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: /* flag CPU mask for C */
112: #if defined(PETSC_HAVE_DEVICE)
113: if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
114: if (c->A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->A->offloadmask = PETSC_OFFLOAD_CPU;
115: if (c->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->B->offloadmask = PETSC_OFFLOAD_CPU;
116: #endif
118: /* 1) get P_oth = ptap->P_oth and P_loc = ptap->P_loc */
119: /*-----------------------------------------------------*/
120: /* update numerical values of P_oth and P_loc */
121: MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
122: MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);
124: /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
125: /*----------------------------------------------------------*/
126: /* get data from symbolic products */
127: p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
128: p_oth = NULL;
129: if (size >1) {
130: p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
131: }
133: /* get apa for storing dense row A[i,:]*P */
134: apa = ptap->apa;
136: api = ptap->api;
137: apj = ptap->apj;
138: /* trigger copy to CPU */
139: MatSeqAIJGetArrayRead(a->A,&dummy);
140: MatSeqAIJRestoreArrayRead(a->A,&dummy);
141: MatSeqAIJGetArrayRead(a->B,&dummy);
142: MatSeqAIJRestoreArrayRead(a->B,&dummy);
143: for (i=0; i<cm; i++) {
144: /* compute apa = A[i,:]*P */
145: AProw_nonscalable(i,ad,ao,p_loc,p_oth,apa);
147: /* set values in C */
148: apJ = apj + api[i];
149: cdnz = cd->i[i+1] - cd->i[i];
150: conz = co->i[i+1] - co->i[i];
152: /* 1st off-diagonal part of C */
153: ca = coa + co->i[i];
154: k = 0;
155: for (k0=0; k0<conz; k0++) {
156: if (apJ[k] >= cstart) break;
157: ca[k0] = apa[apJ[k]];
158: apa[apJ[k++]] = 0.0;
159: }
161: /* diagonal part of C */
162: ca = cda + cd->i[i];
163: for (k1=0; k1<cdnz; k1++) {
164: ca[k1] = apa[apJ[k]];
165: apa[apJ[k++]] = 0.0;
166: }
168: /* 2nd off-diagonal part of C */
169: ca = coa + co->i[i];
170: for (; k0<conz; k0++) {
171: ca[k0] = apa[apJ[k]];
172: apa[apJ[k++]] = 0.0;
173: }
174: }
175: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
176: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
177: return(0);
178: }
180: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,PetscReal fill,Mat C)
181: {
182: PetscErrorCode ierr;
183: MPI_Comm comm;
184: PetscMPIInt size;
185: Mat_APMPI *ptap;
186: PetscFreeSpaceList free_space=NULL,current_space=NULL;
187: Mat_MPIAIJ *a=(Mat_MPIAIJ*)A->data;
188: Mat_SeqAIJ *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
189: PetscInt *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
190: PetscInt *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
191: PetscInt *lnk,i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi;
192: PetscInt am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n;
193: PetscBT lnkbt;
194: PetscReal afill;
195: MatType mtype;
198: MatCheckProduct(C,4);
199: if (C->product->data) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
200: PetscObjectGetComm((PetscObject)A,&comm);
201: MPI_Comm_size(comm,&size);
203: /* create struct Mat_APMPI and attached it to C later */
204: PetscNew(&ptap);
206: /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
207: MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
209: /* get P_loc by taking all local rows of P */
210: MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);
212: p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
213: pi_loc = p_loc->i; pj_loc = p_loc->j;
214: if (size > 1) {
215: p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
216: pi_oth = p_oth->i; pj_oth = p_oth->j;
217: } else {
218: p_oth = NULL;
219: pi_oth = NULL; pj_oth = NULL;
220: }
222: /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
223: /*-------------------------------------------------------------------*/
224: PetscMalloc1(am+2,&api);
225: ptap->api = api;
226: api[0] = 0;
228: /* create and initialize a linked list */
229: PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);
231: /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
232: PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space);
233: current_space = free_space;
235: MatPreallocateInitialize(comm,am,pn,dnz,onz);
236: for (i=0; i<am; i++) {
237: /* diagonal portion of A */
238: nzi = adi[i+1] - adi[i];
239: for (j=0; j<nzi; j++) {
240: row = *adj++;
241: pnz = pi_loc[row+1] - pi_loc[row];
242: Jptr = pj_loc + pi_loc[row];
243: /* add non-zero cols of P into the sorted linked list lnk */
244: PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);
245: }
246: /* off-diagonal portion of A */
247: nzi = aoi[i+1] - aoi[i];
248: for (j=0; j<nzi; j++) {
249: row = *aoj++;
250: pnz = pi_oth[row+1] - pi_oth[row];
251: Jptr = pj_oth + pi_oth[row];
252: PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);
253: }
254: /* add possible missing diagonal entry */
255: if (C->force_diagonals) {
256: j = i + rstart; /* column index */
257: PetscLLCondensedAddSorted(1,&j,lnk,lnkbt);
258: }
260: apnz = lnk[0];
261: api[i+1] = api[i] + apnz;
263: /* if free space is not available, double the total space in the list */
264: if (current_space->local_remaining<apnz) {
265: PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),¤t_space);
266: nspacedouble++;
267: }
269: /* Copy data into free space, then initialize lnk */
270: PetscLLCondensedClean(pN,apnz,current_space->array,lnk,lnkbt);
271: MatPreallocateSet(i+rstart,apnz,current_space->array,dnz,onz);
273: current_space->array += apnz;
274: current_space->local_used += apnz;
275: current_space->local_remaining -= apnz;
276: }
278: /* Allocate space for apj, initialize apj, and */
279: /* destroy list of free space and other temporary array(s) */
280: PetscMalloc1(api[am]+1,&ptap->apj);
281: apj = ptap->apj;
282: PetscFreeSpaceContiguous(&free_space,ptap->apj);
283: PetscLLDestroy(lnk,lnkbt);
285: /* malloc apa to store dense row A[i,:]*P */
286: PetscCalloc1(pN,&ptap->apa);
288: /* set and assemble symbolic parallel matrix C */
289: /*---------------------------------------------*/
290: MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
291: MatSetBlockSizesFromMats(C,A,P);
293: MatGetType(A,&mtype);
294: MatSetType(C,mtype);
295: MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
296: MatPreallocateFinalize(dnz,onz);
298: MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);
299: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
300: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
301: MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
303: C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
304: C->ops->productnumeric = MatProductNumeric_AB;
306: /* attach the supporting struct to C for reuse */
307: C->product->data = ptap;
308: C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;
310: /* set MatInfo */
311: afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
312: if (afill < 1.0) afill = 1.0;
313: C->info.mallocs = nspacedouble;
314: C->info.fill_ratio_given = fill;
315: C->info.fill_ratio_needed = afill;
317: #if defined(PETSC_USE_INFO)
318: if (api[am]) {
319: PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
320: PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
321: } else {
322: PetscInfo(C,"Empty matrix product\n");
323: }
324: #endif
325: return(0);
326: }
328: /* ------------------------------------------------------- */
329: static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat,Mat,PetscReal,Mat);
330: static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat,Mat,Mat);
332: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AB(Mat C)
333: {
334: Mat_Product *product = C->product;
335: Mat A = product->A,B=product->B;
338: if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend)
339: 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);
341: C->ops->matmultsymbolic = MatMatMultSymbolic_MPIAIJ_MPIDense;
342: C->ops->productsymbolic = MatProductSymbolic_AB;
343: return(0);
344: }
345: /* -------------------------------------------------------------------- */
346: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(Mat C)
347: {
348: Mat_Product *product = C->product;
349: Mat A = product->A,B=product->B;
352: if (A->rmap->rstart != B->rmap->rstart || A->rmap->rend != B->rmap->rend)
353: 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);
355: C->ops->transposematmultsymbolic = MatTransposeMatMultSymbolic_MPIAIJ_MPIDense;
356: C->ops->productsymbolic = MatProductSymbolic_AtB;
357: return(0);
358: }
360: /* --------------------------------------------------------------------- */
361: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense(Mat C)
362: {
364: Mat_Product *product = C->product;
367: switch (product->type) {
368: case MATPRODUCT_AB:
369: MatProductSetFromOptions_MPIAIJ_MPIDense_AB(C);
370: break;
371: case MATPRODUCT_AtB:
372: MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(C);
373: break;
374: default:
375: break;
376: }
377: return(0);
378: }
379: /* ------------------------------------------------------- */
381: typedef struct {
382: Mat workB,workB1;
383: MPI_Request *rwaits,*swaits;
384: PetscInt nsends,nrecvs;
385: MPI_Datatype *stype,*rtype;
386: PetscInt blda;
387: } MPIAIJ_MPIDense;
389: PetscErrorCode MatMPIAIJ_MPIDenseDestroy(void *ctx)
390: {
391: MPIAIJ_MPIDense *contents = (MPIAIJ_MPIDense*)ctx;
392: PetscErrorCode ierr;
393: PetscInt i;
396: MatDestroy(&contents->workB);
397: MatDestroy(&contents->workB1);
398: for (i=0; i<contents->nsends; i++) {
399: MPI_Type_free(&contents->stype[i]);
400: }
401: for (i=0; i<contents->nrecvs; i++) {
402: MPI_Type_free(&contents->rtype[i]);
403: }
404: PetscFree4(contents->stype,contents->rtype,contents->rwaits,contents->swaits);
405: PetscFree(contents);
406: return(0);
407: }
409: static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat A,Mat B,PetscReal fill,Mat C)
410: {
411: PetscErrorCode ierr;
412: Mat_MPIAIJ *aij=(Mat_MPIAIJ*)A->data;
413: PetscInt nz=aij->B->cmap->n,nsends,nrecvs,i,nrows_to,j,blda,clda,m,M,n,N;
