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(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]) caj[k] += (*pA) * apa[apj[nextap++]];
255: }
256: PetscLogFlops(2.0 * apnzj);
257: pA++;
258: }
260: /* Zero the current row info for A*P */
261: for (j = 0; j < apnzj; j++) {
262: apa[apj[j]] = 0.;
263: apjdense[apj[j]] = 0;
264: }
265: }
267: /* Assemble the final matrix and clean up */
268: MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY);
269: MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY);
271: PetscFree2(apa, apjdense);
272: PetscFree(apj);
273: return 0;
274: }
276: PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ(Mat A, Mat P, Mat C)
277: {
278: Mat_MatTransMatMult *atb;
280: MatCheckProduct(C, 3);
281: atb = (Mat_MatTransMatMult *)C->product->data;
283: MatTranspose(P, MAT_REUSE_MATRIX, &atb->At);
285: /* when using rap, MatMatMatMultSymbolic used a different data */
286: if (atb->data) C->product->data = atb->data;
287: (*C->ops->matmatmultnumeric)(atb->At, A, P, C);
288: C->product->data = atb;
289: return 0;
290: }