Actual source code: mpimatmatmult.c
1: /*
2: Defines matrix-matrix product routines for pairs of MPIAIJ matrices
3: C = A * B
4: */
5: #include <../src/mat/impls/aij/seq/aij.h>
6: #include <../src/mat/utils/freespace.h>
7: #include <../src/mat/impls/aij/mpi/mpiaij.h>
8: #include <petscbt.h>
9: #include <../src/mat/impls/dense/mpi/mpidense.h>
10: #include <petsc/private/vecimpl.h>
11: #include <petsc/private/sfimpl.h>
13: #if PetscDefined(HAVE_HYPRE)
14: PETSC_INTERN PetscErrorCode MatMatMultSymbolic_AIJ_AIJ_wHYPRE(Mat, Mat, PetscReal, Mat);
15: #endif
17: PETSC_INTERN PetscErrorCode MatProductSymbolic_ABt_MPIAIJ_MPIAIJ(Mat C)
18: {
19: Mat_Product *product = C->product;
20: Mat B = product->B;
22: PetscFunctionBegin;
23: PetscCall(MatTranspose(B, MAT_INITIAL_MATRIX, &product->B));
24: PetscCall(MatDestroy(&B));
25: PetscCall(MatProductSymbolic_AB_MPIAIJ_MPIAIJ(C));
26: PetscFunctionReturn(PETSC_SUCCESS);
27: }
29: PETSC_INTERN PetscErrorCode MatProductSymbolic_AB_MPIAIJ_MPIAIJ(Mat C)
30: {
31: Mat_Product *product = C->product;
32: Mat A = product->A, B = product->B;
33: MatProductAlgorithm alg = product->alg;
34: PetscReal fill = product->fill;
35: PetscBool flg;
37: PetscFunctionBegin;
38: /* scalable */
39: PetscCall(PetscStrcmp(alg, "scalable", &flg));
40: if (flg || C->structure_only) {
41: if (C->structure_only) PetscCall(MatProductSetAlgorithm(C, "scalable"));
42: PetscCall(MatMatMultSymbolic_MPIAIJ_MPIAIJ(A, B, fill, C));
43: PetscFunctionReturn(PETSC_SUCCESS);
44: }
46: /* nonscalable */
47: PetscCall(PetscStrcmp(alg, "nonscalable", &flg));
48: if (flg) {
49: PetscCall(MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A, B, fill, C));
50: PetscFunctionReturn(PETSC_SUCCESS);
51: }
53: /* seqmpi */
54: PetscCall(PetscStrcmp(alg, "seqmpi", &flg));
55: if (flg) {
56: PetscCall(MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(A, B, fill, C));
57: PetscFunctionReturn(PETSC_SUCCESS);
58: }
60: /* backend general code */
61: PetscCall(PetscStrcmp(alg, "backend", &flg));
62: if (flg) {
63: PetscCall(MatProductSymbolic_MPIAIJBACKEND(C));
64: PetscFunctionReturn(PETSC_SUCCESS);
65: }
67: #if PetscDefined(HAVE_HYPRE)
68: PetscCall(PetscStrcmp(alg, "hypre", &flg));
69: if (flg) {
70: PetscCall(MatMatMultSymbolic_AIJ_AIJ_wHYPRE(A, B, fill, C));
71: PetscFunctionReturn(PETSC_SUCCESS);
72: }
73: #endif
74: SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_SUP, "Mat Product Algorithm is not supported");
75: }
77: PetscErrorCode MatProductCtxDestroy_MPIAIJ_MatMatMult(PetscCtxRt data)
78: {
79: MatProductCtx_APMPI *ptap = *(MatProductCtx_APMPI **)data;
81: PetscFunctionBegin;
82: PetscCall(PetscFree2(ptap->startsj_s, ptap->startsj_r));
83: PetscCall(PetscFree(ptap->bufa));
84: PetscCall(MatDestroy(&ptap->P_loc));
85: PetscCall(MatDestroy(&ptap->P_oth));
86: PetscCall(MatDestroy(&ptap->Pt));
87: PetscCall(PetscFree(ptap->api));
88: PetscCall(PetscFree(ptap->apj));
89: PetscCall(PetscFree(ptap->apa));
90: PetscCall(PetscFree(ptap));
91: PetscFunctionReturn(PETSC_SUCCESS);
92: }
94: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat A, Mat P, Mat C)
95: {
96: Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data, *c = (Mat_MPIAIJ *)C->data;
97: Mat_SeqAIJ *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data;
98: Mat_SeqAIJ *cd = (Mat_SeqAIJ *)c->A->data, *co = (Mat_SeqAIJ *)c->B->data;
99: PetscScalar *cda, *coa;
100: Mat_SeqAIJ *p_loc, *p_oth;
101: PetscScalar *apa, *ca;
102: PetscInt cm = C->rmap->n;
103: MatProductCtx_APMPI *ptap;
104: PetscInt *api, *apj, *apJ, i, k;
105: PetscInt cstart = C->cmap->rstart;
106: PetscInt cdnz, conz, k0, k1;
107: const PetscScalar *dummy1, *dummy2, *dummy3, *dummy4;
108: MPI_Comm comm;
109: PetscMPIInt size;
111: PetscFunctionBegin;
112: MatCheckProduct(C, 3);
113: ptap = (MatProductCtx_APMPI *)C->product->data;
114: PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
115: PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
116: PetscCallMPI(MPI_Comm_size(comm, &size));
117: PetscCheck(ptap->P_oth || size <= 1, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "AP cannot be reused. Do not call MatProductClear()");
119: /* flag CPU mask for C */
120: #if PetscDefined(HAVE_DEVICE)
121: if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
122: if (c->A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->A->offloadmask = PETSC_OFFLOAD_CPU;
123: if (c->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->B->offloadmask = PETSC_OFFLOAD_CPU;
124: #endif
126: /* 1) get P_oth = ptap->P_oth and P_loc = ptap->P_loc */
127: /* update numerical values of P_oth and P_loc */
128: PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_REUSE_MATRIX, &ptap->startsj_s, &ptap->startsj_r, &ptap->bufa, &ptap->P_oth));
129: PetscCall(MatMPIAIJGetLocalMat(P, MAT_REUSE_MATRIX, &ptap->P_loc));
131: /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
132: /* get data from symbolic products */
133: p_loc = (Mat_SeqAIJ *)ptap->P_loc->data;
134: p_oth = NULL;
135: if (size > 1) p_oth = (Mat_SeqAIJ *)ptap->P_oth->data;
137: /* get apa for storing dense row A[i,:]*P */
138: apa = ptap->apa;
140: api = ptap->api;
141: apj = ptap->apj;
142: /* trigger copy to CPU */
143: PetscCall(MatSeqAIJGetArrayRead(a->A, &dummy1));
144: PetscCall(MatSeqAIJGetArrayRead(a->B, &dummy2));
145: PetscCall(MatSeqAIJGetArrayRead(ptap->P_loc, &dummy3));
146: if (ptap->P_oth) PetscCall(MatSeqAIJGetArrayRead(ptap->P_oth, &dummy4));
147: PetscCall(MatSeqAIJGetArrayWrite(c->A, &cda));
148: PetscCall(MatSeqAIJGetArrayWrite(c->B, &coa));
149: for (i = 0; i < cm; i++) {
150: /* compute apa = A[i,:]*P */
151: AProw_nonscalable(i, ad, ao, p_loc, p_oth, apa);
153: /* set values in C */
154: apJ = PetscSafePointerPlusOffset(apj, api[i]);
155: cdnz = cd->i[i + 1] - cd->i[i];
156: conz = co->i[i + 1] - co->i[i];
158: /* 1st off-diagonal part of C */
159: ca = PetscSafePointerPlusOffset(coa, co->i[i]);
160: k = 0;
161: for (k0 = 0; k0 < conz; k0++) {
162: if (apJ[k] >= cstart) break;
163: ca[k0] = apa[apJ[k]];
164: apa[apJ[k++]] = 0.0;
165: }
167: /* diagonal part of C */
168: ca = PetscSafePointerPlusOffset(cda, cd->i[i]);
169: for (k1 = 0; k1 < cdnz; k1++) {
170: ca[k1] = apa[apJ[k]];
171: apa[apJ[k++]] = 0.0;
172: }
174: /* 2nd off-diagonal part of C */
175: ca = PetscSafePointerPlusOffset(coa, co->i[i]);
176: for (; k0 < conz; k0++) {
177: ca[k0] = apa[apJ[k]];
178: apa[apJ[k++]] = 0.0;
179: }
180: }
181: PetscCall(MatSeqAIJRestoreArrayRead(a->A, &dummy1));
182: PetscCall(MatSeqAIJRestoreArrayRead(a->B, &dummy2));
183: PetscCall(MatSeqAIJRestoreArrayRead(ptap->P_loc, &dummy3));
184: if (ptap->P_oth) PetscCall(MatSeqAIJRestoreArrayRead(ptap->P_oth, &dummy4));
185: PetscCall(MatSeqAIJRestoreArrayWrite(c->A, &cda));
186: PetscCall(MatSeqAIJRestoreArrayWrite(c->B, &coa));
188: PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
189: PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
190: PetscFunctionReturn(PETSC_SUCCESS);
191: }
193: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat A, Mat P, PetscReal fill, Mat C)
194: {
195: MPI_Comm comm;
196: PetscMPIInt size;
197: MatProductCtx_APMPI *ptap;
198: PetscFreeSpaceList free_space = NULL, current_space = NULL;
199: Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
200: Mat_SeqAIJ *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data, *p_loc, *p_oth;
201: PetscInt *pi_loc, *pj_loc, *pi_oth, *pj_oth, *dnz, *onz;
202: PetscInt *adi = ad->i, *adj = ad->j, *aoi = ao->i, *aoj = ao->j, rstart = A->rmap->rstart;
203: PetscInt *lnk, i, pnz, row, *api, *apj, *Jptr, apnz, nspacedouble = 0, j, nzi;
204: PetscInt am = A->rmap->n, pN = P->cmap->N, pn = P->cmap->n, pm = P->rmap->n;
205: PetscBT lnkbt;
206: PetscReal afill;
207: MatType mtype;
209: PetscFunctionBegin;
210: MatCheckProduct(C, 4);
211: PetscCheck(!C->product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");
212: PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
213: PetscCallMPI(MPI_Comm_size(comm, &size));
215: /* create struct MatProductCtx_APMPI and attached it to C later */
216: PetscCall(PetscNew(&ptap));
218: /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
219: PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_INITIAL_MATRIX, &ptap->startsj_s, &ptap->startsj_r, &ptap->bufa, &ptap->P_oth));
221: /* get P_loc by taking all local rows of P */
222: PetscCall(MatMPIAIJGetLocalMat(P, MAT_INITIAL_MATRIX, &ptap->P_loc));
224: p_loc = (Mat_SeqAIJ *)ptap->P_loc->data;
225: pi_loc = p_loc->i;
226: pj_loc = p_loc->j;
227: if (size > 1) {
228: p_oth = (Mat_SeqAIJ *)ptap->P_oth->data;
229: pi_oth = p_oth->i;
230: pj_oth = p_oth->j;
231: } else {
232: p_oth = NULL;
233: pi_oth = NULL;
234: pj_oth = NULL;
235: }
237: /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
238: PetscCall(PetscMalloc1(am + 1, &api));
239: ptap->api = api;
240: api[0] = 0;
242: /* create and initialize a linked list */
243: PetscCall(PetscLLCondensedCreate(pN, pN, &lnk, &lnkbt));
245: /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
246: PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(adi[am], PetscIntSumTruncate(aoi[am], pi_loc[pm]))), &free_space));
247: current_space = free_space;
249: MatPreallocateBegin(comm, am, pn, dnz, onz);
250: for (i = 0; i < am; i++) {
251: /* diagonal portion of A */
252: nzi = adi[i + 1] - adi[i];
253: for (j = 0; j < nzi; j++) {
254: row = *adj++;
255: pnz = pi_loc[row + 1] - pi_loc[row];
256: Jptr = pj_loc + pi_loc[row];
257: /* add non-zero cols of P into the sorted linked list lnk */
258: PetscCall(PetscLLCondensedAddSorted(pnz, Jptr, lnk, lnkbt));
259: }
260: /* off-diagonal portion of A */
261: nzi = aoi[i + 1] - aoi[i];
262: for (j = 0; j < nzi; j++) {
263: row = *aoj++;
264: pnz = pi_oth[row + 1] - pi_oth[row];
265: Jptr = pj_oth + pi_oth[row];
266: PetscCall(PetscLLCondensedAddSorted(pnz, Jptr, lnk, lnkbt));
267: }
268: /* add possible missing diagonal entry */
269: if (C->force_diagonals) {
270: j = i + rstart; /* column index */
271: PetscCall(PetscLLCondensedAddSorted(1, &j, lnk, lnkbt));
272: }
274: apnz = lnk[0];
275: api[i + 1] = api[i] + apnz;
277: /* if free space is not available, double the total space in the list */
278: if (current_space->local_remaining < apnz) {
279: PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(apnz, current_space->total_array_size), ¤t_space));
280: nspacedouble++;
281: }
283: /* Copy data into free space, then initialize lnk */
284: PetscCall(PetscLLCondensedClean(pN, apnz, current_space->array, lnk, lnkbt));
285: PetscCall(MatPreallocateSet(i + rstart, apnz, current_space->array, dnz, onz));
287: current_space->array += apnz;
288: current_space->local_used += apnz;
289: current_space->local_remaining -= apnz;
290: }
292: /* Allocate space for apj, initialize apj, and */
293: /* destroy list of free space and other temporary array(s) */
294: PetscCall(PetscMalloc1(api[am], &ptap->apj));
295: apj = ptap->apj;
296: PetscCall(PetscFreeSpaceContiguous(&free_space, ptap->apj));
297: PetscCall(PetscLLDestroy(lnk, lnkbt));
299: /* malloc apa to store dense row A[i,:]*P */
300: PetscCall(PetscCalloc1(pN, &ptap->apa));
302: /* set and assemble symbolic parallel matrix C */
303: PetscCall(MatSetSizes(C, am, pn, PETSC_DETERMINE, PETSC_DETERMINE));
304: PetscCall(MatSetBlockSizesFromMats(C, A, P));
306: PetscCall(MatGetType(A, &mtype));
307: PetscCall(MatSetType(C, mtype));
308: PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
309: MatPreallocateEnd(dnz, onz);
311: PetscCall(MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api));
312: PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
313: PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
314: PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
315: PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
317: C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
318: C->ops->productnumeric = MatProductNumeric_AB;
320: /* attach the supporting struct to C for reuse */
321: C->product->data = ptap;
322: C->product->destroy = MatProductCtxDestroy_MPIAIJ_MatMatMult;
324: /* set MatInfo */
325: afill = (PetscReal)api[am] / (adi[am] + aoi[am] + pi_loc[pm] + 1) + 1.e-5;
326: if (afill < 1.0) afill = 1.0;
327: C->info.mallocs = nspacedouble;
328: C->info.fill_ratio_given = fill;
