Actual source code: matptap.c
petsc-3.14.6 2021-03-30
2: /*
3: Defines projective product routines where A is a SeqAIJ matrix
4: C = P^T * A * P
5: */
7: #include <../src/mat/impls/aij/seq/aij.h>
8: #include <../src/mat/utils/freespace.h>
9: #include <petscbt.h>
10: #include <petsctime.h>
12: #if defined(PETSC_HAVE_HYPRE)
13: PETSC_INTERN PetscErrorCode MatPtAPSymbolic_AIJ_AIJ_wHYPRE(Mat,Mat,PetscReal,Mat);
14: #endif
16: PetscErrorCode MatProductSymbolic_PtAP_SeqAIJ_SeqAIJ(Mat C)
17: {
18: PetscErrorCode ierr;
19: Mat_Product *product = C->product;
20: Mat A=product->A,P=product->B;
21: MatProductAlgorithm alg=product->alg;
22: PetscReal fill=product->fill;
23: PetscBool flg;
24: Mat Pt;
27: /* "scalable" */
28: PetscStrcmp(alg,"scalable",&flg);
29: if (flg) {
30: MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(A,P,fill,C);
31: C->ops->productnumeric = MatProductNumeric_PtAP;
32: return(0);
33: }
35: /* "rap" */
36: PetscStrcmp(alg,"rap",&flg);
37: if (flg) {
38: Mat_MatTransMatMult *atb;
40: PetscNew(&atb);
41: MatTranspose_SeqAIJ(P,MAT_INITIAL_MATRIX,&Pt);
42: MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ(Pt,A,P,fill,C);
44: atb->At = Pt;
45: atb->data = C->product->data;
46: atb->destroy = C->product->destroy;
47: C->product->data = atb;
48: C->product->destroy = MatDestroy_SeqAIJ_MatTransMatMult;
49: C->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ;
50: C->ops->productnumeric = MatProductNumeric_PtAP;
51: return(0);
52: }
54: /* hypre */
55: #if defined(PETSC_HAVE_HYPRE)
56: PetscStrcmp(alg,"hypre",&flg);
57: if (flg) {
58: MatPtAPSymbolic_AIJ_AIJ_wHYPRE(A,P,fill,C);
59: return(0);
60: }
61: #endif
63: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatProductType is not supported");
64: }
66: PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,PetscReal fill,Mat C)
67: {
68: PetscErrorCode ierr;
69: PetscFreeSpaceList free_space=NULL,current_space=NULL;
70: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*p = (Mat_SeqAIJ*)P->data,*c;
71: PetscInt *pti,*ptj,*ptJ,*ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj;
72: PetscInt *ci,*cj,*ptadenserow,*ptasparserow,*ptaj,nspacedouble=0;
73: PetscInt an=A->cmap->N,am=A->rmap->N,pn=P->cmap->N,pm=P->rmap->N;
74: PetscInt i,j,k,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi,nlnk,*lnk;
75: MatScalar *ca;
76: PetscBT lnkbt;
77: PetscReal afill;
80: /* Get ij structure of P^T */
81: MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);
82: ptJ = ptj;
84: /* Allocate ci array, arrays for fill computation and */
85: /* free space for accumulating nonzero column info */
86: PetscMalloc1(pn+1,&ci);
87: ci[0] = 0;
89: PetscCalloc1(2*an+1,&ptadenserow);
90: ptasparserow = ptadenserow + an;
92: /* create and initialize a linked list */
93: nlnk = pn+1;
94: PetscLLCreate(pn,pn,nlnk,lnk,lnkbt);
96: /* Set initial free space to be fill*(nnz(A)+ nnz(P)) */
97: PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],pi[pm])),&free_space);
98: current_space = free_space;
100: /* Determine symbolic info for each row of C: */
101: for (i=0; i<pn; i++) {
102: ptnzi = pti[i+1] - pti[i];
103: ptanzi = 0;
104: /* Determine symbolic row of PtA: */
105: for (j=0; j<ptnzi; j++) {
106: arow = *ptJ++;
107: anzj = ai[arow+1] - ai[arow];
108: ajj = aj + ai[arow];
109: for (k=0; k<anzj; k++) {
110: if (!ptadenserow[ajj[k]]) {
111: ptadenserow[ajj[k]] = -1;
112: ptasparserow[ptanzi++] = ajj[k];
113: }
114: }
115: }
116: /* Using symbolic info for row of PtA, determine symbolic info for row of C: */
117: ptaj = ptasparserow;
118: cnzi = 0;
119: for (j=0; j<ptanzi; j++) {
120: prow = *ptaj++;
121: pnzj = pi[prow+1] - pi[prow];
122: pjj = pj + pi[prow];
123: /* add non-zero cols of P into the sorted linked list lnk */
124: PetscLLAddSorted(pnzj,pjj,pn,nlnk,lnk,lnkbt);
125: cnzi += nlnk;
126: }
128: /* If free space is not available, make more free space */
129: /* Double the amount of total space in the list */
130: if (current_space->local_remaining<cnzi) {
131: PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),¤t_space);
132: nspacedouble++;
133: }
135: /* Copy data into free space, and zero out denserows */
136: PetscLLClean(pn,pn,cnzi,lnk,current_space->array,lnkbt);
138: current_space->array += cnzi;
139: current_space->local_used += cnzi;
140: current_space->local_remaining -= cnzi;
142: for (j=0; j<ptanzi; j++) ptadenserow[ptasparserow[j]] = 0;
144: /* Aside: Perhaps we should save the pta info for the numerical factorization. */
145: /* For now, we will recompute what is needed. */
146: ci[i+1] = ci[i] + cnzi;
147: }
