Actual source code: matptap.c
petsc-3.9.4 2018-09-11
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: PetscObjectOptionsBegin((PetscObject)A);
40: PetscOptionsObject->alreadyprinted = PETSC_FALSE; /* a hack to ensure the option shows in '-help' */
41: PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[0],&alg,NULL);
42: PetscOptionsEnd();
43: switch (alg) {
44: case 1:
45: PetscNew(&atb);
46: MatTranspose_SeqAIJ(P,MAT_INITIAL_MATRIX,&Pt);
47: MatMatMatMult(Pt,A,P,MAT_INITIAL_MATRIX,fill,C);
49: c = (Mat_SeqAIJ*)(*C)->data;
50: c->atb = atb;
51: atb->At = Pt;
52: atb->destroy = (*C)->ops->destroy;
53: (*C)->ops->destroy = MatDestroy_SeqAIJ_MatTransMatMult;
54: (*C)->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ;
55: return(0);
56: break;
57: #if defined(PETSC_HAVE_HYPRE)
58: case 2:
59: MatPtAPSymbolic_AIJ_AIJ_wHYPRE(A,P,fill,C);
60: break;
61: #endif
62: default:
63: MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(A,P,fill,C);
64: break;
65: }
66: }
67: (*(*C)->ops->ptapnumeric)(A,P,*C);
68: return(0);
69: }
71: PetscErrorCode MatDestroy_SeqAIJ_PtAP(Mat A)
72: {
74: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
75: Mat_PtAP *ptap = a->ptap;
78: PetscFree(ptap->apa);
79: PetscFree(ptap->api);
80: PetscFree(ptap->apj);
81: (ptap->destroy)(A);
82: PetscFree(ptap);
83: return(0);
84: }
86: PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,PetscReal fill,Mat *C)
87: {
88: PetscErrorCode ierr;
89: PetscFreeSpaceList free_space=NULL,current_space=NULL;
90: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*p = (Mat_SeqAIJ*)P->data,*c;
91: PetscInt *pti,*ptj,*ptJ,*ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj;
92: PetscInt *ci,*cj,*ptadenserow,*ptasparserow,*ptaj,nspacedouble=0;
93: PetscInt an=A->cmap->N,am=A->rmap->N,pn=P->cmap->N,pm=P->rmap->N;
94: PetscInt i,j,k,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi,nlnk,*lnk;
95: MatScalar *ca;
96: PetscBT lnkbt;
97: PetscReal afill;
100: /* Get ij structure of P^T */
101: MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);
102: ptJ = ptj;
104: /* Allocate ci array, arrays for fill computation and */
105: /* free space for accumulating nonzero column info */
106: PetscMalloc1(pn+1,&ci);
107: ci[0] = 0;
109: PetscCalloc1(2*an+1,&ptadenserow);
110: ptasparserow = ptadenserow + an;
112: /* create and initialize a linked list */
113: nlnk = pn+1;
114: PetscLLCreate(pn,pn,nlnk,lnk,lnkbt);
116: /* Set initial free space to be fill*(nnz(A)+ nnz(P)) */
117: PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],pi[pm])),&free_space);
118: current_space = free_space;
120: /* Determine symbolic info for each row of C: */
121: for (i=0; i<pn; i++) {
122: ptnzi = pti[i+1] - pti[i];
123: ptanzi = 0;
124: /* Determine symbolic row of PtA: */
125: for (j=0; j<ptnzi; j++) {
126: arow = *ptJ++;
127: anzj = ai[arow+1] - ai[arow];
128: ajj = aj + ai[arow];
129: for (k=0; k<anzj; k++) {
130: if (!ptadenserow[ajj[k]]) {
131: ptadenserow[ajj[k]] = -1;
132: ptasparserow[ptanzi++] = ajj[k];
133: }
134: }
135: }
136: /* Using symbolic info for row of PtA, determine symbolic info for row of C: */
137: ptaj = ptasparserow;
138: cnzi = 0;
139: for (j=0; j<ptanzi; j++) {
140: prow = *ptaj++;
141: pnzj = pi[prow+1] - pi[prow];
142: pjj = pj + pi[prow];
143: /* add non-zero cols of P into the sorted linked list lnk */
144: PetscLLAddSorted(pnzj,pjj,pn,nlnk,lnk,lnkbt);
145: cnzi += nlnk;
146: }
148: /* If free space is not available, make more free space */
149: /* Double the amount of total space in the list */
150: if (current_space->local_remaining<cnzi) {
151: PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),¤t_space);
152: nspacedouble++;
153: }
155: /* Copy data into free space, and zero out denserows */
156: PetscLLClean(pn,pn,cnzi,lnk,current_space->array,lnkbt);
158: current_space->array += cnzi;
159: current_space->local_used += cnzi;
160: current_space->local_remaining -= cnzi;
162: for (j=0; j<ptanzi; j++) ptadenserow[ptasparserow[j]] = 0;
164: /* Aside: Perhaps we should save the pta info for the numerical factorization. */
165: /* For now, we will recompute what is needed. */
166: ci[i+1] = ci[i] + cnzi;
167: }
168: /* nnz is now stored in ci[ptm], column indices are in the list of free space */