329: C->info.fill_ratio_needed = afill;
331: if (PetscDefined(USE_INFO)) {
332: if (api[am]) {
333: PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
334: PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
335: } else PetscCall(PetscInfo(C, "Empty matrix product\n"));
336: }
337: PetscFunctionReturn(PETSC_SUCCESS);
338: }
340: static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat, Mat, PetscReal, Mat);
341: static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat, Mat, Mat);
343: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AB(Mat C)
344: {
345: Mat_Product *product = C->product;
346: Mat A = product->A, B = product->B;
348: PetscFunctionBegin;
349: if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend)
350: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, (%" PetscInt_FMT ", %" PetscInt_FMT ") != (%" PetscInt_FMT ",%" PetscInt_FMT ")", A->cmap->rstart, A->cmap->rend, B->rmap->rstart, B->rmap->rend);
352: C->ops->matmultsymbolic = MatMatMultSymbolic_MPIAIJ_MPIDense;
353: C->ops->productsymbolic = MatProductSymbolic_AB;
354: PetscFunctionReturn(PETSC_SUCCESS);
355: }
357: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(Mat C)
358: {
359: Mat_Product *product = C->product;
360: Mat A = product->A, B = product->B;
362: PetscFunctionBegin;
363: if (A->rmap->rstart != B->rmap->rstart || A->rmap->rend != B->rmap->rend)
364: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, (%" PetscInt_FMT ", %" PetscInt_FMT ") != (%" PetscInt_FMT ",%" PetscInt_FMT ")", A->rmap->rstart, A->rmap->rend, B->rmap->rstart, B->rmap->rend);
366: C->ops->transposematmultsymbolic = MatTransposeMatMultSymbolic_MPIAIJ_MPIDense;
367: C->ops->productsymbolic = MatProductSymbolic_AtB;
368: PetscFunctionReturn(PETSC_SUCCESS);
369: }
371: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense(Mat C)
372: {
373: Mat_Product *product = C->product;
375: PetscFunctionBegin;
376: switch (product->type) {
377: case MATPRODUCT_AB:
378: PetscCall(MatProductSetFromOptions_MPIAIJ_MPIDense_AB(C));
379: break;
380: case MATPRODUCT_AtB:
381: PetscCall(MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(C));
382: break;
383: default:
384: break;
385: }
386: PetscFunctionReturn(PETSC_SUCCESS);
387: }
389: PETSC_INTERN PetscErrorCode MatMPIDenseScatterDestroy_Private(MPIAIJ_MPIDense *contents)
390: {
391: PetscFunctionBegin;
392: PetscCall(MatDestroy(&contents->workB));
393: PetscCall(PetscSFDestroy(&contents->sf[0]));
394: PetscCall(PetscSFDestroy(&contents->sf[1]));
395: for (PetscInt i = 0; i < contents->nsends; i++) PetscCallMPI(MPI_Type_free(&contents->stype[i]));
396: for (PetscInt i = 0; i < contents->nrecvs; i++) PetscCallMPI(MPI_Type_free(&contents->rtype[i]));
397: PetscCall(PetscFree4(contents->stype, contents->rtype, contents->rwaits, contents->swaits));
398: PetscFunctionReturn(PETSC_SUCCESS);
399: }
401: typedef struct {
402: MPIAIJ_MPIDense scatter;
403: Mat workC; /* off-diagonal contribution A_o * workB on the device route, NULL otherwise */
404: } MPIAIJ_MPIDense_AB;
406: static PetscErrorCode MatMPIAIJ_MPIDenseDestroy(PetscCtxRt ctx)
407: {
408: MPIAIJ_MPIDense_AB *data = *(MPIAIJ_MPIDense_AB **)ctx;
410: PetscFunctionBegin;
411: PetscCall(MatDestroy(&data->workC));
412: PetscCall(MatMPIDenseScatterDestroy_Private(&data->scatter));
413: PetscCall(PetscFree(data));
414: PetscFunctionReturn(PETSC_SUCCESS);
415: }
417: PETSC_INTERN PetscErrorCode MatMPIDenseScatterSetUp_Private(VecScatter ctx, PetscInt nrows, PetscInt bs, PetscInt Am, Mat B, Mat C, MPIAIJ_MPIDense *contents, PetscInt *batchSize, PetscInt *numBatches)
418: {
419: PetscInt Bm = B->rmap->n, BN = B->cmap->N, Bbn, Bbs, numBb, ncols;
420: MPI_Comm comm;
421: MPI_Datatype type1;
422: const PetscInt *sindices, *sstarts, *rstarts;
423: PetscMPIInt *disp;
424: PetscMPIInt nsends, nrecvs, nrows_to, nrows_from, bs_mpi;
425: PetscBool flg;
427: PetscFunctionBegin;
428: PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
429: PetscCall(MatDenseGetLDA(B, &contents->blda));
431: /* Create column block of B and C for memory scalability when BN is too large */
432: /* Estimate Bbn, column size of Bb */
433: if (nrows) {
434: Bbn = 2 * Am * BN / nrows;
435: if (!Bbn) Bbn = 1;
436: } else Bbn = BN;
437: Bbs = B->cmap->bs;
438: Bbn = Bbn / Bbs * Bbs;
439: if (Bbn > BN) Bbn = BN;
440: PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &Bbn, 1, MPIU_INT, MPI_MAX, comm));
442: /* Enable runtime option for Bbn */
443: PetscOptionsBegin(comm, ((PetscObject)C)->prefix, "MatProduct", "Mat");
444: PetscCall(PetscOptionsDeprecated("-matmatmult_Bbn", "-matproduct_batch_size", "3.25", NULL));
445: PetscCall(PetscOptionsBoundedInt("-matproduct_batch_size", "Number of dense columns per batch", "MatProduct", Bbn, &Bbn, NULL, 0));
446: PetscOptionsEnd();
447: Bbn = PetscMin(Bbn, BN);
449: if (Bbn > 0 && Bbn < BN) numBb = BN / Bbn;
450: else numBb = 0;
451: if (numBb) PetscCall(PetscInfo(C, "Using column batches of size %" PetscInt_FMT " for %" PetscInt_FMT " dense columns\n", Bbn, BN));
452: ncols = Bbn ? Bbn : BN;
454: /* Create work matrix used to store off processor rows of B needed for local product, with the same type as the local block of B */
455: PetscCall(MatCreate(PETSC_COMM_SELF, &contents->workB));
456: PetscCall(MatSetSizes(contents->workB, nrows, ncols, nrows, ncols));
457: PetscCall(MatSetType(contents->workB, ((PetscObject)((Mat_MPIDense *)B->data)->A)->type_name));
458: PetscCall(MatSetUp(contents->workB));
460: PetscCall(PetscObjectTypeCompare((PetscObject)((Mat_MPIDense *)B->data)->A, MATSEQDENSE, &flg));
461: contents->ondevice = (PetscBool)!flg;
462: if (contents->ondevice) {
463: /* Use strided PetscSFs, which support device memory, instead of the MPI derived data types below */
464: PetscCheck(ctx->vscat.bs <= 1 || contents->blda % ctx->vscat.bs == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Leading dimension %" PetscInt_FMT " of the dense matrix must be a multiple of the block size %" PetscInt_FMT, contents->blda, ctx->vscat.bs);
465: contents->ncols[0] = ncols;
466: PetscCall(PetscSFCreateStridedSF(ctx, ncols, contents->blda, nrows, &contents->sf[0]));
467: if (numBb && BN % Bbn) {
468: contents->ncols[1] = BN % Bbn;
469: PetscCall(PetscSFCreateStridedSF(ctx, BN % Bbn, contents->blda, nrows, &contents->sf[1]));
470: }
471: } else {
472: PetscCall(VecScatterGetRemote_Private(ctx, PETSC_TRUE, &nsends, &sstarts, &sindices, NULL, NULL));
473: PetscCall(VecScatterGetRemoteOrdered_Private(ctx, PETSC_FALSE, &nrecvs, &rstarts, NULL, NULL, NULL));
475: /* Use MPI derived data type to reduce memory required by the send/recv buffers */
476: PetscCall(PetscMalloc4(nsends, &contents->stype, nrecvs, &contents->rtype, nrecvs, &contents->rwaits, nsends, &contents->swaits));
477: contents->nsends = nsends;
478: contents->nrecvs = nrecvs;
480: PetscCall(PetscMalloc1(PetscMax(Bm, 1), &disp));
481: PetscCall(PetscMPIIntCast(bs, &bs_mpi));
482: for (PetscMPIInt i = 0; i < nsends; i++) {
483: PetscCall(PetscMPIIntCast(sstarts[i + 1] - sstarts[i], &nrows_to));
484: for (PetscInt j = 0; j < nrows_to; j++) PetscCall(PetscMPIIntCast(sindices[sstarts[i] + j] * bs, &disp[j]));
485: PetscCallMPI(MPI_Type_create_indexed_block(nrows_to, bs_mpi, disp, MPIU_SCALAR, &type1));
486: PetscCallMPI(MPI_Type_create_resized(type1, 0, contents->blda * sizeof(PetscScalar), &contents->stype[i]));
487: PetscCallMPI(MPI_Type_commit(&contents->stype[i]));
488: PetscCallMPI(MPI_Type_free(&type1));
489: }
491: for (PetscMPIInt i = 0; i < nrecvs; i++) {
492: /* received values from a process form a (nrows_from x Bbn) row block in workB (column-wise) */
493: PetscCall(PetscMPIIntCast((rstarts[i + 1] - rstarts[i]) * bs, &nrows_from));
494: disp[0] = 0;
495: PetscCallMPI(MPI_Type_create_indexed_block(1, nrows_from, disp, MPIU_SCALAR, &type1));
496: PetscCallMPI(MPI_Type_create_resized(type1, 0, nrows * sizeof(PetscScalar), &contents->rtype[i]));
497: PetscCallMPI(MPI_Type_commit(&contents->rtype[i]));
498: PetscCallMPI(MPI_Type_free(&type1));
499: }
501: PetscCall(PetscFree(disp));
502: PetscCall(VecScatterRestoreRemote_Private(ctx, PETSC_TRUE /*send*/, &nsends, &sstarts, &sindices, NULL, NULL));
503: PetscCall(VecScatterRestoreRemoteOrdered_Private(ctx, PETSC_FALSE /*recv*/, &nrecvs, &rstarts, NULL, NULL, NULL));
504: }
505: if (batchSize) *batchSize = Bbn;
506: if (numBatches) *numBatches = numBb;
507: PetscFunctionReturn(PETSC_SUCCESS);
508: }
510: static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat A, Mat B, PetscReal fill, Mat C)
511: {
512: Mat_MPIAIJ *aij = (Mat_MPIAIJ *)A->data;
513: MPIAIJ_MPIDense_AB *data;
514: PetscInt nz = aij->B->cmap->n;
515: VecScatter ctx = aij->Mvctx;
516: PetscInt Am = A->rmap->n, BN = B->cmap->N, Bbn, numBb;
517: Mat workB1, workC1;
518: const char *ctype;
519: PetscBool cisdense;
521: PetscFunctionBegin;
522: MatCheckProduct(C, 4);
523: PetscCheck(!C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data not empty");
524: PetscCall(PetscObjectBaseTypeCompare((PetscObject)C, MATMPIDENSE, &cisdense));
525: if (!cisdense) {
526: PetscCall(MatSetType(C, ((PetscObject)B)->type_name));
527: PetscCall(MatSetVecType(C, B->defaultvectype));
528: }
529: PetscCall(MatSetSizes(C, Am, B->cmap->n, A->rmap->N, BN));
530: PetscCall(MatSetBlockSizesFromMats(C, A, B));
531: PetscCall(MatSetUp(C));
532: /* The cuSPARSE and hipSPARSE symbolic below re-types a host local block of C in place, so capture the type
533: of the local block of C now to give the work matrix the type the numeric will add it to */
534: ctype = ((PetscObject)((Mat_MPIDense *)C->data)->A)->type_name;
535: PetscCall(PetscNew(&data));
536: PetscCall(MatMPIDenseScatterSetUp_Private(ctx, nz, 1, Am, B, C, &data->scatter, &Bbn, &numBb));
537: PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
538: PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
539: PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
540: PetscCall(MatProductClear(aij->A));
541: PetscCall(MatProductClear(((Mat_MPIDense *)B->data)->A));
542: PetscCall(MatProductClear(((Mat_MPIDense *)C->data)->A));
543: if (data->scatter.ondevice && nz) {
544: /* On the device route the off-diagonal contribution is computed into a work matrix and added to the local
545: block of C, rather than accumulated in place by a host kernel */
546: PetscCall(MatCreate(PETSC_COMM_SELF, &data->workC));
547: PetscCall(MatSetSizes(data->workC, Am, Bbn ? Bbn : BN, Am, Bbn ? Bbn : BN));
548: PetscCall(MatSetType(data->workC, ctype));
549: PetscCall(MatSetUp(data->workC));
550: PetscCall(MatProductCreateWithMat(aij->B, data->scatter.workB, NULL, data->workC));
551: PetscCall(MatProductSetType(data->workC, MATPRODUCT_AB));
552: PetscCall(MatProductSetFromOptions(data->workC));
553: PetscCall(MatProductSymbolic(data->workC));
554: if (numBb && BN % Bbn) {
555: /* the last column batch is smaller, set up the product on the sub-matrices the numeric will use for it */
556: PetscCall(MatDenseGetSubMatrix(data->scatter.workB, PETSC_DECIDE, PETSC_DECIDE, 0, BN % Bbn, &workB1));
557: PetscCall(MatDenseGetSubMatrix(data->workC, PETSC_DECIDE, PETSC_DECIDE, 0, BN % Bbn, &workC1));
558: PetscCall(MatProductCreateWithMat(aij->B, workB1, NULL, workC1));
559: PetscCall(MatProductSetType(workC1, MATPRODUCT_AB));
560: PetscCall(MatProductSetFromOptions(workC1));
561: PetscCall(MatProductSymbolic(workC1));
562: PetscCall(MatDenseRestoreSubMatrix(data->workC, &workC1));
563: PetscCall(MatDenseRestoreSubMatrix(data->scatter.workB, &workB1));
564: }
565: }
566: PetscCall(MatProductCreateWithMat(aij->A, ((Mat_MPIDense *)B->data)->A, NULL, ((Mat_MPIDense *)C->data)->A));
567: PetscCall(MatProductSetType(((Mat_MPIDense *)C->data)->A, MATPRODUCT_AB));
568: PetscCall(MatProductSetFromOptions(((Mat_MPIDense *)C->data)->A));
569: PetscCall(MatProductSymbolic(((Mat_MPIDense *)C->data)->A));
570: C->product->data = data;
571: C->product->destroy = MatMPIAIJ_MPIDenseDestroy;
572: C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense;
573: PetscFunctionReturn(PETSC_SUCCESS);
574: }
576: PETSC_INTERN PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat, Mat, Mat, const PetscBool);
578: /*
579: Performs an efficient scatter on the rows of B needed by this process; this is
580: a modification of the VecScatterBegin_() routines.
