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 if (a->inode.size) { 274 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace; 275 } 276 PetscFunctionReturn(0); 277 } 278 279 #undef __FUNCT__ 280 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ" 281 PetscErrorCode MatLUFactorSymbolic_SeqAIJ(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 282 { 283 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 284 IS isicol; 285 PetscErrorCode ierr; 286 const PetscInt *r,*ic; 287 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j; 288 PetscInt *bi,*bj,*ajtmp; 289 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 290 PetscReal f; 291 PetscInt nlnk,*lnk,k,**bi_ptr; 292 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 293 PetscBT lnkbt; 294 PetscTruth olddatastruct=PETSC_FALSE; 295 296 PetscFunctionBegin; 297 /* Uncomment the oldatastruct part only while testing new data structure for MatSolve() */ 298 ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_old",&olddatastruct,PETSC_NULL);CHKERRQ(ierr); 299 if(olddatastruct){ 300 ierr = MatLUFactorSymbolic_SeqAIJ_inplace(B,A,isrow,iscol,info);CHKERRQ(ierr); 301 PetscFunctionReturn(0); 302 } 303 304 305 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square"); 306 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 307 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 308 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 309 310 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 311 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 312 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 313 bi[0] = bdiag[0] = 0; 314 315 /* linked list for storing column indices of the active row */ 316 nlnk = n + 1; 317 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 318 319 ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr); 320 321 /* initial FreeSpace size is f*(ai[n]+1) */ 322 f = info->fill; 323 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 324 current_space = free_space; 325 326 for (i=0; i<n; i++) { 327 /* copy previous fill into linked list */ 328 nzi = 0; 329 nnz = ai[r[i]+1] - ai[r[i]]; 330 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 331 ajtmp = aj + ai[r[i]]; 332 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 333 nzi += nlnk; 334 335 /* add pivot rows into linked list */ 336 row = lnk[n]; 337 while (row < i){ 338 nzbd = bdiag[row] + 1; /* num of entries in the row with column index <= row */ 339 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 340 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 341 nzi += nlnk; 342 row = lnk[row]; 343 } 344 bi[i+1] = bi[i] + nzi; 345 im[i] = nzi; 346 347 /* mark bdiag */ 348 nzbd = 0; 349 nnz = nzi; 350 k = lnk[n]; 351 while (nnz-- && k < i){ 352 nzbd++; 353 k = lnk[k]; 354 } 355 bdiag[i] = nzbd; /* note: bdiag[i] = nnzL as input for PetscFreeSpaceContiguous_LU() */ 356 357 /* if free space is not available, make more free space */ 358 if (current_space->local_remaining<nzi) { 359 nnz = 2*(n - i)*nzi; /* estimated and max additional space needed */ 360 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 361 reallocs++; 362 } 363 364 /* copy data into free space, then initialize lnk */ 365 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 366 bi_ptr[i] = current_space->array; 367 current_space->array += nzi; 368 current_space->local_used += nzi; 369 current_space->local_remaining -= nzi; 370 } 371 #if defined(PETSC_USE_INFO) 372 if (ai[n] != 0) { 373 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 374 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 375 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 376 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr); 377 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 378 } else { 379 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 380 } 381 #endif 382 383 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 384 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 385 386 /* destroy list of free space and other temporary array(s) */ 387 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 388 ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 389 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 390 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 391 392 /* put together the new matrix */ 393 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 394 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 395 b = (Mat_SeqAIJ*)(B)->data; 396 b->free_a = PETSC_TRUE; 397 b->free_ij = PETSC_TRUE; 398 b->singlemalloc = PETSC_FALSE; 399 ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 400 b->j = bj; 401 b->i = bi; 402 b->diag = bdiag; 403 b->ilen = 0; 404 b->imax = 0; 405 b->row = isrow; 406 b->col = iscol; 407 