Actual source code: matptap.c
1: #define PETSCMAT_DLL
3: /*
4: Defines projective product routines where A is a SeqAIJ matrix
5: C = P^T * A * P
6: */
8: #include src/mat/impls/aij/seq/aij.h
9: #include src/mat/utils/freespace.h
10: #include petscbt.h
14: PetscErrorCode MatPtAPSymbolic_SeqAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
15: {
19: if (!P->ops->ptapsymbolic_seqaij) {
20: SETERRQ2(PETSC_ERR_SUP,"Not implemented for A=%s and P=%s",A->type_name,P->type_name);
21: }
22: (*P->ops->ptapsymbolic_seqaij)(A,P,fill,C);
23: return(0);
24: }
28: PetscErrorCode MatPtAPNumeric_SeqAIJ(Mat A,Mat P,Mat C)
29: {
33: if (!P->ops->ptapnumeric_seqaij) {
34: SETERRQ2(PETSC_ERR_SUP,"Not implemented for A=%s and P=%s",A->type_name,P->type_name);
35: }
36: (*P->ops->ptapnumeric_seqaij)(A,P,C);
37: return(0);
38: }
42: PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
43: {
44: PetscErrorCode ierr;
45: PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
46: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*p = (Mat_SeqAIJ*)P->data,*c;
47: PetscInt *pti,*ptj,*ptJ,*ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj;
48: PetscInt *ci,*cj,*ptadenserow,*ptasparserow,*ptaj;
49: PetscInt an=A->cmap.N,am=A->rmap.N,pn=P->cmap.N,pm=P->rmap.N;
50: PetscInt i,j,k,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi,nlnk,*lnk;
51: MatScalar *ca;
52: PetscBT lnkbt;
55: /* Get ij structure of P^T */
56: MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);
57: ptJ=ptj;
59: /* Allocate ci array, arrays for fill computation and */
60: /* free space for accumulating nonzero column info */
61: PetscMalloc((pn+1)*sizeof(PetscInt),&ci);
62: ci[0] = 0;
64: PetscMalloc((2*an+1)*sizeof(PetscInt),&ptadenserow);
65: PetscMemzero(ptadenserow,(2*an+1)*sizeof(PetscInt));
66: ptasparserow = ptadenserow + an;
68: /* create and initialize a linked list */
69: nlnk = pn+1;
70: PetscLLCreate(pn,pn,nlnk,lnk,lnkbt);
72: /* Set initial free space to be nnz(A) scaled by aspect ratio of P. */
73: /* This should be reasonable if sparsity of PtAP is similar to that of A. */
74: PetscFreeSpaceGet((ai[am]/pm)*pn,&free_space);
75: current_space = free_space;
77: /* Determine symbolic info for each row of C: */
78: for (i=0;i<pn;i++) {
79: ptnzi = pti[i+1] - pti[i];
80: ptanzi = 0;
81: /* Determine symbolic row of PtA: */
82: for (j=0;j<ptnzi;j++) {
83: arow = *ptJ++;
84: anzj = ai[arow+1] - ai[arow];
85: ajj = aj + ai[arow];
86: for (k=0;k<anzj;k++) {
87: if (!ptadenserow[ajj[k]]) {
88: ptadenserow[ajj[k]] = -1;
89: ptasparserow[ptanzi++] = ajj[k];
90: }
91: }
92: }
93: /* Using symbolic info for row of PtA, determine symbolic info for row of C: */
94: ptaj = ptasparserow;
95: cnzi = 0;
96: for (j=0;j<ptanzi;j++) {
97: prow = *ptaj++;
98: pnzj = pi[prow+1] - pi[prow];
99: pjj = pj + pi[prow];
100: /* add non-zero cols of P into the sorted linked list lnk */
101: PetscLLAdd(pnzj,pjj,pn,nlnk,lnk,lnkbt);
102: cnzi += nlnk;
103: }
104:
105: /* If free space is not available, make more free space */
106: /* Double the amount of total space in the list */
107: if (current_space->local_remaining<cnzi) {
108: PetscFreeSpaceGet(current_space->total_array_size,¤t_space);
109: }
111: /* Copy data into free space, and zero out denserows */
112: PetscLLClean(pn,pn,cnzi,lnk,current_space->array,lnkbt);
113: current_space->array += cnzi;
114: current_space->local_used += cnzi;
115: current_space->local_remaining -= cnzi;
116:
117: for (j=0;j<ptanzi;j++) {
118: ptadenserow[ptasparserow[j]] = 0;
119: }
