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: /* "scalable" */
26: PetscStrcmp(alg,"scalable",&flg);
27: if (flg) {
28: MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(A,P,fill,C);
29: C->ops->productnumeric = MatProductNumeric_PtAP;
30: return 0;
31: }
33: /* "rap" */
34: PetscStrcmp(alg,"rap",&flg);
35: if (flg) {
36: Mat_MatTransMatMult *atb;
38: PetscNew(&atb);
39: MatTranspose_SeqAIJ(P,MAT_INITIAL_MATRIX,&Pt);
40: 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: return 0;
50: }
52: /* hypre */
53: #if defined(PETSC_HAVE_HYPRE)
54: PetscStrcmp(alg,"hypre",&flg);
55: if (flg) {
56: MatPtAPSymbolic_AIJ_AIJ_wHYPRE(A,P,fill,C);
57: return 0;
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: /* Get ij structure of P^T */
77: MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);
78: ptJ = ptj;
80: /* Allocate ci array, arrays for fill computation and */
81: /* free space for accumulating nonzero column info */
82: PetscMalloc1(pn+1,&ci);
83: ci[0] = 0;
85: PetscCalloc1(2*an+1,&ptadenserow);
86: ptasparserow = ptadenserow + an;
88: /* create and initialize a linked list */
89: nlnk = pn+1;
90: PetscLLCreate(pn,pn,nlnk,lnk,lnkbt);
92: /* Set initial free space to be fill*(nnz(A)+ nnz(P)) */
93: PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],pi[pm])),&free_space);
94: current_space = free_space;
96: /* Determine symbolic info for each row of C: */
97: for (i=0; i<pn; i++) {
98: ptnzi = pti[i+1] - pti[i];
99: ptanzi = 0;
100: /* Determine symbolic row of PtA: */
101: for (j=0; j<ptnzi; j++) {
102: arow = *ptJ++;
103: anzj = ai[arow+1] - ai[arow];
104: ajj = aj + ai[arow];
105: for (k=0; k<anzj; k++) {
106: if (!ptadenserow[ajj[k]]) {
107: ptadenserow[ajj[k]] = -1;
108: ptasparserow[ptanzi++] = ajj[k];
109: }
110: }
111: }
112: /* Using symbolic info for row of PtA, determine symbolic info for row of C: */
113: ptaj = ptasparserow;
114: cnzi = 0;
115: for (j=0; j<ptanzi; j++) {
116: prow = *ptaj++;
117: pnzj = pi[prow+1] - pi[prow];
118: pjj = pj + pi[prow];
119: /* add non-zero cols of P into the sorted linked list lnk */
120: PetscLLAddSorted(pnzj,pjj,pn,&nlnk,lnk,lnkbt);
121: cnzi += nlnk;
122: }
124: /* If free space is not available, make more free space */
125: /* Double the amount of total space in the list */
126: if (current_space->local_remaining<cnzi) {
127: PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),¤t_space);
128: nspacedouble++;
129: }
131: /* Copy data into free space, and zero out denserows */
132: PetscLLClean(pn,pn,cnzi,lnk,current_space->array,lnkbt);
134: current_space->array += cnzi;
135: current_space->local_used += cnzi;
136: current_space->local_remaining -= cnzi;
138: for (j=0; j<ptanzi; j++) ptadenserow[ptasparserow[j]] = 0;
140: /* Aside: Perhaps we should save the pta info for the numerical factorization. */
141: /* For now, we will recompute what is needed. */
142: ci[i+1] = ci[i] + cnzi;
143: }
144: /* nnz is now stored in ci[ptm], column indices are in the list of free space */
145: /* Allocate space for cj, initialize cj, and */
146: /* destroy list of free space and other temporary array(s) */
147: PetscMalloc1(ci[pn]+1,&cj);
148: PetscFreeSpaceContiguous(&free_space,cj);
149: PetscFree(ptadenserow);
150: PetscLLDestroy(lnk,lnkbt);
152: PetscCalloc1(ci[pn]+1,&ca);
154: /* put together the new matrix */
155: MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A),pn,pn,ci,cj,ca,((PetscObject)A)->type_name,C);
156: MatSetBlockSizes(C,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));
158: /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
159: /* Since these are PETSc arrays, change flags to free them as necessary. */
160: c = (Mat_SeqAIJ*)((C)->data);
161: c->free_a = PETSC_TRUE;