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 408 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 409 b->icol = isicol; 410 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 411 412 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 413 ierr = PetscLogObjectMemory(B,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 414 b->maxnz = b->nz = bdiag[0]+1; 415 B->factor = MAT_FACTOR_LU; 416 B->info.factor_mallocs = reallocs; 417 B->info.fill_ratio_given = f; 418 419 if (ai[n]) { 420 B->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 421 } else { 422 B->info.fill_ratio_needed = 0.0; 423 } 424 B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 425 if (a->inode.size) { 426 B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode; 427 } 428 PetscFunctionReturn(0); 429 } 430 431 /* 432 Trouble in factorization, should we dump the original matrix? 433 */ 434 #undef __FUNCT__ 435 #define __FUNCT__ "MatFactorDumpMatrix" 436 PetscErrorCode MatFactorDumpMatrix(Mat A) 437 { 438 PetscErrorCode ierr; 439 PetscTruth flg = PETSC_FALSE; 440 441 PetscFunctionBegin; 442 ierr = PetscOptionsGetTruth(PETSC_NULL,"-mat_factor_dump_on_error",&flg,PETSC_NULL);CHKERRQ(ierr); 443 if (flg) { 444 PetscViewer viewer; 445 char filename[PETSC_MAX_PATH_LEN]; 446 447 ierr = PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);CHKERRQ(ierr); 448 ierr = PetscViewerBinaryOpen(((PetscObject)A)->comm,filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr); 449 ierr = MatView(A,viewer);CHKERRQ(ierr); 450 ierr = PetscViewerDestroy(viewer);CHKERRQ(ierr); 451 } 452 PetscFunctionReturn(0); 453 } 454 455 #undef __FUNCT__ 456 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ" 457 PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 458 { 459 Mat C=B; 460 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 461 IS isrow = b->row,isicol = b->icol; 462 PetscErrorCode ierr; 463 const PetscInt *r,*ic,*ics; 464 const PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bdiag=b->diag; 465 PetscInt i,j,k,nz,nzL,row,*pj; 466 const PetscInt *ajtmp,*bjtmp; 467 MatScalar *rtmp,*pc,multiplier,*pv; 468 const MatScalar *aa=a->a,*v; 469 PetscTruth row_identity,col_identity; 470 FactorShiftCtx sctx; 471 const PetscInt *ddiag; 472 PetscReal rs; 473 MatScalar d; 474 475 PetscFunctionBegin; 476 /* MatPivotSetUp(): initialize shift context sctx */ 477 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 478 479 if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 480 ddiag = a->diag; 481 sctx.shift_top = info->zeropivot; 482 for (i=0; i<n; i++) { 483 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 484 d = (aa)[ddiag[i]]; 485 rs = -PetscAbsScalar(d) - PetscRealPart(d); 486 v = aa+ai[i]; 487 nz = ai[i+1] - ai[i]; 488 for (j=0; j<nz; j++) 489 rs += PetscAbsScalar(v[j]); 490 if (rs>sctx.shift_top) sctx.shift_top = rs; 491 } 492 sctx.shift_top *= 1.1; 493 sctx.nshift_max = 5; 494 sctx.shift_lo = 0.; 495 sctx.shift_hi = 1.; 496 } 497 498 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 499 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 500 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 501 ics = ic; 502 503 do { 504 sctx.useshift = PETSC_FALSE; 505 for (i=0; i<n; i++){ 506 /* zero rtmp */ 507 /* L part */ 508 nz = bi[i+1] - bi[i]; 509 bjtmp = bj + bi[i]; 510 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 511 512 /* U part */ 513 nz = bdiag[i]-bdiag[i+1]; 514 bjtmp = bj + bdiag[i+1]+1; 515 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 516 517 /* load in initial (unfactored row) */ 518 nz = ai[r[i]+1] - ai[r[i]]; 519 ajtmp = aj + ai[r[i]]; 520 v = aa + ai[r[i]]; 521 for (j=0; j<nz; j++) { 522 rtmp[ics[ajtmp[j]]] = v[j]; 523 } 524 /* ZeropivotApply() */ 525 rtmp[i] += sctx.shift_amount; /* shift the diagonal of the matrix */ 526 527 /* elimination */ 528 bjtmp = bj + bi[i]; 529 row = *bjtmp++; 530 nzL = bi[i+1] - bi[i]; 531 for(k=0; k < nzL;k++) { 532 pc = rtmp + row; 533 if (*pc != 0.0) { 534 pv = b->a + bdiag[row]; 535 multiplier = *pc * (*pv); 536 *pc = multiplier; 537 pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */ 538 pv = b->a + bdiag[row+1]+1; 539 nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */ 540 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 541 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 542 } 543 row = *bjtmp++; 544 } 545 546 /* finished row so stick it into b->a */ 547 rs = 0.0; 548 /* L part */ 549 pv = b->a + bi[i] ; 550 pj = b->j + bi[i] ; 551 nz = bi[i+1] - bi[i]; 552 for (j=0; j<nz; j++) { 553 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 554 } 555 556 /* U part */ 557 pv = b->a + bdiag[i+1]+1; 558 pj = b->j + bdiag[i+1]+1; 559 nz = bdiag[i] - bdiag[i+1]-1; 560 for (j=0; j<nz; j++) { 561 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 