Actual source code: matptap.c
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> /*I "petscmat.h" I*/
8: #include <../src/mat/utils/freespace.h>
9: #include <petscbt.h>
13: PetscErrorCode MatPtAPSymbolic_SeqAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
14: {
18: if (!P->ops->ptapsymbolic_seqaij) SETERRQ2(((PetscObject)A)->comm,PETSC_ERR_SUP,"Not implemented for A=%s and P=%s",((PetscObject)A)->type_name,((PetscObject)P)->type_name);
19: (*P->ops->ptapsymbolic_seqaij)(A,P,fill,C);
20: return(0);
21: }
25: PetscErrorCode MatPtAPNumeric_SeqAIJ(Mat A,Mat P,Mat C)
26: {
30: if (!P->ops->ptapnumeric_seqaij) SETERRQ2(((PetscObject)A)->comm,PETSC_ERR_SUP,"Not implemented for A=%s and P=%s",((PetscObject)A)->type_name,((PetscObject)P)->type_name);
31: (*P->ops->ptapnumeric_seqaij)(A,P,C);
32: return(0);
33: }
37: PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
38: {
39: PetscErrorCode ierr;
40: PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
41: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*p = (Mat_SeqAIJ*)P->data,*c;
42: PetscInt *pti,*ptj,*ptJ,*ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj;
43: PetscInt *ci,*cj,*ptadenserow,*ptasparserow,*ptaj,nspacedouble=0;
44: PetscInt an=A->cmap->N,am=A->rmap->N,pn=P->cmap->N;
45: PetscInt i,j,k,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi,nlnk,*lnk;
46: MatScalar *ca;
47: PetscBT lnkbt;
50: /* Get ij structure of P^T */
51: MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);
52: ptJ=ptj;
54: /* Allocate ci array, arrays for fill computation and */
55: /* free space for accumulating nonzero column info */
56: PetscMalloc((pn+1)*sizeof(PetscInt),&ci);
57: ci[0] = 0;
59: PetscMalloc((2*an+1)*sizeof(PetscInt),&ptadenserow);
60: PetscMemzero(ptadenserow,(2*an+1)*sizeof(PetscInt));
61: ptasparserow = ptadenserow + an;
63: /* create and initialize a linked list */
64: nlnk = pn+1;
65: PetscLLCreate(pn,pn,nlnk,lnk,lnkbt);
67: /* Set initial free space to be fill*nnz(A). */
68: /* This should be reasonable if sparsity of PtAP is similar to that of A. */
69: PetscFreeSpaceGet((PetscInt)(fill*ai[am]),&free_space);
70: current_space = free_space;
72: /* Determine symbolic info for each row of C: */
73: for (i=0;i<pn;i++) {
74: ptnzi = pti[i+1] - pti[i];
75: ptanzi = 0;
76: /* Determine symbolic row of PtA: */
77: for (j=0;j<ptnzi;j++) {
78: arow = *ptJ++;
79: anzj = ai[arow+1] - ai[arow];
80: ajj = aj + ai[arow];
81: for (k=0;k<anzj;k++) {
82: if (!ptadenserow[ajj[k]]) {
83: ptadenserow[ajj[k]] = -1;
84: ptasparserow[ptanzi++] = ajj[k];
85: }
86: }
87: }
88: /* Using symbolic info for row of PtA, determine symbolic info for row of C: */
89: ptaj = ptasparserow;
90: cnzi = 0;
91: for (j=0;j<ptanzi;j++) {
92: prow = *ptaj++;
93: pnzj = pi[prow+1] - pi[prow];
94: pjj = pj + pi[prow];
95: /* add non-zero cols of P into the sorted linked list lnk */
96: PetscLLAdd(pnzj,pjj,pn,nlnk,lnk,lnkbt);
97: cnzi += nlnk;
98: }
99:
100: /* If free space is not available, make more free space */
101: /* Double the amount of total space in the list */
102: if (current_space->local_remaining<cnzi) {
103: PetscFreeSpaceGet(cnzi+current_space->total_array_size,¤t_space);
104: nspacedouble++;
105: }
107: /* Copy data into free space, and zero out denserows */
108: PetscLLClean(pn,pn,cnzi,lnk,current_space->array,lnkbt);
109: current_space->array += cnzi;
110: current_space->local_used += cnzi;
111: current_space->local_remaining -= cnzi;
112:
113: for (j=0;j<ptanzi;j++) {
114: ptadenserow[ptasparserow[j]] = 0;
115: }
116: /* Aside: Perhaps we should save the pta info for the numerical factorization. */
117: /* For now, we will recompute what is needed. */
118: ci[i+1] = ci[i] + cnzi;
119: }
120: /* nnz is now stored in ci[ptm], column indices are in the list of free space */
