Actual source code: matptap.c
petsc-3.7.1 2016-05-15
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      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>   /*I "petscmat.h" I*/
      8: #include <../src/mat/utils/freespace.h>
      9: #include <petscbt.h>
     10: #include <petsctime.h>

     14: PETSC_INTERN PetscErrorCode MatPtAP_SeqAIJ_SeqAIJ(Mat A,Mat P,MatReuse scall,PetscReal fill,Mat *C)
     15: {
     17:   const char     *algTypes[2] = {"scalable","nonscalable"};
     18:   PetscInt       alg=0; /* set default algorithm */

     21:   if (scall == MAT_INITIAL_MATRIX) {
     22:     /*
     23:      Alg 'scalable' determines which implementations to be used:
     24:        "nonscalable": do dense axpy in MatPtAPNumeric() - fastest, but requires storage of struct A*P;
     25:        "scalable":    do two sparse axpy in MatPtAPNumeric() - might slow, does not store structure of A*P.
     26:      */
     27:     PetscObjectOptionsBegin((PetscObject)A);
     28:     PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,2,algTypes[0],&alg,NULL);
     29:     PetscOptionsEnd();
     30:     PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);
     31:     switch (alg) {
     32:     case 1:
     33:       MatPtAPSymbolic_SeqAIJ_SeqAIJ_DenseAxpy(A,P,fill,C);
     34:       break;
     35:     default:
     36:       MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(A,P,fill,C);
     37:       break;
     38:     }
     39:     PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);
     40:   }
     41:   PetscLogEventBegin(MAT_PtAPNumeric,A,P,0,0);
     42:   (*(*C)->ops->ptapnumeric)(A,P,*C);
     43:   PetscLogEventEnd(MAT_PtAPNumeric,A,P,0,0);
     44:   return(0);
     45: }

     49: PetscErrorCode MatDestroy_SeqAIJ_PtAP(Mat A)
     50: {
     52:   Mat_SeqAIJ     *a    = (Mat_SeqAIJ*)A->data;
     53:   Mat_PtAP       *ptap = a->ptap;

     56:   PetscFree(ptap->apa);
     57:   PetscFree(ptap->api);
     58:   PetscFree(ptap->apj);
     59:   (ptap->destroy)(A);
     60:   PetscFree(ptap);
     61:   return(0);
     62: }

     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:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),pn,pn,ci,cj,ca,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;
    168:   (*C)->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy;

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

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

    194: PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,Mat C)
    195: {
    197:   Mat_SeqAIJ     *a = (Mat_SeqAIJ*) A->data;
    198:   Mat_SeqAIJ     *p = (Mat_SeqAIJ*) P->data;
    199:   Mat_SeqAIJ     *c = (Mat_SeqAIJ*) C->data;
    200:   PetscInt       *ai=a->i,*aj=a->j,*apj,*apjdense,*pi=p->i,*pj=p->j,*pJ=p->j,*pjj;
    201:   PetscInt       *ci=c->i,*cj=c->j,*cjj;
    202:   PetscInt       am =A->rmap->N,cn=C->cmap->N,cm=C->rmap->N;
    203:   PetscInt       i,j,k,anzi,pnzi,apnzj,nextap,pnzj,prow,crow;
    204:   MatScalar      *aa=a->a,*apa,*pa=p->a,*pA=p->a,*paj,*ca=c->a,*caj;

    207:   /* Allocate temporary array for storage of one row of A*P (cn: non-scalable) */
    208:   PetscMalloc3(cn,&apa,cn,&apjdense,c->rmax,&apj);
    209:   PetscMemzero(apa,cn*sizeof(MatScalar));
    210:   PetscMemzero(apjdense,cn*sizeof(PetscInt));

    212:   /* Clear old values in C */
    213:   PetscMemzero(ca,ci[cm]*sizeof(MatScalar));

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

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

    239:     /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */
    240:     pnzi = pi[i+1] - pi[i];
    241:     for (j=0; j<pnzi; j++) {
    242:       nextap = 0;
    243:       crow   = *pJ++;
    244:       cjj    = cj + ci[crow];
    245:       caj    = ca + ci[crow];
    246:       /* Perform sparse axpy operation.  Note cjj includes apj. */
    247:       for (k=0; nextap<apnzj; k++) {
    248: #if defined(PETSC_USE_DEBUG)
    249:         if (k >= ci[crow+1] - ci[crow]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"k too large k %d, crow %d",k,crow);
    250: #endif
    251:         if (cjj[k]==apj[nextap]) {
    252:           caj[k] += (*pA)*apa[apj[nextap++]];
    253:         }
    254:       }
    255:       PetscLogFlops(2.0*apnzj);
    256:       pA++;
    257:     }

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

    266:   /* Assemble the final matrix and clean up */
    267:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    268:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

    270:   PetscFree3(apa,apjdense,apj);
    271:   return(0);
    272: }

    276: PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ_DenseAxpy(Mat A,Mat P,PetscReal fill,Mat *C)
    277: {
    279:   Mat_SeqAIJ     *ap,*c;
    280:   PetscInt       *api,*apj,*ci,pn=P->cmap->N;
    281:   MatScalar      *ca;
    282:   Mat_PtAP       *ptap;
    283:   Mat            Pt,AP;

    286:   /* Get symbolic Pt = P^T */
    287:   MatTransposeSymbolic_SeqAIJ(P,&Pt);

    289:   /* Get symbolic AP = A*P */
    290:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,P,fill,&AP);

    292:   ap          = (Mat_SeqAIJ*)AP->data;
    293:   api         = ap->i;
    294:   apj         = ap->j;
    295:   ap->free_ij = PETSC_FALSE; /* api and apj are kept in struct ptap, cannot be destroyed with AP */

