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