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