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 PETSC_INTERN PetscErrorCode MatPtAP_SeqAIJ_SeqAIJ(Mat A,Mat P,MatReuse scall,PetscReal fill,Mat *C) 17 { 18 PetscErrorCode ierr; 19 #if !defined(PETSC_HAVE_HYPRE) 20 const char *algTypes[2] = {"scalable","rap"}; 21 PetscInt nalg = 2; 22 #else 23 const char *algTypes[3] = {"scalable","rap","hypre"}; 24 PetscInt nalg = 3; 25 #endif 26 PetscInt alg = 1; /* set default algorithm */ 27 Mat Pt; 28 Mat_MatTransMatMult *atb; 29 Mat_SeqAIJ *c; 30 31 PetscFunctionBegin; 32 if (scall == MAT_INITIAL_MATRIX) { 33 /* 34 Alg 'scalable' determines which implementations to be used: 35 "rap": Pt = P^T and C = Pt*A*P 36 "scalable": do outer product and two sparse axpy in MatPtAPNumeric() - might slow, does not store structure of A*P. 37 "hypre": use boomerAMGBuildCoarseOperator. 38 */ 39 ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)A),((PetscObject)A)->prefix,"MatPtAP","Mat");CHKERRQ(ierr); 40 ierr = PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[0],&alg,NULL);CHKERRQ(ierr); 41 ierr = PetscOptionsEnd();CHKERRQ(ierr); 42 switch (alg) { 43 case 1: 44 ierr = PetscNew(&atb);CHKERRQ(ierr); 45 ierr = MatTranspose_SeqAIJ(P,MAT_INITIAL_MATRIX,&Pt);CHKERRQ(ierr); 46 ierr = MatMatMatMult(Pt,A,P,MAT_INITIAL_MATRIX,fill,C);CHKERRQ(ierr); 47 48 c = (Mat_SeqAIJ*)(*C)->data; 49 c->atb = atb; 50 atb->At = Pt; 51 atb->destroy = (*C)->ops->destroy; 52 (*C)->ops->destroy = MatDestroy_SeqAIJ_MatTransMatMult; 53 (*C)->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ; 54 PetscFunctionReturn(0); 55 break; 56 #if defined(PETSC_HAVE_HYPRE) 57 case 2: 58 ierr = MatPtAPSymbolic_AIJ_AIJ_wHYPRE(A,P,fill,C);CHKERRQ(ierr); 59 break; 60 #endif 61 default: 62 ierr = MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(A,P,fill,C);CHKERRQ(ierr); 63 break; 64 } 65 } 66 ierr = (*(*C)->ops->ptapnumeric)(A,P,*C);CHKERRQ(ierr); 67 PetscFunctionReturn(0); 68 } 69 70 PetscErrorCode MatDestroy_SeqAIJ_PtAP(Mat A) 71 { 72 PetscErrorCode ierr; 73 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 74 Mat_AP *ap = a->ap; 75 76 PetscFunctionBegin; 77 ierr = PetscFree(ap->apa);CHKERRQ(ierr); 78 ierr = PetscFree(ap->api);CHKERRQ(ierr); 79 ierr = PetscFree(ap->apj);CHKERRQ(ierr); 80 ierr = (ap->destroy)(A);CHKERRQ(ierr); 81 ierr = PetscFree(ap);CHKERRQ(ierr); 82 PetscFunctionReturn(0); 83 } 84 85 PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,PetscReal fill,Mat *C) 86 { 87 PetscErrorCode ierr; 88 PetscFreeSpaceList free_space=NULL,current_space=NULL; 89 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*p = (Mat_SeqAIJ*)P->data,*c; 90 PetscInt *pti,*ptj,*ptJ,*ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj; 91 PetscInt *ci,*cj,*ptadenserow,*ptasparserow,*ptaj,nspacedouble=0; 92 PetscInt an=A->cmap->N,am=A->rmap->N,pn=P->cmap->N,pm=P->rmap->N; 93 PetscInt i,j,k,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi,nlnk,*lnk; 94 MatScalar *ca; 95 PetscBT lnkbt; 96 PetscReal afill; 97 98 PetscFunctionBegin; 99 /* Get ij structure of P^T */ 100 ierr = MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr); 101 ptJ = ptj; 102 103 /* Allocate ci array, arrays for fill computation and */ 104 /* free space for accumulating nonzero column info */ 105 ierr = PetscMalloc1(pn+1,&ci);CHKERRQ(ierr); 106 ci[0] = 0; 107 108 ierr = PetscCalloc1(2*an+1,&ptadenserow);CHKERRQ(ierr); 109 ptasparserow = ptadenserow + an; 110 111 /* create and initialize a linked list */ 112 nlnk = pn+1; 113 ierr = PetscLLCreate(pn,pn,nlnk,lnk,lnkbt);CHKERRQ(ierr); 114 115 /* Set initial free space to be fill*(nnz(A)+ nnz(P)) */ 116 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],pi[pm])),&free_space);CHKERRQ(ierr); 117 current_space = free_space; 118 119 /* Determine symbolic info for each row of C: */ 120 for (i=0; i<pn; i++) { 121 ptnzi = pti[i+1] - pti[i]; 122 ptanzi = 0; 123 /* Determine symbolic row of PtA: */ 124 for (j=0; j<ptnzi; j++) { 125 arow = *ptJ++; 126 anzj = ai[arow+1] - ai[arow]; 127 ajj = aj + ai[arow]; 128 for (k=0; k<anzj; k++) { 129 if (!ptadenserow[ajj[k]]) { 130 ptadenserow[ajj[k]] = -1; 131 ptasparserow[ptanzi++] = ajj[k]; 132 } 133 } 134 } 135 /* Using symbolic info for row of PtA, determine symbolic info for row of C: */ 136 ptaj = ptasparserow; 137 cnzi = 0; 138 for (j=0; j<ptanzi; j++) { 139 prow = *ptaj++; 140 pnzj = pi[prow+1] - pi[prow]; 141 pjj = pj + pi[prow]; 142 /* add non-zero cols of P into the sorted linked list lnk */ 143 ierr = PetscLLAddSorted(pnzj,pjj,pn,nlnk,lnk,lnkbt);CHKERRQ(ierr); 144 cnzi += nlnk; 145 } 146 147 /* If free space is not available, make more free space */ 148 /* Double the amount of total space in the list */ 149 if (current_space->local_remaining<cnzi) { 150 ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),¤t_space);CHKERRQ(ierr); 151 nspacedouble++; 152 } 153 154 /* Copy data into free space, and zero out denserows */ 155 ierr = PetscLLClean(pn,pn,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 156 157 current_space->array += cnzi; 158 current_space->local_used += cnzi; 159 current_space->local_remaining -= cnzi; 160 161 for (j=0; j<ptanzi; j++) ptadenserow[ptasparserow[j]] = 0; 162 163 /* Aside: Perhaps we should save the pta info for the numerical factorization. */ 164 /* For now, we will recompute what is needed. */ 165 ci[i+1] = ci[i] + cnzi; 166 } 167 /* nnz is now stored in ci[ptm], column indices are in the list of free space */ 168 /* Allocate space for cj, initialize cj, and */ 169 /* destroy list of free space and other temporary array(s) */ 170 ierr = PetscMalloc1(ci[pn]+1,&cj);CHKERRQ(ierr); 171 ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr); 172 ierr = PetscFree(ptadenserow);CHKERRQ(ierr); 173 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 174 175 ierr = PetscCalloc1(ci[pn]+1,&ca);CHKERRQ(ierr); 176 177 /* put together the new matrix */ 178 ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),pn,pn,ci,cj,ca,C);CHKERRQ(ierr); 179 ierr = MatSetBlockSizes(*C,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));CHKERRQ(ierr); 180 181 /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */ 182 /* Since these are PETSc arrays, change flags to free them as necessary. */ 183 c = (Mat_SeqAIJ*)((*C)->data); 184 c->free_a = PETSC_TRUE; 185 c->free_ij = PETSC_TRUE; 186 c->nonew = 0; 187 (*C)->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy; 188 189 /* set MatInfo */ 190 afill = (PetscReal)ci[pn]/(ai[am]+pi[pm] + 1.e-5); 191 if (afill < 1.0) afill = 1.0; 192 c->maxnz = ci[pn]; 193 c->nz = ci[pn]; 194 (*C)->info.mallocs = nspacedouble; 195 (*C)->info.fill_ratio_given = fill; 196 (*C)->info.fill_ratio_needed = afill; 197 198 /* Clean up. */ 199 ierr = MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr); 200 #if defined(PETSC_USE_INFO) 201 if (ci[pn] != 0) { 202 ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr); 203 ierr = PetscInfo1((*C),"Use MatPtAP(A,P,MatReuse,%g,&C) for best performance.