169: /* Allocate space for cj, initialize cj, and */
170: /* destroy list of free space and other temporary array(s) */
171: PetscMalloc1(ci[pn]+1,&cj);
172: PetscFreeSpaceContiguous(&free_space,cj);
173: PetscFree(ptadenserow);
174: PetscLLDestroy(lnk,lnkbt);
176: PetscCalloc1(ci[pn]+1,&ca);
178: /* put together the new matrix */
179: MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),pn,pn,ci,cj,ca,C);
180: MatSetBlockSizes(*C,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));
182: /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
183: /* Since these are PETSc arrays, change flags to free them as necessary. */
184: c = (Mat_SeqAIJ*)((*C)->data);
185: c->free_a = PETSC_TRUE;
186: c->free_ij = PETSC_TRUE;
187: c->nonew = 0;
188: (*C)->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy;
190: /* set MatInfo */
191: afill = (PetscReal)ci[pn]/(ai[am]+pi[pm] + 1.e-5);
192: if (afill < 1.0) afill = 1.0;
193: c->maxnz = ci[pn];
194: c->nz = ci[pn];
195: (*C)->info.mallocs = nspacedouble;
196: (*C)->info.fill_ratio_given = fill;
197: (*C)->info.fill_ratio_needed = afill;
199: /* Clean up. */
200: MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);
201: #if defined(PETSC_USE_INFO)
202: if (ci[pn] != 0) {
203: PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
204: PetscInfo1((*C),"Use MatPtAP(A,P,MatReuse,%g,&C) for best performance.\n",(double)afill);
205: } else {
206: PetscInfo((*C),"Empty matrix product\n");
207: }
208: #endif
209: return(0);
210: }
212: PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,Mat C)
213: {
215: Mat_SeqAIJ *a = (Mat_SeqAIJ*) A->data;
216: Mat_SeqAIJ *p = (Mat_SeqAIJ*) P->data;
217: Mat_SeqAIJ *c = (Mat_SeqAIJ*) C->data;
218: PetscInt *ai=a->i,*aj=a->j,*apj,*apjdense,*pi=p->i,*pj=p->j,*pJ=p->j,*pjj;
219: PetscInt *ci=c->i,*cj=c->j,*cjj;
220: PetscInt am =A->rmap->N,cn=C->cmap->N,cm=C->rmap->N;
221: PetscInt i,j,k,anzi,pnzi,apnzj,nextap,pnzj,prow,crow;
222: MatScalar *aa=a->a,*apa,*pa=p->a,*pA=p->a,*paj,*ca=c->a,*caj;
225: /* Allocate temporary array for storage of one row of A*P (cn: non-scalable) */
226: PetscMalloc3(cn,&apa,cn,&apjdense,cn,&apj);
227: PetscMemzero(apa,cn*sizeof(MatScalar));
228: PetscMemzero(apjdense,cn*sizeof(PetscInt));
230: /* Clear old values in C */
231: PetscMemzero(ca,ci[cm]*sizeof(MatScalar));
233: for (i=0; i<am; i++) {
234: /* Form sparse row of A*P */
235: anzi = ai[i+1] - ai[i];
236: apnzj = 0;
237: for (j=0; j<anzi; j++) {
238: prow = *aj++;
239: pnzj = pi[prow+1] - pi[prow];
240: pjj = pj + pi[prow];
241: paj = pa + pi[prow];
242: for (k=0; k<pnzj; k++) {
243: if (!apjdense[pjj[k]]) {
244: apjdense[pjj[k]] = -1;
245: apj[apnzj++] = pjj[k];
246: }
247: apa[pjj[k]] += (*aa)*paj[k];
248: }
249: PetscLogFlops(2.0*pnzj);
250: aa++;
251: }
253: /* Sort the j index array for quick sparse axpy. */
254: /* Note: a array does not need sorting as it is in dense storage locations. */
255: PetscSortInt(apnzj,apj);
257: /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */
258: pnzi = pi[i+1] - pi[i];
259: for (j=0; j<pnzi; j++) {
260: nextap = 0;
261: crow = *pJ++;
262: cjj = cj + ci[crow];
263: caj = ca + ci[crow];
264: /* Perform sparse axpy operation. Note cjj includes apj. */
265: for (k=0; nextap<apnzj; k++) {
266: #if defined(PETSC_USE_DEBUG)
267: if (k >= ci[crow+1] - ci[crow]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"k too large k %d, crow %d",k,crow);
268: #endif
269: if (cjj[k]==apj[nextap]) {
270: caj[k] += (*pA)*apa[apj[nextap++]];
271: }
272: }
273: PetscLogFlops(2.0*apnzj);
274: pA++;
275: }
277: /* Zero the current row info for A*P */
278: for (j=0; j<apnzj; j++) {
279: apa[apj[j]] = 0.;
280: apjdense[apj[j]] = 0;
281: }
282: }
284: /* Assemble the final matrix and clean up */
285: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
286: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
288: PetscFree3(apa,apjdense,apj);
289: return(0);
290: }
292: PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat C)
293: {
294: PetscErrorCode ierr;
295: Mat_SeqAIJ *c = (Mat_SeqAIJ*)C->data;
296: Mat_MatTransMatMult *atb = c->atb;
297: Mat Pt = atb->At;
300: MatTranspose_SeqAIJ(P,MAT_REUSE_MATRIX,&Pt);
301: (C->ops->matmatmultnumeric)(Pt,A,P,C);
302: return(0);
303: }