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 = PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr); 59 ierr = MatPtAPSymbolic_AIJ_AIJ_wHYPRE(A,P,fill,C);CHKERRQ(ierr); 60 ierr = PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr); 61 break; 62 #endif 63 default: 64 ierr = PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr); 65 ierr = MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(A,P,fill,C);CHKERRQ(ierr); 66 ierr = PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr); 67 break; 68 } 69 } 70 ierr = PetscLogEventBegin(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr); 71 ierr = (*(*C)->ops->ptapnumeric)(A,P,*C);CHKERRQ(ierr); 72 ierr = PetscLogEventEnd(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr); 73 PetscFunctionReturn(0); 74 } 75 76 PetscErrorCode MatDestroy_SeqAIJ_PtAP(Mat A) 77 { 78 PetscErrorCode ierr; 79 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 80 Mat_AP *ap = a->ap; 81 82 PetscFunctionBegin; 83 ierr = PetscFree(ap->apa);CHKERRQ(ierr); 84 ierr = PetscFree(ap->api);CHKERRQ(ierr); 85 ierr = PetscFree(ap->apj);CHKERRQ(ierr); 86 ierr = (ap->destroy)(A);CHKERRQ(ierr); 87 ierr = PetscFree(ap);CHKERRQ(ierr); 88 PetscFunctionReturn(0); 89 } 90 91 PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,PetscReal fill,Mat *C) 92 { 93 PetscErrorCode ierr; 94 PetscFreeSpaceList free_space=NULL,current_space=NULL; 95 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*p = (Mat_SeqAIJ*)P->data,*c; 96 PetscInt *pti,*ptj,*ptJ,*ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj; 97 PetscInt *ci,*cj,*ptadenserow,*ptasparserow,*ptaj,nspacedouble=0; 98 PetscInt an=A->cmap->N,am=A->rmap->N,pn=P->cmap->N,pm=P->rmap->N; 99 PetscInt i,j,k,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi,nlnk,*lnk; 100 MatScalar *ca; 101 PetscBT lnkbt; 102 PetscReal afill; 103 104 PetscFunctionBegin; 105 /* Get ij structure of P^T */ 106 ierr = MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr); 107 ptJ = ptj; 108 109 /* Allocate ci array, arrays for fill computation and */ 110 /* free space for accumulating nonzero column info */ 111 ierr = PetscMalloc1(pn+1,&ci);CHKERRQ(ierr); 112 ci[0] = 0; 113 114 ierr = PetscCalloc1(2*an+1,&ptadenserow);CHKERRQ(ierr); 115 ptasparserow = ptadenserow + an; 116 117 /* create and initialize a linked list */ 118 nlnk = pn+1; 119 ierr = PetscLLCreate(pn,pn,nlnk,lnk,lnkbt);CHKERRQ(ierr); 120 121 /* Set initial free space to be fill*(nnz(A)+ nnz(P)) */ 122 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],pi[pm])),&free_space);CHKERRQ(ierr); 123 current_space = free_space; 124 125 /* Determine symbolic info for each row of C: */ 126 for (i=0; i<pn; i++) { 127 ptnzi = pti[i+1] - pti[i]; 128 ptanzi = 0; 129 /* Determine symbolic row of PtA: */ 130 for (j=0; j<ptnzi; j++) { 131 arow = *ptJ++; 132 anzj = ai[arow+1] - ai[arow]; 133 ajj = aj + ai[arow]; 134 for (k=0; k<anzj; k++) { 135 if (!ptadenserow[ajj[k]]) { 136 ptadenserow[ajj[k]] = -1; 137 ptasparserow[ptanzi++] = ajj[k]; 138 } 139 } 140 } 141 /* Using symbolic info for row of PtA, determine symbolic info for row of C: */ 142 ptaj = ptasparserow; 143 cnzi = 0; 144 for (j=0; j<ptanzi; j++) { 145 prow = *ptaj++; 146 pnzj = pi[prow+1] - pi[prow]; 147 pjj = pj + pi[prow]; 148 /* add non-zero cols of P into the sorted linked list lnk */ 149 ierr = PetscLLAddSorted(pnzj,pjj,pn,nlnk,lnk,lnkbt);CHKERRQ(ierr); 150 cnzi += nlnk; 151 } 152 153 /* If free space is not available, make more free space */ 154 /* Double the amount of total space in the list */ 155 if (current_space->local_remaining<cnzi) { 156 ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),¤t_space);CHKERRQ(ierr); 157 nspacedouble++; 158 } 159 160 /* Copy data into free space, and zero out denserows */ 161 ierr = PetscLLClean(pn,pn,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 162 163 current_space->array += cnzi; 164 current_space->local_used += cnzi; 165 current_space->local_remaining -= cnzi; 166 167 for (j=0; j<ptanzi; j++) ptadenserow[ptasparserow[j]] = 0; 168 169 /* Aside: Perhaps we should save the pta info for the numerical factorization. */ 170 /* For now, we will recompute what is needed. */ 171 ci[i+1] = ci[i] + cnzi; 172 } 173 /* nnz is now stored in ci[ptm], column indices are in the list of free space */ 174 /* Allocate space for cj, initialize cj, and */ 175 /* destroy list of free space and other temporary array(s) */ 176 ierr = PetscMalloc1(ci[pn]+1,&cj);CHKERRQ(ierr); 177 ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr); 178 ierr = PetscFree(ptadenserow);CHKERRQ(ierr); 179 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 180 181 ierr = PetscCalloc1(ci[pn]+1,&ca);CHKERRQ(ierr); 182 183 /* put together the new matrix */ 184 ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),pn,pn,ci,cj,ca,C);CHKERRQ(ierr); 185 ierr = MatSetBlockSizes(*C,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));CHKERRQ(ierr); 186 187 /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */ 188 /* Since these are PETSc arrays, change flags to free them as necessary. */ 189 c = (Mat_SeqAIJ*)((*C)->data); 190 c->free_a = PETSC_TRUE; 191 c->free_ij = PETSC_TRUE; 192 c->nonew = 0; 193 (*C)->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy; 194 195 /* set MatInfo */ 196 afill = (PetscReal)ci[pn]/(ai[am]+pi[pm] + 1.e-5); 197 if (afill < 1.0) afill = 1.0; 198 c->maxnz = ci[pn]; 199 c->nz = ci[pn]; 200 (*C)->info.mallocs = nspacedouble; 201 (*C)->info.fill_ratio_given = fill; 202 (*C)->info.fill_ratio_needed = afill; 203 204 /* Clean up. */ 205 ierr = MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr); 206 #if defined(PETSC_USE_INFO) 207 if (ci[pn] != 0) { 208 ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr); 209 ierr = PetscInfo1((*C),"Use MatPtAP(A,P,MatReuse,%g,&C) for best performance.\n",(double)afill);CHKERRQ(ierr); 210 } else { 211 ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr); 212 } 213 #endif 214 PetscFunctionReturn(0); 215 } 216 217 PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,Mat C) 218 { 219 PetscErrorCode ierr; 220 Mat_SeqAIJ *a = (Mat_SeqAIJ*) A->data; 221 Mat_SeqAIJ *p = (Mat_SeqAIJ*) P->data; 222 Mat_SeqAIJ *c = (Mat_SeqAIJ*) C->data; 223 PetscInt *ai=a->i,*aj=a->j,*apj,*apjdense,*pi=p->i,*pj=p->j,*pJ=p->j,*pjj; 224 PetscInt *ci=c->i,*cj=c->j,*cjj; 225 PetscInt am =A->rmap->N,cn=C->cmap->N,cm=C->rmap->N; 226 PetscInt i,j,k,anzi,pnzi,apnzj,nextap,pnzj,prow,crow; 227 MatScalar *aa=a->a,*apa,*pa=p->a,*pA=p->a,*paj,*ca=c->a,*caj; 228 229 PetscFunctionBegin; 230 /* Allocate temporary array for storage of one row of A*P (cn: non-scalable) */ 231 ierr = PetscMalloc3(cn,&apa,cn,&apjdense,cn,&apj);CHKERRQ(ierr); 232 ierr = PetscMemzero(apa,cn*sizeof(MatScalar));CHKERRQ(ierr); 233 ierr = PetscMemzero(apjdense,cn*sizeof(PetscInt));CHKERRQ(ierr); 234 235 /* Clear old values in C */ 236 ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr); 237 238 for (i=0; i<am; i++) { 239 /* Form sparse row of A*P */ 240 anzi = ai[i+1] - ai[i]; 241 apnzj = 0; 242 for (j=0; j<anzi; j++) { 243 prow = *aj++; 244 pnzj = pi[prow+1] - pi[prow]; 245 pjj = pj + pi[prow]; 246 paj = pa + pi[prow]; 247 for (k=0; k<pnzj; k++) { 248 if (!apjdense[pjj[k]]) { 249 apjdense[pjj[k]] = -1; 250 apj[apnzj++] = pjj[k]; 251 } 252 apa[pjj[k]] += (*aa)*paj[k]; 253 } 254 ierr = PetscLogFlops(2.0*pnzj);CHKERRQ(ierr); 255 aa++; 256 } 257 258 /* Sort the j index array for quick sparse axpy. */ 259 /* Note: a array does not need sorting as it is in dense storage locations. */ 260 ierr = PetscSortInt(apnzj,apj);CHKERRQ(ierr); 261 262 /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */ 263 pnzi = pi[i+1] - pi[i]; 264 for (j=0; j<pnzi; j++) { 265 nextap = 0; 266 crow = *pJ++; 267 cjj = cj + ci[crow]; 268 caj = ca + ci[crow]; 269 /* Perform sparse axpy operation. Note cjj includes apj. */ 270 for (k=0; nextap<apnzj; k++) { 271 #if defined(PETSC_USE_DEBUG) 272 if (k >= ci[crow+1] - ci[crow]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"k too large k %d, crow %d",k,crow); 273 #endif 274 if (cjj[k]==apj[nextap]) { 275 caj[k] += (*pA)*apa[apj[nextap++]]; 276 } 277 } 278 ierr = PetscLogFlops(2.0*apnzj);CHKERRQ(ierr); 279 pA++; 280 } 281 282 /* Zero the current row info for A*P */ 283 for (j=0; j<apnzj; j++) { 284 apa[apj[j]] = 0.; 285 apjdense[apj[j]] = 0; 286 } 287 } 288 289 /* Assemble the final matrix and clean up */ 290 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 291 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 292 293 ierr = PetscFree3(apa,apjdense,apj);CHKERRQ(ierr); 294 PetscFunctionReturn(0); 295 } 296 297 PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat C) 298 { 299 PetscErrorCode ierr; 300 Mat_SeqAIJ *c = (Mat_SeqAIJ*)C->data; 301 Mat_MatTransMatMult *atb = c->atb; 302 Mat Pt = atb->At; 303 304 PetscFunctionBegin; 305 ierr = MatTranspose_SeqAIJ(P,MAT_REUSE_MATRIX,&Pt);CHKERRQ(ierr); 306 ierr = (C->ops->matmatmultnumeric)(Pt,A,P,C);CHKERRQ(ierr); 307 PetscFunctionReturn(0); 308 } 309