\n",(double)afill);CHKERRQ(ierr); 204 } else { 205 ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr); 206 } 207 #endif 208 PetscFunctionReturn(0); 209 } 210 211 PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,Mat C) 212 { 213 PetscErrorCode ierr; 214 Mat_SeqAIJ *a = (Mat_SeqAIJ*) A->data; 215 Mat_SeqAIJ *p = (Mat_SeqAIJ*) P->data; 216 Mat_SeqAIJ *c = (Mat_SeqAIJ*) C->data; 217 PetscInt *ai=a->i,*aj=a->j,*apj,*apjdense,*pi=p->i,*pj=p->j,*pJ=p->j,*pjj; 218 PetscInt *ci=c->i,*cj=c->j,*cjj; 219 PetscInt am =A->rmap->N,cn=C->cmap->N,cm=C->rmap->N; 220 PetscInt i,j,k,anzi,pnzi,apnzj,nextap,pnzj,prow,crow; 221 MatScalar *aa=a->a,*apa,*pa=p->a,*pA=p->a,*paj,*ca=c->a,*caj; 222 223 PetscFunctionBegin; 224 /* Allocate temporary array for storage of one row of A*P (cn: non-scalable) */ 225 ierr = PetscMalloc3(cn,&apa,cn,&apjdense,cn,&apj);CHKERRQ(ierr); 226 ierr = PetscMemzero(apa,cn*sizeof(MatScalar));CHKERRQ(ierr); 227 ierr = PetscMemzero(apjdense,cn*sizeof(PetscInt));CHKERRQ(ierr); 228 229 /* Clear old values in C */ 230 ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr); 231 232 for (i=0; i<am; i++) { 233 /* Form sparse row of A*P */ 234 anzi = ai[i+1] - ai[i]; 235 apnzj = 0; 236 for (j=0; j<anzi; j++) { 237 prow = *aj++; 238 pnzj = pi[prow+1] - pi[prow]; 239 pjj = pj + pi[prow]; 240 paj = pa + pi[prow]; 241 for (k=0; k<pnzj; k++) { 242 if (!apjdense[pjj[k]]) { 243 apjdense[pjj[k]] = -1; 244 apj[apnzj++] = pjj[k]; 245 } 246 apa[pjj[k]] += (*aa)*paj[k]; 247 } 248 ierr = PetscLogFlops(2.0*pnzj);CHKERRQ(ierr); 249 aa++; 250 } 251 252 /* Sort the j index array for quick sparse axpy. */ 253 /* Note: a array does not need sorting as it is in dense storage locations. */ 254 ierr = PetscSortInt(apnzj,apj);CHKERRQ(ierr); 255 256 /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */ 257 pnzi = pi[i+1] - pi[i]; 258 for (j=0; j<pnzi; j++) { 259 nextap = 0; 260 crow = *pJ++; 261 cjj = cj + ci[crow]; 262 caj = ca + ci[crow]; 263 /* Perform sparse axpy operation. Note cjj includes apj. */ 264 for (k=0; nextap<apnzj; k++) { 265 #if defined(PETSC_USE_DEBUG) 266 if (k >= ci[crow+1] - ci[crow]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"k too large k %d, crow %d",k,crow); 267 #endif 268 if (cjj[k]==apj[nextap]) { 269 caj[k] += (*pA)*apa[apj[nextap++]]; 270 } 271 } 272 ierr = PetscLogFlops(2.0*apnzj);CHKERRQ(ierr); 273 pA++; 274 } 275 276 /* Zero the current row info for A*P */ 277 for (j=0; j<apnzj; j++) { 278 apa[apj[j]] = 0.; 279 apjdense[apj[j]] = 0; 280 } 281 } 282 283 /* Assemble the final matrix and clean up */ 284 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 285 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 286 287 ierr = PetscFree3(apa,apjdense,apj);CHKERRQ(ierr); 288 PetscFunctionReturn(0); 289 } 290 291 PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat C) 292 { 293 PetscErrorCode ierr; 294 Mat_SeqAIJ *c = (Mat_SeqAIJ*)C->data; 295 Mat_MatTransMatMult *atb = c->atb; 296 Mat Pt = atb->At; 297 298 PetscFunctionBegin; 299 ierr = MatTranspose_SeqAIJ(P,MAT_REUSE_MATRIX,&Pt);CHKERRQ(ierr); 300 ierr = (C->ops->matmatmultnumeric)(Pt,A,P,C);CHKERRQ(ierr); 301 PetscFunctionReturn(0); 302 } 303