121: /* Allocate space for cj, initialize cj, and */
122: /* destroy list of free space and other temporary array(s) */
123: PetscMalloc((ci[pn]+1)*sizeof(PetscInt),&cj);
124: PetscFreeSpaceContiguous(&free_space,cj);
125: PetscFree(ptadenserow);
126: PetscLLDestroy(lnk,lnkbt);
127:
128: /* Allocate space for ca */
129: PetscMalloc((ci[pn]+1)*sizeof(MatScalar),&ca);
130: PetscMemzero(ca,(ci[pn]+1)*sizeof(MatScalar));
131:
132: /* put together the new matrix */
133: MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,pn,pn,ci,cj,ca,C);
135: /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
136: /* Since these are PETSc arrays, change flags to free them as necessary. */
137: c = (Mat_SeqAIJ *)((*C)->data);
138: c->free_a = PETSC_TRUE;
139: c->free_ij = PETSC_TRUE;
140: c->nonew = 0;
142: /* Clean up. */
143: MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);
144: #if defined(PETSC_USE_INFO)
145: if (ci[pn] != 0) {
146: PetscReal afill = ((PetscReal)ci[pn])/ai[am];
147: if (afill < 1.0) afill = 1.0;
148: PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);
149: PetscInfo1((*C),"Use MatPtAP(A,P,MatReuse,%G,&C) for best performance.\n",afill);
150: } else {
151: PetscInfo((*C),"Empty matrix product\n");
152: }
153: #endif
154: return(0);
155: }
159: PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat C)
160: {
162: Mat_SeqAIJ *a = (Mat_SeqAIJ *) A->data;
163: Mat_SeqAIJ *p = (Mat_SeqAIJ *) P->data;
164: Mat_SeqAIJ *c = (Mat_SeqAIJ *) C->data;
165: PetscInt *ai=a->i,*aj=a->j,*apj,*apjdense,*pi=p->i,*pj=p->j,*pJ=p->j,*pjj;
166: PetscInt *ci=c->i,*cj=c->j,*cjj;
167: PetscInt am=A->rmap->N,cn=C->cmap->N,cm=C->rmap->N;
168: PetscInt i,j,k,anzi,pnzi,apnzj,nextap,pnzj,prow,crow;
169: MatScalar *aa=a->a,*apa,*pa=p->a,*pA=p->a,*paj,*ca=c->a,*caj;
172: /* Allocate temporary array for storage of one row of A*P */
173: PetscMalloc(cn*(sizeof(MatScalar)+2*sizeof(PetscInt)),&apa);
174: PetscMemzero(apa,cn*(sizeof(MatScalar)+2*sizeof(PetscInt)));
176: apj = (PetscInt *)(apa + cn);
177: apjdense = apj + cn;
179: /* Clear old values in C */
180: PetscMemzero(ca,ci[cm]*sizeof(MatScalar));
182: for (i=0;i<am;i++) {
183: /* Form sparse row of A*P */
184: anzi = ai[i+1] - ai[i];
185: apnzj = 0;
186: for (j=0;j<anzi;j++) {
187: prow = *aj++;
188: pnzj = pi[prow+1] - pi[prow];
189: pjj = pj + pi[prow];
190: paj = pa + pi[prow];
191: for (k=0;k<pnzj;k++) {
192: if (!apjdense[pjj[k]]) {
193: apjdense[pjj[k]] = -1;
194: apj[apnzj++] = pjj[k];
195: }
196: apa[pjj[k]] += (*aa)*paj[k];
197: }
198: PetscLogFlops(2.0*pnzj);
199: aa++;
200: }
202: /* Sort the j index array for quick sparse axpy. */
203: /* Note: a array does not need sorting as it is in dense storage locations. */
204: PetscSortInt(apnzj,apj);
206: /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */
207: pnzi = pi[i+1] - pi[i];
208: for (j=0;j<pnzi;j++) {
209: nextap = 0;
210: crow = *pJ++;
211: cjj = cj + ci[crow];
212: caj = ca + ci[crow];
213: /* Perform sparse axpy operation. Note cjj includes apj. */
214: for (k=0;nextap<apnzj;k++) {
215: #if defined(PETSC_USE_DEBUG)
216: if (k >= ci[crow+1] - ci[crow]) {
217: SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"k too large k %d, crow %d",k,crow);
218: }
219: #endif
220: if (cjj[k]==apj[nextap]) {
221: caj[k] += (*pA)*apa[apj[nextap++]];
222: }
223: }
224: PetscLogFlops(2.0*apnzj);
225: pA++;
226: }
228: /* Zero the current row info for A*P */
229: for (j=0;j<apnzj;j++) {
230: apa[apj[j]] = 0.;
231: apjdense[apj[j]] = 0;
232: }
233: }
235: /* Assemble the final matrix and clean up */
236: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
237: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
238: PetscFree(apa);
239: return(0);
240: }