Actual source code: mpimatmatmult.c
2: /*
3: Defines matrix-matrix product routines for pairs of MPIAIJ matrices
4: C = A * B
5: */
6: #include <../src/mat/impls/aij/seq/aij.h>
7: #include <../src/mat/utils/freespace.h>
8: #include <../src/mat/impls/aij/mpi/mpiaij.h>
9: #include <petscbt.h>
10: #include <../src/mat/impls/dense/mpi/mpidense.h>
11: #include <petsc/private/vecimpl.h>
12: #include <petsc/private/sfimpl.h>
14: #if defined(PETSC_HAVE_HYPRE)
15: PETSC_INTERN PetscErrorCode MatMatMultSymbolic_AIJ_AIJ_wHYPRE(Mat,Mat,PetscReal,Mat);
16: #endif
18: PETSC_INTERN PetscErrorCode MatProductSymbolic_AB_MPIAIJ_MPIAIJ(Mat C)
19: {
20: PetscErrorCode ierr;
21: Mat_Product *product = C->product;
22: Mat A=product->A,B=product->B;
23: MatProductAlgorithm alg=product->alg;
24: PetscReal fill=product->fill;
25: PetscBool flg;
28: /* scalable */
29: PetscStrcmp(alg,"scalable",&flg);
30: if (flg) {
31: MatMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);
32: return(0);
33: }
35: /* nonscalable */
36: PetscStrcmp(alg,"nonscalable",&flg);
37: if (flg) {
38: MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C);
39: return(0);
40: }
42: /* seqmpi */
43: PetscStrcmp(alg,"seqmpi",&flg);
44: if (flg) {
45: MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(A,B,fill,C);
46: return(0);
47: }
49: /* backend general code */
50: PetscStrcmp(alg,"backend",&flg);
51: if (flg) {
52: MatProductSymbolic_MPIAIJBACKEND(C);
53: return(0);
54: }
56: #if defined(PETSC_HAVE_HYPRE)
57: PetscStrcmp(alg,"hypre",&flg);
58: if (flg) {
59: MatMatMultSymbolic_AIJ_AIJ_wHYPRE(A,B,fill,C);
60: return(0);
61: }
62: #endif
63: SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_SUP,"Mat Product Algorithm is not supported");
64: }
66: PetscErrorCode MatDestroy_MPIAIJ_MatMatMult(void *data)
67: {
69: Mat_APMPI *ptap = (Mat_APMPI*)data;
72: PetscFree2(ptap->startsj_s,ptap->startsj_r);
73: PetscFree(ptap->bufa);
74: MatDestroy(&ptap->P_loc);
75: MatDestroy(&ptap->P_oth);
76: MatDestroy(&ptap->Pt);
77: PetscFree(ptap->api);
78: PetscFree(ptap->apj);
79: PetscFree(ptap->apa);
80: PetscFree(ptap);
81: return(0);
82: }
84: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,Mat C)
85: {
86: PetscErrorCode ierr;
87: Mat_MPIAIJ *a =(Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
88: Mat_SeqAIJ *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
89: Mat_SeqAIJ *cd =(Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
90: PetscScalar *cda=cd->a,*coa=co->a;
91: Mat_SeqAIJ *p_loc,*p_oth;
92: PetscScalar *apa,*ca;
93: PetscInt cm =C->rmap->n;
94: Mat_APMPI *ptap;
95: PetscInt *api,*apj,*apJ,i,k;
96: PetscInt cstart=C->cmap->rstart;
97: PetscInt cdnz,conz,k0,k1;
98: const PetscScalar *dummy;
99: MPI_Comm comm;
100: PetscMPIInt size;
103: MatCheckProduct(C,3);
104: ptap = (Mat_APMPI*)C->product->data;
105: if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
106: PetscObjectGetComm((PetscObject)A,&comm);
107: MPI_Comm_size(comm,&size);
109: if (!ptap->P_oth && size>1) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"AP cannot be reused. Do not call MatProductClear()");
111: /* 1) get P_oth = ptap->P_oth and P_loc = ptap->P_loc */
112: /*-----------------------------------------------------*/
113: /* update numerical values of P_oth and P_loc */
114: MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
115: MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);
117: /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
118: /*----------------------------------------------------------*/
119: /* get data from symbolic products */
120: p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
121: p_oth = NULL;
122: if (size >1) {
123: p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
124: }
126: /* get apa for storing dense row A[i,:]*P */
127: apa = ptap->apa;
129: api = ptap->api;
130: apj = ptap->apj;
131: /* trigger copy to CPU */
132: MatSeqAIJGetArrayRead(a->A,&dummy);
133: MatSeqAIJRestoreArrayRead(a->A,&dummy);
134: MatSeqAIJGetArrayRead(a->B,&dummy);
135: MatSeqAIJRestoreArrayRead(a->B,&dummy);
136: for (i=0; i<cm; i++) {
137: /* compute apa = A[i,:]*P */
138: AProw_nonscalable(i,ad,ao,p_loc,p_oth,apa);
140: /* set values in C */
141: apJ = apj + api[i];
142: cdnz = cd->i[i+1] - cd->i[i];
143: conz = co->i[i+1] - co->i[i];
145: /* 1st off-diagonal part of C */
146: ca = coa + co->i[i];
147: k = 0;
148: for (k0=0; k0<conz; k0++) {
149: if (apJ[k] >= cstart) break;
150: ca[k0] = apa[apJ[k]];
151: apa[apJ[k++]] = 0.0;
152: }
154: /* diagonal part of C */
155: ca = cda + cd->i[i];
156: for (k1=0; k1<cdnz; k1++) {
157: ca[k1] = apa[apJ[k]];
158: apa[apJ[k++]] = 0.0;
159: }
161: /* 2nd off-diagonal part of C */
162: ca = coa + co->i[i];
163: for (; k0<conz; k0++) {
164: ca[k0] = apa[apJ[k]];
165: apa[apJ[k++]] = 0.0;
166: }
167: }
168: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
169: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
170: return(0);
171: }
173: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,PetscReal fill,Mat C)
174: {
175: PetscErrorCode ierr;
176: MPI_Comm comm;
177: PetscMPIInt size;
178: Mat_APMPI *ptap;
179: PetscFreeSpaceList free_space=NULL,current_space=NULL;
180: Mat_MPIAIJ *a=(Mat_MPIAIJ*)A->data;
181: Mat_SeqAIJ *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
182: PetscInt *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
183: PetscInt *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
184: PetscInt *lnk,i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi;
185: PetscInt am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n;
186: PetscBT lnkbt;
187: PetscReal afill;
188: MatType mtype;
191: MatCheckProduct(C,4);
192: if (C->product->data) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
193: PetscObjectGetComm((PetscObject)A,&comm);
194: MPI_Comm_size(comm,&size);
196: /* create struct Mat_APMPI and attached it to C later */
197: PetscNew(&ptap);
199: /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
200: MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
202: /* get P_loc by taking all local rows of P */
203: MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);
205: p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
206: pi_loc = p_loc->i; pj_loc = p_loc->j;
207: if (size > 1) {
208: p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
209: pi_oth = p_oth->i; pj_oth = p_oth->j;
210: } else {
211: p_oth = NULL;
212: pi_oth = NULL; pj_oth = NULL;
213: }
215: /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
216: /*-------------------------------------------------------------------*/
217: PetscMalloc1(am+2,&api);
218: ptap->api = api;
219: api[0] = 0;
221: /* create and initialize a linked list */
222: PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);
224: /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
225: PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space);
226: current_space = free_space;
228: MatPreallocateInitialize(comm,am,pn,dnz,onz);
229: for (i=0; i<am; i++) {
230: /* diagonal portion of A */
231: nzi = adi[i+1] - adi[i];
232: for (j=0; j<nzi; j++) {
233: row = *adj++;
234: pnz = pi_loc[row+1] - pi_loc[row];
235: Jptr = pj_loc + pi_loc[row];
236: /* add non-zero cols of P into the sorted linked list lnk */
237: PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);
238: }
239: /* off-diagonal portion of A */
240: nzi = aoi[i+1] - aoi[i];
241: for (j=0; j<nzi; j++) {
242: row = *aoj++;
243: pnz = pi_oth[row+1] - pi_oth[row];
244: Jptr = pj_oth + pi_oth[row];
245: PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);
246: }
247: /* add possible missing diagonal entry */
248: if (C->force_diagonals) {
249: j = i + rstart; /* column index */
250: PetscLLCondensedAddSorted(1,&j,lnk,lnkbt);
251: }
253: apnz = lnk[0];
254: api[i+1] = api[i] + apnz;
256: /* if free space is not available, double the total space in the list */
257: if (current_space->local_remaining<apnz) {
258: PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),¤t_space);
259: nspacedouble++;
260: }
262: /* Copy data into free space, then initialize lnk */
263: PetscLLCondensedClean(pN,apnz,current_space->array,lnk,lnkbt);
264: MatPreallocateSet(i+rstart,apnz,current_space->array,dnz,onz);
266: current_space->array += apnz;
267: current_space->local_used += apnz;
268: current_space->local_remaining -= apnz;
269: }
271: /* Allocate space for apj, initialize apj, and */
272: /* destroy list of free space and other temporary array(s) */
273: PetscMalloc1(api[am]+1,&ptap->apj);
274: apj = ptap->apj;
275: PetscFreeSpaceContiguous(&free_space,ptap->apj);
276: PetscLLDestroy(lnk,lnkbt);
278: /* malloc apa to store dense row A[i,:]*P */
279: PetscCalloc1(pN,&ptap->apa);
281: /* set and assemble symbolic parallel matrix C */
282: /*---------------------------------------------*/
283: MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
284: MatSetBlockSizesFromMats(C,A,P);
286: MatGetType(A,&mtype);
287: MatSetType(C,mtype);
288: MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
289: MatPreallocateFinalize(dnz,onz);
291: MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);
292: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
293: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
294: MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
296: C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
297: C->ops->productnumeric = MatProductNumeric_AB;
299: /* attach the supporting struct to C for reuse */
300: C->product->data = ptap;
301: C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;
303: /* set MatInfo */
304: afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
305: if (afill < 1.0) afill = 1.0;
306: C->info.mallocs = nspacedouble;
307: C->info.fill_ratio_given = fill;
308: C->info.fill_ratio_needed = afill;
310: #if defined(PETSC_USE_INFO)
311: if (api[am]) {
312: PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
313: PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
314: } else {
315: PetscInfo(C,"Empty matrix product\n");
316: }
317: #endif
318: return(0);
319: }
321: /* ------------------------------------------------------- */
322: static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat,Mat,PetscReal,Mat);
323: static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat,Mat,Mat);
325: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AB(Mat C)
326: {
327: Mat_Product *product = C->product;
328: Mat A = product->A,B=product->B;
331: if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend)
