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 = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr); 40 PetscOptionsObject->alreadyprinted = PETSC_FALSE; /* a hack to ensure the option shows in '-help' */ 41 ierr = PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[0],&alg,NULL);CHKERRQ(ierr); 42 ierr = PetscOptionsEnd();CHKERRQ(ierr); 43 switch (alg) { 44 case 1: 45 ierr = PetscNew(&atb);CHKERRQ(ierr); 46 ierr = MatTranspose_SeqAIJ(P,MAT_INITIAL_MATRIX,&Pt);CHKERRQ(ierr); 47 ierr = MatMatMatMult(Pt,A,P,MAT_INITIAL_MATRIX,fill,C);CHKERRQ(ierr); 48 49 c = (Mat_SeqAIJ*)(*C)->data; 50 c->atb = atb; 51 atb->At = Pt; 52 atb->destroy = (*C)->ops->destroy; 53 (*C)->ops->destroy = MatDestroy_SeqAIJ_MatTransMatMult; 54 (*C)->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ; 55 PetscFunctionReturn(0); 56 break; 57 #if defined(PETSC_HAVE_HYPRE) 58 case 2: 59 ierr = MatPtAPSymbolic_AIJ_AIJ_wHYPRE(A,P,fill,C);CHKERRQ(ierr); 60 break; 61 #endif 62 default: 63 ierr = MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(A,P,fill,C);CHKERRQ(ierr); 64 break; 65 } 66 } 67 ierr = (*(*C)->ops->ptapnumeric)(A,P,*C);CHKERRQ(ierr); 68 PetscFunctionReturn(0); 69 } 70 71 PetscErrorCode MatDestroy_SeqAIJ_PtAP(Mat A) 72 { 73 PetscErrorCode ierr; 74 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 75 Mat_PtAP *ptap = a->ptap; 76 77 PetscFunctionBegin; 78 ierr = PetscFree(ptap->apa);CHKERRQ(ierr); 79 ierr = PetscFree(ptap->api);CHKERRQ(ierr); 80 ierr = PetscFree(ptap->apj);CHKERRQ(ierr); 81 ierr = (ptap->destroy)(A);CHKERRQ(ierr); 82 ierr = PetscFree(ptap);CHKERRQ(ierr); 83 PetscFunctionReturn(0); 84 } 85 86 PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,PetscReal fill,Mat *C) 87 { 88 PetscErrorCode ierr; 89 PetscFreeSpaceList free_space=NULL,current_space=NULL; 90 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*p = (Mat_SeqAIJ*)P->data,*c; 91 PetscInt *pti,*ptj,*ptJ,*ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj; 92 PetscInt *ci,*cj,*ptadenserow,*ptasparserow,*ptaj,nspacedouble=0; 93 PetscInt an=A->cmap->N,am=A->rmap->N,pn=P->cmap->N,pm=P->rmap->N; 94 PetscInt i,j,k,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi,nlnk,*lnk; 95 MatScalar *ca; 96 PetscBT lnkbt; 97 PetscReal afill; 98 99 PetscFunctionBegin; 100 /* Get ij structure of P^T */ 101 ierr = MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr); 102 ptJ = ptj; 103 104 /* Allocate ci array, arrays for fill computation and */ 105 /* free space for accumulating nonzero column info */ 106 ierr = PetscMalloc1(pn+1,&ci);CHKERRQ(ierr); 107 ci[0] = 0; 108 109 ierr = PetscCalloc1(2*an+1,&ptadenserow);CHKERRQ(ierr); 110 ptasparserow = ptadenserow + an; 111 112 /* create and initialize a linked list */ 113 nlnk = pn+1; 114 ierr = PetscLLCreate(pn,pn,nlnk,lnk,lnkbt);CHKERRQ(ierr); 115 116 /* Set initial free space to be fill*(nnz(A)+ nnz(P)) */ 117 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],pi[pm])),&free_space);CHKERRQ(ierr); 118 current_space = free_space; 119 120 /* Determine symbolic info for each row of C: */ 121 for (i=0; i<pn; i++) { 122 ptnzi = pti[i+1] - pti[i]; 123 ptanzi = 0; 