1 2 /* 3 Defines projective product routines where A is a SeqAIJ matrix 4 C = P^T * A * P 5 */ 6 7 #include <../src/mat/impls/aij/seq/aij.h> /*I "petscmat.h" I*/ 8 #include <../src/mat/utils/freespace.h> 9 #include <petscbt.h> 10 #include <petsctime.h> 11 12 #if defined(PETSC_HAVE_HYPRE) 13 PETSC_INTERN PetscErrorCode MatPtAPSymbolic_AIJ_AIJ_wHYPRE(Mat,Mat,PetscReal,Mat); 14 #endif 15 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; 25 Mat_MatTransMatMult *atb; 26 Mat_SeqAIJ *c; 27 28 PetscFunctionBegin; 29 /* "scalable" */ 30 ierr = PetscStrcmp(alg,"scalable",&flg);CHKERRQ(ierr); 31 if (flg) { 32 ierr = MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(A,P,fill,C);CHKERRQ(ierr); 33 C->ops->productnumeric = MatProductNumeric_PtAP; 34 PetscFunctionReturn(0); 35 } 36 37 /* "rap" */ 38 ierr = PetscStrcmp(alg,"rap",&flg);CHKERRQ(ierr); 39 if (flg) { /* Set default algorithm */ 40 ierr = PetscNew(&atb);CHKERRQ(ierr); 41 ierr = MatTranspose_SeqAIJ(P,MAT_INITIAL_MATRIX,&Pt);CHKERRQ(ierr); 42 ierr = MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ(Pt,A,P,fill,C);CHKERRQ(ierr); 43 44 c = (Mat_SeqAIJ*)C->data; 45 c->atb = atb; 46 atb->At = Pt; 47 atb->destroy = C->ops->destroy; 48 C->ops->destroy = MatDestroy_SeqAIJ_MatTransMatMult; 49 C->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ; 50 C->ops->productnumeric = MatProductNumeric_PtAP; 51 PetscFunctionReturn(0); 52 } 53 54 /* hypre */ 55 #if defined(PETSC_HAVE_HYPRE) 56 ierr = PetscStrcmp(alg,"hypre",&flg);CHKERRQ(ierr); 57 if (flg) { 58 ierr = MatPtAPSymbolic_AIJ_AIJ_wHYPRE(A,P,fill,C);CHKERRQ(ierr); 59 PetscFunctionReturn(0); 60 } 61 #endif 62 63 SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatProductType is not supported"); 64 PetscFunctionReturn(0); 65 } 66 67 PetscErrorCode MatDestroy_SeqAIJ_PtAP(Mat A) 68 { 69 PetscErrorCode ierr; 70 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 71 Mat_AP *ap = a->ap; 72 73 PetscFunctionBegin; 74 ierr = PetscFree(ap->apa);CHKERRQ(ierr); 75 ierr = PetscFree(ap->api);CHKERRQ(ierr); 76 ierr = PetscFree(ap->apj);CHKERRQ(ierr); 77 ierr = (ap->destroy)(A);CHKERRQ(ierr); 78 ierr = PetscFree(ap);CHKERRQ(ierr); 79 PetscFunctionReturn(0); 80 } 81 82 PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,PetscReal fill,Mat C) 83 { 84 PetscErrorCode ierr; 85 PetscFreeSpaceList free_space=NULL,current_space=NULL; 86 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*p = (Mat_SeqAIJ*)P->data,*c; 87 PetscInt *pti,*ptj,*ptJ,*ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj; 88 PetscInt *ci,*cj,*ptadenserow,*ptasparserow,*ptaj,nspacedouble=0; 89 PetscInt an=A->cmap->N,am=A->rmap->N,pn=P->cmap->N,pm=P->rmap->N; 90 PetscInt i,j,k,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi,nlnk,*lnk; 91 MatScalar *ca; 92 PetscBT lnkbt; 93 PetscReal afill; 94 95 PetscFunctionBegin; 96 /* Get ij structure of P^T */ 97 ierr = MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr); 98 ptJ = ptj; 99 100 /* Allocate ci array, arrays for fill computation and */ 101 /* free space for accumulating nonzero column info */ 102 ierr = PetscMalloc1(pn+1,&ci);CHKERRQ(ierr); 103 ci[0] = 0; 104 105 ierr = PetscCalloc1(2*an+1,&ptadenserow);CHKERRQ(ierr); 106 ptasparserow = ptadenserow + an; 107 108 /* create and initialize a linked list */ 109 nlnk = pn+1; 110 ierr = PetscLLCreate(pn,pn,nlnk,lnk,lnkbt);CHKERRQ(ierr); 111 112 /* Set initial free space to be fill*(nnz(A)+ nnz(P)) */ 113 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],pi[pm])),&free_space);CHKERRQ(ierr); 114 current_space = free_space; 115 116 /* Determine symbolic info for each row of C: */ 117 for (i=0; i<pn; i++) { 118 ptnzi = pti[i+1] - pti[i]; 119 ptanzi = 0; 120 /* Determine symbolic row of PtA: */ 121 for (j=0; j<ptnzi; j++) { 122 arow = *ptJ++; 123 anzj = ai[arow+1] - ai[arow]; 124 ajj = aj + ai[arow]; 125 for (k=0; k<anzj; k++) { 126 if (!ptadenserow[ajj[k]]) { 127 ptadenserow[ajj[k]] = -1; 128 ptasparserow[ptanzi++] = ajj[k]; 129 } 130 } 131 } 132 /* Using symbolic info for row of PtA, determine symbolic info for row of C: */ 133 ptaj = ptasparserow; 134 cnzi = 0; 135 for (j=0; j<ptanzi; j++) { 136 prow = *ptaj++; 137 pnzj = pi[prow+1] - pi[prow]; 138 pjj = pj + pi[prow]; 139 /* add non-zero cols of P into the sorted linked list lnk */ 140 ierr = PetscLLAddSorted(pnzj,pjj,pn,nlnk,lnk,lnkbt);CHKERRQ(ierr); 141 cnzi += nlnk; 142 } 143 144 /* If free space is not available, make more free space */ 145 /* Double the amount of total space in the list */ 146 if (current_space->local_remaining<cnzi) { 147 ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),¤t_space);CHKERRQ(ierr); 148 nspacedouble++; 149 } 150 151 /* Copy data into free space, and zero out denserows */ 152 ierr = PetscLLClean(pn,pn,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 153 154 current_space->array += cnzi; 155 current_space->local_used += cnzi; 156 current_space->local_remaining -= cnzi; 157 158 for (j=0; j<ptanzi; j++) ptadenserow[ptasparserow[j]] = 0; 159 160 /* Aside: Perhaps we should save the pta info for the numerical factorization. */ 161 /* For now, we will recompute what is needed. */ 162 ci[i+1] = ci[i] + cnzi; 163 } 164 /* nnz is now stored in ci[ptm], column indices are in the list of free space */ 165 /* Allocate space for cj, initialize cj, and */ 166 /* destroy list of free space and other temporary array(s) */ 167 ierr = PetscMalloc1(ci[pn]+1,&cj);CHKERRQ(ierr); 168 ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr); 169 ierr = PetscFree(ptadenserow);CHKERRQ(ierr); 170 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 171 172 ierr = PetscCalloc1(ci[pn]+1,&ca);CHKERRQ(ierr); 173 174 /* put together the new matrix */ 175 ierr = MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A),pn,pn,ci,cj,ca,((PetscObject)A)->type_name,C);CHKERRQ(ierr); 176 ierr = MatSetBlockSizes(C,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));CHKERRQ(ierr); 177 178 /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */ 179 /* Since these are PETSc arrays, change flags to free them as necessary. */ 180 c = (Mat_SeqAIJ*)((C)->data); 181 c->free_a = PETSC_TRUE; 182 c->free_ij = PETSC_TRUE; 183 c->nonew = 0; 184 C->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy; 185 186 /* set MatInfo */ 187 afill = (PetscReal)ci[pn]/(ai[am]+pi[pm] + 1.e-5); 188 if (afill < 1.0) afill = 1.0; 189 c->maxnz = ci[pn]; 190 c->nz = ci[pn]; 191 C->info.mallocs = nspacedouble; 192 C->info.fill_ratio_given = fill; 193 C->info.fill_ratio_needed = afill; 194 195 /* Clean up. */ 196 ierr = MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr); 197 #if defined(PETSC_USE_INFO) 198 if (ci[pn] != 0) { 199 ierr = PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr); 200 ierr = PetscInfo1(C,"Use MatPtAP(A,P,MatReuse,%g,&C) for best performance.