414: MPIAIJ_MPIDense *contents;
415: VecScatter ctx=aij->Mvctx;
416: PetscInt Am=A->rmap->n,Bm=B->rmap->n,BN=B->cmap->N,Bbn,Bbn1,bs,nrows_from,numBb;
417: MPI_Comm comm;
418: MPI_Datatype type1,*stype,*rtype;
419: const PetscInt *sindices,*sstarts,*rstarts;
420: PetscMPIInt *disp;
421: PetscBool cisdense;
424: MatCheckProduct(C,4);
425: if (C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data not empty");
426: PetscObjectGetComm((PetscObject)A,&comm);
427: PetscObjectBaseTypeCompare((PetscObject)C,MATMPIDENSE,&cisdense);
428: if (!cisdense) {
429: MatSetType(C,((PetscObject)B)->type_name);
430: }
431: MatGetLocalSize(C,&m,&n);
432: MatGetSize(C,&M,&N);
433: if (m == PETSC_DECIDE || n == PETSC_DECIDE || M == PETSC_DECIDE || N == PETSC_DECIDE) {
434: MatSetSizes(C,Am,B->cmap->n,A->rmap->N,BN);
435: }
436: MatSetBlockSizesFromMats(C,A,B);
437: MatSetUp(C);
438: MatDenseGetLDA(B,&blda);
439: MatDenseGetLDA(C,&clda);
440: PetscNew(&contents);
442: VecScatterGetRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,NULL,NULL);
443: VecScatterGetRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,NULL,NULL);
445: /* Create column block of B and C for memory scalability when BN is too large */
446: /* Estimate Bbn, column size of Bb */
447: if (nz) {
448: Bbn1 = 2*Am*BN/nz;
449: if (!Bbn1) Bbn1 = 1;
450: } else Bbn1 = BN;
452: bs = PetscAbs(B->cmap->bs);
453: Bbn1 = Bbn1/bs *bs; /* Bbn1 is a multiple of bs */
454: if (Bbn1 > BN) Bbn1 = BN;
455: MPI_Allreduce(&Bbn1,&Bbn,1,MPIU_INT,MPI_MAX,comm);
457: /* Enable runtime option for Bbn */
458: PetscOptionsBegin(comm,((PetscObject)C)->prefix,"MatMatMult","Mat");
459: PetscOptionsInt("-matmatmult_Bbn","Number of columns in Bb","MatMatMult",Bbn,&Bbn,NULL);
460: PetscOptionsEnd();
461: Bbn = PetscMin(Bbn,BN);
463: if (Bbn > 0 && Bbn < BN) {
464: numBb = BN/Bbn;
465: Bbn1 = BN - numBb*Bbn;
466: } else numBb = 0;
468: if (numBb) {
469: PetscInfo3(C,"use Bb, BN=%D, Bbn=%D; numBb=%D\n",BN,Bbn,numBb);
470: if (Bbn1) { /* Create workB1 for the remaining columns */
471: PetscInfo2(C,"use Bb1, BN=%D, Bbn1=%D\n",BN,Bbn1);
472: /* Create work matrix used to store off processor rows of B needed for local product */
473: MatCreateSeqDense(PETSC_COMM_SELF,nz,Bbn1,NULL,&contents->workB1);
474: } else contents->workB1 = NULL;
475: }
477: /* Create work matrix used to store off processor rows of B needed for local product */
478: MatCreateSeqDense(PETSC_COMM_SELF,nz,Bbn,NULL,&contents->workB);
480: /* Use MPI derived data type to reduce memory required by the send/recv buffers */
481: PetscMalloc4(nsends,&stype,nrecvs,&rtype,nrecvs,&contents->rwaits,nsends,&contents->swaits);
482: contents->stype = stype;
483: contents->nsends = nsends;
485: contents->rtype = rtype;
486: contents->nrecvs = nrecvs;
487: contents->blda = blda;
489: PetscMalloc1(Bm+1,&disp);
490: for (i=0; i<nsends; i++) {
491: nrows_to = sstarts[i+1]-sstarts[i];
492: for (j=0; j<nrows_to; j++) {
493: disp[j] = sindices[sstarts[i]+j]; /* rowB to be sent */
494: }
495: MPI_Type_create_indexed_block(nrows_to,1,(const PetscMPIInt *)disp,MPIU_SCALAR,&type1);
497: MPI_Type_create_resized(type1,0,blda*sizeof(PetscScalar),&stype[i]);
498: MPI_Type_commit(&stype[i]);
499: MPI_Type_free(&type1);
500: }
502: for (i=0; i<nrecvs; i++) {
503: /* received values from a process form a (nrows_from x Bbn) row block in workB (column-wise) */
504: nrows_from = rstarts[i+1]-rstarts[i];
505: disp[0] = 0;
506: MPI_Type_create_indexed_block(1, nrows_from, (const PetscMPIInt *)disp, MPIU_SCALAR, &type1);
507: MPI_Type_create_resized(type1, 0, nz*sizeof(PetscScalar), &rtype[i]);
508: MPI_Type_commit(&rtype[i]);
509: MPI_Type_free(&type1);
510: }
512: PetscFree(disp);
513: VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,NULL,NULL);
514: VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,NULL,NULL);
515: MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);
516: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
517: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
518: MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
520: C->product->data = contents;
521: C->product->destroy = MatMPIAIJ_MPIDenseDestroy;
522: C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense;
523: return(0);
524: }
526: PETSC_INTERN PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat,Mat,Mat,const PetscBool);
527: /*
528: Performs an efficient scatter on the rows of B needed by this process; this is
529: a modification of the VecScatterBegin_() routines.
531: Input: Bbidx = 0: B = Bb
532: = 1: B = Bb1, see MatMatMultSymbolic_MPIAIJ_MPIDense()
533: */
534: PetscErrorCode MatMPIDenseScatter(Mat A,Mat B,PetscInt Bbidx,Mat C,Mat *outworkB)
535: {
536: Mat_MPIAIJ *aij = (Mat_MPIAIJ*)A->data;
537: PetscErrorCode ierr;
538: const PetscScalar *b;
539: PetscScalar *rvalues;
540: VecScatter ctx = aij->Mvctx;
541: const PetscInt *sindices,*sstarts,*rstarts;
542: const PetscMPIInt *sprocs,*rprocs;
543: PetscInt i,nsends,nrecvs;
544: MPI_Request *swaits,*rwaits;
545: MPI_Comm comm;
546: PetscMPIInt tag=((PetscObject)ctx)->tag,ncols=B->cmap->N,nrows=aij->B->cmap->n,nsends_mpi,nrecvs_mpi;
547: MPIAIJ_MPIDense *contents;
548: Mat workB;
549: MPI_Datatype *stype,*rtype;
550: PetscInt blda;
553: MatCheckProduct(C,4);
554: if (!C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
555: contents = (MPIAIJ_MPIDense*)C->product->data;
556: VecScatterGetRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL/*bs*/);
557: VecScatterGetRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL/*bs*/);
558: PetscMPIIntCast(nsends,&nsends_mpi);
559: PetscMPIIntCast(nrecvs,&nrecvs_mpi);
560: if (Bbidx == 0) {
561: workB = *outworkB = contents->workB;
562: } else {
563: workB = *outworkB = contents->workB1;
564: }
565: 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);
566: swaits = contents->swaits;
567: rwaits = contents->rwaits;
569: MatDenseGetArrayRead(B,&b);
570: MatDenseGetLDA(B,&blda);
571: if (blda != contents->blda) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Cannot reuse an input matrix with lda %D != %D",blda,contents->blda);
572: MatDenseGetArray(workB,&rvalues);
574: /* Post recv, use MPI derived data type to save memory */
575: PetscObjectGetComm((PetscObject)C,&comm);
576: rtype = contents->rtype;
577: for (i=0; i<nrecvs; i++) {
578: MPI_Irecv(rvalues+(rstarts[i]-rstarts[0]),ncols,rtype[i],rprocs[i],tag,comm,rwaits+i);
579: }
581: stype = contents->stype;
582: for (i=0; i<nsends; i++) {
583: MPI_Isend(b,ncols,stype[i],sprocs[i],tag,comm,swaits+i);
584: }
586: if (nrecvs) {MPI_Waitall(nrecvs_mpi,rwaits,MPI_STATUSES_IGNORE);}
587: if (nsends) {MPI_Waitall(nsends_mpi,swaits,MPI_STATUSES_IGNORE);}
589: VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL);
590: VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL);
591: MatDenseRestoreArrayRead(B,&b);
592: MatDenseRestoreArray(workB,&rvalues);
593: return(0);
594: }
596: static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A,Mat B,Mat C)
597: {
598: PetscErrorCode ierr;
599: Mat_MPIAIJ *aij = (Mat_MPIAIJ*)A->data;
600: Mat_MPIDense *bdense = (Mat_MPIDense*)B->data;
601: Mat_MPIDense *cdense = (Mat_MPIDense*)C->data;
602: Mat workB;
603: MPIAIJ_MPIDense *contents;
606: MatCheckProduct(C,3);
607: if (!C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
608: contents = (MPIAIJ_MPIDense*)C->product->data;
609: /* diagonal block of A times all local rows of B */
610: /* TODO: this calls a symbolic multiplication every time, which could be avoided */
611: MatMatMult(aij->A,bdense->A,MAT_REUSE_MATRIX,PETSC_DEFAULT,&cdense->A);
612: if (contents->workB->cmap->n == B->cmap->N) {
613: /* get off processor parts of B needed to complete C=A*B */
614: MatMPIDenseScatter(A,B,0,C,&workB);
616: /* off-diagonal block of A times nonlocal rows of B */
617: MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A,PETSC_TRUE);
618: } else {
619: Mat Bb,Cb;
620: PetscInt BN=B->cmap->N,n=contents->workB->cmap->n,i;
621: if (n <= 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Column block size %D must be positive",n);
623: for (i=0; i<BN; i+=n) {
624: MatDenseGetSubMatrix(B,i,PetscMin(i+n,BN),&Bb);
625: MatDenseGetSubMatrix(C,i,PetscMin(i+n,BN),&Cb);
627: /* get off processor parts of B needed to complete C=A*B */
628: MatMPIDenseScatter(A,Bb,i+n>BN,C,&workB);
630: /* off-diagonal block of A times nonlocal rows of B */
631: cdense = (Mat_MPIDense*)Cb->data;
632: MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A,PETSC_TRUE);
634: MatDenseRestoreSubMatrix(B,&Bb);
635: MatDenseRestoreSubMatrix(C,&Cb);
636: }
637: }
638: return(0);
639: }
641: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
642: {
643: PetscErrorCode ierr;
644: Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
645: Mat_SeqAIJ *ad = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
646: Mat_SeqAIJ *cd = (Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
647: PetscInt *adi = ad->i,*adj,*aoi=ao->i,*aoj;
648: PetscScalar *ada,*aoa,*cda=cd->a,*coa=co->a;
649: Mat_SeqAIJ *p_loc,*p_oth;
650: PetscInt *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pj;
651: PetscScalar *pa_loc,*pa_oth,*pa,valtmp,*ca;
652: PetscInt cm = C->rmap->n,anz,pnz;
653: Mat_APMPI *ptap;
654: PetscScalar *apa_sparse;
655: const PetscScalar *dummy;
656: PetscInt *api,*apj,*apJ,i,j,k,row;
657: PetscInt cstart = C->cmap->rstart;
658: PetscInt cdnz,conz,k0,k1,nextp;
659: MPI_Comm comm;
660: PetscMPIInt size;
663: MatCheckProduct(C,3);
664: ptap = (Mat_APMPI*)C->product->data;
665: if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
666: PetscObjectGetComm((PetscObject)C,&comm);
667: MPI_Comm_size(comm,&size);
668: if (!ptap->P_oth && size>1) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"AP cannot be reused. Do not call MatProductClear()");
670: /* flag CPU mask for C */
671: #if defined(PETSC_HAVE_DEVICE)
672: if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
673: if (c->A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->A->offloadmask = PETSC_OFFLOAD_CPU;
