Actual source code: matptap.c

petsc-master 2019-06-12
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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>
  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: PETSC_INTERN PetscErrorCode MatPtAP_SeqAIJ_SeqAIJ(Mat A,Mat P,MatReuse scall,PetscReal fill,Mat *C)
 17: {
 18:   PetscErrorCode      ierr;
 19: #if !defined(PETSC_HAVE_HYPRE)
 20:   const char          *algTypes[2] = {"scalable","rap"};
 21:   PetscInt            nalg = 2;
 22: #else
 23:   const char          *algTypes[3] = {"scalable","rap","hypre"};
 24:   PetscInt            nalg = 3;
 25: #endif
 26:   PetscInt            alg = 1; /* set default algorithm */
 27:   Mat                 Pt;
 28:   Mat_MatTransMatMult *atb;
 29:   Mat_SeqAIJ          *c;

 32:   if (scall == MAT_INITIAL_MATRIX) {
 33:     /*
 34:      Alg 'scalable' determines which implementations to be used:
 35:        "rap":      Pt = P^T and C = Pt*A*P
 36:        "scalable": do outer product and two sparse axpy in MatPtAPNumeric() - might slow, does not store structure of A*P.
 37:        "hypre":    use boomerAMGBuildCoarseOperator.
 38:      */
 39:     PetscOptionsBegin(PetscObjectComm((PetscObject)A),((PetscObject)A)->prefix,"MatPtAP","Mat");
 40:     PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[0],&alg,NULL);
 41:     PetscOptionsEnd();
 42:     switch (alg) {
 43:     case 1:
 44:       PetscNew(&atb);
 45:       MatTranspose_SeqAIJ(P,MAT_INITIAL_MATRIX,&Pt);
 46:       MatMatMatMult(Pt,A,P,MAT_INITIAL_MATRIX,fill,C);

 48:       c                      = (Mat_SeqAIJ*)(*C)->data;
 49:       c->atb                 = atb;
 50:       atb->At                = Pt;
 51:       atb->destroy           = (*C)->ops->destroy;
 52:       (*C)->ops->destroy     = MatDestroy_SeqAIJ_MatTransMatMult;
 53:       (*C)->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ;
 54:       return(0);
 55:       break;
 56: #if defined(PETSC_HAVE_HYPRE)
 57:     case 2:
 58:       PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);
 59:       MatPtAPSymbolic_AIJ_AIJ_wHYPRE(A,P,fill,C);
 60:       PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);
 61:       break;
 62: #endif
 63:     default:
 64:       PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);
 65:       MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(A,P,fill,C);
 66:       PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);
 67:       break;
 68:     }
 69:   }
 70:   PetscLogEventBegin(MAT_PtAPNumeric,A,P,0,0);
 71:   (*(*C)->ops->ptapnumeric)(A,P,*C);
 72:   PetscLogEventEnd(MAT_PtAPNumeric,A,P,0,0);
 73:   return(0);
 74: }

 76: PetscErrorCode MatDestroy_SeqAIJ_PtAP(Mat A)
 77: {
 79:   Mat_SeqAIJ     *a  = (Mat_SeqAIJ*)A->data;
 80:   Mat_AP         *ap = a->ap;

 83:   PetscFree(ap->apa);
 84:   PetscFree(ap->api);
 85:   PetscFree(ap->apj);
 86:   (ap->destroy)(A);
 87:   PetscFree(ap);
 88:   return(0);
 89: }

 91: PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,PetscReal fill,Mat *C)
 92: {
 93:   PetscErrorCode     ierr;
 94:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
 95:   Mat_SeqAIJ         *a        = (Mat_SeqAIJ*)A->data,*p = (Mat_SeqAIJ*)P->data,*c;
 96:   PetscInt           *pti,*ptj,*ptJ,*ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj;
 97:   PetscInt           *ci,*cj,*ptadenserow,*ptasparserow,*ptaj,nspacedouble=0;
 98:   PetscInt           an=A->cmap->N,am=A->rmap->N,pn=P->cmap->N,pm=P->rmap->N;
 99:   PetscInt           i,j,k,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi,nlnk,*lnk;
100:   MatScalar          *ca;
101:   PetscBT            lnkbt;
102:   PetscReal          afill;