332: SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%D, %D) != (%D,%D)",A->cmap->rstart,A->cmap->rend,B->rmap->rstart,B->rmap->rend);
334: C->ops->matmultsymbolic = MatMatMultSymbolic_MPIAIJ_MPIDense;
335: C->ops->productsymbolic = MatProductSymbolic_AB;
336: return(0);
337: }
338: /* -------------------------------------------------------------------- */
339: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(Mat C)
340: {
341: Mat_Product *product = C->product;
342: Mat A = product->A,B=product->B;
345: if (A->rmap->rstart != B->rmap->rstart || A->rmap->rend != B->rmap->rend)
346: SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%D, %D) != (%D,%D)",A->rmap->rstart,A->rmap->rend,B->rmap->rstart,B->rmap->rend);
348: C->ops->transposematmultsymbolic = MatTransposeMatMultSymbolic_MPIAIJ_MPIDense;
349: C->ops->productsymbolic = MatProductSymbolic_AtB;
350: return(0);
351: }
353: /* --------------------------------------------------------------------- */
354: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense(Mat C)
355: {
357: Mat_Product *product = C->product;
360: switch (product->type) {
361: case MATPRODUCT_AB:
362: MatProductSetFromOptions_MPIAIJ_MPIDense_AB(C);
363: break;
364: case MATPRODUCT_AtB:
365: MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(C);
366: break;
367: default:
368: break;
369: }
370: return(0);
371: }
372: /* ------------------------------------------------------- */
374: typedef struct {
375: Mat workB,workB1;
376: MPI_Request *rwaits,*swaits;
377: PetscInt nsends,nrecvs;
378: MPI_Datatype *stype,*rtype;
379: PetscInt blda;
380: } MPIAIJ_MPIDense;
382: PetscErrorCode MatMPIAIJ_MPIDenseDestroy(void *ctx)
383: {
384: MPIAIJ_MPIDense *contents = (MPIAIJ_MPIDense*)ctx;
385: PetscErrorCode ierr;
386: PetscInt i;
389: MatDestroy(&contents->workB);
390: MatDestroy(&contents->workB1);
391: for (i=0; i<contents->nsends; i++) {
392: MPI_Type_free(&contents->stype[i]);
393: }
394: for (i=0; i<contents->nrecvs; i++) {
395: MPI_Type_free(&contents->rtype[i]);
396: }
397: PetscFree4(contents->stype,contents->rtype,contents->rwaits,contents->swaits);
398: PetscFree(contents);
399: return(0);
400: }
402: static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat A,Mat B,PetscReal fill,Mat C)
403: {
404: PetscErrorCode ierr;
405: Mat_MPIAIJ *aij=(Mat_MPIAIJ*)A->data;
406: PetscInt nz=aij->B->cmap->n,nsends,nrecvs,i,nrows_to,j,blda,clda,m,M,n,N;
407: MPIAIJ_MPIDense *contents;
408: VecScatter ctx=aij->Mvctx;
409: PetscInt Am=A->rmap->n,Bm=B->rmap->n,BN=B->cmap->N,Bbn,Bbn1,bs,nrows_from,numBb;
410: MPI_Comm comm;
411: MPI_Datatype type1,*stype,*rtype;
412: const PetscInt *sindices,*sstarts,*rstarts;
413: PetscMPIInt *disp;
414: PetscBool cisdense;
417: MatCheckProduct(C,4);
418: if (C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data not empty");
419: PetscObjectGetComm((PetscObject)A,&comm);
420: PetscObjectBaseTypeCompare((PetscObject)C,MATMPIDENSE,&cisdense);
421: if (!cisdense) {
422: MatSetType(C,((PetscObject)B)->type_name);
423: }
424: MatGetLocalSize(C,&m,&n);
425: MatGetSize(C,&M,&N);
426: if (m == PETSC_DECIDE || n == PETSC_DECIDE || M == PETSC_DECIDE || N == PETSC_DECIDE) {
427: MatSetSizes(C,Am,B->cmap->n,A->rmap->N,BN);
428: }
429: MatSetBlockSizesFromMats(C,A,B);
430: MatSetUp(C);
431: MatDenseGetLDA(B,&blda);
432: MatDenseGetLDA(C,&clda);
433: PetscNew(&contents);
435: VecScatterGetRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,NULL,NULL);
436: VecScatterGetRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,NULL,NULL);
438: /* Create column block of B and C for memory scalability when BN is too large */
439: /* Estimate Bbn, column size of Bb */
440: if (nz) {
441: Bbn1 = 2*Am*BN/nz;
442: if (!Bbn1) Bbn1 = 1;
443: } else Bbn1 = BN;
445: bs = PetscAbs(B->cmap->bs);
446: Bbn1 = Bbn1/bs *bs; /* Bbn1 is a multiple of bs */
447: if (Bbn1 > BN) Bbn1 = BN;
448: MPI_Allreduce(&Bbn1,&Bbn,1,MPIU_INT,MPI_MAX,comm);
450: /* Enable runtime option for Bbn */
451: PetscOptionsBegin(comm,((PetscObject)C)->prefix,"MatMatMult","Mat");
452: PetscOptionsInt("-matmatmult_Bbn","Number of columns in Bb","MatMatMult",Bbn,&Bbn,NULL);
453: PetscOptionsEnd();
454: Bbn = PetscMin(Bbn,BN);
456: if (Bbn > 0 && Bbn < BN) {
457: numBb = BN/Bbn;
458: Bbn1 = BN - numBb*Bbn;
459: } else numBb = 0;
461: if (numBb) {
462: PetscInfo3(C,"use Bb, BN=%D, Bbn=%D; numBb=%D\n",BN,Bbn,numBb);
463: if (Bbn1) { /* Create workB1 for the remaining columns */
464: PetscInfo2(C,"use Bb1, BN=%D, Bbn1=%D\n",BN,Bbn1);
465: /* Create work matrix used to store off processor rows of B needed for local product */
466: MatCreateSeqDense(PETSC_COMM_SELF,nz,Bbn1,NULL,&contents->workB1);
467: } else contents->workB1 = NULL;
468: }
470: /* Create work matrix used to store off processor rows of B needed for local product */
471: MatCreateSeqDense(PETSC_COMM_SELF,nz,Bbn,NULL,&contents->workB);
473: /* Use MPI derived data type to reduce memory required by the send/recv buffers */
474: PetscMalloc4(nsends,&stype,nrecvs,&rtype,nrecvs,&contents->rwaits,nsends,&contents->swaits);
475: contents->stype = stype;
476: contents->nsends = nsends;
478: contents->rtype = rtype;
479: contents->nrecvs = nrecvs;
480: contents->blda = blda;
482: PetscMalloc1(Bm+1,&disp);
483: for (i=0; i<nsends; i++) {
484: nrows_to = sstarts[i+1]-sstarts[i];
485: for (j=0; j<nrows_to; j++){
486: disp[j] = sindices[sstarts[i]+j]; /* rowB to be sent */
487: }
488: MPI_Type_create_indexed_block(nrows_to,1,(const PetscMPIInt *)disp,MPIU_SCALAR,&type1);
490: MPI_Type_create_resized(type1,0,blda*sizeof(PetscScalar),&stype[i]);
491: MPI_Type_commit(&stype[i]);
492: MPI_Type_free(&type1);
493: }
495: for (i=0; i<nrecvs; i++) {
496: /* received values from a process form a (nrows_from x Bbn) row block in workB (column-wise) */
497: nrows_from = rstarts[i+1]-rstarts[i];
498: disp[0] = 0;
499: MPI_Type_create_indexed_block(1, nrows_from, (const PetscMPIInt *)disp, MPIU_SCALAR, &type1);
500: MPI_Type_create_resized(type1, 0, nz*sizeof(PetscScalar), &rtype[i]);
501: MPI_Type_commit(&rtype[i]);
502: MPI_Type_free(&type1);
503: }
505: PetscFree(disp);
506: VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,NULL,NULL);
507: VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,NULL,NULL);
508: MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);
509: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
510: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
511: MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
513: C->product->data = contents;
514: C->product->destroy = MatMPIAIJ_MPIDenseDestroy;
515: C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense;
516: return(0);
517: }
519: PETSC_INTERN PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat,Mat,Mat,const PetscBool);
520: /*
521: Performs an efficient scatter on the rows of B needed by this process; this is
522: a modification of the VecScatterBegin_() routines.
524: Input: Bbidx = 0: B = Bb
525: = 1: B = Bb1, see MatMatMultSymbolic_MPIAIJ_MPIDense()
526: */
527: PetscErrorCode MatMPIDenseScatter(Mat A,Mat B,PetscInt Bbidx,Mat C,Mat *outworkB)
528: {
529: Mat_MPIAIJ *aij = (Mat_MPIAIJ*)A->data;
530: PetscErrorCode ierr;
531: const PetscScalar *b;
532: PetscScalar *rvalues;
533: VecScatter ctx = aij->Mvctx;
534: const PetscInt *sindices,*sstarts,*rstarts;
535: const PetscMPIInt *sprocs,*rprocs;
536: PetscInt i,nsends,nrecvs;
537: MPI_Request *swaits,*rwaits;
538: MPI_Comm comm;
539: PetscMPIInt tag=((PetscObject)ctx)->tag,ncols=B->cmap->N,nrows=aij->B->cmap->n,nsends_mpi,nrecvs_mpi;
540: MPIAIJ_MPIDense *contents;
541: Mat workB;
542: MPI_Datatype *stype,*rtype;
543: PetscInt blda;
546: MatCheckProduct(C,4);
547: if (!C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
548: contents = (MPIAIJ_MPIDense*)C->product->data;
549: VecScatterGetRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL/*bs*/);
550: VecScatterGetRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL/*bs*/);
551: PetscMPIIntCast(nsends,&nsends_mpi);
552: PetscMPIIntCast(nrecvs,&nrecvs_mpi);
553: if (Bbidx == 0) {
554: workB = *outworkB = contents->workB;
555: } else {
556: workB = *outworkB = contents->workB1;
557: }
558: if (nrows != workB->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Number of rows of workB %D not equal to columns of aij->B %D",workB->cmap->n,nrows);
559: swaits = contents->swaits;
560: rwaits = contents->rwaits;
562: MatDenseGetArrayRead(B,&b);
563: MatDenseGetLDA(B,&blda);
564: if (blda != contents->blda) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Cannot reuse an input matrix with lda %D != %D",blda,contents->blda);
565: MatDenseGetArray(workB,&rvalues);
567: /* Post recv, use MPI derived data type to save memory */
568: PetscObjectGetComm((PetscObject)C,&comm);
569: rtype = contents->rtype;
570: for (i=0; i<nrecvs; i++) {
571: MPI_Irecv(rvalues+(rstarts[i]-rstarts[0]),ncols,rtype[i],rprocs[i],tag,comm,rwaits+i);
572: }
574: stype = contents->stype;
575: for (i=0; i<nsends; i++) {
576: MPI_Isend(b,ncols,stype[i],sprocs[i],tag,comm,swaits+i);
577: }
579: if (nrecvs) {MPI_Waitall(nrecvs_mpi,rwaits,MPI_STATUSES_IGNORE);}
580: if (nsends) {MPI_Waitall(nsends_mpi,swaits,MPI_STATUSES_IGNORE);}
582: VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL);
583: VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL);
584: MatDenseRestoreArrayRead(B,&b);
585: MatDenseRestoreArray(workB,&rvalues);
586: return(0);
587: }
589: static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A,Mat B,Mat C)
590: {
591: PetscErrorCode ierr;
592: Mat_MPIAIJ *aij = (Mat_MPIAIJ*)A->data;
593: Mat_MPIDense *bdense = (Mat_MPIDense*)B->data;
594: Mat_MPIDense *cdense = (Mat_MPIDense*)C->data;
595: Mat workB;
596: MPIAIJ_MPIDense *contents;
599: MatCheckProduct(C,3);
600: if (!C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
601: contents = (MPIAIJ_MPIDense*)C->product->data;
602: /* diagonal block of A times all local rows of B */
603: /* TODO: this calls a symbolic multiplication every time, which could be avoided */
604: MatMatMult(aij->A,bdense->A,MAT_REUSE_MATRIX,PETSC_DEFAULT,&cdense->A);
605: if (contents->workB->cmap->n == B->cmap->N) {
606: /* get off processor parts of B needed to complete C=A*B */
607: MatMPIDenseScatter(A,B,0,C,&workB);
609: /* off-diagonal block of A times nonlocal rows of B */
610: MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A,PETSC_TRUE);
611: } else {
612: Mat Bb,Cb;
613: PetscInt BN=B->cmap->N,n=contents->workB->cmap->n,i;
