1 #define PETSCMAT_DLL 2 3 4 #include "../src/mat/impls/aij/seq/aij.h" 5 #include "../src/mat/impls/sbaij/seq/sbaij.h" 6 #include "petscbt.h" 7 #include "../src/mat/utils/freespace.h" 8 9 EXTERN_C_BEGIN 10 #undef __FUNCT__ 11 #define __FUNCT__ "MatOrdering_Flow_SeqAIJ" 12 /* 13 Computes an ordering to get most of the large numerical values in the lower triangular part of the matrix 14 */ 15 PetscErrorCode MatOrdering_Flow_SeqAIJ(Mat mat,const MatOrderingType type,IS *irow,IS *icol) 16 { 17 Mat_SeqAIJ *a = (Mat_SeqAIJ*)mat->data; 18 PetscErrorCode ierr; 19 PetscInt i,j,jj,k, kk,n = mat->rmap->n, current = 0, newcurrent = 0,*order; 20 const PetscInt *ai = a->i, *aj = a->j; 21 const PetscScalar *aa = a->a; 22 PetscTruth *done; 23 PetscReal best,past = 0,future; 24 25 PetscFunctionBegin; 26 /* pick initial row */ 27 best = -1; 28 for (i=0; i<n; i++) { 29 future = 0.0; 30 for (j=ai[i]; j<ai[i+1]; j++) { 31 if (aj[j] != i) future += PetscAbsScalar(aa[j]); else past = PetscAbsScalar(aa[j]); 32 } 33 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 34 if (past/future > best) { 35 best = past/future; 36 current = i; 37 } 38 } 39 40 ierr = PetscMalloc(n*sizeof(PetscTruth),&done);CHKERRQ(ierr); 41 ierr = PetscMemzero(done,n*sizeof(PetscTruth));CHKERRQ(ierr); 42 ierr = PetscMalloc(n*sizeof(PetscInt),&order);CHKERRQ(ierr); 43 order[0] = current; 44 for (i=0; i<n-1; i++) { 45 done[current] = PETSC_TRUE; 46 best = -1; 47 /* loop over all neighbors of current pivot */ 48 for (j=ai[current]; j<ai[current+1]; j++) { 49 jj = aj[j]; 50 if (done[jj]) continue; 51 /* loop over columns of potential next row computing weights for below and above diagonal */ 52 past = future = 0.0; 53 for (k=ai[jj]; k<ai[jj+1]; k++) { 54 kk = aj[k]; 55 if (done[kk]) past += PetscAbsScalar(aa[k]); 56 else if (kk != jj) future += PetscAbsScalar(aa[k]); 57 } 58 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 59 if (past/future > best) { 60 best = past/future; 61 newcurrent = jj; 62 } 63 } 64 if (best == -1) { /* no neighbors to select from so select best of all that remain */ 65 best = -1; 66 for (k=0; k<n; k++) { 67 if (done[k]) continue; 68 future = 0.0; 69 past = 0.0; 70 for (j=ai[k]; j<ai[k+1]; j++) { 71 kk = aj[j]; 72 if (done[kk]) past += PetscAbsScalar(aa[j]); 73 else if (kk != k) future += PetscAbsScalar(aa[j]); 74 } 75 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 76 if (past/future > best) { 77 best = past/future; 78 newcurrent = k; 79 } 80 } 81 } 82 if (current == newcurrent) SETERRQ(PETSC_ERR_PLIB,"newcurrent cannot be current"); 83 current = newcurrent; 84 order[i+1] = current; 85 } 86 ierr = ISCreateGeneral(PETSC_COMM_SELF,n,order,irow);CHKERRQ(ierr); 87 *icol = *irow; 88 ierr = PetscObjectReference((PetscObject)*irow);CHKERRQ(ierr); 89 ierr = PetscFree(done);CHKERRQ(ierr); 90 ierr = PetscFree(order);CHKERRQ(ierr); 91 PetscFunctionReturn(0); 92 } 93 EXTERN_C_END 94 95 EXTERN_C_BEGIN 96 #undef __FUNCT__ 97 #define __FUNCT__ "MatGetFactorAvailable_seqaij_petsc" 98 PetscErrorCode MatGetFactorAvailable_seqaij_petsc(Mat A,MatFactorType ftype,PetscTruth *flg) 99 { 100 PetscFunctionBegin; 101 *flg = PETSC_TRUE; 102 PetscFunctionReturn(0); 103 } 104 EXTERN_C_END 105 106 EXTERN_C_BEGIN 107 #undef __FUNCT__ 108 #define __FUNCT__ "MatGetFactor_seqaij_petsc" 109 PetscErrorCode MatGetFactor_seqaij_petsc(Mat A,MatFactorType ftype,Mat *B) 110 { 111 PetscInt n = A->rmap->n; 112 PetscErrorCode ierr; 113 114 PetscFunctionBegin; 115 ierr = MatCreate(((PetscObject)A)->comm,B);CHKERRQ(ierr); 116 ierr = MatSetSizes(*B,n,n,n,n);CHKERRQ(ierr); 117 if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT){ 118 ierr = MatSetType(*B,MATSEQAIJ);CHKERRQ(ierr); 119 (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJ; 120 (*B)->ops->lufactorsymbolic = MatLUFactorSymbolic_SeqAIJ; 121 } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) { 122 ierr = MatSetType(*B,MATSEQSBAIJ);CHKERRQ(ierr); 123 ierr = MatSeqSBAIJSetPreallocation(*B,1,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 124 (*B)->ops->iccfactorsymbolic = MatICCFactorSymbolic_SeqAIJ; 125 (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJ; 126 } else SETERRQ(PETSC_ERR_SUP,"Factor type not supported"); 127 (*B)->factor = ftype; 128 PetscFunctionReturn(0); 129 } 130 EXTERN_C_END 131 132 #undef __FUNCT__ 133 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ_inplace" 134 PetscErrorCode MatLUFactorSymbolic_SeqAIJ_inplace(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 135 { 136 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 137 IS isicol; 138 PetscErrorCode ierr; 139 const PetscInt *r,*ic; 140 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j; 141 PetscInt *bi,*bj,*ajtmp; 142 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 143 PetscReal f; 144 PetscInt nlnk,*lnk,k,**bi_ptr; 145 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 146 PetscBT lnkbt; 147 148 PetscFunctionBegin; 149 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square"); 150 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 151 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 152 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 153 154 /* get new row pointers */ 155 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 156 bi[0] = 0; 157 158 /* bdiag is location of diagonal in factor */ 159 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 160 bdiag[0] = 0; 161 162 /* linked list for storing column indices of the active row */ 163 nlnk = n + 1; 164 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 165 166 ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr); 167 168 /* initial FreeSpace size is f*(ai[n]+1) */ 169 f = info->fill; 170 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 171 current_space = free_space; 172 173 for (i=0; i<n; i++) { 174 /* copy previous fill into linked list */ 175 nzi = 0; 176 nnz = ai[r[i]+1] - ai[r[i]]; 177 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 178 ajtmp = aj + ai[r[i]]; 179 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 180 nzi += nlnk; 181 182 /* add pivot rows into linked list */ 183 row = lnk[n]; 184 while (row < i) { 185 nzbd = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */ 186 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 187 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 188 nzi += nlnk; 189 row = lnk[row]; 190 } 191 bi[i+1] = bi[i] + nzi; 192 im[i] = nzi; 193 194 /* mark bdiag */ 195 nzbd = 0; 196 nnz = nzi; 197 k = lnk[n]; 198 while (nnz-- && k < i){ 199 nzbd++; 200 k = lnk[k]; 201 } 202 bdiag[i] = bi[i] + nzbd; 203 204 /* if free space is not available, make more free space */ 205 if (current_space->local_remaining<nzi) { 206 nnz = (n - i)*nzi; /* estimated and max additional space needed */ 207 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 208 reallocs++; 209 } 210 211 /* copy data into free space, then initialize lnk */ 212 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 213 bi_ptr[i] = current_space->array; 214 current_space->array += nzi; 215 current_space->local_used += nzi; 216 current_space->local_remaining -= nzi; 217 } 218 #if defined(PETSC_USE_INFO) 219 if (ai[n] != 0) { 220 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 221 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 222 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 223 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr); 224 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 225 } else { 226 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 227 } 228 #endif 229 230 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 231 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 232 233 /* destroy list of free space and other temporary array(s) */ 234 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 235 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); 236 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 237 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 238 239 /* put together the new matrix */ 240 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 241 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 242 b = (Mat_SeqAIJ*)(B)->data; 243 b->free_a = PETSC_TRUE; 244 b->free_ij = PETSC_TRUE; 245 b->singlemalloc = PETSC_FALSE; 246 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 247 b->j = bj; 248 b->i = bi; 249 b->diag = bdiag; 250 b->ilen = 0; 251 b->imax = 0; 252 b->row = isrow; 253 b->col = iscol; 254 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 255 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 256 b->icol = isicol; 257 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 258 259 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 260 ierr = PetscLogObjectMemory(B,(bi[n]-n)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 261 b->maxnz = b->nz = bi[n] ; 262 263 (B)->factor = MAT_FACTOR_LU; 264 (B)->info.factor_mallocs = reallocs; 265 (B)->info.fill_ratio_given = f; 266 267 if (ai[n]) { 268 (B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 269 } else { 270 (B)->info.fill_ratio_needed = 0.0; 271 } 272 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace; 273 (B)->ops->solve = MatSolve_SeqAIJ_inplace; 274 (B)->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace; 275 /* switch to inodes if appropriate */ 276 ierr = MatLUFactorSymbolic_SeqAIJ_Inode(B,A,isrow,iscol,info);CHKERRQ(ierr); 277 PetscFunctionReturn(0); 278 } 279 280 #undef __FUNCT__ 281 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ" 282 PetscErrorCode MatLUFactorSymbolic_SeqAIJ(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 283 { 284 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 285 IS isicol; 286 PetscErrorCode ierr; 287 const PetscInt *r,*ic; 288 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j; 289 PetscInt *bi,*bj,*ajtmp; 290 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 291 PetscReal f; 292 PetscInt nlnk,*lnk,k,**bi_ptr; 293 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 294 PetscBT lnkbt; 295 296 PetscFunctionBegin; 297 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square"); 298 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 299 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 300 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 301 302 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 303 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 304 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 305 bi[0] = bdiag[0] = 0; 306 307 /* linked list for storing column indices of the active row */ 308 nlnk = n + 1; 309 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 310 311 ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr); 312 313 /* initial FreeSpace size is f*(ai[n]+1) */ 314 f = info->fill; 315 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 316 current_space = free_space; 317 318 for (i=0; i<n; i++) { 319 /* copy previous fill into linked list */ 320 nzi = 0; 321 nnz = ai[r[i]+1] - ai[r[i]]; 322 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 323 ajtmp = aj + ai[r[i]]; 324 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 325 nzi += nlnk; 326 327 /* add pivot rows into linked list */ 328 row = lnk[n]; 329 while (row < i){ 330 nzbd = bdiag[row] + 1; /* num of entries in the row with column index <= row */ 331 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 332 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 333 nzi += nlnk; 334 row = lnk[row]; 335 } 336 bi[i+1] = bi[i] + nzi; 337 im[i] = nzi; 338 339 /* mark bdiag */ 340 nzbd = 0; 341 nnz = nzi; 342 k = lnk[n]; 343 while (nnz-- && k < i){ 344 nzbd++; 345 k = lnk[k]; 346 } 347 bdiag[i] = nzbd; /* note: bdiag[i] = nnzL as input for PetscFreeSpaceContiguous_LU() */ 348 349 /* if free space is not available, make more free space */ 350 if (current_space->local_remaining<nzi) { 351 nnz = 2*(n - i)*nzi; /* estimated and max additional space needed */ 352 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 353 reallocs++; 354 } 355 356 /* copy data into free space, then initialize lnk */ 357 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 358 bi_ptr[i] = current_space->array; 359 current_space->array += nzi; 360 current_space->local_used += nzi; 361 current_space->local_remaining -= nzi; 362 } 363 #if defined(PETSC_USE_INFO) 364 if (ai[n] != 0) { 365 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 366 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 367 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 368 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr); 369 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 370 } else { 371 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 372 } 373 #endif 374 375 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 376 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 377 378 /* destroy list of free space and other temporary array(s) */ 379 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 380 ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 381 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 382 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 383 384 /* put together the new matrix */ 385 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 386 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 387 b = (Mat_SeqAIJ*)(B)->data; 388 b->free_a = PETSC_TRUE; 389 b->free_ij = PETSC_TRUE; 390 b->singlemalloc = PETSC_FALSE; 391 ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 392 b->j = bj; 393 b->i = bi; 394 b->diag = bdiag; 395 b->ilen = 0; 396 b->imax = 0; 397 b->row = isrow; 398 b->col = iscol; 399 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 400 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 401 b->icol = isicol; 402 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 403 404 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 405 ierr = PetscLogObjectMemory(B,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 406 b->maxnz = b->nz = bdiag[0]+1; 407 B->factor = MAT_FACTOR_LU; 408 B->info.factor_mallocs = reallocs; 409 B->info.fill_ratio_given = f; 410 411 if (ai[n]) { 412 B->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 413 } else { 414 B->info.fill_ratio_needed = 0.0; 415 } 416 B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 417 /* switch to inodes if appropriate */ 418 ierr = Mat_CheckInode_FactorLU(B,PETSC_FALSE);CHKERRQ(ierr); 419 PetscFunctionReturn(0); 420 } 421 422 /* 423 Trouble in factorization, should we dump the original matrix? 