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>
8: #include <petscbt.h>
9: #include <petsctime.h>
11: #if defined(PETSC_HAVE_HYPRE)
12: PETSC_INTERN PetscErrorCode MatPtAPSymbolic_AIJ_AIJ_wHYPRE(Mat, Mat, PetscReal, Mat);
13: #endif
15: PetscErrorCode MatProductSymbolic_PtAP_SeqAIJ_SeqAIJ(Mat C)
16: {
17: Mat_Product *product = C->product;
18: Mat A = product->A, P = product->B;
19: MatProductAlgorithm alg = product->alg;
20: PetscReal fill = product->fill;
21: PetscBool flg;
22: Mat Pt;
24: PetscFunctionBegin;
25: /* "scalable" */
26: PetscCall(PetscStrcmp(alg, "scalable", &flg));
27: if (flg) {
28: PetscCall(MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(A, P, fill, C));
29: C->ops->productnumeric = MatProductNumeric_PtAP;
30: PetscFunctionReturn(PETSC_SUCCESS);
31: }
33: /* "rap" */
34: PetscCall(PetscStrcmp(alg, "rap", &flg));
35: if (flg) {
36: Mat_MatTransMatMult *atb;
38: PetscCall(PetscNew(&atb));
39: PetscCall(MatTranspose(P, MAT_INITIAL_MATRIX, &Pt));
40: PetscCall(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: PetscFunctionReturn(PETSC_SUCCESS);
50: }
52: /* hypre */
53: #if defined(PETSC_HAVE_HYPRE)
54: PetscCall(PetscStrcmp(alg, "hypre", &flg));
55: if (flg) {
56: PetscCall(MatPtAPSymbolic_AIJ_AIJ_wHYPRE(A, P, fill, C));
57: PetscFunctionReturn(PETSC_SUCCESS);
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: PetscFunctionBegin;
77: /* Get ij structure of P^T */
78: PetscCall(MatGetSymbolicTranspose_SeqAIJ(P, &pti, &ptj));
79: ptJ = ptj;
81: /* Allocate ci array, arrays for fill computation and */
82: /* free space for accumulating nonzero column info */
83: PetscCall(PetscMalloc1(pn + 1, &ci));
84: ci[0] = 0;
86: PetscCall(PetscCalloc1(2 * an + 1, &ptadenserow));
87: ptasparserow = ptadenserow + an;
89: /* create and initialize a linked list */
90: nlnk = pn + 1;
91: PetscCall(PetscLLCreate(pn, pn, nlnk, lnk, lnkbt));
93: /* Set initial free space to be fill*(nnz(A)+ nnz(P)) */
94: PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(ai[am], pi[pm])), &free_space));
95: current_space = free_space;
97: /* Determine symbolic info for each row of C: */
98: for (i = 0; i < pn; i++) {
99: ptnzi = pti[i + 1] - pti[i];
100: ptanzi = 0;
101: /* Determine symbolic row of PtA: */
102: for (j = 0; j < ptnzi; j++) {
103: arow = *ptJ++;
104: anzj = ai[arow + 1] - ai[arow];
105: ajj = aj + ai[arow];
106: for (k = 0; k < anzj; k++) {
107: if (!ptadenserow[ajj[k]]) {
108: ptadenserow[ajj[k]] = -1;
109: ptasparserow[ptanzi++] = ajj[k];
110: }
111: }
112: }
113: /* Using symbolic info for row of PtA, determine symbolic info for row of C: */
114: ptaj = ptasparserow;
115: cnzi = 0;
116: for (j = 0; j < ptanzi; j++) {
117: prow = *ptaj++;
118: pnzj = pi[prow + 1] - pi[prow];
119: pjj = pj + pi[prow];
120: /* add non-zero cols of P into the sorted linked list lnk */
121: PetscCall(PetscLLAddSorted(pnzj, pjj, pn, &nlnk, lnk, lnkbt));
122: cnzi += nlnk;
123: }
125: /* If free space is not available, make more free space */
126: /* Double the amount of total space in the list */
127: if (current_space->local_remaining < cnzi) {
128: PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(cnzi, current_space->total_array_size), ¤t_space));
129: nspacedouble++;
130: }
132: /* Copy data into free space, and zero out denserows */
133: PetscCall(PetscLLClean(pn, pn, cnzi, lnk, current_space->array, lnkbt));
135: current_space->array += cnzi;
136: current_space->local_used += cnzi;
137: current_space->local_remaining -= cnzi;
139: for (j = 0; j < ptanzi; j++) ptadenserow[ptasparserow[j]] = 0;
141: /* Aside: Perhaps we should save the pta info for the numerical factorization. */
142: /* For now, we will recompute what is needed. */
143: ci[i + 1] = ci[i] + cnzi;
144: }
145: /* nnz is now stored in ci[ptm], column indices are in the list of free space */
146: /* Allocate space for cj, initialize cj, and */
147: /* destroy list of free space and other temporary array(s) */
148: PetscCall(PetscMalloc1(ci[pn] + 1, &cj));
149: PetscCall(PetscFreeSpaceContiguous(&free_space, cj));
150: PetscCall(PetscFree(ptadenserow));
151: PetscCall(PetscLLDestroy(lnk, lnkbt));
153: PetscCall(PetscCalloc1(ci[pn] + 1, &ca));
155: /* put together the new matrix */
156: PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), pn, pn, ci, cj, ca, ((PetscObject)A)->type_name, C));
157: PetscCall(MatSetBlockSizes(C, PetscAbs(P->cmap->bs), PetscAbs(P->cmap->bs)));
159: /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