614: if (n <= 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Column block size %D must be positive",n);
616: for (i=0; i<BN; i+=n) {
617: MatDenseGetSubMatrix(B,i,PetscMin(i+n,BN),&Bb);
618: MatDenseGetSubMatrix(C,i,PetscMin(i+n,BN),&Cb);
620: /* get off processor parts of B needed to complete C=A*B */
621: MatMPIDenseScatter(A,Bb,i+n>BN,C,&workB);
623: /* off-diagonal block of A times nonlocal rows of B */
624: cdense = (Mat_MPIDense*)Cb->data;
625: MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A,PETSC_TRUE);
627: MatDenseRestoreSubMatrix(B,&Bb);
628: MatDenseRestoreSubMatrix(C,&Cb);
629: }
630: }
631: return(0);
632: }
634: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
635: {
636: PetscErrorCode ierr;
637: Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
638: Mat_SeqAIJ *ad = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
639: Mat_SeqAIJ *cd = (Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
640: PetscInt *adi = ad->i,*adj,*aoi=ao->i,*aoj;
641: PetscScalar *ada,*aoa,*cda=cd->a,*coa=co->a;
642: Mat_SeqAIJ *p_loc,*p_oth;
643: PetscInt *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pj;
644: PetscScalar *pa_loc,*pa_oth,*pa,valtmp,*ca;
645: PetscInt cm = C->rmap->n,anz,pnz;
646: Mat_APMPI *ptap;
647: PetscScalar *apa_sparse;
648: const PetscScalar *dummy;
649: PetscInt *api,*apj,*apJ,i,j,k,row;
650: PetscInt cstart = C->cmap->rstart;
651: PetscInt cdnz,conz,k0,k1,nextp;
652: MPI_Comm comm;
653: PetscMPIInt size;
656: MatCheckProduct(C,3);
657: ptap = (Mat_APMPI*)C->product->data;
658: if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
659: PetscObjectGetComm((PetscObject)C,&comm);
660: MPI_Comm_size(comm,&size);
661: if (!ptap->P_oth && size>1) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"AP cannot be reused. Do not call MatProductClear()");
663: apa_sparse = ptap->apa;
665: /* 1) get P_oth = ptap->P_oth and P_loc = ptap->P_loc */
666: /*-----------------------------------------------------*/
667: /* update numerical values of P_oth and P_loc */
668: MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
669: MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);
671: /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
672: /*----------------------------------------------------------*/
673: /* get data from symbolic products */
674: p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
675: pi_loc = p_loc->i; pj_loc = p_loc->j; pa_loc = p_loc->a;
676: if (size >1) {
677: p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
678: pi_oth = p_oth->i; pj_oth = p_oth->j; pa_oth = p_oth->a;
679: } else {
680: p_oth = NULL; pi_oth = NULL; pj_oth = NULL; pa_oth = NULL;
681: }
683: /* trigger copy to CPU */
684: MatSeqAIJGetArrayRead(a->A,&dummy);
685: MatSeqAIJRestoreArrayRead(a->A,&dummy);
686: MatSeqAIJGetArrayRead(a->B,&dummy);
687: MatSeqAIJRestoreArrayRead(a->B,&dummy);
688: api = ptap->api;
689: apj = ptap->apj;
690: for (i=0; i<cm; i++) {
691: apJ = apj + api[i];
693: /* diagonal portion of A */
694: anz = adi[i+1] - adi[i];
695: adj = ad->j + adi[i];
696: ada = ad->a + adi[i];
697: for (j=0; j<anz; j++) {
698: row = adj[j];
699: pnz = pi_loc[row+1] - pi_loc[row];
700: pj = pj_loc + pi_loc[row];
701: pa = pa_loc + pi_loc[row];
702: /* perform sparse axpy */
703: valtmp = ada[j];
704: nextp = 0;
705: for (k=0; nextp<pnz; k++) {
706: if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
707: apa_sparse[k] += valtmp*pa[nextp++];
708: }
709: }
710: PetscLogFlops(2.0*pnz);
711: }
713: /* off-diagonal portion of A */
714: anz = aoi[i+1] - aoi[i];
715: aoj = ao->j + aoi[i];
716: aoa = ao->a + aoi[i];
717: for (j=0; j<anz; j++) {
718: row = aoj[j];
719: pnz = pi_oth[row+1] - pi_oth[row];
720: pj = pj_oth + pi_oth[row];
721: pa = pa_oth + pi_oth[row];
722: /* perform sparse axpy */
723: valtmp = aoa[j];
724: nextp = 0;
725: for (k=0; nextp<pnz; k++) {
726: if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
727: apa_sparse[k] += valtmp*pa[nextp++];
728: }
729: }
730: PetscLogFlops(2.0*pnz);
731: }
733: /* set values in C */
734: cdnz = cd->i[i+1] - cd->i[i];
735: conz = co->i[i+1] - co->i[i];
737: /* 1st off-diagonal part of C */
738: ca = coa + co->i[i];
739: k = 0;
740: for (k0=0; k0<conz; k0++) {
741: if (apJ[k] >= cstart) break;
742: ca[k0] = apa_sparse[k];
743: apa_sparse[k] = 0.0;
744: k++;
745: }
747: /* diagonal part of C */
748: ca = cda + cd->i[i];
749: for (k1=0; k1<cdnz; k1++) {
750: ca[k1] = apa_sparse[k];
751: apa_sparse[k] = 0.0;
752: k++;
753: }
755: /* 2nd off-diagonal part of C */
756: ca = coa + co->i[i];
757: for (; k0<conz; k0++) {
758: ca[k0] = apa_sparse[k];
759: apa_sparse[k] = 0.0;
760: k++;
761: }
762: }
763: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
764: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
765: return(0);
766: }
768: /* same as MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(), except using LLCondensed to avoid O(BN) memory requirement */
769: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat C)
770: {
771: PetscErrorCode ierr;
772: MPI_Comm comm;
773: PetscMPIInt size;
774: Mat_APMPI *ptap;
775: PetscFreeSpaceList free_space = NULL,current_space=NULL;
776: Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
777: Mat_SeqAIJ *ad = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
778: PetscInt *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
779: PetscInt *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
780: PetscInt i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi,*lnk,apnz_max=1;
781: PetscInt am=A->rmap->n,pn=P->cmap->n,pm=P->rmap->n,lsize=pn+20;
782: PetscReal afill;
783: MatType mtype;
786: MatCheckProduct(C,4);
787: if (C->product->data) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
788: PetscObjectGetComm((PetscObject)A,&comm);
789: MPI_Comm_size(comm,&size);
791: /* create struct Mat_APMPI and attached it to C later */
792: PetscNew(&ptap);
794: /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
795: MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
797: /* get P_loc by taking all local rows of P */
798: MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);
800: p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
801: pi_loc = p_loc->i; pj_loc = p_loc->j;
802: if (size > 1) {
803: p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
804: pi_oth = p_oth->i; pj_oth = p_oth->j;
805: } else {
806: p_oth = NULL;
807: pi_oth = NULL; pj_oth = NULL;
808: }
810: /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
811: /*-------------------------------------------------------------------*/
812: PetscMalloc1(am+2,&api);
813: ptap->api = api;
814: api[0] = 0;
816: PetscLLCondensedCreate_Scalable(lsize,&lnk);
818: /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
819: PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space);
820: current_space = free_space;
821: MatPreallocateInitialize(comm,am,pn,dnz,onz);
822: for (i=0; i<am; i++) {
823: /* diagonal portion of A */
824: nzi = adi[i+1] - adi[i];
825: for (j=0; j<nzi; j++) {
826: row = *adj++;
827: pnz = pi_loc[row+1] - pi_loc[row];
828: Jptr = pj_loc + pi_loc[row];
829: /* Expand list if it is not long enough */
830: if (pnz+apnz_max > lsize) {
831: lsize = pnz+apnz_max;
832: PetscLLCondensedExpand_Scalable(lsize, &lnk);
833: }
834: /* add non-zero cols of P into the sorted linked list lnk */
835: PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);
836: apnz = *lnk; /* The first element in the list is the number of items in the list */
837: api[i+1] = api[i] + apnz;
838: if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
839: }
840: /* off-diagonal portion of A */
841: nzi = aoi[i+1] - aoi[i];
842: for (j=0; j<nzi; j++) {
843: row = *aoj++;
844: pnz = pi_oth[row+1] - pi_oth[row];
845: Jptr = pj_oth + pi_oth[row];
846: /* Expand list if it is not long enough */
847: if (pnz+apnz_max > lsize) {
848: lsize = pnz + apnz_max;
849: PetscLLCondensedExpand_Scalable(lsize, &lnk);
850: }
851: /* add non-zero cols of P into the sorted linked list lnk */
852: PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);
853: apnz = *lnk; /* The first element in the list is the number of items in the list */
854: api[i+1] = api[i] + apnz;
855: if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
856: }
858: /* add missing diagonal entry */
859: if (C->force_diagonals) {
860: j = i + rstart; /* column index */
861: PetscLLCondensedAddSorted_Scalable(1,&j,lnk);
862: }
864: apnz = *lnk;
865: api[i+1] = api[i] + apnz;
866: if (apnz > apnz_max) apnz_max = apnz;
868: /* if free space is not available, double the total space in the list */
869: if (current_space->local_remaining<apnz) {
870: PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),¤t_space);
871: nspacedouble++;
872: }
874: /* Copy data into free space, then initialize lnk */
875: PetscLLCondensedClean_Scalable(apnz,current_space->array,lnk);
876: MatPreallocateSet(i+rstart,apnz,current_space->array,dnz,onz);
878: current_space->array += apnz;
879: current_space->local_used += apnz;
880: current_space->local_remaining -= apnz;
881: }
883: /* Allocate space for apj, initialize apj, and */
884: /* destroy list of free space and other temporary array(s) */
885: PetscMalloc1(api[am]+1,&ptap->apj);
886: apj = ptap->apj;
887: PetscFreeSpaceContiguous(&free_space,ptap->apj);
888: PetscLLCondensedDestroy_Scalable(lnk);
890: /* create and assemble symbolic parallel matrix C */
891: /*----------------------------------------------------*/
892: MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
893: MatSetBlockSizesFromMats(C,A,P);
894: MatGetType(A,&mtype);
895: MatSetType(C,mtype);
896: MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
897: MatPreallocateFinalize(dnz,onz);
899: /* malloc apa for assembly C */
900: PetscCalloc1(apnz_max,&ptap->apa);
902: MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);
903: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
904: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
905: MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
907: C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
908: C->ops->productnumeric = MatProductNumeric_AB;
910: /* attach the supporting struct to C for reuse */
911: C->product->data = ptap;
912: C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;
914: /* set MatInfo */
915: afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
916: if (afill < 1.0) afill = 1.0;
917: C->info.mallocs = nspacedouble;