674: if (c->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->B->offloadmask = PETSC_OFFLOAD_CPU;
675: #endif
676: apa_sparse = ptap->apa;
678: /* 1) get P_oth = ptap->P_oth and P_loc = ptap->P_loc */
679: /*-----------------------------------------------------*/
680: /* update numerical values of P_oth and P_loc */
681: MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
682: MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);
684: /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
685: /*----------------------------------------------------------*/
686: /* get data from symbolic products */
687: p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
688: pi_loc = p_loc->i; pj_loc = p_loc->j; pa_loc = p_loc->a;
689: if (size >1) {
690: p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
691: pi_oth = p_oth->i; pj_oth = p_oth->j; pa_oth = p_oth->a;
692: } else {
693: p_oth = NULL; pi_oth = NULL; pj_oth = NULL; pa_oth = NULL;
694: }
696: /* trigger copy to CPU */
697: MatSeqAIJGetArrayRead(a->A,&dummy);
698: MatSeqAIJRestoreArrayRead(a->A,&dummy);
699: MatSeqAIJGetArrayRead(a->B,&dummy);
700: MatSeqAIJRestoreArrayRead(a->B,&dummy);
701: api = ptap->api;
702: apj = ptap->apj;
703: for (i=0; i<cm; i++) {
704: apJ = apj + api[i];
706: /* diagonal portion of A */
707: anz = adi[i+1] - adi[i];
708: adj = ad->j + adi[i];
709: ada = ad->a + adi[i];
710: for (j=0; j<anz; j++) {
711: row = adj[j];
712: pnz = pi_loc[row+1] - pi_loc[row];
713: pj = pj_loc + pi_loc[row];
714: pa = pa_loc + pi_loc[row];
715: /* perform sparse axpy */
716: valtmp = ada[j];
717: nextp = 0;
718: for (k=0; nextp<pnz; k++) {
719: if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
720: apa_sparse[k] += valtmp*pa[nextp++];
721: }
722: }
723: PetscLogFlops(2.0*pnz);
724: }
726: /* off-diagonal portion of A */
727: anz = aoi[i+1] - aoi[i];
728: aoj = ao->j + aoi[i];
729: aoa = ao->a + aoi[i];
730: for (j=0; j<anz; j++) {
731: row = aoj[j];
732: pnz = pi_oth[row+1] - pi_oth[row];
733: pj = pj_oth + pi_oth[row];
734: pa = pa_oth + pi_oth[row];
735: /* perform sparse axpy */
736: valtmp = aoa[j];
737: nextp = 0;
738: for (k=0; nextp<pnz; k++) {
739: if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
740: apa_sparse[k] += valtmp*pa[nextp++];
741: }
742: }
743: PetscLogFlops(2.0*pnz);
744: }
746: /* set values in C */
747: cdnz = cd->i[i+1] - cd->i[i];
748: conz = co->i[i+1] - co->i[i];
750: /* 1st off-diagonal part of C */
751: ca = coa + co->i[i];
752: k = 0;
753: for (k0=0; k0<conz; k0++) {
754: if (apJ[k] >= cstart) break;
755: ca[k0] = apa_sparse[k];
756: apa_sparse[k] = 0.0;
757: k++;
758: }
760: /* diagonal part of C */
761: ca = cda + cd->i[i];
762: for (k1=0; k1<cdnz; k1++) {
763: ca[k1] = apa_sparse[k];
764: apa_sparse[k] = 0.0;
765: k++;
766: }
768: /* 2nd off-diagonal part of C */
769: ca = coa + co->i[i];
770: for (; k0<conz; k0++) {
771: ca[k0] = apa_sparse[k];
772: apa_sparse[k] = 0.0;
773: k++;
774: }
775: }
776: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
777: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
778: return(0);
779: }
781: /* same as MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(), except using LLCondensed to avoid O(BN) memory requirement */
782: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat C)
783: {
784: PetscErrorCode ierr;
785: MPI_Comm comm;
786: PetscMPIInt size;
787: Mat_APMPI *ptap;
788: PetscFreeSpaceList free_space = NULL,current_space=NULL;
789: Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
790: Mat_SeqAIJ *ad = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
791: PetscInt *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
792: PetscInt *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
793: PetscInt i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi,*lnk,apnz_max=1;
794: PetscInt am=A->rmap->n,pn=P->cmap->n,pm=P->rmap->n,lsize=pn+20;
795: PetscReal afill;
796: MatType mtype;
799: MatCheckProduct(C,4);
800: if (C->product->data) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
801: PetscObjectGetComm((PetscObject)A,&comm);
802: MPI_Comm_size(comm,&size);
804: /* create struct Mat_APMPI and attached it to C later */
805: PetscNew(&ptap);
807: /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
808: MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
810: /* get P_loc by taking all local rows of P */
811: MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);
813: p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
814: pi_loc = p_loc->i; pj_loc = p_loc->j;
815: if (size > 1) {
816: p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
817: pi_oth = p_oth->i; pj_oth = p_oth->j;
818: } else {
819: p_oth = NULL;
820: pi_oth = NULL; pj_oth = NULL;
821: }
823: /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
824: /*-------------------------------------------------------------------*/
825: PetscMalloc1(am+2,&api);
826: ptap->api = api;
827: api[0] = 0;
829: PetscLLCondensedCreate_Scalable(lsize,&lnk);
831: /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
832: PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space);
833: current_space = free_space;
834: MatPreallocateInitialize(comm,am,pn,dnz,onz);
835: for (i=0; i<am; i++) {
836: /* diagonal portion of A */
837: nzi = adi[i+1] - adi[i];
838: for (j=0; j<nzi; j++) {
839: row = *adj++;
840: pnz = pi_loc[row+1] - pi_loc[row];
841: Jptr = pj_loc + pi_loc[row];
842: /* Expand list if it is not long enough */
843: if (pnz+apnz_max > lsize) {
844: lsize = pnz+apnz_max;
845: PetscLLCondensedExpand_Scalable(lsize, &lnk);
846: }
847: /* add non-zero cols of P into the sorted linked list lnk */
848: PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);
849: apnz = *lnk; /* The first element in the list is the number of items in the list */
850: api[i+1] = api[i] + apnz;
851: if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
852: }
853: /* off-diagonal portion of A */
854: nzi = aoi[i+1] - aoi[i];
855: for (j=0; j<nzi; j++) {
856: row = *aoj++;
857: pnz = pi_oth[row+1] - pi_oth[row];
858: Jptr = pj_oth + pi_oth[row];
859: /* Expand list if it is not long enough */
860: if (pnz+apnz_max > lsize) {
861: lsize = pnz + apnz_max;
862: PetscLLCondensedExpand_Scalable(lsize, &lnk);
863: }
864: /* add non-zero cols of P into the sorted linked list lnk */
865: PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);
866: apnz = *lnk; /* The first element in the list is the number of items in the list */
867: api[i+1] = api[i] + apnz;
868: if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
869: }
871: /* add missing diagonal entry */
872: if (C->force_diagonals) {
873: j = i + rstart; /* column index */
874: PetscLLCondensedAddSorted_Scalable(1,&j,lnk);
875: }
877: apnz = *lnk;
878: api[i+1] = api[i] + apnz;
879: if (apnz > apnz_max) apnz_max = apnz;
881: /* if free space is not available, double the total space in the list */
882: if (current_space->local_remaining<apnz) {
883: PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),¤t_space);
884: nspacedouble++;
885: }
887: /* Copy data into free space, then initialize lnk */
888: PetscLLCondensedClean_Scalable(apnz,current_space->array,lnk);
889: MatPreallocateSet(i+rstart,apnz,current_space->array,dnz,onz);
891: current_space->array += apnz;
892: current_space->local_used += apnz;
893: current_space->local_remaining -= apnz;
894: }
896: /* Allocate space for apj, initialize apj, and */
897: /* destroy list of free space and other temporary array(s) */
898: PetscMalloc1(api[am]+1,&ptap->apj);
899: apj = ptap->apj;
900: PetscFreeSpaceContiguous(&free_space,ptap->apj);
901: PetscLLCondensedDestroy_Scalable(lnk);
903: /* create and assemble symbolic parallel matrix C */
904: /*----------------------------------------------------*/
905: MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
906: MatSetBlockSizesFromMats(C,A,P);
907: MatGetType(A,&mtype);
908: MatSetType(C,mtype);
909: MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
910: MatPreallocateFinalize(dnz,onz);
912: /* malloc apa for assembly C */
913: PetscCalloc1(apnz_max,&ptap->apa);
915: MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);
916: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
917: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
918: MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
920: C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
921: C->ops->productnumeric = MatProductNumeric_AB;
923: /* attach the supporting struct to C for reuse */
924: C->product->data = ptap;
925: C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;
927: /* set MatInfo */
928: afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
929: if (afill < 1.0) afill = 1.0;
930: C->info.mallocs = nspacedouble;
931: C->info.fill_ratio_given = fill;
932: C->info.fill_ratio_needed = afill;
934: #if defined(PETSC_USE_INFO)
935: if (api[am]) {
936: PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
937: PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
938: } else {
939: PetscInfo(C,"Empty matrix product\n");
940: }
941: #endif
942: return(0);
943: }
945: /* This function is needed for the seqMPI matrix-matrix multiplication. */
946: /* Three input arrays are merged to one output array. The size of the */
947: /* output array is also output. Duplicate entries only show up once. */
948: static void Merge3SortedArrays(PetscInt size1, PetscInt *in1,
949: PetscInt size2, PetscInt *in2,
950: PetscInt size3, PetscInt *in3,
951: PetscInt *size4, PetscInt *out)
952: {
953: int i = 0, j = 0, k = 0, l = 0;
955: /* Traverse all three arrays */
956: while (i<size1 && j<size2 && k<size3) {
957: if (in1[i] < in2[j] && in1[i] < in3[k]) {
958: out[l++] = in1[i++];
959: }
960: else if (in2[j] < in1[i] && in2[j] < in3[k]) {
961: out[l++] = in2[j++];
962: }
963: else if (in3[k] < in1[i] && in3[k] < in2[j]) {
964: out[l++] = in3[k++];
965: }
966: else if (in1[i] == in2[j] && in1[i] < in3[k]) {
967: out[l++] = in1[i];
968: i++, j++;
969: }
970: else if (in1[i] == in3[k] && in1[i] < in2[j]) {
971: out[l++] = in1[i];
972: i++, k++;
973: }