581: */
582: static PetscErrorCode MatMPIDenseScatterHost_Private(VecScatter ctx, PetscInt bs, Mat workB, MPIAIJ_MPIDense *contents, Mat B, Mat C)
583: {
584: const PetscScalar *b;
585: PetscScalar *rvalues;
586: const PetscInt *sindices, *sstarts, *rstarts;
587: const PetscMPIInt *sprocs, *rprocs;
588: PetscMPIInt nsends, nrecvs;
589: MPI_Comm comm;
590: PetscMPIInt tag = ((PetscObject)ctx)->tag, ncols, nsends_mpi, nrecvs_mpi;
592: PetscFunctionBegin;
593: PetscCall(PetscMPIIntCast(B->cmap->N, &ncols));
594: PetscCall(VecScatterGetRemote_Private(ctx, PETSC_TRUE /*send*/, &nsends, &sstarts, &sindices, &sprocs, NULL /*bs*/));
595: PetscCall(VecScatterGetRemoteOrdered_Private(ctx, PETSC_FALSE /*recv*/, &nrecvs, &rstarts, NULL, &rprocs, NULL /*bs*/));
596: PetscCall(PetscMPIIntCast(nsends, &nsends_mpi));
597: PetscCall(PetscMPIIntCast(nrecvs, &nrecvs_mpi));
599: PetscCall(MatDenseGetArrayRead(B, &b));
600: PetscCall(MatDenseGetArray(workB, &rvalues));
602: /* Post recv, use MPI derived data type to save memory */
603: PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
604: for (PetscMPIInt i = 0; i < nrecvs; i++) PetscCallMPI(MPIU_Irecv(rvalues + ((rstarts[i] - rstarts[0]) * bs), ncols, contents->rtype[i], rprocs[i], tag, comm, contents->rwaits + i));
605: for (PetscMPIInt i = 0; i < nsends; i++) PetscCallMPI(MPIU_Isend(b, ncols, contents->stype[i], sprocs[i], tag, comm, contents->swaits + i));
607: if (nrecvs) PetscCallMPI(MPI_Waitall(nrecvs_mpi, contents->rwaits, MPI_STATUSES_IGNORE));
608: if (nsends) PetscCallMPI(MPI_Waitall(nsends_mpi, contents->swaits, MPI_STATUSES_IGNORE));
610: PetscCall(VecScatterRestoreRemote_Private(ctx, PETSC_TRUE /*send*/, &nsends, &sstarts, &sindices, &sprocs, NULL));
611: PetscCall(VecScatterRestoreRemoteOrdered_Private(ctx, PETSC_FALSE /*recv*/, &nrecvs, &rstarts, NULL, &rprocs, NULL));
612: PetscCall(MatDenseRestoreArrayRead(B, &b));
613: PetscCall(MatDenseRestoreArray(workB, &rvalues));
614: PetscFunctionReturn(PETSC_SUCCESS);
615: }
617: /*
618: Same as MatMPIDenseScatterHost_Private(), but using the strided PetscSFs set up in
619: MatMPIDenseScatterSetUp_Private() so that the data never leaves the device. The scatter is split in two
620: halves so that a caller can run other work while the off-process rows of B are in flight
621: */
622: static PetscErrorCode MatMPIDenseScatterDeviceBegin_Private(Mat workB, MPIAIJ_MPIDense *contents, Mat B)
623: {
624: PetscSF sf;
625: PetscInt k = 0;
626: PetscMemType bmtype, wmtype;
628: PetscFunctionBegin;
629: PetscCheck(!contents->sfinuse, PETSC_COMM_SELF, PETSC_ERR_PLIB, "A scatter is already in flight");
630: if (B->cmap->N != contents->ncols[0]) k = 1;
631: PetscCheck(contents->sf[k] && contents->ncols[k] == B->cmap->N, PETSC_COMM_SELF, PETSC_ERR_PLIB, "No scatter set up for %" PetscInt_FMT " columns", B->cmap->N);
632: sf = contents->sf[k];
633: /* every entry of workB is overwritten, so write-only access is enough */
634: PetscCall(MatDenseGetArrayReadAndMemType(B, &contents->barray, &bmtype));
635: PetscCall(MatDenseGetArrayWriteAndMemType(workB, &contents->warray, &wmtype));
636: PetscCall(PetscSFBcastWithMemTypeBegin(sf, sf->vscat.unit, bmtype, contents->barray, wmtype, contents->warray, MPI_REPLACE));
637: contents->sfinuse = sf;
638: PetscFunctionReturn(PETSC_SUCCESS);
639: }
641: static PetscErrorCode MatMPIDenseScatterDeviceEnd_Private(Mat workB, MPIAIJ_MPIDense *contents, Mat B)
642: {
643: PetscSF sf = contents->sfinuse;
645: PetscFunctionBegin;
646: PetscCheck(sf, PETSC_COMM_SELF, PETSC_ERR_PLIB, "No scatter in flight");
647: PetscCall(PetscSFBcastEnd(sf, sf->vscat.unit, contents->barray, contents->warray, MPI_REPLACE));
648: PetscCall(MatDenseRestoreArrayWriteAndMemType(workB, &contents->warray));
649: PetscCall(MatDenseRestoreArrayReadAndMemType(B, &contents->barray));
650: contents->sfinuse = NULL;
651: PetscFunctionReturn(PETSC_SUCCESS);
652: }
654: /*
655: The checks the host and device scatters share; on the device route they are done by the begin half
656: */
657: static PetscErrorCode MatMPIDenseScatterCheck_Private(PetscInt nrows, Mat workB, MPIAIJ_MPIDense *contents, Mat B, Mat C)
658: {
659: PetscInt blda;
661: PetscFunctionBegin;
662: MatCheckProduct(C, 5);
663: PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data empty");
664: PetscCheck(nrows == workB->rmap->n, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Number of rows of workB %" PetscInt_FMT " not equal to columns of off-diagonal block %" PetscInt_FMT, workB->rmap->n, nrows);
665: PetscCall(MatDenseGetLDA(B, &blda));
666: PetscCheck(blda == contents->blda, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot reuse an input matrix with lda %" PetscInt_FMT " != %" PetscInt_FMT, blda, contents->blda);
667: PetscFunctionReturn(PETSC_SUCCESS);
668: }
670: PETSC_INTERN PetscErrorCode MatMPIDenseScatter_Private(VecScatter ctx, PetscInt nrows, PetscInt bs, Mat workB, MPIAIJ_MPIDense *contents, Mat B, Mat C)
671: {
672: PetscFunctionBegin;
673: PetscCall(MatMPIDenseScatterCheck_Private(nrows, workB, contents, B, C));
674: if (contents->ondevice) {
675: PetscCall(MatMPIDenseScatterDeviceBegin_Private(workB, contents, B));
676: PetscCall(MatMPIDenseScatterDeviceEnd_Private(workB, contents, B));
677: } else PetscCall(MatMPIDenseScatterHost_Private(ctx, bs, workB, contents, B, C));
678: PetscFunctionReturn(PETSC_SUCCESS);
679: }
681: /*
682: Starts the scatter of the off-process rows of B into workB. On the device route only the begin half of the
683: PetscSF broadcast is posted, so the caller must complete it with MatMPIDenseScatterEnd(); the host scatter
684: is blocking and is done entirely here
685: */
686: static PetscErrorCode MatMPIDenseScatterBegin(Mat A, Mat B, Mat workB, Mat C)
687: {
688: Mat_MPIAIJ *aij = (Mat_MPIAIJ *)A->data;
689: MPIAIJ_MPIDense *contents = &((MPIAIJ_MPIDense_AB *)C->product->data)->scatter;
691: PetscFunctionBegin;
692: if (contents->ondevice) {
693: PetscCall(MatMPIDenseScatterCheck_Private(aij->B->cmap->n, workB, contents, B, C));
694: PetscCall(MatMPIDenseScatterDeviceBegin_Private(workB, contents, B));
695: } else PetscCall(MatMPIDenseScatter_Private(aij->Mvctx, aij->B->cmap->n, 1, workB, contents, B, C));
696: PetscFunctionReturn(PETSC_SUCCESS);
697: }
699: static PetscErrorCode MatMPIDenseScatterEnd(Mat B, Mat workB, Mat C)
700: {
701: MPIAIJ_MPIDense *contents = &((MPIAIJ_MPIDense_AB *)C->product->data)->scatter;
703: PetscFunctionBegin;
704: if (contents->ondevice) PetscCall(MatMPIDenseScatterDeviceEnd_Private(workB, contents, B));
705: PetscFunctionReturn(PETSC_SUCCESS);
706: }
708: /*
709: Computes C = A * B, creating the nested product and its symbolic the first time. When clear is true the
710: product is cleared by the numeric, so that the symbolic is redone on the next call
711: */
712: static PetscErrorCode MatMPIAIJ_MPIDenseProductNumeric_Private(Mat A, Mat B, Mat C, PetscBool clear)
713: {
714: PetscFunctionBegin;
715: if (!C->product) {
716: PetscCall(MatProductCreateWithMat(A, B, NULL, C));
717: PetscCall(MatProductSetType(C, MATPRODUCT_AB));
718: PetscCall(MatProductSetFromOptions(C));
719: PetscCall(MatProductSymbolic(C));
720: } else PetscCall(MatProductReplaceMats(A, B, NULL, C));
721: if (clear && !C->product->clear) C->product->clear = PETSC_TRUE;
722: PetscCall(MatProductNumeric(C));
723: PetscFunctionReturn(PETSC_SUCCESS);
724: }
726: static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A, Mat B, Mat C)
727: {
728: Mat_MPIAIJ *aij = (Mat_MPIAIJ *)A->data;
729: Mat_MPIDense *bdense = (Mat_MPIDense *)B->data;
730: Mat_MPIDense *cdense = (Mat_MPIDense *)C->data;
731: Mat workB;
732: MPIAIJ_MPIDense *contents;
733: MPIAIJ_MPIDense_AB *data;
734: PetscBool clear = PETSC_FALSE, flg, overlap;
736: PetscFunctionBegin;
737: MatCheckProduct(C, 3);
738: PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data empty");
739: data = (MPIAIJ_MPIDense_AB *)C->product->data;
740: contents = &data->scatter;
741: if (PetscDefined(HAVE_CUPM)) {
742: PetscCall(PetscObjectTypeCompare((PetscObject)C, MATMPIDENSE, &flg));
743: if (flg) PetscCall(PetscObjectTypeCompare((PetscObject)A, MATMPIAIJ, &flg));
744: clear = (PetscBool)!flg; /* if either A or C is a device Mat, make sure MatProductClear() is called */
745: }
746: /* The device scatter is non-blocking, so when there are no column batches start it before the product of the
747: diagonal block below to overlap the communication with that product, as MatMult_MPIAIJ() does. The host
748: scatter is blocking, so it is left where it is */
749: overlap = (PetscBool)(contents->ondevice && contents->workB->cmap->n == B->cmap->N);
750: if (overlap) PetscCall(MatMPIDenseScatterBegin(A, B, contents->workB, C));
751: /* diagonal block of A times all local rows of B, first make sure that everything is up-to-date */
752: PetscCall(MatMPIAIJ_MPIDenseProductNumeric_Private(aij->A, bdense->A, cdense->A, clear));
753: if (contents->workB->cmap->n == B->cmap->N) {
754: /* get off processor parts of B needed to complete C=A*B */
755: workB = contents->workB;
756: if (!overlap) PetscCall(MatMPIDenseScatterBegin(A, B, workB, C));
757: PetscCall(MatMPIDenseScatterEnd(B, workB, C));
759: /* off-diagonal block of A times nonlocal rows of B */
760: if (data->workC) {
761: PetscCall(MatMPIAIJ_MPIDenseProductNumeric_Private(aij->B, workB, data->workC, clear));
762: PetscCall(MatAXPY(cdense->A, 1.0, data->workC, SAME_NONZERO_PATTERN));
763: } else if (!contents->ondevice) PetscCall(MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B, workB, cdense->A, PETSC_TRUE)); /* the device route has no work matrix only when the off-diagonal block has no columns */
764: } else {
765: Mat Bb, Cb, workC;
766: PetscInt BN = B->cmap->N, n = contents->workB->cmap->n, cols;
767: PetscBool ccpu = PETSC_FALSE;
769: PetscCheck(n > 0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Column block size %" PetscInt_FMT " must be positive", n);
770: /* The host route accumulates into the local block of C on the host, bind C to the CPU to avoid copies back
771: and forth from the device when getting and restoring the sub-matrices */
772: if (!contents->ondevice) {
773: PetscCall(MatBoundToCPU(C, &ccpu));
774: PetscCall(MatBindToCPU(C, PETSC_TRUE));
775: }
776: for (PetscInt i = 0; i < BN; i += n) {
777: cols = PetscMin(n, BN - i);
778: workB = contents->workB;
779: workC = data->workC;
780: if (cols != n) {
781: PetscCall(MatDenseGetSubMatrix(contents->workB, PETSC_DECIDE, PETSC_DECIDE, 0, cols, &workB));
782: if (workC) PetscCall(MatDenseGetSubMatrix(data->workC, PETSC_DECIDE, PETSC_DECIDE, 0, cols, &workC));
783: }
784: PetscCall(MatDenseGetSubMatrix(B, PETSC_DECIDE, PETSC_DECIDE, i, i + cols, &Bb));
785: PetscCall(MatDenseGetSubMatrix(C, PETSC_DECIDE, PETSC_DECIDE, i, i + cols, &Cb));
787: /* get off processor parts of B needed to complete C=A*B */
788: PetscCall(MatMPIDenseScatterBegin(A, Bb, workB, C));
789: PetscCall(MatMPIDenseScatterEnd(Bb, workB, C));
791: /* off-diagonal block of A times nonlocal rows of B */
792: if (workC) {
793: PetscCall(MatMPIAIJ_MPIDenseProductNumeric_Private(aij->B, workB, workC, clear));
794: PetscCall(MatAXPY(((Mat_MPIDense *)Cb->data)->A, 1.0, workC, SAME_NONZERO_PATTERN));
795: } else if (!contents->ondevice) PetscCall(MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B, workB, ((Mat_MPIDense *)Cb->data)->A, PETSC_TRUE));
796: if (cols != n) {
797: if (workC) PetscCall(MatDenseRestoreSubMatrix(data->workC, &workC));
798: PetscCall(MatDenseRestoreSubMatrix(contents->workB, &workB));
799: }
800: PetscCall(MatDenseRestoreSubMatrix(B, &Bb));
801: PetscCall(MatDenseRestoreSubMatrix(C, &Cb));
802: }
803: if (!contents->ondevice) PetscCall(MatBindToCPU(C, ccpu));
804: }
805: PetscFunctionReturn(PETSC_SUCCESS);
806: }
808: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A, Mat P, Mat C)
809: {
810: Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data, *c = (Mat_MPIAIJ *)C->data;
811: Mat_SeqAIJ *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data;
812: Mat_SeqAIJ *cd = (Mat_SeqAIJ *)c->A->data, *co = (Mat_SeqAIJ *)c->B->data;
813: PetscInt *adi = ad->i, *adj, *aoi = ao->i, *aoj;
814: PetscScalar *ada, *aoa, *cda = cd->a, *coa = co->a;
815: Mat_SeqAIJ *p_loc, *p_oth;
816: PetscInt *pi_loc, *pj_loc, *pi_oth, *pj_oth, *pj;
817: PetscScalar *pa_loc, *pa_oth, *pa, valtmp, *ca;
818: PetscInt cm = C->rmap->n, anz, pnz;
819: MatProductCtx_APMPI *ptap;
820: PetscScalar *apa_sparse;
821: const PetscScalar *dummy;
822: PetscInt *api, *apj, *apJ, i, j, k, row;
823: PetscInt cstart = C->cmap->rstart;
824: PetscInt cdnz, conz, k0, k1, nextp;
825: MPI_Comm comm;
826: PetscMPIInt size;
828: PetscFunctionBegin;
829: MatCheckProduct(C, 3);
830: ptap = (MatProductCtx_APMPI *)C->product->data;
831: PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
832: PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
833: PetscCallMPI(MPI_Comm_size(comm, &size));
834: PetscCheck(ptap->P_oth || size <= 1, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "AP cannot be reused. Do not call MatProductClear()");
836: /* flag CPU mask for C */
837: #if PetscDefined(HAVE_DEVICE)
838: if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
839: if (c->A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->A->offloadmask = PETSC_OFFLOAD_CPU;