918: C->info.fill_ratio_given = fill;
919: C->info.fill_ratio_needed = afill;
921: #if defined(PETSC_USE_INFO)
922: if (api[am]) {
923: PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
924: PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
925: } else {
926: PetscInfo(C,"Empty matrix product\n");
927: }
928: #endif
929: return(0);
930: }
932: /* This function is needed for the seqMPI matrix-matrix multiplication. */
933: /* Three input arrays are merged to one output array. The size of the */
934: /* output array is also output. Duplicate entries only show up once. */
935: static void Merge3SortedArrays(PetscInt size1, PetscInt *in1,
936: PetscInt size2, PetscInt *in2,
937: PetscInt size3, PetscInt *in3,
938: PetscInt *size4, PetscInt *out)
939: {
940: int i = 0, j = 0, k = 0, l = 0;
942: /* Traverse all three arrays */
943: while (i<size1 && j<size2 && k<size3) {
944: if (in1[i] < in2[j] && in1[i] < in3[k]) {
945: out[l++] = in1[i++];
946: }
947: else if (in2[j] < in1[i] && in2[j] < in3[k]) {
948: out[l++] = in2[j++];
949: }
950: else if (in3[k] < in1[i] && in3[k] < in2[j]) {
951: out[l++] = in3[k++];
952: }
953: else if (in1[i] == in2[j] && in1[i] < in3[k]) {
954: out[l++] = in1[i];
955: i++, j++;
956: }
957: else if (in1[i] == in3[k] && in1[i] < in2[j]) {
958: out[l++] = in1[i];
959: i++, k++;
960: }
961: else if (in3[k] == in2[j] && in2[j] < in1[i]) {
962: out[l++] = in2[j];
963: k++, j++;
964: }
965: else if (in1[i] == in2[j] && in1[i] == in3[k]) {
966: out[l++] = in1[i];
967: i++, j++, k++;
968: }
969: }
971: /* Traverse two remaining arrays */
972: while (i<size1 && j<size2) {
973: if (in1[i] < in2[j]) {
974: out[l++] = in1[i++];
975: }
976: else if (in1[i] > in2[j]) {
977: out[l++] = in2[j++];
978: }
979: else {
980: out[l++] = in1[i];
981: i++, j++;
982: }
983: }
985: while (i<size1 && k<size3) {
986: if (in1[i] < in3[k]) {
987: out[l++] = in1[i++];
988: }
989: else if (in1[i] > in3[k]) {
990: out[l++] = in3[k++];
991: }
992: else {
993: out[l++] = in1[i];
994: i++, k++;
995: }
996: }
998: while (k<size3 && j<size2) {
999: if (in3[k] < in2[j]) {
1000: out[l++] = in3[k++];
1001: }
1002: else if (in3[k] > in2[j]) {
1003: out[l++] = in2[j++];
1004: }
1005: else {
1006: out[l++] = in3[k];
1007: k++, j++;
1008: }
1009: }
1011: /* Traverse one remaining array */
1012: while (i<size1) out[l++] = in1[i++];
1013: while (j<size2) out[l++] = in2[j++];
1014: while (k<size3) out[l++] = in3[k++];
1016: *size4 = l;
1017: }
1019: /* This matrix-matrix multiplication algorithm divides the multiplication into three multiplications and */
1020: /* adds up the products. Two of these three multiplications are performed with existing (sequential) */
1021: /* matrix-matrix multiplications. */
1022: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(Mat A, Mat P, PetscReal fill, Mat C)
1023: {
1024: PetscErrorCode ierr;
1025: MPI_Comm comm;
1026: PetscMPIInt size;
1027: Mat_APMPI *ptap;
1028: PetscFreeSpaceList free_space_diag=NULL, current_space=NULL;
1029: Mat_MPIAIJ *a =(Mat_MPIAIJ*)A->data;
1030: Mat_SeqAIJ *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc;
1031: Mat_MPIAIJ *p =(Mat_MPIAIJ*)P->data;
1032: Mat_SeqAIJ *adpd_seq, *p_off, *aopoth_seq;
1033: PetscInt adponz, adpdnz;
1034: PetscInt *pi_loc,*dnz,*onz;
1035: PetscInt *adi=ad->i,*adj=ad->j,*aoi=ao->i,rstart=A->rmap->rstart;
1036: PetscInt *lnk,i, i1=0,pnz,row,*adpoi,*adpoj, *api, *adpoJ, *aopJ, *apJ,*Jptr, aopnz, nspacedouble=0,j,nzi,
1037: *apj,apnz, *adpdi, *adpdj, *adpdJ, *poff_i, *poff_j, *j_temp, *aopothi, *aopothj;
1038: PetscInt am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n, p_colstart, p_colend;
1039: PetscBT lnkbt;
1040: PetscReal afill;
1041: PetscMPIInt rank;
1042: Mat adpd, aopoth;
1043: MatType mtype;
1044: const char *prefix;
1047: MatCheckProduct(C,4);
1048: if (C->product->data) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
1049: PetscObjectGetComm((PetscObject)A,&comm);
1050: MPI_Comm_size(comm,&size);
1051: MPI_Comm_rank(comm, &rank);
1052: MatGetOwnershipRangeColumn(P, &p_colstart, &p_colend);
1054: /* create struct Mat_APMPI and attached it to C later */
1055: PetscNew(&ptap);
1057: /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
1058: MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
1060: /* get P_loc by taking all local rows of P */
1061: MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);
1064: p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
1065: pi_loc = p_loc->i;
1067: /* Allocate memory for the i arrays of the matrices A*P, A_diag*P_off and A_offd * P */
1068: PetscMalloc1(am+2,&api);
1069: PetscMalloc1(am+2,&adpoi);
1071: adpoi[0] = 0;
1072: ptap->api = api;
1073: api[0] = 0;
1075: /* create and initialize a linked list, will be used for both A_diag * P_loc_off and A_offd * P_oth */
1076: PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);
1077: MatPreallocateInitialize(comm,am,pn,dnz,onz);
1079: /* Symbolic calc of A_loc_diag * P_loc_diag */
1080: MatGetOptionsPrefix(A,&prefix);
1081: MatProductCreate(a->A,p->A,NULL,&adpd);
1082: MatGetOptionsPrefix(A,&prefix);
1083: MatSetOptionsPrefix(adpd,prefix);
1084: MatAppendOptionsPrefix(adpd,"inner_diag_");
1086: MatProductSetType(adpd,MATPRODUCT_AB);
1087: MatProductSetAlgorithm(adpd,"sorted");
1088: MatProductSetFill(adpd,fill);
1089: MatProductSetFromOptions(adpd);
1091: adpd->force_diagonals = C->force_diagonals;
1092: MatProductSymbolic(adpd);
1094: adpd_seq = (Mat_SeqAIJ*)((adpd)->data);
1095: adpdi = adpd_seq->i; adpdj = adpd_seq->j;
1096: p_off = (Mat_SeqAIJ*)((p->B)->data);
1097: poff_i = p_off->i; poff_j = p_off->j;
1099: /* j_temp stores indices of a result row before they are added to the linked list */
1100: PetscMalloc1(pN+2,&j_temp);
1103: /* Symbolic calc of the A_diag * p_loc_off */
1104: /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
1105: PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space_diag);
1106: current_space = free_space_diag;
1108: for (i=0; i<am; i++) {
1109: /* A_diag * P_loc_off */
1110: nzi = adi[i+1] - adi[i];
1111: for (j=0; j<nzi; j++) {
1112: row = *adj++;
1113: pnz = poff_i[row+1] - poff_i[row];
1114: Jptr = poff_j + poff_i[row];
1115: for (i1 = 0; i1 < pnz; i1++) {
1116: j_temp[i1] = p->garray[Jptr[i1]];
1117: }
1118: /* add non-zero cols of P into the sorted linked list lnk */
1119: PetscLLCondensedAddSorted(pnz,j_temp,lnk,lnkbt);
1120: }
1122: adponz = lnk[0];
1123: adpoi[i+1] = adpoi[i] + adponz;
1125: /* if free space is not available, double the total space in the list */
1126: if (current_space->local_remaining<adponz) {
1127: PetscFreeSpaceGet(PetscIntSumTruncate(adponz,current_space->total_array_size),¤t_space);
1128: nspacedouble++;
1129: }
1131: /* Copy data into free space, then initialize lnk */
1132: PetscLLCondensedClean(pN,adponz,current_space->array,lnk,lnkbt);
1134: current_space->array += adponz;
1135: current_space->local_used += adponz;
1136: current_space->local_remaining -= adponz;
1137: }
1139: /* Symbolic calc of A_off * P_oth */
1140: MatSetOptionsPrefix(a->B,prefix);
1141: MatAppendOptionsPrefix(a->B,"inner_offdiag_");
1142: MatCreate(PETSC_COMM_SELF,&aopoth);
1143: MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, aopoth);
1144: aopoth_seq = (Mat_SeqAIJ*)((aopoth)->data);
1145: aopothi = aopoth_seq->i; aopothj = aopoth_seq->j;
1147: /* Allocate space for apj, adpj, aopj, ... */
1148: /* destroy lists of free space and other temporary array(s) */
1150: PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am]+2, &ptap->apj);
1151: PetscMalloc1(adpoi[am]+2, &adpoj);
1153: /* Copy from linked list to j-array */
1154: PetscFreeSpaceContiguous(&free_space_diag,adpoj);
1155: PetscLLDestroy(lnk,lnkbt);
1157: adpoJ = adpoj;
1158: adpdJ = adpdj;
1159: aopJ = aopothj;
1160: apj = ptap->apj;
1161: apJ = apj; /* still empty */
1163: /* Merge j-arrays of A_off * P, A_diag * P_loc_off, and */
1164: /* A_diag * P_loc_diag to get A*P */
1165: for (i = 0; i < am; i++) {
1166: aopnz = aopothi[i+1] - aopothi[i];
1167: adponz = adpoi[i+1] - adpoi[i];
1168: adpdnz = adpdi[i+1] - adpdi[i];
1170: /* Correct indices from A_diag*P_diag */
1171: for (i1 = 0; i1 < adpdnz; i1++) {
1172: adpdJ[i1] += p_colstart;
1173: }
1174: /* Merge j-arrays of A_diag * P_loc_off and A_diag * P_loc_diag and A_off * P_oth */
1175: Merge3SortedArrays(adponz, adpoJ, adpdnz, adpdJ, aopnz, aopJ, &apnz, apJ);
1176: MatPreallocateSet(i+rstart, apnz, apJ, dnz, onz);
1178: aopJ += aopnz;
1179: adpoJ += adponz;
1180: adpdJ += adpdnz;
1181: apJ += apnz;
1182: api[i+1] = api[i] + apnz;
1183: }
1185: /* malloc apa to store dense row A[i,:]*P */
1186: PetscCalloc1(pN+2,&ptap->apa);
1188: /* create and assemble symbolic parallel matrix C */
1189: MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
1190: MatSetBlockSizesFromMats(C,A,P);
1191: MatGetType(A,&mtype);
1192: MatSetType(C,mtype);
1193: MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
1194: MatPreallocateFinalize(dnz,onz);
1196: MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);
1197: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1198: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
1199: MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
1201: C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1202: C->ops->productnumeric = MatProductNumeric_AB;
1204: /* attach the supporting struct to C for reuse */
1205: C->product->data = ptap;
1206: C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;
1208: /* set MatInfo */
1209: afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
1210: if (afill < 1.0) afill = 1.0;
1211: C->info.mallocs = nspacedouble;
1212: C->info.fill_ratio_given = fill;
1213: C->info.fill_ratio_needed = afill;
1215: #if defined(PETSC_USE_INFO)
1216: if (api[am]) {
1217: PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
1218: PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
1219: } else {
1220: PetscInfo(C,"Empty matrix product\n");
1221: }
1222: #endif
1224: MatDestroy(&aopoth);
1225: MatDestroy(&adpd);
1226: PetscFree(j_temp);
1227: PetscFree(adpoj);
1228: PetscFree(adpoi);
1229: return(0);
1230: }
1232: /*-------------------------------------------------------------------------*/
1233: /* This routine only works when scall=MAT_REUSE_MATRIX! */
1234: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P,Mat A,Mat C)
1235: {
1237: Mat_APMPI *ptap;
1238: Mat Pt;
1241: MatCheckProduct(C,3);
1242: ptap = (Mat_APMPI*)C->product->data;