424 */ 425 #undef __FUNCT__ 426 #define __FUNCT__ "MatFactorDumpMatrix" 427 PetscErrorCode MatFactorDumpMatrix(Mat A) 428 { 429 PetscErrorCode ierr; 430 PetscTruth flg = PETSC_FALSE; 431 432 PetscFunctionBegin; 433 ierr = PetscOptionsGetTruth(PETSC_NULL,"-mat_factor_dump_on_error",&flg,PETSC_NULL);CHKERRQ(ierr); 434 if (flg) { 435 PetscViewer viewer; 436 char filename[PETSC_MAX_PATH_LEN]; 437 438 ierr = PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);CHKERRQ(ierr); 439 ierr = PetscViewerBinaryOpen(((PetscObject)A)->comm,filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr); 440 ierr = MatView(A,viewer);CHKERRQ(ierr); 441 ierr = PetscViewerDestroy(viewer);CHKERRQ(ierr); 442 } 443 PetscFunctionReturn(0); 444 } 445 446 #undef __FUNCT__ 447 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ" 448 PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 449 { 450 Mat C=B; 451 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 452 IS isrow = b->row,isicol = b->icol; 453 PetscErrorCode ierr; 454 const PetscInt *r,*ic,*ics; 455 const PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bdiag=b->diag; 456 PetscInt i,j,k,nz,nzL,row,*pj; 457 const PetscInt *ajtmp,*bjtmp; 458 MatScalar *rtmp,*pc,multiplier,*pv; 459 const MatScalar *aa=a->a,*v; 460 PetscTruth row_identity,col_identity; 461 462 FactorShiftCtx sctx; 463 PetscInt *ddiag; 464 PetscReal rs; 465 MatScalar d; 466 467 PetscFunctionBegin; 468 /* MatPivotSetUp(): initialize shift context sctx */ 469 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 470 471 if (info->shifttype == MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 472 ddiag = a->diag; 473 sctx.shift_top = info->zeropivot; 474 for (i=0; i<n; i++) { 475 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 476 d = (aa)[ddiag[i]]; 477 rs = -PetscAbsScalar(d) - PetscRealPart(d); 478 v = aa+ai[i]; 479 nz = ai[i+1] - ai[i]; 480 for (j=0; j<nz; j++) 481 rs += PetscAbsScalar(v[j]); 482 if (rs>sctx.shift_top) sctx.shift_top = rs; 483 } 484 sctx.shift_top *= 1.1; 485 sctx.nshift_max = 5; 486 sctx.shift_lo = 0.; 487 sctx.shift_hi = 1.; 488 } 489 490 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 491 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 492 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 493 ics = ic; 494 495 do { 496 sctx.useshift = PETSC_FALSE; 497 for (i=0; i<n; i++){ 498 /* zero rtmp */ 499 /* L part */ 500 nz = bi[i+1] - bi[i]; 501 bjtmp = bj + bi[i]; 502 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 503 504 /* U part */ 505 nz = bdiag[i]-bdiag[i+1]; 506 bjtmp = bj + bdiag[i+1]+1; 507 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 508 509 /* load in initial (unfactored row) */ 510 nz = ai[r[i]+1] - ai[r[i]]; 511 ajtmp = aj + ai[r[i]]; 512 v = aa + ai[r[i]]; 513 for (j=0; j<nz; j++) { 514 rtmp[ics[ajtmp[j]]] = v[j]; 515 } 516 /* ZeropivotApply() */ 517 rtmp[i] += sctx.shift_amount; /* shift the diagonal of the matrix */ 518 519 /* elimination */ 520 bjtmp = bj + bi[i]; 521 row = *bjtmp++; 522 nzL = bi[i+1] - bi[i]; 523 for(k=0; k < nzL;k++) { 524 pc = rtmp + row; 525 if (*pc != 0.0) { 526 pv = b->a + bdiag[row]; 527 multiplier = *pc * (*pv); 528 *pc = multiplier; 529 pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */ 530 pv = b->a + bdiag[row+1]+1; 531 nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */ 532 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 533 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 534 } 535 row = *bjtmp++; 536 } 537 538 /* finished row so stick it into b->a */ 539 rs = 0.0; 540 /* L part */ 541 pv = b->a + bi[i] ; 542 pj = b->j + bi[i] ; 543 nz = bi[i+1] - bi[i]; 544 for (j=0; j<nz; j++) { 545 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 546 } 547 548 /* U part */ 549 pv = b->a + bdiag[i+1]+1; 550 pj = b->j + bdiag[i+1]+1; 551 nz = bdiag[i] - bdiag[i+1]-1; 552 for (j=0; j<nz; j++) { 553 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 554 } 555 556 /* MatPivotCheck() */ 557 sctx.rs = rs; 558 sctx.pv = rtmp[i]; 559 if (info->shifttype == MAT_SHIFT_NONZERO){ 560 ierr = MatPivotCheck_nz(info,sctx,i);CHKERRQ(ierr); 561 } else if (info->shifttype == MAT_SHIFT_POSITIVE_DEFINITE){ 562 ierr = MatPivotCheck_pd(info,sctx,i);CHKERRQ(ierr); 563 } else if (info->shifttype == MAT_SHIFT_INBLOCKS){ 564 ierr = MatPivotCheck_inblocks(info,sctx,i);CHKERRQ(ierr); 565 } else { 566 ierr = MatPivotCheck_none(info,sctx,i);CHKERRQ(ierr); 567 } 568 rtmp[i] = sctx.pv; 569 570 /* Mark diagonal and invert diagonal for simplier triangular solves */ 571 pv = b->a + bdiag[i]; 572 *pv = 1.0/rtmp[i]; 573 574 } /* endof for (i=0; i<n; i++){ */ 575 576 /* MatPivotRefine() */ 577 if (info->shifttype == MAT_SHIFT_POSITIVE_DEFINITE && !sctx.useshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max){ 578 /* 579 * if no shift in this attempt & shifting & started shifting & can refine, 580 * then try lower shift 581 */ 582 sctx.shift_hi = sctx.shift_fraction; 583 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 584 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 585 sctx.useshift = PETSC_TRUE; 586 sctx.nshift++; 587 } 588 } while (sctx.useshift); 589 590 ierr = PetscFree(rtmp);CHKERRQ(ierr); 591 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 592 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 593 if (b->inode.use){ 594 C->ops->solve = MatSolve_SeqAIJ_Inode; 595 } else { 596 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 597 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 598 if (row_identity && col_identity) { 599 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 600 } else { 601 C->ops->solve = MatSolve_SeqAIJ; 602 } 603 } 604 C->ops->solveadd = MatSolveAdd_SeqAIJ; 605 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 606 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 607 C->ops->matsolve = MatMatSolve_SeqAIJ; 608 C->assembled = PETSC_TRUE; 609 C->preallocated = PETSC_TRUE; 610 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 611 612 /* MatPivotView() */ 613 if (sctx.nshift){ 614 if (info->shifttype == MAT_SHIFT_POSITIVE_DEFINITE) { 615 ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %G, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,sctx.shift_amount,sctx.shift_fraction,sctx.shift_top);CHKERRQ(ierr); 616 } else if (info->shifttype == MAT_SHIFT_NONZERO) { 617 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 618 } else if (info->shifttype == MAT_SHIFT_INBLOCKS){ 619 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftamount);CHKERRQ(ierr); 620 } 621 } 622 PetscFunctionReturn(0); 623 } 624 625 #undef __FUNCT__ 626 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_inplace" 627 PetscErrorCode MatLUFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info) 628 { 629 Mat C=B; 630 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 631 IS isrow = b->row,isicol = b->icol; 632 PetscErrorCode ierr; 633 const PetscInt *r,*ic,*ics; 634 PetscInt nz,row,i,j,n=A->rmap->n,diag; 635 const PetscInt *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 636 const PetscInt *ajtmp,*bjtmp,*diag_offset = b->diag,*pj; 637 MatScalar *pv,*rtmp,*pc,multiplier,d; 638 const MatScalar *v,*aa=a->a; 639 PetscReal rs=0.0; 640 FactorShiftCtx sctx; 641 PetscInt newshift,*ddiag; 642 643 PetscFunctionBegin; 644 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 645 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 646 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 647 ics = ic; 648 649 /* initialize shift context sctx */ 650 sctx.nshift = 0; 651 sctx.nshift_max = 0; 652 sctx.shift_top = 0.0; 653 sctx.shift_lo = 0.0; 654 sctx.shift_hi = 0.0; 655 sctx.shift_fraction = 0.0; 656 sctx.shift_amount = 0.0; 657 658 /* if both shift schemes are chosen by user, only use info->shiftpd */ 659 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 660 ddiag = a->diag; 661 sctx.shift_top = info->zeropivot; 662 for (i=0; i<n; i++) { 663 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 664 d = (aa)[ddiag[i]]; 665 rs = -PetscAbsScalar(d) - PetscRealPart(d); 666 v = aa+ai[i]; 667 nz = ai[i+1] - ai[i]; 668 for (j=0; j<nz; j++) 669 rs += PetscAbsScalar(v[j]); 670 if (rs>sctx.shift_top) sctx.shift_top = rs; 671 } 672 sctx.shift_top *= 1.1; 673 sctx.nshift_max = 5; 674 sctx.shift_lo = 0.; 675 sctx.shift_hi = 1.; 676 } 677 678 do { 679 sctx.useshift = PETSC_FALSE; 680 for (i=0; i<n; i++){ 681 nz = bi[i+1] - bi[i]; 682 bjtmp = bj + bi[i]; 683 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 684 685 /* load in initial (unfactored row) */ 686 nz = ai[r[i]+1] - ai[r[i]]; 687 ajtmp = aj + ai[r[i]]; 688 v = aa + ai[r[i]]; 689 for (j=0; j<nz; j++) { 690 rtmp[ics[ajtmp[j]]] = v[j]; 691 } 692 rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 693 /* if (sctx.shift_amount > 0.0) printf("row %d, shift %g\n",i,sctx.shift_amount); */ 694 695 row = *bjtmp++; 696 while (row < i) { 697 pc = rtmp + row; 698 if (*pc != 0.0) { 699 pv = b->a + diag_offset[row]; 700 pj = b->j + diag_offset[row] + 1; 701 multiplier = *pc / *pv++; 702 *pc = multiplier; 703 nz = bi[row+1] - diag_offset[row] - 1; 704 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 705 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 706 } 707 row = *bjtmp++; 708 } 709 /* finished row so stick it into b->a */ 710 pv = b->a + bi[i] ; 711 pj = b->j + bi[i] ; 712 nz = bi[i+1] - bi[i]; 713 diag = diag_offset[i] - bi[i]; 714 rs = 0.0; 715 for (j=0; j<nz; j++) { 716 pv[j] = rtmp[pj[j]]; 717 rs += PetscAbsScalar(pv[j]); 718 } 719 rs -= PetscAbsScalar(pv[diag]); 720 721 /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */ 722 sctx.rs = rs; 723 sctx.pv = pv[diag]; 724 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 725 if (newshift == 1) break; 726 } 727 728 if (info->shiftpd && !sctx.useshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 729 /* 730 * if no shift in this attempt & shifting & started shifting & can refine, 731 * then try lower shift 732 */ 733 sctx.shift_hi = sctx.shift_fraction; 734 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 735 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 736 sctx.useshift = PETSC_TRUE; 737 sctx.nshift++; 738 } 739 } while (sctx.useshift); 740 741 /* invert diagonal entries for simplier triangular solves */ 742 for (i=0; i<n; i++) { 743 b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]]; 744 } 745 ierr = PetscFree(rtmp);CHKERRQ(ierr); 746 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 747 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 748 if (b->inode.use) { 749 C->ops->solve = MatSolve_SeqAIJ_Inode_inplace; 750 } else { 751 PetscTruth row_identity, col_identity; 752 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 753 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 754 if (row_identity && col_identity) { 755 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_inplace; 756 } else { 757 C->ops->solve = MatSolve_SeqAIJ_inplace; 758 } 759 } 760 C->ops->solveadd = MatSolveAdd_SeqAIJ_inplace; 761 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace; 762 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace; 763 C->ops->matsolve = MatMatSolve_SeqAIJ_inplace; 764 C->assembled = PETSC_TRUE; 765 C->preallocated = PETSC_TRUE; 766 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 767 if (sctx.nshift){ 768 if (info->shiftpd) { 769 ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %G, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,sctx.shift_amount,sctx.shift_fraction,sctx.shift_top);CHKERRQ(ierr); 770 } else if (info->shiftnz) { 771 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 772 } 773 } 774 PetscFunctionReturn(0); 775 } 776 777 /* 778 This routine implements inplace ILU(0) with row or/and column permutations. 779 Input: 780 A - original matrix 781 Output; 782 A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i] 783 a->j (col index) is permuted by the inverse of colperm, then sorted 784 a->a reordered accordingly with a->j 785 a->diag (ptr to diagonal elements) is updated. 786 */ 787 #undef __FUNCT__ 788 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_InplaceWithPerm" 789 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info) 790 { 791 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 792 IS isrow = a->row,isicol = a->icol; 793 PetscErrorCode ierr; 794 const PetscInt *r,*ic,*ics; 795 PetscInt i,j,n=A->rmap->n,*ai=a->i,*aj=a->j; 796 PetscInt *ajtmp,nz,row; 797 PetscInt *diag = a->diag,nbdiag,*pj; 798 PetscScalar *rtmp,*pc,multiplier,d; 799 MatScalar *v,*pv; 800 PetscReal rs; 801 FactorShiftCtx sctx; 802 PetscInt newshift; 803 804 PetscFunctionBegin; 805 if (A != B) SETERRQ(PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address"); 806 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 807 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 808 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&rtmp);CHKERRQ(ierr); 809 ierr = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr); 810 ics = ic; 811 812 sctx.shift_top = 0.; 813 sctx.nshift_max = 0; 814 sctx.shift_lo = 0.; 815 sctx.shift_hi = 0.; 816 sctx.shift_fraction = 0.; 817 818 /* if both shift schemes are chosen by user, only use info->shiftpd */ 819 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 820 sctx.shift_top = 0.; 821 for (i=0; i<n; i++) { 822 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 823 d = (a->a)[diag[i]]; 824 rs = -PetscAbsScalar(d) - PetscRealPart(d); 825 v = a->a+ai[i]; 826 nz = ai[i+1] - ai[i]; 827 for (j=0; j<nz; j++) 828 rs += PetscAbsScalar(v[j]); 829 if (rs>sctx.shift_top) sctx.shift_top = rs; 830 } 831 if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot; 832 sctx.shift_top *= 1.1; 833 sctx.nshift_max = 5; 834 sctx.shift_lo = 0.; 835 sctx.shift_hi = 1.; 836 } 837 838 sctx.shift_amount = 0.; 839 sctx.nshift = 0; 840 do { 841 sctx.useshift = PETSC_FALSE; 842 for (i=0; i<n; i++){ 843 /* load in initial unfactored row */ 844 nz = ai[r[i]+1] - ai[r[i]]; 845 ajtmp = aj + ai[r[i]]; 846 v = a->a + ai[r[i]]; 847 /* sort permuted ajtmp and values v accordingly */ 848 for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]]; 849 ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr); 850 851 diag[r[i]] = ai[r[i]]; 852 for (j=0; j<nz; j++) { 853 rtmp[ajtmp[j]] = v[j]; 854 if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */ 855 } 856 rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 857 858 row = *ajtmp++; 859 while (row < i) { 860 pc = rtmp + row; 861 if (*pc != 0.0) { 862 pv = a->a + diag[r[row]]; 863 pj = aj + diag[r[row]] + 1; 864 865 multiplier = *pc / *pv++; 866 *pc = multiplier; 867 nz = ai[r[row]+1] - diag[r[row]] - 1; 868 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 869 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 870 } 871 row = *ajtmp++; 872 } 873 /* finished row so overwrite it onto a->a */ 874 pv = a->a + ai[r[i]] ; 875 pj = aj + ai[r[i]] ; 876 nz = ai[r[i]+1] - ai[r[i]]; 877 nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */ 878 879 rs = 0.0; 880 for (j=0; j<nz; j++) { 881 pv[j] = rtmp[pj[j]]; 882 if (j != nbdiag) rs += PetscAbsScalar(pv[j]); 883 } 884 885 /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */ 886 sctx.rs = rs; 887 sctx.pv = pv[nbdiag]; 888 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 889 if (newshift == 1) break; 890 } 891 892 if (info->shiftpd && !sctx.useshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 893 /* 894 * if no shift in this attempt & shifting & started shifting & can refine, 895 * then try lower shift 896 */ 897 sctx.shift_hi = sctx.shift_fraction; 898 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 899 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 900 sctx.useshift = PETSC_TRUE; 901 sctx.nshift++; 902 } 903 } while (sctx.useshift); 904 905 /* invert diagonal entries for simplier triangular solves */ 906 for (i=0; i<n; i++) { 907 a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]]; 908 } 909 910 ierr = PetscFree(rtmp);CHKERRQ(ierr); 911 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 912 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 913 A->ops->solve = MatSolve_SeqAIJ_InplaceWithPerm; 914 A->ops->solveadd = MatSolveAdd_SeqAIJ_inplace; 915 A->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace; 916 A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace; 917 A->assembled = PETSC_TRUE; 918 A->preallocated = PETSC_TRUE; 919 ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr); 920 if (sctx.nshift){ 921 if (info->shiftpd) { 922 ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %G, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,sctx.shift_amount,sctx.shift_fraction,sctx.shift_top);CHKERRQ(ierr); 923 } else if (info->shiftnz) { 924 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 925 } 926 } 927 PetscFunctionReturn(0); 928 } 929 930 /* ----------------------------------------------------------- */ 931 #undef __FUNCT__ 932 #define __FUNCT__ "MatLUFactor_SeqAIJ" 933 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info) 934 { 935 PetscErrorCode ierr; 936 Mat C; 937 938 PetscFunctionBegin; 939 ierr = MatGetFactor(A,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr); 940 ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr); 941 ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr); 942 A->ops->solve = C->ops->solve; 943 A->ops->solvetranspose = C->ops->solvetranspose; 944 ierr = MatHeaderCopy(A,C);CHKERRQ(ierr); 945 ierr = PetscLogObjectParent(A,((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr); 946 PetscFunctionReturn(0); 947 } 948 /* ----------------------------------------------------------- */ 949 950 951 #undef __FUNCT__ 952 #define __FUNCT__ "MatSolve_SeqAIJ_inplace" 953 PetscErrorCode MatSolve_SeqAIJ_inplace(Mat A,Vec bb,Vec xx) 954 { 955 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 956 IS iscol = a->col,isrow = a->row; 957 PetscErrorCode ierr; 958 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 959 PetscInt nz; 960 const PetscInt *rout,*cout,*r,*c; 961 PetscScalar *x,*tmp,*tmps,sum; 962 const PetscScalar *b; 963 const MatScalar *aa = a->a,*v; 964 965 PetscFunctionBegin; 966 if (!n) PetscFunctionReturn(0); 967 968 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 969 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 970 tmp = a->solve_work; 971 972 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 973 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 974 975 /* forward solve the lower triangular */ 976 tmp[0] = b[*r++]; 977 tmps = tmp; 978 for (i=1; i<n; i++) { 979 v = aa + ai[i] ; 980 vi = aj + ai[i] ; 981 nz = a->diag[i] - ai[i]; 982 sum = b[*r++]; 983 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 984 tmp[i] = sum; 985 } 986 987 /* backward solve the upper triangular */ 988 for (i=n-1; i>=0; i--){ 989 v = aa + a->diag[i] + 1; 990 vi = aj + a->diag[i] + 1; 991 nz = ai[i+1] - a->diag[i] - 1; 992 sum = tmp[i]; 993 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 994 x[*c--] = tmp[i] = sum*aa[a->diag[i]]; 995 } 996 997 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 998 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 999 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1000 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1001 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1002 PetscFunctionReturn(0); 1003 } 1004 1005 #undef __FUNCT__ 1006 #define __FUNCT__ "MatMatSolve_SeqAIJ_inplace" 1007 PetscErrorCode MatMatSolve_SeqAIJ_inplace(Mat A,Mat B,Mat X) 1008 { 1009 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1010 IS iscol = a->col,isrow = a->row; 1011 PetscErrorCode ierr; 1012 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1013 PetscInt nz,neq; 1014 const PetscInt *rout,*cout,*r,*c; 1015 PetscScalar *x,*b,*tmp,*tmps,sum; 1016 const MatScalar *aa = a->a,*v; 1017 PetscTruth bisdense,xisdense; 1018 1019 PetscFunctionBegin; 1020 if (!n) PetscFunctionReturn(0); 1021 1022 ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr); 1023 if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 1024 ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr); 1025 if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 1026 1027 ierr = MatGetArray(B,&b);CHKERRQ(ierr); 1028 ierr = MatGetArray(X,&x);CHKERRQ(ierr); 1029 1030 tmp = a->solve_work; 1031 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1032 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1033 1034 for (neq=0; neq<B->cmap->n; neq++){ 1035 /* forward solve the lower triangular */ 1036 tmp[0] = b[r[0]]; 1037 tmps = tmp; 1038 for (i=1; i<n; i++) { 1039 v = aa + ai[i] ; 1040 vi = aj + ai[i] ; 1041 nz = a->diag[i] - ai[i]; 1042 sum = b[r[i]]; 1043 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1044 tmp[i] = sum; 1045 } 1046 /* backward solve the upper triangular */ 1047 for (i=n-1; i>=0; i--){ 1048 v = aa + a->diag[i] + 1; 1049 vi = aj + a->diag[i] + 1; 1050 nz = ai[i+1] - a->diag[i] - 1; 1051 sum = tmp[i]; 1052 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1053 x[c[i]] = tmp[i] = sum*aa[a->diag[i]]; 1054 } 1055 1056 b += n; 1057 x += n; 1058 } 1059 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1060 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1061 ierr = MatRestoreArray(B,&b);CHKERRQ(ierr); 1062 ierr = MatRestoreArray(X,&x);CHKERRQ(ierr); 1063 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 1064 PetscFunctionReturn(0); 1065 } 1066 1067 #undef __FUNCT__ 1068 #define __FUNCT__ "MatMatSolve_SeqAIJ" 1069 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X) 1070 { 1071 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1072 IS iscol = a->col,isrow = a->row; 1073 PetscErrorCode ierr; 1074 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag; 1075 PetscInt nz,neq; 1076 const PetscInt *rout,*cout,*r,*c; 1077 PetscScalar *x,*b,*tmp,sum; 1078 const MatScalar *aa = a->a,*v; 1079 PetscTruth bisdense,xisdense; 1080 1081 PetscFunctionBegin; 1082 if (!n) PetscFunctionReturn(0); 1083 1084 ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr); 1085 if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 1086 ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr); 1087 if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 1088 1089 ierr = MatGetArray(B,&b);CHKERRQ(ierr); 1090 ierr = MatGetArray(X,&x);CHKERRQ(ierr); 1091 1092 tmp = a->solve_work; 1093 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1094 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1095 1096 for (neq=0; neq<B->cmap->n; neq++){ 1097 /* forward solve the lower triangular */ 1098 tmp[0] = b[r[0]]; 1099 v = aa; 1100 vi = aj; 1101 for (i=1; i<n; i++) { 1102 nz = ai[i+1] - ai[i]; 1103 sum = b[r[i]]; 1104 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 1105 tmp[i] = sum; 1106 v += nz; vi += nz; 1107 } 1108 1109 /* backward solve the upper triangular */ 1110 for (i=n-1; i>=0; i--){ 1111 v = aa + adiag[i+1]+1; 1112 vi = aj + adiag[i+1]+1; 1113 nz = adiag[i]-adiag[i+1]-1; 1114 sum = tmp[i]; 1115 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 1116 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 1117 } 1118 1119 b += n; 1120 x += n; 1121 } 1122 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1123 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1124 ierr = MatRestoreArray(B,&b);CHKERRQ(ierr); 1125 ierr = MatRestoreArray(X,&x);CHKERRQ(ierr); 1126 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 1127 PetscFunctionReturn(0); 1128 } 1129 1130 #undef __FUNCT__ 1131 #define __FUNCT__ "MatSolve_SeqAIJ_InplaceWithPerm" 1132 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx) 1133 { 1134 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1135 IS iscol = a->col,isrow = a->row; 1136 PetscErrorCode ierr; 1137 const PetscInt *r,*c,*rout,*cout; 1138 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1139 PetscInt nz,row; 1140 PetscScalar *x,*b,*tmp,*tmps,sum; 1141 const MatScalar *aa = a->a,*v; 1142 1143 PetscFunctionBegin; 1144 if (!n) PetscFunctionReturn(0); 1145 1146 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1147 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1148 tmp = a->solve_work; 1149 1150 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1151 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1152 1153 /* forward solve the lower triangular */ 1154 tmp[0] = b[*r++]; 1155 tmps = tmp; 1156 for (row=1; row<n; row++) { 1157 i = rout[row]; /* permuted row */ 1158 v = aa + ai[i] ; 1159 vi = aj + ai[i] ; 1160 nz = a->diag[i] - ai[i]; 1161 sum = b[*r++]; 1162 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1163 tmp[row] = sum; 1164 } 1165 1166 /* backward solve the upper triangular */ 1167 for (row=n-1; row>=0; row--){ 1168 i = rout[row]; /* permuted row */ 1169 v = aa + a->diag[i] + 1; 1170 vi = aj + a->diag[i] + 1; 1171 nz = ai[i+1] - a->diag[i] - 1; 1172 sum = tmp[row]; 1173 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1174 x[*c--] = tmp[row] = sum*aa[a->diag[i]]; 1175 } 1176 1177 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1178 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1179 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1180 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1181 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1182 PetscFunctionReturn(0); 1183 } 1184 1185 /* ----------------------------------------------------------- */ 1186 #include "../src/mat/impls/aij/seq/ftn-kernels/fsolve.h" 1187 #undef __FUNCT__ 1188 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_inplace" 1189 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_inplace(Mat A,Vec bb,Vec xx) 1190 { 1191 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1192 PetscErrorCode ierr; 1193 PetscInt n = A->rmap->n; 1194 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag; 1195 PetscScalar *x; 1196 const PetscScalar *b; 1197 const MatScalar *aa = a->a; 1198 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1199 PetscInt adiag_i,i,nz,ai_i; 1200 const PetscInt *vi; 1201 const MatScalar *v; 1202 PetscScalar sum; 1203 #endif 1204 1205 PetscFunctionBegin; 1206 if (!n) PetscFunctionReturn(0); 1207 1208 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1209 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1210 1211 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1212 fortransolveaij_(&n,x,ai,aj,adiag,aa,b); 1213 #else 1214 /* forward solve the lower triangular */ 1215 x[0] = b[0]; 1216 for (i=1; i<n; i++) { 1217 ai_i = ai[i]; 1218 v = aa + ai_i; 1219 vi = aj + ai_i; 1220 nz = adiag[i] - ai_i; 1221 sum = b[i]; 1222 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1223 x[i] = sum; 1224 } 1225 1226 /* backward solve the upper triangular */ 1227 for (i=n-1; i>=0; i--){ 1228 adiag_i = adiag[i]; 1229 v = aa + adiag_i + 1; 1230 vi = aj + adiag_i + 1; 1231 nz = ai[i+1] - adiag_i - 1; 1232 sum = x[i]; 1233 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1234 x[i] = sum*aa[adiag_i]; 1235 } 1236 #endif 1237 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1238 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1239 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1240 PetscFunctionReturn(0); 1241 } 1242 1243 #undef __FUNCT__ 1244 #define __FUNCT__ "MatSolveAdd_SeqAIJ_inplace" 1245 PetscErrorCode MatSolveAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec yy,Vec xx) 1246 { 1247 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1248 IS iscol = a->col,isrow = a->row; 1249 PetscErrorCode ierr; 1250 PetscInt i, n = A->rmap->n,j; 1251 PetscInt nz; 1252 const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j; 1253 PetscScalar *x,*tmp,sum; 1254 const PetscScalar *b; 1255 const MatScalar *aa = a->a,*v; 1256 1257 PetscFunctionBegin; 1258 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 1259 1260 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1261 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1262 tmp = a->solve_work; 1263 1264 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1265 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1266 1267 /* forward solve the lower triangular */ 1268 tmp[0] = b[*r++]; 1269 for (i=1; i<n; i++) { 1270 v = aa + ai[i] ; 1271 vi = aj + ai[i] ; 1272 nz = a->diag[i] - ai[i]; 1273 sum = b[*r++]; 1274 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1275 tmp[i] = sum; 1276 } 1277 1278 /* backward solve the upper triangular */ 1279 for (i=n-1; i>=0; i--){ 1280 v = aa + a->diag[i] + 1; 1281 vi = aj + a->diag[i] + 1; 1282 nz = ai[i+1] - a->diag[i] - 1; 1283 sum = tmp[i]; 1284 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1285 tmp[i] = sum*aa[a->diag[i]]; 1286 x[*c--] += tmp[i]; 1287 } 1288 1289 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1290 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1291 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1292 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1293 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1294 1295 PetscFunctionReturn(0); 1296 } 1297 1298 #undef __FUNCT__ 1299 #define __FUNCT__ "MatSolveAdd_SeqAIJ" 1300 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx) 1301 { 1302 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1303 IS iscol = a->col,isrow = a->row; 1304 PetscErrorCode ierr; 1305 PetscInt i, n = A->rmap->n,j; 1306 PetscInt nz; 1307 const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag; 1308 PetscScalar *x,*tmp,sum; 1309 const PetscScalar *b; 1310 const MatScalar *aa = a->a,*v; 1311 1312 PetscFunctionBegin; 1313 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 1314 1315 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1316 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1317 tmp = a->solve_work; 1318 1319 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1320 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1321 1322 /* forward solve the lower triangular */ 1323 tmp[0] = b[r[0]]; 1324 v = aa; 1325 vi = aj; 1326 for (i=1; i<n; i++) { 1327 nz = ai[i+1] - ai[i]; 1328 sum = b[r[i]]; 1329 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1330 tmp[i] = sum; 1331 v += nz; vi += nz; 1332 } 1333 1334 /* backward solve the upper triangular */ 1335 v = aa + adiag[n-1]; 1336 vi = aj + adiag[n-1]; 1337 for (i=n-1; i>=0; i--){ 1338 nz = adiag[i] - adiag[i+1] - 1; 1339 sum = tmp[i]; 1340 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1341 tmp[i] = sum*v[nz]; 1342 x[c[i]] += tmp[i]; 1343 v += nz+1; vi += nz+1; 1344 } 1345 1346 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1347 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1348 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1349 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1350 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1351 1352 PetscFunctionReturn(0); 1353 } 1354 1355 #undef __FUNCT__ 1356 #define __FUNCT__ "MatSolveTranspose_SeqAIJ_inplace" 1357 PetscErrorCode MatSolveTranspose_SeqAIJ_inplace(Mat A,Vec bb,Vec xx) 1358 { 1359 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1360 IS iscol = a->col,isrow = a->row; 1361 PetscErrorCode ierr; 1362 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1363 PetscInt i,n = A->rmap->n,j; 1364 PetscInt nz; 1365 PetscScalar *x,*tmp,s1; 1366 const MatScalar *aa = a->a,*v; 1367 const PetscScalar *b; 1368 1369 PetscFunctionBegin; 1370 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1371 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1372 tmp = a->solve_work; 1373 1374 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1375 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1376 1377 /* copy the b into temp work space according to permutation */ 1378 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1379 1380 /* forward solve the U^T */ 1381 for (i=0; i<n; i++) { 1382 v = aa + diag[i] ; 1383 vi = aj + diag[i] + 1; 1384 nz = ai[i+1] - diag[i] - 1; 1385 s1 = tmp[i]; 1386 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1387 