120: /* Aside: Perhaps we should save the pta info for the numerical factorization. */
121: /* For now, we will recompute what is needed. */
122: ci[i+1] = ci[i] + cnzi;
123: }
124: /* nnz is now stored in ci[ptm], column indices are in the list of free space */
125: /* Allocate space for cj, initialize cj, and */
126: /* destroy list of free space and other temporary array(s) */
127: PetscMalloc((ci[pn]+1)*sizeof(PetscInt),&cj);
128: PetscFreeSpaceContiguous(&free_space,cj);
129: PetscFree(ptadenserow);
130: PetscLLDestroy(lnk,lnkbt);
131:
132: /* Allocate space for ca */
133: PetscMalloc((ci[pn]+1)*sizeof(MatScalar),&ca);
134: PetscMemzero(ca,(ci[pn]+1)*sizeof(MatScalar));
135:
136: /* put together the new matrix */
137: MatCreateSeqAIJWithArrays(A->comm,pn,pn,ci,cj,ca,C);
139: /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
140: /* Since these are PETSc arrays, change flags to free them as necessary. */
141: c = (Mat_SeqAIJ *)((*C)->data);
142: c->freedata = PETSC_TRUE;
143: c->nonew = 0;
145: /* Clean up. */
146: MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);
148: return(0);
149: }
153: PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat C)
154: {
156: PetscInt flops=0;
157: Mat_SeqAIJ *a = (Mat_SeqAIJ *) A->data;
158: Mat_SeqAIJ *p = (Mat_SeqAIJ *) P->data;
159: Mat_SeqAIJ *c = (Mat_SeqAIJ *) C->data;
160: PetscInt *ai=a->i,*aj=a->j,*apj,*apjdense,*pi=p->i,*pj=p->j,*pJ=p->j,*pjj;
161: PetscInt *ci=c->i,*cj=c->j,*cjj;
162: PetscInt am=A->rmap.N,cn=C->cmap.N,cm=C->rmap.N;
163: PetscInt i,j,k,anzi,pnzi,apnzj,nextap,pnzj,prow,crow;
164: MatScalar *aa=a->a,*apa,*pa=p->a,*pA=p->a,*paj,*ca=c->a,*caj;
167: /* Allocate temporary array for storage of one row of A*P */
168: PetscMalloc(cn*(sizeof(MatScalar)+2*sizeof(PetscInt)),&apa);
169: PetscMemzero(apa,cn*(sizeof(MatScalar)+2*sizeof(PetscInt)));
171: apj = (PetscInt *)(apa + cn);
172: apjdense = apj + cn;
174: /* Clear old values in C */
175: PetscMemzero(ca,ci[cm]*sizeof(MatScalar));
177: for (i=0;i<am;i++) {
178: /* Form sparse row of A*P */
179: anzi = ai[i+1] - ai[i];
180: apnzj = 0;
181: for (j=0;j<anzi;j++) {
182: prow = *aj++;
183: pnzj = pi[prow+1] - pi[prow];
184: pjj = pj + pi[prow];
185: paj = pa + pi[prow];
186: for (k=0;k<pnzj;k++) {
187: if (!apjdense[pjj[k]]) {
188: apjdense[pjj[k]] = -1;
189: apj[apnzj++] = pjj[k];
190: }
191: apa[pjj[k]] += (*aa)*paj[k];
192: }
193: flops += 2*pnzj;
194: aa++;
195: }
197: /* Sort the j index array for quick sparse axpy. */
198: /* Note: a array does not need sorting as it is in dense storage locations. */
199: PetscSortInt(apnzj,apj);
201: /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */
202: pnzi = pi[i+1] - pi[i];
203: for (j=0;j<pnzi;j++) {
204: nextap = 0;
205: crow = *pJ++;
206: cjj = cj + ci[crow];
207: caj = ca + ci[crow];
208: /* Perform sparse axpy operation. Note cjj includes apj. */
209: for (k=0;nextap<apnzj;k++) {
210: #if defined(PETSC_USE_DEBUG)
211: if (k >= ci[crow+1] - ci[crow]) {
212: SETERRQ2(PETSC_ERR_PLIB,"k too large k %d, crow %d",k,crow);
213: }
214: #endif
215: if (cjj[k]==apj[nextap]) {
216: caj[k] += (*pA)*apa[apj[nextap++]];
217: }
218: }
219: flops += 2*apnzj;
220: pA++;
221: }
223: /* Zero the current row info for A*P */
224: for (j=0;j<apnzj;j++) {
225: apa[apj[j]] = 0.;
226: apjdense[apj[j]] = 0;
227: }
228: }
230: /* Assemble the final matrix and clean up */
231: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
232: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
233: PetscFree(apa);
234: PetscLogFlops(flops);
236: return(0);
237: }