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

  9: EXTERN int MatSeqAIJPtAP(Mat,Mat,Mat*);
 10: EXTERN int MatSeqAIJPtAPSymbolic(Mat,Mat,Mat*);
 11: EXTERN int MatSeqAIJPtAPNumeric(Mat,Mat,Mat);
 12: EXTERN int RegisterMatMatMultRoutines_Private(Mat);

 14: static int MATSeqAIJ_PtAP         = 0;
 15: static int MATSeqAIJ_PtAPSymbolic = 0;
 16: static int MATSeqAIJ_PtAPNumeric  = 0;

 18: /*
 19:      MatSeqAIJPtAP - Creates the SeqAIJ matrix product, C,
 20:            of SeqAIJ matrix A and matrix P:
 21:                  C = P^T * A * P;

 23:      Note: C is assumed to be uncreated.
 24:            If this is not the case, Destroy C before calling this routine.
 25: */
 28: int MatSeqAIJPtAP(Mat A,Mat P,Mat *C) {
 30:   char funct[80];

 33:   PetscLogEventBegin(MATSeqAIJ_PtAP,A,P,0,0);

 35:   MatSeqAIJPtAPSymbolic(A,P,C);

 37:   /* Avoid additional error checking included in */
 38: /*   MatSeqAIJApplyPtAPNumeric(A,P,*C); */

 40:   /* Query A for ApplyPtAPNumeric implementation based on types of P */
 41:   PetscStrcpy(funct,"MatApplyPtAPNumeric_seqaij_");
 42:   PetscStrcat(funct,P->type_name);
 43:   PetscUseMethod(A,funct,(Mat,Mat,Mat),(A,P,*C));

 45:   PetscLogEventEnd(MATSeqAIJ_PtAP,A,P,0,0);
 46:   return(0);
 47: }

 49: /*
 50:      MatSeqAIJPtAPSymbolic - Creates the (i,j) structure of the SeqAIJ matrix product, C,
 51:            of SeqAIJ matrix A and matrix P, according to:
 52:                  C = P^T * A * P;

 54:      Note: C is assumed to be uncreated.
 55:            If this is not the case, Destroy C before calling this routine.
 56: */
 59: int MatSeqAIJPtAPSymbolic(Mat A,Mat P,Mat *C) {
 61:   char funct[80];


 67:   MatPreallocated(A);
 68:   if (!A->assembled) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
 69:   if (A->factor) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");

 73:   MatPreallocated(P);
 74:   if (!P->assembled) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
 75:   if (P->factor) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");


 79:   if (P->M!=A->N) SETERRQ2(PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %d != %d",P->M,A->N);
 80:   if (A->M!=A->N) SETERRQ2(PETSC_ERR_ARG_SIZ,"Matrix 'A' must be square, %d != %d",A->M,A->N);

 82:   /* Query A for ApplyPtAP implementation based on types of P */
 83:   PetscStrcpy(funct,"MatApplyPtAPSymbolic_seqaij_");
 84:   PetscStrcat(funct,P->type_name);
 85:   PetscUseMethod(A,funct,(Mat,Mat,Mat*),(A,P,C));

 87:   return(0);
 88: }

 90: EXTERN_C_BEGIN
 93: int MatApplyPtAPSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat *C) {
 94:   int            ierr;
 95:   FreeSpaceList  free_space=PETSC_NULL,current_space=PETSC_NULL;
 96:   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*p=(Mat_SeqAIJ*)P->data,*c;
 97:   int            *pti,*ptj,*ptJ,*ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj;
 98:   int            *ci,*cj,*denserow,*sparserow,*ptadenserow,*ptasparserow,*ptaj;
 99:   int            an=A->N,am=A->M,pn=P->N,pm=P->M;
100:   int            i,j,k,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi;
101:   MatScalar      *ca;


105:   /* Start timer */
106:   PetscLogEventBegin(MATSeqAIJ_PtAPSymbolic,A,P,0,0);

108:   /* Get ij structure of P^T */
109:   MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);
110:   ptJ=ptj;

112:   /* Allocate ci array, arrays for fill computation and */
113:   /* free space for accumulating nonzero column info */
114:   PetscMalloc((pn+1)*sizeof(int),&ci);
115:   ci[0] = 0;