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1388 tmp[i] = s1; 1389 } 1390 1391 /* backward solve the L^T */ 1392 for (i=n-1; i>=0; i--){ 1393 v = aa + diag[i] - 1 ; 1394 vi = aj + diag[i] - 1 ; 1395 nz = diag[i] - ai[i]; 1396 s1 = tmp[i]; 1397 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1398 } 1399 1400 /* copy tmp into x according to permutation */ 1401 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1402 1403 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1404 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1405 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1406 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1407 1408 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1409 PetscFunctionReturn(0); 1410 } 1411 1412 #undef __FUNCT__ 1413 #define __FUNCT__ "MatSolveTranspose_SeqAIJ" 1414 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx) 1415 { 1416 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1417 IS iscol = a->col,isrow = a->row; 1418 PetscErrorCode ierr; 1419 const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi; 1420 PetscInt i,n = A->rmap->n,j; 1421 PetscInt nz; 1422 PetscScalar *x,*tmp,s1; 1423 const MatScalar *aa = a->a,*v; 1424 const PetscScalar *b; 1425 1426 PetscFunctionBegin; 1427 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1428 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1429 tmp = a->solve_work; 1430 1431 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1432 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1433 1434 /* copy the b into temp work space according to permutation */ 1435 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1436 1437 /* forward solve the U^T */ 1438 for (i=0; i<n; i++) { 1439 v = aa + adiag[i+1] + 1; 1440 vi = aj + adiag[i+1] + 1; 1441 nz = adiag[i] - adiag[i+1] - 1; 1442 s1 = tmp[i]; 1443 s1 *= v[nz]; /* multiply by inverse of diagonal entry */ 1444 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1445 tmp[i] = s1; 1446 } 1447 1448 /* backward solve the L^T */ 1449 for (i=n-1; i>=0; i--){ 1450 v = aa + ai[i]; 1451 vi = aj + ai[i]; 1452 nz = ai[i+1] - ai[i]; 1453 s1 = tmp[i]; 1454 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1455 } 1456 1457 /* copy tmp into x according to permutation */ 1458 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1459 1460 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1461 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1462 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1463 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1464 1465 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1466 PetscFunctionReturn(0); 1467 } 1468 1469 #undef __FUNCT__ 1470 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ_inplace" 1471 PetscErrorCode MatSolveTransposeAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec zz,Vec xx) 1472 { 1473 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1474 IS iscol = a->col,isrow = a->row; 1475 PetscErrorCode ierr; 1476 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1477 PetscInt i,n = A->rmap->n,j; 1478 PetscInt nz; 1479 PetscScalar *x,*tmp,s1; 1480 const MatScalar *aa = a->a,*v; 1481 const PetscScalar *b; 1482 1483 PetscFunctionBegin; 1484 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1485 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1486 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1487 tmp = a->solve_work; 1488 1489 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1490 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1491 1492 /* copy the b into temp work space according to permutation */ 1493 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1494 1495 /* forward solve the U^T */ 1496 for (i=0; i<n; i++) { 1497 v = aa + diag[i] ; 1498 vi = aj + diag[i] + 1; 1499 nz = ai[i+1] - diag[i] - 1; 1500 s1 = tmp[i]; 1501 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1502 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1503 tmp[i] = s1; 1504 } 1505 1506 /* backward solve the L^T */ 1507 for (i=n-1; i>=0; i--){ 1508 v = aa + diag[i] - 1 ; 1509 vi = aj + diag[i] - 1 ; 1510 nz = diag[i] - ai[i]; 1511 s1 = tmp[i]; 1512 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1513 } 1514 1515 /* copy tmp into x according to permutation */ 1516 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1517 1518 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1519 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1520 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1521 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1522 1523 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1524 PetscFunctionReturn(0); 1525 } 1526 1527 #undef __FUNCT__ 1528 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ" 1529 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx) 1530 { 1531 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1532 IS iscol = a->col,isrow = a->row; 1533 PetscErrorCode ierr; 1534 const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi; 1535 PetscInt i,n = A->rmap->n,j; 1536 PetscInt nz; 1537 PetscScalar *x,*tmp,s1; 1538 const MatScalar *aa = a->a,*v; 1539 const PetscScalar *b; 1540 1541 PetscFunctionBegin; 1542 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1543 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1544 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1545 tmp = a->solve_work; 1546 1547 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1548 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1549 1550 /* copy the b into temp work space according to permutation */ 1551 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1552 1553 /* forward solve the U^T */ 1554 for (i=0; i<n; i++) { 1555 v = aa + adiag[i+1] + 1; 1556 vi = aj + adiag[i+1] + 1; 1557 nz = adiag[i] - adiag[i+1] - 1; 1558 s1 = tmp[i]; 1559 s1 *= v[nz]; /* multiply by inverse of diagonal entry */ 1560 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1561 tmp[i] = s1; 1562 } 1563 1564 1565 /* backward solve the L^T */ 1566 for (i=n-1; i>=0; i--){ 1567 v = aa + ai[i] ; 1568 vi = aj + ai[i]; 1569 nz = ai[i+1] - ai[i]; 1570 s1 = tmp[i]; 1571 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1572 } 1573 1574 /* copy tmp into x according to permutation */ 1575 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1576 1577 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1578 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1579 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1580 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1581 1582 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1583 PetscFunctionReturn(0); 1584 } 1585 1586 /* ----------------------------------------------------------------*/ 1587 1588 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth); 1589 1590 /* 1591 ilu() under revised new data structure. 1592 Factored arrays bj and ba are stored as 1593 L(0,:), L(1,:), ...,L(n-1,:), U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:) 1594 1595 bi=fact->i is an array of size n+1, in which 1596 bi+ 1597 bi[i]: points to 1st entry of L(i,:),i=0,...,n-1 1598 bi[n]: points to L(n-1,n-1)+1 1599 1600 bdiag=fact->diag is an array of size n+1,in which 1601 bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1 1602 bdiag[n]: points to entry of U(n-1,0)-1 1603 1604 U(i,:) contains bdiag[i] as its last entry, i.e., 1605 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 1606 */ 1607 #undef __FUNCT__ 1608 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0" 1609 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1610 { 1611 1612 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1613 PetscErrorCode ierr; 1614 const PetscInt n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag; 1615 PetscInt i,j,k=0,nz,*bi,*bj,*bdiag; 1616 PetscTruth missing; 1617 IS isicol; 1618 1619 PetscFunctionBegin; 1620 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 1621 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 1622 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 1623 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1624 1625 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr); 1626 b = (Mat_SeqAIJ*)(fact)->data; 1627 1628 /* allocate matrix arrays for new data structure */ 1629 ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,n+1,PetscInt,&b->i);CHKERRQ(ierr); 1630 ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1631 b->singlemalloc = PETSC_TRUE; 1632 if (!b->diag){ 1633 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr); 1634 ierr = PetscLogObjectMemory(fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1635 } 1636 bdiag = b->diag; 1637 1638 if (n > 0) { 1639 ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr); 1640 } 1641 1642 /* set bi and bj with new data structure */ 1643 bi = b->i; 1644 bj = b->j; 1645 1646 /* L part */ 1647 bi[0] = 0; 1648 for (i=0; i<n; i++){ 1649 nz = adiag[i] - ai[i]; 1650 bi[i+1] = bi[i] + nz; 1651 aj = a->j + ai[i]; 1652 for (j=0; j<nz; j++){ 1653 /* *bj = aj[j]; bj++; */ 1654 bj[k++] = aj[j]; 1655 } 1656 } 1657 1658 /* U part */ 1659 bdiag[n] = bi[n]-1; 1660 for (i=n-1; i>=0; i--){ 1661 nz = ai[i+1] - adiag[i] - 1; 1662 aj = a->j + adiag[i] + 1; 1663 for (j=0; j<nz; j++){ 1664 /* *bj = aj[j]; bj++; */ 1665 bj[k++] = aj[j]; 1666 } 1667 /* diag[i] */ 1668 /* *bj = i; bj++; */ 1669 bj[k++] = i; 1670 bdiag[i] = bdiag[i+1] + nz + 1; 1671 } 1672 1673 fact->factor = MAT_FACTOR_ILU; 1674 fact->info.factor_mallocs = 0; 1675 fact->info.fill_ratio_given = info->fill; 1676 fact->info.fill_ratio_needed = 1.0; 1677 fact->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1678 1679 b = (Mat_SeqAIJ*)(fact)->data; 1680 b->row = isrow; 1681 b->col = iscol; 1682 b->icol = isicol; 1683 ierr = PetscMalloc((fact->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1684 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1685 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1686 PetscFunctionReturn(0); 1687 } 1688 1689 #undef __FUNCT__ 1690 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ" 1691 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1692 { 1693 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1694 IS isicol; 1695 PetscErrorCode ierr; 1696 const PetscInt *r,*ic; 1697 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j; 1698 PetscInt *bi,*cols,nnz,*cols_lvl; 1699 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1700 PetscInt i,levels,diagonal_fill; 1701 PetscTruth col_identity,row_identity; 1702 PetscReal f; 1703 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1704 PetscBT lnkbt; 1705 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1706 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1707 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1708 1709 PetscFunctionBegin; 1710 /* // Testing new data structure for MatSolve() 1711 PetscTruth olddatastruct=PETSC_FALSE 1712 ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_old",&olddatastruct,PETSC_NULL);CHKERRQ(ierr); 1713 if(olddatastruct){ 1714 ierr = MatILUFactorSymbolic_SeqAIJ_inplace(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1715 PetscFunctionReturn(0); 1716 } 1717 */ 1718 1719 levels = (PetscInt)info->levels; 1720 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1721 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1722 1723 if (!levels && row_identity && col_identity) { 1724 /* special case: ilu(0) with natural ordering */ 1725 ierr = MatILUFactorSymbolic_SeqAIJ_ilu0(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1726 ierr = Mat_CheckInode_FactorLU(fact,PETSC_FALSE);CHKERRQ(ierr); 1727 PetscFunctionReturn(0); 1728 } 1729 1730 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 1731 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1732 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1733 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1734 1735 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1736 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1737 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1738 bi[0] = bdiag[0] = 0; 1739 1740 ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr); 1741 1742 /* create a linked list for storing column indices of the active row */ 1743 nlnk = n + 1; 1744 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1745 1746 /* initial FreeSpace size is f*(ai[n]+1) */ 1747 f = info->fill; 1748 diagonal_fill = (PetscInt)info->diagonal_fill; 1749 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1750 current_space = free_space; 1751 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1752 current_space_lvl = free_space_lvl; 1753 1754 for (i=0; i<n; i++) { 1755 nzi = 0; 1756 /* copy current row into linked list */ 1757 nnz = ai[r[i]+1] - ai[r[i]]; 1758 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1759 cols = aj + ai[r[i]]; 1760 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1761 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1762 nzi += nlnk; 1763 1764 /* make sure diagonal entry is included */ 1765 if (diagonal_fill && lnk[i] == -1) { 1766 fm = n; 1767 while (lnk[fm] < i) fm = lnk[fm]; 1768 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1769 lnk[fm] = i; 1770 lnk_lvl[i] = 0; 1771 nzi++; dcount++; 1772 } 1773 1774 /* add pivot rows into the active row */ 1775 nzbd = 0; 1776 prow = lnk[n]; 1777 while (prow < i) { 1778 nnz = bdiag[prow]; 1779 cols = bj_ptr[prow] + nnz + 1; 1780 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1781 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1782 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1783 nzi += nlnk; 1784 prow = lnk[prow]; 1785 nzbd++; 1786 } 1787 bdiag[i] = nzbd; 1788 bi[i+1] = bi[i] + nzi; 1789 1790 /* if free space is not available, make more free space */ 1791 if (current_space->local_remaining<nzi) { 1792 nnz = 2*nzi*(n - i); /* estimated and max additional space needed */ 1793 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1794 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1795 reallocs++; 1796 } 1797 1798 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1799 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1800 bj_ptr[i] = current_space->array; 1801 bjlvl_ptr[i] = current_space_lvl->array; 1802 1803 /* make sure the active row i has diagonal entry */ 1804 if (*(bj_ptr[i]+bdiag[i]) != i) { 1805 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 1806 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1807 } 1808 1809 current_space->array += nzi; 1810 current_space->local_used += nzi; 1811 current_space->local_remaining -= nzi; 1812 current_space_lvl->array += nzi; 1813 current_space_lvl->local_used += nzi; 1814 current_space_lvl->local_remaining -= nzi; 1815 } 1816 1817 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1818 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1819 1820 /* destroy list of free space and other temporary arrays */ 1821 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 1822 1823 /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */ 1824 ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 1825 1826 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1827 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1828 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 1829 1830 #if defined(PETSC_USE_INFO) 1831 { 1832 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1833 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 1834 