1243: if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1244: if (!ptap->Pt) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
1246: Pt = ptap->Pt;
1247: MatTranspose(P,MAT_REUSE_MATRIX,&Pt);
1248: MatMatMultNumeric_MPIAIJ_MPIAIJ(Pt,A,C);
1249: return(0);
1250: }
1252: /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
1253: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,PetscReal fill,Mat C)
1254: {
1255: PetscErrorCode ierr;
1256: Mat_APMPI *ptap;
1257: Mat_MPIAIJ *p=(Mat_MPIAIJ*)P->data;
1258: MPI_Comm comm;
1259: PetscMPIInt size,rank;
1260: PetscFreeSpaceList free_space=NULL,current_space=NULL;
1261: PetscInt pn=P->cmap->n,aN=A->cmap->N,an=A->cmap->n;
1262: PetscInt *lnk,i,k,nsend,rstart;
1263: PetscBT lnkbt;
1264: PetscMPIInt tagi,tagj,*len_si,*len_s,*len_ri,nrecv;
1265: PETSC_UNUSED PetscMPIInt icompleted=0;
1266: PetscInt **buf_rj,**buf_ri,**buf_ri_k,row,ncols,*cols;
1267: PetscInt len,proc,*dnz,*onz,*owners,nzi;
1268: PetscInt nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1269: MPI_Request *swaits,*rwaits;
1270: MPI_Status *sstatus,rstatus;
1271: PetscLayout rowmap;
1272: PetscInt *owners_co,*coi,*coj; /* i and j array of (p->B)^T*A*P - used in the communication */
1273: PetscMPIInt *len_r,*id_r; /* array of length of comm->size, store send/recv matrix values */
1274: PetscInt *Jptr,*prmap=p->garray,con,j,Crmax;
1275: Mat_SeqAIJ *a_loc,*c_loc,*c_oth;
1276: PetscTable ta;
1277: MatType mtype;
1278: const char *prefix;
1281: PetscObjectGetComm((PetscObject)A,&comm);
1282: MPI_Comm_size(comm,&size);
1283: MPI_Comm_rank(comm,&rank);
1285: /* create symbolic parallel matrix C */
1286: MatGetType(A,&mtype);
1287: MatSetType(C,mtype);
1289: C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1291: /* create struct Mat_APMPI and attached it to C later */
1292: PetscNew(&ptap);
1293: ptap->reuse = MAT_INITIAL_MATRIX;
1295: /* (0) compute Rd = Pd^T, Ro = Po^T */
1296: /* --------------------------------- */
1297: MatTranspose_SeqAIJ(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);
1298: MatTranspose_SeqAIJ(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);
1300: /* (1) compute symbolic A_loc */
1301: /* ---------------------------*/
1302: MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&ptap->A_loc);
1304: /* (2-1) compute symbolic C_oth = Ro*A_loc */
1305: /* ------------------------------------ */
1306: MatGetOptionsPrefix(A,&prefix);
1307: MatSetOptionsPrefix(ptap->Ro,prefix);
1308: MatAppendOptionsPrefix(ptap->Ro,"inner_offdiag_");
1309: MatCreate(PETSC_COMM_SELF,&ptap->C_oth);
1310: MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->A_loc,fill,ptap->C_oth);
1312: /* (3) send coj of C_oth to other processors */
1313: /* ------------------------------------------ */
1314: /* determine row ownership */
1315: PetscLayoutCreate(comm,&rowmap);
1316: rowmap->n = pn;
1317: rowmap->bs = 1;
1318: PetscLayoutSetUp(rowmap);
1319: owners = rowmap->range;
1321: /* determine the number of messages to send, their lengths */
1322: PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);
1323: PetscArrayzero(len_s,size);
1324: PetscArrayzero(len_si,size);
1326: c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
1327: coi = c_oth->i; coj = c_oth->j;
1328: con = ptap->C_oth->rmap->n;
1329: proc = 0;
1330: for (i=0; i<con; i++) {
1331: while (prmap[i] >= owners[proc+1]) proc++;
1332: len_si[proc]++; /* num of rows in Co(=Pt*A) to be sent to [proc] */
1333: len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
1334: }
1336: len = 0; /* max length of buf_si[], see (4) */
1337: owners_co[0] = 0;
1338: nsend = 0;
1339: for (proc=0; proc<size; proc++) {
1340: owners_co[proc+1] = owners_co[proc] + len_si[proc];
1341: if (len_s[proc]) {
1342: nsend++;
1343: len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
1344: len += len_si[proc];
1345: }
1346: }
1348: /* determine the number and length of messages to receive for coi and coj */
1349: PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);
1350: PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);
1352: /* post the Irecv and Isend of coj */
1353: PetscCommGetNewTag(comm,&tagj);
1354: PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);
1355: PetscMalloc1(nsend+1,&swaits);
1356: for (proc=0, k=0; proc<size; proc++) {
1357: if (!len_s[proc]) continue;
1358: i = owners_co[proc];
1359: MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);
1360: k++;
1361: }
1363: /* (2-2) compute symbolic C_loc = Rd*A_loc */
1364: /* ---------------------------------------- */
1365: MatSetOptionsPrefix(ptap->Rd,prefix);
1366: MatAppendOptionsPrefix(ptap->Rd,"inner_diag_");
1367: MatCreate(PETSC_COMM_SELF,&ptap->C_loc);
1368: MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->A_loc,fill,ptap->C_loc);
1369: c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;
1371: /* receives coj are complete */
1372: for (i=0; i<nrecv; i++) {
1373: MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);
1374: }
1375: PetscFree(rwaits);
1376: if (nsend) {MPI_Waitall(nsend,swaits,sstatus);}
1378: /* add received column indices into ta to update Crmax */
1379: a_loc = (Mat_SeqAIJ*)(ptap->A_loc)->data;
1381: /* create and initialize a linked list */
1382: PetscTableCreate(an,aN,&ta); /* for compute Crmax */
1383: MatRowMergeMax_SeqAIJ(a_loc,ptap->A_loc->rmap->N,ta);
1385: for (k=0; k<nrecv; k++) {/* k-th received message */
1386: Jptr = buf_rj[k];
1387: for (j=0; j<len_r[k]; j++) {
1388: PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);
1389: }
1390: }
1391: PetscTableGetCount(ta,&Crmax);
1392: PetscTableDestroy(&ta);
1394: /* (4) send and recv coi */
1395: /*-----------------------*/
1396: PetscCommGetNewTag(comm,&tagi);
1397: PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);
1398: PetscMalloc1(len+1,&buf_s);
1399: buf_si = buf_s; /* points to the beginning of k-th msg to be sent */
1400: for (proc=0,k=0; proc<size; proc++) {
1401: if (!len_s[proc]) continue;
1402: /* form outgoing message for i-structure:
1403: buf_si[0]: nrows to be sent
1404: [1:nrows]: row index (global)
1405: [nrows+1:2*nrows+1]: i-structure index
1406: */
1407: /*-------------------------------------------*/
1408: nrows = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
1409: buf_si_i = buf_si + nrows+1;
1410: buf_si[0] = nrows;
1411: buf_si_i[0] = 0;
1412: nrows = 0;
1413: for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
1414: nzi = coi[i+1] - coi[i];
1415: buf_si_i[nrows+1] = buf_si_i[nrows] + nzi; /* i-structure */
1416: buf_si[nrows+1] = prmap[i] -owners[proc]; /* local row index */
1417: nrows++;
1418: }
1419: MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);
1420: k++;
1421: buf_si += len_si[proc];
1422: }
1423: for (i=0; i<nrecv; i++) {
1424: MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);
1425: }
1426: PetscFree(rwaits);
1427: if (nsend) {MPI_Waitall(nsend,swaits,sstatus);}
1429: PetscFree4(len_s,len_si,sstatus,owners_co);
1430: PetscFree(len_ri);
1431: PetscFree(swaits);
1432: PetscFree(buf_s);
1434: /* (5) compute the local portion of C */
1435: /* ------------------------------------------ */
1436: /* set initial free space to be Crmax, sufficient for holding nozeros in each row of C */
1437: PetscFreeSpaceGet(Crmax,&free_space);
1438: current_space = free_space;
1440: PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);
1441: for (k=0; k<nrecv; k++) {
1442: buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1443: nrows = *buf_ri_k[k];
1444: nextrow[k] = buf_ri_k[k] + 1; /* next row number of k-th recved i-structure */
1445: nextci[k] = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure */
1446: }
1448: MatPreallocateInitialize(comm,pn,an,dnz,onz);
1449: PetscLLCondensedCreate(Crmax,aN,&lnk,&lnkbt);
1450: for (i=0; i<pn; i++) { /* for each local row of C */
1451: /* add C_loc into C */
1452: nzi = c_loc->i[i+1] - c_loc->i[i];
1453: Jptr = c_loc->j + c_loc->i[i];
1454: PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);
1456: /* add received col data into lnk */
1457: for (k=0; k<nrecv; k++) { /* k-th received message */
1458: if (i == *nextrow[k]) { /* i-th row */
1459: nzi = *(nextci[k]+1) - *nextci[k];
1460: Jptr = buf_rj[k] + *nextci[k];
1461: PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);
1462: nextrow[k]++; nextci[k]++;
1463: }
1464: }
1466: /* add missing diagonal entry */
1467: if (C->force_diagonals) {
1468: k = i + owners[rank]; /* column index */
1469: PetscLLCondensedAddSorted(1,&k,lnk,lnkbt);
1470: }
1472: nzi = lnk[0];
1474: /* copy data into free space, then initialize lnk */
1475: PetscLLCondensedClean(aN,nzi,current_space->array,lnk,lnkbt);
1476: MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);
1477: }
1478: PetscFree3(buf_ri_k,nextrow,nextci);
1479: PetscLLDestroy(lnk,lnkbt);
1480: PetscFreeSpaceDestroy(free_space);
1482: /* local sizes and preallocation */
1483: MatSetSizes(C,pn,an,PETSC_DETERMINE,PETSC_DETERMINE);
1484: if (P->cmap->bs > 0) {PetscLayoutSetBlockSize(C->rmap,P->cmap->bs);}
1485: if (A->cmap->bs > 0) {PetscLayoutSetBlockSize(C->cmap,A->cmap->bs);}
1486: MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
1487: MatPreallocateFinalize(dnz,onz);
1489: /* add C_loc and C_oth to C */
1490: MatGetOwnershipRange(C,&rstart,NULL);
1491: for (i=0; i<pn; i++) {
1492: ncols = c_loc->i[i+1] - c_loc->i[i];
1493: cols = c_loc->j + c_loc->i[i];
1494: row = rstart + i;
1495: MatSetValues(C,1,(const PetscInt*)&row,ncols,(const PetscInt*)cols,NULL,INSERT_VALUES);
1497: if (C->force_diagonals) {
1498: MatSetValues(C,1,(const PetscInt*)&row,1,(const PetscInt*)&row,NULL,INSERT_VALUES);
1499: }
1500: }
1501: for (i=0; i<con; i++) {
1502: ncols = c_oth->i[i+1] - c_oth->i[i];
1503: cols = c_oth->j + c_oth->i[i];
1504: row = prmap[i];
1505: MatSetValues(C,1,(const PetscInt*)&row,ncols,(const PetscInt*)cols,NULL,INSERT_VALUES);
1506: }
1507: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1508: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
1509: MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
1511: /* members in merge */
1512: PetscFree(id_r);
1513: PetscFree(len_r);
1514: PetscFree(buf_ri[0]);
1515: PetscFree(buf_ri);
1516: PetscFree(buf_rj[0]);
1517: PetscFree(buf_rj);
1518: PetscLayoutDestroy(&rowmap);
1520: /* attach the supporting struct to C for reuse */
1521: C->product->data = ptap;
1522: C->product->destroy = MatDestroy_MPIAIJ_PtAP;
1523: return(0);
1524: }
1526: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,Mat C)
1527: {
1528: PetscErrorCode ierr;