117:   PetscMalloc((2*pn+2*an+1)*sizeof(int),&ptadenserow);
118:   PetscMemzero(ptadenserow,(2*pn+2*an+1)*sizeof(int));
119:   ptasparserow = ptadenserow  + an;
120:   denserow     = ptasparserow + an;
121:   sparserow    = denserow     + pn;

123:   /* Set initial free space to be nnz(A) scaled by aspect ratio of P. */
124:   /* This should be reasonable if sparsity of PtAP is similar to that of A. */
125:   GetMoreSpace((ai[am]/pm)*pn,&free_space);
126:   current_space = free_space;

128:   /* Determine symbolic info for each row of C: */
129:   for (i=0;i<pn;i++) {
130:     ptnzi  = pti[i+1] - pti[i];
131:     ptanzi = 0;
132:     /* Determine symbolic row of PtA: */
133:     for (j=0;j<ptnzi;j++) {
134:       arow = *ptJ++;
135:       anzj = ai[arow+1] - ai[arow];
136:       ajj  = aj + ai[arow];
137:       for (k=0;k<anzj;k++) {
138:         if (!ptadenserow[ajj[k]]) {
139:           ptadenserow[ajj[k]]    = -1;
140:           ptasparserow[ptanzi++] = ajj[k];
141:         }
142:       }
143:     }
144:       /* Using symbolic info for row of PtA, determine symbolic info for row of C: */
145:     ptaj = ptasparserow;
146:     cnzi   = 0;
147:     for (j=0;j<ptanzi;j++) {
148:       prow = *ptaj++;
149:       pnzj = pi[prow+1] - pi[prow];
150:       pjj  = pj + pi[prow];
151:       for (k=0;k<pnzj;k++) {
152:         if (!denserow[pjj[k]]) {
153:             denserow[pjj[k]]  = -1;
154:             sparserow[cnzi++] = pjj[k];
155:         }
156:       }
157:     }

159:     /* sort sparserow */
160:     PetscSortInt(cnzi,sparserow);
161: 
162:     /* If free space is not available, make more free space */
163:     /* Double the amount of total space in the list */
164:     if (current_space->local_remaining<cnzi) {
165:       GetMoreSpace(current_space->total_array_size,&current_space);
166:     }

168:     /* Copy data into free space, and zero out denserows */
169:     PetscMemcpy(current_space->array,sparserow,cnzi*sizeof(int));
170:     current_space->array           += cnzi;
171:     current_space->local_used      += cnzi;
172:     current_space->local_remaining -= cnzi;
173: 
174:     for (j=0;j<ptanzi;j++) {
175:       ptadenserow[ptasparserow[j]] = 0;
176:     }
177:     for (j=0;j<cnzi;j++) {
178:       denserow[sparserow[j]] = 0;
179:     }
180:       /* Aside: Perhaps we should save the pta info for the numerical factorization. */
181:       /*        For now, we will recompute what is needed. */
182:     ci[i+1] = ci[i] + cnzi;
183:   }
184:   /* nnz is now stored in ci[ptm], column indices are in the list of free space */
185:   /* Allocate space for cj, initialize cj, and */
186:   /* destroy list of free space and other temporary array(s) */
187:   PetscMalloc((ci[pn]+1)*sizeof(int),&cj);
188:   MakeSpaceContiguous(&free_space,cj);
189:   PetscFree(ptadenserow);
190: 
191:   /* Allocate space for ca */
192:   PetscMalloc((ci[pn]+1)*sizeof(MatScalar),&ca);
193:   PetscMemzero(ca,(ci[pn]+1)*sizeof(MatScalar));
194: 
195:   /* put together the new matrix */
196:   MatCreateSeqAIJWithArrays(A->comm,pn,pn,ci,cj,ca,C);

198:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
199:   /* Since these are PETSc arrays, change flags to free them as necessary. */
200:   c = (Mat_SeqAIJ *)((*C)->data);
201:   c->freedata = PETSC_TRUE;
202:   c->nonew    = 0;

204:   /* Clean up. */
205:   MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);