\n",(double)afill);CHKERRQ(ierr); 201 } else { 202 ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr); 203 } 204 #endif 205 PetscFunctionReturn(0); 206 } 207 208 PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,Mat C) 209 { 210 PetscErrorCode ierr; 211 Mat_SeqAIJ *a = (Mat_SeqAIJ*) A->data; 212 Mat_SeqAIJ *p = (Mat_SeqAIJ*) P->data; 213 Mat_SeqAIJ *c = (Mat_SeqAIJ*) C->data; 214 PetscInt *ai=a->i,*aj=a->j,*apj,*apjdense,*pi=p->i,*pj=p->j,*pJ=p->j,*pjj; 215 PetscInt *ci=c->i,*cj=c->j,*cjj; 216 PetscInt am =A->rmap->N,cn=C->cmap->N,cm=C->rmap->N; 217 PetscInt i,j,k,anzi,pnzi,apnzj,nextap,pnzj,prow,crow; 218 MatScalar *aa=a->a,*apa,*pa=p->a,*pA=p->a,*paj,*ca=c->a,*caj; 219 220 PetscFunctionBegin; 221 /* Allocate temporary array for storage of one row of A*P (cn: non-scalable) */ 222 ierr = PetscCalloc2(cn,&apa,cn,&apjdense);CHKERRQ(ierr); 223 ierr = PetscMalloc1(cn,&apj);CHKERRQ(ierr); 224 225 /* Clear old values in C */ 226 ierr = PetscArrayzero(ca,ci[cm]);CHKERRQ(ierr); 227 228 for (i=0; i<am; i++) { 229 /* Form sparse row of A*P */ 230 anzi = ai[i+1] - ai[i]; 231 apnzj = 0; 232 for (j=0; j<anzi; j++) { 233 prow = *aj++; 234 pnzj = pi[prow+1] - pi[prow]; 235 pjj = pj + pi[prow]; 236 paj = pa + pi[prow]; 237 for (k=0; k<pnzj; k++) { 238 if (!apjdense[pjj[k]]) { 239 apjdense[pjj[k]] = -1; 240 apj[apnzj++] = pjj[k]; 241 } 242 apa[pjj[k]] += (*aa)*paj[k]; 243 } 244 ierr = PetscLogFlops(2.0*pnzj);CHKERRQ(ierr); 245 aa++; 246 } 247 248 /* Sort the j index array for quick sparse axpy. */ 249 /* Note: a array does not need sorting as it is in dense storage locations. */ 250 ierr = PetscSortInt(apnzj,apj);CHKERRQ(ierr); 251 252 /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */ 253 pnzi = pi[i+1] - pi[i]; 254 for (j=0; j<pnzi; j++) { 255 nextap = 0; 256 crow = *pJ++; 257 cjj = cj + ci[crow]; 258 caj = ca + ci[crow]; 259 /* Perform sparse axpy operation. Note cjj includes apj. */ 260 for (k=0; nextap<apnzj; k++) { 261 if (PetscUnlikelyDebug(k >= ci[crow+1] - ci[crow])) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"k too large k %d, crow %d",k,crow); 262 if (cjj[k]==apj[nextap]) { 263 caj[k] += (*pA)*apa[apj[nextap++]]; 264 } 265 } 266 ierr = PetscLogFlops(2.0*apnzj);CHKERRQ(ierr); 267 pA++; 268 } 269 270 /* Zero the current row info for A*P */ 271 for (j=0; j<apnzj; j++) { 272 apa[apj[j]] = 0.; 273 apjdense[apj[j]] = 0; 274 } 275 } 276 277 /* Assemble the final matrix and clean up */ 278 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 279 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 280 281 ierr = PetscFree2(apa,apjdense);CHKERRQ(ierr); 282 ierr = PetscFree(apj);CHKERRQ(ierr); 283 PetscFunctionReturn(0); 284 } 285 286 PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat C) 287 { 288 PetscErrorCode ierr; 289 Mat_SeqAIJ *c = (Mat_SeqAIJ*)C->data; 290 Mat_MatTransMatMult *atb = c->atb; 291 Mat Pt = atb->At; 292 293 PetscFunctionBegin; 294 ierr = MatTranspose_SeqAIJ(P,MAT_REUSE_MATRIX,&Pt);CHKERRQ(ierr); 295 ierr = (C->ops->matmatmultnumeric)(Pt,A,P,C);CHKERRQ(ierr); 296 PetscFunctionReturn(0); 297 } 298