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: PetscFunctionBegin;
26: /* "scalable" */
27: PetscCall(PetscStrcmp(alg, "scalable", &flg));
28: if (flg) {
29: PetscCall(MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(A, P, fill, C));
30: C->ops->productnumeric = MatProductNumeric_PtAP;
31: PetscFunctionReturn(PETSC_SUCCESS);
32: }
34: /* "rap" */
35: PetscCall(PetscStrcmp(alg, "rap", &flg));
36: if (flg) {
37: Mat_MatTransMatMult *atb;
39: PetscCall(PetscNew(&atb));
40: PetscCall(MatTranspose(P, MAT_INITIAL_MATRIX, &Pt));
41: PetscCall(MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ(Pt, A, P, fill, C));
43: atb->At = Pt;
44: atb->data = C->product->data;
45: atb->destroy = C->product->destroy;
46: C->product->data = atb;
47: C->product->destroy = MatDestroy_SeqAIJ_MatTransMatMult;
48: C->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ;
49: C->ops->productnumeric = MatProductNumeric_PtAP;
50: PetscFunctionReturn(PETSC_SUCCESS);
51: }
53: /* hypre */
54: #if defined(PETSC_HAVE_HYPRE)
55: PetscCall(PetscStrcmp(alg, "hypre", &flg));
56: if (flg) {
57: PetscCall(MatPtAPSymbolic_AIJ_AIJ_wHYPRE(A, P, fill, C));
58: PetscFunctionReturn(PETSC_SUCCESS);
59: }
60: #endif
62: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatProductType is not supported");
63: }
65: PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(Mat A, Mat P, PetscReal fill, Mat C)
66: {
67: PetscFreeSpaceList free_space = NULL, current_space = NULL;
68: Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data, *p = (Mat_SeqAIJ *)P->data, *c;
69: PetscInt *pti, *ptj, *ptJ, *ai = a->i, *aj = a->j, *ajj, *pi = p->i, *pj = p->j, *pjj;
70: PetscInt *ci, *cj, *ptadenserow, *ptasparserow, *ptaj, nspacedouble = 0;
71: PetscInt an = A->cmap->N, am = A->rmap->N, pn = P->cmap->N, pm = P->rmap->N;
72: PetscInt i, j, k, ptnzi, arow, anzj, ptanzi, prow, pnzj, cnzi, nlnk, *lnk;
73: MatScalar *ca;
74: PetscBT lnkbt;
75: PetscReal afill;
77: PetscFunctionBegin;
78: /* Get ij structure of P^T */
79: PetscCall(MatGetSymbolicTranspose_SeqAIJ(P, &pti, &ptj));
80: ptJ = ptj;
82: /* Allocate ci array, arrays for fill computation and */
83: /* free space for accumulating nonzero column info */
84: PetscCall(PetscMalloc1(pn + 1, &ci));
85: ci[0] = 0;
87: PetscCall(PetscCalloc1(2 * an + 1, &ptadenserow));
88: ptasparserow = ptadenserow + an;
90: /* create and initialize a linked list */
91: nlnk = pn + 1;
92: PetscCall(PetscLLCreate(pn, pn, nlnk, lnk, lnkbt));
94: /* Set initial free space to be fill*(nnz(A)+ nnz(P)) */
95: PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(ai[am], pi[pm])), &free_space));
96: current_space = free_space;
98: /* Determine symbolic info for each row of C: */
99: for (i = 0; i < pn; i++) {
100: ptnzi = pti[i + 1] - pti[i];
101: ptanzi = 0;
102: /* Determine symbolic row of PtA: */
103: for (j = 0; j < ptnzi; j++) {
104: arow = *ptJ++;
105: anzj = ai[arow + 1] - ai[arow];
106: ajj = aj + ai[arow];
107: for (k = 0; k < anzj; k++) {
108: if (!ptadenserow[ajj[k]]) {
109: ptadenserow[ajj[k]] = -1;
110: ptasparserow[ptanzi++] = ajj[k];
111: }
112: }
113: }
114: /* Using symbolic info for row of PtA, determine symbolic info for row of C: */
115: ptaj = ptasparserow;
116: cnzi = 0;
117: for (j = 0; j < ptanzi; j++) {