162: c->free_ij = PETSC_TRUE;
163: c->nonew = 0;
165: C->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy;
167: /* set MatInfo */
168: afill = (PetscReal)ci[pn]/(ai[am]+pi[pm] + 1.e-5);
169: if (afill < 1.0) afill = 1.0;
170: C->info.mallocs = nspacedouble;
171: C->info.fill_ratio_given = fill;
172: C->info.fill_ratio_needed = afill;
174: /* Clean up. */
175: MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);
176: #if defined(PETSC_USE_INFO)
177: if (ci[pn] != 0) {
178: PetscInfo(C,"Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
179: PetscInfo(C,"Use MatPtAP(A,P,MatReuse,%g,&C) for best performance.\n",(double)afill);
180: } else {
181: PetscInfo(C,"Empty matrix product\n");
182: }
183: #endif
184: return 0;
185: }
187: PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,Mat C)
188: {
189: Mat_SeqAIJ *a = (Mat_SeqAIJ*) A->data;
190: Mat_SeqAIJ *p = (Mat_SeqAIJ*) P->data;
191: Mat_SeqAIJ *c = (Mat_SeqAIJ*) C->data;
192: PetscInt *ai=a->i,*aj=a->j,*apj,*apjdense,*pi=p->i,*pj=p->j,*pJ=p->j,*pjj;
193: PetscInt *ci=c->i,*cj=c->j,*cjj;
194: PetscInt am =A->rmap->N,cn=C->cmap->N,cm=C->rmap->N;
195: PetscInt i,j,k,anzi,pnzi,apnzj,nextap,pnzj,prow,crow;
196: MatScalar *aa,*apa,*pa,*pA,*paj,*ca,*caj;
198: /* Allocate temporary array for storage of one row of A*P (cn: non-scalable) */
199: PetscCalloc2(cn,&apa,cn,&apjdense);
200: PetscMalloc1(cn,&apj);
201: /* trigger CPU copies if needed and flag CPU mask for C */
202: #if defined(PETSC_HAVE_DEVICE)
203: {
204: const PetscScalar *dummy;
205: MatSeqAIJGetArrayRead(A,&dummy);
206: MatSeqAIJRestoreArrayRead(A,&dummy);
207: MatSeqAIJGetArrayRead(P,&dummy);
208: MatSeqAIJRestoreArrayRead(P,&dummy);
209: if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
210: }
211: #endif
212: aa = a->a;
213: pa = p->a;
214: pA = p->a;
215: ca = c->a;
217: /* Clear old values in C */
218: PetscArrayzero(ca,ci[cm]);
220: for (i=0; i<am; i++) {
221: /* Form sparse row of A*P */
222: anzi = ai[i+1] - ai[i];
223: apnzj = 0;
224: for (j=0; j<anzi; j++) {
225: prow = *aj++;
226: pnzj = pi[prow+1] - pi[prow];
227: pjj = pj + pi[prow];
228: paj = pa + pi[prow];
229: for (k=0; k<pnzj; k++) {
230: if (!apjdense[pjj[k]]) {
231: apjdense[pjj[k]] = -1;
232: apj[apnzj++] = pjj[k];
233: }
234: apa[pjj[k]] += (*aa)*paj[k];
235: }
236: PetscLogFlops(2.0*pnzj);
237: aa++;
238: }
240: /* Sort the j index array for quick sparse axpy. */
241: /* Note: a array does not need sorting as it is in dense storage locations. */
242: PetscSortInt(apnzj,apj);
244: /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */
245: pnzi = pi[i+1] - pi[i];
246: for (j=0; j<pnzi; j++) {
247: nextap = 0;
248: crow = *pJ++;
249: cjj = cj + ci[crow];
250: caj = ca + ci[crow];
251: /* Perform sparse axpy operation. Note cjj includes apj. */
252: for (k=0; nextap<apnzj; k++) {
253: PetscAssert(k < ci[crow+1] - ci[crow],PETSC_COMM_SELF,PETSC_ERR_PLIB,"k too large k %" PetscInt_FMT ", crow %" PetscInt_FMT,k,crow);
254: if (cjj[k]==apj[nextap]) {
255: caj[k] += (*pA)*apa[apj[nextap++]];
256: }
257: }
258: 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: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
271: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
273: PetscFree2(apa,apjdense);
274: PetscFree(apj);
275: return 0;
276: }
278: PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat C)
279: {
280: Mat_MatTransMatMult *atb;
282: MatCheckProduct(C,3);
283: atb = (Mat_MatTransMatMult*)C->product->data;
285: MatTranspose_SeqAIJ(P,MAT_REUSE_MATRIX,&atb->At);
287: /* when using rap, MatMatMatMultSymbolic used a different data */
288: if (atb->data) C->product->data = atb->data;
289: (*C->ops->matmatmultnumeric)(atb->At,A,P,C);
290: C->product->data = atb;
291: return 0;
292: }