105:   /* Get ij structure of P^T */
106:   MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);
107:   ptJ  = ptj;

109:   /* Allocate ci array, arrays for fill computation and */
110:   /* free space for accumulating nonzero column info */
111:   PetscMalloc1(pn+1,&ci);
112:   ci[0] = 0;

114:   PetscCalloc1(2*an+1,&ptadenserow);
115:   ptasparserow = ptadenserow  + an;

117:   /* create and initialize a linked list */
118:   nlnk = pn+1;
119:   PetscLLCreate(pn,pn,nlnk,lnk,lnkbt);

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

125:   /* Determine symbolic info for each row of C: */
126:   for (i=0; i<pn; i++) {
127:     ptnzi  = pti[i+1] - pti[i];
128:     ptanzi = 0;
129:     /* Determine symbolic row of PtA: */
130:     for (j=0; j<ptnzi; j++) {
131:       arow = *ptJ++;
132:       anzj = ai[arow+1] - ai[arow];
133:       ajj  = aj + ai[arow];
134:       for (k=0; k<anzj; k++) {
135:         if (!ptadenserow[ajj[k]]) {
136:           ptadenserow[ajj[k]]    = -1;
137:           ptasparserow[ptanzi++] = ajj[k];
138:         }
139:       }
140:     }
141:     /* Using symbolic info for row of PtA, determine symbolic info for row of C: */
142:     ptaj = ptasparserow;
143:     cnzi = 0;
144:     for (j=0; j<ptanzi; j++) {
145:       prow = *ptaj++;
146:       pnzj = pi[prow+1] - pi[prow];
147:       pjj  = pj + pi[prow];
148:       /* add non-zero cols of P into the sorted linked list lnk */
149:       PetscLLAddSorted(pnzj,pjj,pn,nlnk,lnk,lnkbt);
150:       cnzi += nlnk;
151:     }

153:     /* If free space is not available, make more free space */
154:     /* Double the amount of total space in the list */
155:     if (current_space->local_remaining<cnzi) {
156:       PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);
157:       nspacedouble++;
158:     }

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

163:     current_space->array           += cnzi;
164:     current_space->local_used      += cnzi;
165:     current_space->local_remaining -= cnzi;

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

169:     /* Aside: Perhaps we should save the pta info for the numerical factorization. */
170:     /*        For now, we will recompute what is needed. */
171:     ci[i+1] = ci[i] + cnzi;
172:   }
173:   /* nnz is now stored in ci[ptm], column indices are in the list of free space */
174:   /* Allocate space for cj, initialize cj, and */
175:   /* destroy list of free space and other temporary array(s) */
176:   PetscMalloc1(ci[pn]+1,&cj);
177:   PetscFreeSpaceContiguous(&free_space,cj);
178:   PetscFree(ptadenserow);
179:   PetscLLDestroy(lnk,lnkbt);

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

183:   /* put together the new matrix */
184:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),pn,pn,ci,cj,ca,C);
185:   MatSetBlockSizes(*C,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));

187:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
188:   /* Since these are PETSc arrays, change flags to free them as necessary. */
189:   c          = (Mat_SeqAIJ*)((*C)->data);
190:   c->free_a  = PETSC_TRUE;
191:   c->free_ij = PETSC_TRUE;
192:   c->nonew   = 0;
193:   (*C)->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy;

195:   /* set MatInfo */
196:   afill = (PetscReal)ci[pn]/(ai[am]+pi[pm] + 1.e-5);
197:   if (afill < 1.0) afill = 1.0;
198:   c->maxnz                     = ci[pn];
199:   c->nz                        = ci[pn];
200:   (*C)->info.mallocs           = nspacedouble;
201:   (*C)->info.fill_ratio_given  = fill;
202:   (*C)->info.fill_ratio_needed = afill;