124 /* Determine symbolic row of PtA: */ 125 for (j=0; j<ptnzi; j++) { 126 arow = *ptJ++; 127 anzj = ai[arow+1] - ai[arow]; 128 ajj = aj + ai[arow]; 129 for (k=0; k<anzj; k++) { 130 if (!ptadenserow[ajj[k]]) { 131 ptadenserow[ajj[k]] = -1; 132 ptasparserow[ptanzi++] = ajj[k]; 133 } 134 } 135 } 136 /* Using symbolic info for row of PtA, determine symbolic info for row of C: */ 137 ptaj = ptasparserow; 138 cnzi = 0; 139 for (j=0; j<ptanzi; j++) { 140 prow = *ptaj++; 141 pnzj = pi[prow+1] - pi[prow]; 142 pjj = pj + pi[prow]; 143 /* add non-zero cols of P into the sorted linked list lnk */ 144 ierr = PetscLLAddSorted(pnzj,pjj,pn,nlnk,lnk,lnkbt);CHKERRQ(ierr); 145 cnzi += nlnk; 146 } 147 148 /* If free space is not available, make more free space */ 149 /* Double the amount of total space in the list */ 150 if (current_space->local_remaining<cnzi) { 151 ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),¤t_space);CHKERRQ(ierr); 152 nspacedouble++; 153 } 154 155 /* Copy data into free space, and zero out denserows */ 156 ierr = PetscLLClean(pn,pn,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 157 158 current_space->array += cnzi; 159 current_space->local_used += cnzi; 160 current_space->local_remaining -= cnzi; 161 162 for (j=0; j<ptanzi; j++) ptadenserow[ptasparserow[j]] = 0; 163 164 /* Aside: Perhaps we should save the pta info for the numerical factorization. */ 165 /* For now, we will recompute what is needed. */ 166 ci[i+1] = ci[i] + cnzi; 167 } 168 /* nnz is now stored in ci[ptm], column indices are in the list of free space */ 169 /* Allocate space for cj, initialize cj, and */ 170 /* destroy list of free space and other temporary array(s) */ 171 ierr = PetscMalloc1(ci[pn]+1,&cj);CHKERRQ(ierr); 172 ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr); 173 ierr = PetscFree(ptadenserow);CHKERRQ(ierr); 174 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 175 176 ierr = PetscCalloc1(ci[pn]+1,&ca);CHKERRQ(ierr); 177 178 /* put together the new matrix */ 179 ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),pn,pn,ci,cj,ca,C);CHKERRQ(ierr); 180 ierr = MatSetBlockSizes(*C,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));CHKERRQ(ierr); 181 182 /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */ 183 /* Since these are PETSc arrays, change flags to free them as necessary. */ 184 c = (Mat_SeqAIJ*)((*C)->data); 185 c->free_a = PETSC_TRUE; 186 c->free_ij = PETSC_TRUE; 187 c->nonew = 0; 188 (*C)->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy; 189 190 /* set MatInfo */ 191 afill = (PetscReal)ci[pn]/(ai[am]+pi[pm] + 1.e-5); 192 if (afill < 1.0) afill = 1.0; 193 c->maxnz = ci[pn]; 194 c->nz = ci[pn]; 195 (*C)->info.mallocs = nspacedouble; 196 (*C)->info.fill_ratio_given = fill; 197 (*C)->info.fill_ratio_needed = afill; 198 199 /* Clean up. */ 200 ierr = MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr); 201 #if defined(PETSC_USE_INFO) 202 if (ci[pn] != 0) { 203 ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr); 204 ierr = PetscInfo1((*C),"Use MatPtAP(A,P,MatReuse,%g,&C) for best performance.