1529: Mat_MPIAIJ *p=(Mat_MPIAIJ*)P->data;
1530: Mat_SeqAIJ *c_seq;
1531: Mat_APMPI *ptap;
1532: Mat A_loc,C_loc,C_oth;
1533: PetscInt i,rstart,rend,cm,ncols,row;
1534: const PetscInt *cols;
1535: const PetscScalar *vals;
1538: MatCheckProduct(C,3);
1539: ptap = (Mat_APMPI*)C->product->data;
1540: if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1541: if (!ptap->A_loc) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
1542: MatZeroEntries(C);
1544: if (ptap->reuse == MAT_REUSE_MATRIX) {
1545: /* These matrices are obtained in MatTransposeMatMultSymbolic() */
1546: /* 1) get R = Pd^T, Ro = Po^T */
1547: /*----------------------------*/
1548: MatTranspose_SeqAIJ(p->A,MAT_REUSE_MATRIX,&ptap->Rd);
1549: MatTranspose_SeqAIJ(p->B,MAT_REUSE_MATRIX,&ptap->Ro);
1551: /* 2) compute numeric A_loc */
1552: /*--------------------------*/
1553: MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&ptap->A_loc);
1554: }
1556: /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */
1557: A_loc = ptap->A_loc;
1558: ((ptap->C_loc)->ops->matmultnumeric)(ptap->Rd,A_loc,ptap->C_loc);
1559: ((ptap->C_oth)->ops->matmultnumeric)(ptap->Ro,A_loc,ptap->C_oth);
1560: C_loc = ptap->C_loc;
1561: C_oth = ptap->C_oth;
1563: /* add C_loc and C_oth to C */
1564: MatGetOwnershipRange(C,&rstart,&rend);
1566: /* C_loc -> C */
1567: cm = C_loc->rmap->N;
1568: c_seq = (Mat_SeqAIJ*)C_loc->data;
1569: cols = c_seq->j;
1570: vals = c_seq->a;
1571: for (i=0; i<cm; i++) {
1572: ncols = c_seq->i[i+1] - c_seq->i[i];
1573: row = rstart + i;
1574: MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);
1575: cols += ncols; vals += ncols;
1576: }
1578: /* Co -> C, off-processor part */
1579: cm = C_oth->rmap->N;
1580: c_seq = (Mat_SeqAIJ*)C_oth->data;
1581: cols = c_seq->j;
1582: vals = c_seq->a;
1583: for (i=0; i<cm; i++) {
1584: ncols = c_seq->i[i+1] - c_seq->i[i];
1585: row = p->garray[i];
1586: MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);
1587: cols += ncols; vals += ncols;
1588: }
1589: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1590: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
1591: MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
1593: ptap->reuse = MAT_REUSE_MATRIX;
1594: return(0);
1595: }
1597: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P,Mat A,Mat C)
1598: {
1599: PetscErrorCode ierr;
1600: Mat_Merge_SeqsToMPI *merge;
1601: Mat_MPIAIJ *p =(Mat_MPIAIJ*)P->data;
1602: Mat_SeqAIJ *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
1603: Mat_APMPI *ptap;
1604: PetscInt *adj;
1605: PetscInt i,j,k,anz,pnz,row,*cj,nexta;
1606: MatScalar *ada,*ca,valtmp;
1607: PetscInt am=A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
1608: MPI_Comm comm;
1609: PetscMPIInt size,rank,taga,*len_s;
1610: PetscInt *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
1611: PetscInt **buf_ri,**buf_rj;
1612: PetscInt cnz=0,*bj_i,*bi,*bj,bnz,nextcj; /* bi,bj,ba: local array of C(mpi mat) */
1613: MPI_Request *s_waits,*r_waits;
1614: MPI_Status *status;
1615: MatScalar **abuf_r,*ba_i,*pA,*coa,*ba;
1616: const PetscScalar *dummy;
1617: PetscInt *ai,*aj,*coi,*coj,*poJ,*pdJ;
1618: Mat A_loc;
1619: Mat_SeqAIJ *a_loc;
1622: MatCheckProduct(C,3);
1623: ptap = (Mat_APMPI*)C->product->data;
1624: if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1625: if (!ptap->A_loc) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
1626: PetscObjectGetComm((PetscObject)C,&comm);
1627: MPI_Comm_size(comm,&size);
1628: MPI_Comm_rank(comm,&rank);
1630: merge = ptap->merge;
1632: /* 2) compute numeric C_seq = P_loc^T*A_loc */
1633: /*------------------------------------------*/
1634: /* get data from symbolic products */
1635: coi = merge->coi; coj = merge->coj;
1636: PetscCalloc1(coi[pon]+1,&coa);
1637: bi = merge->bi; bj = merge->bj;
1638: owners = merge->rowmap->range;
1639: PetscCalloc1(bi[cm]+1,&ba);
1641: /* get A_loc by taking all local rows of A */
1642: A_loc = ptap->A_loc;
1643: MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&A_loc);
1644: a_loc = (Mat_SeqAIJ*)(A_loc)->data;
1645: ai = a_loc->i;
1646: aj = a_loc->j;
1648: /* trigger copy to CPU */
1649: MatSeqAIJGetArrayRead(p->A,&dummy);
1650: MatSeqAIJRestoreArrayRead(p->A,&dummy);
1651: MatSeqAIJGetArrayRead(p->B,&dummy);
1652: MatSeqAIJRestoreArrayRead(p->B,&dummy);
1653: for (i=0; i<am; i++) {
1654: anz = ai[i+1] - ai[i];
1655: adj = aj + ai[i];
1656: ada = a_loc->a + ai[i];
1658: /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
1659: /*-------------------------------------------------------------*/
1660: /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
1661: pnz = po->i[i+1] - po->i[i];
1662: poJ = po->j + po->i[i];
1663: pA = po->a + po->i[i];
1664: for (j=0; j<pnz; j++) {
1665: row = poJ[j];
1666: cj = coj + coi[row];
1667: ca = coa + coi[row];
1668: /* perform sparse axpy */
1669: nexta = 0;
1670: valtmp = pA[j];
1671: for (k=0; nexta<anz; k++) {
1672: if (cj[k] == adj[nexta]) {
1673: ca[k] += valtmp*ada[nexta];
1674: nexta++;
1675: }
1676: }
1677: PetscLogFlops(2.0*anz);
1678: }
1680: /* put the value into Cd (diagonal part) */
1681: pnz = pd->i[i+1] - pd->i[i];
1682: pdJ = pd->j + pd->i[i];
1683: pA = pd->a + pd->i[i];
1684: for (j=0; j<pnz; j++) {
1685: row = pdJ[j];
1686: cj = bj + bi[row];
1687: ca = ba + bi[row];
1688: /* perform sparse axpy */
1689: nexta = 0;
1690: valtmp = pA[j];
1691: for (k=0; nexta<anz; k++) {
1692: if (cj[k] == adj[nexta]) {
1693: ca[k] += valtmp*ada[nexta];
1694: nexta++;
1695: }
1696: }
1697: PetscLogFlops(2.0*anz);
1698: }
1699: }
1701: /* 3) send and recv matrix values coa */
1702: /*------------------------------------*/
1703: buf_ri = merge->buf_ri;
1704: buf_rj = merge->buf_rj;
1705: len_s = merge->len_s;
1706: PetscCommGetNewTag(comm,&taga);
1707: PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);
1709: PetscMalloc2(merge->nsend+1,&s_waits,size,&status);
1710: for (proc=0,k=0; proc<size; proc++) {
1711: if (!len_s[proc]) continue;
1712: i = merge->owners_co[proc];
1713: MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);
1714: k++;
1715: }
1716: if (merge->nrecv) {MPI_Waitall(merge->nrecv,r_waits,status);}
1717: if (merge->nsend) {MPI_Waitall(merge->nsend,s_waits,status);}
1719: PetscFree2(s_waits,status);
1720: PetscFree(r_waits);
1721: PetscFree(coa);
1723: /* 4) insert local Cseq and received values into Cmpi */
1724: /*----------------------------------------------------*/
1725: PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
1726: for (k=0; k<merge->nrecv; k++) {
1727: buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1728: nrows = *(buf_ri_k[k]);
1729: nextrow[k] = buf_ri_k[k]+1; /* next row number of k-th recved i-structure */
1730: nextci[k] = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure */
1731: }
1733: for (i=0; i<cm; i++) {
1734: row = owners[rank] + i; /* global row index of C_seq */
1735: bj_i = bj + bi[i]; /* col indices of the i-th row of C */
1736: ba_i = ba + bi[i];
1737: bnz = bi[i+1] - bi[i];
1738: /* add received vals into ba */
1739: for (k=0; k<merge->nrecv; k++) { /* k-th received message */
1740: /* i-th row */
1741: if (i == *nextrow[k]) {
1742: cnz = *(nextci[k]+1) - *nextci[k];
1743: cj = buf_rj[k] + *(nextci[k]);
1744: ca = abuf_r[k] + *(nextci[k]);
1745: nextcj = 0;
1746: for (j=0; nextcj<cnz; j++) {
1747: if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
1748: ba_i[j] += ca[nextcj++];
1749: }
1750: }
1751: nextrow[k]++; nextci[k]++;
1752: PetscLogFlops(2.0*cnz);
1753: }
1754: }
1755: MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);
1756: }
1757: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1758: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
1760: PetscFree(ba);
1761: PetscFree(abuf_r[0]);
1762: PetscFree(abuf_r);
1763: PetscFree3(buf_ri_k,nextrow,nextci);
1764: return(0);
1765: }
1767: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P,Mat A,PetscReal fill,Mat C)
1768: {
1769: PetscErrorCode ierr;
1770: Mat A_loc;
1771: Mat_APMPI *ptap;
1772: PetscFreeSpaceList free_space=NULL,current_space=NULL;
1773: Mat_MPIAIJ *p=(Mat_MPIAIJ*)P->data,*a=(Mat_MPIAIJ*)A->data;
1774: PetscInt *pdti,*pdtj,*poti,*potj,*ptJ;
1775: PetscInt nnz;
1776: PetscInt *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
1777: PetscInt am =A->rmap->n,pn=P->cmap->n;
1778: MPI_Comm comm;
1779: PetscMPIInt size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
1780: PetscInt **buf_rj,**buf_ri,**buf_ri_k;
1781: PetscInt len,proc,*dnz,*onz,*owners;
1782: PetscInt nzi,*bi,*bj;
1783: PetscInt nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1784: MPI_Request *swaits,*rwaits;
1785: MPI_Status *sstatus,rstatus;
1786: Mat_Merge_SeqsToMPI *merge;
1787: PetscInt *ai,*aj,*Jptr,anz,*prmap=p->garray,pon,nspacedouble=0,j;
1788: PetscReal afill =1.0,afill_tmp;
1789: PetscInt rstart = P->cmap->rstart,rmax,aN=A->cmap->N,Armax;
1790: Mat_SeqAIJ *a_loc;
1791: PetscTable ta;
1792: MatType mtype;
1795: PetscObjectGetComm((PetscObject)A,&comm);
1796: /* check if matrix local sizes are compatible */
1797: if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend) SETERRQ4(comm,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, A (%D, %D) != P (%D,%D)",A->rmap->rstart,A->rmap->rend,P->rmap->rstart,P->rmap->rend);
1799: MPI_Comm_size(comm,&size);
1800: MPI_Comm_rank(comm,&rank);
1802: /* create struct Mat_APMPI and attached it to C later */
1803: PetscNew(&ptap);
1805: /* get A_loc by taking all local rows of A */
1806: MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&A_loc);
1808: ptap->A_loc = A_loc;
1809: a_loc = (Mat_SeqAIJ*)(A_loc)->data;
1810: ai = a_loc->i;
1811: aj = a_loc->j;
1813: /* determine symbolic Co=(p->B)^T*A - send to others */
1814: /*----------------------------------------------------*/
1815: MatGetSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);
1816: MatGetSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);
1817: pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
1818: >= (num of nonzero rows of C_seq) - pn */
1819: PetscMalloc1(pon+1,&coi);
1820: coi[0] = 0;
1822: /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
1823: nnz = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(poti[pon],ai[am]));
1824: PetscFreeSpaceGet(nnz,&free_space);
1825: current_space = free_space;
1827: /* create and initialize a linked list */
1828: PetscTableCreate(A->cmap->n + a->B->cmap->N,aN,&ta);
1829: MatRowMergeMax_SeqAIJ(a_loc,am,ta);
1830: PetscTableGetCount(ta,&Armax);
1832: PetscLLCondensedCreate_Scalable(Armax,&lnk);