207:   PetscLogEventEnd(MATSeqAIJ_PtAPSymbolic,A,P,0,0);
208:   return(0);
209: }
210: EXTERN_C_END

212:  #include src/mat/impls/maij/maij.h
213: EXTERN_C_BEGIN
216: int MatApplyPtAPSymbolic_SeqAIJ_SeqMAIJ(Mat A,Mat PP,Mat *C) {
217:   /* This routine requires testing -- I don't think it works. */
218:   int            ierr;
219:   FreeSpaceList  free_space=PETSC_NULL,current_space=PETSC_NULL;
220:   Mat_SeqMAIJ    *pp=(Mat_SeqMAIJ*)PP->data;
221:   Mat            P=pp->AIJ;
222:   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*p=(Mat_SeqAIJ*)P->data,*c;
223:   int            *pti,*ptj,*ptJ,*ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj;
224:   int            *ci,*cj,*denserow,*sparserow,*ptadenserow,*ptasparserow,*ptaj;
225:   int            an=A->N,am=A->M,pn=P->N,pm=P->M,ppdof=pp->dof;
226:   int            i,j,k,dof,pdof,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi;
227:   MatScalar      *ca;

230:   /* Start timer */
231:   PetscLogEventBegin(MATSeqAIJ_PtAPSymbolic,A,PP,0,0);

233:   /* Get ij structure of P^T */
234:   MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);

236:   /* Allocate ci array, arrays for fill computation and */
237:   /* free space for accumulating nonzero column info */
238:   PetscMalloc((pn+1)*sizeof(int),&ci);
239:   ci[0] = 0;

241:   PetscMalloc((2*pn+2*an+1)*sizeof(int),&ptadenserow);
242:   PetscMemzero(ptadenserow,(2*pn+2*an+1)*sizeof(int));
243:   ptasparserow = ptadenserow  + an;
244:   denserow     = ptasparserow + an;
245:   sparserow    = denserow     + pn;

247:   /* Set initial free space to be nnz(A) scaled by aspect ratio of P. */
248:   /* This should be reasonable if sparsity of PtAP is similar to that of A. */
249:   GetMoreSpace((ai[am]/pm)*pn,&free_space);
250:   current_space = free_space;

252:   /* Determine symbolic info for each row of C: */
253:   for (i=0;i<pn/ppdof;i++) {
254:     ptnzi  = pti[i+1] - pti[i];
255:     ptanzi = 0;
256:     ptJ    = ptj + pti[i];
257:     for (dof=0;dof<ppdof;dof++) {
258:     /* Determine symbolic row of PtA: */
259:       for (j=0;j<ptnzi;j++) {
260:         arow = ptJ[j] + dof;
261:         anzj = ai[arow+1] - ai[arow];
262:         ajj  = aj + ai[arow];
263:         for (k=0;k<anzj;k++) {
264:           if (!ptadenserow[ajj[k]]) {
265:             ptadenserow[ajj[k]]    = -1;
266:             ptasparserow[ptanzi++] = ajj[k];
267:           }
268:         }
269:       }
270:       /* Using symbolic info for row of PtA, determine symbolic info for row of C: */
271:       ptaj = ptasparserow;
272:       cnzi   = 0;
273:       for (j=0;j<ptanzi;j++) {
274:         pdof = *ptaj%dof;
275:         prow = (*ptaj++)/dof;
276:         pnzj = pi[prow+1] - pi[prow];
277:         pjj  = pj + pi[prow];
278:         for (k=0;k<pnzj;k++) {
279:           if (!denserow[pjj[k]+pdof]) {
280:             denserow[pjj[k]+pdof] = -1;
281:             sparserow[cnzi++]     = pjj[k]+pdof;
282:           }
283:         }
284:       }

286:       /* sort sparserow */
287:       PetscSortInt(cnzi,sparserow);
288: 
289:       /* If free space is not available, make more free space */
290:       /* Double the amount of total space in the list */
291:       if (current_space->local_remaining<cnzi) {
292:         GetMoreSpace(current_space->total_array_size,&current_space);
293:       }

295:       /* Copy data into free space, and zero out denserows */
296:       PetscMemcpy(current_space->array,sparserow,cnzi*sizeof(int));
297:       current_space->array           += cnzi;
298:       current_space->local_used      += cnzi;
299:       current_space->local_remaining -= cnzi;