974: else if (in3[k] == in2[j] && in2[j] < in1[i]) {
975: out[l++] = in2[j];
976: k++, j++;
977: }
978: else if (in1[i] == in2[j] && in1[i] == in3[k]) {
979: out[l++] = in1[i];
980: i++, j++, k++;
981: }
982: }
984: /* Traverse two remaining arrays */
985: while (i<size1 && j<size2) {
986: if (in1[i] < in2[j]) {
987: out[l++] = in1[i++];
988: }
989: else if (in1[i] > in2[j]) {
990: out[l++] = in2[j++];
991: }
992: else {
993: out[l++] = in1[i];
994: i++, j++;
995: }
996: }
998: while (i<size1 && k<size3) {
999: if (in1[i] < in3[k]) {
1000: out[l++] = in1[i++];
1001: }
1002: else if (in1[i] > in3[k]) {
1003: out[l++] = in3[k++];
1004: }
1005: else {
1006: out[l++] = in1[i];
1007: i++, k++;
1008: }
1009: }
1011: while (k<size3 && j<size2) {
1012: if (in3[k] < in2[j]) {
1013: out[l++] = in3[k++];
1014: }
1015: else if (in3[k] > in2[j]) {
1016: out[l++] = in2[j++];
1017: }
1018: else {
1019: out[l++] = in3[k];
1020: k++, j++;
1021: }
1022: }
1024: /* Traverse one remaining array */
1025: while (i<size1) out[l++] = in1[i++];
1026: while (j<size2) out[l++] = in2[j++];
1027: while (k<size3) out[l++] = in3[k++];
1029: *size4 = l;
1030: }
1032: /* This matrix-matrix multiplication algorithm divides the multiplication into three multiplications and */
1033: /* adds up the products. Two of these three multiplications are performed with existing (sequential) */
1034: /* matrix-matrix multiplications. */
1035: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(Mat A, Mat P, PetscReal fill, Mat C)
1036: {
1037: PetscErrorCode ierr;
1038: MPI_Comm comm;
1039: PetscMPIInt size;
1040: Mat_APMPI *ptap;
1041: PetscFreeSpaceList free_space_diag=NULL, current_space=NULL;
1042: Mat_MPIAIJ *a =(Mat_MPIAIJ*)A->data;
1043: Mat_SeqAIJ *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc;
1044: Mat_MPIAIJ *p =(Mat_MPIAIJ*)P->data;
1045: Mat_SeqAIJ *adpd_seq, *p_off, *aopoth_seq;
1046: PetscInt adponz, adpdnz;
1047: PetscInt *pi_loc,*dnz,*onz;
1048: PetscInt *adi=ad->i,*adj=ad->j,*aoi=ao->i,rstart=A->rmap->rstart;
1049: PetscInt *lnk,i, i1=0,pnz,row,*adpoi,*adpoj, *api, *adpoJ, *aopJ, *apJ,*Jptr, aopnz, nspacedouble=0,j,nzi,
1050: *apj,apnz, *adpdi, *adpdj, *adpdJ, *poff_i, *poff_j, *j_temp, *aopothi, *aopothj;
1051: PetscInt am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n, p_colstart, p_colend;
1052: PetscBT lnkbt;
1053: PetscReal afill;
1054: PetscMPIInt rank;
1055: Mat adpd, aopoth;
1056: MatType mtype;
1057: const char *prefix;
1060: MatCheckProduct(C,4);
1061: if (C->product->data) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
1062: PetscObjectGetComm((PetscObject)A,&comm);
1063: MPI_Comm_size(comm,&size);
1064: MPI_Comm_rank(comm, &rank);
1065: MatGetOwnershipRangeColumn(P, &p_colstart, &p_colend);
1067: /* create struct Mat_APMPI and attached it to C later */
1068: PetscNew(&ptap);
1070: /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
1071: MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
1073: /* get P_loc by taking all local rows of P */
1074: MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);
1076: p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
1077: pi_loc = p_loc->i;
1079: /* Allocate memory for the i arrays of the matrices A*P, A_diag*P_off and A_offd * P */
1080: PetscMalloc1(am+2,&api);
1081: PetscMalloc1(am+2,&adpoi);
1083: adpoi[0] = 0;
1084: ptap->api = api;
1085: api[0] = 0;
1087: /* create and initialize a linked list, will be used for both A_diag * P_loc_off and A_offd * P_oth */
1088: PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);
1089: MatPreallocateInitialize(comm,am,pn,dnz,onz);
1091: /* Symbolic calc of A_loc_diag * P_loc_diag */
1092: MatGetOptionsPrefix(A,&prefix);
1093: MatProductCreate(a->A,p->A,NULL,&adpd);
1094: MatGetOptionsPrefix(A,&prefix);
1095: MatSetOptionsPrefix(adpd,prefix);
1096: MatAppendOptionsPrefix(adpd,"inner_diag_");
1098: MatProductSetType(adpd,MATPRODUCT_AB);
1099: MatProductSetAlgorithm(adpd,"sorted");
1100: MatProductSetFill(adpd,fill);
1101: MatProductSetFromOptions(adpd);
1103: adpd->force_diagonals = C->force_diagonals;
1104: MatProductSymbolic(adpd);
1106: adpd_seq = (Mat_SeqAIJ*)((adpd)->data);
1107: adpdi = adpd_seq->i; adpdj = adpd_seq->j;
1108: p_off = (Mat_SeqAIJ*)((p->B)->data);
1109: poff_i = p_off->i; poff_j = p_off->j;
1111: /* j_temp stores indices of a result row before they are added to the linked list */
1112: PetscMalloc1(pN+2,&j_temp);
1114: /* Symbolic calc of the A_diag * p_loc_off */
1115: /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
1116: PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space_diag);
1117: current_space = free_space_diag;
1119: for (i=0; i<am; i++) {
1120: /* A_diag * P_loc_off */
1121: nzi = adi[i+1] - adi[i];
1122: for (j=0; j<nzi; j++) {
1123: row = *adj++;
1124: pnz = poff_i[row+1] - poff_i[row];
1125: Jptr = poff_j + poff_i[row];
1126: for (i1 = 0; i1 < pnz; i1++) {
1127: j_temp[i1] = p->garray[Jptr[i1]];
1128: }
1129: /* add non-zero cols of P into the sorted linked list lnk */
1130: PetscLLCondensedAddSorted(pnz,j_temp,lnk,lnkbt);
1131: }
1133: adponz = lnk[0];
1134: adpoi[i+1] = adpoi[i] + adponz;
1136: /* if free space is not available, double the total space in the list */
1137: if (current_space->local_remaining<adponz) {
1138: PetscFreeSpaceGet(PetscIntSumTruncate(adponz,current_space->total_array_size),¤t_space);
1139: nspacedouble++;
1140: }
1142: /* Copy data into free space, then initialize lnk */
1143: PetscLLCondensedClean(pN,adponz,current_space->array,lnk,lnkbt);
1145: current_space->array += adponz;
1146: current_space->local_used += adponz;
1147: current_space->local_remaining -= adponz;
1148: }
1150: /* Symbolic calc of A_off * P_oth */
1151: MatSetOptionsPrefix(a->B,prefix);
1152: MatAppendOptionsPrefix(a->B,"inner_offdiag_");
1153: MatCreate(PETSC_COMM_SELF,&aopoth);
1154: MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, aopoth);
1155: aopoth_seq = (Mat_SeqAIJ*)((aopoth)->data);
1156: aopothi = aopoth_seq->i; aopothj = aopoth_seq->j;
1158: /* Allocate space for apj, adpj, aopj, ... */
1159: /* destroy lists of free space and other temporary array(s) */
1161: PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am]+2, &ptap->apj);
1162: PetscMalloc1(adpoi[am]+2, &adpoj);
1164: /* Copy from linked list to j-array */
1165: PetscFreeSpaceContiguous(&free_space_diag,adpoj);
1166: PetscLLDestroy(lnk,lnkbt);
1168: adpoJ = adpoj;
1169: adpdJ = adpdj;
1170: aopJ = aopothj;
1171: apj = ptap->apj;
1172: apJ = apj; /* still empty */
1174: /* Merge j-arrays of A_off * P, A_diag * P_loc_off, and */
1175: /* A_diag * P_loc_diag to get A*P */
1176: for (i = 0; i < am; i++) {
1177: aopnz = aopothi[i+1] - aopothi[i];
1178: adponz = adpoi[i+1] - adpoi[i];
1179: adpdnz = adpdi[i+1] - adpdi[i];
1181: /* Correct indices from A_diag*P_diag */
1182: for (i1 = 0; i1 < adpdnz; i1++) {
1183: adpdJ[i1] += p_colstart;
1184: }
1185: /* Merge j-arrays of A_diag * P_loc_off and A_diag * P_loc_diag and A_off * P_oth */
1186: Merge3SortedArrays(adponz, adpoJ, adpdnz, adpdJ, aopnz, aopJ, &apnz, apJ);
1187: MatPreallocateSet(i+rstart, apnz, apJ, dnz, onz);
1189: aopJ += aopnz;
1190: adpoJ += adponz;
1191: adpdJ += adpdnz;
1192: apJ += apnz;
1193: api[i+1] = api[i] + apnz;
1194: }
1196: /* malloc apa to store dense row A[i,:]*P */
1197: PetscCalloc1(pN+2,&ptap->apa);
1199: /* create and assemble symbolic parallel matrix C */
1200: MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
1201: MatSetBlockSizesFromMats(C,A,P);
1202: MatGetType(A,&mtype);
1203: MatSetType(C,mtype);
1204: MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
1205: MatPreallocateFinalize(dnz,onz);
1207: MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);
1208: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1209: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
1210: MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
1212: C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1213: C->ops->productnumeric = MatProductNumeric_AB;
1215: /* attach the supporting struct to C for reuse */
1216: C->product->data = ptap;
1217: C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;
1219: /* set MatInfo */
1220: afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
1221: if (afill < 1.0) afill = 1.0;
1222: C->info.mallocs = nspacedouble;
1223: C->info.fill_ratio_given = fill;
1224: C->info.fill_ratio_needed = afill;
1226: #if defined(PETSC_USE_INFO)
1227: if (api[am]) {
1228: PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
1229: PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
1230: } else {
1231: PetscInfo(C,"Empty matrix product\n");
1232: }
1233: #endif
1235: MatDestroy(&aopoth);
1236: MatDestroy(&adpd);
1237: PetscFree(j_temp);
1238: PetscFree(adpoj);
1239: PetscFree(adpoi);
1240: return(0);
1241: }
1243: /*-------------------------------------------------------------------------*/
1244: /* This routine only works when scall=MAT_REUSE_MATRIX! */
1245: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P,Mat A,Mat C)
1246: {
1248: Mat_APMPI *ptap;
1249: Mat Pt;
1252: MatCheckProduct(C,3);
1253: ptap = (Mat_APMPI*)C->product->data;
1254: if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1255: if (!ptap->Pt) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
1257: Pt = ptap->Pt;
1258: MatTranspose(P,MAT_REUSE_MATRIX,&Pt);
1259: MatMatMultNumeric_MPIAIJ_MPIAIJ(Pt,A,C);
1260: return(0);
1261: }
1263: /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
1264: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,PetscReal fill,Mat C)
1265: {
1266: PetscErrorCode ierr;
1267: Mat_APMPI *ptap;
1268: Mat_MPIAIJ *p=(Mat_MPIAIJ*)P->data;
1269: MPI_Comm comm;
1270: PetscMPIInt size,rank;
1271: PetscFreeSpaceList free_space=NULL,current_space=NULL;
1272: PetscInt pn=P->cmap->n,aN=A->cmap->N,an=A->cmap->n;
1273: PetscInt *lnk,i,k,nsend,rstart;
1274: PetscBT lnkbt;
1275: PetscMPIInt tagi,tagj,*len_si,*len_s,*len_ri,nrecv;
1276: PETSC_UNUSED PetscMPIInt icompleted=0;
1277: PetscInt **buf_rj,**buf_ri,**buf_ri_k,row,ncols,*cols;
