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 LUShift_Ctx sctx; 463 PetscInt *ddiag; 464 PetscReal rs; 465 MatScalar d; 466 467 PetscFunctionBegin; 468 /* MatPivotSetUp(): initialize shift context sctx */ 469 ierr = PetscMemzero(&sctx,sizeof(LUShift_Ctx));CHKERRQ(ierr); 470 471 /* if both shift schemes are chosen by user, only use info->shiftpd */ 472 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 473 ddiag = a->diag; 474 sctx.shift_top = info->zeropivot; 475 for (i=0; i<n; i++) { 476 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 477 d = (aa)[ddiag[i]]; 478 rs = -PetscAbsScalar(d) - PetscRealPart(d); 479 v = aa+ai[i]; 480 nz = ai[i+1] - ai[i]; 481 for (j=0; j<nz; j++) 482 rs += PetscAbsScalar(v[j]); 483 if (rs>sctx.shift_top) sctx.shift_top = rs; 484 } 485 sctx.shift_top *= 1.1; 486 sctx.nshift_max = 5; 487 sctx.shift_lo = 0.; 488 sctx.shift_hi = 1.; 489 } 490 491 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 492 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 493 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 494 ics = ic; 495 496 do { 497 sctx.lushift = PETSC_FALSE; 498 for (i=0; i<n; i++){ 499 /* zero rtmp */ 500 /* L part */ 501 nz = bi[i+1] - bi[i]; 502 bjtmp = bj + bi[i]; 503 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 504 505 /* U part */ 506 nz = bdiag[i]-bdiag[i+1]; 507 bjtmp = bj + bdiag[i+1]+1; 508 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 509 510 /* load in initial (unfactored row) */ 511 nz = ai[r[i]+1] - ai[r[i]]; 512 ajtmp = aj + ai[r[i]]; 513 v = aa + ai[r[i]]; 514 for (j=0; j<nz; j++) { 515 rtmp[ics[ajtmp[j]]] = v[j]; 516 } 517 /* ZeropivotApply() */ 518 rtmp[i] += sctx.shift_amount; /* shift the diagonal of the matrix */ 519 520 /* elimination */ 521 bjtmp = bj + bi[i]; 522 row = *bjtmp++; 523 nzL = bi[i+1] - bi[i]; 524 for(k=0; k < nzL;k++) { 525 pc = rtmp + row; 526 if (*pc != 0.0) { 527 pv = b->a + bdiag[row]; 528 multiplier = *pc * (*pv); 529 *pc = multiplier; 530 pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */ 531 pv = b->a + bdiag[row+1]+1; 532 nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */ 533 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 534 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 535 } 536 row = *bjtmp++; 537 } 538 539 /* finished row so stick it into b->a */ 540 rs = 0.0; 541 /* L part */ 542 pv = b->a + bi[i] ; 543 pj = b->j + bi[i] ; 544 nz = bi[i+1] - bi[i]; 545 for (j=0; j<nz; j++) { 546 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 547 } 548 549 /* U part */ 550 pv = b->a + bdiag[i+1]+1; 551 pj = b->j + bdiag[i+1]+1; 552 nz = bdiag[i] - bdiag[i+1]-1; 553 for (j=0; j<nz; j++) { 554 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 555 } 556 557 /* MatPivotCheck() */ 558 sctx.rs = rs; 559 sctx.pv = rtmp[i]; 560 if (info->shiftnz){ 561 ierr = MatPivotCheck_nz(info,sctx,i);CHKERRQ(ierr); 562 } else if (info->shiftpd){ 563 ierr = MatPivotCheck_pd(info,sctx,i);CHKERRQ(ierr); 564 } else if (info->shiftinblocks){ 565 ierr = MatPivotCheck_inblocks(info,sctx,i);CHKERRQ(ierr); 566 } else { 567 ierr = MatPivotCheck_none(info,sctx,i);CHKERRQ(ierr); 568 } 569 rtmp[i] = sctx.pv; 570 // if (newshift == 1) break; 571 572 /* Mark diagonal and invert diagonal for simplier triangular solves */ 573 pv = b->a + bdiag[i]; 574 *pv = 1.0/rtmp[i]; 575 576 } /* endof for (i=0; i<n; i++){ */ 577 578 /* MatPivotRefine() */ 579 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max){ 580 /* 581 * if no shift in this attempt & shifting & started shifting & can refine, 582 * then try lower shift 583 */ 584 sctx.shift_hi = sctx.shift_fraction; 585 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 586 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 587 sctx.lushift = PETSC_TRUE; 588 sctx.nshift++; 589 } 590 } while (sctx.lushift); 591 592 ierr = PetscFree(rtmp);CHKERRQ(ierr); 593 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 594 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 595 if (b->inode.use){ 596 C->ops->solve = MatSolve_SeqAIJ_Inode; 597 } else { 598 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 599 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 600 if (row_identity && col_identity) { 601 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 602 } else { 603 C->ops->solve = MatSolve_SeqAIJ; 604 } 605 } 606 C->ops->solveadd = MatSolveAdd_SeqAIJ; 607 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 608 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 609 C->ops->matsolve = MatMatSolve_SeqAIJ; 610 C->assembled = PETSC_TRUE; 611 C->preallocated = PETSC_TRUE; 612 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 613 614 /* MatPivotView() */ 615 if (sctx.nshift){ 616 if (info->shiftpd) { 617 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); 618 } else if (info->shiftnz) { 619 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 620 } else if (info->shiftinblocks){ 621 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftinblocks);CHKERRQ(ierr); 622 } 623 } 624 PetscFunctionReturn(0); 625 } 626 627 #undef __FUNCT__ 628 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_inplace" 629 PetscErrorCode MatLUFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info) 630 { 631 Mat C=B; 632 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 633 IS isrow = b->row,isicol = b->icol; 634 PetscErrorCode ierr; 635 const PetscInt *r,*ic,*ics; 636 PetscInt nz,row,i,j,n=A->rmap->n,diag; 637 const PetscInt *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 638 const PetscInt *ajtmp,*bjtmp,*diag_offset = b->diag,*pj; 639 MatScalar *pv,*rtmp,*pc,multiplier,d; 640 const MatScalar *v,*aa=a->a; 641 PetscReal rs=0.0; 642 LUShift_Ctx sctx; 643 PetscInt newshift,*ddiag; 644 645 PetscFunctionBegin; 646 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 647 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 648 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 649 ics = ic; 650 651 /* initialize shift context sctx */ 652 sctx.nshift = 0; 653 sctx.nshift_max = 0; 654 sctx.shift_top = 0.0; 655 sctx.shift_lo = 0.0; 656 sctx.shift_hi = 0.0; 657 sctx.shift_fraction = 0.0; 658 sctx.shift_amount = 0.0; 659 660 /* if both shift schemes are chosen by user, only use info->shiftpd */ 661 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 662 ddiag = a->diag; 663 sctx.shift_top = info->zeropivot; 664 for (i=0; i<n; i++) { 665 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 666 d = (aa)[ddiag[i]]; 667 rs = -PetscAbsScalar(d) - PetscRealPart(d); 668 v = aa+ai[i]; 669 nz = ai[i+1] - ai[i]; 670 for (j=0; j<nz; j++) 671 rs += PetscAbsScalar(v[j]); 672 if (rs>sctx.shift_top) sctx.shift_top = rs; 673 } 674 sctx.shift_top *= 1.1; 675 sctx.nshift_max = 5; 676 sctx.shift_lo = 0.; 677 sctx.shift_hi = 1.; 678 } 679 680 do { 681 sctx.lushift = PETSC_FALSE; 682 for (i=0; i<n; i++){ 683 nz = bi[i+1] - bi[i]; 684 bjtmp = bj + bi[i]; 685 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 686 687 /* load in initial (unfactored row) */ 688 nz = ai[r[i]+1] - ai[r[i]]; 689 ajtmp = aj + ai[r[i]]; 690 v = aa + ai[r[i]]; 691 for (j=0; j<nz; j++) { 692 rtmp[ics[ajtmp[j]]] = v[j]; 693 } 694 rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 695 /* if (sctx.shift_amount > 0.0) printf("row %d, shift %g\n",i,sctx.shift_amount); */ 696 697 row = *bjtmp++; 698 while (row < i) { 699 pc = rtmp + row; 700 if (*pc != 0.0) { 701 pv = b->a + diag_offset[row]; 702 pj = b->j + diag_offset[row] + 1; 703 multiplier = *pc / *pv++; 704 *pc = multiplier; 705 nz = bi[row+1] - diag_offset[row] - 1; 706 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 707 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 708 } 709 row = *bjtmp++; 710 } 711 /* finished row so stick it into b->a */ 712 pv = b->a + bi[i] ; 713 pj = b->j + bi[i] ; 714 nz = bi[i+1] - bi[i]; 715 diag = diag_offset[i] - bi[i]; 716 rs = 0.0; 717 for (j=0; j<nz; j++) { 718 pv[j] = rtmp[pj[j]]; 719 rs += PetscAbsScalar(pv[j]); 720 } 721 rs -= PetscAbsScalar(pv[diag]); 722 723 /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */ 724 sctx.rs = rs; 725 sctx.pv = pv[diag]; 726 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 727 if (newshift == 1) break; 728 } 729 730 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 731 /* 732 * if no shift in this attempt & shifting & started shifting & can refine, 733 * then try lower shift 734 */ 735 sctx.shift_hi = sctx.shift_fraction; 736 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 737 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 738 sctx.lushift = PETSC_TRUE; 739 sctx.nshift++; 740 } 741 } while (sctx.lushift); 742 743 /* invert diagonal entries for simplier triangular solves */ 744 for (i=0; i<n; i++) { 745 b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]]; 746 } 747 ierr = PetscFree(rtmp);CHKERRQ(ierr); 748 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 749 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 750 if (b->inode.use) { 751 C->ops->solve = MatSolve_SeqAIJ_Inode_inplace; 752 } else { 753 PetscTruth row_identity, col_identity; 754 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 755 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 756 if (row_identity && col_identity) { 757 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_inplace; 758 } else { 759 C->ops->solve = MatSolve_SeqAIJ_inplace; 760 } 761 } 762 C->ops->solveadd = MatSolveAdd_SeqAIJ_inplace; 763 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace; 764 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace; 765 C->ops->matsolve = MatMatSolve_SeqAIJ_inplace; 766 C->assembled = PETSC_TRUE; 767 C->preallocated = PETSC_TRUE; 768 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 769 if (sctx.nshift){ 770 if (info->shiftpd) { 771 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); 772 } else if (info->shiftnz) { 773 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 774 } 775 } 776 PetscFunctionReturn(0); 777 } 778 779 /* 780 This routine implements inplace ILU(0) with row or/and column permutations. 781 Input: 782 A - original matrix 783 Output; 784 A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i] 785 a->j (col index) is permuted by the inverse of colperm, then sorted 786 a->a reordered accordingly with a->j 787 a->diag (ptr to diagonal elements) is updated. 788 */ 789 #undef __FUNCT__ 790 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_InplaceWithPerm" 791 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info) 792 { 793 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 794 IS isrow = a->row,isicol = a->icol; 795 PetscErrorCode ierr; 796 const PetscInt *r,*ic,*ics; 797 PetscInt i,j,n=A->rmap->n,*ai=a->i,*aj=a->j; 798 PetscInt *ajtmp,nz,row; 799 PetscInt *diag = a->diag,nbdiag,*pj; 800 PetscScalar *rtmp,*pc,multiplier,d; 801 MatScalar *v,*pv; 802 PetscReal rs; 803 LUShift_Ctx sctx; 804 PetscInt newshift; 805 806 PetscFunctionBegin; 807 if (A != B) SETERRQ(PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address"); 808 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 809 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 810 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&rtmp);CHKERRQ(ierr); 811 ierr = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr); 812 ics = ic; 813 814 sctx.shift_top = 0.; 815 sctx.nshift_max = 0; 816 sctx.shift_lo = 0.; 817 sctx.shift_hi = 0.; 818 sctx.shift_fraction = 0.; 819 820 /* if both shift schemes are chosen by user, only use info->shiftpd */ 821 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 822 sctx.shift_top = 0.; 823 for (i=0; i<n; i++) { 824 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 825 d = (a->a)[diag[i]]; 826 rs = -PetscAbsScalar(d) - PetscRealPart(d); 827 v = a->a+ai[i]; 828 nz = ai[i+1] - ai[i]; 829 for (j=0; j<nz; j++) 830 rs += PetscAbsScalar(v[j]); 831 if (rs>sctx.shift_top) sctx.shift_top = rs; 832 } 833 if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot; 834 sctx.shift_top *= 1.1; 835 sctx.nshift_max = 5; 836 sctx.shift_lo = 0.; 837 sctx.shift_hi = 1.; 838 } 839 840 sctx.shift_amount = 0.; 841 sctx.nshift = 0; 842 do { 843 sctx.lushift = PETSC_FALSE; 844 for (i=0; i<n; i++){ 845 /* load in initial unfactored row */ 846 nz = ai[r[i]+1] - ai[r[i]]; 847 ajtmp = aj + ai[r[i]]; 848 v = a->a + ai[r[i]]; 849 /* sort permuted ajtmp and values v accordingly */ 850 for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]]; 851 ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr); 852 853 diag[r[i]] = ai[r[i]]; 854 for (j=0; j<nz; j++) { 855 rtmp[ajtmp[j]] = v[j]; 856 if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */ 857 } 858 rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 859 860 row = *ajtmp++; 861 while (row < i) { 862 pc = rtmp + row; 863 if (*pc != 0.0) { 864 pv = a->a + diag[r[row]]; 865 pj = aj + diag[r[row]] + 1; 866 867 multiplier = *pc / *pv++; 868 *pc = multiplier; 869 nz = ai[r[row]+1] - diag[r[row]] - 1; 870 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 871 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 872 } 873 row = *ajtmp++; 874 } 875 /* finished row so overwrite it onto a->a */ 876 pv = a->a + ai[r[i]] ; 877 pj = aj + ai[r[i]] ; 878 nz = ai[r[i]+1] - ai[r[i]]; 879 nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */ 880 881 rs = 0.0; 882 for (j=0; j<nz; j++) { 883 