160: /* Since these are PETSc arrays, change flags to free them as necessary. */
161: c = (Mat_SeqAIJ *)((C)->data);
162: c->free_a = PETSC_TRUE;
163: c->free_ij = PETSC_TRUE;
164: c->nonew = 0;
166: C->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy;
168: /* set MatInfo */
169: afill = (PetscReal)ci[pn] / (ai[am] + pi[pm] + 1.e-5);
170: if (afill < 1.0) afill = 1.0;
171: C->info.mallocs = nspacedouble;
172: C->info.fill_ratio_given = fill;
173: C->info.fill_ratio_needed = afill;
175: /* Clean up. */
176: PetscCall(MatRestoreSymbolicTranspose_SeqAIJ(P, &pti, &ptj));
177: #if defined(PETSC_USE_INFO)
178: if (ci[pn] != 0) {
179: PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
180: PetscCall(PetscInfo(C, "Use MatPtAP(A,P,MatReuse,%g,&C) for best performance.\n", (double)afill));
181: } else {
182: PetscCall(PetscInfo(C, "Empty matrix product\n"));
183: }
184: #endif
185: PetscFunctionReturn(PETSC_SUCCESS);
186: }
188: PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy(Mat A, Mat P, Mat C)
189: {
190: Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
191: Mat_SeqAIJ *p = (Mat_SeqAIJ *)P->data;
192: Mat_SeqAIJ *c = (Mat_SeqAIJ *)C->data;
193: PetscInt *ai = a->i, *aj = a->j, *apj, *apjdense, *pi = p->i, *pj = p->j, *pJ = p->j, *pjj;
194: PetscInt *ci = c->i, *cj = c->j, *cjj;
195: PetscInt am = A->rmap->N, cn = C->cmap->N, cm = C->rmap->N;
196: PetscInt i, j, k, anzi, pnzi, apnzj, nextap, pnzj, prow, crow;
197: MatScalar *aa, *apa, *pa, *pA, *paj, *ca, *caj;
199: PetscFunctionBegin;
200: /* Allocate temporary array for storage of one row of A*P (cn: non-scalable) */
201: PetscCall(PetscCalloc2(cn, &apa, cn, &apjdense));
202: PetscCall(PetscMalloc1(cn, &apj));
203: /* trigger CPU copies if needed and flag CPU mask for C */
204: #if defined(PETSC_HAVE_DEVICE)
205: {
206: const PetscScalar *dummy;
207: PetscCall(MatSeqAIJGetArrayRead(A, &dummy));
208: PetscCall(MatSeqAIJRestoreArrayRead(A, &dummy));
209: PetscCall(MatSeqAIJGetArrayRead(P, &dummy));
210: PetscCall(MatSeqAIJRestoreArrayRead(P, &dummy));
211: if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
212: }
213: #endif
214: aa = a->a;
215: pa = p->a;
216: pA = p->a;
217: ca = c->a;
219: /* Clear old values in C */
220: PetscCall(PetscArrayzero(ca, ci[cm]));
222: for (i = 0; i < am; i++) {
223: /* Form sparse row of A*P */
224: anzi = ai[i + 1] - ai[i];
225: apnzj = 0;
226: for (j = 0; j < anzi; j++) {
227: prow = *aj++;
228: pnzj = pi[prow + 1] - pi[prow];
229: pjj = pj + pi[prow];
230: paj = pa + pi[prow];
231: for (k = 0; k < pnzj; k++) {
232: if (!apjdense[pjj[k]]) {
233: apjdense[pjj[k]] = -1;
234: apj[apnzj++] = pjj[k];
235: }
236: apa[pjj[k]] += (*aa) * paj[k];
237: }
238: PetscCall(PetscLogFlops(2.0 * pnzj));
239: aa++;
240: }
242: /* Sort the j index array for quick sparse axpy. */
243: /* Note: a array does not need sorting as it is in dense storage locations. */
244: PetscCall(PetscSortInt(apnzj, apj));
246: /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */
247: pnzi = pi[i + 1] - pi[i];
248: for (j = 0; j < pnzi; j++) {
249: nextap = 0;
250: crow = *pJ++;
251: cjj = cj + ci[crow];
252: caj = ca + ci[crow];
253: /* Perform sparse axpy operation. Note cjj includes apj. */
254: for (k = 0; nextap < apnzj; k++) {
255: PetscAssert(k < ci[crow + 1] - ci[crow], PETSC_COMM_SELF, PETSC_ERR_PLIB, "k too large k %" PetscInt_FMT ", crow %" PetscInt_FMT, k, crow);
256: if (cjj[k] == apj[nextap]) caj[k] += (*pA) * apa[apj[nextap++]];
257: }
258: PetscCall(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: PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
271: PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
273: PetscCall(PetscFree2(apa, apjdense));
274: PetscCall(PetscFree(apj));
275: PetscFunctionReturn(PETSC_SUCCESS);
276: }
278: PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ(Mat A, Mat P, Mat C)
279: {
280: Mat_MatTransMatMult *atb;
282: PetscFunctionBegin;
283: MatCheckProduct(C, 3);
284: atb = (Mat_MatTransMatMult *)C->product->data;
285: PetscCheck(atb, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Missing data structure");
286: PetscCall(MatTranspose(P, MAT_REUSE_MATRIX, &atb->At));
287: PetscCheck(C->ops->matmultnumeric, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Missing numeric operation");
288: /* when using rap, MatMatMatMultSymbolic used a different data */
289: if (atb->data) C->product->data = atb->data;
290: PetscCall((*C->ops->matmatmultnumeric)(atb->At, A, P, C));
291: C->product->data = atb;
292: PetscFunctionReturn(PETSC_SUCCESS);
293: }