1278: PetscInt len,proc,*dnz,*onz,*owners,nzi;
1279: PetscInt nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1280: MPI_Request *swaits,*rwaits;
1281: MPI_Status *sstatus,rstatus;
1282: PetscLayout rowmap;
1283: PetscInt *owners_co,*coi,*coj; /* i and j array of (p->B)^T*A*P - used in the communication */
1284: PetscMPIInt *len_r,*id_r; /* array of length of comm->size, store send/recv matrix values */
1285: PetscInt *Jptr,*prmap=p->garray,con,j,Crmax;
1286: Mat_SeqAIJ *a_loc,*c_loc,*c_oth;
1287: PetscTable ta;
1288: MatType mtype;
1289: const char *prefix;
1292: PetscObjectGetComm((PetscObject)A,&comm);
1293: MPI_Comm_size(comm,&size);
1294: MPI_Comm_rank(comm,&rank);
1296: /* create symbolic parallel matrix C */
1297: MatGetType(A,&mtype);
1298: MatSetType(C,mtype);
1300: C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1302: /* create struct Mat_APMPI and attached it to C later */
1303: PetscNew(&ptap);
1304: ptap->reuse = MAT_INITIAL_MATRIX;
1306: /* (0) compute Rd = Pd^T, Ro = Po^T */
1307: /* --------------------------------- */
1308: MatTranspose_SeqAIJ(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);
1309: MatTranspose_SeqAIJ(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);
1311: /* (1) compute symbolic A_loc */
1312: /* ---------------------------*/
1313: MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&ptap->A_loc);
1315: /* (2-1) compute symbolic C_oth = Ro*A_loc */
1316: /* ------------------------------------ */
1317: MatGetOptionsPrefix(A,&prefix);
1318: MatSetOptionsPrefix(ptap->Ro,prefix);
1319: MatAppendOptionsPrefix(ptap->Ro,"inner_offdiag_");
1320: MatCreate(PETSC_COMM_SELF,&ptap->C_oth);
1321: MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->A_loc,fill,ptap->C_oth);
1323: /* (3) send coj of C_oth to other processors */
1324: /* ------------------------------------------ */
1325: /* determine row ownership */
1326: PetscLayoutCreate(comm,&rowmap);
1327: rowmap->n = pn;
1328: rowmap->bs = 1;
1329: PetscLayoutSetUp(rowmap);
1330: owners = rowmap->range;
1332: /* determine the number of messages to send, their lengths */
1333: PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);
1334: PetscArrayzero(len_s,size);
1335: PetscArrayzero(len_si,size);
1337: c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
1338: coi = c_oth->i; coj = c_oth->j;
1339: con = ptap->C_oth->rmap->n;
1340: proc = 0;
1341: for (i=0; i<con; i++) {
1342: while (prmap[i] >= owners[proc+1]) proc++;
1343: len_si[proc]++; /* num of rows in Co(=Pt*A) to be sent to [proc] */
1344: len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
1345: }
1347: len = 0; /* max length of buf_si[], see (4) */
1348: owners_co[0] = 0;
1349: nsend = 0;
1350: for (proc=0; proc<size; proc++) {
1351: owners_co[proc+1] = owners_co[proc] + len_si[proc];
1352: if (len_s[proc]) {
1353: nsend++;
1354: len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
1355: len += len_si[proc];
1356: }
1357: }
1359: /* determine the number and length of messages to receive for coi and coj */
1360: PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);
1361: PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);
1363: /* post the Irecv and Isend of coj */
1364: PetscCommGetNewTag(comm,&tagj);
1365: PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);
1366: PetscMalloc1(nsend+1,&swaits);
1367: for (proc=0, k=0; proc<size; proc++) {
1368: if (!len_s[proc]) continue;
1369: i = owners_co[proc];
1370: MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);
1371: k++;
1372: }
1374: /* (2-2) compute symbolic C_loc = Rd*A_loc */
1375: /* ---------------------------------------- */
1376: MatSetOptionsPrefix(ptap->Rd,prefix);
1377: MatAppendOptionsPrefix(ptap->Rd,"inner_diag_");
1378: MatCreate(PETSC_COMM_SELF,&ptap->C_loc);
1379: MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->A_loc,fill,ptap->C_loc);
1380: c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;
1382: /* receives coj are complete */
1383: for (i=0; i<nrecv; i++) {
1384: MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);
1385: }
1386: PetscFree(rwaits);
1387: if (nsend) {MPI_Waitall(nsend,swaits,sstatus);}
1389: /* add received column indices into ta to update Crmax */
1390: a_loc = (Mat_SeqAIJ*)(ptap->A_loc)->data;
1392: /* create and initialize a linked list */
1393: PetscTableCreate(an,aN,&ta); /* for compute Crmax */
1394: MatRowMergeMax_SeqAIJ(a_loc,ptap->A_loc->rmap->N,ta);
1396: for (k=0; k<nrecv; k++) {/* k-th received message */
1397: Jptr = buf_rj[k];
1398: for (j=0; j<len_r[k]; j++) {
1399: PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);
1400: }
1401: }
1402: PetscTableGetCount(ta,&Crmax);
1403: PetscTableDestroy(&ta);
1405: /* (4) send and recv coi */
1406: /*-----------------------*/
1407: PetscCommGetNewTag(comm,&tagi);
1408: PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);
1409: PetscMalloc1(len+1,&buf_s);
1410: buf_si = buf_s; /* points to the beginning of k-th msg to be sent */
1411: for (proc=0,k=0; proc<size; proc++) {
1412: if (!len_s[proc]) continue;
1413: /* form outgoing message for i-structure:
1414: buf_si[0]: nrows to be sent
1415: [1:nrows]: row index (global)
1416: [nrows+1:2*nrows+1]: i-structure index
1417: */
1418: /*-------------------------------------------*/
1419: nrows = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
1420: buf_si_i = buf_si + nrows+1;
1421: buf_si[0] = nrows;
1422: buf_si_i[0] = 0;
1423: nrows = 0;
1424: for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
1425: nzi = coi[i+1] - coi[i];
1426: buf_si_i[nrows+1] = buf_si_i[nrows] + nzi; /* i-structure */
1427: buf_si[nrows+1] = prmap[i] -owners[proc]; /* local row index */
1428: nrows++;
1429: }
1430: MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);
1431: k++;
1432: buf_si += len_si[proc];
1433: }
1434: for (i=0; i<nrecv; i++) {
1435: MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);
1436: }
1437: PetscFree(rwaits);
1438: if (nsend) {MPI_Waitall(nsend,swaits,sstatus);}
1440: PetscFree4(len_s,len_si,sstatus,owners_co);
1441: PetscFree(len_ri);
1442: PetscFree(swaits);
1443: PetscFree(buf_s);
1445: /* (5) compute the local portion of C */
1446: /* ------------------------------------------ */
1447: /* set initial free space to be Crmax, sufficient for holding nozeros in each row of C */
1448: PetscFreeSpaceGet(Crmax,&free_space);
1449: current_space = free_space;
1451: PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);
1452: for (k=0; k<nrecv; k++) {
1453: buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1454: nrows = *buf_ri_k[k];
1455: nextrow[k] = buf_ri_k[k] + 1; /* next row number of k-th recved i-structure */
1456: nextci[k] = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure */
1457: }
1459: MatPreallocateInitialize(comm,pn,an,dnz,onz);
1460: PetscLLCondensedCreate(Crmax,aN,&lnk,&lnkbt);
1461: for (i=0; i<pn; i++) { /* for each local row of C */
1462: /* add C_loc into C */
1463: nzi = c_loc->i[i+1] - c_loc->i[i];
1464: Jptr = c_loc->j + c_loc->i[i];
1465: PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);
1467: /* add received col data into lnk */
1468: for (k=0; k<nrecv; k++) { /* k-th received message */
1469: if (i == *nextrow[k]) { /* i-th row */
1470: nzi = *(nextci[k]+1) - *nextci[k];
1471: Jptr = buf_rj[k] + *nextci[k];
1472: PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);
1473: nextrow[k]++; nextci[k]++;
1474: }
1475: }
1477: /* add missing diagonal entry */
1478: if (C->force_diagonals) {
1479: k = i + owners[rank]; /* column index */
1480: PetscLLCondensedAddSorted(1,&k,lnk,lnkbt);
1481: }
1483: nzi = lnk[0];
1485: /* copy data into free space, then initialize lnk */
1486: PetscLLCondensedClean(aN,nzi,current_space->array,lnk,lnkbt);
1487: MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);
1488: }
1489: PetscFree3(buf_ri_k,nextrow,nextci);
1490: PetscLLDestroy(lnk,lnkbt);
1491: PetscFreeSpaceDestroy(free_space);
1493: /* local sizes and preallocation */
1494: MatSetSizes(C,pn,an,PETSC_DETERMINE,PETSC_DETERMINE);
1495: if (P->cmap->bs > 0) {PetscLayoutSetBlockSize(C->rmap,P->cmap->bs);}
1496: if (A->cmap->bs > 0) {PetscLayoutSetBlockSize(C->cmap,A->cmap->bs);}
1497: MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
1498: MatPreallocateFinalize(dnz,onz);
1500: /* add C_loc and C_oth to C */
1501: MatGetOwnershipRange(C,&rstart,NULL);
1502: for (i=0; i<pn; i++) {
1503: ncols = c_loc->i[i+1] - c_loc->i[i];
1504: cols = c_loc->j + c_loc->i[i];
1505: row = rstart + i;
1506: MatSetValues(C,1,(const PetscInt*)&row,ncols,(const PetscInt*)cols,NULL,INSERT_VALUES);
1508: if (C->force_diagonals) {
1509: MatSetValues(C,1,(const PetscInt*)&row,1,(const PetscInt*)&row,NULL,INSERT_VALUES);
1510: }
1511: }
1512: for (i=0; i<con; i++) {
1513: ncols = c_oth->i[i+1] - c_oth->i[i];
1514: cols = c_oth->j + c_oth->i[i];
1515: row = prmap[i];
1516: MatSetValues(C,1,(const PetscInt*)&row,ncols,(const PetscInt*)cols,NULL,INSERT_VALUES);
1517: }
1518: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1519: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
1520: MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
1522: /* members in merge */
1523: PetscFree(id_r);
1524: PetscFree(len_r);
1525: PetscFree(buf_ri[0]);
1526: PetscFree(buf_ri);
1527: PetscFree(buf_rj[0]);
1528: PetscFree(buf_rj);
1529: PetscLayoutDestroy(&rowmap);
1531: /* attach the supporting struct to C for reuse */
1532: C->product->data = ptap;
1533: C->product->destroy = MatDestroy_MPIAIJ_PtAP;
1534: return(0);
1535: }
1537: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,Mat C)
1538: {
1539: PetscErrorCode ierr;
1540: Mat_MPIAIJ *p=(Mat_MPIAIJ*)P->data;
1541: Mat_SeqAIJ *c_seq;
1542: Mat_APMPI *ptap;
1543: Mat A_loc,C_loc,C_oth;
1544: PetscInt i,rstart,rend,cm,ncols,row;
1545: const PetscInt *cols;
1546: const PetscScalar *vals;
1549: MatCheckProduct(C,3);
1550: ptap = (Mat_APMPI*)C->product->data;
1551: if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1552: if (!ptap->A_loc) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
1553: MatZeroEntries(C);