pv[j] = rtmp[pj[j]]; 884 if (j != nbdiag) rs += PetscAbsScalar(pv[j]); 885 } 886 887 /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */ 888 sctx.rs = rs; 889 sctx.pv = pv[nbdiag]; 890 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 891 if (newshift == 1) break; 892 } 893 894 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 895 /* 896 * if no shift in this attempt & shifting & started shifting & can refine, 897 * then try lower shift 898 */ 899 sctx.shift_hi = sctx.shift_fraction; 900 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 901 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 902 sctx.lushift = PETSC_TRUE; 903 sctx.nshift++; 904 } 905 } while (sctx.lushift); 906 907 /* invert diagonal entries for simplier triangular solves */ 908 for (i=0; i<n; i++) { 909 a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]]; 910 } 911 912 ierr = PetscFree(rtmp);CHKERRQ(ierr); 913 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 914 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 915 A->ops->solve = MatSolve_SeqAIJ_InplaceWithPerm; 916 A->ops->solveadd = MatSolveAdd_SeqAIJ_inplace; 917 A->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace; 918 A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace; 919 A->assembled = PETSC_TRUE; 920 A->preallocated = PETSC_TRUE; 921 ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr); 922 if (sctx.nshift){ 923 if (info->shiftpd) { 924 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); 925 } else if (info->shiftnz) { 926 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 927 } 928 } 929 PetscFunctionReturn(0); 930 } 931 932 /* ----------------------------------------------------------- */ 933 #undef __FUNCT__ 934 #define __FUNCT__ "MatLUFactor_SeqAIJ" 935 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info) 936 { 937 PetscErrorCode ierr; 938 Mat C; 939 940 PetscFunctionBegin; 941 ierr = MatGetFactor(A,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr); 942 ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr); 943 ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr); 944 A->ops->solve = C->ops->solve; 945 A->ops->solvetranspose = C->ops->solvetranspose; 946 ierr = MatHeaderCopy(A,C);CHKERRQ(ierr); 947 ierr = PetscLogObjectParent(A,((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr); 948 PetscFunctionReturn(0); 949 } 950 /* ----------------------------------------------------------- */ 951 952 953 #undef __FUNCT__ 954 #define __FUNCT__ "MatSolve_SeqAIJ_inplace" 955 PetscErrorCode MatSolve_SeqAIJ_inplace(Mat A,Vec bb,Vec xx) 956 { 957 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 958 IS iscol = a->col,isrow = a->row; 959 PetscErrorCode ierr; 960 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 961 PetscInt nz; 962 const PetscInt *rout,*cout,*r,*c; 963 PetscScalar *x,*tmp,*tmps,sum; 964 const PetscScalar *b; 965 const MatScalar *aa = a->a,*v; 966 967 PetscFunctionBegin; 968 if (!n) PetscFunctionReturn(0); 969 970 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 971 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 972 tmp = a->solve_work; 973 974 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 975 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 976 977 /* forward solve the lower triangular */ 978 tmp[0] = b[*r++]; 979 tmps = tmp; 980 for (i=1; i<n; i++) { 981 v = aa + ai[i] ; 982 vi = aj + ai[i] ; 983 nz = a->diag[i] - ai[i]; 984 sum = b[*r++]; 985 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 986 tmp[i] = sum; 987 } 988 989 /* backward solve the upper triangular */ 990 for (i=n-1; i>=0; i--){ 991 v = aa + a->diag[i] + 1; 992 vi = aj + a->diag[i] + 1; 993 nz = ai[i+1] - a->diag[i] - 1; 994 sum = tmp[i]; 995 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 996 x[*c--] = tmp[i] = sum*aa[a->diag[i]]; 997 } 998 999 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1000 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1001 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1002 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1003 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1004 PetscFunctionReturn(0); 1005 } 1006 1007 #undef __FUNCT__ 1008 #define __FUNCT__ "MatMatSolve_SeqAIJ_inplace" 1009 PetscErrorCode MatMatSolve_SeqAIJ_inplace(Mat A,Mat B,Mat X) 1010 { 1011 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1012 IS iscol = a->col,isrow = a->row; 1013 PetscErrorCode ierr; 1014 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1015 PetscInt nz,neq; 1016 const PetscInt *rout,*cout,*r,*c; 1017 PetscScalar *x,*b,*tmp,*tmps,sum; 1018 const MatScalar *aa = a->a,*v; 1019 PetscTruth bisdense,xisdense; 1020 1021 PetscFunctionBegin; 1022 if (!n) PetscFunctionReturn(0); 1023 1024 ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr); 1025 if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 1026 ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr); 1027 if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 1028 1029 ierr = MatGetArray(B,&b);CHKERRQ(ierr); 1030 ierr = MatGetArray(X,&x);CHKERRQ(ierr); 1031 1032 tmp = a->solve_work; 1033 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1034 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1035 1036 for (neq=0; neq<B->cmap->n; neq++){ 1037 /* forward solve the lower triangular */ 1038 tmp[0] = b[r[0]]; 1039 tmps = tmp; 1040 for (i=1; i<n; i++) { 1041 v = aa + ai[i] ; 1042 vi = aj + ai[i] ; 1043 nz = a->diag[i] - ai[i]; 1044 sum = b[r[i]]; 1045 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1046 tmp[i] = sum; 1047 } 1048 /* backward solve the upper triangular */ 1049 for (i=n-1; i>=0; i--){ 1050 v = aa + a->diag[i] + 1; 1051 vi = aj + a->diag[i] + 1; 1052 nz = ai[i+1] - a->diag[i] - 1; 1053 sum = tmp[i]; 1054 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1055 x[c[i]] = tmp[i] = sum*aa[a->diag[i]]; 1056 } 1057 1058 b += n; 1059 x += n; 1060 } 1061 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1062 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1063 ierr = MatRestoreArray(B,&b);CHKERRQ(ierr); 1064 ierr = MatRestoreArray(X,&x);CHKERRQ(ierr); 1065 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 1066 PetscFunctionReturn(0); 1067 } 1068 1069 #undef __FUNCT__ 1070 #define __FUNCT__ "MatMatSolve_SeqAIJ" 1071 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X) 1072 { 1073 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1074 IS iscol = a->col,isrow = a->row; 1075 PetscErrorCode ierr; 1076 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag; 1077 PetscInt nz,neq; 1078 const PetscInt *rout,*cout,*r,*c; 1079 PetscScalar *x,*b,*tmp,sum; 1080 const MatScalar *aa = a->a,*v; 1081 PetscTruth bisdense,xisdense; 1082 1083 PetscFunctionBegin; 1084 if (!n) PetscFunctionReturn(0); 1085 1086 ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr); 1087 if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 1088 ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr); 1089 if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 1090 1091 ierr = MatGetArray(B,&b);CHKERRQ(ierr); 1092 ierr = MatGetArray(X,&x);CHKERRQ(ierr); 1093 1094 tmp = a->solve_work; 1095 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1096 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1097 1098 for (neq=0; neq<B->cmap->n; neq++){ 1099 /* forward solve the lower triangular */ 1100 tmp[0] = b[r[0]]; 1101 v = aa; 1102 vi = aj; 1103 for (i=1; i<n; i++) { 1104 nz = ai[i+1] - ai[i]; 1105 sum = b[r[i]]; 1106 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 1107 tmp[i] = sum; 1108 v += nz; vi += nz; 1109 } 1110 1111 /* backward solve the upper triangular */ 1112 for (i=n-1; i>=0; i--){ 1113 v = aa + adiag[i+1]+1; 1114 vi = aj + adiag[i+1]+1; 1115 nz = adiag[i]-adiag[i+1]-1; 1116 sum = tmp[i]; 1117 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 1118 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 1119 } 1120 1121 b += n; 1122 x += n; 1123 } 1124 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1125 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1126 ierr = MatRestoreArray(B,&b);CHKERRQ(ierr); 1127 ierr = MatRestoreArray(X,&x);CHKERRQ(ierr); 1128 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 1129 PetscFunctionReturn(0); 1130 } 1131 1132 #undef __FUNCT__ 1133 #define __FUNCT__ "MatSolve_SeqAIJ_InplaceWithPerm" 1134 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx) 1135 { 1136 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1137 IS iscol = a->col,isrow = a->row; 1138 PetscErrorCode ierr; 1139 const PetscInt *r,*c,*rout,*cout; 1140 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1141 PetscInt nz,row; 1142 PetscScalar *x,*b,*tmp,*tmps,sum; 1143 const MatScalar *aa = a->a,*v; 1144 1145 PetscFunctionBegin; 1146 if (!n) PetscFunctionReturn(0); 1147 1148 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1149 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1150 tmp = a->solve_work; 1151 1152 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1153 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1154 1155 /* forward solve the lower triangular */ 1156 tmp[0] = b[*r++]; 1157 tmps = tmp; 1158 for (row=1; row<n; row++) { 1159 i = rout[row]; /* permuted row */ 1160 v = aa + ai[i] ; 1161 vi = aj + ai[i] ; 1162 nz = a->diag[i] - ai[i]; 1163 sum = b[*r++]; 1164 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1165 tmp[row] = sum; 1166 } 1167 1168 /* backward solve the upper triangular */ 1169 for (row=n-1; row>=0; row--){ 1170 i = rout[row]; /* permuted row */ 1171 v = aa + a->diag[i] + 1; 1172 vi = aj + a->diag[i] + 1; 1173 nz = ai[i+1] - a->diag[i] - 1; 1174 sum = tmp[row]; 1175 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1176 x[*c--] = tmp[row] = sum*aa[a->diag[i]]; 1177 } 1178 1179 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1180 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1181 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1182 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1183 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1184 PetscFunctionReturn(0); 1185 } 1186 1187 /* ----------------------------------------------------------- */ 1188 #include "../src/mat/impls/aij/seq/ftn-kernels/fsolve.h" 1189 #undef __FUNCT__ 1190 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_inplace" 1191 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_inplace(Mat A,Vec bb,Vec xx) 1192 { 1193 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1194 PetscErrorCode ierr; 1195 PetscInt n = A->rmap->n; 1196 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag; 1197 PetscScalar *x; 1198 const PetscScalar *b; 1199 const MatScalar *aa = a->a; 1200 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1201 PetscInt adiag_i,i,nz,ai_i; 1202 const PetscInt *vi; 1203 const MatScalar *v; 1204 PetscScalar sum; 1205 #endif 1206 1207 PetscFunctionBegin; 1208 if (!n) PetscFunctionReturn(0); 1209 1210 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1211 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1212 1213 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1214 fortransolveaij_(&n,x,ai,aj,adiag,aa,b); 1215 #else 1216 /* forward solve the lower triangular */ 1217 x[0] = b[0]; 1218 for (i=1; i<n; i++) { 1219 ai_i = ai[i]; 1220 v = aa + ai_i; 1221 vi = aj + ai_i; 1222 nz = adiag[i] - ai_i; 1223 sum = b[i]; 1224 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1225 x[i] = sum; 1226 } 1227 1228 /* backward solve the upper triangular */ 1229 for (i=n-1; i>=0; i--){ 1230 adiag_i = adiag[i]; 1231 v = aa + adiag_i + 1; 1232 vi = aj + adiag_i + 1; 1233 nz = ai[i+1] - adiag_i - 1; 1234 sum = x[i]; 1235 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1236 x[i] = sum*aa[adiag_i]; 1237 } 1238 #endif 1239 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1240 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1241 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1242 PetscFunctionReturn(0); 1243 } 1244 1245 #undef __FUNCT__ 1246 #define __FUNCT__ "MatSolveAdd_SeqAIJ_inplace" 1247 PetscErrorCode MatSolveAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec yy,Vec xx) 1248 { 1249 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1250 IS iscol = a->col,isrow = a->row; 1251 PetscErrorCode ierr; 1252 PetscInt i, n = A->rmap->n,j; 1253 PetscInt nz; 1254 const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j; 1255 PetscScalar *x,*tmp,sum; 1256 const PetscScalar *b; 1257 const MatScalar *aa = a->a,*v; 1258 1259 PetscFunctionBegin; 1260 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 1261 1262 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1263 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1264 tmp = a->solve_work; 1265 1266 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1267 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1268 1269 /* forward solve the lower triangular */ 1270 tmp[0] = b[*r++]; 1271 for (i=1; i<n; i++) { 1272 v = aa + ai[i] ; 1273 vi = aj + ai[i] ; 1274 nz = a->diag[i] - ai[i]; 1275 sum = b[*r++]; 1276 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1277 tmp[i] = sum; 1278 } 1279 1280 /* backward solve the upper triangular */ 1281 for (i=n-1; i>=0; i--){ 1282 v = aa + a->diag[i] + 1; 1283 vi = aj + a->diag[i] + 1; 1284 nz = ai[i+1] - a->diag[i] - 1; 1285 sum = tmp[i]; 1286 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1287 