1834: for (i=0; i<pon; i++) {
1835: pnz = poti[i+1] - poti[i];
1836: ptJ = potj + poti[i];
1837: for (j=0; j<pnz; j++) {
1838: row = ptJ[j]; /* row of A_loc == col of Pot */
1839: anz = ai[row+1] - ai[row];
1840: Jptr = aj + ai[row];
1841: /* add non-zero cols of AP into the sorted linked list lnk */
1842: PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);
1843: }
1844: nnz = lnk[0];
1846: /* If free space is not available, double the total space in the list */
1847: if (current_space->local_remaining<nnz) {
1848: PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),¤t_space);
1849: nspacedouble++;
1850: }
1852: /* Copy data into free space, and zero out denserows */
1853: PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);
1855: current_space->array += nnz;
1856: current_space->local_used += nnz;
1857: current_space->local_remaining -= nnz;
1859: coi[i+1] = coi[i] + nnz;
1860: }
1862: PetscMalloc1(coi[pon]+1,&coj);
1863: PetscFreeSpaceContiguous(&free_space,coj);
1864: PetscLLCondensedDestroy_Scalable(lnk); /* must destroy to get a new one for C */
1866: afill_tmp = (PetscReal)coi[pon]/(poti[pon] + ai[am]+1);
1867: if (afill_tmp > afill) afill = afill_tmp;
1869: /* send j-array (coj) of Co to other processors */
1870: /*----------------------------------------------*/
1871: /* determine row ownership */
1872: PetscNew(&merge);
1873: PetscLayoutCreate(comm,&merge->rowmap);
1875: merge->rowmap->n = pn;
1876: merge->rowmap->bs = 1;
1878: PetscLayoutSetUp(merge->rowmap);
1879: owners = merge->rowmap->range;
1881: /* determine the number of messages to send, their lengths */
1882: PetscCalloc1(size,&len_si);
1883: PetscCalloc1(size,&merge->len_s);
1885: len_s = merge->len_s;
1886: merge->nsend = 0;
1888: PetscMalloc1(size+2,&owners_co);
1890: proc = 0;
1891: for (i=0; i<pon; i++) {
1892: while (prmap[i] >= owners[proc+1]) proc++;
1893: len_si[proc]++; /* num of rows in Co to be sent to [proc] */
1894: len_s[proc] += coi[i+1] - coi[i];
1895: }
1897: len = 0; /* max length of buf_si[] */
1898: owners_co[0] = 0;
1899: for (proc=0; proc<size; proc++) {
1900: owners_co[proc+1] = owners_co[proc] + len_si[proc];
1901: if (len_si[proc]) {
1902: merge->nsend++;
1903: len_si[proc] = 2*(len_si[proc] + 1);
1904: len += len_si[proc];
1905: }
1906: }
1908: /* determine the number and length of messages to receive for coi and coj */
1909: PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);
1910: PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);
1912: /* post the Irecv and Isend of coj */
1913: PetscCommGetNewTag(comm,&tagj);
1914: PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);
1915: PetscMalloc1(merge->nsend+1,&swaits);
1916: for (proc=0, k=0; proc<size; proc++) {
1917: if (!len_s[proc]) continue;
1918: i = owners_co[proc];
1919: MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);
1920: k++;
1921: }
1923: /* receives and sends of coj are complete */
1924: PetscMalloc1(size,&sstatus);
1925: for (i=0; i<merge->nrecv; i++) {
1926: PETSC_UNUSED PetscMPIInt icompleted;
1927: MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
1928: }
1929: PetscFree(rwaits);
1930: if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}
1932: /* add received column indices into table to update Armax */
1933: /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/tutorials/ex56.c! */
1934: for (k=0; k<merge->nrecv; k++) {/* k-th received message */
1935: Jptr = buf_rj[k];
1936: for (j=0; j<merge->len_r[k]; j++) {
1937: PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);
1938: }
1939: }
1940: PetscTableGetCount(ta,&Armax);
1941: /* printf("Armax %d, an %d + Bn %d = %d, aN %d\n",Armax,A->cmap->n,a->B->cmap->N,A->cmap->n+a->B->cmap->N,aN); */
1943: /* send and recv coi */
1944: /*-------------------*/
1945: PetscCommGetNewTag(comm,&tagi);
1946: PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);
1947: PetscMalloc1(len+1,&buf_s);
1948: buf_si = buf_s; /* points to the beginning of k-th msg to be sent */
1949: for (proc=0,k=0; proc<size; proc++) {
1950: if (!len_s[proc]) continue;
1951: /* form outgoing message for i-structure:
1952: buf_si[0]: nrows to be sent
1953: [1:nrows]: row index (global)
1954: [nrows+1:2*nrows+1]: i-structure index
1955: */
1956: /*-------------------------------------------*/
1957: nrows = len_si[proc]/2 - 1;
1958: buf_si_i = buf_si + nrows+1;
1959: buf_si[0] = nrows;
1960: buf_si_i[0] = 0;
1961: nrows = 0;
1962: for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
1963: nzi = coi[i+1] - coi[i];
1964: buf_si_i[nrows+1] = buf_si_i[nrows] + nzi; /* i-structure */
1965: buf_si[nrows+1] = prmap[i] -owners[proc]; /* local row index */
1966: nrows++;
1967: }
1968: MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);
1969: k++;
1970: buf_si += len_si[proc];
1971: }
1972: i = merge->nrecv;
1973: while (i--) {
1974: PETSC_UNUSED PetscMPIInt icompleted;
1975: MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
1976: }
1977: PetscFree(rwaits);
1978: if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}
1979: PetscFree(len_si);
1980: PetscFree(len_ri);
1981: PetscFree(swaits);
1982: PetscFree(sstatus);
1983: PetscFree(buf_s);
1985: /* compute the local portion of C (mpi mat) */
1986: /*------------------------------------------*/
1987: /* allocate bi array and free space for accumulating nonzero column info */
1988: PetscMalloc1(pn+1,&bi);
1989: bi[0] = 0;
1991: /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
1992: nnz = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(pdti[pn],PetscIntSumTruncate(poti[pon],ai[am])));
1993: PetscFreeSpaceGet(nnz,&free_space);
1994: current_space = free_space;
1996: PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
1997: for (k=0; k<merge->nrecv; k++) {
1998: buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1999: nrows = *buf_ri_k[k];
2000: nextrow[k] = buf_ri_k[k] + 1; /* next row number of k-th recved i-structure */
2001: nextci[k] = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th received i-structure */
2002: }
2004: PetscLLCondensedCreate_Scalable(Armax,&lnk);
2005: MatPreallocateInitialize(comm,pn,A->cmap->n,dnz,onz);
2006: rmax = 0;
2007: for (i=0; i<pn; i++) {
2008: /* add pdt[i,:]*AP into lnk */
2009: pnz = pdti[i+1] - pdti[i];
2010: ptJ = pdtj + pdti[i];
2011: for (j=0; j<pnz; j++) {
2012: row = ptJ[j]; /* row of AP == col of Pt */
2013: anz = ai[row+1] - ai[row];
2014: Jptr = aj + ai[row];
2015: /* add non-zero cols of AP into the sorted linked list lnk */
2016: PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);
2017: }
2019: /* add received col data into lnk */
2020: for (k=0; k<merge->nrecv; k++) { /* k-th received message */
2021: if (i == *nextrow[k]) { /* i-th row */
2022: nzi = *(nextci[k]+1) - *nextci[k];
2023: Jptr = buf_rj[k] + *nextci[k];
2024: PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);
2025: nextrow[k]++; nextci[k]++;
2026: }
2027: }
2029: /* add missing diagonal entry */
2030: if (C->force_diagonals) {
2031: k = i + owners[rank]; /* column index */
2032: PetscLLCondensedAddSorted_Scalable(1,&k,lnk);
2033: }
2035: nnz = lnk[0];
2037: /* if free space is not available, make more free space */
2038: if (current_space->local_remaining<nnz) {
2039: PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),¤t_space);
2040: nspacedouble++;
2041: }
2042: /* copy data into free space, then initialize lnk */
2043: PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);
2044: MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);
2046: current_space->array += nnz;
2047: current_space->local_used += nnz;
2048: current_space->local_remaining -= nnz;
2050: bi[i+1] = bi[i] + nnz;
2051: if (nnz > rmax) rmax = nnz;
2052: }
2053: PetscFree3(buf_ri_k,nextrow,nextci);
2055: PetscMalloc1(bi[pn]+1,&bj);
2056: PetscFreeSpaceContiguous(&free_space,bj);
2057: afill_tmp = (PetscReal)bi[pn]/(pdti[pn] + poti[pon] + ai[am]+1);
2058: if (afill_tmp > afill) afill = afill_tmp;
2059: PetscLLCondensedDestroy_Scalable(lnk);
2060: PetscTableDestroy(&ta);
2061: MatRestoreSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);
2062: MatRestoreSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);
2064: /* create symbolic parallel matrix C - why cannot be assembled in Numeric part */
2065: /*-------------------------------------------------------------------------------*/
2066: MatSetSizes(C,pn,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);
2067: MatSetBlockSizes(C,PetscAbs(P->cmap->bs),PetscAbs(A->cmap->bs));
2068: MatGetType(A,&mtype);
2069: MatSetType(C,mtype);
2070: MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
2071: MatPreallocateFinalize(dnz,onz);
2072: MatSetBlockSize(C,1);
2073: MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);
2074: for (i=0; i<pn; i++) {
2075: row = i + rstart;
2076: nnz = bi[i+1] - bi[i];
2077: Jptr = bj + bi[i];
2078: MatSetValues(C,1,&row,nnz,Jptr,NULL,INSERT_VALUES);
2079: }
2080: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
2081: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
2082: MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
2083: merge->bi = bi;
2084: merge->bj = bj;
2085: merge->coi = coi;
2086: merge->coj = coj;
2087: merge->buf_ri = buf_ri;
2088: merge->buf_rj = buf_rj;
2089: merge->owners_co = owners_co;
2091: /* attach the supporting struct to C for reuse */
2092: C->product->data = ptap;
2093: C->product->destroy = MatDestroy_MPIAIJ_PtAP;
2094: ptap->merge = merge;
2096: C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;
2098: #if defined(PETSC_USE_INFO)
2099: if (bi[pn] != 0) {
2100: PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
2101: PetscInfo1(C,"Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n",(double)afill);
2102: } else {
2103: PetscInfo(C,"Empty matrix product\n");
2104: }
2105: #endif
2106: return(0);
2107: }
2109: /* ---------------------------------------------------------------- */
2110: static PetscErrorCode MatProductSymbolic_AtB_MPIAIJ_MPIAIJ(Mat C)
2111: {
2113: Mat_Product *product = C->product;
2114: Mat A=product->A,B=product->B;
2115: PetscReal fill=product->fill;
2116: PetscBool flg;
2119: /* scalable */
2120: PetscStrcmp(product->alg,"scalable",&flg);
2121: if (flg) {
2122: MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);
2123: goto next;
2124: }
2126: /* nonscalable */
2127: PetscStrcmp(product->alg,"nonscalable",&flg);
2128: if (flg) {
2129: MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C);
2130: goto next;
2131: }
2133: /* matmatmult */