1555: if (ptap->reuse == MAT_REUSE_MATRIX) {
1556: /* These matrices are obtained in MatTransposeMatMultSymbolic() */
1557: /* 1) get R = Pd^T, Ro = Po^T */
1558: /*----------------------------*/
1559: MatTranspose_SeqAIJ(p->A,MAT_REUSE_MATRIX,&ptap->Rd);
1560: MatTranspose_SeqAIJ(p->B,MAT_REUSE_MATRIX,&ptap->Ro);
1562: /* 2) compute numeric A_loc */
1563: /*--------------------------*/
1564: MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&ptap->A_loc);
1565: }
1567: /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */
1568: A_loc = ptap->A_loc;
1569: ((ptap->C_loc)->ops->matmultnumeric)(ptap->Rd,A_loc,ptap->C_loc);
1570: ((ptap->C_oth)->ops->matmultnumeric)(ptap->Ro,A_loc,ptap->C_oth);
1571: C_loc = ptap->C_loc;
1572: C_oth = ptap->C_oth;
1574: /* add C_loc and C_oth to C */
1575: MatGetOwnershipRange(C,&rstart,&rend);
1577: /* C_loc -> C */
1578: cm = C_loc->rmap->N;
1579: c_seq = (Mat_SeqAIJ*)C_loc->data;
1580: cols = c_seq->j;
1581: vals = c_seq->a;
1582: for (i=0; i<cm; i++) {
1583: ncols = c_seq->i[i+1] - c_seq->i[i];
1584: row = rstart + i;
1585: MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);
1586: cols += ncols; vals += ncols;
1587: }
1589: /* Co -> C, off-processor part */
1590: cm = C_oth->rmap->N;
1591: c_seq = (Mat_SeqAIJ*)C_oth->data;
1592: cols = c_seq->j;
1593: vals = c_seq->a;
1594: for (i=0; i<cm; i++) {
1595: ncols = c_seq->i[i+1] - c_seq->i[i];
1596: row = p->garray[i];
1597: MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);
1598: cols += ncols; vals += ncols;
1599: }
1600: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1601: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
1602: MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
1604: ptap->reuse = MAT_REUSE_MATRIX;
1605: return(0);
1606: }
1608: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P,Mat A,Mat C)
1609: {
1610: PetscErrorCode ierr;
1611: Mat_Merge_SeqsToMPI *merge;
1612: Mat_MPIAIJ *p =(Mat_MPIAIJ*)P->data;
1613: Mat_SeqAIJ *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
1614: Mat_APMPI *ptap;
1615: PetscInt *adj;
1616: PetscInt i,j,k,anz,pnz,row,*cj,nexta;
1617: MatScalar *ada,*ca,valtmp;
1618: PetscInt am=A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
1619: MPI_Comm comm;
1620: PetscMPIInt size,rank,taga,*len_s;
1621: PetscInt *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
1622: PetscInt **buf_ri,**buf_rj;
1623: PetscInt cnz=0,*bj_i,*bi,*bj,bnz,nextcj; /* bi,bj,ba: local array of C(mpi mat) */
1624: MPI_Request *s_waits,*r_waits;
1625: MPI_Status *status;
1626: MatScalar **abuf_r,*ba_i,*pA,*coa,*ba;
1627: const PetscScalar *dummy;
1628: PetscInt *ai,*aj,*coi,*coj,*poJ,*pdJ;
1629: Mat A_loc;
1630: Mat_SeqAIJ *a_loc;
1633: MatCheckProduct(C,3);
1634: ptap = (Mat_APMPI*)C->product->data;
1635: if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1636: if (!ptap->A_loc) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
1637: PetscObjectGetComm((PetscObject)C,&comm);
1638: MPI_Comm_size(comm,&size);
1639: MPI_Comm_rank(comm,&rank);
1641: merge = ptap->merge;
1643: /* 2) compute numeric C_seq = P_loc^T*A_loc */
1644: /*------------------------------------------*/
1645: /* get data from symbolic products */
1646: coi = merge->coi; coj = merge->coj;
1647: PetscCalloc1(coi[pon]+1,&coa);
1648: bi = merge->bi; bj = merge->bj;
1649: owners = merge->rowmap->range;
1650: PetscCalloc1(bi[cm]+1,&ba);
1652: /* get A_loc by taking all local rows of A */
1653: A_loc = ptap->A_loc;
1654: MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&A_loc);
1655: a_loc = (Mat_SeqAIJ*)(A_loc)->data;
1656: ai = a_loc->i;
1657: aj = a_loc->j;
1659: /* trigger copy to CPU */
1660: MatSeqAIJGetArrayRead(p->A,&dummy);
1661: MatSeqAIJRestoreArrayRead(p->A,&dummy);
1662: MatSeqAIJGetArrayRead(p->B,&dummy);
1663: MatSeqAIJRestoreArrayRead(p->B,&dummy);
1664: for (i=0; i<am; i++) {
1665: anz = ai[i+1] - ai[i];
1666: adj = aj + ai[i];
1667: ada = a_loc->a + ai[i];
1669: /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
1670: /*-------------------------------------------------------------*/
1671: /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
1672: pnz = po->i[i+1] - po->i[i];
1673: poJ = po->j + po->i[i];
1674: pA = po->a + po->i[i];
1675: for (j=0; j<pnz; j++) {
1676: row = poJ[j];
1677: cj = coj + coi[row];
1678: ca = coa + coi[row];
1679: /* perform sparse axpy */
1680: nexta = 0;
1681: valtmp = pA[j];
1682: for (k=0; nexta<anz; k++) {
1683: if (cj[k] == adj[nexta]) {
1684: ca[k] += valtmp*ada[nexta];
1685: nexta++;
1686: }
1687: }
1688: PetscLogFlops(2.0*anz);
1689: }
1691: /* put the value into Cd (diagonal part) */
1692: pnz = pd->i[i+1] - pd->i[i];
1693: pdJ = pd->j + pd->i[i];
1694: pA = pd->a + pd->i[i];
1695: for (j=0; j<pnz; j++) {
1696: row = pdJ[j];
1697: cj = bj + bi[row];
1698: ca = ba + bi[row];
1699: /* perform sparse axpy */
1700: nexta = 0;
1701: valtmp = pA[j];
1702: for (k=0; nexta<anz; k++) {
1703: if (cj[k] == adj[nexta]) {
1704: ca[k] += valtmp*ada[nexta];
1705: nexta++;
1706: }
1707: }
1708: PetscLogFlops(2.0*anz);
1709: }
1710: }
1712: /* 3) send and recv matrix values coa */
1713: /*------------------------------------*/
1714: buf_ri = merge->buf_ri;
1715: buf_rj = merge->buf_rj;
1716: len_s = merge->len_s;
1717: PetscCommGetNewTag(comm,&taga);
1718: PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);
1720: PetscMalloc2(merge->nsend+1,&s_waits,size,&status);
1721: for (proc=0,k=0; proc<size; proc++) {
1722: if (!len_s[proc]) continue;
1723: i = merge->owners_co[proc];
1724: MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);
1725: k++;
1726: }
1727: if (merge->nrecv) {MPI_Waitall(merge->nrecv,r_waits,status);}
1728: if (merge->nsend) {MPI_Waitall(merge->nsend,s_waits,status);}
1730: PetscFree2(s_waits,status);
1731: PetscFree(r_waits);
1732: PetscFree(coa);
1734: /* 4) insert local Cseq and received values into Cmpi */
1735: /*----------------------------------------------------*/
1736: PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
1737: for (k=0; k<merge->nrecv; k++) {
1738: buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1739: nrows = *(buf_ri_k[k]);
1740: nextrow[k] = buf_ri_k[k]+1; /* next row number of k-th recved i-structure */
1741: nextci[k] = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure */
1742: }
1744: for (i=0; i<cm; i++) {
1745: row = owners[rank] + i; /* global row index of C_seq */
1746: bj_i = bj + bi[i]; /* col indices of the i-th row of C */
1747: ba_i = ba + bi[i];
1748: bnz = bi[i+1] - bi[i];
1749: /* add received vals into ba */
1750: for (k=0; k<merge->nrecv; k++) { /* k-th received message */
1751: /* i-th row */
1752: if (i == *nextrow[k]) {
1753: cnz = *(nextci[k]+1) - *nextci[k];
1754: cj = buf_rj[k] + *(nextci[k]);
1755: ca = abuf_r[k] + *(nextci[k]);
1756: nextcj = 0;
1757: for (j=0; nextcj<cnz; j++) {
1758: if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
1759: ba_i[j] += ca[nextcj++];
1760: }
1761: }
1762: nextrow[k]++; nextci[k]++;
1763: PetscLogFlops(2.0*cnz);
1764: }
1765: }
1766: MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);
1767: }
1768: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1769: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
1771: PetscFree(ba);
1772: PetscFree(abuf_r[0]);
1773: PetscFree(abuf_r);
1774: PetscFree3(buf_ri_k,nextrow,nextci);
1775: return(0);
1776: }
1778: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P,Mat A,PetscReal fill,Mat C)
1779: {
1780: PetscErrorCode ierr;
1781: Mat A_loc;
1782: Mat_APMPI *ptap;
1783: PetscFreeSpaceList free_space=NULL,current_space=NULL;
1784: Mat_MPIAIJ *p=(Mat_MPIAIJ*)P->data,*a=(Mat_MPIAIJ*)A->data;
1785: PetscInt *pdti,*pdtj,*poti,*potj,*ptJ;
1786: PetscInt nnz;
1787: PetscInt *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
1788: PetscInt am =A->rmap->n,pn=P->cmap->n;
1789: MPI_Comm comm;
1790: PetscMPIInt size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
1791: PetscInt **buf_rj,**buf_ri,**buf_ri_k;
1792: PetscInt len,proc,*dnz,*onz,*owners;
1793: PetscInt nzi,*bi,*bj;
1794: PetscInt nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1795: MPI_Request *swaits,*rwaits;
1796: MPI_Status *sstatus,rstatus;
1797: Mat_Merge_SeqsToMPI *merge;
1798: PetscInt *ai,*aj,*Jptr,anz,*prmap=p->garray,pon,nspacedouble=0,j;
1799: PetscReal afill =1.0,afill_tmp;
1800: PetscInt rstart = P->cmap->rstart,rmax,aN=A->cmap->N,Armax;
1801: Mat_SeqAIJ *a_loc;
1802: PetscTable ta;
1803: MatType mtype;
1806: PetscObjectGetComm((PetscObject)A,&comm);
1807: /* check if matrix local sizes are compatible */
1808: 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);
1810: MPI_Comm_size(comm,&size);
1811: MPI_Comm_rank(comm,&rank);
1813: /* create struct Mat_APMPI and attached it to C later */
1814: PetscNew(&ptap);
1816: /* get A_loc by taking all local rows of A */
1817: MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&A_loc);
1819: ptap->A_loc = A_loc;
1820: a_loc = (Mat_SeqAIJ*)(A_loc)->data;
1821: ai = a_loc->i;
1822: aj = a_loc->j;
1824: /* determine symbolic Co=(p->B)^T*A - send to others */
1825: /*----------------------------------------------------*/
1826: MatGetSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);
1827: MatGetSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);
1828: pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
1829: >= (num of nonzero rows of C_seq) - pn */
1830: PetscMalloc1(pon+1,&coi);
1831: coi[0] = 0;
1833: /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
1834: nnz = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(poti[pon],ai[am]));
1835: PetscFreeSpaceGet(nnz,&free_space);
1836: current_space = free_space;
1838: /* create and initialize a linked list */
1839: PetscTableCreate(A->cmap->n + a->B->cmap->N,aN,&ta);
1840: MatRowMergeMax_SeqAIJ(a_loc,am,ta);
1841: PetscTableGetCount(ta,&Armax);
1843: PetscLLCondensedCreate_Scalable(Armax,&lnk);
1845: for (i=0; i<pon; i++) {
1846: pnz = poti[i+1] - poti[i];
1847: ptJ = potj + poti[i];
1848: for (j=0; j<pnz; j++) {
1849: row = ptJ[j]; /* row of A_loc == col of Pot */