tmp[i] = sum*aa[a->diag[i]]; 1288 x[*c--] += tmp[i]; 1289 } 1290 1291 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1292 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1293 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1294 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1295 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1296 1297 PetscFunctionReturn(0); 1298 } 1299 1300 #undef __FUNCT__ 1301 #define __FUNCT__ "MatSolveAdd_SeqAIJ" 1302 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx) 1303 { 1304 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1305 IS iscol = a->col,isrow = a->row; 1306 PetscErrorCode ierr; 1307 PetscInt i, n = A->rmap->n,j; 1308 PetscInt nz; 1309 const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag; 1310 PetscScalar *x,*tmp,sum; 1311 const PetscScalar *b; 1312 const MatScalar *aa = a->a,*v; 1313 1314 PetscFunctionBegin; 1315 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 1316 1317 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1318 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1319 tmp = a->solve_work; 1320 1321 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1322 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1323 1324 /* forward solve the lower triangular */ 1325 tmp[0] = b[r[0]]; 1326 v = aa; 1327 vi = aj; 1328 for (i=1; i<n; i++) { 1329 nz = ai[i+1] - ai[i]; 1330 sum = b[r[i]]; 1331 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1332 tmp[i] = sum; 1333 v += nz; vi += nz; 1334 } 1335 1336 /* backward solve the upper triangular */ 1337 v = aa + adiag[n-1]; 1338 vi = aj + adiag[n-1]; 1339 for (i=n-1; i>=0; i--){ 1340 nz = adiag[i] - adiag[i+1] - 1; 1341 sum = tmp[i]; 1342 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1343 tmp[i] = sum*v[nz]; 1344 x[c[i]] += tmp[i]; 1345 v += nz+1; vi += nz+1; 1346 } 1347 1348 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1349 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1350 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1351 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1352 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1353 1354 PetscFunctionReturn(0); 1355 } 1356 1357 #undef __FUNCT__ 1358 #define __FUNCT__ "MatSolveTranspose_SeqAIJ_inplace" 1359 PetscErrorCode MatSolveTranspose_SeqAIJ_inplace(Mat A,Vec bb,Vec xx) 1360 { 1361 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1362 IS iscol = a->col,isrow = a->row; 1363 PetscErrorCode ierr; 1364 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1365 PetscInt i,n = A->rmap->n,j; 1366 PetscInt nz; 1367 PetscScalar *x,*tmp,s1; 1368 const MatScalar *aa = a->a,*v; 1369 const PetscScalar *b; 1370 1371 PetscFunctionBegin; 1372 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1373 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1374 tmp = a->solve_work; 1375 1376 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1377 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1378 1379 /* copy the b into temp work space according to permutation */ 1380 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1381 1382 /* forward solve the U^T */ 1383 for (i=0; i<n; i++) { 1384 v = aa + diag[i] ; 1385 vi = aj + diag[i] + 1; 1386 nz = ai[i+1] - diag[i] - 1; 1387 s1 = tmp[i]; 1388 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1389 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1390 tmp[i] = s1; 1391 } 1392 1393 /* backward solve the L^T */ 1394 for (i=n-1; i>=0; i--){ 1395 v = aa + diag[i] - 1 ; 1396 vi = aj + diag[i] - 1 ; 1397 nz = diag[i] - ai[i]; 1398 s1 = tmp[i]; 1399 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1400 } 1401 1402 /* copy tmp into x according to permutation */ 1403 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1404 1405 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1406 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1407 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1408 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1409 1410 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1411 PetscFunctionReturn(0); 1412 } 1413 1414 #undef __FUNCT__ 1415 #define __FUNCT__ "MatSolveTranspose_SeqAIJ" 1416 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx) 1417 { 1418 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1419 IS iscol = a->col,isrow = a->row; 1420 PetscErrorCode ierr; 1421 const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi; 1422 PetscInt i,n = A->rmap->n,j; 1423 PetscInt nz; 1424 PetscScalar *x,*tmp,s1; 1425 const MatScalar *aa = a->a,*v; 1426 const PetscScalar *b; 1427 1428 PetscFunctionBegin; 1429 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1430 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1431 tmp = a->solve_work; 1432 1433 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1434 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1435 1436 /* copy the b into temp work space according to permutation */ 1437 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1438 1439 /* forward solve the U^T */ 1440 for (i=0; i<n; i++) { 1441 v = aa + adiag[i+1] + 1; 1442 vi = aj + adiag[i+1] + 1; 1443 nz = adiag[i] - adiag[i+1] - 1; 1444 s1 = tmp[i]; 1445 s1 *= v[nz]; /* multiply by inverse of diagonal entry */ 1446 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1447 tmp[i] = s1; 1448 } 1449 1450 /* backward solve the L^T */ 1451 for (i=n-1; i>=0; i--){ 1452 v = aa + ai[i]; 1453 vi = aj + ai[i]; 1454 nz = ai[i+1] - ai[i]; 1455 s1 = tmp[i]; 1456 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1457 } 1458 1459 /* copy tmp into x according to permutation */ 1460 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1461 1462 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1463 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1464 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1465 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1466 1467 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1468 PetscFunctionReturn(0); 1469 } 1470 1471 #undef __FUNCT__ 1472 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ_inplace" 1473 PetscErrorCode MatSolveTransposeAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec zz,Vec xx) 1474 { 1475 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1476 IS iscol = a->col,isrow = a->row; 1477 PetscErrorCode ierr; 1478 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1479 PetscInt i,n = A->rmap->n,j; 1480 PetscInt nz; 1481 PetscScalar *x,*tmp,s1; 1482 const MatScalar *aa = a->a,*v; 1483 const PetscScalar *b; 1484 1485 PetscFunctionBegin; 1486 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1487 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1488 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1489 tmp = a->solve_work; 1490 1491 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1492 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1493 1494 /* copy the b into temp work space according to permutation */ 1495 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1496 1497 /* forward solve the U^T */ 1498 for (i=0; i<n; i++) { 1499 v = aa + diag[i] ; 1500 vi = aj + diag[i] + 1; 1501 nz = ai[i+1] - diag[i] - 1; 1502 s1 = tmp[i]; 1503 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1504 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1505 tmp[i] = s1; 1506 } 1507 1508 /* backward solve the L^T */ 1509 for (i=n-1; i>=0; i--){ 1510 v = aa + diag[i] - 1 ; 1511 vi = aj + diag[i] - 1 ; 1512 nz = diag[i] - ai[i]; 1513 s1 = tmp[i]; 1514 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1515 } 1516 1517 /* copy tmp into x according to permutation */ 1518 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1519 1520 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1521 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1522 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1523 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1524 1525 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1526 PetscFunctionReturn(0); 1527 } 1528 1529 #undef __FUNCT__ 1530 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ" 1531 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx) 1532 { 1533 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1534 IS iscol = a->col,isrow = a->row; 1535 PetscErrorCode ierr; 1536 const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi; 1537 PetscInt i,n = A->rmap->n,j; 1538 PetscInt nz; 1539 PetscScalar *x,*tmp,s1; 1540 const MatScalar *aa = a->a,*v; 1541 const PetscScalar *b; 1542 1543 PetscFunctionBegin; 1544 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1545 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1546 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1547 tmp = a->solve_work; 1548 1549 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1550 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1551 1552 /* copy the b into temp work space according to permutation */ 1553 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1554 1555 /* forward solve the U^T */ 1556 for (i=0; i<n; i++) { 1557 v = aa + adiag[i+1] + 1; 1558 vi = aj + adiag[i+1] + 1; 1559 nz = adiag[i] - adiag[i+1] - 1; 1560 s1 = tmp[i]; 1561 s1 *= v[nz]; /* multiply by inverse of diagonal entry */ 1562 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1563 tmp[i] = s1; 1564 } 1565 1566 1567 /* backward solve the L^T */ 1568 for (i=n-1; i>=0; i--){ 1569 v = aa + ai[i] ; 1570 vi = aj + ai[i]; 1571 nz = ai[i+1] - ai[i]; 1572 s1 = tmp[i]; 1573 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1574 } 1575 1576 /* copy tmp into x according to permutation */ 1577 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1578 1579 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1580 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1581 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1582 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1583 1584 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1585 PetscFunctionReturn(0); 1586 } 1587 1588 /* ----------------------------------------------------------------*/ 1589 1590 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth); 1591 1592 /* 1593 ilu() under revised new data structure. 1594 Factored arrays bj and ba are stored as 1595 L(0,:), L(1,:), ...,L(n-1,:), U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:) 1596 1597 bi=fact->i is an array of size n+1, in which 1598 bi+ 1599 bi[i]: points to 1st entry of L(i,:),i=0,...,n-1 1600 bi[n]: points to L(n-1,n-1)+1 1601 1602 bdiag=fact->diag is an array of size n+1,in which 1603 bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1 1604 bdiag[n]: points to entry of U(n-1,0)-1 1605 1606 U(i,:) contains bdiag[i] as its last entry, i.e., 1607 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 1608 */ 1609 #undef __FUNCT__ 1610 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0" 1611 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1612 { 1613 1614 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1615 PetscErrorCode ierr; 1616 const PetscInt n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag; 1617 PetscInt i,j,k=0,nz,*bi,*bj,*bdiag; 1618 PetscTruth missing; 1619 IS isicol; 1620 1621 PetscFunctionBegin; 1622 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); 1623 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 1624 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 1625 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1626 1627 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr); 1628 b = (Mat_SeqAIJ*)(fact)->data; 1629 1630 /* allocate matrix arrays for new data structure */ 1631 ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,n+1,PetscInt,&b->i);CHKERRQ(ierr); 1632 ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1633 b->singlemalloc = PETSC_TRUE; 1634 if (!b->diag){ 1635 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr); 1636 ierr = PetscLogObjectMemory(fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1637 } 1638 bdiag = b->diag; 1639 1640 if (n > 0) { 1641 ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr); 1642 } 1643 1644 /* set bi and bj with new data structure */ 1645 bi = b->i; 1646 bj = b->j; 1647 1648 /* L part */ 1649 bi[0] = 0; 1650 for (i=0; i<n; i++){ 1651 nz = adiag[i] - ai[i]; 1652 bi[i+1] = bi[i] + nz; 1653 aj = a->j + ai[i]; 1654 for (j=0; j<nz; j++){ 1655 /* *bj = aj[j]; bj++; */ 1656 bj[k++] = aj[j]; 1657 } 1658 } 1659 1660 /* U part */ 1661 bdiag[n] = bi[n]-1; 1662 for (i=n-1; i>=0; i--){ 1663 nz = ai[i+1] - adiag[i] - 1; 1664 aj = a->j + adiag[i] + 1; 1665 for (j=0; j<nz; j++){ 1666 /* *bj = aj[j]; bj++; */ 1667 bj[k++] = aj[j]; 1668 } 1669 /* diag[i] */ 1670 /* *bj = i; bj++; */ 1671 bj[k++] = i; 1672 bdiag[i] = bdiag[i+1] + nz + 1; 1673 } 1674 1675 fact->factor = MAT_FACTOR_ILU; 1676 fact->info.factor_mallocs = 0; 1677 fact->info.fill_ratio_given = info->fill; 1678 fact->info.fill_ratio_needed = 1.0; 1679 fact->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1680 1681 b = (Mat_SeqAIJ*)(fact)->data; 1682 b->row = isrow; 1683 b->col = iscol; 1684 b->icol = isicol; 1685 ierr = PetscMalloc((fact->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1686 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1687 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1688 PetscFunctionReturn(0); 1689 } 1690 1691 #undef __FUNCT__ 1692 