2134: PetscStrcmp(product->alg,"at*b",&flg);
2135: if (flg) {
2136: Mat At;
2137: Mat_APMPI *ptap;
2139: MatTranspose(A,MAT_INITIAL_MATRIX,&At);
2140: MatMatMultSymbolic_MPIAIJ_MPIAIJ(At,B,fill,C);
2141: ptap = (Mat_APMPI*)C->product->data;
2142: if (ptap) {
2143: ptap->Pt = At;
2144: C->product->destroy = MatDestroy_MPIAIJ_PtAP;
2145: }
2146: C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
2147: goto next;
2148: }
2150: /* backend general code */
2151: PetscStrcmp(product->alg,"backend",&flg);
2152: if (flg) {
2153: MatProductSymbolic_MPIAIJBACKEND(C);
2154: return(0);
2155: }
2157: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatProduct type is not supported");
2159: next:
2160: C->ops->productnumeric = MatProductNumeric_AtB;
2161: return(0);
2162: }
2164: /* ---------------------------------------------------------------- */
2165: /* Set options for MatMatMultxxx_MPIAIJ_MPIAIJ */
2166: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AB(Mat C)
2167: {
2169: Mat_Product *product = C->product;
2170: Mat A=product->A,B=product->B;
2171: #if defined(PETSC_HAVE_HYPRE)
2172: const char *algTypes[5] = {"scalable","nonscalable","seqmpi","backend","hypre"};
2173: PetscInt nalg = 5;
2174: #else
2175: const char *algTypes[4] = {"scalable","nonscalable","seqmpi","backend",};
2176: PetscInt nalg = 4;
2177: #endif
2178: PetscInt alg = 1; /* set nonscalable algorithm as default */
2179: PetscBool flg;
2180: MPI_Comm comm;
2183: /* Check matrix local sizes */
2184: PetscObjectGetComm((PetscObject)C,&comm);
2185: if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%D, %D) != (%D,%D)",A->cmap->rstart,A->cmap->rend,B->rmap->rstart,B->rmap->rend);
2187: /* Set "nonscalable" as default algorithm */
2188: PetscStrcmp(C->product->alg,"default",&flg);
2189: if (flg) {
2190: MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2192: /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2193: if (B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2194: MatInfo Ainfo,Binfo;
2195: PetscInt nz_local;
2196: PetscBool alg_scalable_loc=PETSC_FALSE,alg_scalable;
2198: MatGetInfo(A,MAT_LOCAL,&Ainfo);
2199: MatGetInfo(B,MAT_LOCAL,&Binfo);
2200: nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);
2202: if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2203: MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);
2205: if (alg_scalable) {
2206: alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2207: MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2208: PetscInfo2(B,"Use scalable algorithm, BN %D, fill*nz_allocated %g\n",B->cmap->N,product->fill*nz_local);
2209: }
2210: }
2211: }
2213: /* Get runtime option */
2214: if (product->api_user) {
2215: PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMult","Mat");
2216: PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
2217: PetscOptionsEnd();
2218: } else {
2219: PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AB","Mat");
2220: PetscOptionsEList("-matproduct_ab_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
2221: PetscOptionsEnd();
2222: }
2223: if (flg) {
2224: MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2225: }
2227: C->ops->productsymbolic = MatProductSymbolic_AB_MPIAIJ_MPIAIJ;
2228: return(0);
2229: }
2231: /* Set options for MatTransposeMatMultXXX_MPIAIJ_MPIAIJ */
2232: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AtB(Mat C)
2233: {
2235: Mat_Product *product = C->product;
2236: Mat A=product->A,B=product->B;
2237: const char *algTypes[4] = {"scalable","nonscalable","at*b","backend"};
2238: PetscInt nalg = 4;
2239: PetscInt alg = 1; /* set default algorithm */
2240: PetscBool flg;
2241: MPI_Comm comm;
2244: /* Check matrix local sizes */
2245: PetscObjectGetComm((PetscObject)C,&comm);
2246: if (A->rmap->rstart != B->rmap->rstart || A->rmap->rend != B->rmap->rend) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, A (%D, %D) != B (%D,%D)",A->rmap->rstart,A->rmap->rend,B->rmap->rstart,B->rmap->rend);
2248: /* Set default algorithm */
2249: PetscStrcmp(C->product->alg,"default",&flg);
2250: if (flg) {
2251: MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2252: }
2254: /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2255: if (alg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2256: MatInfo Ainfo,Binfo;
2257: PetscInt nz_local;
2258: PetscBool alg_scalable_loc=PETSC_FALSE,alg_scalable;
2260: MatGetInfo(A,MAT_LOCAL,&Ainfo);
2261: MatGetInfo(B,MAT_LOCAL,&Binfo);
2262: nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);
2264: if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2265: MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);
2267: if (alg_scalable) {
2268: alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2269: MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2270: PetscInfo2(B,"Use scalable algorithm, BN %D, fill*nz_allocated %g\n",B->cmap->N,product->fill*nz_local);
2271: }
2272: }
2274: /* Get runtime option */
2275: if (product->api_user) {
2276: PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatTransposeMatMult","Mat");
2277: PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
2278: PetscOptionsEnd();
2279: } else {
2280: PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AtB","Mat");
2281: PetscOptionsEList("-matproduct_atb_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
2282: PetscOptionsEnd();
2283: }
2284: if (flg) {
2285: MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2286: }
2288: C->ops->productsymbolic = MatProductSymbolic_AtB_MPIAIJ_MPIAIJ;
2289: return(0);
2290: }
2292: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_PtAP(Mat C)
2293: {
2295: Mat_Product *product = C->product;
2296: Mat A=product->A,P=product->B;
2297: MPI_Comm comm;
2298: PetscBool flg;
2299: PetscInt alg=1; /* set default algorithm */
2300: #if !defined(PETSC_HAVE_HYPRE)
2301: const char *algTypes[5] = {"scalable","nonscalable","allatonce","allatonce_merged","backend"};
2302: PetscInt nalg=5;
2303: #else
2304: const char *algTypes[6] = {"scalable","nonscalable","allatonce","allatonce_merged","backend","hypre"};
2305: PetscInt nalg=6;
2306: #endif
2307: PetscInt pN=P->cmap->N;
2310: /* Check matrix local sizes */
2311: PetscObjectGetComm((PetscObject)C,&comm);
2312: if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, Arow (%D, %D) != Prow (%D,%D)",A->rmap->rstart,A->rmap->rend,P->rmap->rstart,P->rmap->rend);
2313: if (A->cmap->rstart != P->rmap->rstart || A->cmap->rend != P->rmap->rend) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, Acol (%D, %D) != Prow (%D,%D)",A->cmap->rstart,A->cmap->rend,P->rmap->rstart,P->rmap->rend);
2315: /* Set "nonscalable" as default algorithm */
2316: PetscStrcmp(C->product->alg,"default",&flg);
2317: if (flg) {
2318: MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2320: /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2321: if (pN > 100000) {
2322: MatInfo Ainfo,Pinfo;
2323: PetscInt nz_local;
2324: PetscBool alg_scalable_loc=PETSC_FALSE,alg_scalable;
2326: MatGetInfo(A,MAT_LOCAL,&Ainfo);
2327: MatGetInfo(P,MAT_LOCAL,&Pinfo);
2328: nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);
2330: if (pN > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2331: MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);
2333: if (alg_scalable) {
2334: alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2335: MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2336: }
2337: }
2338: }
2340: /* Get runtime option */
2341: if (product->api_user) {
2342: PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatPtAP","Mat");
2343: PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);
2344: PetscOptionsEnd();
2345: } else {
2346: PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_PtAP","Mat");
2347: PetscOptionsEList("-matproduct_ptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);
2348: PetscOptionsEnd();
2349: }
2350: if (flg) {
2351: MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2352: }
2354: C->ops->productsymbolic = MatProductSymbolic_PtAP_MPIAIJ_MPIAIJ;
2355: return(0);
2356: }
2358: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_RARt(Mat C)
2359: {
2360: Mat_Product *product = C->product;
2361: Mat A = product->A,R=product->B;
2364: /* Check matrix local sizes */
2365: if (A->cmap->n != R->cmap->n || A->rmap->n != R->cmap->n) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, A local (%D, %D), R local (%D,%D)",A->rmap->n,A->rmap->n,R->rmap->n,R->cmap->n);
2367: C->ops->productsymbolic = MatProductSymbolic_RARt_MPIAIJ_MPIAIJ;
2368: return(0);
2369: }
2371: /*
2372: Set options for ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm
2373: */
2374: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABC(Mat C)
2375: {
2377: Mat_Product *product = C->product;
2378: PetscBool flg = PETSC_FALSE;
2379: PetscInt alg = 1; /* default algorithm */
2380: const char *algTypes[3] = {"scalable","nonscalable","seqmpi"};
2381: PetscInt nalg = 3;
2384: /* Set default algorithm */
2385: PetscStrcmp(C->product->alg,"default",&flg);
2386: if (flg) {
2387: MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2388: }
2390: /* Get runtime option */
2391: if (product->api_user) {
2392: PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMatMult","Mat");
2393: PetscOptionsEList("-matmatmatmult_via","Algorithmic approach","MatMatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
2394: PetscOptionsEnd();
2395: } else {
2396: PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_ABC","Mat");
2397: PetscOptionsEList("-matproduct_abc_via","Algorithmic approach","MatProduct_ABC",algTypes,nalg,algTypes[alg],&alg,&flg);
2398: PetscOptionsEnd();
2399: }
2400: if (flg) {
2401: MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2402: }
2404: C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ;
2405: C->ops->productsymbolic = MatProductSymbolic_ABC;
2406: return(0);
2407: }
2409: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ(Mat C)
2410: {
2412: Mat_Product *product = C->product;
2415: switch (product->type) {
2416: case MATPRODUCT_AB:
2417: MatProductSetFromOptions_MPIAIJ_AB(C);
2418: break;
2419: case MATPRODUCT_AtB:
2420: MatProductSetFromOptions_MPIAIJ_AtB(C);
2421: break;
2422: case MATPRODUCT_PtAP:
2423: MatProductSetFromOptions_MPIAIJ_PtAP(C);
2424: break;
2425: case MATPRODUCT_RARt:
2426: MatProductSetFromOptions_MPIAIJ_RARt(C);
2427: break;
2428: case MATPRODUCT_ABC:
2429: MatProductSetFromOptions_MPIAIJ_ABC(C);
2430: break;
2431: default:
2432: break;
2433: }
2434: return(0);
2435: }