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1835 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 1836 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1837 if (diagonal_fill) { 1838 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 1839 } 1840 } 1841 #endif 1842 1843 /* put together the new matrix */ 1844 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 1845 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 1846 b = (Mat_SeqAIJ*)(fact)->data; 1847 b->free_a = PETSC_TRUE; 1848 b->free_ij = PETSC_TRUE; 1849 b->singlemalloc = PETSC_FALSE; 1850 ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 1851 b->j = bj; 1852 b->i = bi; 1853 b->diag = bdiag; 1854 b->ilen = 0; 1855 b->imax = 0; 1856 b->row = isrow; 1857 b->col = iscol; 1858 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1859 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1860 b->icol = isicol; 1861 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1862 /* In b structure: Free imax, ilen, old a, old j. 1863 Allocate bdiag, solve_work, new a, new j */ 1864 ierr = PetscLogObjectMemory(fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1865 b->maxnz = b->nz = bdiag[0]+1; 1866 (fact)->info.factor_mallocs = reallocs; 1867 (fact)->info.fill_ratio_given = f; 1868 (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 1869 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1870 ierr = Mat_CheckInode_FactorLU(fact,PETSC_FALSE);CHKERRQ(ierr); 1871 PetscFunctionReturn(0); 1872 } 1873 1874 #undef __FUNCT__ 1875 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_inplace" 1876 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1877 { 1878 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1879 IS isicol; 1880 PetscErrorCode ierr; 1881 const PetscInt *r,*ic; 1882 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,d; 1883 PetscInt *bi,*cols,nnz,*cols_lvl; 1884 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1885 PetscInt i,levels,diagonal_fill; 1886 PetscTruth col_identity,row_identity; 1887 PetscReal f; 1888 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1889 PetscBT lnkbt; 1890 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1891 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1892 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1893 PetscTruth missing; 1894 1895 PetscFunctionBegin; 1896 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 1897 f = info->fill; 1898 levels = (PetscInt)info->levels; 1899 diagonal_fill = (PetscInt)info->diagonal_fill; 1900 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1901 1902 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1903 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1904 if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */ 1905 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr); 1906 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace; 1907 1908 fact->factor = MAT_FACTOR_ILU; 1909 (fact)->info.factor_mallocs = 0; 1910 (fact)->info.fill_ratio_given = info->fill; 1911 (fact)->info.fill_ratio_needed = 1.0; 1912 b = (Mat_SeqAIJ*)(fact)->data; 1913 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 1914 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 1915 b->row = isrow; 1916 b->col = iscol; 1917 b->icol = isicol; 1918 ierr = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1919 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1920 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1921 ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1922 PetscFunctionReturn(0); 1923 } 1924 1925 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1926 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1927 1928 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1929 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1930 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1931 bi[0] = bdiag[0] = 0; 1932 1933 ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr); 1934 1935 /* create a linked list for storing column indices of the active row */ 1936 nlnk = n + 1; 1937 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1938 1939 /* initial FreeSpace size is f*(ai[n]+1) */ 1940 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1941 current_space = free_space; 1942 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1943 current_space_lvl = free_space_lvl; 1944 1945 for (i=0; i<n; i++) { 1946 nzi = 0; 1947 /* copy current row into linked list */ 1948 nnz = ai[r[i]+1] - ai[r[i]]; 1949 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1950 cols = aj + ai[r[i]]; 1951 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1952 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1953 nzi += nlnk; 1954 1955 /* make sure diagonal entry is included */ 1956 if (diagonal_fill && lnk[i] == -1) { 1957 fm = n; 1958 while (lnk[fm] < i) fm = lnk[fm]; 1959 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1960 lnk[fm] = i; 1961 lnk_lvl[i] = 0; 1962 nzi++; dcount++; 1963 } 1964 1965 /* add pivot rows into the active row */ 1966 nzbd = 0; 1967 prow = lnk[n]; 1968 while (prow < i) { 1969 nnz = bdiag[prow]; 1970 cols = bj_ptr[prow] + nnz + 1; 1971 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1972 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1973 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1974 nzi += nlnk; 1975 prow = lnk[prow]; 1976 nzbd++; 1977 } 1978 bdiag[i] = nzbd; 1979 bi[i+1] = bi[i] + nzi; 1980 1981 /* if free space is not available, make more free space */ 1982 if (current_space->local_remaining<nzi) { 1983 nnz = nzi*(n - i); /* estimated and max additional space needed */ 1984 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1985 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1986 reallocs++; 1987 } 1988 1989 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1990 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1991 bj_ptr[i] = current_space->array; 1992 bjlvl_ptr[i] = current_space_lvl->array; 1993 1994 /* make sure the active row i has diagonal entry */ 1995 if (*(bj_ptr[i]+bdiag[i]) != i) { 1996 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 1997 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1998 } 1999 2000 current_space->array += nzi; 2001 current_space->local_used += nzi; 2002 current_space->local_remaining -= nzi; 2003 current_space_lvl->array += nzi; 2004 current_space_lvl->local_used += nzi; 2005 current_space_lvl->local_remaining -= nzi; 2006 } 2007 2008 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 2009 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 2010 2011 /* destroy list of free space and other temporary arrays */ 2012 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 2013 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */ 2014 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2015 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2016 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 2017 2018 #if defined(PETSC_USE_INFO) 2019 { 2020 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 2021 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 2022 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2023 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 2024 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 2025 if (diagonal_fill) { 2026 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 2027 } 2028 } 2029 #endif 2030 2031 /* put together the new matrix */ 2032 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 2033 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 2034 b = (Mat_SeqAIJ*)(fact)->data; 2035 b->free_a = PETSC_TRUE; 2036 b->free_ij = PETSC_TRUE; 2037 b->singlemalloc = PETSC_FALSE; 2038 ierr = PetscMalloc(bi[n]*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 2039 b->j = bj; 2040 b->i = bi; 2041 for (i=0; i<n; i++) bdiag[i] += bi[i]; 2042 b->diag = bdiag; 2043 b->ilen = 0; 2044 b->imax = 0; 2045 b->row = isrow; 2046 b->col = iscol; 2047 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 2048 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 2049 b->icol = isicol; 2050 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2051 /* In b structure: Free imax, ilen, old a, old j. 2052 Allocate bdiag, solve_work, new a, new j */ 2053 ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 2054 b->maxnz = b->nz = bi[n] ; 2055 (fact)->info.factor_mallocs = reallocs; 2056 (fact)->info.fill_ratio_given = f; 2057 (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 2058 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace; 2059 ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); 2060 PetscFunctionReturn(0); 2061 } 2062 2063 #undef __FUNCT__ 2064 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ" 2065 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 2066 { 2067 Mat C = B; 2068 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2069 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2070 IS ip=b->row,iip = b->icol; 2071 PetscErrorCode ierr; 2072 const PetscInt *rip,*riip; 2073 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp; 2074 PetscInt *ai=a->i,*aj=a->j; 2075 PetscInt k,jmin,jmax,*c2r,*il,col,nexti,ili,nz; 2076 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2077 PetscTruth perm_identity; 2078 2079 FactorShiftCtx sctx; 2080 PetscReal rs; 2081 MatScalar d,*v; 2082 2083 PetscFunctionBegin; 2084 /* MatPivotSetUp(): initialize shift context sctx */ 2085 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 2086 2087 /* if both shift schemes are chosen by user, only use info->shiftpd */ 2088 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 2089 sctx.shift_top = info->zeropivot; 2090 for (i=0; i<mbs; i++) { 2091 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 2092 d = (aa)[a->diag[i]]; 2093 rs = -PetscAbsScalar(d) - PetscRealPart(d); 2094 v = aa+ai[i]; 2095 nz = ai[i+1] - ai[i]; 2096 for (j=0; j<nz; j++) 2097 rs += PetscAbsScalar(v[j]); 2098 if (rs>sctx.shift_top) sctx.shift_top = rs; 2099 } 2100 sctx.shift_top *= 1.1; 2101 sctx.nshift_max = 5; 2102 sctx.shift_lo = 0.; 2103 sctx.shift_hi = 1.; 2104 } 2105 2106 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2107 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2108 2109 /* allocate working arrays 2110 c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col 2111 il: for active k row, il[i] gives the index of the 1st nonzero entry in U[i,k:n-1] in bj and ba arrays 2112 */ 2113 ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&c2r);CHKERRQ(ierr); 2114 2115 do { 2116 sctx.useshift = PETSC_FALSE; 2117 2118 for (i=0; i<mbs; i++) c2r[i] = mbs; 2119 il[0] = 0; 2120 2121 for (k = 0; k<mbs; k++){ 2122 /* zero rtmp */ 2123 nz = bi[k+1] - bi[k]; 2124 bjtmp = bj + bi[k]; 2125 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2126 2127 /* load in initial unfactored row */ 2128 bval = ba + bi[k]; 2129 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2130 for (j = jmin; j < jmax; j++){ 2131 col = riip[aj[j]]; 2132 if (col >= k){ /* only take upper triangular entry */ 2133 rtmp[col] = aa[j]; 2134 *bval++ = 0.0; /* for in-place factorization */ 2135 } 2136 } 2137 /* shift the diagonal of the matrix: ZeropivotApply() */ 2138 rtmp[k] += sctx.shift_amount; /* shift the diagonal of the matrix */ 2139 2140 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2141 dk = rtmp[k]; 2142 i = c2r[k]; /* first row to be added to k_th row */ 2143 2144 while (i < k){ 2145 nexti = c2r[i]; /* next row to be added to k_th row */ 2146 2147 /* compute multiplier, update diag(k) and U(i,k) */ 2148 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2149 uikdi = - ba[ili]*ba[bdiag[i]]; /* diagonal(k) */ 2150 dk += uikdi*ba[ili]; /* update diag[k] */ 2151 ba[ili] = uikdi; /* -U(i,k) */ 2152 2153 /* add multiple of row i to k-th row */ 2154 jmin = ili + 1; jmax = bi[i+1]; 2155 if (jmin < jmax){ 2156 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2157 /* update il and c2r for row i */ 2158 il[i] = jmin; 2159 j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i; 2160 } 2161 i = nexti; 2162 } 2163 2164 /* copy data into U(k,:) */ 2165 rs = 0.0; 2166 jmin = bi[k]; jmax = bi[k+1]-1; 2167 if (jmin < jmax) { 2168 for (j=jmin; j<jmax; j++){ 2169 col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]); 2170 } 2171 /* add the k-th row into il and c2r */ 2172 il[k] = jmin; 2173 i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k; 2174 } 2175 2176 /* MatPivotCheck() */ 2177 sctx.rs = rs; 2178 sctx.pv = dk; 2179 if (info->shiftnz){ 2180 ierr = MatPivotCheck_nz(info,sctx,k);CHKERRQ(ierr); 2181 } else if (info->shiftpd){ 2182 ierr = MatPivotCheck_pd(info,sctx,k);CHKERRQ(ierr); 2183 } else if (info->shiftinblocks){ 2184 ierr = MatPivotCheck_inblocks(info,sctx,k);CHKERRQ(ierr); 2185 } else { 2186 ierr = MatPivotCheck_none(info,sctx,k);CHKERRQ(ierr); 2187 } 2188 dk = sctx.pv; 2189 2190 ba[bdiag[k]] = 1.0/dk; /* U(k,k) */ 2191 } 2192 } while (sctx.useshift); 2193 2194 ierr = PetscFree3(rtmp,il,c2r);CHKERRQ(ierr); 2195 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2196 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2197 2198 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2199 if (perm_identity){ 2200 B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2201 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2202 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering; 2203 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering; 2204 } else { 2205 B->ops->solve = MatSolve_SeqSBAIJ_1; 2206 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1; 2207 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1; 2208 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1; 2209 } 2210 2211 C->assembled = PETSC_TRUE; 2212 C->preallocated = PETSC_TRUE; 2213 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2214 2215 /* MatPivotView() */ 2216 if (sctx.nshift){ 2217 if (info->shiftpd) { 2218 ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %G, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,sctx.shift_amount,sctx.shift_fraction,sctx.shift_top);CHKERRQ(ierr); 2219 } else if (info->shiftnz) { 2220 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2221 } else if (info->shiftinblocks){ 2222 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftinblocks);CHKERRQ(ierr); 2223 } 2224 } 2225 PetscFunctionReturn(0); 2226 } 2227 2228 #undef __FUNCT__ 2229 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ_inplace" 2230 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info) 2231 { 2232 Mat C = B; 2233 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2234 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2235 IS ip=b->row,iip = b->icol; 2236 PetscErrorCode ierr; 2237 const PetscInt *rip,*riip; 2238 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol,*bjtmp; 2239 PetscInt *ai=a->i,*aj=a->j; 2240 PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz; 2241 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2242 PetscReal zeropivot,rs,shiftnz; 2243 PetscReal shiftpd; 2244 ChShift_Ctx sctx; 2245 PetscInt newshift; 2246 PetscTruth perm_identity; 2247 2248 PetscFunctionBegin; 2249 shiftnz = info->shiftnz; 2250 shiftpd = info->shiftpd; 2251 zeropivot = info->zeropivot; 2252 2253 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2254 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2255 2256 /* initialization */ 2257 ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr); 2258 sctx.shift_amount = 0; 2259 sctx.nshift = 0; 2260 do { 2261 