    297:   /* Get C = Pt*AP */
    298:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(Pt,AP,fill,C);

    300:   c         = (Mat_SeqAIJ*)(*C)->data;
    301:   ci        = c->i;
    302:   PetscCalloc1(ci[pn]+1,&ca);
    303:   c->a      = ca;
    304:   c->free_a = PETSC_TRUE;

    306:   /* Create a supporting struct for reuse by MatPtAPNumeric() */
    307:   PetscNew(&ptap);

    309:   c->ptap            = ptap;
    310:   ptap->destroy      = (*C)->ops->destroy;
    311:   (*C)->ops->destroy = MatDestroy_SeqAIJ_PtAP;

    313:   /* Allocate temporary array for storage of one row of A*P */
    314:   PetscCalloc1(pn+1,&ptap->apa);

    316:   (*C)->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ;

    318:   ptap->api = api;
    319:   ptap->apj = apj;

    321:   /* Clean up. */
    322:   MatDestroy(&Pt);
    323:   MatDestroy(&AP);
    324: #if defined(PETSC_USE_INFO)
    325:   PetscInfo1((*C),"given fill %g\n",(double)fill);
    326: #endif
    327:   return(0);
    328: }

    330: /* #define PROFILE_MatPtAPNumeric */
    333: PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat C)
    334: {
    335:   PetscErrorCode    ierr;
    336:   Mat_SeqAIJ        *a = (Mat_SeqAIJ*) A->data;
    337:   Mat_SeqAIJ        *p = (Mat_SeqAIJ*) P->data;
    338:   Mat_SeqAIJ        *c = (Mat_SeqAIJ*) C->data;
    339:   const PetscInt    *ai=a->i,*aj=a->j,*pi=p->i,*pj=p->j,*ci=c->i,*cj=c->j;
    340:   const PetscScalar *aa=a->a,*pa=p->a,*pval;
    341:   const PetscInt    *apj,*pcol,*cjj;
    342:   const PetscInt    am=A->rmap->N,cm=C->rmap->N;
    343:   PetscInt          i,j,k,anz,apnz,pnz,prow,crow,cnz;
    344:   PetscScalar       *apa,*ca=c->a,*caj,pvalj;
    345:   Mat_PtAP          *ptap = c->ptap;
    346: #if defined(PROFILE_MatPtAPNumeric)
    347:   PetscLogDouble t0,tf,time_Cseq0=0.0,time_Cseq1=0.0;
    348:   PetscInt       flops0=0,flops1=0;
    349: #endif

    352:   /* Get temporary array for storage of one row of A*P */
    353:   apa = ptap->apa;

    355:   /* Clear old values in C */
    356:   PetscMemzero(ca,ci[cm]*sizeof(MatScalar));

    358:   for (i=0; i<am; i++) {
    359:     /* Form sparse row of AP[i,:] = A[i,:]*P */
    360: #if defined(PROFILE_MatPtAPNumeric)
    361:     PetscTime(&t0);
    362: #endif
    363:     anz  = ai[i+1] - ai[i];
    364:     for (j=0; j<anz; j++) {
    365:       prow = aj[j];
    366:       pnz  = pi[prow+1] - pi[prow];
    367:       pcol = pj + pi[prow];
    368:       pval = pa + pi[prow];
    369:       for (k=0; k<pnz; k++) {
    370:         apa[pcol[k]] += aa[j]*pval[k];
    371:       }
    372:       PetscLogFlops(2.0*pnz);
    373: #if defined(PROFILE_MatPtAPNumeric)
    374:       flops0 += 2.0*pnz;
    375: #endif
    376:     }
    377:     aj += anz; aa += anz;
    378: #if defined(PROFILE_MatPtAPNumeric)
    379:     PetscTime(&tf);

    381:     time_Cseq0 += tf - t0;
    382: #endif

    384:     /* Compute P^T*A*P using outer product P[i,:]^T*AP[i,:]. */
    385: #if defined(PROFILE_MatPtAPNumeric)
    386:     PetscTime(&t0);
    387: #endif
    388:     apj  = ptap->apj + ptap->api[i];
    389:     apnz = ptap->api[i+1] - ptap->api[i];
    390:     pnz  = pi[i+1] - pi[i];
    391:     pcol = pj + pi[i];
    392:     pval = pa + pi[i];

    394:     /* Perform dense axpy */
    395:     for (j=0; j<pnz; j++) {
    396:       crow  = pcol[j];
    397:       cjj   = cj + ci[crow];
    398:       caj   = ca + ci[crow];
    399:       pvalj = pval[j];
    400:       cnz   = ci[crow+1] - ci[crow];
    401:       for (k=0; k<cnz; k++) caj[k] += pvalj*apa[cjj[k]];
    402:       PetscLogFlops(2.0*cnz);
    403: #if defined(PROFILE_MatPtAPNumeric)
    404:       flops1 += 2.0*cnz;
    405: #endif
    406:     }
    407: #if defined(PROFILE_MatPtAPNumeric)
    408:     PetscTime(&tf);
    409:     time_Cseq1 += tf - t0;
    410: #endif

    412:     /* Zero the current row info for A*P */
    413:     for (j=0; j<apnz; j++) apa[apj[j]] = 0.0;
    414:   }

    416:   /* Assemble the final matrix and clean up */
    417:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    418:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    419: #if defined(PROFILE_MatPtAPNumeric)
    420:   printf("PtAPNumeric_SeqAIJ time %g + %g, flops %d %d\n",time_Cseq0,time_Cseq1,flops0,flops1);
    421: #endif
    422:   return(0);
    423: }