301:       for (j=0;j<ptanzi;j++) {
302:         ptadenserow[ptasparserow[j]] = 0;
303:       }
304:       for (j=0;j<cnzi;j++) {
305:         denserow[sparserow[j]] = 0;
306:       }
307:       /* Aside: Perhaps we should save the pta info for the numerical factorization. */
308:       /*        For now, we will recompute what is needed. */
309:       ci[i+1+dof] = ci[i+dof] + cnzi;
310:     }
311:   }
312:   /* nnz is now stored in ci[ptm], column indices are in the list of free space */
313:   /* Allocate space for cj, initialize cj, and */
314:   /* destroy list of free space and other temporary array(s) */
315:   PetscMalloc((ci[pn]+1)*sizeof(int),&cj);
316:   MakeSpaceContiguous(&free_space,cj);
317:   PetscFree(ptadenserow);
318: 
319:   /* Allocate space for ca */
320:   PetscMalloc((ci[pn]+1)*sizeof(MatScalar),&ca);
321:   PetscMemzero(ca,(ci[pn]+1)*sizeof(MatScalar));
322: 
323:   /* put together the new matrix */
324:   MatCreateSeqAIJWithArrays(A->comm,pn,pn,ci,cj,ca,C);

326:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
327:   /* Since these are PETSc arrays, change flags to free them as necessary. */
328:   c = (Mat_SeqAIJ *)((*C)->data);
329:   c->freedata = PETSC_TRUE;
330:   c->nonew    = 0;

332:   /* Clean up. */
333:   MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);

335:   PetscLogEventEnd(MATSeqAIJ_PtAPSymbolic,A,PP,0,0);
336:   return(0);
337: }
338: EXTERN_C_END

340: /*
341:      MatSeqAIJPtAPNumeric - Computes the SeqAIJ matrix product, C,
342:            of SeqAIJ matrix A and matrix P, according to:
343:                  C = P^T * A * P
344:      Note: C must have been created by calling MatSeqAIJApplyPtAPSymbolic.
345: */
348: int MatSeqAIJPtAPNumeric(Mat A,Mat P,Mat C) {
350:   char funct[80];


356:   MatPreallocated(A);
357:   if (!A->assembled) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
358:   if (A->factor) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");

362:   MatPreallocated(P);
363:   if (!P->assembled) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
364:   if (P->factor) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");

368:   MatPreallocated(C);
369:   if (!C->assembled) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
370:   if (C->factor) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");

372:   if (P->N!=C->M) SETERRQ2(PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %d != %d",P->N,C->M);
373:   if (P->M!=A->N) SETERRQ2(PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %d != %d",P->M,A->N);
374:   if (A->M!=A->N) SETERRQ2(PETSC_ERR_ARG_SIZ,"Matrix 'A' must be square, %d != %d",A->M,A->N);
375:   if (P->N!=C->N) SETERRQ2(PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %d != %d",P->N,C->N);

377:   /* Query A for ApplyPtAP implementation based on types of P */
378:   PetscStrcpy(funct,"MatApplyPtAPNumeric_seqaij_");
379:   PetscStrcat(funct,P->type_name);
380:   PetscUseMethod(A,funct,(Mat,Mat,Mat),(A,P,C));

382:   return(0);
383: }

385: EXTERN_C_BEGIN
388: int MatApplyPtAPNumeric_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat C) {
389:   int        ierr,flops=0;
390:   Mat_SeqAIJ *a  = (Mat_SeqAIJ *) A->data;
391:   Mat_SeqAIJ *p  = (Mat_SeqAIJ *) P->data;
392:   Mat_SeqAIJ *c  = (Mat_SeqAIJ *) C->data;
393:   int        *ai=a->i,*aj=a->j,*apj,*apjdense,*pi=p->i,*pj=p->j,*pJ=p->j,*pjj;
394:   int        *ci=c->i,*cj=c->j,*cjj;
395:   int        am=A->M,cn=C->N,cm=C->M;
396:   int        i,j,k,anzi,pnzi,apnzj,nextap,pnzj,prow,crow;
397:   MatScalar  *aa=a->a,*apa,*pa=p->a,*pA=p->a,*paj,*ca=c->a,*caj;