sctx.chshift = PETSC_FALSE; 2262 for (i=0; i<mbs; i++) jl[i] = mbs; 2263 il[0] = 0; 2264 2265 for (k = 0; k<mbs; k++){ 2266 /* zero rtmp */ 2267 nz = bi[k+1] - bi[k]; 2268 bjtmp = bj + bi[k]; 2269 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2270 2271 bval = ba + bi[k]; 2272 /* initialize k-th row by the perm[k]-th row of A */ 2273 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2274 for (j = jmin; j < jmax; j++){ 2275 col = riip[aj[j]]; 2276 if (col >= k){ /* only take upper triangular entry */ 2277 rtmp[col] = aa[j]; 2278 *bval++ = 0.0; /* for in-place factorization */ 2279 } 2280 } 2281 /* shift the diagonal of the matrix */ 2282 if (sctx.nshift) rtmp[k] += sctx.shift_amount; 2283 2284 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2285 dk = rtmp[k]; 2286 i = jl[k]; /* first row to be added to k_th row */ 2287 2288 while (i < k){ 2289 nexti = jl[i]; /* next row to be added to k_th row */ 2290 2291 /* compute multiplier, update diag(k) and U(i,k) */ 2292 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2293 uikdi = - ba[ili]*ba[bi[i]]; /* diagonal(k) */ 2294 dk += uikdi*ba[ili]; 2295 ba[ili] = uikdi; /* -U(i,k) */ 2296 2297 /* add multiple of row i to k-th row */ 2298 jmin = ili + 1; jmax = bi[i+1]; 2299 if (jmin < jmax){ 2300 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2301 /* update il and jl for row i */ 2302 il[i] = jmin; 2303 j = bj[jmin]; jl[i] = jl[j]; jl[j] = i; 2304 } 2305 i = nexti; 2306 } 2307 2308 /* shift the diagonals when zero pivot is detected */ 2309 /* compute rs=sum of abs(off-diagonal) */ 2310 rs = 0.0; 2311 jmin = bi[k]+1; 2312 nz = bi[k+1] - jmin; 2313 bcol = bj + jmin; 2314 for (j=0; j<nz; j++) { 2315 rs += PetscAbsScalar(rtmp[bcol[j]]); 2316 } 2317 2318 sctx.rs = rs; 2319 sctx.pv = dk; 2320 ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr); 2321 2322 if (newshift == 1) { 2323 if (!sctx.shift_amount) { 2324 sctx.shift_amount = 1e-5; 2325 } 2326 break; 2327 } 2328 2329 /* copy data into U(k,:) */ 2330 ba[bi[k]] = 1.0/dk; /* U(k,k) */ 2331 jmin = bi[k]+1; jmax = bi[k+1]; 2332 if (jmin < jmax) { 2333 for (j=jmin; j<jmax; j++){ 2334 col = bj[j]; ba[j] = rtmp[col]; 2335 } 2336 /* add the k-th row into il and jl */ 2337 il[k] = jmin; 2338 i = bj[jmin]; jl[k] = jl[i]; jl[i] = k; 2339 } 2340 } 2341 } while (sctx.chshift); 2342 ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr); 2343 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2344 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2345 2346 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2347 if (perm_identity){ 2348 B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2349 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2350 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2351 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2352 } else { 2353 B->ops->solve = MatSolve_SeqSBAIJ_1_inplace; 2354 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_inplace; 2355 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_inplace; 2356 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_inplace; 2357 } 2358 2359 C->assembled = PETSC_TRUE; 2360 C->preallocated = PETSC_TRUE; 2361 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2362 if (sctx.nshift){ 2363 if (shiftnz) { 2364 ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2365 } else if (shiftpd) { 2366 ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2367 } 2368 } 2369 PetscFunctionReturn(0); 2370 } 2371 2372 /* 2373 icc() under revised new data structure. 2374 Factored arrays bj and ba are stored as 2375 U(0,:),...,U(i,:),U(n-1,:) 2376 2377 ui=fact->i is an array of size n+1, in which 2378 ui+ 2379 ui[i]: points to 1st entry of U(i,:),i=0,...,n-1 2380 ui[n]: points to U(n-1,n-1)+1 2381 2382 udiag=fact->diag is an array of size n,in which 2383 udiag[i]: points to diagonal of U(i,:), i=0,...,n-1 2384 2385 U(i,:) contains udiag[i] as its last entry, i.e., 2386 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 2387 */ 2388 2389 #undef __FUNCT__ 2390 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ" 2391 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2392 { 2393 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2394 Mat_SeqSBAIJ *b; 2395 PetscErrorCode ierr; 2396 PetscTruth perm_identity,missing; 2397 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2398 const PetscInt *rip,*riip; 2399 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2400 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2401 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2402 PetscReal fill=info->fill,levels=info->levels; 2403 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2404 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2405 PetscBT lnkbt; 2406 IS iperm; 2407 2408 PetscFunctionBegin; 2409 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 2410 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2411 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2412 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2413 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2414 2415 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2416 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2417 ui[0] = 0; 2418 2419 /* ICC(0) without matrix ordering: simply rearrange column indices */ 2420 if (!levels && perm_identity) { 2421 for (i=0; i<am; i++) { 2422 ncols = ai[i+1] - a->diag[i]; 2423 ui[i+1] = ui[i] + ncols; 2424 udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */ 2425 } 2426 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2427 cols = uj; 2428 for (i=0; i<am; i++) { 2429 aj = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */ 2430 ncols = ai[i+1] - a->diag[i] -1; 2431 for (j=0; j<ncols; j++) *cols++ = aj[j]; 2432 *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */ 2433 } 2434 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2435 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2436 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2437 2438 /* initialization */ 2439 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2440 2441 /* jl: linked list for storing indices of the pivot rows 2442 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2443 ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr); 2444 for (i=0; i<am; i++){ 2445 jl[i] = am; il[i] = 0; 2446 } 2447 2448 /* create and initialize a linked list for storing column indices of the active row k */ 2449 nlnk = am + 1; 2450 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2451 2452 /* initial FreeSpace size is fill*(ai[am]+1) */ 2453 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2454 current_space = free_space; 2455 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2456 current_space_lvl = free_space_lvl; 2457 2458 for (k=0; k<am; k++){ /* for each active row k */ 2459 /* initialize lnk by the column indices of row rip[k] of A */ 2460 nzk = 0; 2461 ncols = ai[rip[k]+1] - ai[rip[k]]; 2462 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2463 ncols_upper = 0; 2464 for (j=0; j<ncols; j++){ 2465 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2466 if (riip[i] >= k){ /* only take upper triangular entry */ 2467 ajtmp[ncols_upper] = i; 2468 ncols_upper++; 2469 } 2470 } 2471 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2472 nzk += nlnk; 2473 2474 /* update lnk by computing fill-in for each pivot row to be merged in */ 2475 prow = jl[k]; /* 1st pivot row */ 2476 2477 while (prow < k){ 2478 nextprow = jl[prow]; 2479 2480 /* merge prow into k-th row */ 2481 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2482 jmax = ui[prow+1]; 2483 ncols = jmax-jmin; 2484 i = jmin - ui[prow]; 2485 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2486 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2487 j = *(uj - 1); 2488 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2489 nzk += nlnk; 2490 2491 /* update il and jl for prow */ 2492 if (jmin < jmax){ 2493 il[prow] = jmin; 2494 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2495 } 2496 prow = nextprow; 2497 } 2498 2499 /* if free space is not available, make more free space */ 2500 if (current_space->local_remaining<nzk) { 2501 i = am - k + 1; /* num of unfactored rows */ 2502 i *= PetscMin(nzk, i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2503 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2504 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2505 reallocs++; 2506 } 2507 2508 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2509 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2510 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2511 2512 /* add the k-th row into il and jl */ 2513 if (nzk > 1){ 2514 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2515 jl[k] = jl[i]; jl[i] = k; 2516 il[k] = ui[k] + 1; 2517 } 2518 uj_ptr[k] = current_space->array; 2519 uj_lvl_ptr[k] = current_space_lvl->array; 2520 2521 current_space->array += nzk; 2522 current_space->local_used += nzk; 2523 current_space->local_remaining -= nzk; 2524 2525 current_space_lvl->array += nzk; 2526 current_space_lvl->local_used += nzk; 2527 current_space_lvl->local_remaining -= nzk; 2528 2529 ui[k+1] = ui[k] + nzk; 2530 } 2531 2532 #if defined(PETSC_USE_INFO) 2533 if (ai[am] != 0) { 2534 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2535 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2536 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2537 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2538 } else { 2539 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2540 } 2541 #endif 2542 2543 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2544 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2545 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2546 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2547 2548 /* destroy list of free space and other temporary array(s) */ 2549 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2550 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor */ 2551 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2552 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2553 2554 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2555 2556 /* put together the new matrix in MATSEQSBAIJ format */ 2557 b = (Mat_SeqSBAIJ*)(fact)->data; 2558 b->singlemalloc = PETSC_FALSE; 2559 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2560 b->j = uj; 2561 b->i = ui; 2562 b->diag = udiag; 2563 b->free_diag = PETSC_TRUE; 2564 b->ilen = 0; 2565 b->imax = 0; 2566 b->row = perm; 2567 b->col = perm; 2568 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2569 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2570 b->icol = iperm; 2571 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2572 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2573 ierr = PetscLogObjectMemory(fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2574 b->maxnz = b->nz = ui[am]; 2575 b->free_a = PETSC_TRUE; 2576 b->free_ij = PETSC_TRUE; 2577 2578 fact->info.factor_mallocs = reallocs; 2579 fact->info.fill_ratio_given = fill; 2580 if (ai[am] != 0) { 2581 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2582 } else { 2583 fact->info.fill_ratio_needed = 0.0; 2584 } 2585 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2586 PetscFunctionReturn(0); 2587 } 2588 2589 #undef __FUNCT__ 2590 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ_inplace" 2591 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2592 { 2593 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2594 Mat_SeqSBAIJ *b; 2595 PetscErrorCode ierr; 2596 PetscTruth perm_identity,missing; 2597 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2598 const PetscInt *rip,*riip; 2599 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2600 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2601 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2602 PetscReal fill=info->fill,levels=info->levels; 2603 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2604 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2605 PetscBT lnkbt; 2606 IS iperm; 2607 2608 PetscFunctionBegin; 2609 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 2610 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2611 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2612 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2613 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2614 2615 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2616 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2617 ui[0] = 0; 2618 2619 /* ICC(0) without matrix ordering: simply copies fill pattern */ 2620 if (!levels && perm_identity) { 2621 2622 for (i=0; i<am; i++) { 2623 ui[i+1] = ui[i] + ai[i+1] - a->diag[i]; 2624 udiag[i] = ui[i]; 2625 } 2626 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2627 cols = uj; 2628 for (i=0; i<am; i++) { 2629 aj = a->j + a->diag[i]; 2630 ncols = ui[i+1] - ui[i]; 2631 for (j=0; j<ncols; j++) *cols++ = *aj++; 2632 } 2633 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2634 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2635 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2636 2637 /* initialization */ 2638 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2639 2640 /* jl: linked list for storing indices of the pivot rows 2641 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2642 ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr); 2643 for (i=0; i<am; i++){ 2644 jl[i] = am; il[i] = 0; 2645 } 2646 2647 /* create and initialize a linked list for storing column indices of the active row k */ 2648 nlnk = am + 1; 2649 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2650 2651 /* initial FreeSpace size is fill*(ai[am]+1) */ 2652 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2653 current_space = free_space; 2654 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2655 current_space_lvl = free_space_lvl; 2656 2657 for (k=0; k<am; k++){ /* for each active row k */ 2658 /* initialize lnk by the column indices of row rip[k] of A */ 2659 nzk = 0; 2660 ncols = ai[rip[k]+1] - ai[rip[k]]; 2661 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2662 ncols_upper = 0; 2663 for (j=0; j<ncols; j++){ 2664 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2665 if (riip[i] >= k){ /* only take upper triangular entry */ 2666 ajtmp[ncols_upper] = i; 2667 ncols_upper++; 2668 } 2669 } 2670 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2671 nzk += nlnk; 2672 2673 /* update lnk by computing fill-in for each pivot row to be merged in */ 2674 prow = jl[k]; /* 1st pivot row */ 2675 2676 while (prow < k){ 2677 nextprow = jl[prow]; 2678 2679 /* merge prow into k-th row */ 2680 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2681 jmax = ui[prow+1]; 2682 ncols = jmax-jmin; 2683 i = jmin - ui[prow]; 2684 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2685 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2686 j = *(uj - 1); 2687 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2688 nzk += nlnk; 2689 2690 /* update il and jl for prow */ 2691 if (jmin < jmax){ 2692 il[prow] = jmin; 2693 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2694 } 2695 prow = nextprow; 2696 } 2697 2698 /* if free space is not available, make more free space */ 2699 if (current_space->local_remaining<nzk) { 2700 i = am - k + 1; /* num of unfactored rows */ 2701 i *= PetscMin(nzk, (i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2702 