118: prow = *ptaj++;
119: pnzj = pi[prow + 1] - pi[prow];
120: pjj = pj + pi[prow];
121: /* add non-zero cols of P into the sorted linked list lnk */
122: PetscCall(PetscLLAddSorted(pnzj, pjj, pn, &nlnk, lnk, lnkbt));
123: cnzi += nlnk;
124: }
126: /* If free space is not available, make more free space */
127: /* Double the amount of total space in the list */
128: if (current_space->local_remaining < cnzi) {
129: PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(cnzi, current_space->total_array_size), ¤t_space));
130: nspacedouble++;
131: }
133: /* Copy data into free space, and zero out denserows */
134: PetscCall(PetscLLClean(pn, pn, cnzi, lnk, current_space->array, lnkbt));
136: current_space->array += cnzi;
137: current_space->local_used += cnzi;
138: current_space->local_remaining -= cnzi;
140: for (j = 0; j < ptanzi; j++) ptadenserow[ptasparserow[j]] = 0;
142: /* Aside: Perhaps we should save the pta info for the numerical factorization. */
143: /* For now, we will recompute what is needed. */
144: ci[i + 1] = ci[i] + cnzi;
145: }
146: /* nnz is now stored in ci[ptm], column indices are in the list of free space */
147: /* Allocate space for cj, initialize cj, and */
148: /* destroy list of free space and other temporary array(s) */
149: PetscCall(PetscMalloc1(ci[pn] + 1, &cj));
150: PetscCall(PetscFreeSpaceContiguous(&free_space, cj));
151: PetscCall(PetscFree(ptadenserow));
152: PetscCall(PetscLLDestroy(lnk, lnkbt));
154: PetscCall(PetscCalloc1(ci[pn] + 1, &ca));
156: /* put together the new matrix */
157: PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), pn, pn, ci, cj, ca, ((PetscObject)A)->type_name, C));
158: PetscCall(MatSetBlockSizes(C, PetscAbs(P->cmap->bs), PetscAbs(P->cmap->bs)));
160: /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
161: /* Since these are PETSc arrays, change flags to free them as necessary. */
162: c = (Mat_SeqAIJ *)((C)->data);
163: c->free_a = PETSC_TRUE;
164: c->free_ij = PETSC_TRUE;
165: c->nonew = 0;
167: C->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy;
169: /* set MatInfo */
170: afill = (PetscReal)ci[pn] / (ai[am] + pi[pm] + 1.e-5);
171: if (afill < 1.0) afill = 1.0;
172: C->info.mallocs = nspacedouble;
173: C->info.fill_ratio_given = fill;
174: C->info.fill_ratio_needed = afill;
176: /* Clean up. */
177: PetscCall(MatRestoreSymbolicTranspose_SeqAIJ(P, &pti, &ptj));
178: #if defined(PETSC_USE_INFO)
179: if (ci[pn] != 0) {
180: PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
181: PetscCall(PetscInfo(C, "Use MatPtAP(A,P,MatReuse,%g,&C) for best performance.\n", (double)afill));
182: } else {
183: PetscCall(PetscInfo(C, "Empty matrix product\n"));
184: }
185: #endif
186: PetscFunctionReturn(PETSC_SUCCESS);
187: }
189: PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy(Mat A, Mat P, Mat C)
190: {
191: Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
192: Mat_SeqAIJ *p = (Mat_SeqAIJ *)P->data;
193: Mat_SeqAIJ *c = (Mat_SeqAIJ *)C->data;
194: PetscInt *ai = a->i, *aj = a->j, *apj, *apjdense, *pi = p->i, *pj = p->j, *pJ = p->j, *pjj;
195: PetscInt *ci = c->i, *cj = c->j, *cjj;
196: PetscInt am = A->rmap->N, cn = C->cmap->N, cm = C->rmap->N;
197: PetscInt i, j, k, anzi, pnzi, apnzj, nextap, pnzj, prow, crow;
198: MatScalar *aa, *apa, *pa, *pA, *paj, *ca, *caj;