840: if (c->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->B->offloadmask = PETSC_OFFLOAD_CPU;
841: #endif
842: apa_sparse = ptap->apa;
844: /* 1) get P_oth = ptap->P_oth and P_loc = ptap->P_loc */
845: /* update numerical values of P_oth and P_loc */
846: PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_REUSE_MATRIX, &ptap->startsj_s, &ptap->startsj_r, &ptap->bufa, &ptap->P_oth));
847: PetscCall(MatMPIAIJGetLocalMat(P, MAT_REUSE_MATRIX, &ptap->P_loc));
849: /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
850: /* get data from symbolic products */
851: p_loc = (Mat_SeqAIJ *)ptap->P_loc->data;
852: pi_loc = p_loc->i;
853: pj_loc = p_loc->j;
854: pa_loc = p_loc->a;
855: if (size > 1) {
856: p_oth = (Mat_SeqAIJ *)ptap->P_oth->data;
857: pi_oth = p_oth->i;
858: pj_oth = p_oth->j;
859: pa_oth = p_oth->a;
860: } else {
861: p_oth = NULL;
862: pi_oth = NULL;
863: pj_oth = NULL;
864: pa_oth = NULL;
865: }
867: /* trigger copy to CPU */
868: PetscCall(MatSeqAIJGetArrayRead(a->A, &dummy));
869: PetscCall(MatSeqAIJRestoreArrayRead(a->A, &dummy));
870: PetscCall(MatSeqAIJGetArrayRead(a->B, &dummy));
871: PetscCall(MatSeqAIJRestoreArrayRead(a->B, &dummy));
872: api = ptap->api;
873: apj = ptap->apj;
874: for (i = 0; i < cm; i++) {
875: apJ = apj + api[i];
877: /* diagonal portion of A */
878: anz = adi[i + 1] - adi[i];
879: adj = ad->j + adi[i];
880: ada = ad->a + adi[i];
881: for (j = 0; j < anz; j++) {
882: row = adj[j];
883: pnz = pi_loc[row + 1] - pi_loc[row];
884: pj = pj_loc + pi_loc[row];
885: pa = pa_loc + pi_loc[row];
886: /* perform sparse axpy */
887: valtmp = ada[j];
888: nextp = 0;
889: for (k = 0; nextp < pnz; k++) {
890: if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
891: apa_sparse[k] += valtmp * pa[nextp++];
892: }
893: }
894: PetscCall(PetscLogFlops(2.0 * pnz));
895: }
897: /* off-diagonal portion of A */
898: anz = aoi[i + 1] - aoi[i];
899: aoj = PetscSafePointerPlusOffset(ao->j, aoi[i]);
900: aoa = PetscSafePointerPlusOffset(ao->a, aoi[i]);
901: for (j = 0; j < anz; j++) {
902: row = aoj[j];
903: pnz = pi_oth[row + 1] - pi_oth[row];
904: pj = pj_oth + pi_oth[row];
905: pa = pa_oth + pi_oth[row];
906: /* perform sparse axpy */
907: valtmp = aoa[j];
908: nextp = 0;
909: for (k = 0; nextp < pnz; k++) {
910: if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
911: apa_sparse[k] += valtmp * pa[nextp++];
912: }
913: }
914: PetscCall(PetscLogFlops(2.0 * pnz));
915: }
917: /* set values in C */
918: cdnz = cd->i[i + 1] - cd->i[i];
919: conz = co->i[i + 1] - co->i[i];
921: /* 1st off-diagonal part of C */
922: ca = PetscSafePointerPlusOffset(coa, co->i[i]);
923: k = 0;
924: for (k0 = 0; k0 < conz; k0++) {
925: if (apJ[k] >= cstart) break;
926: ca[k0] = apa_sparse[k];
927: apa_sparse[k] = 0.0;
928: k++;
929: }
931: /* diagonal part of C */
932: ca = cda + cd->i[i];
933: for (k1 = 0; k1 < cdnz; k1++) {
934: ca[k1] = apa_sparse[k];
935: apa_sparse[k] = 0.0;
936: k++;
937: }
939: /* 2nd off-diagonal part of C */
940: ca = PetscSafePointerPlusOffset(coa, co->i[i]);
941: for (; k0 < conz; k0++) {
942: ca[k0] = apa_sparse[k];
943: apa_sparse[k] = 0.0;
944: k++;
945: }
946: }
947: PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
948: PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
949: PetscFunctionReturn(PETSC_SUCCESS);
950: }
952: /* same as MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(), except using LLCondensed to avoid O(BN) memory requirement */
953: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A, Mat P, PetscReal fill, Mat C)
954: {
955: MPI_Comm comm;
956: PetscMPIInt size;
957: MatProductCtx_APMPI *ptap;
958: PetscFreeSpaceList free_space = NULL, current_space = NULL;
959: Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
960: Mat_SeqAIJ *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data, *p_loc, *p_oth;
961: PetscInt *pi_loc, *pj_loc, *pi_oth, *pj_oth, *dnz, *onz;
962: PetscInt *adi = ad->i, *adj = ad->j, *aoi = ao->i, *aoj = ao->j, rstart = A->rmap->rstart;
963: PetscInt i, pnz, row, *api, *apj, *Jptr, apnz, nspacedouble = 0, j, nzi, *lnk, apnz_max = 1;
964: PetscInt am = A->rmap->n, pn = P->cmap->n, pm = P->rmap->n, lsize = pn + 20;
965: PetscReal afill;
966: MatType mtype;
968: PetscFunctionBegin;
969: MatCheckProduct(C, 4);
970: PetscCheck(!C->product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");
971: PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
972: PetscCallMPI(MPI_Comm_size(comm, &size));
974: /* create struct MatProductCtx_APMPI and attached it to C later */
975: PetscCall(PetscNew(&ptap));
977: /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
978: PetscCall(MatGetBrowsOfAoCols_MPIAIJ_Private(A, P, MAT_INITIAL_MATRIX, C->structure_only, &ptap->startsj_s, &ptap->startsj_r, &ptap->bufa, &ptap->P_oth));
980: /* get P_loc by taking all local rows of P */
981: PetscCall(MatMPIAIJGetLocalMat_Private(P, MAT_INITIAL_MATRIX, C->structure_only, &ptap->P_loc));
983: p_loc = (Mat_SeqAIJ *)ptap->P_loc->data;
984: pi_loc = p_loc->i;
985: pj_loc = p_loc->j;
986: if (size > 1) {
987: p_oth = (Mat_SeqAIJ *)ptap->P_oth->data;
988: pi_oth = p_oth->i;
989: pj_oth = p_oth->j;
990: } else {
991: p_oth = NULL;
992: pi_oth = NULL;
993: pj_oth = NULL;
994: }
996: /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
997: PetscCall(PetscMalloc1(am + 1, &api));
998: ptap->api = api;
999: api[0] = 0;
1001: PetscCall(PetscLLCondensedCreate_Scalable(lsize, &lnk));
1003: /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
1004: PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(adi[am], PetscIntSumTruncate(aoi[am], pi_loc[pm]))), &free_space));
1005: current_space = free_space;
1006: MatPreallocateBegin(comm, am, pn, dnz, onz);
1007: for (i = 0; i < am; i++) {
1008: /* diagonal portion of A */
1009: nzi = adi[i + 1] - adi[i];
1010: for (j = 0; j < nzi; j++) {
1011: row = *adj++;
1012: pnz = pi_loc[row + 1] - pi_loc[row];
1013: Jptr = pj_loc + pi_loc[row];
1014: /* Expand list if it is not long enough */
1015: if (pnz + apnz_max > lsize) {
1016: lsize = pnz + apnz_max;
1017: PetscCall(PetscLLCondensedExpand_Scalable(lsize, &lnk));
1018: }
1019: /* add non-zero cols of P into the sorted linked list lnk */
1020: PetscCall(PetscLLCondensedAddSorted_Scalable(pnz, Jptr, lnk));
1021: apnz = *lnk; /* The first element in the list is the number of items in the list */
1022: api[i + 1] = api[i] + apnz;
1023: if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
1024: }
1025: /* off-diagonal portion of A */
1026: nzi = aoi[i + 1] - aoi[i];
1027: for (j = 0; j < nzi; j++) {
1028: row = *aoj++;
1029: pnz = pi_oth[row + 1] - pi_oth[row];
1030: Jptr = pj_oth + pi_oth[row];
1031: /* Expand list if it is not long enough */
1032: if (pnz + apnz_max > lsize) {
1033: lsize = pnz + apnz_max;
1034: PetscCall(PetscLLCondensedExpand_Scalable(lsize, &lnk));
1035: }
1036: /* add non-zero cols of P into the sorted linked list lnk */
1037: PetscCall(PetscLLCondensedAddSorted_Scalable(pnz, Jptr, lnk));
1038: apnz = *lnk; /* The first element in the list is the number of items in the list */
1039: api[i + 1] = api[i] + apnz;
1040: if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
1041: }
1043: /* add missing diagonal entry */
1044: if (C->force_diagonals) {
1045: j = i + rstart; /* column index */
1046: PetscCall(PetscLLCondensedAddSorted_Scalable(1, &j, lnk));
1047: }
1049: apnz = *lnk;
1050: api[i + 1] = api[i] + apnz;
1051: if (apnz > apnz_max) apnz_max = apnz;
1053: /* if free space is not available, double the total space in the list */
1054: if (current_space->local_remaining < apnz) {
1055: PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(apnz, current_space->total_array_size), ¤t_space));
1056: nspacedouble++;
1057: }
1059: /* Copy data into free space, then initialize lnk */
1060: PetscCall(PetscLLCondensedClean_Scalable(apnz, current_space->array, lnk));
1061: PetscCall(MatPreallocateSet(i + rstart, apnz, current_space->array, dnz, onz));
1063: current_space->array += apnz;
1064: current_space->local_used += apnz;
1065: current_space->local_remaining -= apnz;
1066: }
1068: /* Allocate space for apj, initialize apj, and */
1069: /* destroy list of free space and other temporary array(s) */
1070: PetscCall(PetscMalloc1(api[am], &ptap->apj));
1071: apj = ptap->apj;
1072: PetscCall(PetscFreeSpaceContiguous(&free_space, ptap->apj));
1073: PetscCall(PetscLLCondensedDestroy_Scalable(lnk));
1075: /* create and assemble symbolic parallel matrix C */
1076: PetscCall(MatSetSizes(C, am, pn, PETSC_DETERMINE, PETSC_DETERMINE));
1077: PetscCall(MatSetBlockSizesFromMats(C, A, P));
1078: PetscCall(MatGetType(A, &mtype));
1079: PetscCall(MatSetType(C, C->structure_only ? MATMPIAIJ : mtype));
1080: PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
1081: MatPreallocateEnd(dnz, onz);
1083: /* malloc apa for assembly C */
1084: if (!C->structure_only) PetscCall(PetscCalloc1(apnz_max, &ptap->apa));
1086: PetscCall(MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api));
1087: PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
1088: PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1089: PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1090: PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
1092: C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
1093: C->ops->productnumeric = MatProductNumeric_AB;
1095: /* attach the supporting struct to C for reuse */
1096: C->product->data = ptap;
1097: C->product->destroy = MatProductCtxDestroy_MPIAIJ_MatMatMult;
1099: /* set MatInfo */
1100: afill = (PetscReal)api[am] / (adi[am] + aoi[am] + pi_loc[pm] + 1) + 1.e-5;
1101: if (afill < 1.0) afill = 1.0;
1102: C->info.mallocs = nspacedouble;
1103: C->info.fill_ratio_given = fill;
1104: C->info.fill_ratio_needed = afill;
1106: if (PetscDefined(USE_INFO)) {
1107: if (api[am]) {
1108: PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
1109: PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
1110: } else PetscCall(PetscInfo(C, "Empty matrix product\n"));
1111: }
1112: PetscFunctionReturn(PETSC_SUCCESS);
1113: }
1115: /* This function is needed for the seqMPI matrix-matrix multiplication. */
1116: /* Three input arrays are merged to one output array. The size of the */
1117: /* output array is also output. Duplicate entries only show up once. */
1118: static void Merge3SortedArrays(PetscInt size1, PetscInt *in1, PetscInt size2, PetscInt *in2, PetscInt size3, PetscInt *in3, PetscInt *size4, PetscInt *out)
1119: {
1120: int i = 0, j = 0, k = 0, l = 0;
1122: /* Traverse all three arrays */
1123: while (i < size1 && j < size2 && k < size3) {
1124: if (in1[i] < in2[j] && in1[i] < in3[k]) {
1125: out[l++] = in1[i++];
1126: } else if (in2[j] < in1[i] && in2[j] < in3[k]) {
1127: out[l++] = in2[j++];
1128: } else if (in3[k] < in1[i] && in3[k] < in2[j]) {
1129: out[l++] = in3[k++];
1130: } else if (in1[i] == in2[j] && in1[i] < in3[k]) {
1131: out[l++] = in1[i];
1132: i++, j++;
1133: } else if (in1[i] == in3[k] && in1[i] < in2[j]) {
1134: out[l++] = in1[i];
1135: i++, k++;
1136: } else if (in3[k] == in2[j] && in2[j] < in1[i]) {
1137: out[l++] = in2[j];
1138: k++, j++;
1139: } else if (in1[i] == in2[j] && in1[i] == in3[k]) {
1140: out[l++] = in1[i];
1141: i++, j++, k++;
1142: }
1143: }
1145: /* Traverse two remaining arrays */
1146: while (i < size1 && j < size2) {
1147: if (in1[i] < in2[j]) {
1148: out[l++] = in1[i++];
1149: } else if (in1[i] > in2[j]) {
1150: out[l++] = in2[j++];
1151: } else {
1152: out[l++] = in1[i];
1153: i++, j++;
1154: }
1155: }
1157: while (i < size1 && k < size3) {
1158: if (in1[i] < in3[k]) {
1159: out[l++] = in1[i++];
1160: } else if (in1[i] > in3[k]) {
1161: out[l++] = in3[k++];
1162: } else {
1163: out[l++] = in1[i];
1164: i++, k++;
1165: }
1166: }
1168: while (k < size3 && j < size2) {
1169: if (in3[k] < in2[j]) {
1170: out[l++] = in3[k++];
1171: } else if (in3[k] > in2[j]) {
1172: out[l++] = in2[j++];
1173: } else {
1174: out[l++] = in3[k];
1175: k++, j++;
1176: }
1177: }
1179: /* Traverse one remaining array */
1180: while (i < size1) out[l++] = in1[i++];
1181: while (j < size2) out[l++] = in2[j++];
1182: while (k < size3) out[l++] = in3[k++];
1184: *size4 = l;
1185: }
1187: /* This matrix-matrix multiplication algorithm divides the multiplication into three multiplications and */
1188: /* adds up the products. Two of these three multiplications are performed with existing (sequential) */
1189: /* matrix-matrix multiplications. */
1190: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(Mat A, Mat P, PetscReal fill, Mat C)
1191: {
1192: MPI_Comm comm;
1193: PetscMPIInt size;
1194: MatProductCtx_APMPI *ptap;
1195: PetscFreeSpaceList free_space_diag = NULL, current_space = NULL;
1196: Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
1197: Mat_SeqAIJ *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data, *p_loc;
1198: Mat_MPIAIJ *p = (Mat_MPIAIJ *)P->data;
1199: Mat_SeqAIJ *adpd_seq, *p_off, *aopoth_seq;
1200: PetscInt adponz, adpdnz;
1201: PetscInt *pi_loc, *dnz, *onz;
1202: PetscInt *adi = ad->i, *adj = ad->j, *aoi = ao->i, rstart = A->rmap->rstart;
1203: PetscInt *lnk, i, i1 = 0, pnz, row, *adpoi, *adpoj, *api, *adpoJ, *aopJ, *apJ, *Jptr, aopnz, nspacedouble = 0, j, nzi, *apj, apnz, *adpdi, *adpdj, *adpdJ, *poff_i, *poff_j, *j_temp, *aopothi, *aopothj;
1204: PetscInt am = A->rmap->n, pN = P->cmap->N, pn = P->cmap->n, pm = P->rmap->n, p_colstart, p_colend;