400:   PetscLogEventBegin(MATSeqAIJ_PtAPNumeric,A,P,C,0);

402:   /* Allocate temporary array for storage of one row of A*P */
403:   PetscMalloc(cn*(sizeof(MatScalar)+2*sizeof(int)),&apa);
404:   PetscMemzero(apa,cn*(sizeof(MatScalar)+2*sizeof(int)));

406:   apj      = (int *)(apa + cn);
407:   apjdense = apj + cn;

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

412:   for (i=0;i<am;i++) {
413:     /* Form sparse row of A*P */
414:     anzi  = ai[i+1] - ai[i];
415:     apnzj = 0;
416:     for (j=0;j<anzi;j++) {
417:       prow = *aj++;
418:       pnzj = pi[prow+1] - pi[prow];
419:       pjj  = pj + pi[prow];
420:       paj  = pa + pi[prow];
421:       for (k=0;k<pnzj;k++) {
422:         if (!apjdense[pjj[k]]) {
423:           apjdense[pjj[k]] = -1;
424:           apj[apnzj++]     = pjj[k];
425:         }
426:         apa[pjj[k]] += (*aa)*paj[k];
427:       }
428:       flops += 2*pnzj;
429:       aa++;
430:     }

432:     /* Sort the j index array for quick sparse axpy. */
433:     PetscSortInt(apnzj,apj);

435:     /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */
436:     pnzi = pi[i+1] - pi[i];
437:     for (j=0;j<pnzi;j++) {
438:       nextap = 0;
439:       crow   = *pJ++;
440:       cjj    = cj + ci[crow];
441:       caj    = ca + ci[crow];
442:       /* Perform sparse axpy operation.  Note cjj includes apj. */
443:       for (k=0;nextap<apnzj;k++) {
444:         if (cjj[k]==apj[nextap]) {
445:           caj[k] += (*pA)*apa[apj[nextap++]];
446:         }
447:       }
448:       flops += 2*apnzj;
449:       pA++;
450:     }

452:     /* Zero the current row info for A*P */
453:     for (j=0;j<apnzj;j++) {
454:       apa[apj[j]]      = 0.;
455:       apjdense[apj[j]] = 0;
456:     }
457:   }

459:   /* Assemble the final matrix and clean up */
460:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
461:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
462:   PetscFree(apa);
463:   PetscLogFlops(flops);
464:   PetscLogEventEnd(MATSeqAIJ_PtAPNumeric,A,P,C,0);

466:   return(0);
467: }
468: EXTERN_C_END

472: int RegisterApplyPtAPRoutines_Private(Mat A) {


477:   if (!MATSeqAIJ_PtAP) {
478:     PetscLogEventRegister(&MATSeqAIJ_PtAP,"MatSeqAIJApplyPtAP",MAT_COOKIE);
479:   }

481:   if (!MATSeqAIJ_PtAPSymbolic) {
482:     PetscLogEventRegister(&MATSeqAIJ_PtAPSymbolic,"MatSeqAIJApplyPtAPSymbolic",MAT_COOKIE);
483:   }
484:   PetscObjectComposeFunctionDynamic((PetscObject)A,"MatApplyPtAPSymbolic_seqaij_seqaij",
485:                                            "MatApplyPtAPSymbolic_SeqAIJ_SeqAIJ",
486:                                            MatApplyPtAPSymbolic_SeqAIJ_SeqAIJ);

488:   if (!MATSeqAIJ_PtAPNumeric) {
489:     PetscLogEventRegister(&MATSeqAIJ_PtAPNumeric,"MatSeqAIJApplyPtAPNumeric",MAT_COOKIE);
490:   }
491:   PetscObjectComposeFunctionDynamic((PetscObject)A,"MatApplyPtAPNumeric_seqaij_seqaij",
492:                                            "MatApplyPtAPNumeric_SeqAIJ_SeqAIJ",
493:                                            MatApplyPtAPNumeric_SeqAIJ_SeqAIJ);
494:   RegisterMatMatMultRoutines_Private(A);
495:   return(0);
496: }