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2703 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2704 reallocs++; 2705 } 2706 2707 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2708 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2709 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2710 2711 /* add the k-th row into il and jl */ 2712 if (nzk > 1){ 2713 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2714 jl[k] = jl[i]; jl[i] = k; 2715 il[k] = ui[k] + 1; 2716 } 2717 uj_ptr[k] = current_space->array; 2718 uj_lvl_ptr[k] = current_space_lvl->array; 2719 2720 current_space->array += nzk; 2721 current_space->local_used += nzk; 2722 current_space->local_remaining -= nzk; 2723 2724 current_space_lvl->array += nzk; 2725 current_space_lvl->local_used += nzk; 2726 current_space_lvl->local_remaining -= nzk; 2727 2728 ui[k+1] = ui[k] + nzk; 2729 } 2730 2731 #if defined(PETSC_USE_INFO) 2732 if (ai[am] != 0) { 2733 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2734 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2735 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2736 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2737 } else { 2738 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2739 } 2740 #endif 2741 2742 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2743 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2744 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2745 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2746 2747 /* destroy list of free space and other temporary array(s) */ 2748 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2749 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 2750 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2751 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2752 2753 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2754 2755 /* put together the new matrix in MATSEQSBAIJ format */ 2756 2757 b = (Mat_SeqSBAIJ*)fact->data; 2758 b->singlemalloc = PETSC_FALSE; 2759 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2760 b->j = uj; 2761 b->i = ui; 2762 b->diag = udiag; 2763 b->free_diag = PETSC_TRUE; 2764 b->ilen = 0; 2765 b->imax = 0; 2766 b->row = perm; 2767 b->col = perm; 2768 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2769 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2770 b->icol = iperm; 2771 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2772 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2773 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2774 b->maxnz = b->nz = ui[am]; 2775 b->free_a = PETSC_TRUE; 2776 b->free_ij = PETSC_TRUE; 2777 2778 fact->info.factor_mallocs = reallocs; 2779 fact->info.fill_ratio_given = fill; 2780 if (ai[am] != 0) { 2781 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2782 } else { 2783 fact->info.fill_ratio_needed = 0.0; 2784 } 2785 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace; 2786 PetscFunctionReturn(0); 2787 } 2788 2789 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2790 { 2791 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2792 Mat_SeqSBAIJ *b; 2793 PetscErrorCode ierr; 2794 PetscTruth perm_identity; 2795 PetscReal fill = info->fill; 2796 const PetscInt *rip,*riip; 2797 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2798 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2799 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr,*udiag; 2800 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2801 PetscBT lnkbt; 2802 IS iperm; 2803 2804 PetscFunctionBegin; 2805 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 2806 /* check whether perm is the identity mapping */ 2807 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2808 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2809 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2810 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2811 2812 /* initialization */ 2813 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2814 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2815 ui[0] = 0; 2816 2817 /* jl: linked list for storing indices of the pivot rows 2818 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2819 ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr); 2820 for (i=0; i<am; i++){ 2821 jl[i] = am; il[i] = 0; 2822 } 2823 2824 /* create and initialize a linked list for storing column indices of the active row k */ 2825 nlnk = am + 1; 2826 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2827 2828 /* initial FreeSpace size is fill*(ai[am]+1) */ 2829 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2830 current_space = free_space; 2831 2832 for (k=0; k<am; k++){ /* for each active row k */ 2833 /* initialize lnk by the column indices of row rip[k] of A */ 2834 nzk = 0; 2835 ncols = ai[rip[k]+1] - ai[rip[k]]; 2836 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2837 ncols_upper = 0; 2838 for (j=0; j<ncols; j++){ 2839 i = riip[*(aj + ai[rip[k]] + j)]; 2840 if (i >= k){ /* only take upper triangular entry */ 2841 cols[ncols_upper] = i; 2842 ncols_upper++; 2843 } 2844 } 2845 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2846 nzk += nlnk; 2847 2848 /* update lnk by computing fill-in for each pivot row to be merged in */ 2849 prow = jl[k]; /* 1st pivot row */ 2850 2851 while (prow < k){ 2852 nextprow = jl[prow]; 2853 /* merge prow into k-th row */ 2854 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2855 jmax = ui[prow+1]; 2856 ncols = jmax-jmin; 2857 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2858 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2859 nzk += nlnk; 2860 2861 /* update il and jl for prow */ 2862 if (jmin < jmax){ 2863 il[prow] = jmin; 2864 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 2865 } 2866 prow = nextprow; 2867 } 2868 2869 /* if free space is not available, make more free space */ 2870 if (current_space->local_remaining<nzk) { 2871 i = am - k + 1; /* num of unfactored rows */ 2872 i *= PetscMin(nzk,i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2873 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2874 reallocs++; 2875 } 2876 2877 /* copy data into free space, then initialize lnk */ 2878 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 2879 2880 /* add the k-th row into il and jl */ 2881 if (nzk > 1){ 2882 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2883 jl[k] = jl[i]; jl[i] = k; 2884 il[k] = ui[k] + 1; 2885 } 2886 ui_ptr[k] = current_space->array; 2887 current_space->array += nzk; 2888 current_space->local_used += nzk; 2889 current_space->local_remaining -= nzk; 2890 2891 ui[k+1] = ui[k] + nzk; 2892 } 2893 2894 #if defined(PETSC_USE_INFO) 2895 if (ai[am] != 0) { 2896 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 2897 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2898 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2899 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2900 } else { 2901 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2902 } 2903 #endif 2904 2905 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2906 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2907 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 2908 2909 /* destroy list of free space and other temporary array(s) */ 2910 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2911 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor */ 2912 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2913 2914 /* put together the new matrix in MATSEQSBAIJ format */ 2915 2916 b = (Mat_SeqSBAIJ*)fact->data; 2917 b->singlemalloc = PETSC_FALSE; 2918 b->free_a = PETSC_TRUE; 2919 b->free_ij = PETSC_TRUE; 2920 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2921 b->j = uj; 2922 b->i = ui; 2923 b->diag = udiag; 2924 b->free_diag = PETSC_TRUE; 2925 b->ilen = 0; 2926 b->imax = 0; 2927 b->row = perm; 2928 b->col = perm; 2929 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2930 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2931 b->icol = iperm; 2932 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2933 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2934 ierr = PetscLogObjectMemory(fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2935 b->maxnz = b->nz = ui[am]; 2936 2937 fact->info.factor_mallocs = reallocs; 2938 fact->info.fill_ratio_given = fill; 2939 if (ai[am] != 0) { 2940 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2941 } else { 2942 fact->info.fill_ratio_needed = 0.0; 2943 } 2944 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2945 PetscFunctionReturn(0); 2946 } 2947 2948 #undef __FUNCT__ 2949 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ_inplace" 2950 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2951 { 2952 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2953 Mat_SeqSBAIJ *b; 2954 PetscErrorCode ierr; 2955 PetscTruth perm_identity; 2956 PetscReal fill = info->fill; 2957 const PetscInt *rip,*riip; 2958 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2959 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2960 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr; 2961 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2962 PetscBT lnkbt; 2963 IS iperm; 2964 2965 PetscFunctionBegin; 2966 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 2967 /* check whether perm is the identity mapping */ 2968 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2969 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2970 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2971 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2972 2973 /* initialization */ 2974 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2975 ui[0] = 0; 2976 2977 /* jl: linked list for storing indices of the pivot rows 2978 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2979 ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr); 2980 for (i=0; i<am; i++){ 2981 jl[i] = am; il[i] = 0; 2982 } 2983 2984 /* create and initialize a linked list for storing column indices of the active row k */ 2985 nlnk = am + 1; 2986 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2987 2988 /* initial FreeSpace size is fill*(ai[am]+1) */ 2989 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2990 current_space = free_space; 2991 2992 for (k=0; k<am; k++){ /* for each active row k */ 2993 /* initialize lnk by the column indices of row rip[k] of A */ 2994 nzk = 0; 2995 ncols = ai[rip[k]+1] - ai[rip[k]]; 2996 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2997 ncols_upper = 0; 2998 for (j=0; j<ncols; j++){ 2999 i = riip[*(aj + ai[rip[k]] + j)]; 3000 if (i >= k){ /* only take upper triangular entry */ 3001 cols[ncols_upper] = i; 3002 ncols_upper++; 3003 } 3004 } 3005 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3006 nzk += nlnk; 3007 3008 /* update lnk by computing fill-in for each pivot row to be merged in */ 3009 prow = jl[k]; /* 1st pivot row */ 3010 3011 while (prow < k){ 3012 nextprow = jl[prow]; 3013 /* merge prow into k-th row */ 3014 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 3015 jmax = ui[prow+1]; 3016 ncols = jmax-jmin; 3017 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 3018 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3019 nzk += nlnk; 3020 3021 /* update il and jl for prow */ 3022 if (jmin < jmax){ 3023 il[prow] = jmin; 3024 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 3025 } 3026 prow = nextprow; 3027 } 3028 3029 /* if free space is not available, make more free space */ 3030 if (current_space->local_remaining<nzk) { 3031 i = am - k + 1; /* num of unfactored rows */ 3032 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 3033 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 3034 reallocs++; 3035 } 3036 3037 /* copy data into free space, then initialize lnk */ 3038 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 3039 3040 /* add the k-th row into il and jl */ 3041 if (nzk-1 > 0){ 3042 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 3043 jl[k] = jl[i]; jl[i] = k; 3044 il[k] = ui[k] + 1; 3045 } 3046 ui_ptr[k] = current_space->array; 3047 current_space->array += nzk; 3048 current_space->local_used += nzk; 3049 current_space->local_remaining -= nzk; 3050 3051 ui[k+1] = ui[k] + nzk; 3052 } 3053 3054 #if defined(PETSC_USE_INFO) 3055 if (ai[am] != 0) { 3056 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 3057 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 3058 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 3059 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 3060 } else { 3061 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 3062 } 3063 #endif 3064 3065 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 3066 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 3067 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 3068 3069 /* destroy list of free space and other temporary array(s) */ 3070 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 3071 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 3072 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3073 3074 /* put together the new matrix in MATSEQSBAIJ format */ 3075 3076 b = (Mat_SeqSBAIJ*)fact->data; 3077 b->singlemalloc = PETSC_FALSE; 3078 b->free_a = PETSC_TRUE; 3079 b->free_ij = PETSC_TRUE; 3080 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 3081 b->j = uj; 3082 b->i = ui; 3083 b->diag = 0; 3084 b->ilen = 0; 3085 b->imax = 0; 3086 b->row = perm; 3087 b->col = perm; 3088 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3089 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3090 b->icol = iperm; 3091 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 3092 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 3093 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3094 b->maxnz = b->nz = ui[am]; 3095 3096 fact->info.factor_mallocs = reallocs; 3097 fact->info.fill_ratio_given = fill; 3098 if (ai[am] != 0) { 3099 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 3100 } else { 3101 fact->info.fill_ratio_needed = 0.0; 3102 } 3103 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace; 3104 PetscFunctionReturn(0); 3105 } 3106 3107 #undef __FUNCT__ 3108 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering" 3109 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx) 3110 { 3111 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3112 PetscErrorCode ierr; 3113 PetscInt n = A->rmap->n; 3114 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag,*vi; 3115 PetscScalar *x,sum; 3116 const PetscScalar *b; 3117 const MatScalar *aa = a->a,*v; 3118 PetscInt i,nz; 3119 3120 PetscFunctionBegin; 3121 if (!n) PetscFunctionReturn(0); 3122 3123 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3124 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3125 3126 /* forward solve the lower triangular */ 3127 x[0] = b[0]; 3128 v = aa; 3129 vi = aj; 3130 for (i=1; i<n; i++) { 3131 nz = ai[i+1] - ai[i]; 3132 sum = b[i]; 3133 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3134 v += nz; 3135 vi += nz; 3136 x[i] = sum; 3137 } 3138 3139 /* backward solve the upper triangular */ 3140 for (i=n-1; i>=0; i--){ 3141 v = aa + adiag[i+1] + 1; 3142 vi = aj + adiag[i+1] + 1; 3143 nz = adiag[i] - adiag[i+1]-1; 3144 sum = x[i]; 3145 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3146 x[i] = sum*v[nz]; /* x[i]=aa[adiag[i]]*sum; v++; */ 3147 } 3148 3149 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 3150 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3151 