1205: PetscBT lnkbt;
1206: PetscReal afill;
1207: PetscMPIInt rank;
1208: Mat adpd, aopoth;
1209: MatType mtype;
1210: const char *prefix;
1212: PetscFunctionBegin;
1213: MatCheckProduct(C, 4);
1214: PetscCheck(!C->product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");
1215: PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
1216: PetscCallMPI(MPI_Comm_size(comm, &size));
1217: PetscCallMPI(MPI_Comm_rank(comm, &rank));
1218: PetscCall(MatGetOwnershipRangeColumn(P, &p_colstart, &p_colend));
1220: /* create struct MatProductCtx_APMPI and attached it to C later */
1221: PetscCall(PetscNew(&ptap));
1223: /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
1224: PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_INITIAL_MATRIX, &ptap->startsj_s, &ptap->startsj_r, &ptap->bufa, &ptap->P_oth));
1226: /* get P_loc by taking all local rows of P */
1227: PetscCall(MatMPIAIJGetLocalMat(P, MAT_INITIAL_MATRIX, &ptap->P_loc));
1229: p_loc = (Mat_SeqAIJ *)ptap->P_loc->data;
1230: pi_loc = p_loc->i;
1232: /* Allocate memory for the i arrays of the matrices A*P, A_diag*P_off and A_offd * P */
1233: PetscCall(PetscMalloc1(am + 1, &api));
1234: PetscCall(PetscMalloc1(am + 1, &adpoi));
1236: adpoi[0] = 0;
1237: ptap->api = api;
1238: api[0] = 0;
1240: /* create and initialize a linked list, will be used for both A_diag * P_loc_off and A_offd * P_oth */
1241: PetscCall(PetscLLCondensedCreate(pN, pN, &lnk, &lnkbt));
1242: MatPreallocateBegin(comm, am, pn, dnz, onz);
1244: /* Symbolic calc of A_loc_diag * P_loc_diag */
1245: PetscCall(MatGetOptionsPrefix(A, &prefix));
1246: PetscCall(MatProductCreate(a->A, p->A, NULL, &adpd));
1247: PetscCall(MatGetOptionsPrefix(A, &prefix));
1248: PetscCall(MatSetOptionsPrefix(adpd, prefix));
1249: PetscCall(MatAppendOptionsPrefix(adpd, "inner_diag_"));
1251: PetscCall(MatProductSetType(adpd, MATPRODUCT_AB));
1252: PetscCall(MatProductSetAlgorithm(adpd, "sorted"));
1253: PetscCall(MatProductSetFill(adpd, fill));
1254: PetscCall(MatProductSetFromOptions(adpd));
1256: adpd->force_diagonals = C->force_diagonals;
1257: PetscCall(MatProductSymbolic(adpd));
1259: adpd_seq = (Mat_SeqAIJ *)adpd->data;
1260: adpdi = adpd_seq->i;
1261: adpdj = adpd_seq->j;
1262: p_off = (Mat_SeqAIJ *)p->B->data;
1263: poff_i = p_off->i;
1264: poff_j = p_off->j;
1266: /* j_temp stores indices of a result row before they are added to the linked list */
1267: PetscCall(PetscMalloc1(pN, &j_temp));
1269: /* Symbolic calc of the A_diag * p_loc_off */
1270: /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
1271: PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(adi[am], PetscIntSumTruncate(aoi[am], pi_loc[pm]))), &free_space_diag));
1272: current_space = free_space_diag;
1274: for (i = 0; i < am; i++) {
1275: /* A_diag * P_loc_off */
1276: nzi = adi[i + 1] - adi[i];
1277: for (j = 0; j < nzi; j++) {
1278: row = *adj++;
1279: pnz = poff_i[row + 1] - poff_i[row];
1280: Jptr = poff_j + poff_i[row];
1281: for (i1 = 0; i1 < pnz; i1++) j_temp[i1] = p->garray[Jptr[i1]];
1282: /* add non-zero cols of P into the sorted linked list lnk */
1283: PetscCall(PetscLLCondensedAddSorted(pnz, j_temp, lnk, lnkbt));
1284: }
1286: adponz = lnk[0];
1287: adpoi[i + 1] = adpoi[i] + adponz;
1289: /* if free space is not available, double the total space in the list */
1290: if (current_space->local_remaining < adponz) {
1291: PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(adponz, current_space->total_array_size), ¤t_space));
1292: nspacedouble++;
1293: }
1295: /* Copy data into free space, then initialize lnk */
1296: PetscCall(PetscLLCondensedClean(pN, adponz, current_space->array, lnk, lnkbt));
1298: current_space->array += adponz;
1299: current_space->local_used += adponz;
1300: current_space->local_remaining -= adponz;
1301: }
1303: /* Symbolic calc of A_off * P_oth */
1304: PetscCall(MatSetOptionsPrefix(a->B, prefix));
1305: PetscCall(MatAppendOptionsPrefix(a->B, "inner_offdiag_"));
1306: PetscCall(MatCreate(PETSC_COMM_SELF, &aopoth));
1307: PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, aopoth));
1308: aopoth_seq = (Mat_SeqAIJ *)aopoth->data;
1309: aopothi = aopoth_seq->i;
1310: aopothj = aopoth_seq->j;
1312: /* Allocate space for apj, adpj, aopj, ... */
1313: /* destroy lists of free space and other temporary array(s) */
1315: PetscCall(PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am], &ptap->apj));
1316: PetscCall(PetscMalloc1(adpoi[am], &adpoj));
1318: /* Copy from linked list to j-array */
1319: PetscCall(PetscFreeSpaceContiguous(&free_space_diag, adpoj));
1320: PetscCall(PetscLLDestroy(lnk, lnkbt));
1322: adpoJ = adpoj;
1323: adpdJ = adpdj;
1324: aopJ = aopothj;
1325: apj = ptap->apj;
1326: apJ = apj; /* still empty */
1328: /* Merge j-arrays of A_off * P, A_diag * P_loc_off, and */
1329: /* A_diag * P_loc_diag to get A*P */
1330: for (i = 0; i < am; i++) {
1331: aopnz = aopothi[i + 1] - aopothi[i];
1332: adponz = adpoi[i + 1] - adpoi[i];
1333: adpdnz = adpdi[i + 1] - adpdi[i];
1335: /* Correct indices from A_diag*P_diag */
1336: for (i1 = 0; i1 < adpdnz; i1++) adpdJ[i1] += p_colstart;
1337: /* Merge j-arrays of A_diag * P_loc_off and A_diag * P_loc_diag and A_off * P_oth */
1338: Merge3SortedArrays(adponz, adpoJ, adpdnz, adpdJ, aopnz, aopJ, &apnz, apJ);
1339: PetscCall(MatPreallocateSet(i + rstart, apnz, apJ, dnz, onz));
1341: aopJ += aopnz;
1342: adpoJ += adponz;
1343: adpdJ += adpdnz;
1344: apJ += apnz;
1345: api[i + 1] = api[i] + apnz;
1346: }
1348: /* malloc apa to store dense row A[i,:]*P */
1349: PetscCall(PetscCalloc1(pN, &ptap->apa));
1351: /* create and assemble symbolic parallel matrix C */
1352: PetscCall(MatSetSizes(C, am, pn, PETSC_DETERMINE, PETSC_DETERMINE));
1353: PetscCall(MatSetBlockSizesFromMats(C, A, P));
1354: PetscCall(MatGetType(A, &mtype));
1355: PetscCall(MatSetType(C, mtype));
1356: PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
1357: MatPreallocateEnd(dnz, onz);
1359: PetscCall(MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api));
1360: PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
1361: PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1362: PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1363: PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
1365: C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1366: C->ops->productnumeric = MatProductNumeric_AB;
1368: /* attach the supporting struct to C for reuse */
1369: C->product->data = ptap;
1370: C->product->destroy = MatProductCtxDestroy_MPIAIJ_MatMatMult;
1372: /* set MatInfo */
1373: afill = (PetscReal)api[am] / (adi[am] + aoi[am] + pi_loc[pm] + 1) + 1.e-5;
1374: if (afill < 1.0) afill = 1.0;
1375: C->info.mallocs = nspacedouble;
1376: C->info.fill_ratio_given = fill;
1377: C->info.fill_ratio_needed = afill;
1379: if (PetscDefined(USE_INFO)) {
1380: if (api[am]) {
1381: PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
1382: PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
1383: } else PetscCall(PetscInfo(C, "Empty matrix product\n"));
1384: }
1386: PetscCall(MatDestroy(&aopoth));
1387: PetscCall(MatDestroy(&adpd));
1388: PetscCall(PetscFree(j_temp));
1389: PetscCall(PetscFree(adpoj));
1390: PetscCall(PetscFree(adpoi));
1391: PetscFunctionReturn(PETSC_SUCCESS);
1392: }
1394: /* This routine only works when scall=MAT_REUSE_MATRIX! */
1395: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P, Mat A, Mat C)
1396: {
1397: MatProductCtx_APMPI *ptap;
1398: Mat Pt;
1400: PetscFunctionBegin;
1401: MatCheckProduct(C, 3);
1402: ptap = (MatProductCtx_APMPI *)C->product->data;
1403: PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
1404: PetscCheck(ptap->Pt, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");
1406: Pt = ptap->Pt;
1407: PetscCall(MatTransposeSetPrecursor(P, Pt));
1408: PetscCall(MatTranspose(P, MAT_REUSE_MATRIX, &Pt));
1409: PetscCall(MatMatMultNumeric_MPIAIJ_MPIAIJ(Pt, A, C));
1410: PetscFunctionReturn(PETSC_SUCCESS);
1411: }
1413: /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
1414: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P, Mat A, PetscReal fill, Mat C)
1415: {
1416: MatProductCtx_APMPI *ptap;
1417: Mat_MPIAIJ *p = (Mat_MPIAIJ *)P->data;
1418: MPI_Comm comm;
1419: PetscMPIInt size, rank;
1420: PetscFreeSpaceList free_space = NULL, current_space = NULL;
1421: PetscInt pn = P->cmap->n, aN = A->cmap->N, an = A->cmap->n;
1422: PetscInt *lnk, i, k, rstart;
1423: PetscBT lnkbt;
1424: PetscMPIInt tagi, tagj, *len_si, *len_s, *len_ri, nrecv, proc, nsend;
1425: PETSC_UNUSED PetscMPIInt icompleted = 0;
1426: PetscInt **buf_rj, **buf_ri, **buf_ri_k, row, ncols, *cols;
1427: PetscInt len, *dnz, *onz, *owners, nzi;
1428: PetscInt nrows, *buf_s, *buf_si, *buf_si_i, **nextrow, **nextci;
1429: MPI_Request *swaits, *rwaits;
1430: MPI_Status *sstatus, rstatus;
1431: PetscLayout rowmap;
1432: PetscInt *owners_co, *coi, *coj; /* i and j array of (p->B)^T*A*P - used in the communication */
1433: PetscMPIInt *len_r, *id_r; /* array of length of comm->size, store send/recv matrix values */
1434: PetscInt *Jptr, *prmap = p->garray, con, j, Crmax;
1435: Mat_SeqAIJ *a_loc, *c_loc, *c_oth;
1436: PetscHMapI ta;
1437: MatType mtype;
1438: const char *prefix;
1440: PetscFunctionBegin;
1441: PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
1442: PetscCallMPI(MPI_Comm_size(comm, &size));
1443: PetscCallMPI(MPI_Comm_rank(comm, &rank));
1445: /* create symbolic parallel matrix C */
1446: PetscCall(MatGetType(A, &mtype));
1447: PetscCall(MatSetType(C, mtype));
1449: C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1451: /* create struct MatProductCtx_APMPI and attached it to C later */
1452: PetscCall(PetscNew(&ptap));
1454: /* (0) compute Rd = Pd^T, Ro = Po^T */
1455: PetscCall(MatTranspose(p->A, MAT_INITIAL_MATRIX, &ptap->Rd));
1456: PetscCall(MatTranspose(p->B, MAT_INITIAL_MATRIX, &ptap->Ro));
1458: /* (1) compute symbolic A_loc */
1459: PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, &ptap->A_loc));
1461: /* (2-1) compute symbolic C_oth = Ro*A_loc */
1462: PetscCall(MatGetOptionsPrefix(A, &prefix));
1463: PetscCall(MatSetOptionsPrefix(ptap->Ro, prefix));
1464: PetscCall(MatAppendOptionsPrefix(ptap->Ro, "inner_offdiag_"));
1465: PetscCall(MatCreate(PETSC_COMM_SELF, &ptap->C_oth));
1466: PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro, ptap->A_loc, fill, ptap->C_oth));
1468: /* (3) send coj of C_oth to other processors */
1469: /* determine row ownership */
1470: PetscCall(PetscLayoutCreate(comm, &rowmap));
1471: rowmap->n = pn;
1472: rowmap->bs = 1;
1473: PetscCall(PetscLayoutSetUp(rowmap));
1474: owners = rowmap->range;
1476: /* determine the number of messages to send, their lengths */
1477: PetscCall(PetscMalloc4(size, &len_s, size, &len_si, size, &sstatus, size + 1, &owners_co));
1478: PetscCall(PetscArrayzero(len_s, size));
1479: PetscCall(PetscArrayzero(len_si, size));
1481: c_oth = (Mat_SeqAIJ *)ptap->C_oth->data;
1482: coi = c_oth->i;
1483: coj = c_oth->j;
1484: con = ptap->C_oth->rmap->n;
1485: proc = 0;
1486: for (i = 0; i < con; i++) {
1487: while (prmap[i] >= owners[proc + 1]) proc++;
1488: len_si[proc]++; /* num of rows in Co(=Pt*A) to be sent to [proc] */
1489: len_s[proc] += coi[i + 1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
1490: }
1492: len = 0; /* max length of buf_si[], see (4) */
1493: owners_co[0] = 0;
1494: nsend = 0;
1495: for (proc = 0; proc < size; proc++) {
1496: owners_co[proc + 1] = owners_co[proc] + len_si[proc];
1497: if (len_s[proc]) {
1498: nsend++;
1499: len_si[proc] = 2 * (len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
1500: len += len_si[proc];
1501: }
1502: }
1504: /* determine the number and length of messages to receive for coi and coj */
1505: PetscCall(PetscGatherNumberOfMessages(comm, NULL, len_s, &nrecv));
1506: PetscCall(PetscGatherMessageLengths2(comm, nsend, nrecv, len_s, len_si, &id_r, &len_r, &len_ri));
1508: /* post the Irecv and Isend of coj */
1509: PetscCall(PetscCommGetNewTag(comm, &tagj));
1510: PetscCall(PetscPostIrecvInt(comm, tagj, nrecv, id_r, len_r, &buf_rj, &rwaits));
1511: PetscCall(PetscMalloc1(nsend, &swaits));
1512: for (proc = 0, k = 0; proc < size; proc++) {
1513: if (!len_s[proc]) continue;
1514: i = owners_co[proc];
1515: PetscCallMPI(MPIU_Isend(coj + coi[i], len_s[proc], MPIU_INT, proc, tagj, comm, swaits + k));
1516: k++;
1517: }
1519: /* (2-2) compute symbolic C_loc = Rd*A_loc */
1520: PetscCall(MatSetOptionsPrefix(ptap->Rd, prefix));
1521: PetscCall(MatAppendOptionsPrefix(ptap->Rd, "inner_diag_"));
1522: PetscCall(MatCreate(PETSC_COMM_SELF, &ptap->C_loc));
1523: PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd, ptap->A_loc, fill, ptap->C_loc));
1524: c_loc = (Mat_SeqAIJ *)ptap->C_loc->data;
1526: /* receives coj are complete */
1527: for (i = 0; i < nrecv; i++) PetscCallMPI(MPI_Waitany(nrecv, rwaits, &icompleted, &rstatus));
1528: PetscCall(PetscFree(rwaits));
1529: if (nsend) PetscCallMPI(MPI_Waitall(nsend, swaits, sstatus));
1531: /* add received column indices into ta to update Crmax */
1532: a_loc = (Mat_SeqAIJ *)ptap->A_loc->data;
1534: /* create and initialize a linked list */
1535: PetscCall(PetscHMapICreateWithSize(an, &ta)); /* for compute Crmax */
1536: MatRowMergeMax_SeqAIJ(a_loc, ptap->A_loc->rmap->N, ta);
1538: for (k = 0; k < nrecv; k++) { /* k-th received message */