148: /* nnz is now stored in ci[ptm], column indices are in the list of free space */
149: /* Allocate space for cj, initialize cj, and */
150: /* destroy list of free space and other temporary array(s) */
151: PetscMalloc1(ci[pn]+1,&cj);
152: PetscFreeSpaceContiguous(&free_space,cj);
153: PetscFree(ptadenserow);
154: PetscLLDestroy(lnk,lnkbt);
156: PetscCalloc1(ci[pn]+1,&ca);
158: /* put together the new matrix */
159: MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A),pn,pn,ci,cj,ca,((PetscObject)A)->type_name,C);
160: MatSetBlockSizes(C,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));
162: /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
163: /* Since these are PETSc arrays, change flags to free them as necessary. */
164: c = (Mat_SeqAIJ*)((C)->data);
165: c->free_a = PETSC_TRUE;
166: c->free_ij = PETSC_TRUE;
167: c->nonew = 0;
169: C->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy;
171: /* set MatInfo */
172: afill = (PetscReal)ci[pn]/(ai[am]+pi[pm] + 1.e-5);
173: if (afill < 1.0) afill = 1.0;
174: c->maxnz = ci[pn];
175: c->nz = ci[pn];
176: C->info.mallocs = nspacedouble;
177: C->info.fill_ratio_given = fill;
178: C->info.fill_ratio_needed = afill;
180: /* Clean up. */
181: MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);
182: #if defined(PETSC_USE_INFO)
183: if (ci[pn] != 0) {
184: PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
185: PetscInfo1(C,"Use MatPtAP(A,P,MatReuse,%g,&C) for best performance.\n",(double)afill);
186: } else {
187: PetscInfo(C,"Empty matrix product\n");
188: }
189: #endif
190: return(0);
191: }
193: PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,Mat C)
194: {
196: Mat_SeqAIJ *a = (Mat_SeqAIJ*) A->data;
197: Mat_SeqAIJ *p = (Mat_SeqAIJ*) P->data;
198: Mat_SeqAIJ *c = (Mat_SeqAIJ*) C->data;
199: PetscInt *ai=a->i,*aj=a->j,*apj,*apjdense,*pi=p->i,*pj=p->j,*pJ=p->j,*pjj;
200: PetscInt *ci=c->i,*cj=c->j,*cjj;
201: PetscInt am =A->rmap->N,cn=C->cmap->N,cm=C->rmap->N;
202: PetscInt i,j,k,anzi,pnzi,apnzj,nextap,pnzj,prow,crow;
203: MatScalar *aa=a->a,*apa,*pa=p->a,*pA=p->a,*paj,*ca=c->a,*caj;
206: /* Allocate temporary array for storage of one row of A*P (cn: non-scalable) */
207: PetscCalloc2(cn,&apa,cn,&apjdense);
208: PetscMalloc1(cn,&apj);
210: /* Clear old values in C */
211: PetscArrayzero(ca,ci[cm]);
213: for (i=0; i<am; i++) {
214: /* Form sparse row of A*P */
215: anzi = ai[i+1] - ai[i];
216: apnzj = 0;
217: for (j=0; j<anzi; j++) {
218: prow = *aj++;
219: pnzj = pi[prow+1] - pi[prow];
220: pjj = pj + pi[prow];
221: paj = pa + pi[prow];
222: for (k=0; k<pnzj; k++) {
223: if (!apjdense[pjj[k]]) {
224: apjdense[pjj[k]] = -1;
225: apj[apnzj++] = pjj[k];
226: }
227: apa[pjj[k]] += (*aa)*paj[k];
228: }
229: PetscLogFlops(2.0*pnzj);
230: aa++;
231: }
233: /* Sort the j index array for quick sparse axpy. */
234: /* Note: a array does not need sorting as it is in dense storage locations. */
235: PetscSortInt(apnzj,apj);
237: /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */
238: pnzi = pi[i+1] - pi[i];
239: for (j=0; j<pnzi; j++) {
240: nextap = 0;
241: crow = *pJ++;
242: cjj = cj + ci[crow];
243: caj = ca + ci[crow];
244: /* Perform sparse axpy operation. Note cjj includes apj. */
245: for (k=0; nextap<apnzj; k++) {
246: if (PetscUnlikelyDebug(k >= ci[crow+1] - ci[crow])) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"k too large k %d, crow %d",k,crow);
247: if (cjj[k]==apj[nextap]) {
248: caj[k] += (*pA)*apa[apj[nextap++]];
249: }
250: }
251: PetscLogFlops(2.0*apnzj);
252: pA++;
253: }
255: /* Zero the current row info for A*P */
256: for (j=0; j<apnzj; j++) {
257: apa[apj[j]] = 0.;
258: apjdense[apj[j]] = 0;
259: }
260: }
262: /* Assemble the final matrix and clean up */
263: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
264: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
266: PetscFree2(apa,apjdense);
267: PetscFree(apj);
268: return(0);
269: }
271: PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat C)
272: {
273: PetscErrorCode ierr;
274: Mat_MatTransMatMult *atb;
277: MatCheckProduct(C,3);
278: atb = (Mat_MatTransMatMult*)C->product->data;
279: if (!atb) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Missing data structure");
280: MatTranspose_SeqAIJ(P,MAT_REUSE_MATRIX,&atb->At);
281: if (!C->ops->matmultnumeric) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Missing numeric operation");
282: /* when using rap, MatMatMatMultSymbolic used a different data */
283: if (atb->data) C->product->data = atb->data;
284: (*C->ops->matmatmultnumeric)(atb->At,A,P,C);
285: C->product->data = atb;
286: return(0);
287: }