Actual source code: matptap.c

      1: /*
      2:   Defines projective product routines where A is a SeqAIJ matrix
      3:           C = P^T * A * P
      4: */

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

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

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

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

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

     38:     PetscCall(PetscNew(&atb));
     39:     PetscCall(MatTranspose(P, MAT_INITIAL_MATRIX, &Pt));
     40:     PetscCall(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:     PetscFunctionReturn(PETSC_SUCCESS);
     50:   }

     52:   /* hypre */
     53: #if defined(PETSC_HAVE_HYPRE)
     54:   PetscCall(PetscStrcmp(alg, "hypre", &flg));
     55:   if (flg) {
     56:     PetscCall(MatPtAPSymbolic_AIJ_AIJ_wHYPRE(A, P, fill, C));
     57:     PetscFunctionReturn(PETSC_SUCCESS);
     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:   PetscFunctionBegin;
     77:   /* Get ij structure of P^T */
     78:   PetscCall(MatGetSymbolicTranspose_SeqAIJ(P, &pti, &ptj));
     79:   ptJ = ptj;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    219:   /* Clear old values in C */
    220:   PetscCall(PetscArrayzero(ca, ci[cm]));

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

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

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

    273:   PetscCall(PetscFree2(apa, apjdense));
    274:   PetscCall(PetscFree(apj));
    275:   PetscFunctionReturn(PETSC_SUCCESS);
    276: }

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

    282:   PetscFunctionBegin;
    283:   MatCheckProduct(C, 3);
    284:   atb = (Mat_MatTransMatMult *)C->product->data;
    285:   PetscCheck(atb, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Missing data structure");
    286:   PetscCall(MatTranspose(P, MAT_REUSE_MATRIX, &atb->At));
    287:   PetscCheck(C->ops->matmultnumeric, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Missing numeric operation");
    288:   /* when using rap, MatMatMatMultSymbolic used a different data */
    289:   if (atb->data) C->product->data = atb->data;
    290:   PetscCall((*C->ops->matmatmultnumeric)(atb->At, A, P, C));
    291:   C->product->data = atb;
    292:   PetscFunctionReturn(PETSC_SUCCESS);
    293: }