1539: Jptr = buf_rj[k];
1540: for (j = 0; j < len_r[k]; j++) PetscCall(PetscHMapISet(ta, *(Jptr + j) + 1, 1));
1541: }
1542: PetscCall(PetscHMapIGetSize(ta, &Crmax));
1543: PetscCall(PetscHMapIDestroy(&ta));
1545: /* (4) send and recv coi */
1546: PetscCall(PetscCommGetNewTag(comm, &tagi));
1547: PetscCall(PetscPostIrecvInt(comm, tagi, nrecv, id_r, len_ri, &buf_ri, &rwaits));
1548: PetscCall(PetscMalloc1(len, &buf_s));
1549: buf_si = buf_s; /* points to the beginning of k-th msg to be sent */
1550: for (proc = 0, k = 0; proc < size; proc++) {
1551: if (!len_s[proc]) continue;
1552: /* form outgoing message for i-structure:
1553: buf_si[0]: nrows to be sent
1554: [1:nrows]: row index (global)
1555: [nrows+1:2*nrows+1]: i-structure index
1556: */
1557: nrows = len_si[proc] / 2 - 1; /* num of rows in Co to be sent to [proc] */
1558: buf_si_i = buf_si + nrows + 1;
1559: buf_si[0] = nrows;
1560: buf_si_i[0] = 0;
1561: nrows = 0;
1562: for (i = owners_co[proc]; i < owners_co[proc + 1]; i++) {
1563: nzi = coi[i + 1] - coi[i];
1564: buf_si_i[nrows + 1] = buf_si_i[nrows] + nzi; /* i-structure */
1565: buf_si[nrows + 1] = prmap[i] - owners[proc]; /* local row index */
1566: nrows++;
1567: }
1568: PetscCallMPI(MPIU_Isend(buf_si, len_si[proc], MPIU_INT, proc, tagi, comm, swaits + k));
1569: k++;
1570: buf_si += len_si[proc];
1571: }
1572: for (i = 0; i < nrecv; i++) PetscCallMPI(MPI_Waitany(nrecv, rwaits, &icompleted, &rstatus));
1573: PetscCall(PetscFree(rwaits));
1574: if (nsend) PetscCallMPI(MPI_Waitall(nsend, swaits, sstatus));
1576: PetscCall(PetscFree4(len_s, len_si, sstatus, owners_co));
1577: PetscCall(PetscFree(len_ri));
1578: PetscCall(PetscFree(swaits));
1579: PetscCall(PetscFree(buf_s));
1581: /* (5) compute the local portion of C */
1582: /* set initial free space to be Crmax, sufficient for holding nonzeros in each row of C */
1583: PetscCall(PetscFreeSpaceGet(Crmax, &free_space));
1584: current_space = free_space;
1586: PetscCall(PetscMalloc3(nrecv, &buf_ri_k, nrecv, &nextrow, nrecv, &nextci));
1587: for (k = 0; k < nrecv; k++) {
1588: buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1589: nrows = *buf_ri_k[k];
1590: nextrow[k] = buf_ri_k[k] + 1; /* next row number of k-th recved i-structure */
1591: nextci[k] = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure */
1592: }
1594: MatPreallocateBegin(comm, pn, an, dnz, onz);
1595: PetscCall(PetscLLCondensedCreate(Crmax, aN, &lnk, &lnkbt));
1596: for (i = 0; i < pn; i++) { /* for each local row of C */
1597: /* add C_loc into C */
1598: nzi = c_loc->i[i + 1] - c_loc->i[i];
1599: Jptr = c_loc->j + c_loc->i[i];
1600: PetscCall(PetscLLCondensedAddSorted(nzi, Jptr, lnk, lnkbt));
1602: /* add received col data into lnk */
1603: for (k = 0; k < nrecv; k++) { /* k-th received message */
1604: if (i == *nextrow[k]) { /* i-th row */
1605: nzi = *(nextci[k] + 1) - *nextci[k];
1606: Jptr = buf_rj[k] + *nextci[k];
1607: PetscCall(PetscLLCondensedAddSorted(nzi, Jptr, lnk, lnkbt));
1608: nextrow[k]++;
1609: nextci[k]++;
1610: }
1611: }
1613: /* add missing diagonal entry */
1614: if (C->force_diagonals) {
1615: k = i + owners[rank]; /* column index */
1616: PetscCall(PetscLLCondensedAddSorted(1, &k, lnk, lnkbt));
1617: }
1619: nzi = lnk[0];
1621: /* copy data into free space, then initialize lnk */
1622: PetscCall(PetscLLCondensedClean(aN, nzi, current_space->array, lnk, lnkbt));
1623: PetscCall(MatPreallocateSet(i + owners[rank], nzi, current_space->array, dnz, onz));
1624: }
1625: PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));
1626: PetscCall(PetscLLDestroy(lnk, lnkbt));
1627: PetscCall(PetscFreeSpaceDestroy(free_space));
1629: /* local sizes and preallocation */
1630: PetscCall(MatSetSizes(C, pn, an, PETSC_DETERMINE, PETSC_DETERMINE));
1631: PetscCall(PetscLayoutSetBlockSize(C->rmap, P->cmap->bs));
1632: PetscCall(PetscLayoutSetBlockSize(C->cmap, A->cmap->bs));
1633: PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
1634: MatPreallocateEnd(dnz, onz);
1636: /* add C_loc and C_oth to C */
1637: PetscCall(MatGetOwnershipRange(C, &rstart, NULL));
1638: for (i = 0; i < pn; i++) {
1639: ncols = c_loc->i[i + 1] - c_loc->i[i];
1640: cols = c_loc->j + c_loc->i[i];
1641: row = rstart + i;
1642: PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, ncols, (const PetscInt *)cols, NULL, INSERT_VALUES));
1644: if (C->force_diagonals) PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, 1, (const PetscInt *)&row, NULL, INSERT_VALUES));
1645: }
1646: for (i = 0; i < con; i++) {
1647: ncols = c_oth->i[i + 1] - c_oth->i[i];
1648: cols = c_oth->j + c_oth->i[i];
1649: row = prmap[i];
1650: PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, ncols, (const PetscInt *)cols, NULL, INSERT_VALUES));
1651: }
1652: PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1653: PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1654: PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
1656: /* members in merge */
1657: PetscCall(PetscFree(id_r));
1658: PetscCall(PetscFree(len_r));
1659: PetscCall(PetscFree(buf_ri[0]));
1660: PetscCall(PetscFree(buf_ri));
1661: PetscCall(PetscFree(buf_rj[0]));
1662: PetscCall(PetscFree(buf_rj));
1663: PetscCall(PetscLayoutDestroy(&rowmap));
1665: /* attach the supporting struct to C for reuse */
1666: C->product->data = ptap;
1667: C->product->destroy = MatProductCtxDestroy_MPIAIJ_PtAP;
1668: PetscFunctionReturn(PETSC_SUCCESS);
1669: }
1671: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P, Mat A, Mat C)
1672: {
1673: Mat_MPIAIJ *p = (Mat_MPIAIJ *)P->data;
1674: Mat_SeqAIJ *c_seq;
1675: MatProductCtx_APMPI *ptap;
1676: Mat A_loc, C_loc, C_oth;
1677: PetscInt i, rstart, rend, cm, ncols, row;
1678: const PetscInt *cols;
1679: const PetscScalar *vals;
1681: PetscFunctionBegin;
1682: MatCheckProduct(C, 3);
1683: ptap = (MatProductCtx_APMPI *)C->product->data;
1684: PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
1685: PetscCheck(ptap->A_loc, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");
1686: PetscCall(MatZeroEntries(C));
1688: /* These matrices are obtained in MatTransposeMatMultSymbolic() */
1689: /* 1) get R = Pd^T, Ro = Po^T */
1690: PetscCall(MatTransposeSetPrecursor(p->A, ptap->Rd));
1691: PetscCall(MatTranspose(p->A, MAT_REUSE_MATRIX, &ptap->Rd));
1692: PetscCall(MatTransposeSetPrecursor(p->B, ptap->Ro));
1693: PetscCall(MatTranspose(p->B, MAT_REUSE_MATRIX, &ptap->Ro));
1695: /* 2) compute numeric A_loc */
1696: PetscCall(MatMPIAIJGetLocalMat(A, MAT_REUSE_MATRIX, &ptap->A_loc));
1698: /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */
1699: A_loc = ptap->A_loc;
1700: PetscCall(ptap->C_loc->ops->matmultnumeric(ptap->Rd, A_loc, ptap->C_loc));
1701: PetscCall(ptap->C_oth->ops->matmultnumeric(ptap->Ro, A_loc, ptap->C_oth));
1702: C_loc = ptap->C_loc;
1703: C_oth = ptap->C_oth;
1705: /* add C_loc and C_oth to C */
1706: PetscCall(MatGetOwnershipRange(C, &rstart, &rend));
1708: /* C_loc -> C */
1709: cm = C_loc->rmap->N;
1710: c_seq = (Mat_SeqAIJ *)C_loc->data;
1711: cols = c_seq->j;
1712: vals = c_seq->a;
1713: for (i = 0; i < cm; i++) {
1714: ncols = c_seq->i[i + 1] - c_seq->i[i];
1715: row = rstart + i;
1716: PetscCall(MatSetValues(C, 1, &row, ncols, cols, vals, ADD_VALUES));
1717: cols += ncols;
1718: vals += ncols;
1719: }
1721: /* Co -> C, off-processor part */
1722: cm = C_oth->rmap->N;
1723: c_seq = (Mat_SeqAIJ *)C_oth->data;
1724: cols = c_seq->j;
1725: vals = c_seq->a;
1726: for (i = 0; i < cm; i++) {
1727: ncols = c_seq->i[i + 1] - c_seq->i[i];
1728: row = p->garray[i];
1729: PetscCall(MatSetValues(C, 1, &row, ncols, cols, vals, ADD_VALUES));
1730: cols += ncols;
1731: vals += ncols;
1732: }
1733: PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1734: PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1735: PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
1736: PetscFunctionReturn(PETSC_SUCCESS);
1737: }
1739: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P, Mat A, Mat C)
1740: {
1741: MatMergeSeqsToMPI *merge;
1742: Mat_MPIAIJ *p = (Mat_MPIAIJ *)P->data;
1743: Mat_SeqAIJ *pd = (Mat_SeqAIJ *)p->A->data, *po = (Mat_SeqAIJ *)p->B->data;
1744: MatProductCtx_APMPI *ap;
1745: PetscInt *adj;
1746: PetscInt i, j, k, anz, pnz, row, *cj, nexta;
1747: MatScalar *ada, *ca, valtmp;
1748: PetscInt am = A->rmap->n, cm = C->rmap->n, pon = p->B->cmap->n;
1749: MPI_Comm comm;
1750: PetscMPIInt size, rank, taga, *len_s, proc;
1751: PetscInt *owners, nrows, **buf_ri_k, **nextrow, **nextci;
1752: PetscInt **buf_ri, **buf_rj;
1753: PetscInt cnz = 0, *bj_i, *bi, *bj, bnz, nextcj; /* bi,bj,ba: local array of C(mpi mat) */
1754: MPI_Request *s_waits, *r_waits;
1755: MPI_Status *status;
1756: MatScalar **abuf_r, *ba_i, *pA, *coa, *ba;
1757: const PetscScalar *dummy;
1758: PetscInt *ai, *aj, *coi, *coj, *poJ, *pdJ;
1759: Mat A_loc;
1760: Mat_SeqAIJ *a_loc;
1762: PetscFunctionBegin;
1763: MatCheckProduct(C, 3);
1764: ap = (MatProductCtx_APMPI *)C->product->data;
1765: PetscCheck(ap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be computed. Missing data");
1766: PetscCheck(ap->A_loc, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");
1767: PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
1768: PetscCallMPI(MPI_Comm_size(comm, &size));
1769: PetscCallMPI(MPI_Comm_rank(comm, &rank));
1771: merge = ap->merge;
1773: /* 2) compute numeric C_seq = P_loc^T*A_loc */
1774: /* get data from symbolic products */
1775: coi = merge->coi;
1776: coj = merge->coj;
1777: PetscCall(PetscCalloc1(coi[pon], &coa));
1778: bi = merge->bi;
1779: bj = merge->bj;
1780: owners = merge->rowmap->range;
1781: PetscCall(PetscCalloc1(bi[cm], &ba));
1783: /* get A_loc by taking all local rows of A */
1784: A_loc = ap->A_loc;
1785: PetscCall(MatMPIAIJGetLocalMat(A, MAT_REUSE_MATRIX, &A_loc));
1786: a_loc = (Mat_SeqAIJ *)A_loc->data;
1787: ai = a_loc->i;
1788: aj = a_loc->j;
1790: /* trigger copy to CPU */
1791: PetscCall(MatSeqAIJGetArrayRead(p->A, &dummy));
1792: PetscCall(MatSeqAIJRestoreArrayRead(p->A, &dummy));
1793: PetscCall(MatSeqAIJGetArrayRead(p->B, &dummy));
1794: PetscCall(MatSeqAIJRestoreArrayRead(p->B, &dummy));
1795: for (i = 0; i < am; i++) {
1796: anz = ai[i + 1] - ai[i];
1797: adj = aj + ai[i];
1798: ada = a_loc->a + ai[i];
1800: /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
1801: /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
1802: pnz = po->i[i + 1] - po->i[i];
1803: poJ = po->j + po->i[i];
1804: pA = po->a + po->i[i];
1805: for (j = 0; j < pnz; j++) {
1806: row = poJ[j];
1807: cj = coj + coi[row];
1808: ca = coa + coi[row];
1809: /* perform sparse axpy */
1810: nexta = 0;
1811: valtmp = pA[j];
1812: for (k = 0; nexta < anz; k++) {
1813: if (cj[k] == adj[nexta]) {
1814: ca[k] += valtmp * ada[nexta];
1815: nexta++;
1816: }
1817: }
1818: PetscCall(PetscLogFlops(2.0 * anz));
1819: }
1821: /* put the value into Cd (diagonal part) */
1822: pnz = pd->i[i + 1] - pd->i[i];
1823: pdJ = pd->j + pd->i[i];
1824: pA = pd->a + pd->i[i];
1825: for (j = 0; j < pnz; j++) {
1826: row = pdJ[j];
1827: cj = bj + bi[row];
1828: ca = ba + bi[row];
1829: /* perform sparse axpy */
1830: nexta = 0;
1831: valtmp = pA[j];
1832: for (k = 0; nexta < anz; k++) {
1833: if (cj[k] == adj[nexta]) {
1834: ca[k] += valtmp * ada[nexta];
1835: nexta++;
1836: }
1837: }
1838: PetscCall(PetscLogFlops(2.0 * anz));
1839: }
1840: }
1842: /* 3) send and recv matrix values coa */
1843: buf_ri = merge->buf_ri;
1844: buf_rj = merge->buf_rj;
1845: len_s = merge->len_s;
1846: PetscCall(PetscCommGetNewTag(comm, &taga));
1847: PetscCall(PetscPostIrecvScalar(comm, taga, merge->nrecv, merge->id_r, merge->len_r, &abuf_r, &r_waits));
1849: PetscCall(PetscMalloc2(merge->nsend, &s_waits, size, &status));
1850: for (proc = 0, k = 0; proc < size; proc++) {
1851: if (!len_s[proc]) continue;
1852: i = merge->owners_co[proc];
1853: PetscCallMPI(MPIU_Isend(coa + coi[i], len_s[proc], MPIU_MATSCALAR, proc, taga, comm, s_waits + k));
1854: k++;
1855: }
1856: if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv, r_waits, status));
1857: if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, s_waits, status));
1859: PetscCall(PetscFree2(s_waits, status));
1860: PetscCall(PetscFree(r_waits));
1861: PetscCall(PetscFree(coa));
1863: /* 4) insert local Cseq and received values into Cmpi */
1864: PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextci));
1865: for (k = 0; k < merge->nrecv; k++) {
1866: buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1867: nrows = *buf_ri_k[k];
1868: nextrow[k] = buf_ri_k[k] + 1; /* next row number of k-th recved i-structure */
1869: nextci[k] = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure */
1870: }
1872: for (i = 0; i < cm; i++) {
1873: row = owners[rank] + i; /* global row index of C_seq */
1874: bj_i = bj + bi[i]; /* col indices of the i-th row of C */
1875: ba_i = ba + bi[i];
1876: bnz = bi[i + 1] - bi[i];
1877: /* add received vals into ba */
1878: for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
1879: /* i-th row */
1880: if (i == *nextrow[k]) {
1881: cnz = *(nextci[k] + 1) - *nextci[k];
1882: cj = buf_rj[k] + *nextci[k];
1883: ca = abuf_r[k] + *nextci[k];
1884: nextcj = 0;
1885: for (j = 0; nextcj < cnz; j++) {
1886: if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
1887: ba_i[j] += ca[nextcj++];
1888: }
1889: }
1890: nextrow[k]++;
1891: nextci[k]++;
