;

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

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

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

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

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

     61:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatProductType is not supported");
     62: }

     64: PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,PetscReal fill,Mat C)
     65: {
     66:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
     67:   Mat_SeqAIJ         *a        = (Mat_SeqAIJ*)A->data,*p = (Mat_SeqAIJ*)P->data,*c;
     68:   PetscInt           *pti,*ptj,*ptJ,*ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj;
     69:   PetscInt           *ci,*cj,*ptadenserow,*ptasparserow,*ptaj,nspacedouble=0;
     70:   PetscInt           an=A->cmap->N,am=A->rmap->N,pn=P->cmap->N,pm=P->rmap->N;
     71:   PetscInt           i,j,k,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi,nlnk,*lnk;
     72:   MatScalar          *ca;
     73:   PetscBT            lnkbt;
     74:   PetscReal          afill;

     76:   /* Get ij structure of P^T */
     77:   MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);
     78:   ptJ  = ptj;

     80:   /* Allocate ci array, arrays for fill computation and */
     81:   /* free space for accumulating nonzero column info */
     82:   PetscMalloc1(pn+1,&ci);
     83:   ci[0] = 0;

     85:   PetscCalloc1(2*an+1,&ptadenserow);
     86:   ptasparserow = ptadenserow  + an;

     88:   /* create and initialize a linked list */
     89:   nlnk = pn+1;
     90:   PetscLLCreate(pn,pn,nlnk,lnk,lnkbt);

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

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

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

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

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

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

    140:     /* Aside: Perhaps we should save the pta info for the numerical factorization. */
    141:     /*        For now, we will recompute what is needed. */
    142:     ci[i+1] = ci[i] + cnzi;
    143:   }
    144:   /* nnz is now stored in ci[ptm], column indices are in the list of free space */
    145:   /* Allocate space for cj, initialize cj, and */
    146:   /* destroy list of free space and other temporary array(s) */
    147:   PetscMalloc1(ci[pn]+1,&cj);
    148:   PetscFreeSpaceContiguous(&free_space,cj);
    149:   PetscFree(ptadenserow);
    150:   PetscLLDestroy(lnk,lnkbt);

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

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

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

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

    167:   /* set MatInfo */
    168:   afill = (PetscReal)ci[pn]/(ai[am]+pi[pm] + 1.e-5);
    169:   if (afill < 1.0) afill = 1.0;
    170:   C->info.mallocs           = nspacedouble;
    171:   C->info.fill_ratio_given  = fill;
    172:   C->info.fill_ratio_needed = afill;

    174:   /* Clean up. */
    175:   MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);
    176: #if defined(PETSC_USE_INFO)
    177:   if (ci[pn] != 0) {
    178:     PetscInfo(C,"Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    179:     PetscInfo(C,"Use MatPtAP(A,P,MatReuse,%g,&C) for best performance.\n",(double)afill);
    180:   } else {
    181:     PetscInfo(C,"Empty matrix product\n");
    182:   }
    183: #endif
    184:   return 0;
    185: }

    187: PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,Mat C)
    188: {
    189:   Mat_SeqAIJ     *a = (Mat_SeqAIJ*) A->data;
    190:   Mat_SeqAIJ     *p = (Mat_SeqAIJ*) P->data;
    191:   Mat_SeqAIJ     *c = (Mat_SeqAIJ*) C->data;
    192:   PetscInt       *ai=a->i,*aj=a->j,*apj,*apjdense,*pi=p->i,*pj=p->j,*pJ=p->j,*pjj;
    193:   PetscInt       *ci=c->i,*cj=c->j,*cjj;
    194:   PetscInt       am =A->rmap->N,cn=C->cmap->N,cm=C->rmap->N;
    195:   PetscInt       i,j,k,anzi,pnzi,apnzj,nextap,pnzj,prow,crow;
    196:   MatScalar      *aa,*apa,*pa,*pA,*paj,*ca,*caj;

    198:   /* Allocate temporary array for storage of one row of A*P (cn: non-scalable) */
    199:   PetscCalloc2(cn,&apa,cn,&apjdense);
    200:   PetscMalloc1(cn,&apj);
    201:   /* trigger CPU copies if needed and flag CPU mask for C */
    202: #if defined(PETSC_HAVE_DEVICE)
    203:   {
    204:     const PetscScalar *dummy;
    205:     MatSeqAIJGetArrayRead(A,&dummy);
    206:     MatSeqAIJRestoreArrayRead(A,&dummy);
    207:     MatSeqAIJGetArrayRead(P,&dummy);
    208:     MatSeqAIJRestoreArrayRead(P,&dummy);
    209:     if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
    210:   }
    211: #endif
    212:   aa = a->a;
    213:   pa = p->a;
    214:   pA = p->a;
    215:   ca = c->a;

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

    220:   for (i=0; i<am; i++) {
    221:     /* Form sparse row of A*P */
    222:     anzi  = ai[i+1] - ai[i];
    223:     apnzj = 0;
    224:     for (j=0; j<anzi; j++) {
    225:       prow = *aj++;
    226:       pnzj = pi[prow+1] - pi[prow];
    227:       pjj  = pj + pi[prow];
    228:       paj  = pa + pi[prow];
    229:       for (k=0; k<pnzj; k++) {
    230:         if (!apjdense[pjj[k]]) {
    231:           apjdense[pjj[k]] = -1;
    232:           apj[apnzj++]     = pjj[k];
    233:         }
    234:         apa[pjj[k]] += (*aa)*paj[k];
    235:       }
    236:       PetscLogFlops(2.0*pnzj);
    237:       aa++;
    238:     }

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

    244:     /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */
    245:     pnzi = pi[i+1] - pi[i];
    246:     for (j=0; j<pnzi; j++) {
    247:       nextap = 0;
    248:       crow   = *pJ++;
    249:       cjj    = cj + ci[crow];
    250:       caj    = ca + ci[crow];
    251:       /* Perform sparse axpy operation.  Note cjj includes apj. */
    252:       for (k=0; nextap<apnzj; k++) {
    253:         PetscAssert(k < ci[crow+1] - ci[crow],PETSC_COMM_SELF,PETSC_ERR_PLIB,"k too large k %" PetscInt_FMT ", crow %" PetscInt_FMT,k,crow);
    254:         if (cjj[k]==apj[nextap]) {
    255:           caj[k] += (*pA)*apa[apj[nextap++]];
    256:         }
    257:       }
    258:       PetscLogFlops(2.0*apnzj);
    259:       pA++;
    260:     }

    262:     /* Zero the current row info for A*P */
    263:     for (j=0; j<apnzj; j++) {
    264:       apa[apj[j]]      = 0.;
    265:       apjdense[apj[j]] = 0;
    266:     }
    267:   }

    269:   /* Assemble the final matrix and clean up */
    270:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    271:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

    273:   PetscFree2(apa,apjdense);
    274:   PetscFree(apj);
    275:   return 0;
    276: }

    278: PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat C)
    279: {
    280:   Mat_MatTransMatMult *atb;

    282:   MatCheckProduct(C,3);
    283:   atb  = (Mat_MatTransMatMult*)C->product->data;
    285:   MatTranspose_SeqAIJ(P,MAT_REUSE_MATRIX,&atb->At);
    287:   /* when using rap, MatMatMatMultSymbolic used a different data */
    288:   if (atb->data) C->product->data = atb->data;
    289:   (*C->ops->matmatmultnumeric)(atb->At,A,P,C);
    290:   C->product->data = atb;
    291:   return 0;
    292: }