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

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

 39:     PetscCall(PetscNew(&atb));
 40:     PetscCall(MatTranspose(P, MAT_INITIAL_MATRIX, &Pt));
 41:     PetscCall(MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ(Pt, A, P, fill, C));

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

247:     /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */
248:     pnzi = pi[i + 1] - pi[i];
249:     for (j = 0; j < pnzi; j++) {
250:       nextap = 0;
251:       crow   = *pJ++;
252:       cjj    = cj + ci[crow];
253:       caj    = ca + ci[crow];
254:       /* Perform sparse axpy operation.  Note cjj includes apj. */
255:       for (k = 0; nextap < apnzj; k++) {
256:         PetscAssert(k < ci[crow + 1] - ci[crow], PETSC_COMM_SELF, PETSC_ERR_PLIB, "k too large k %" PetscInt_FMT ", crow %" PetscInt_FMT, k, crow);
257:         if (cjj[k] == apj[nextap]) caj[k] += (*pA) * apa[apj[nextap++]];
258:       }
259:       PetscCall(PetscLogFlops(2.0 * apnzj));
260:       pA++;
261:     }

263:     /* Zero the current row info for A*P */
264:     for (j = 0; j < apnzj; j++) {
265:       apa[apj[j]]      = 0.;
266:       apjdense[apj[j]] = 0;
267:     }
268:   }

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

274:   PetscCall(PetscFree2(apa, apjdense));
275:   PetscCall(PetscFree(apj));
276:   PetscFunctionReturn(PETSC_SUCCESS);
277: }

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

283:   PetscFunctionBegin;
284:   MatCheckProduct(C, 3);
285:   atb = (Mat_MatTransMatMult *)C->product->data;
286:   PetscCheck(atb, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Missing data structure");
287:   PetscCall(MatTranspose(P, MAT_REUSE_MATRIX, &atb->At));
288:   PetscCheck(C->ops->matmultnumeric, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Missing numeric operation");
289:   /* when using rap, MatMatMatMultSymbolic used a different data */
290:   if (atb->data) C->product->data = atb->data;
291:   PetscCall((*C->ops->matmatmultnumeric)(atb->At, A, P, C));
292:   C->product->data = atb;
293:   PetscFunctionReturn(PETSC_SUCCESS);
294: }