\n",(double)afill);CHKERRQ(ierr); 205 } else { 206 ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr); 207 } 208 #endif 209 PetscFunctionReturn(0); 210 } 211 212 PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,Mat C) 213 { 214 PetscErrorCode ierr; 215 Mat_SeqAIJ *a = (Mat_SeqAIJ*) A->data; 216 Mat_SeqAIJ *p = (Mat_SeqAIJ*) P->data; 217 Mat_SeqAIJ *c = (Mat_SeqAIJ*) C->data; 218 PetscInt *ai=a->i,*aj=a->j,*apj,*apjdense,*pi=p->i,*pj=p->j,*pJ=p->j,*pjj; 219 PetscInt *ci=c->i,*cj=c->j,*cjj; 220 PetscInt am =A->rmap->N,cn=C->cmap->N,cm=C->rmap->N; 221 PetscInt i,j,k,anzi,pnzi,apnzj,nextap,pnzj,prow,crow; 222 MatScalar *aa=a->a,*apa,*pa=p->a,*pA=p->a,*paj,*ca=c->a,*caj; 223 224 PetscFunctionBegin; 225 /* Allocate temporary array for storage of one row of A*P (cn: non-scalable) */ 226 ierr = PetscMalloc3(cn,&apa,cn,&apjdense,cn,&apj);CHKERRQ(ierr); 227 ierr = PetscMemzero(apa,cn*sizeof(MatScalar));CHKERRQ(ierr); 228 ierr = PetscMemzero(apjdense,cn*sizeof(PetscInt));CHKERRQ(ierr); 229 230 /* Clear old values in C */ 231 ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr); 232 233 for (i=0; i<am; i++) { 234 /* Form sparse row of A*P */ 235 anzi = ai[i+1] - ai[i]; 236 apnzj = 0; 237 for (j=0; j<anzi; j++) { 238 prow = *aj++; 239 pnzj = pi[prow+1] - pi[prow]; 240 pjj = pj + pi[prow]; 241 paj = pa + pi[prow]; 242 for (k=0; k<pnzj; k++) { 243 if (!apjdense[pjj[k]]) { 244 apjdense[pjj[k]] = -1; 245 apj[apnzj++] = pjj[k]; 246 } 247 apa[pjj[k]] += (*aa)*paj[k]; 248 } 249 ierr = PetscLogFlops(2.0*pnzj);CHKERRQ(ierr); 250 aa++; 251 } 252 253 /* Sort the j index array for quick sparse axpy. */ 254 /* Note: a array does not need sorting as it is in dense storage locations. */ 255 ierr = PetscSortInt(apnzj,apj);CHKERRQ(ierr); 256 257 /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */ 258 pnzi = pi[i+1] - pi[i]; 259 for (j=0; j<pnzi; j++) { 260 nextap = 0; 261 crow = *pJ++; 262 cjj = cj + ci[crow]; 263 caj = ca + ci[crow]; 264 /* Perform sparse axpy operation. Note cjj includes apj. */ 265 for (k=0; nextap<apnzj; k++) { 266 #if defined(PETSC_USE_DEBUG) 267 if (k >= ci[crow+1] - ci[crow]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"k too large k %d, crow %d",k,crow); 268 #endif 269 if (cjj[k]==apj[nextap]) { 270 caj[k] += (*pA)*apa[apj[nextap++]]; 271 } 272 } 273 ierr = PetscLogFlops(2.0*apnzj);CHKERRQ(ierr); 274 pA++; 275 } 276 277 /* Zero the current row info for A*P */ 278 for (j=0; j<apnzj; j++) { 279 apa[apj[j]] = 0.; 280 apjdense[apj[j]] = 0; 281 } 282 } 283 284 /* Assemble the final matrix and clean up */ 285 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 286 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 287 288 ierr = PetscFree3(apa,apjdense,apj);CHKERRQ(ierr); 289 PetscFunctionReturn(0); 290 } 291 292 PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat C) 293 { 294 PetscErrorCode ierr; 295 Mat_SeqAIJ *c = (Mat_SeqAIJ*)C->data; 296 Mat_MatTransMatMult *atb = c->atb; 297 Mat Pt = atb->At; 298 299 PetscFunctionBegin; 300 ierr = MatTranspose_SeqAIJ(P,MAT_REUSE_MATRIX,&Pt);CHKERRQ(ierr); 301 ierr = (C->ops->matmatmultnumeric)(Pt,A,P,C);CHKERRQ(ierr); 302 PetscFunctionReturn(0); 303 } 304