1892: PetscCall(PetscLogFlops(2.0 * cnz));
1893: }
1894: }
1895: PetscCall(MatSetValues(C, 1, &row, bnz, bj_i, ba_i, INSERT_VALUES));
1896: }
1897: PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1898: PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1900: PetscCall(PetscFree(ba));
1901: PetscCall(PetscFree(abuf_r[0]));
1902: PetscCall(PetscFree(abuf_r));
1903: PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));
1904: PetscFunctionReturn(PETSC_SUCCESS);
1905: }
1907: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P, Mat A, PetscReal fill, Mat C)
1908: {
1909: Mat A_loc;
1910: MatProductCtx_APMPI *ap;
1911: PetscFreeSpaceList free_space = NULL, current_space = NULL;
1912: Mat_MPIAIJ *p = (Mat_MPIAIJ *)P->data, *a = (Mat_MPIAIJ *)A->data;
1913: PetscInt *pdti, *pdtj, *poti, *potj, *ptJ;
1914: PetscInt nnz;
1915: PetscInt *lnk, *owners_co, *coi, *coj, i, k, pnz, row;
1916: PetscInt am = A->rmap->n, pn = P->cmap->n;
1917: MPI_Comm comm;
1918: PetscMPIInt size, rank, tagi, tagj, *len_si, *len_s, *len_ri, proc;
1919: PetscInt **buf_rj, **buf_ri, **buf_ri_k;
1920: PetscInt len, *dnz, *onz, *owners;
1921: PetscInt nzi, *bi, *bj;
1922: PetscInt nrows, *buf_s, *buf_si, *buf_si_i, **nextrow, **nextci;
1923: MPI_Request *swaits, *rwaits;
1924: MPI_Status *sstatus, rstatus;
1925: MatMergeSeqsToMPI *merge;
1926: PetscInt *ai, *aj, *Jptr, anz, *prmap = p->garray, pon, nspacedouble = 0, j;
1927: PetscReal afill = 1.0, afill_tmp;
1928: PetscInt rstart = P->cmap->rstart, rmax, Armax;
1929: Mat_SeqAIJ *a_loc;
1930: PetscHMapI ta;
1931: MatType mtype;
1933: PetscFunctionBegin;
1934: PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
1935: /* check if matrix local sizes are compatible */
1936: PetscCheck(A->rmap->rstart == P->rmap->rstart && A->rmap->rend == P->rmap->rend, comm, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, A (%" PetscInt_FMT ", %" PetscInt_FMT ") != P (%" PetscInt_FMT ",%" PetscInt_FMT ")", A->rmap->rstart,
1937: A->rmap->rend, P->rmap->rstart, P->rmap->rend);
1939: PetscCallMPI(MPI_Comm_size(comm, &size));
1940: PetscCallMPI(MPI_Comm_rank(comm, &rank));
1942: /* create struct MatProductCtx_APMPI and attached it to C later */
1943: PetscCall(PetscNew(&ap));
1945: /* get A_loc by taking all local rows of A */
1946: PetscCall(MatMPIAIJGetLocalMat_Private(A, MAT_INITIAL_MATRIX, C->structure_only, &A_loc));
1948: ap->A_loc = A_loc;
1949: a_loc = (Mat_SeqAIJ *)A_loc->data;
1950: ai = a_loc->i;
1951: aj = a_loc->j;
1953: /* determine symbolic Co=(p->B)^T*A - send to others */
1954: PetscCall(MatGetSymbolicTranspose_SeqAIJ(p->A, &pdti, &pdtj));
1955: PetscCall(MatGetSymbolicTranspose_SeqAIJ(p->B, &poti, &potj));
1956: pon = p->B->cmap->n; /* total num of rows to be sent to other processors
1957: >= (num of nonzero rows of C_seq) - pn */
1958: PetscCall(PetscMalloc1(pon + 1, &coi));
1959: coi[0] = 0;
1961: /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
1962: nnz = PetscRealIntMultTruncate(fill, PetscIntSumTruncate(poti[pon], ai[am]));
1963: PetscCall(PetscFreeSpaceGet(nnz, &free_space));
1964: current_space = free_space;
1966: /* create and initialize a linked list */
1967: PetscCall(PetscHMapICreateWithSize(A->cmap->n + a->B->cmap->N, &ta));
1968: MatRowMergeMax_SeqAIJ(a_loc, am, ta);
1969: PetscCall(PetscHMapIGetSize(ta, &Armax));
1971: PetscCall(PetscLLCondensedCreate_Scalable(Armax, &lnk));
1973: for (i = 0; i < pon; i++) {
1974: pnz = poti[i + 1] - poti[i];
1975: ptJ = potj + poti[i];
1976: for (j = 0; j < pnz; j++) {
1977: row = ptJ[j]; /* row of A_loc == col of Pot */
1978: anz = ai[row + 1] - ai[row];
1979: Jptr = aj + ai[row];
1980: /* add non-zero cols of AP into the sorted linked list lnk */
1981: PetscCall(PetscLLCondensedAddSorted_Scalable(anz, Jptr, lnk));
1982: }
1983: nnz = lnk[0];
1985: /* If free space is not available, double the total space in the list */
1986: if (current_space->local_remaining < nnz) {
1987: PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(nnz, current_space->total_array_size), ¤t_space));
1988: nspacedouble++;
1989: }
1991: /* Copy data into free space, and zero out denserows */
1992: PetscCall(PetscLLCondensedClean_Scalable(nnz, current_space->array, lnk));
1994: current_space->array += nnz;
1995: current_space->local_used += nnz;
1996: current_space->local_remaining -= nnz;
1998: coi[i + 1] = coi[i] + nnz;
1999: }
2001: PetscCall(PetscMalloc1(coi[pon], &coj));
2002: PetscCall(PetscFreeSpaceContiguous(&free_space, coj));
2003: PetscCall(PetscLLCondensedDestroy_Scalable(lnk)); /* must destroy to get a new one for C */
2005: afill_tmp = (PetscReal)coi[pon] / (poti[pon] + ai[am] + 1);
2006: if (afill_tmp > afill) afill = afill_tmp;
2008: /* send j-array (coj) of Co to other processors */
2009: /* determine row ownership */
2010: PetscCall(PetscNew(&merge));
2011: PetscCall(PetscLayoutCreate(comm, &merge->rowmap));
2013: merge->rowmap->n = pn;
2014: merge->rowmap->bs = 1;
2016: PetscCall(PetscLayoutSetUp(merge->rowmap));
2017: owners = merge->rowmap->range;
2019: /* determine the number of messages to send, their lengths */
2020: PetscCall(PetscCalloc1(size, &len_si));
2021: PetscCall(PetscCalloc1(size, &merge->len_s));
2023: len_s = merge->len_s;
2024: merge->nsend = 0;
2026: PetscCall(PetscMalloc1(size + 1, &owners_co));
2028: proc = 0;
2029: for (i = 0; i < pon; i++) {
2030: while (prmap[i] >= owners[proc + 1]) proc++;
2031: len_si[proc]++; /* num of rows in Co to be sent to [proc] */
2032: len_s[proc] += coi[i + 1] - coi[i];
2033: }
2035: len = 0; /* max length of buf_si[] */
2036: owners_co[0] = 0;
2037: for (proc = 0; proc < size; proc++) {
2038: owners_co[proc + 1] = owners_co[proc] + len_si[proc];
2039: if (len_s[proc]) {
2040: merge->nsend++;
2041: len_si[proc] = 2 * (len_si[proc] + 1);
2042: len += len_si[proc];
2043: }
2044: }
2046: /* determine the number and length of messages to receive for coi and coj */
2047: PetscCall(PetscGatherNumberOfMessages(comm, NULL, len_s, &merge->nrecv));
2048: PetscCall(PetscGatherMessageLengths2(comm, merge->nsend, merge->nrecv, len_s, len_si, &merge->id_r, &merge->len_r, &len_ri));
2050: /* post the Irecv and Isend of coj */
2051: PetscCall(PetscCommGetNewTag(comm, &tagj));
2052: PetscCall(PetscPostIrecvInt(comm, tagj, merge->nrecv, merge->id_r, merge->len_r, &buf_rj, &rwaits));
2053: PetscCall(PetscMalloc1(merge->nsend, &swaits));
2054: for (proc = 0, k = 0; proc < size; proc++) {
2055: if (!len_s[proc]) continue;
2056: i = owners_co[proc];
2057: PetscCallMPI(MPIU_Isend(coj + coi[i], len_s[proc], MPIU_INT, proc, tagj, comm, swaits + k));
2058: k++;
2059: }
2061: /* receives and sends of coj are complete */
2062: PetscCall(PetscMalloc1(size, &sstatus));
2063: for (i = 0; i < merge->nrecv; i++) {
2064: PETSC_UNUSED PetscMPIInt icompleted;
2065: PetscCallMPI(MPI_Waitany(merge->nrecv, rwaits, &icompleted, &rstatus));
2066: }
2067: PetscCall(PetscFree(rwaits));
2068: if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, swaits, sstatus));
2070: /* add received column indices into table to update Armax */
2071: /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/tutorials/ex56.c! */
2072: for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
2073: Jptr = buf_rj[k];
2074: for (j = 0; j < merge->len_r[k]; j++) PetscCall(PetscHMapISet(ta, *(Jptr + j) + 1, 1));
2075: }
2076: PetscCall(PetscHMapIGetSize(ta, &Armax));
2078: /* send and recv coi */
2079: PetscCall(PetscCommGetNewTag(comm, &tagi));
2080: PetscCall(PetscPostIrecvInt(comm, tagi, merge->nrecv, merge->id_r, len_ri, &buf_ri, &rwaits));
2081: PetscCall(PetscMalloc1(len, &buf_s));
2082: buf_si = buf_s; /* points to the beginning of k-th msg to be sent */
2083: for (proc = 0, k = 0; proc < size; proc++) {
2084: if (!len_s[proc]) continue;
2085: /* form outgoing message for i-structure:
2086: buf_si[0]: nrows to be sent
2087: [1:nrows]: row index (global)
2088: [nrows+1:2*nrows+1]: i-structure index
2089: */
2090: nrows = len_si[proc] / 2 - 1;
2091: buf_si_i = buf_si + nrows + 1;
2092: buf_si[0] = nrows;
2093: buf_si_i[0] = 0;
2094: nrows = 0;
2095: for (i = owners_co[proc]; i < owners_co[proc + 1]; i++) {
2096: nzi = coi[i + 1] - coi[i];
2097: buf_si_i[nrows + 1] = buf_si_i[nrows] + nzi; /* i-structure */
2098: buf_si[nrows + 1] = prmap[i] - owners[proc]; /* local row index */
2099: nrows++;
2100: }
2101: PetscCallMPI(MPIU_Isend(buf_si, len_si[proc], MPIU_INT, proc, tagi, comm, swaits + k));
2102: k++;
2103: buf_si += len_si[proc];
2104: }
2105: i = merge->nrecv;
2106: while (i--) {
2107: PETSC_UNUSED PetscMPIInt icompleted;
2108: PetscCallMPI(MPI_Waitany(merge->nrecv, rwaits, &icompleted, &rstatus));
2109: }
2110: PetscCall(PetscFree(rwaits));
2111: if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, swaits, sstatus));
2112: PetscCall(PetscFree(len_si));
2113: PetscCall(PetscFree(len_ri));
2114: PetscCall(PetscFree(swaits));
2115: PetscCall(PetscFree(sstatus));
2116: PetscCall(PetscFree(buf_s));
2118: /* compute the local portion of C (mpi mat) */
2119: /* allocate bi array and free space for accumulating nonzero column info */
2120: PetscCall(PetscMalloc1(pn + 1, &bi));
2121: bi[0] = 0;
2123: /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
2124: nnz = PetscRealIntMultTruncate(fill, PetscIntSumTruncate(pdti[pn], PetscIntSumTruncate(poti[pon], ai[am])));
2125: PetscCall(PetscFreeSpaceGet(nnz, &free_space));
2126: current_space = free_space;
2128: PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextci));
2129: for (k = 0; k < merge->nrecv; k++) {
2130: buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
2131: nrows = *buf_ri_k[k];
2132: nextrow[k] = buf_ri_k[k] + 1; /* next row number of k-th recved i-structure */
2133: nextci[k] = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th received i-structure */
2134: }
2136: PetscCall(PetscLLCondensedCreate_Scalable(Armax, &lnk));
2137: MatPreallocateBegin(comm, pn, A->cmap->n, dnz, onz);
2138: rmax = 0;
2139: for (i = 0; i < pn; i++) {
2140: /* add pdt[i,:]*AP into lnk */
2141: pnz = pdti[i + 1] - pdti[i];
2142: ptJ = pdtj + pdti[i];
2143: for (j = 0; j < pnz; j++) {
2144: row = ptJ[j]; /* row of AP == col of Pt */
2145: anz = ai[row + 1] - ai[row];
2146: Jptr = aj + ai[row];
2147: /* add non-zero cols of AP into the sorted linked list lnk */
2148: PetscCall(PetscLLCondensedAddSorted_Scalable(anz, Jptr, lnk));
2149: }
2151: /* add received col data into lnk */
2152: for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
2153: if (i == *nextrow[k]) { /* i-th row */
2154: nzi = *(nextci[k] + 1) - *nextci[k];
2155: Jptr = buf_rj[k] + *nextci[k];
2156: PetscCall(PetscLLCondensedAddSorted_Scalable(nzi, Jptr, lnk));
2157: nextrow[k]++;
2158: nextci[k]++;
2159: }
2160: }
2162: /* add missing diagonal entry */
2163: if (C->force_diagonals) {
2164: k = i + owners[rank]; /* column index */
2165: PetscCall(PetscLLCondensedAddSorted_Scalable(1, &k, lnk));
2166: }
2168: nnz = lnk[0];
2170: /* if free space is not available, make more free space */
2171: if (current_space->local_remaining < nnz) {
2172: PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(nnz, current_space->total_array_size), ¤t_space));
2173: nspacedouble++;
2174: }
2175: /* copy data into free space, then initialize lnk */
2176: PetscCall(PetscLLCondensedClean_Scalable(nnz, current_space->array, lnk));
2177: PetscCall(MatPreallocateSet(i + owners[rank], nnz, current_space->array, dnz, onz));
2179: current_space->array += nnz;
2180: current_space->local_used += nnz;
2181: current_space->local_remaining -= nnz;
2183: bi[i + 1] = bi[i] + nnz;
2184: if (nnz > rmax) rmax = nnz;
2185: }
2186: PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));
2188: PetscCall(PetscMalloc1(bi[pn], &bj));
2189: PetscCall(PetscFreeSpaceContiguous(&free_space, bj));
2190: afill_tmp = (PetscReal)bi[pn] / (pdti[pn] + poti[pon] + ai[am] + 1);
2191: if (afill_tmp > afill) afill = afill_tmp;
2192: PetscCall(PetscLLCondensedDestroy_Scalable(lnk));
2193: PetscCall(PetscHMapIDestroy(&ta));
2194: PetscCall(MatRestoreSymbolicTranspose_SeqAIJ(p->A, &pdti, &pdtj));
2195: PetscCall(MatRestoreSymbolicTranspose_SeqAIJ(p->B, &poti, &potj));
2197: /* create symbolic parallel matrix C - why cannot be assembled in Numeric part */
2198: PetscCall(MatSetSizes(C, pn, A->cmap->n, PETSC_DETERMINE, PETSC_DETERMINE));
2199: PetscCall(MatSetBlockSizes(C, P->cmap->bs, A->cmap->bs));
2200: PetscCall(MatGetType(A, &mtype));
2201: PetscCall(MatSetType(C, C->structure_only ? MATMPIAIJ : mtype));
2202: PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
2203: MatPreallocateEnd(dnz, onz);
2204: PetscCall(MatSetBlockSize(C, 1));
2205: PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
2206: for (i = 0; i < pn; i++) {
2207: row = i + rstart;
2208: nnz = bi[i + 1] - bi[i];
2209: Jptr = bj + bi[i];
2210: PetscCall(MatSetValues(C, 1, &row, nnz, Jptr, NULL, INSERT_VALUES));
2211: }
2212: PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
2213: PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
2214: PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
2215: merge->bi = bi;
2216: merge->bj = bj;
2217: merge->coi = coi;
2218: merge->coj = coj;
2219: merge->buf_ri = buf_ri;
2220: merge->buf_rj = buf_rj;
2221: merge->owners_co = owners_co;
2223: /* attach the supporting struct to C for reuse */
2224: C->product->data = ap;
2225: C->product->destroy = MatProductCtxDestroy_MPIAIJ_PtAP;