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ" 1693 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1694 { 1695 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1696 IS isicol; 1697 PetscErrorCode ierr; 1698 const PetscInt *r,*ic; 1699 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j; 1700 PetscInt *bi,*cols,nnz,*cols_lvl; 1701 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1702 PetscInt i,levels,diagonal_fill; 1703 PetscTruth col_identity,row_identity; 1704 PetscReal f; 1705 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1706 PetscBT lnkbt; 1707 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1708 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1709 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1710 1711 PetscFunctionBegin; 1712 /* // Testing new data structure for MatSolve() 1713 PetscTruth olddatastruct=PETSC_FALSE 1714 ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_old",&olddatastruct,PETSC_NULL);CHKERRQ(ierr); 1715 if(olddatastruct){ 1716 ierr = MatILUFactorSymbolic_SeqAIJ_inplace(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1717 PetscFunctionReturn(0); 1718 } 1719 */ 1720 1721 levels = (PetscInt)info->levels; 1722 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1723 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1724 1725 if (!levels && row_identity && col_identity) { 1726 /* special case: ilu(0) with natural ordering */ 1727 ierr = MatILUFactorSymbolic_SeqAIJ_ilu0(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1728 ierr = Mat_CheckInode_FactorLU(fact,PETSC_FALSE);CHKERRQ(ierr); 1729 PetscFunctionReturn(0); 1730 } 1731 1732 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); 1733 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1734 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1735 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1736 1737 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1738 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1739 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1740 bi[0] = bdiag[0] = 0; 1741 1742 ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr); 1743 1744 /* create a linked list for storing column indices of the active row */ 1745 nlnk = n + 1; 1746 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1747 1748 /* initial FreeSpace size is f*(ai[n]+1) */ 1749 f = info->fill; 1750 diagonal_fill = (PetscInt)info->diagonal_fill; 1751 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1752 current_space = free_space; 1753 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1754 current_space_lvl = free_space_lvl; 1755 1756 for (i=0; i<n; i++) { 1757 nzi = 0; 1758 /* copy current row into linked list */ 1759 nnz = ai[r[i]+1] - ai[r[i]]; 1760 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1761 cols = aj + ai[r[i]]; 1762 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1763 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1764 nzi += nlnk; 1765 1766 /* make sure diagonal entry is included */ 1767 if (diagonal_fill && lnk[i] == -1) { 1768 fm = n; 1769 while (lnk[fm] < i) fm = lnk[fm]; 1770 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1771 lnk[fm] = i; 1772 lnk_lvl[i] = 0; 1773 nzi++; dcount++; 1774 } 1775 1776 /* add pivot rows into the active row */ 1777 nzbd = 0; 1778 prow = lnk[n]; 1779 while (prow < i) { 1780 nnz = bdiag[prow]; 1781 cols = bj_ptr[prow] + nnz + 1; 1782 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1783 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1784 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1785 nzi += nlnk; 1786 prow = lnk[prow]; 1787 nzbd++; 1788 } 1789 bdiag[i] = nzbd; 1790 bi[i+1] = bi[i] + nzi; 1791 1792 /* if free space is not available, make more free space */ 1793 if (current_space->local_remaining<nzi) { 1794 nnz = 2*nzi*(n - i); /* estimated and max additional space needed */ 1795 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1796 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1797 reallocs++; 1798 } 1799 1800 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1801 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1802 bj_ptr[i] = current_space->array; 1803 bjlvl_ptr[i] = current_space_lvl->array; 1804 1805 /* make sure the active row i has diagonal entry */ 1806 if (*(bj_ptr[i]+bdiag[i]) != i) { 1807 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 1808 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1809 } 1810 1811 current_space->array += nzi; 1812 current_space->local_used += nzi; 1813 current_space->local_remaining -= nzi; 1814 current_space_lvl->array += nzi; 1815 current_space_lvl->local_used += nzi; 1816 current_space_lvl->local_remaining -= nzi; 1817 } 1818 1819 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1820 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1821 1822 /* destroy list of free space and other temporary arrays */ 1823 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 1824 1825 /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */ 1826 ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 1827 1828 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1829 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1830 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 1831 1832 #if defined(PETSC_USE_INFO) 1833 { 1834 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1835 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 1836 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1837 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 1838 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1839 if (diagonal_fill) { 1840 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 1841 } 1842 } 1843 #endif 1844 1845 /* put together the new matrix */ 1846 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 1847 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 1848 b = (Mat_SeqAIJ*)(fact)->data; 1849 b->free_a = PETSC_TRUE; 1850 b->free_ij = PETSC_TRUE; 1851 b->singlemalloc = PETSC_FALSE; 1852 ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 1853 b->j = bj; 1854 b->i = bi; 1855 b->diag = bdiag; 1856 b->ilen = 0; 1857 b->imax = 0; 1858 b->row = isrow; 1859 b->col = iscol; 1860 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1861 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1862 b->icol = isicol; 1863 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1864 /* In b structure: Free imax, ilen, old a, old j. 1865 Allocate bdiag, solve_work, new a, new j */ 1866 ierr = PetscLogObjectMemory(fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1867 b->maxnz = b->nz = bdiag[0]+1; 1868 (fact)->info.factor_mallocs = reallocs; 1869 (fact)->info.fill_ratio_given = f; 1870 (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 1871 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1872 ierr = Mat_CheckInode_FactorLU(fact,PETSC_FALSE);CHKERRQ(ierr); 1873 PetscFunctionReturn(0); 1874 } 1875 1876 #undef __FUNCT__ 1877 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_inplace" 1878 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1879 { 1880 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1881 IS isicol; 1882 PetscErrorCode ierr; 1883 const PetscInt *r,*ic; 1884 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,d; 1885 PetscInt *bi,*cols,nnz,*cols_lvl; 1886 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1887 PetscInt i,levels,diagonal_fill; 1888 PetscTruth col_identity,row_identity; 1889 PetscReal f; 1890 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1891 PetscBT lnkbt; 1892 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1893 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1894 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1895 PetscTruth missing; 1896 1897 PetscFunctionBegin; 1898 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); 1899 f = info->fill; 1900 levels = (PetscInt)info->levels; 1901 diagonal_fill = (PetscInt)info->diagonal_fill; 1902 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1903 1904 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1905 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1906 if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */ 1907 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr); 1908 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace; 1909 1910 fact->factor = MAT_FACTOR_ILU; 1911 (fact)->info.factor_mallocs = 0; 1912 (fact)->info.fill_ratio_given = info->fill; 1913 (fact)->info.fill_ratio_needed = 1.0; 1914 b = (Mat_SeqAIJ*)(fact)->data; 1915 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 1916 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 1917 b->row = isrow; 1918 b->col = iscol; 1919 b->icol = isicol; 1920 ierr = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1921 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1922 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1923 ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1924 PetscFunctionReturn(0); 1925 } 1926 1927 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1928 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1929 1930 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1931 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1932 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1933 bi[0] = bdiag[0] = 0; 1934 1935 ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr); 1936 1937 /* create a linked list for storing column indices of the active row */ 1938 nlnk = n + 1; 1939 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1940 1941 /* initial FreeSpace size is f*(ai[n]+1) */ 1942 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1943 current_space = free_space; 1944 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1945 current_space_lvl = free_space_lvl; 1946 1947 for (i=0; i<n; i++) { 1948 nzi = 0; 1949 /* copy current row into linked list */ 1950 nnz = ai[r[i]+1] - ai[r[i]]; 1951 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1952 cols = aj + ai[r[i]]; 1953 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1954 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1955 nzi += nlnk; 1956 1957 /* make sure diagonal entry is included */ 1958 if (diagonal_fill && lnk[i] == -1) { 1959 fm = n; 1960 while (lnk[fm] < i) fm = lnk[fm]; 1961 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1962 lnk[fm] = i; 1963 lnk_lvl[i] = 0; 1964 nzi++; dcount++; 1965 } 1966 1967 /* add pivot rows into the active row */ 1968 nzbd = 0; 1969 prow = lnk[n]; 1970 while (prow < i) { 1971 nnz = bdiag[prow]; 1972 cols = bj_ptr[prow] + nnz + 1; 1973 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1974 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1975 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1976 nzi += nlnk; 1977 prow = lnk[prow]; 1978 nzbd++; 1979 } 1980 bdiag[i] = nzbd; 1981 bi[i+1] = bi[i] + nzi; 1982 1983 /* if free space is not available, make more free space */ 1984 if (current_space->local_remaining<nzi) { 1985 nnz = nzi*(n - i); /* estimated and max additional space needed */ 1986 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1987 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1988 reallocs++; 1989 } 1990 1991 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1992 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1993 bj_ptr[i] = current_space->array; 1994 bjlvl_ptr[i] = current_space_lvl->array; 1995 1996 /* make sure the active row i has diagonal entry */ 1997 if (*(bj_ptr[i]+bdiag[i]) != i) { 1998 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 1999 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 2000 } 2001 2002 current_space->array += nzi; 2003 current_space->local_used += nzi; 2004 current_space->local_remaining -= nzi; 2005 current_space_lvl->array += nzi; 2006 current_space_lvl->local_used += nzi; 2007 current_space_lvl->local_remaining -= nzi; 2008 } 2009 2010 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 2011 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 2012 2013 /* destroy list of free space and other temporary arrays */ 2014 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 2015 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */ 2016 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2017 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2018 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 2019 2020 #if defined(PETSC_USE_INFO) 2021 { 2022 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 2023 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 2024 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2025 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 2026 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 2027 if (diagonal_fill) { 2028 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 2029 } 2030 } 2031 #endif 2032 2033 /* put together the new matrix */ 2034 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 2035 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 2036 b = (Mat_SeqAIJ*)(fact)->data; 2037 b->free_a = PETSC_TRUE; 2038 b->free_ij = PETSC_TRUE; 2039 b->singlemalloc = PETSC_FALSE; 2040 ierr = PetscMalloc(bi[n]*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 2041 b->j = bj; 2042 b->i = bi; 2043 for (i=0; i<n; i++) bdiag[i] += bi[i]; 2044 b->diag = bdiag; 2045 b->ilen = 0; 2046 b->imax = 0; 2047 b->row = isrow; 2048 b->col = iscol; 2049 