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3152 PetscFunctionReturn(0); 3153 } 3154 3155 #undef __FUNCT__ 3156 #define __FUNCT__ "MatSolve_SeqAIJ" 3157 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx) 3158 { 3159 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3160 IS iscol = a->col,isrow = a->row; 3161 PetscErrorCode ierr; 3162 PetscInt i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz; 3163 const PetscInt *rout,*cout,*r,*c; 3164 PetscScalar *x,*tmp,sum; 3165 const PetscScalar *b; 3166 const MatScalar *aa = a->a,*v; 3167 3168 PetscFunctionBegin; 3169 if (!n) PetscFunctionReturn(0); 3170 3171 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3172 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3173 tmp = a->solve_work; 3174 3175 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 3176 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 3177 3178 /* forward solve the lower triangular */ 3179 tmp[0] = b[r[0]]; 3180 v = aa; 3181 vi = aj; 3182 for (i=1; i<n; i++) { 3183 nz = ai[i+1] - ai[i]; 3184 sum = b[r[i]]; 3185 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3186 tmp[i] = sum; 3187 v += nz; vi += nz; 3188 } 3189 3190 /* backward solve the upper triangular */ 3191 for (i=n-1; i>=0; i--){ 3192 v = aa + adiag[i+1]+1; 3193 vi = aj + adiag[i+1]+1; 3194 nz = adiag[i]-adiag[i+1]-1; 3195 sum = tmp[i]; 3196 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3197 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 3198 } 3199 3200 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 3201 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 3202 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3203 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3204 ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr); 3205 PetscFunctionReturn(0); 3206 } 3207 3208 #undef __FUNCT__ 3209 #define __FUNCT__ "MatILUDTFactor_SeqAIJ" 3210 /* 3211 This will get a new name and become a varient of MatILUFactor_SeqAIJ() there is no longer seperate functions in the matrix function table for dt factors 3212 */ 3213 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact) 3214 { 3215 Mat B = *fact; 3216 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b; 3217 IS isicol; 3218 PetscErrorCode ierr; 3219 const PetscInt *r,*ic; 3220 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag; 3221 PetscInt *bi,*bj,*bdiag,*bdiag_rev; 3222 PetscInt row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au; 3223 PetscInt nlnk,*lnk; 3224 PetscBT lnkbt; 3225 PetscTruth row_identity,icol_identity,both_identity; 3226 MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp; 3227 const PetscInt *ics; 3228 PetscInt j,nz,*pj,*bjtmp,k,ncut,*jtmp; 3229 PetscReal dt=info->dt,dtcol=info->dtcol,shift=info->shiftinblocks; 3230 PetscInt dtcount=(PetscInt)info->dtcount,nnz_max; 3231 PetscTruth missing; 3232 3233 PetscFunctionBegin; 3234 3235 if (dt == PETSC_DEFAULT) dt = 0.005; 3236 if (dtcol == PETSC_DEFAULT) dtcol = 0.01; /* XXX unused! */ 3237 if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax); 3238 3239 /* ------- symbolic factorization, can be reused ---------*/ 3240 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 3241 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 3242 adiag=a->diag; 3243 3244 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 3245 3246 /* bdiag is location of diagonal in factor */ 3247 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); /* becomes b->diag */ 3248 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag_rev);CHKERRQ(ierr); /* temporary */ 3249 3250 /* allocate row pointers bi */ 3251 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 3252 3253 /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */ 3254 if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */ 3255 nnz_max = ai[n]+2*n*dtcount+2; 3256 3257 ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 3258 ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr); 3259 3260 /* put together the new matrix */ 3261 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 3262 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 3263 b = (Mat_SeqAIJ*)B->data; 3264 b->free_a = PETSC_TRUE; 3265 b->free_ij = PETSC_TRUE; 3266 b->singlemalloc = PETSC_FALSE; 3267 b->a = ba; 3268 b->j = bj; 3269 b->i = bi; 3270 b->diag = bdiag; 3271 b->ilen = 0; 3272 b->imax = 0; 3273 b->row = isrow; 3274 b->col = iscol; 3275 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 3276 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 3277 b->icol = isicol; 3278 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 3279 3280 ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3281 b->maxnz = nnz_max; 3282 3283 B->factor = MAT_FACTOR_ILUDT; 3284 B->info.factor_mallocs = 0; 3285 B->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]); 3286 CHKMEMQ; 3287 /* ------- end of symbolic factorization ---------*/ 3288 3289 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3290 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3291 ics = ic; 3292 3293 /* linked list for storing column indices of the active row */ 3294 nlnk = n + 1; 3295 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3296 3297 /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */ 3298 ierr = PetscMalloc2(n,PetscInt,&im,n,PetscInt,&jtmp);CHKERRQ(ierr); 3299 /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */ 3300 ierr = PetscMalloc2(n,MatScalar,&rtmp,n,MatScalar,&vtmp);CHKERRQ(ierr); 3301 ierr = PetscMemzero(rtmp,n*sizeof(MatScalar));CHKERRQ(ierr); 3302 3303 bi[0] = 0; 3304 bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */ 3305 bdiag_rev[n] = bdiag[0]; 3306 bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */ 3307 for (i=0; i<n; i++) { 3308 /* copy initial fill into linked list */ 3309 nzi = 0; /* nonzeros for active row i */ 3310 nzi = ai[r[i]+1] - ai[r[i]]; 3311 if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 3312 nzi_al = adiag[r[i]] - ai[r[i]]; 3313 nzi_au = ai[r[i]+1] - adiag[r[i]] -1; 3314 ajtmp = aj + ai[r[i]]; 3315 ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3316 3317 /* load in initial (unfactored row) */ 3318 aatmp = a->a + ai[r[i]]; 3319 for (j=0; j<nzi; j++) { 3320 rtmp[ics[*ajtmp++]] = *aatmp++; 3321 } 3322 3323 /* add pivot rows into linked list */ 3324 row = lnk[n]; 3325 while (row < i ) { 3326 nzi_bl = bi[row+1] - bi[row] + 1; 3327 bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */ 3328 ierr = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr); 3329 nzi += nlnk; 3330 row = lnk[row]; 3331 } 3332 3333 /* copy data from lnk into jtmp, then initialize lnk */ 3334 ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr); 3335 3336 /* numerical factorization */ 3337 bjtmp = jtmp; 3338 row = *bjtmp++; /* 1st pivot row */ 3339 while ( row < i ) { 3340 pc = rtmp + row; 3341 pv = ba + bdiag[row]; /* 1./(diag of the pivot row) */ 3342 multiplier = (*pc) * (*pv); 3343 *pc = multiplier; 3344 if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */ 3345 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3346 pv = ba + bdiag[row+1] + 1; 3347 /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */ 3348 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3349 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3350 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 3351 } 3352 row = *bjtmp++; 3353 } 3354 3355 /* copy sparse rtmp into contiguous vtmp; separate L and U part */ 3356 diag_tmp = rtmp[i]; /* save diagonal value - may not needed?? */ 3357 nzi_bl = 0; j = 0; 3358 while (jtmp[j] < i){ /* Note: jtmp is sorted */ 3359 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3360 nzi_bl++; j++; 3361 } 3362 nzi_bu = nzi - nzi_bl -1; 3363 while (j < nzi){ 3364 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3365 j++; 3366 } 3367 3368 bjtmp = bj + bi[i]; 3369 batmp = ba + bi[i]; 3370 /* apply level dropping rule to L part */ 3371 ncut = nzi_al + dtcount; 3372 if (ncut < nzi_bl){ 3373 ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr); 3374 ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr); 3375 } else { 3376 ncut = nzi_bl; 3377 } 3378 for (j=0; j<ncut; j++){ 3379 bjtmp[j] = jtmp[j]; 3380 batmp[j] = vtmp[j]; 3381 /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */ 3382 } 3383 bi[i+1] = bi[i] + ncut; 3384 nzi = ncut + 1; 3385 3386 /* apply level dropping rule to U part */ 3387 ncut = nzi_au + dtcount; 3388 if (ncut < nzi_bu){ 3389 ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr); 3390 ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr); 3391 } else { 3392 ncut = nzi_bu; 3393 } 3394 nzi += ncut; 3395 3396 /* mark bdiagonal */ 3397 bdiag[i+1] = bdiag[i] - (ncut + 1); 3398 bdiag_rev[n-i-1] = bdiag[i+1]; 3399 bi[2*n - i] = bi[2*n - i +1] - (ncut + 1); 3400 bjtmp = bj + bdiag[i]; 3401 batmp = ba + bdiag[i]; 3402 *bjtmp = i; 3403 *batmp = diag_tmp; /* rtmp[i]; */ 3404 if (*batmp == 0.0) { 3405 *batmp = dt+shift; 3406 /* printf(" row %d add shift %g\n",i,shift); */ 3407 } 3408 *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */ 3409 /* printf(" (%d,%g),",*bjtmp,*batmp); */ 3410 3411 bjtmp = bj + bdiag[i+1]+1; 3412 batmp = ba + bdiag[i+1]+1; 3413 for (k=0; k<ncut; k++){ 3414 bjtmp[k] = jtmp[nzi_bl+1+k]; 3415 batmp[k] = vtmp[nzi_bl+1+k]; 3416 /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */ 3417 } 3418 /* printf("\n"); */ 3419 3420 im[i] = nzi; /* used by PetscLLAddSortedLU() */ 3421 /* 3422 printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]); 3423 printf(" ----------------------------\n"); 3424 */ 3425 } /* for (i=0; i<n; i++) */ 3426 /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */ 3427 if (bi[n] >= bdiag[n]) SETERRQ2(PETSC_ERR_ARG_SIZ,"end of L array %d cannot >= the beginning of U array %d",bi[n],bdiag[n]); 3428 3429 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3430 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3431 3432 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3433 ierr = PetscFree2(im,jtmp);CHKERRQ(ierr); 3434 ierr = PetscFree2(rtmp,vtmp);CHKERRQ(ierr); 3435 ierr = PetscFree(bdiag_rev);CHKERRQ(ierr); 3436 3437 ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr); 3438 b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n]; 3439 3440 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3441 ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr); 3442 both_identity = (PetscTruth) (row_identity && icol_identity); 3443 if (row_identity && icol_identity) { 3444 B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 3445 } else { 3446 B->ops->solve = MatSolve_SeqAIJ; 3447 } 3448 3449 B->ops->solveadd = 0; 3450 B->ops->solvetranspose = 0; 3451 B->ops->solvetransposeadd = 0; 3452 B->ops->matsolve = 0; 3453 B->assembled = PETSC_TRUE; 3454 B->preallocated = PETSC_TRUE; 3455 PetscFunctionReturn(0); 3456 } 3457 3458 /* a wraper of MatILUDTFactor_SeqAIJ() */ 3459 #undef __FUNCT__ 3460 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ" 3461 /* 3462 This will get a new name and become a varient of MatILUFactor_SeqAIJ() there is no longer seperate functions in the matrix function table for dt factors 3463 */ 3464 3465 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info) 3466 { 3467 PetscErrorCode ierr; 3468 3469 PetscFunctionBegin; 3470 ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr); 3471 PetscFunctionReturn(0); 3472 } 3473 3474 /* 3475 same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors 3476 - intend to replace existing MatLUFactorNumeric_SeqAIJ() 3477 */ 3478 #undef __FUNCT__ 3479 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ" 3480 /* 3481 This will get a new name and become a varient of MatILUFactor_SeqAIJ() there is no longer seperate functions in the matrix function table for dt factors 3482 */ 3483 3484 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info) 3485 { 3486 Mat C=fact; 3487 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 3488 IS isrow = b->row,isicol = b->icol; 3489 PetscErrorCode ierr; 3490 const PetscInt *r,*ic,*ics; 3491 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 3492 PetscInt *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj; 3493 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 3494 PetscReal dt=info->dt,shift=info->shiftinblocks; 3495 PetscTruth row_identity, col_identity; 3496 3497 PetscFunctionBegin; 3498 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3499 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3500 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 3501 ics = ic; 3502 3503 for (i=0; i<n; i++){ 3504 /* initialize rtmp array */ 3505 nzl = bi[i+1] - bi[i]; /* num of nozeros in L(i,:) */ 3506 bjtmp = bj + bi[i]; 3507 for (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0; 3508 rtmp[i] = 0.0; 3509 nzu = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */ 3510 bjtmp = bj + bdiag[i+1] + 1; 3511 for (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0; 3512 3513 /* load in initial unfactored row of A */ 3514 /* printf("row %d\n",i); */ 3515 nz = ai[r[i]+1] - ai[r[i]]; 3516 ajtmp = aj + ai[r[i]]; 3517 v = aa + ai[r[i]]; 3518 for (j=0; j<nz; j++) { 3519 rtmp[ics[*ajtmp++]] = v[j]; 3520 /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */ 3521 } 3522 /* printf("\n"); */ 3523 3524 /* numerical factorization */ 3525 bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */ 3526 nzl = bi[i+1] - bi[i]; /* num of entries in L(i,:) */ 3527 k = 0; 3528 while (k < nzl){ 3529 row = *bjtmp++; 3530 /* printf(" prow %d\n",row); */ 3531 pc = rtmp + row; 3532 pv = b->a + bdiag[row]; /* 1./(diag of the pivot row) */ 3533 multiplier = (*pc) * (*pv); 3534 *pc = multiplier; 3535 if (PetscAbsScalar(multiplier) > dt){ 3536 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3537 pv = b->a + bdiag[row+1] + 1; 3538 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3539 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3540 /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */ 3541 } 3542 k++; 3543 } 3544 3545 /* finished row so stick it into b->a */ 3546 /* L-part */ 3547 pv = b->a + bi[i] ; 3548 pj = bj + bi[i] ; 3549 nzl = bi[i+1] - bi[i]; 3550 for (j=0; j<nzl; j++) { 3551 pv[j] = rtmp[pj[j]]; 3552 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3553 } 3554 3555 /* diagonal: invert diagonal entries for simplier triangular solves */ 3556 if (rtmp[i] == 0.0) rtmp[i] = dt+shift; 3557 b->a[bdiag[i]] = 1.0/rtmp[i]; 3558 /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */ 3559 3560 /* U-part */ 3561 pv = b->a + bdiag[i+1] + 1; 3562 pj = bj + bdiag[i+1] + 1; 3563 nzu = bdiag[i] - bdiag[i+1] - 1; 3564 for (j=0; j<nzu; j++) { 3565 pv[j] = rtmp[pj[j]]; 3566 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3567 } 3568 /* printf("\n"); */ 3569 } 3570 3571 ierr = PetscFree(rtmp);CHKERRQ(ierr); 3572 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3573 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3574 3575 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3576 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 3577 if (row_identity && col_identity) { 3578 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 3579 } else { 3580 C->ops->solve = MatSolve_SeqAIJ; 3581 } 3582 C->ops->solveadd = 0; 3583 C->ops->solvetranspose = 0; 3584 C->ops->solvetransposeadd = 0; 3585 C->ops->matsolve = 0; 3586 C->assembled = PETSC_TRUE; 3587 C->preallocated = PETSC_TRUE; 3588 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 3589 PetscFunctionReturn(0); 3590 } 3591