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: {
 45:   FreeSpaceList  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->N,am=A->M,pn=P->N,pm=P->M;
 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:   GetMoreSpace((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:       GetMoreSpace(current_space->total_array_size,&current_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:   MakeSpaceContiguous(&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->M,cn=C->N,cm=C->M;
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 (cjj[k]==apj[nextap]) {
211:           caj[k] += (*pA)*apa[apj[nextap++]];
212:         }
213:       }
214:       flops += 2*apnzj;
215:       pA++;
216:     }

218:     /* Zero the current row info for A*P */
219:     for (j=0;j<apnzj;j++) {
220:       apa[apj[j]]      = 0.;
221:       apjdense[apj[j]] = 0;
222:     }
223:   }

225:   /* Assemble the final matrix and clean up */
226:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
227:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
228:   PetscFree(apa);
229:   PetscLogFlops(flops);

231:   return(0);
232: }