204:   /* Clean up. */
205:   MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);
206: #if defined(PETSC_USE_INFO)
207:   if (ci[pn] != 0) {
208:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
209:     PetscInfo1((*C),"Use MatPtAP(A,P,MatReuse,%g,&C) for best performance.\n",(double)afill);
210:   } else {
211:     PetscInfo((*C),"Empty matrix product\n");
212:   }
213: #endif
214:   return(0);
215: }

217: PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,Mat C)
218: {
220:   Mat_SeqAIJ     *a = (Mat_SeqAIJ*) A->data;
221:   Mat_SeqAIJ     *p = (Mat_SeqAIJ*) P->data;
222:   Mat_SeqAIJ     *c = (Mat_SeqAIJ*) C->data;
223:   PetscInt       *ai=a->i,*aj=a->j,*apj,*apjdense,*pi=p->i,*pj=p->j,*pJ=p->j,*pjj;
224:   PetscInt       *ci=c->i,*cj=c->j,*cjj;
225:   PetscInt       am =A->rmap->N,cn=C->cmap->N,cm=C->rmap->N;
226:   PetscInt       i,j,k,anzi,pnzi,apnzj,nextap,pnzj,prow,crow;
227:   MatScalar      *aa=a->a,*apa,*pa=p->a,*pA=p->a,*paj,*ca=c->a,*caj;

230:   /* Allocate temporary array for storage of one row of A*P (cn: non-scalable) */
231:   PetscMalloc3(cn,&apa,cn,&apjdense,cn,&apj);
232:   PetscMemzero(apa,cn*sizeof(MatScalar));
233:   PetscMemzero(apjdense,cn*sizeof(PetscInt));

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

238:   for (i=0; i<am; i++) {
239:     /* Form sparse row of A*P */
240:     anzi  = ai[i+1] - ai[i];
241:     apnzj = 0;
242:     for (j=0; j<anzi; j++) {
243:       prow = *aj++;
244:       pnzj = pi[prow+1] - pi[prow];
245:       pjj  = pj + pi[prow];
246:       paj  = pa + pi[prow];
247:       for (k=0; k<pnzj; k++) {
248:         if (!apjdense[pjj[k]]) {
249:           apjdense[pjj[k]] = -1;
250:           apj[apnzj++]     = pjj[k];
251:         }
252:         apa[pjj[k]] += (*aa)*paj[k];
253:       }
254:       PetscLogFlops(2.0*pnzj);
255:       aa++;
256:     }

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

262:     /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */
263:     pnzi = pi[i+1] - pi[i];
264:     for (j=0; j<pnzi; j++) {
265:       nextap = 0;
266:       crow   = *pJ++;
267:       cjj    = cj + ci[crow];
268:       caj    = ca + ci[crow];
269:       /* Perform sparse axpy operation.  Note cjj includes apj. */
270:       for (k=0; nextap<apnzj; k++) {
271: #if defined(PETSC_USE_DEBUG)
272:         if (k >= ci[crow+1] - ci[crow]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"k too large k %d, crow %d",k,crow);
273: #endif
274:         if (cjj[k]==apj[nextap]) {
275:           caj[k] += (*pA)*apa[apj[nextap++]];
276:         }
277:       }
278:       PetscLogFlops(2.0*apnzj);
279:       pA++;
280:     }

282:     /* Zero the current row info for A*P */
283:     for (j=0; j<apnzj; j++) {
284:       apa[apj[j]]      = 0.;
285:       apjdense[apj[j]] = 0;
286:     }
287:   }

289:   /* Assemble the final matrix and clean up */
290:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
291:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

293:   PetscFree3(apa,apjdense,apj);
294:   return(0);
295: }

297: PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat C)
298: {
299:   PetscErrorCode      ierr;
300:   Mat_SeqAIJ          *c = (Mat_SeqAIJ*)C->data;
301:   Mat_MatTransMatMult *atb = c->atb;
302:   Mat                 Pt = atb->At;

305:   MatTranspose_SeqAIJ(P,MAT_REUSE_MATRIX,&Pt);
306:   (C->ops->matmatmultnumeric)(Pt,A,P,C);
307:   return(0);
308: }