1 #define PETSCMAT_DLL 2 3 /* 4 Defines projective product routines where A is a SeqAIJ matrix 5 C = P^T * A * P 6 */ 7 8 #include "src/mat/impls/aij/seq/aij.h" /*I "petscmat.h" I*/ 9 #include "src/mat/utils/freespace.h" 10 #include "petscbt.h" 11 12 #undef __FUNCT__ 13 #define __FUNCT__ "MatPtAPSymbolic_SeqAIJ" 14 PetscErrorCode MatPtAPSymbolic_SeqAIJ(Mat A,Mat P,PetscReal fill,Mat *C) 15 { 16 PetscErrorCode ierr; 17 18 PetscFunctionBegin; 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 ierr = (*P->ops->ptapsymbolic_seqaij)(A,P,fill,C);CHKERRQ(ierr); 23 PetscFunctionReturn(0); 24 } 25 26 #undef __FUNCT__ 27 #define __FUNCT__ "MatPtAPNumeric_SeqAIJ" 28 PetscErrorCode MatPtAPNumeric_SeqAIJ(Mat A,Mat P,Mat C) 29 { 30 PetscErrorCode ierr; 31 32 PetscFunctionBegin; 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 ierr = (*P->ops->ptapnumeric_seqaij)(A,P,C);CHKERRQ(ierr); 37 PetscFunctionReturn(0); 38 } 39 40 #undef __FUNCT__ 41 #define __FUNCT__ "MatPtAPSymbolic_SeqAIJ_SeqAIJ" 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->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; 53 54 PetscFunctionBegin; 55 /* Get ij structure of P^T */ 56 ierr = MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr); 57 ptJ=ptj; 58 59 /* Allocate ci array, arrays for fill computation and */ 60 /* free space for accumulating nonzero column info */ 61 ierr = PetscMalloc((pn+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr); 62 ci[0] = 0; 63 64 ierr = PetscMalloc((2*an+1)*sizeof(PetscInt),&ptadenserow);CHKERRQ(ierr); 65 ierr = PetscMemzero(ptadenserow,(2*an+1)*sizeof(PetscInt));CHKERRQ(ierr); 66 ptasparserow = ptadenserow + an; 67 68 /* create and initialize a linked list */ 69 nlnk = pn+1; 70 ierr = PetscLLCreate(pn,pn,nlnk,lnk,lnkbt);CHKERRQ(ierr); 71 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 ierr = PetscFreeSpaceGet((ai[am]/pm)*pn,&free_space); 75 current_space = free_space; 76 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 ierr = PetscLLAdd(pnzj,pjj,pn,nlnk,lnk,lnkbt);CHKERRQ(ierr); 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 ierr = PetscFreeSpaceGet(current_space->total_array_size,¤t_space);CHKERRQ(ierr); 109 } 110 111 /* Copy data into free space, and zero out denserows */ 112 ierr = PetscLLClean(pn,pn,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 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 ierr = PetscMalloc((ci[pn]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr); 128 ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr); 129 ierr = PetscFree(ptadenserow);CHKERRQ(ierr); 130 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 131 132 /* Allocate space for ca */ 133 ierr = PetscMalloc((ci[pn]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr); 134 ierr = PetscMemzero(ca,(ci[pn]+1)*sizeof(MatScalar));CHKERRQ(ierr); 135 136 /* put together the new matrix */ 137 ierr = MatCreateSeqAIJWithArrays(A->comm,pn,pn,ci,cj,ca,C);CHKERRQ(ierr); 138 139 /* 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; 144 145 /* Clean up. */ 146 ierr = MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr); 147 148 PetscFunctionReturn(0); 149 } 150 151 #undef __FUNCT__ 152 #define __FUNCT__ "MatPtAPNumeric_SeqAIJ_SeqAIJ" 153 PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat C) 154 { 155 PetscErrorCode ierr; 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; 165 166 PetscFunctionBegin; 167 /* Allocate temporary array for storage of one row of A*P */ 168 ierr = PetscMalloc(cn*(sizeof(MatScalar)+2*sizeof(PetscInt)),&apa);CHKERRQ(ierr); 169 ierr = PetscMemzero(apa,cn*(sizeof(MatScalar)+2*sizeof(PetscInt)));CHKERRQ(ierr); 170 171 apj = (PetscInt *)(apa + cn); 172 apjdense = apj + cn; 173 174 /* Clear old values in C */ 175 ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr); 176 177 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 } 196 197 /* 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 ierr = PetscSortInt(apnzj,apj);CHKERRQ(ierr); 200 201 /* 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 } 217 218 /* 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 } 224 225 /* Assemble the final matrix and clean up */ 226 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 227 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 228 ierr = PetscFree(apa);CHKERRQ(ierr); 229 ierr = PetscLogFlops(flops);CHKERRQ(ierr); 230 231 PetscFunctionReturn(0); 232 } 233