1850: anz = ai[row+1] - ai[row];
1851: Jptr = aj + ai[row];
1852: /* add non-zero cols of AP into the sorted linked list lnk */
1853: PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);
1854: }
1855: nnz = lnk[0];
1857: /* If free space is not available, double the total space in the list */
1858: if (current_space->local_remaining<nnz) {
1859: PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),¤t_space);
1860: nspacedouble++;
1861: }
1863: /* Copy data into free space, and zero out denserows */
1864: PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);
1866: current_space->array += nnz;
1867: current_space->local_used += nnz;
1868: current_space->local_remaining -= nnz;
1870: coi[i+1] = coi[i] + nnz;
1871: }
1873: PetscMalloc1(coi[pon]+1,&coj);
1874: PetscFreeSpaceContiguous(&free_space,coj);
1875: PetscLLCondensedDestroy_Scalable(lnk); /* must destroy to get a new one for C */
1877: afill_tmp = (PetscReal)coi[pon]/(poti[pon] + ai[am]+1);
1878: if (afill_tmp > afill) afill = afill_tmp;
1880: /* send j-array (coj) of Co to other processors */
1881: /*----------------------------------------------*/
1882: /* determine row ownership */
1883: PetscNew(&merge);
1884: PetscLayoutCreate(comm,&merge->rowmap);
1886: merge->rowmap->n = pn;
1887: merge->rowmap->bs = 1;
1889: PetscLayoutSetUp(merge->rowmap);
1890: owners = merge->rowmap->range;
1892: /* determine the number of messages to send, their lengths */
1893: PetscCalloc1(size,&len_si);
1894: PetscCalloc1(size,&merge->len_s);
1896: len_s = merge->len_s;
1897: merge->nsend = 0;
1899: PetscMalloc1(size+2,&owners_co);
1901: proc = 0;
1902: for (i=0; i<pon; i++) {
1903: while (prmap[i] >= owners[proc+1]) proc++;
1904: len_si[proc]++; /* num of rows in Co to be sent to [proc] */
1905: len_s[proc] += coi[i+1] - coi[i];
1906: }
1908: len = 0; /* max length of buf_si[] */
1909: owners_co[0] = 0;
1910: for (proc=0; proc<size; proc++) {
1911: owners_co[proc+1] = owners_co[proc] + len_si[proc];
1912: if (len_si[proc]) {
1913: merge->nsend++;
1914: len_si[proc] = 2*(len_si[proc] + 1);
1915: len += len_si[proc];
1916: }
1917: }
1919: /* determine the number and length of messages to receive for coi and coj */
1920: PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);
1921: PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);
1923: /* post the Irecv and Isend of coj */
1924: PetscCommGetNewTag(comm,&tagj);
1925: PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);
1926: PetscMalloc1(merge->nsend+1,&swaits);
1927: for (proc=0, k=0; proc<size; proc++) {
1928: if (!len_s[proc]) continue;
1929: i = owners_co[proc];
1930: MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);
1931: k++;
1932: }
1934: /* receives and sends of coj are complete */
1935: PetscMalloc1(size,&sstatus);
1936: for (i=0; i<merge->nrecv; i++) {
1937: PETSC_UNUSED PetscMPIInt icompleted;
1938: MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
1939: }
1940: PetscFree(rwaits);
1941: if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}
1943: /* add received column indices into table to update Armax */
1944: /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/tutorials/ex56.c! */
1945: for (k=0; k<merge->nrecv; k++) {/* k-th received message */
1946: Jptr = buf_rj[k];
1947: for (j=0; j<merge->len_r[k]; j++) {
1948: PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);
1949: }
1950: }
1951: PetscTableGetCount(ta,&Armax);
1952: /* 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); */
1954: /* send and recv coi */
1955: /*-------------------*/
1956: PetscCommGetNewTag(comm,&tagi);
1957: PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);
1958: PetscMalloc1(len+1,&buf_s);
1959: buf_si = buf_s; /* points to the beginning of k-th msg to be sent */
1960: for (proc=0,k=0; proc<size; proc++) {
1961: if (!len_s[proc]) continue;
1962: /* form outgoing message for i-structure:
1963: buf_si[0]: nrows to be sent
1964: [1:nrows]: row index (global)
1965: [nrows+1:2*nrows+1]: i-structure index
1966: */
1967: /*-------------------------------------------*/
1968: nrows = len_si[proc]/2 - 1;
1969: buf_si_i = buf_si + nrows+1;
1970: buf_si[0] = nrows;
1971: buf_si_i[0] = 0;
1972: nrows = 0;
1973: for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
1974: nzi = coi[i+1] - coi[i];
1975: buf_si_i[nrows+1] = buf_si_i[nrows] + nzi; /* i-structure */
1976: buf_si[nrows+1] = prmap[i] -owners[proc]; /* local row index */
1977: nrows++;
1978: }
1979: MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);
1980: k++;
1981: buf_si += len_si[proc];
1982: }
1983: i = merge->nrecv;
1984: while (i--) {
1985: PETSC_UNUSED PetscMPIInt icompleted;
1986: MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
1987: }
1988: PetscFree(rwaits);
1989: if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}
1990: PetscFree(len_si);
1991: PetscFree(len_ri);
1992: PetscFree(swaits);
1993: PetscFree(sstatus);
1994: PetscFree(buf_s);
1996: /* compute the local portion of C (mpi mat) */
1997: /*------------------------------------------*/
1998: /* allocate bi array and free space for accumulating nonzero column info */
1999: PetscMalloc1(pn+1,&bi);
2000: bi[0] = 0;
2002: /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
2003: nnz = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(pdti[pn],PetscIntSumTruncate(poti[pon],ai[am])));
2004: PetscFreeSpaceGet(nnz,&free_space);
2005: current_space = free_space;
2007: PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
2008: for (k=0; k<merge->nrecv; k++) {
2009: buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
2010: nrows = *buf_ri_k[k];
2011: nextrow[k] = buf_ri_k[k] + 1; /* next row number of k-th recved i-structure */
2012: nextci[k] = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th received i-structure */
2013: }
2015: PetscLLCondensedCreate_Scalable(Armax,&lnk);
2016: MatPreallocateInitialize(comm,pn,A->cmap->n,dnz,onz);
2017: rmax = 0;
2018: for (i=0; i<pn; i++) {
2019: /* add pdt[i,:]*AP into lnk */
2020: pnz = pdti[i+1] - pdti[i];
2021: ptJ = pdtj + pdti[i];
2022: for (j=0; j<pnz; j++) {
2023: row = ptJ[j]; /* row of AP == col of Pt */
2024: anz = ai[row+1] - ai[row];
2025: Jptr = aj + ai[row];
2026: /* add non-zero cols of AP into the sorted linked list lnk */
2027: PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);
2028: }
2030: /* add received col data into lnk */
2031: for (k=0; k<merge->nrecv; k++) { /* k-th received message */
2032: if (i == *nextrow[k]) { /* i-th row */
2033: nzi = *(nextci[k]+1) - *nextci[k];
2034: Jptr = buf_rj[k] + *nextci[k];
2035: PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);
2036: nextrow[k]++; nextci[k]++;
2037: }
2038: }
2040: /* add missing diagonal entry */
2041: if (C->force_diagonals) {
2042: k = i + owners[rank]; /* column index */
2043: PetscLLCondensedAddSorted_Scalable(1,&k,lnk);
2044: }
2046: nnz = lnk[0];
2048: /* if free space is not available, make more free space */
2049: if (current_space->local_remaining<nnz) {
2050: PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),¤t_space);
2051: nspacedouble++;
2052: }
2053: /* copy data into free space, then initialize lnk */
2054: PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);
2055: MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);
2057: current_space->array += nnz;
2058: current_space->local_used += nnz;
2059: current_space->local_remaining -= nnz;
2061: bi[i+1] = bi[i] + nnz;
2062: if (nnz > rmax) rmax = nnz;
2063: }
2064: PetscFree3(buf_ri_k,nextrow,nextci);
2066: PetscMalloc1(bi[pn]+1,&bj);
2067: PetscFreeSpaceContiguous(&free_space,bj);
2068: afill_tmp = (PetscReal)bi[pn]/(pdti[pn] + poti[pon] + ai[am]+1);
2069: if (afill_tmp > afill) afill = afill_tmp;
2070: PetscLLCondensedDestroy_Scalable(lnk);
2071: PetscTableDestroy(&ta);
2072: MatRestoreSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);
2073: MatRestoreSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);
2075: /* create symbolic parallel matrix C - why cannot be assembled in Numeric part */
2076: /*-------------------------------------------------------------------------------*/
2077: MatSetSizes(C,pn,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);
2078: MatSetBlockSizes(C,PetscAbs(P->cmap->bs),PetscAbs(A->cmap->bs));
2079: MatGetType(A,&mtype);
2080: MatSetType(C,mtype);
2081: MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
2082: MatPreallocateFinalize(dnz,onz);
2083: MatSetBlockSize(C,1);
2084: MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);
2085: for (i=0; i<pn; i++) {
2086: row = i + rstart;
2087: nnz = bi[i+1] - bi[i];
2088: Jptr = bj + bi[i];
2089: MatSetValues(C,1,&row,nnz,Jptr,NULL,INSERT_VALUES);
2090: }
2091: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
2092: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
2093: MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
2094: merge->bi = bi;
2095: merge->bj = bj;
2096: merge->coi = coi;
2097: merge->coj = coj;
2098: merge->buf_ri = buf_ri;
2099: merge->buf_rj = buf_rj;
2100: merge->owners_co = owners_co;
2102: /* attach the supporting struct to C for reuse */
2103: C->product->data = ptap;
2104: C->product->destroy = MatDestroy_MPIAIJ_PtAP;
2105: ptap->merge = merge;
2107: C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;
2109: #if defined(PETSC_USE_INFO)
2110: if (bi[pn] != 0) {
2111: PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
2112: PetscInfo1(C,"Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n",(double)afill);
2113: } else {
2114: PetscInfo(C,"Empty matrix product\n");
2115: }
2116: #endif
2117: return(0);
2118: }
2120: /* ---------------------------------------------------------------- */
2121: static PetscErrorCode MatProductSymbolic_AtB_MPIAIJ_MPIAIJ(Mat C)
2122: {
2124: Mat_Product *product = C->product;
2125: Mat A=product->A,B=product->B;
2126: PetscReal fill=product->fill;
2127: PetscBool flg;
2130: /* scalable */
2131: PetscStrcmp(product->alg,"scalable",&flg);
2132: if (flg) {
2133: MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);
2134: goto next;
2135: }
2137: /* nonscalable */