2226: ap->merge = merge;
2228: C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;
2230: if (PetscDefined(USE_INFO)) {
2231: if (bi[pn] != 0) {
2232: PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
2233: PetscCall(PetscInfo(C, "Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n", (double)afill));
2234: } else PetscCall(PetscInfo(C, "Empty matrix product\n"));
2235: }
2236: PetscFunctionReturn(PETSC_SUCCESS);
2237: }
2239: static PetscErrorCode MatProductSymbolic_AtB_MPIAIJ_MPIAIJ(Mat C)
2240: {
2241: Mat_Product *product = C->product;
2242: Mat A = product->A, B = product->B;
2243: PetscReal fill = product->fill;
2244: PetscBool flg;
2246: PetscFunctionBegin;
2247: /* scalable */
2248: PetscCall(PetscStrcmp(product->alg, "scalable", &flg));
2249: if (flg || C->structure_only) {
2250: if (C->structure_only) PetscCall(MatProductSetAlgorithm(C, "scalable"));
2251: PetscCall(MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(A, B, fill, C));
2252: goto next;
2253: }
2255: /* nonscalable */
2256: PetscCall(PetscStrcmp(product->alg, "nonscalable", &flg));
2257: if (flg) {
2258: PetscCall(MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A, B, fill, C));
2259: goto next;
2260: }
2262: /* matmatmult */
2263: PetscCall(PetscStrcmp(product->alg, "at*b", &flg));
2264: if (flg) {
2265: Mat At;
2266: MatProductCtx_APMPI *ptap;
2268: PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &At));
2269: PetscCall(MatMatMultSymbolic_MPIAIJ_MPIAIJ(At, B, fill, C));
2270: ptap = (MatProductCtx_APMPI *)C->product->data;
2271: if (ptap) {
2272: ptap->Pt = At;
2273: C->product->destroy = MatProductCtxDestroy_MPIAIJ_PtAP;
2274: }
2275: C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
2276: goto next;
2277: }
2279: /* backend general code */
2280: PetscCall(PetscStrcmp(product->alg, "backend", &flg));
2281: if (flg) {
2282: PetscCall(MatProductSymbolic_MPIAIJBACKEND(C));
2283: PetscFunctionReturn(PETSC_SUCCESS);
2284: }
2286: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatProduct type is not supported");
2288: next:
2289: C->ops->productnumeric = MatProductNumeric_AtB;
2290: PetscFunctionReturn(PETSC_SUCCESS);
2291: }
2293: /* Set options for MatMatMultxxx_MPIAIJ_MPIAIJ */
2294: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AB(Mat C)
2295: {
2296: Mat_Product *product = C->product;
2297: Mat A = product->A, B = product->B;
2298: #if PetscDefined(HAVE_HYPRE)
2299: const char *algTypes[5] = {"scalable", "nonscalable", "seqmpi", "backend", "hypre"};
2300: PetscInt nalg = 5;
2301: #else
2302: const char *algTypes[4] = {
2303: "scalable",
2304: "nonscalable",
2305: "seqmpi",
2306: "backend",
2307: };
2308: PetscInt nalg = 4;
2309: #endif
2310: PetscInt alg = 1; /* set nonscalable algorithm as default */
2311: PetscBool flg;
2312: MPI_Comm comm;
2314: PetscFunctionBegin;
2315: PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
2317: /* Set "nonscalable" as default algorithm */
2318: PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2319: if (flg) {
2320: PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2322: /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2323: if (B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2324: MatInfo Ainfo, Binfo;
2325: PetscInt nz_local;
2326: PetscBool alg_scalable = PETSC_FALSE;
2328: PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
2329: PetscCall(MatGetInfo(B, MAT_LOCAL, &Binfo));
2330: nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);
2332: if (B->cmap->N > product->fill * nz_local) alg_scalable = PETSC_TRUE;
2333: PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &alg_scalable, 1, MPI_C_BOOL, MPI_LOR, comm));
2335: if (alg_scalable) {
2336: alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2337: PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2338: PetscCall(PetscInfo(B, "Use scalable algorithm, BN %" PetscInt_FMT ", fill*nz_allocated %g\n", B->cmap->N, (double)(product->fill * nz_local)));
2339: }
2340: }
2341: }
2343: /* Get runtime option */
2344: if (product->api_user) {
2345: PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMult", "Mat");
2346: PetscCall(PetscOptionsEList("-matmatmult_via", "Algorithmic approach", "MatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2347: PetscOptionsEnd();
2348: } else {
2349: PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AB", "Mat");
2350: PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2351: PetscOptionsEnd();
2352: }
2353: if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2355: C->ops->productsymbolic = MatProductSymbolic_AB_MPIAIJ_MPIAIJ;
2356: PetscFunctionReturn(PETSC_SUCCESS);
2357: }
2359: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABt(Mat C)
2360: {
2361: PetscFunctionBegin;
2362: PetscCall(MatProductSetFromOptions_MPIAIJ_AB(C));
2363: C->ops->productsymbolic = MatProductSymbolic_ABt_MPIAIJ_MPIAIJ;
2364: PetscFunctionReturn(PETSC_SUCCESS);
2365: }
2367: /* Set options for MatTransposeMatMultXXX_MPIAIJ_MPIAIJ */
2368: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AtB(Mat C)
2369: {
2370: Mat_Product *product = C->product;
2371: Mat A = product->A, B = product->B;
2372: const char *algTypes[4] = {"scalable", "nonscalable", "at*b", "backend"};
2373: PetscInt nalg = 4;
2374: PetscInt alg = 1; /* set default algorithm */
2375: PetscBool flg;
2376: MPI_Comm comm;
2378: PetscFunctionBegin;
2379: /* Check matrix local sizes */
2380: PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
2381: PetscCheck(A->rmap->rstart == B->rmap->rstart && A->rmap->rend == B->rmap->rend, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, A (%" PetscInt_FMT ", %" PetscInt_FMT ") != B (%" PetscInt_FMT ",%" PetscInt_FMT ")",
2382: A->rmap->rstart, A->rmap->rend, B->rmap->rstart, B->rmap->rend);
2384: /* Set default algorithm */
2385: PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2386: if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2388: /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2389: if (alg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2390: MatInfo Ainfo, Binfo;
2391: PetscInt nz_local;
2392: PetscBool alg_scalable = PETSC_FALSE;
2394: PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
2395: PetscCall(MatGetInfo(B, MAT_LOCAL, &Binfo));
2396: nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);
2398: if (B->cmap->N > product->fill * nz_local) alg_scalable = PETSC_TRUE;
2399: PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &alg_scalable, 1, MPI_C_BOOL, MPI_LOR, comm));
2401: if (alg_scalable) {
2402: alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2403: PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2404: PetscCall(PetscInfo(B, "Use scalable algorithm, BN %" PetscInt_FMT ", fill*nz_allocated %g\n", B->cmap->N, (double)(product->fill * nz_local)));
2405: }
2406: }
2408: /* Get runtime option */
2409: if (product->api_user) {
2410: PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatTransposeMatMult", "Mat");
2411: PetscCall(PetscOptionsEList("-mattransposematmult_via", "Algorithmic approach", "MatTransposeMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2412: PetscOptionsEnd();
2413: } else {
2414: PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AtB", "Mat");
2415: PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatTransposeMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2416: PetscOptionsEnd();
2417: }
2418: if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2420: C->ops->productsymbolic = MatProductSymbolic_AtB_MPIAIJ_MPIAIJ;
2421: PetscFunctionReturn(PETSC_SUCCESS);
2422: }
2424: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_PtAP(Mat C)
2425: {
2426: Mat_Product *product = C->product;
2427: Mat A = product->A, P = product->B;
2428: MPI_Comm comm;
2429: PetscBool flg;
2430: PetscInt alg = 1; /* set default algorithm */
2431: #if !PetscDefined(HAVE_HYPRE)
2432: const char *algTypes[5] = {"scalable", "nonscalable", "allatonce", "allatonce_merged", "backend"};
2433: PetscInt nalg = 5;
2434: #else
2435: const char *algTypes[6] = {"scalable", "nonscalable", "allatonce", "allatonce_merged", "backend", "hypre"};
2436: PetscInt nalg = 6;
2437: #endif
2438: PetscInt pN = P->cmap->N;
2440: PetscFunctionBegin;
2441: /* Check matrix local sizes */
2442: PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
2443: PetscCheck(A->rmap->rstart == P->rmap->rstart && A->rmap->rend == P->rmap->rend, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, Arow (%" PetscInt_FMT ", %" PetscInt_FMT ") != Prow (%" PetscInt_FMT ",%" PetscInt_FMT ")",
2444: A->rmap->rstart, A->rmap->rend, P->rmap->rstart, P->rmap->rend);
2445: PetscCheck(A->cmap->rstart == P->rmap->rstart && A->cmap->rend == P->rmap->rend, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, Acol (%" PetscInt_FMT ", %" PetscInt_FMT ") != Prow (%" PetscInt_FMT ",%" PetscInt_FMT ")",
2446: A->cmap->rstart, A->cmap->rend, P->rmap->rstart, P->rmap->rend);
2448: /* Set "nonscalable" as default algorithm */
2449: PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2450: if (flg) {
2451: PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2453: /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2454: if (pN > 100000) {
2455: MatInfo Ainfo, Pinfo;
2456: PetscInt nz_local;
2457: PetscBool alg_scalable = PETSC_FALSE;
2459: PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
2460: PetscCall(MatGetInfo(P, MAT_LOCAL, &Pinfo));
2461: nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);
2463: if (pN > product->fill * nz_local) alg_scalable = PETSC_TRUE;
2464: PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &alg_scalable, 1, MPI_C_BOOL, MPI_LOR, comm));
2466: if (alg_scalable) {
2467: alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2468: PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2469: }
2470: }
2471: }
2473: /* Get runtime option */
2474: if (product->api_user) {
2475: PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatPtAP", "Mat");
2476: PetscCall(PetscOptionsEList("-matptap_via", "Algorithmic approach", "MatPtAP", algTypes, nalg, algTypes[alg], &alg, &flg));
2477: PetscOptionsEnd();
2478: } else {
2479: PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_PtAP", "Mat");
2480: PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatPtAP", algTypes, nalg, algTypes[alg], &alg, &flg));
2481: PetscOptionsEnd();
2482: }
2483: if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2485: C->ops->productsymbolic = MatProductSymbolic_PtAP_MPIAIJ_MPIAIJ;
2486: PetscFunctionReturn(PETSC_SUCCESS);
2487: }
2489: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_RARt(Mat C)
2490: {
2491: Mat_Product *product = C->product;
2492: Mat A = product->A, R = product->B;
2494: PetscFunctionBegin;
2495: /* Check matrix local sizes */
2496: PetscCheck(A->cmap->n == R->cmap->n && A->rmap->n == R->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, A local (%" PetscInt_FMT ", %" PetscInt_FMT "), R local (%" PetscInt_FMT ",%" PetscInt_FMT ")", A->rmap->n,
2497: A->rmap->n, R->rmap->n, R->cmap->n);
2499: C->ops->productsymbolic = MatProductSymbolic_RARt_MPIAIJ_MPIAIJ;
2500: PetscFunctionReturn(PETSC_SUCCESS);
2501: }
2503: /*
2504: Set options for ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm
2505: */
2506: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABC(Mat C)
2507: {
2508: Mat_Product *product = C->product;
2509: PetscBool flg = PETSC_FALSE;
2510: PetscInt alg = 1; /* default algorithm */
2511: const char *algTypes[3] = {"scalable", "nonscalable", "seqmpi"};
2512: PetscInt nalg = 3;
2514: PetscFunctionBegin;
2515: /* Set default algorithm */
2516: PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2517: if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2519: /* Get runtime option */
2520: if (product->api_user) {
2521: PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMatMult", "Mat");
2522: PetscCall(PetscOptionsEList("-matmatmatmult_via", "Algorithmic approach", "MatMatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2523: PetscOptionsEnd();
2524: } else {
2525: PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_ABC", "Mat");
2526: PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_ABC", algTypes, nalg, algTypes[alg], &alg, &flg));
2527: PetscOptionsEnd();
2528: }
2529: if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2531: C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ;
2532: C->ops->productsymbolic = MatProductSymbolic_ABC;
2533: PetscFunctionReturn(PETSC_SUCCESS);
2534: }
2536: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ(Mat C)
2537: {
2538: Mat_Product *product = C->product;
2540: PetscFunctionBegin;
2541: switch (product->type) {
2542: case MATPRODUCT_AB:
2543: PetscCall(MatProductSetFromOptions_MPIAIJ_AB(C));
2544: break;
2545: case MATPRODUCT_ABt:
2546: PetscCall(MatProductSetFromOptions_MPIAIJ_ABt(C));
2547: break;
2548: case MATPRODUCT_AtB:
2549: PetscCall(MatProductSetFromOptions_MPIAIJ_AtB(C));
2550: break;
2551: case MATPRODUCT_PtAP:
2552: PetscCall(MatProductSetFromOptions_MPIAIJ_PtAP(C));
2553: break;
2554: case MATPRODUCT_RARt:
2555: PetscCall(MatProductSetFromOptions_MPIAIJ_RARt(C));
2556: break;
2557: case MATPRODUCT_ABC:
2558: PetscCall(MatProductSetFromOptions_MPIAIJ_ABC(C));
2559: break;
2560: default:
2561: break;
2562: }
2563: PetscFunctionReturn(PETSC_SUCCESS);
2564: }