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 2050 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 2051 b->icol = isicol; 2052 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2053 /* In b structure: Free imax, ilen, old a, old j. 2054 Allocate bdiag, solve_work, new a, new j */ 2055 ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 2056 b->maxnz = b->nz = bi[n] ; 2057 (fact)->info.factor_mallocs = reallocs; 2058 (fact)->info.fill_ratio_given = f; 2059 (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 2060 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace; 2061 ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); 2062 PetscFunctionReturn(0); 2063 } 2064 2065 #undef __FUNCT__ 2066 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ" 2067 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 2068 { 2069 Mat C = B; 2070 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2071 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2072 IS ip=b->row,iip = b->icol; 2073 PetscErrorCode ierr; 2074 const PetscInt *rip,*riip; 2075 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp; 2076 PetscInt *ai=a->i,*aj=a->j; 2077 PetscInt k,jmin,jmax,*c2r,*il,col,nexti,ili,nz; 2078 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2079 PetscTruth perm_identity; 2080 2081 LUShift_Ctx sctx; 2082 PetscReal rs; 2083 MatScalar d,*v; 2084 2085 PetscFunctionBegin; 2086 /* MatPivotSetUp(): initialize shift context sctx */ 2087 ierr = PetscMemzero(&sctx,sizeof(LUShift_Ctx));CHKERRQ(ierr); 2088 2089 /* if both shift schemes are chosen by user, only use info->shiftpd */ 2090 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 2091 sctx.shift_top = info->zeropivot; 2092 for (i=0; i<mbs; i++) { 2093 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 2094 d = (aa)[a->diag[i]]; 2095 rs = -PetscAbsScalar(d) - PetscRealPart(d); 2096 v = aa+ai[i]; 2097 nz = ai[i+1] - ai[i]; 2098 for (j=0; j<nz; j++) 2099 rs += PetscAbsScalar(v[j]); 2100 if (rs>sctx.shift_top) sctx.shift_top = rs; 2101 } 2102 sctx.shift_top *= 1.1; 2103 sctx.nshift_max = 5; 2104 sctx.shift_lo = 0.; 2105 sctx.shift_hi = 1.; 2106 } 2107 2108 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2109 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2110 2111 /* allocate working arrays 2112 c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col 2113 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 2114 */ 2115 ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&c2r);CHKERRQ(ierr); 2116 2117 do { 2118 sctx.lushift = PETSC_FALSE; 2119 2120 for (i=0; i<mbs; i++) c2r[i] = mbs; 2121 il[0] = 0; 2122 2123 for (k = 0; k<mbs; k++){ 2124 /* zero rtmp */ 2125 nz = bi[k+1] - bi[k]; 2126 bjtmp = bj + bi[k]; 2127 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2128 2129 /* load in initial unfactored row */ 2130 bval = ba + bi[k]; 2131 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2132 for (j = jmin; j < jmax; j++){ 2133 col = riip[aj[j]]; 2134 if (col >= k){ /* only take upper triangular entry */ 2135 rtmp[col] = aa[j]; 2136 *bval++ = 0.0; /* for in-place factorization */ 2137 } 2138 } 2139 /* shift the diagonal of the matrix: ZeropivotApply() */ 2140 rtmp[k] += sctx.shift_amount; /* shift the diagonal of the matrix */ 2141 2142 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2143 dk = rtmp[k]; 2144 i = c2r[k]; /* first row to be added to k_th row */ 2145 2146 while (i < k){ 2147 nexti = c2r[i]; /* next row to be added to k_th row */ 2148 2149 /* compute multiplier, update diag(k) and U(i,k) */ 2150 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2151 uikdi = - ba[ili]*ba[bdiag[i]]; /* diagonal(k) */ 2152 dk += uikdi*ba[ili]; /* update diag[k] */ 2153 ba[ili] = uikdi; /* -U(i,k) */ 2154 2155 /* add multiple of row i to k-th row */ 2156 jmin = ili + 1; jmax = bi[i+1]; 2157 if (jmin < jmax){ 2158 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2159 /* update il and c2r for row i */ 2160 il[i] = jmin; 2161 j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i; 2162 } 2163 i = nexti; 2164 } 2165 2166 /* copy data into U(k,:) */ 2167 rs = 0.0; 2168 jmin = bi[k]; jmax = bi[k+1]-1; 2169 if (jmin < jmax) { 2170 for (j=jmin; j<jmax; j++){ 2171 col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]); 2172 } 2173 /* add the k-th row into il and c2r */ 2174 il[k] = jmin; 2175 i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k; 2176 } 2177 2178 /* MatPivotCheck() */ 2179 sctx.rs = rs; 2180 sctx.pv = dk; 2181 if (info->shiftnz){ 2182 ierr = MatPivotCheck_nz(info,sctx,k);CHKERRQ(ierr); 2183 } else if (info->shiftpd){ 2184 ierr = MatPivotCheck_pd(info,sctx,k);CHKERRQ(ierr); 2185 } else if (info->shiftinblocks){ 2186 ierr = MatPivotCheck_inblocks(info,sctx,k);CHKERRQ(ierr); 2187 } else { 2188 ierr = MatPivotCheck_none(info,sctx,k);CHKERRQ(ierr); 2189 } 2190 dk = sctx.pv; 2191 // if (newshift == 1) break; 2192 2193 ba[bdiag[k]] = 1.0/dk; /* U(k,k) */ 2194 } 2195 } while (sctx.lushift); 2196 2197 ierr = PetscFree3(rtmp,il,c2r);CHKERRQ(ierr); 2198 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2199 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2200 2201 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2202 if (perm_identity){ 2203 B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2204 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2205 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering; 2206 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering; 2207 } else { 2208 B->ops->solve = MatSolve_SeqSBAIJ_1; 2209 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1; 2210 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1; 2211 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1; 2212 } 2213 2214 C->assembled = PETSC_TRUE; 2215 C->preallocated = PETSC_TRUE; 2216 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2217 2218 /* MatPivotView() */ 2219 if (sctx.nshift){ 2220 if (info->shiftpd) { 2221 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); 2222 } else if (info->shiftnz) { 2223 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2224 } else if (info->shiftinblocks){ 2225 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftinblocks);CHKERRQ(ierr); 2226 } 2227 } 2228 PetscFunctionReturn(0); 2229 } 2230 2231 #undef __FUNCT__ 2232 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ_inplace" 2233 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info) 2234 { 2235 Mat C = B; 2236 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2237 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2238 IS ip=b->row,iip = b->icol; 2239 PetscErrorCode ierr; 2240 const PetscInt *rip,*riip; 2241 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol,*bjtmp; 2242 PetscInt *ai=a->i,*aj=a->j; 2243 PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz; 2244 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2245 PetscReal zeropivot,rs,shiftnz; 2246 PetscReal shiftpd; 2247 ChShift_Ctx sctx; 2248 PetscInt newshift; 2249 PetscTruth perm_identity; 2250 2251 PetscFunctionBegin; 2252 shiftnz = info->shiftnz; 2253 shiftpd = info->shiftpd; 2254 zeropivot = info->zeropivot; 2255 2256 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2257 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2258 2259 /* initialization */ 2260 ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr); 2261 sctx.shift_amount = 0; 2262 sctx.nshift = 0; 2263 do { 2264 sctx.chshift = PETSC_FALSE; 2265 for (i=0; i<mbs; i++) jl[i] = mbs; 2266 il[0] = 0; 2267 2268 for (k = 0; k<mbs; k++){ 2269 /* zero rtmp */ 2270 nz = bi[k+1] - bi[k]; 2271 bjtmp = bj + bi[k]; 2272 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2273 2274 bval = ba + bi[k]; 2275 /* initialize k-th row by the perm[k]-th row of A */ 2276 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2277 for (j = jmin; j < jmax; j++){ 2278 col = riip[aj[j]]; 2279 if (col >= k){ /* only take upper triangular entry */ 2280 rtmp[col] = aa[j]; 2281 *bval++ = 0.0; /* for in-place factorization */ 2282 } 2283 } 2284 /* shift the diagonal of the matrix */ 2285 if (sctx.nshift) rtmp[k] += sctx.shift_amount; 2286 2287 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2288 dk = rtmp[k]; 2289 i = jl[k]; /* first row to be added to k_th row */ 2290 2291 while (i < k){ 2292 nexti = jl[i]; /* next row to be added to k_th row */ 2293 2294 /* compute multiplier, update diag(k) and U(i,k) */ 2295 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2296 uikdi = - ba[ili]*ba[bi[i]]; /* diagonal(k) */ 2297 dk += uikdi*ba[ili]; 2298 ba[ili] = uikdi; /* -U(i,k) */ 2299 2300 /* add multiple of row i to k-th row */ 2301 jmin = ili + 1; jmax = bi[i+1]; 2302 if (jmin < jmax){ 2303 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2304 /* update il and jl for row i */ 2305 il[i] = jmin; 2306 j = bj[jmin]; jl[i] = jl[j]; jl[j] = i; 2307 } 2308 i = nexti; 2309 } 2310 2311 /* shift the diagonals when zero pivot is detected */ 2312 /* compute rs=sum of abs(off-diagonal) */ 2313 rs = 0.0; 2314 jmin = bi[k]+1; 2315 nz = bi[k+1] - jmin; 2316 bcol = bj + jmin; 2317 for (j=0; j<nz; j++) { 2318 rs += PetscAbsScalar(rtmp[bcol[j]]); 2319 } 2320 2321 sctx.rs = rs; 2322 sctx.pv = dk; 2323 ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr); 2324 2325 if (newshift == 1) { 2326 if (!sctx.shift_amount) { 2327 sctx.shift_amount = 1e-5; 2328 } 2329 break; 2330 } 2331 2332 /* copy data into U(k,:) */ 2333 ba[bi[k]] = 1.0/dk; /* U(k,k) */ 2334 jmin = bi[k]+1; jmax = bi[k+1]; 2335 if (jmin < jmax) { 2336 for (j=jmin; j<jmax; j++){ 2337 col = bj[j]; ba[j] = rtmp[col]; 2338 } 2339 /* add the k-th row into il and jl */ 2340 il[k] = jmin; 2341 i = bj[jmin]; jl[k] = jl[i]; jl[i] = k; 2342 } 2343 } 2344 } while (sctx.chshift); 2345 ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr); 2346 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2347 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2348 2349 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2350 if (perm_identity){ 2351 B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2352 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2353 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2354 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2355 } else { 2356 B->ops->solve = MatSolve_SeqSBAIJ_1_inplace; 2357 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_inplace; 2358 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_inplace; 2359 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_inplace; 2360 } 2361 2362 C->assembled = PETSC_TRUE; 2363 C->preallocated = PETSC_TRUE; 2364 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2365 if (sctx.nshift){ 2366 if (shiftnz) { 2367 ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2368 } else if (shiftpd) { 2369 ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2370 } 2371 } 2372 PetscFunctionReturn(0); 2373 } 2374 2375 /* 2376 icc() under revised new data structure. 2377 Factored arrays bj and ba are stored as 2378 U(0,:),...,U(i,:),U(n-1,:) 2379 2380 ui=fact->i is an array of size n+1, in which 2381 ui+ 2382 ui[i]: points to 1st entry of U(i,:),i=0,...,n-1 2383 ui[n]: points to U(n-1,n-1)+1 2384 2385 udiag=fact->diag is an array of size n,in which 2386 udiag[i]: points to diagonal of U(i,:), i=0,...,n-1 2387 2388 U(i,:) contains udiag[i] as its last entry, i.e., 2389 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 2390 */ 2391 2392 #undef __FUNCT__ 2393 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ" 2394 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2395 { 2396 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2397 Mat_SeqSBAIJ *b; 2398 PetscErrorCode ierr; 2399 PetscTruth perm_identity,missing; 2400 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2401 const PetscInt *rip,*riip; 2402 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2403 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2404 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2405 PetscReal fill=info->fill,levels=info->levels; 2406 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2407 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2408 PetscBT lnkbt; 2409 IS iperm; 2410 2411 PetscFunctionBegin; 2412 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); 2413 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2414 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2415 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2416 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2417 2418 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2419 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2420 ui[0] = 0; 2421 2422 /* ICC(0) without matrix ordering: simply rearrange column indices */ 2423 if (!levels && perm_identity) { 2424 for (i=0; i<am; i++) { 2425 ncols = ai[i+1] - a->diag[i]; 2426 ui[i+1] = ui[i] + ncols; 2427 udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */ 2428 } 2429 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2430 cols = uj; 2431 for (i=0; i<am; i++) { 2432 aj = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */ 2433 ncols = ai[i+1] - a->diag[i] -1; 2434 for (j=0; j<ncols; j++) *cols++ = aj[j]; 2435 *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */ 2436 } 2437 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2438 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2439 