2138: PetscStrcmp(product->alg,"nonscalable",&flg);
2139: if (flg) {
2140: MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C);
2141: goto next;
2142: }
2144: /* matmatmult */
2145: PetscStrcmp(product->alg,"at*b",&flg);
2146: if (flg) {
2147: Mat At;
2148: Mat_APMPI *ptap;
2150: MatTranspose(A,MAT_INITIAL_MATRIX,&At);
2151: MatMatMultSymbolic_MPIAIJ_MPIAIJ(At,B,fill,C);
2152: ptap = (Mat_APMPI*)C->product->data;
2153: if (ptap) {
2154: ptap->Pt = At;
2155: C->product->destroy = MatDestroy_MPIAIJ_PtAP;
2156: }
2157: C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
2158: goto next;
2159: }
2161: /* backend general code */
2162: PetscStrcmp(product->alg,"backend",&flg);
2163: if (flg) {
2164: MatProductSymbolic_MPIAIJBACKEND(C);
2165: return(0);
2166: }
2168: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatProduct type is not supported");
2170: next:
2171: C->ops->productnumeric = MatProductNumeric_AtB;
2172: return(0);
2173: }
2175: /* ---------------------------------------------------------------- */
2176: /* Set options for MatMatMultxxx_MPIAIJ_MPIAIJ */
2177: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AB(Mat C)
2178: {
2180: Mat_Product *product = C->product;
2181: Mat A=product->A,B=product->B;
2182: #if defined(PETSC_HAVE_HYPRE)
2183: const char *algTypes[5] = {"scalable","nonscalable","seqmpi","backend","hypre"};
2184: PetscInt nalg = 5;
2185: #else
2186: const char *algTypes[4] = {"scalable","nonscalable","seqmpi","backend",};
2187: PetscInt nalg = 4;
2188: #endif
2189: PetscInt alg = 1; /* set nonscalable algorithm as default */
2190: PetscBool flg;
2191: MPI_Comm comm;
2194: /* Check matrix local sizes */
2195: PetscObjectGetComm((PetscObject)C,&comm);
2196: 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);
2198: /* Set "nonscalable" as default algorithm */
2199: PetscStrcmp(C->product->alg,"default",&flg);
2200: if (flg) {
2201: MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2203: /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2204: if (B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2205: MatInfo Ainfo,Binfo;
2206: PetscInt nz_local;
2207: PetscBool alg_scalable_loc=PETSC_FALSE,alg_scalable;
2209: MatGetInfo(A,MAT_LOCAL,&Ainfo);
2210: MatGetInfo(B,MAT_LOCAL,&Binfo);
2211: nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);
2213: if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2214: MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);
2216: if (alg_scalable) {
2217: alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2218: MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2219: PetscInfo2(B,"Use scalable algorithm, BN %D, fill*nz_allocated %g\n",B->cmap->N,product->fill*nz_local);
2220: }
2221: }
2222: }
2224: /* Get runtime option */
2225: if (product->api_user) {
2226: PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMult","Mat");
2227: PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
2228: PetscOptionsEnd();
2229: } else {
2230: PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AB","Mat");
2231: PetscOptionsEList("-matproduct_ab_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
2232: PetscOptionsEnd();
2233: }
2234: if (flg) {
2235: MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2236: }
2238: C->ops->productsymbolic = MatProductSymbolic_AB_MPIAIJ_MPIAIJ;
2239: return(0);
2240: }
2242: /* Set options for MatTransposeMatMultXXX_MPIAIJ_MPIAIJ */
2243: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AtB(Mat C)
2244: {
2246: Mat_Product *product = C->product;
2247: Mat A=product->A,B=product->B;
2248: const char *algTypes[4] = {"scalable","nonscalable","at*b","backend"};
2249: PetscInt nalg = 4;
2250: PetscInt alg = 1; /* set default algorithm */
2251: PetscBool flg;
2252: MPI_Comm comm;
2255: /* Check matrix local sizes */
2256: PetscObjectGetComm((PetscObject)C,&comm);
2257: 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);
2259: /* Set default algorithm */
2260: PetscStrcmp(C->product->alg,"default",&flg);
2261: if (flg) {
2262: MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2263: }
2265: /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2266: if (alg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2267: MatInfo Ainfo,Binfo;
2268: PetscInt nz_local;
2269: PetscBool alg_scalable_loc=PETSC_FALSE,alg_scalable;
2271: MatGetInfo(A,MAT_LOCAL,&Ainfo);
2272: MatGetInfo(B,MAT_LOCAL,&Binfo);
2273: nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);
2275: if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2276: MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);
2278: if (alg_scalable) {
2279: alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2280: MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2281: PetscInfo2(B,"Use scalable algorithm, BN %D, fill*nz_allocated %g\n",B->cmap->N,product->fill*nz_local);
2282: }
2283: }
2285: /* Get runtime option */
2286: if (product->api_user) {
2287: PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatTransposeMatMult","Mat");
2288: PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
2289: PetscOptionsEnd();
2290: } else {
2291: PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AtB","Mat");
2292: PetscOptionsEList("-matproduct_atb_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
2293: PetscOptionsEnd();
2294: }
2295: if (flg) {
2296: MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2297: }
2299: C->ops->productsymbolic = MatProductSymbolic_AtB_MPIAIJ_MPIAIJ;
2300: return(0);
2301: }
2303: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_PtAP(Mat C)
2304: {
2306: Mat_Product *product = C->product;
2307: Mat A=product->A,P=product->B;
2308: MPI_Comm comm;
2309: PetscBool flg;
2310: PetscInt alg=1; /* set default algorithm */
2311: #if !defined(PETSC_HAVE_HYPRE)
2312: const char *algTypes[5] = {"scalable","nonscalable","allatonce","allatonce_merged","backend"};
2313: PetscInt nalg=5;
2314: #else
2315: const char *algTypes[6] = {"scalable","nonscalable","allatonce","allatonce_merged","backend","hypre"};
2316: PetscInt nalg=6;
2317: #endif
2318: PetscInt pN=P->cmap->N;
2321: /* Check matrix local sizes */
2322: PetscObjectGetComm((PetscObject)C,&comm);
2323: 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);
2324: 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);
2326: /* Set "nonscalable" as default algorithm */
2327: PetscStrcmp(C->product->alg,"default",&flg);
2328: if (flg) {
2329: MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2331: /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2332: if (pN > 100000) {
2333: MatInfo Ainfo,Pinfo;
2334: PetscInt nz_local;
2335: PetscBool alg_scalable_loc=PETSC_FALSE,alg_scalable;
2337: MatGetInfo(A,MAT_LOCAL,&Ainfo);
2338: MatGetInfo(P,MAT_LOCAL,&Pinfo);
2339: nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);
2341: if (pN > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2342: MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);
2344: if (alg_scalable) {
2345: alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2346: MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2347: }
2348: }
2349: }
2351: /* Get runtime option */
2352: if (product->api_user) {
2353: PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatPtAP","Mat");
2354: PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);
2355: PetscOptionsEnd();
2356: } else {
2357: PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_PtAP","Mat");
2358: PetscOptionsEList("-matproduct_ptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);
2359: PetscOptionsEnd();
2360: }
2361: if (flg) {
2362: MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2363: }
2365: C->ops->productsymbolic = MatProductSymbolic_PtAP_MPIAIJ_MPIAIJ;
2366: return(0);
2367: }
2369: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_RARt(Mat C)
2370: {
2371: Mat_Product *product = C->product;
2372: Mat A = product->A,R=product->B;
2375: /* Check matrix local sizes */
2376: 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);
2378: C->ops->productsymbolic = MatProductSymbolic_RARt_MPIAIJ_MPIAIJ;
2379: return(0);
2380: }
2382: /*
2383: Set options for ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm
2384: */
2385: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABC(Mat C)
2386: {
2388: Mat_Product *product = C->product;
2389: PetscBool flg = PETSC_FALSE;
2390: PetscInt alg = 1; /* default algorithm */
2391: const char *algTypes[3] = {"scalable","nonscalable","seqmpi"};
2392: PetscInt nalg = 3;
2395: /* Set default algorithm */
2396: PetscStrcmp(C->product->alg,"default",&flg);
2397: if (flg) {
2398: MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2399: }
2401: /* Get runtime option */
2402: if (product->api_user) {
2403: PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMatMult","Mat");
2404: PetscOptionsEList("-matmatmatmult_via","Algorithmic approach","MatMatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
2405: PetscOptionsEnd();
2406: } else {
2407: PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_ABC","Mat");
2408: PetscOptionsEList("-matproduct_abc_via","Algorithmic approach","MatProduct_ABC",algTypes,nalg,algTypes[alg],&alg,&flg);
2409: PetscOptionsEnd();
2410: }
2411: if (flg) {
2412: MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2413: }
2415: C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ;
2416: C->ops->productsymbolic = MatProductSymbolic_ABC;
2417: return(0);
2418: }
2420: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ(Mat C)
2421: {
2423: Mat_Product *product = C->product;
2426: switch (product->type) {
2427: case MATPRODUCT_AB:
2428: MatProductSetFromOptions_MPIAIJ_AB(C);
2429: break;
2430: case MATPRODUCT_AtB:
2431: MatProductSetFromOptions_MPIAIJ_AtB(C);
2432: break;
2433: case MATPRODUCT_PtAP:
2434: MatProductSetFromOptions_MPIAIJ_PtAP(C);
2435: break;
2436: case MATPRODUCT_RARt:
2437: MatProductSetFromOptions_MPIAIJ_RARt(C);
2438: break;
2439: case MATPRODUCT_ABC:
2440: MatProductSetFromOptions_MPIAIJ_ABC(C);
2441: break;
2442: default:
2443: break;
2444: }
2445: return(0);
2446: }