200: PetscFunctionBegin;
201: /* Allocate temporary array for storage of one row of A*P (cn: non-scalable) */
202: PetscCall(PetscCalloc2(cn, &apa, cn, &apjdense));
203: PetscCall(PetscMalloc1(cn, &apj));
204: /* trigger CPU copies if needed and flag CPU mask for C */
205: #if defined(PETSC_HAVE_DEVICE)
206: {
207: const PetscScalar *dummy;
208: PetscCall(MatSeqAIJGetArrayRead(A, &dummy));
209: PetscCall(MatSeqAIJRestoreArrayRead(A, &dummy));
210: PetscCall(MatSeqAIJGetArrayRead(P, &dummy));
211: PetscCall(MatSeqAIJRestoreArrayRead(P, &dummy));
212: if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
213: }
214: #endif
215: aa = a->a;
216: pa = p->a;
217: pA = p->a;
218: ca = c->a;
220: /* Clear old values in C */
221: PetscCall(PetscArrayzero(ca, ci[cm]));
223: for (i = 0; i < am; i++) {
224: /* Form sparse row of A*P */
225: anzi = ai[i + 1] - ai[i];
226: apnzj = 0;
227: for (j = 0; j < anzi; j++) {
228: prow = *aj++;
229: pnzj = pi[prow + 1] - pi[prow];
230: pjj = pj + pi[prow];
231: paj = pa + pi[prow];
232: for (k = 0; k < pnzj; k++) {
233: if (!apjdense[pjj[k]]) {
234: apjdense[pjj[k]] = -1;
235: apj[apnzj++] = pjj[k];
236: }
237: apa[pjj[k]] += (*aa) * paj[k];
238: }
239: PetscCall(PetscLogFlops(2.0 * pnzj));
240: aa++;
241: }
243: /* Sort the j index array for quick sparse axpy. */
244: /* Note: a array does not need sorting as it is in dense storage locations. */
245: PetscCall(PetscSortInt(apnzj, apj));
247: /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */
248: pnzi = pi[i + 1] - pi[i];
249: for (j = 0; j < pnzi; j++) {
250: nextap = 0;
251: crow = *pJ++;
252: cjj = cj + ci[crow];
253: caj = ca + ci[crow];
254: /* Perform sparse axpy operation. Note cjj includes apj. */
255: for (k = 0; nextap < apnzj; k++) {
256: PetscAssert(k < ci[crow + 1] - ci[crow], PETSC_COMM_SELF, PETSC_ERR_PLIB, "k too large k %" PetscInt_FMT ", crow %" PetscInt_FMT, k, crow);
257: if (cjj[k] == apj[nextap]) caj[k] += (*pA) * apa[apj[nextap++]];
258: }
259: PetscCall(PetscLogFlops(2.0 * apnzj));
260: pA++;
261: }
263: /* Zero the current row info for A*P */
264: for (j = 0; j < apnzj; j++) {
265: apa[apj[j]] = 0.;
266: apjdense[apj[j]] = 0;
267: }
268: }
270: /* Assemble the final matrix and clean up */
271: PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
272: PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
274: PetscCall(PetscFree2(apa, apjdense));
275: PetscCall(PetscFree(apj));
276: PetscFunctionReturn(PETSC_SUCCESS);
277: }
279: PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ(Mat A, Mat P, Mat C)
280: {
281: Mat_MatTransMatMult *atb;
283: PetscFunctionBegin;
284: MatCheckProduct(C, 3);
285: atb = (Mat_MatTransMatMult *)C->product->data;
286: PetscCheck(atb, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Missing data structure");
287: PetscCall(MatTranspose(P, MAT_REUSE_MATRIX, &atb->At));
288: PetscCheck(C->ops->matmultnumeric, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Missing numeric operation");
289: /* when using rap, MatMatMatMultSymbolic used a different data */
290: if (atb->data) C->product->data = atb->data;
291: PetscCall((*C->ops->matmatmultnumeric)(atb->At, A, P, C));
292: C->product->data = atb;
293: PetscFunctionReturn(PETSC_SUCCESS);
294: }