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2440 2441 /* initialization */ 2442 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2443 2444 /* jl: linked list for storing indices of the pivot rows 2445 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2446 ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr); 2447 for (i=0; i<am; i++){ 2448 jl[i] = am; il[i] = 0; 2449 } 2450 2451 /* create and initialize a linked list for storing column indices of the active row k */ 2452 nlnk = am + 1; 2453 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2454 2455 /* initial FreeSpace size is fill*(ai[am]+1) */ 2456 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2457 current_space = free_space; 2458 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2459 current_space_lvl = free_space_lvl; 2460 2461 for (k=0; k<am; k++){ /* for each active row k */ 2462 /* initialize lnk by the column indices of row rip[k] of A */ 2463 nzk = 0; 2464 ncols = ai[rip[k]+1] - ai[rip[k]]; 2465 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2466 ncols_upper = 0; 2467 for (j=0; j<ncols; j++){ 2468 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2469 if (riip[i] >= k){ /* only take upper triangular entry */ 2470 ajtmp[ncols_upper] = i; 2471 ncols_upper++; 2472 } 2473 } 2474 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2475 nzk += nlnk; 2476 2477 /* update lnk by computing fill-in for each pivot row to be merged in */ 2478 prow = jl[k]; /* 1st pivot row */ 2479 2480 while (prow < k){ 2481 nextprow = jl[prow]; 2482 2483 /* merge prow into k-th row */ 2484 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2485 jmax = ui[prow+1]; 2486 ncols = jmax-jmin; 2487 i = jmin - ui[prow]; 2488 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2489 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2490 j = *(uj - 1); 2491 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2492 nzk += nlnk; 2493 2494 /* update il and jl for prow */ 2495 if (jmin < jmax){ 2496 il[prow] = jmin; 2497 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2498 } 2499 prow = nextprow; 2500 } 2501 2502 /* if free space is not available, make more free space */ 2503 if (current_space->local_remaining<nzk) { 2504 i = am - k + 1; /* num of unfactored rows */ 2505 i *= PetscMin(nzk, i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2506 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2507 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2508 reallocs++; 2509 } 2510 2511 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2512 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2513 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2514 2515 /* add the k-th row into il and jl */ 2516 if (nzk > 1){ 2517 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2518 jl[k] = jl[i]; jl[i] = k; 2519 il[k] = ui[k] + 1; 2520 } 2521 uj_ptr[k] = current_space->array; 2522 uj_lvl_ptr[k] = current_space_lvl->array; 2523 2524 current_space->array += nzk; 2525 current_space->local_used += nzk; 2526 current_space->local_remaining -= nzk; 2527 2528 current_space_lvl->array += nzk; 2529 current_space_lvl->local_used += nzk; 2530 current_space_lvl->local_remaining -= nzk; 2531 2532 ui[k+1] = ui[k] + nzk; 2533 } 2534 2535 #if defined(PETSC_USE_INFO) 2536 if (ai[am] != 0) { 2537 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2538 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2539 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2540 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2541 } else { 2542 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2543 } 2544 #endif 2545 2546 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2547 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2548 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2549 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2550 2551 /* destroy list of free space and other temporary array(s) */ 2552 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2553 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor */ 2554 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2555 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2556 2557 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2558 2559 /* put together the new matrix in MATSEQSBAIJ format */ 2560 b = (Mat_SeqSBAIJ*)(fact)->data; 2561 b->singlemalloc = PETSC_FALSE; 2562 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2563 b->j = uj; 2564 b->i = ui; 2565 b->diag = udiag; 2566 b->free_diag = PETSC_TRUE; 2567 b->ilen = 0; 2568 b->imax = 0; 2569 b->row = perm; 2570 b->col = perm; 2571 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2572 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2573 b->icol = iperm; 2574 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2575 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2576 ierr = PetscLogObjectMemory(fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2577 b->maxnz = b->nz = ui[am]; 2578 b->free_a = PETSC_TRUE; 2579 b->free_ij = PETSC_TRUE; 2580 2581 fact->info.factor_mallocs = reallocs; 2582 fact->info.fill_ratio_given = fill; 2583 if (ai[am] != 0) { 2584 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2585 } else { 2586 fact->info.fill_ratio_needed = 0.0; 2587 } 2588 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2589 PetscFunctionReturn(0); 2590 } 2591 2592 #undef __FUNCT__ 2593 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ_inplace" 2594 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2595 { 2596 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2597 Mat_SeqSBAIJ *b; 2598 PetscErrorCode ierr; 2599 PetscTruth perm_identity,missing; 2600 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2601 const PetscInt *rip,*riip; 2602 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2603 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2604 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2605 PetscReal fill=info->fill,levels=info->levels; 2606 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2607 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2608 PetscBT lnkbt; 2609 IS iperm; 2610 2611 PetscFunctionBegin; 2612 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); 2613 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2614 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2615 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2616 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2617 2618 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2619 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2620 ui[0] = 0; 2621 2622 /* ICC(0) without matrix ordering: simply copies fill pattern */ 2623 if (!levels && perm_identity) { 2624 2625 for (i=0; i<am; i++) { 2626 ui[i+1] = ui[i] + ai[i+1] - a->diag[i]; 2627 udiag[i] = ui[i]; 2628 } 2629 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2630 cols = uj; 2631 for (i=0; i<am; i++) { 2632 aj = a->j + a->diag[i]; 2633 ncols = ui[i+1] - ui[i]; 2634 for (j=0; j<ncols; j++) *cols++ = *aj++; 2635 } 2636 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2637 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2638 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2639 2640 /* initialization */ 2641 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2642 2643 /* jl: linked list for storing indices of the pivot rows 2644 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2645 ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr); 2646 for (i=0; i<am; i++){ 2647 jl[i] = am; il[i] = 0; 2648 } 2649 2650 /* create and initialize a linked list for storing column indices of the active row k */ 2651 nlnk = am + 1; 2652 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2653 2654 /* initial FreeSpace size is fill*(ai[am]+1) */ 2655 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2656 current_space = free_space; 2657 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2658 current_space_lvl = free_space_lvl; 2659 2660 for (k=0; k<am; k++){ /* for each active row k */ 2661 /* initialize lnk by the column indices of row rip[k] of A */ 2662 nzk = 0; 2663 ncols = ai[rip[k]+1] - ai[rip[k]]; 2664 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2665 ncols_upper = 0; 2666 for (j=0; j<ncols; j++){ 2667 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2668 if (riip[i] >= k){ /* only take upper triangular entry */ 2669 ajtmp[ncols_upper] = i; 2670 ncols_upper++; 2671 } 2672 } 2673 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2674 nzk += nlnk; 2675 2676 /* update lnk by computing fill-in for each pivot row to be merged in */ 2677 prow = jl[k]; /* 1st pivot row */ 2678 2679 while (prow < k){ 2680 nextprow = jl[prow]; 2681 2682 /* merge prow into k-th row */ 2683 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2684 jmax = ui[prow+1]; 2685 ncols = jmax-jmin; 2686 i = jmin - ui[prow]; 2687 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2688 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2689 j = *(uj - 1); 2690 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2691 nzk += nlnk; 2692 2693 /* update il and jl for prow */ 2694 if (jmin < jmax){ 2695 il[prow] = jmin; 2696 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2697 } 2698 prow = nextprow; 2699 } 2700 2701 /* if free space is not available, make more free space */ 2702 if (current_space->local_remaining<nzk) { 2703 i = am - k + 1; /* num of unfactored rows */ 2704 i *= PetscMin(nzk, (i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2705 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2706 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2707 reallocs++; 2708 } 2709 2710 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2711 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2712 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2713 2714 /* add the k-th row into il and jl */ 2715 if (nzk > 1){ 2716 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2717 jl[k] = jl[i]; jl[i] = k; 2718 il[k] = ui[k] + 1; 2719 } 2720 uj_ptr[k] = current_space->array; 2721 uj_lvl_ptr[k] = current_space_lvl->array; 2722 2723 current_space->array += nzk; 2724 current_space->local_used += nzk; 2725 current_space->local_remaining -= nzk; 2726 2727 current_space_lvl->array += nzk; 2728 current_space_lvl->local_used += nzk; 2729 current_space_lvl->local_remaining -= nzk; 2730 2731 ui[k+1] = ui[k] + nzk; 2732 } 2733 2734 #if defined(PETSC_USE_INFO) 2735 if (ai[am] != 0) { 2736 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2737 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2738 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2739 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2740 } else { 2741 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2742 } 2743 #endif 2744 2745 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2746 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2747 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2748 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2749 2750 /* destroy list of free space and other temporary array(s) */ 2751 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2752 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 2753 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2754 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2755 2756 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2757 2758 /* put together the new matrix in MATSEQSBAIJ format */ 2759 2760 b = (Mat_SeqSBAIJ*)fact->data; 2761 b->singlemalloc = PETSC_FALSE; 2762 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2763 b->j = uj; 2764 b->i = ui; 2765 b->diag = udiag; 2766 b->free_diag = PETSC_TRUE; 2767 b->ilen = 0; 2768 b->imax = 0; 2769 b->row = perm; 2770 b->col = perm; 2771 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2772 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2773 b->icol = iperm; 2774 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2775 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2776 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2777 b->maxnz = b->nz = ui[am]; 2778 b->free_a = PETSC_TRUE; 2779 b->free_ij = PETSC_TRUE; 2780 2781 fact->info.factor_mallocs = reallocs; 2782 fact->info.fill_ratio_given = fill; 2783 if (ai[am] != 0) { 2784 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2785 } else { 2786 fact->info.fill_ratio_needed = 0.0; 2787 } 2788 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace; 2789 PetscFunctionReturn(0); 2790 } 2791 2792 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2793 { 2794 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2795 Mat_SeqSBAIJ *b; 2796 PetscErrorCode ierr; 2797 PetscTruth perm_identity; 2798 PetscReal fill = info->fill; 2799 const PetscInt *rip,*riip; 2800 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2801 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2802 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr,*udiag; 2803 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2804 PetscBT lnkbt; 2805 IS iperm; 2806 2807 PetscFunctionBegin; 2808 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); 2809 /* check whether perm is the identity mapping */ 2810 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2811 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2812 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2813 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2814 2815 /* initialization */ 2816 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2817 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2818 ui[0] = 0; 2819 2820 /* jl: linked list for storing indices of the pivot rows 2821 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2822 ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr); 2823 for (i=0; i<am; i++){ 2824 jl[i] = am; il[i] = 0; 2825 } 2826 2827 /* create and initialize a linked list for storing column indices of the active row k */ 2828 nlnk = am + 1; 2829 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2830 2831 /* initial FreeSpace size is fill*(ai[am]+1) */ 2832 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2833 current_space = free_space; 2834 2835 for (k=0; k<am; k++){ /* for each active row k */ 2836 /* initialize lnk by the column indices of row rip[k] of A */ 2837 nzk = 0; 2838 ncols = ai[rip[k]+1] - ai[rip[k]]; 2839 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2840 ncols_upper = 0; 2841 for (j=0; j<ncols; j++){ 2842 i = riip[*(aj + ai[rip[k]] + j)]; 2843 if (i >= k){ /* only take upper triangular entry */ 2844 cols[ncols_upper] = i; 2845 ncols_upper++; 2846 } 2847 } 2848 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2849 nzk += nlnk; 2850 2851 /* update lnk by computing fill-in for each pivot row to be merged in */ 2852 prow = jl[k]; /* 1st pivot row */ 2853 2854 while (prow < k){ 2855 nextprow = jl[prow]; 2856 /* merge prow into k-th row */ 2857 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2858 jmax = ui[prow+1]; 2859 ncols = jmax-jmin; 2860 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2861 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2862 nzk += nlnk; 2863 2864 /* update il and jl for prow */ 2865 if (jmin < jmax){ 2866 il[prow] = jmin; 2867 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 2868 } 2869 prow = nextprow; 2870 } 2871 2872 /* if free space is not available, make more free space */ 2873 if (current_space->local_remaining<nzk) { 2874 i = am - k + 1; /* num of unfactored rows */ 2875 i *= PetscMin(nzk,i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2876 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2877 reallocs++; 2878 } 2879 2880 /* copy data into free space, then initialize lnk */ 2881 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 2882 2883 /* add the k-th row into il and jl */ 2884 if (nzk > 1){ 2885 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2886 jl[k] = jl[i]; jl[i] = k; 2887 il[k] = ui[k] + 1; 2888 } 2889 ui_ptr[k] = current_space->array; 2890 current_space->array += nzk; 2891 current_space->local_used += nzk; 2892 current_space->local_remaining -= nzk; 2893 2894 ui[k+1] = ui[k] + nzk; 2895 } 2896 2897 #if defined(PETSC_USE_INFO) 2898 if (ai[am] != 0) { 2899 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 2900 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2901 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2902 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2903 } else { 2904 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2905 } 2906 #endif 2907 2908 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2909 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2910 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 2911 2912 /* destroy list of free space and other temporary array(s) */ 2913 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2914 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor */ 2915 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2916 2917 /* put together the new matrix in MATSEQSBAIJ format */ 2918 2919 b = (Mat_SeqSBAIJ*)fact->data; 2920 b->singlemalloc = PETSC_FALSE; 2921 b->free_a = PETSC_TRUE; 2922 b->free_ij = PETSC_TRUE; 2923 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2924 b->j = uj; 2925 b->i = ui; 2926 b->diag = udiag; 2927 b->free_diag = PETSC_TRUE; 2928 b->ilen = 0; 2929 b->imax = 0; 2930 b->row = perm; 2931 b->col = perm; 2932 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2933 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2934 b->icol = iperm; 2935 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2936 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2937 ierr = PetscLogObjectMemory(fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2938 b->maxnz = b->nz = ui[am]; 2939 2940 fact->info.factor_mallocs = reallocs; 2941 fact->info.fill_ratio_given = fill; 2942 if (ai[am] != 0) { 2943 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2944 } else { 2945 fact->info.fill_ratio_needed = 0.0; 2946 } 2947 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2948 PetscFunctionReturn(0); 2949 } 2950 2951 #undef __FUNCT__ 2952 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ_inplace" 2953 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2954 { 2955 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2956 Mat_SeqSBAIJ *b; 2957 PetscErrorCode ierr; 2958 PetscTruth perm_identity; 2959 PetscReal fill = info->fill; 2960 const PetscInt *rip,*riip; 2961 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2962 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2963 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr; 2964 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2965 PetscBT lnkbt; 2966 IS iperm; 2967 2968 PetscFunctionBegin; 2969 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); 2970 /* check whether perm is the identity mapping */ 2971 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2972 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2973 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2974 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2975 2976 /* initialization */ 2977 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2978 ui[0] = 0; 2979 2980 /* jl: linked list for storing indices of the pivot rows 2981 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2982 ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr); 2983 for (i=0; i<am; i++){ 2984 jl[i] = am; il[i] = 0; 2985 } 2986 2987 /* create and initialize a linked list for storing column indices of the active row k */ 2988 nlnk = am + 1; 2989 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2990 2991 /* initial FreeSpace size is fill*(ai[am]+1) */ 2992 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2993 current_space = free_space; 2994 2995 for (k=0; k<am; k++){ /* for each active row k */ 2996 /* initialize lnk by the column indices of row rip[k] of A */ 2997 nzk = 0; 2998 ncols = ai[rip[k]+1] - ai[rip[k]]; 2999 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 3000 ncols_upper = 0; 3001 for (j=0; j<ncols; j++){ 3002 i = riip[*(aj + ai[rip[k]] + j)]; 3003 if (i >= k){ /* only take upper triangular entry */ 3004 cols[ncols_upper] = i; 3005 ncols_upper++; 3006 } 3007 } 3008 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3009 nzk += nlnk; 3010 3011 /* update lnk by computing fill-in for each pivot row to be merged in */ 3012 prow = jl[k]; /* 1st pivot row */ 3013 3014 while (prow < k){ 3015 nextprow = jl[prow]; 3016 /* merge prow into k-th row */ 3017 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 3018 jmax = ui[prow+1]; 3019 ncols = jmax-jmin; 3020 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 3021 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3022 nzk += nlnk; 3023 3024 /* update il and jl for prow */ 3025 if (jmin < jmax){ 3026 il[prow] = jmin; 3027 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 3028 } 3029 prow = nextprow; 3030 } 3031 3032 /* if free space is not available, make more free space */ 3033 if (current_space->local_remaining<nzk) { 3034 i = am - k + 1; /* num of unfactored rows */ 3035 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 3036 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 3037 reallocs++; 3038 } 3039 3040 /* copy data into free space, then initialize lnk */ 3041 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 3042 3043 /* add the k-th row into il and jl */ 3044 if (nzk-1 > 0){ 3045 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 3046 jl[k] = jl[i]; jl[i] = k; 3047 il[k] = ui[k] + 1; 3048 } 3049 ui_ptr[k] = current_space->array; 3050 current_space->array += nzk; 3051 current_space->local_used += nzk; 3052 current_space->local_remaining -= nzk; 3053 3054 ui[k+1] = ui[k] + nzk; 3055 } 3056 3057 #if defined(PETSC_USE_INFO) 3058 if (ai[am] != 0) { 3059 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 3060 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 3061 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 3062 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 3063 } else { 3064 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 3065 } 3066 #endif 3067 3068 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 3069 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 3070 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 3071 3072 /* destroy list of free space and other temporary array(s) */ 3073 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 3074 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 3075 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3076 3077 /* put together the new matrix in MATSEQSBAIJ format */ 3078 3079 b = (Mat_SeqSBAIJ*)fact->data; 3080 b->singlemalloc = PETSC_FALSE; 3081 b->free_a = PETSC_TRUE; 3082 b->free_ij = PETSC_TRUE; 3083 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 3084 b->j = uj; 3085 b->i = ui; 3086 b->diag = 0; 3087 b->ilen = 0; 3088 b->imax = 0; 3089 b->row = perm; 3090 b->col = perm; 3091 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3092 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3093 b->icol = iperm; 3094 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 3095 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 3096 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3097 b->maxnz = b->nz = ui[am]; 3098 3099 fact->info.factor_mallocs = reallocs; 3100 fact->info.fill_ratio_given = fill; 3101 if (ai[am] != 0) { 3102 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 3103 } else { 3104 fact->info.fill_ratio_needed = 0.0; 3105 } 3106 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace; 3107 PetscFunctionReturn(0); 3108 } 3109 3110 #undef __FUNCT__ 3111 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering" 3112 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx) 3113 { 3114 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3115 PetscErrorCode ierr; 3116 PetscInt n = A->rmap->n; 3117 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag,*vi; 3118 PetscScalar *x,sum; 3119 const PetscScalar *b; 3120 const MatScalar *aa = a->a,*v; 3121 PetscInt i,nz; 3122 3123 PetscFunctionBegin; 3124 if (!n) PetscFunctionReturn(0); 3125 3126 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3127 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3128 3129 /* forward solve the lower triangular */ 3130 x[0] = b[0]; 3131 v = aa; 3132 vi = aj; 3133 for (i=1; i<n; i++) { 3134 nz = ai[i+1] - ai[i]; 3135 sum = b[i]; 3136 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3137 v += nz; 3138 vi += nz; 3139 x[i] = sum; 3140 } 3141 3142 /* backward solve the upper triangular */ 3143 for (i=n-1; i>=0; i--){ 3144 v = aa + adiag[i+1] + 1; 3145 vi = aj + adiag[i+1] + 1; 3146 nz = adiag[i] - adiag[i+1]-1; 3147 sum = x[i]; 3148 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3149 x[i] = sum*v[nz]; /* x[i]=aa[adiag[i]]*sum; v++; */ 3150 } 3151 3152 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 3153 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3154 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3155 PetscFunctionReturn(0); 3156 } 3157 3158 #undef __FUNCT__ 3159 #define __FUNCT__ "MatSolve_SeqAIJ" 3160 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx) 3161 { 3162 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3163 IS iscol = a->col,isrow = a->row; 3164 PetscErrorCode ierr; 3165 PetscInt i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz; 3166 const PetscInt *rout,*cout,*r,*c; 3167 PetscScalar *x,*tmp,sum; 3168 const PetscScalar *b; 3169 const MatScalar *aa = a->a,*v; 3170 3171 PetscFunctionBegin; 3172 if (!n) PetscFunctionReturn(0); 3173 3174 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3175 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3176 tmp = a->solve_work; 3177 3178 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 3179 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 3180 3181 /* forward solve the lower triangular */ 3182 tmp[0] = b[r[0]]; 3183 v = aa; 3184 vi = aj; 3185 for (i=1; i<n; i++) { 3186 nz = ai[i+1] - ai[i]; 3187 sum = b[r[i]]; 3188 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3189 tmp[i] = sum; 3190 v += nz; vi += nz; 3191 } 3192 3193 /* backward solve the upper triangular */ 3194 for (i=n-1; i>=0; i--){ 3195 v = aa + adiag[i+1]+1; 3196 vi = aj + adiag[i+1]+1; 3197 nz = adiag[i]-adiag[i+1]-1; 3198 sum = tmp[i]; 3199 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3200 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 3201 } 3202 3203 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 3204 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 3205 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3206 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3207 ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr); 3208 PetscFunctionReturn(0); 3209 } 3210 3211 #undef __FUNCT__ 3212 #define __FUNCT__ "MatILUDTFactor_SeqAIJ" 3213 /* 3214 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 3215 */ 3216 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact) 3217 { 3218 Mat B = *fact; 3219 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b; 3220 IS isicol; 3221 PetscErrorCode ierr; 3222 const PetscInt *r,*ic; 3223 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag; 3224 PetscInt *bi,*bj,*bdiag,*bdiag_rev; 3225 PetscInt row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au; 3226 PetscInt nlnk,*lnk; 3227 PetscBT lnkbt; 3228 PetscTruth row_identity,icol_identity,both_identity; 3229 MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp; 3230 const PetscInt *ics; 3231 PetscInt j,nz,*pj,*bjtmp,k,ncut,*jtmp; 3232 PetscReal dt=info->dt,dtcol=info->dtcol,shift=info->shiftinblocks; 3233 PetscInt dtcount=(PetscInt)info->dtcount,nnz_max; 3234 PetscTruth missing; 3235 3236 PetscFunctionBegin; 3237 3238 if (dt == PETSC_DEFAULT) dt = 0.005; 3239 if (dtcol == PETSC_DEFAULT) dtcol = 0.01; /* XXX unused! */ 3240 if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax); 3241 3242 /* ------- symbolic factorization, can be reused ---------*/ 3243 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 3244 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 3245 adiag=a->diag; 3246 3247 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 3248 3249 /* bdiag is location of diagonal in factor */ 3250 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); /* becomes b->diag */ 3251 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag_rev);CHKERRQ(ierr); /* temporary */ 3252 3253 /* allocate row pointers bi */ 3254 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 3255 3256 /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */ 3257 if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */ 3258 nnz_max = ai[n]+2*n*dtcount+2; 3259 3260 ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 3261 ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr); 3262 3263 /* put together the new matrix */ 3264 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 3265 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 3266 b = (Mat_SeqAIJ*)B->data; 3267 b->free_a = PETSC_TRUE; 3268 b->free_ij = PETSC_TRUE; 3269 b->singlemalloc = PETSC_FALSE; 3270 b->a = ba; 3271 b->j = bj; 3272 b->i = bi; 3273 b->diag = bdiag; 3274 b->ilen = 0; 3275 b->imax = 0; 3276 b->row = isrow; 3277 b->col = iscol; 3278 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 3279 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 3280 b->icol = isicol; 3281 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 3282 3283 ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3284 b->maxnz = nnz_max; 3285 3286 B->factor = MAT_FACTOR_ILUDT; 3287 B->info.factor_mallocs = 0; 3288 B->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]); 3289 CHKMEMQ; 3290 /* ------- end of symbolic factorization ---------*/ 3291 3292 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3293 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3294 ics = ic; 3295 3296 /* linked list for storing column indices of the active row */ 3297 nlnk = n + 1; 3298 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3299 3300 /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */ 3301 ierr = PetscMalloc2(n,PetscInt,&im,n,PetscInt,&jtmp);CHKERRQ(ierr); 3302 /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */ 3303 ierr = PetscMalloc2(n,MatScalar,&rtmp,n,MatScalar,&vtmp);CHKERRQ(ierr); 3304 ierr = PetscMemzero(rtmp,n*sizeof(MatScalar));CHKERRQ(ierr); 3305 3306 bi[0] = 0; 3307 bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */ 3308 bdiag_rev[n] = bdiag[0]; 3309 bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */ 3310 for (i=0; i<n; i++) { 3311 /* copy initial fill into linked list */ 3312 nzi = 0; /* nonzeros for active row i */ 3313 nzi = ai[r[i]+1] - ai[r[i]]; 3314 if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 3315 nzi_al = adiag[r[i]] - ai[r[i]]; 3316 nzi_au = ai[r[i]+1] - adiag[r[i]] -1; 3317 ajtmp = aj + ai[r[i]]; 3318 ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3319 3320 /* load in initial (unfactored row) */ 3321 aatmp = a->a + ai[r[i]]; 3322 for (j=0; j<nzi; j++) { 3323 rtmp[ics[*ajtmp++]] = *aatmp++; 3324 } 3325 3326 /* add pivot rows into linked list */ 3327 row = lnk[n]; 3328 while (row < i ) { 3329 nzi_bl = bi[row+1] - bi[row] + 1; 3330 bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */ 3331 ierr = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr); 3332 nzi += nlnk; 3333 row = lnk[row]; 3334 } 3335 3336 /* copy data from lnk into jtmp, then initialize lnk */ 3337 ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr); 3338 3339 /* numerical factorization */ 3340 bjtmp = jtmp; 3341 row = *bjtmp++; /* 1st pivot row */ 3342 while ( row < i ) { 3343 pc = rtmp + row; 3344 pv = ba + bdiag[row]; /* 1./(diag of the pivot row) */ 3345 multiplier = (*pc) * (*pv); 3346 *pc = multiplier; 3347 if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */ 3348 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3349 pv = ba + bdiag[row+1] + 1; 3350 /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */ 3351 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3352 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3353 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 3354 } 3355 row = *bjtmp++; 3356 } 3357 3358 /* copy sparse rtmp into contiguous vtmp; separate L and U part */ 3359 diag_tmp = rtmp[i]; /* save diagonal value - may not needed?? */ 3360 nzi_bl = 0; j = 0; 3361 while (jtmp[j] < i){ /* Note: jtmp is sorted */ 3362 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3363 nzi_bl++; j++; 3364 } 3365 nzi_bu = nzi - nzi_bl -1; 3366 while (j < nzi){ 3367 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3368 j++; 3369 } 3370 3371 bjtmp = bj + bi[i]; 3372 batmp = ba + bi[i]; 3373 /* apply level dropping rule to L part */ 3374 ncut = nzi_al + dtcount; 3375 if (ncut < nzi_bl){ 3376 ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr); 3377 ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr); 3378 } else { 3379 ncut = nzi_bl; 3380 } 3381 for (j=0; j<ncut; j++){ 3382 bjtmp[j] = jtmp[j]; 3383 batmp[j] = vtmp[j]; 3384 /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */ 3385 } 3386 bi[i+1] = bi[i] + ncut; 3387 nzi = ncut + 1; 3388 3389 /* apply level dropping rule to U part */ 3390 ncut = nzi_au + dtcount; 3391 if (ncut < nzi_bu){ 3392 ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr); 3393 ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr); 3394 } else { 3395 ncut = nzi_bu; 3396 } 3397 nzi += ncut; 3398 3399 /* mark bdiagonal */ 3400 bdiag[i+1] = bdiag[i] - (ncut + 1); 3401 bdiag_rev[n-i-1] = bdiag[i+1]; 3402 bi[2*n - i] = bi[2*n - i +1] - (ncut + 1); 3403 bjtmp = bj + bdiag[i]; 3404 batmp = ba + bdiag[i]; 3405 *bjtmp = i; 3406 *batmp = diag_tmp; /* rtmp[i]; */ 3407 if (*batmp == 0.0) { 3408 *batmp = dt+shift; 3409 /* printf(" row %d add shift %g\n",i,shift); */ 3410 } 3411 *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */ 3412 /* printf(" (%d,%g),",*bjtmp,*batmp); */ 3413 3414 bjtmp = bj + bdiag[i+1]+1; 3415 batmp = ba + bdiag[i+1]+1; 3416 for (k=0; k<ncut; k++){ 3417 bjtmp[k] = jtmp[nzi_bl+1+k]; 3418 batmp[k] = vtmp[nzi_bl+1+k]; 3419 /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */ 3420 } 3421 /* printf("\n"); */ 3422 3423 im[i] = nzi; /* used by PetscLLAddSortedLU() */ 3424 /* 3425 printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]); 3426 printf(" ----------------------------\n"); 3427 */ 3428 } /* for (i=0; i<n; i++) */ 3429 /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */ 3430 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]); 3431 3432 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3433 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3434 3435 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3436 ierr = PetscFree2(im,jtmp);CHKERRQ(ierr); 3437 ierr = PetscFree2(rtmp,vtmp);CHKERRQ(ierr); 3438 ierr = PetscFree(bdiag_rev);CHKERRQ(ierr); 3439 3440 ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr); 3441 b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n]; 3442 3443 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3444 ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr); 3445 both_identity = (PetscTruth) (row_identity && icol_identity); 3446 if (row_identity && icol_identity) { 3447 B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 3448 } else { 3449 B->ops->solve = MatSolve_SeqAIJ; 3450 } 3451 3452 B->ops->solveadd = 0; 3453 B->ops->solvetranspose = 0; 3454 B->ops->solvetransposeadd = 0; 3455 B->ops->matsolve = 0; 3456 B->assembled = PETSC_TRUE; 3457 B->preallocated = PETSC_TRUE; 3458 PetscFunctionReturn(0); 3459 } 3460 3461 /* a wraper of MatILUDTFactor_SeqAIJ() */ 3462 #undef __FUNCT__ 3463 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ" 3464 /* 3465 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 3466 */ 3467 3468 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info) 3469 { 3470 PetscErrorCode ierr; 3471 3472 PetscFunctionBegin; 3473 ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr); 3474 PetscFunctionReturn(0); 3475 } 3476 3477 /* 3478 same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors 3479 - intend to replace existing MatLUFactorNumeric_SeqAIJ() 3480 */ 3481 #undef __FUNCT__ 3482 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ" 3483 /* 3484 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 3485 */ 3486 3487 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info) 3488 { 3489 Mat C=fact; 3490 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 3491 IS isrow = b->row,isicol = b->icol; 3492 PetscErrorCode ierr; 3493 const PetscInt *r,*ic,*ics; 3494 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 3495 PetscInt *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj; 3496 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 3497 PetscReal dt=info->dt,shift=info->shiftinblocks; 3498 PetscTruth row_identity, col_identity; 3499 3500 PetscFunctionBegin; 3501 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3502 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3503 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 3504 ics = ic; 3505 3506 for (i=0; i<n; i++){ 3507 /* initialize rtmp array */ 3508 nzl = bi[i+1] - bi[i]; /* num of nozeros in L(i,:) */ 3509 bjtmp = bj + bi[i]; 3510 for (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0; 3511 rtmp[i] = 0.0; 3512 nzu = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */ 3513 bjtmp = bj + bdiag[i+1] + 1; 3514 for (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0; 3515 3516 /* load in initial unfactored row of A */ 3517 /* printf("row %d\n",i); */ 3518 nz = ai[r[i]+1] - ai[r[i]]; 3519 ajtmp = aj + ai[r[i]]; 3520 v = aa + ai[r[i]]; 3521 for (j=0; j<nz; j++) { 3522 rtmp[ics[*ajtmp++]] = v[j]; 3523 /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */ 3524 } 3525 /* printf("\n"); */ 3526 3527 /* numerical factorization */ 3528 bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */ 3529 nzl = bi[i+1] - bi[i]; /* num of entries in L(i,:) */ 3530 k = 0; 3531 while (k < nzl){ 3532 row = *bjtmp++; 3533 /* printf(" prow %d\n",row); */ 3534 pc = rtmp + row; 3535 pv = b->a + bdiag[row]; /* 1./(diag of the pivot row) */ 3536 multiplier = (*pc) * (*pv); 3537 *pc = multiplier; 3538 if (PetscAbsScalar(multiplier) > dt){ 3539 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3540 pv = b->a + bdiag[row+1] + 1; 3541 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3542 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3543 /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */ 3544 } 3545 k++; 3546 } 3547 3548 /* finished row so stick it into b->a */ 3549 /* L-part */ 3550 pv = b->a + bi[i] ; 3551 pj = bj + bi[i] ; 3552 nzl = bi[i+1] - bi[i]; 3553 for (j=0; j<nzl; j++) { 3554 pv[j] = rtmp[pj[j]]; 3555 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3556 } 3557 3558 /* diagonal: invert diagonal entries for simplier triangular solves */ 3559 if (rtmp[i] == 0.0) rtmp[i] = dt+shift; 3560 b->a[bdiag[i]] = 1.0/rtmp[i]; 3561 /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */ 3562 3563 /* U-part */ 3564 pv = b->a + bdiag[i+1] + 1; 3565 pj = bj + bdiag[i+1] + 1; 3566 nzu = bdiag[i] - bdiag[i+1] - 1; 3567 for (j=0; j<nzu; j++) { 3568 pv[j] = rtmp[pj[j]]; 3569 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3570 } 3571 /* printf("\n"); */ 3572 } 3573 3574 ierr = PetscFree(rtmp);CHKERRQ(ierr); 3575 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3576 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3577 3578 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3579 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 3580 if (row_identity && col_identity) { 3581 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 3582 } else { 3583 C->ops->solve = MatSolve_SeqAIJ; 3584 } 3585 C->ops->solveadd = 0; 3586 C->ops->solvetranspose = 0; 3587 C->ops->solvetransposeadd = 0; 3588 C->ops->matsolve = 0; 3589 C->assembled = PETSC_TRUE; 3590 C->preallocated = PETSC_TRUE; 3591 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 3592 PetscFunctionReturn(0); 3593 } 3594