562 } 563 564 /* MatPivotCheck() */ 565 sctx.rs = rs; 566 sctx.pv = rtmp[i]; 567 if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO){ 568 ierr = MatPivotCheck_nz(info,sctx,i);CHKERRQ(ierr); 569 } else if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE){ 570 ierr = MatPivotCheck_pd(info,sctx,i);CHKERRQ(ierr); 571 } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS){ 572 ierr = MatPivotCheck_inblocks(info,sctx,i);CHKERRQ(ierr); 573 } else { 574 ierr = MatPivotCheck_none(info,sctx,i);CHKERRQ(ierr); 575 } 576 rtmp[i] = sctx.pv; 577 578 /* Mark diagonal and invert diagonal for simplier triangular solves */ 579 pv = b->a + bdiag[i]; 580 *pv = 1.0/rtmp[i]; 581 582 } /* endof for (i=0; i<n; i++){ */ 583 584 /* MatPivotRefine() */ 585 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.useshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max){ 586 /* 587 * if no shift in this attempt & shifting & started shifting & can refine, 588 * then try lower shift 589 */ 590 sctx.shift_hi = sctx.shift_fraction; 591 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 592 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 593 sctx.useshift = PETSC_TRUE; 594 sctx.nshift++; 595 } 596 } while (sctx.useshift); 597 598 ierr = PetscFree(rtmp);CHKERRQ(ierr); 599 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 600 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 601 602 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 603 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 604 if (row_identity && col_identity) { 605 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 606 } else { 607 C->ops->solve = MatSolve_SeqAIJ; 608 } 609 C->ops->solveadd = MatSolveAdd_SeqAIJ; 610 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 611 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 612 C->ops->matsolve = MatMatSolve_SeqAIJ; 613 C->assembled = PETSC_TRUE; 614 C->preallocated = PETSC_TRUE; 615 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 616 617 /* MatShiftView(A,info,&sctx) */ 618 if (sctx.nshift){ 619 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 620 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); 621 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 622 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 623 } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS){ 624 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftamount);CHKERRQ(ierr); 625 } 626 } 627 ierr = Mat_CheckInode_FactorLU(C,PETSC_FALSE);CHKERRQ(ierr); 628 PetscFunctionReturn(0); 629 } 630 631 #undef __FUNCT__ 632 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_inplace" 633 PetscErrorCode MatLUFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info) 634 { 635 Mat C=B; 636 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 637 IS isrow = b->row,isicol = b->icol; 638 PetscErrorCode ierr; 639 const PetscInt *r,*ic,*ics; 640 PetscInt nz,row,i,j,n=A->rmap->n,diag; 641 const PetscInt *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 642 const PetscInt *ajtmp,*bjtmp,*diag_offset = b->diag,*pj; 643 MatScalar *pv,*rtmp,*pc,multiplier,d; 644 const MatScalar *v,*aa=a->a; 645 PetscReal rs=0.0; 646 FactorShiftCtx sctx; 647 PetscInt newshift; 648 const PetscInt *ddiag; 649 PetscTruth row_identity, col_identity; 650 651 PetscFunctionBegin; 652 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 653 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 654 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 655 ics = ic; 656 657 /* initialize shift context sctx */ 658 sctx.nshift = 0; 659 sctx.nshift_max = 0; 660 sctx.shift_top = 0.0; 661 sctx.shift_lo = 0.0; 662 sctx.shift_hi = 0.0; 663 sctx.shift_fraction = 0.0; 664 sctx.shift_amount = 0.0; 665 666 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 667 ddiag = a->diag; 668 sctx.shift_top = info->zeropivot; 669 for (i=0; i<n; i++) { 670 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 671 d = (aa)[ddiag[i]]; 672 rs = -PetscAbsScalar(d) - PetscRealPart(d); 673 v = aa+ai[i]; 674 nz = ai[i+1] - ai[i]; 675 for (j=0; j<nz; j++) 676 rs += PetscAbsScalar(v[j]); 677 if (rs>sctx.shift_top) sctx.shift_top = rs; 678 } 679 sctx.shift_top *= 1.1; 680 sctx.nshift_max = 5; 681 sctx.shift_lo = 0.; 682 sctx.shift_hi = 1.; 683 } 684 685 do { 686 sctx.useshift = PETSC_FALSE; 687 for (i=0; i<n; i++){ 688 nz = bi[i+1] - bi[i]; 689 bjtmp = bj + bi[i]; 690 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 691 692 /* load in initial (unfactored row) */ 693 nz = ai[r[i]+1] - ai[r[i]]; 694 ajtmp = aj + ai[r[i]]; 695 v = aa + ai[r[i]]; 696 for (j=0; j<nz; j++) { 697 rtmp[ics[ajtmp[j]]] = v[j]; 698 } 699 rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 700 /* if (sctx.shift_amount > 0.0) printf("row %d, shift %g\n",i,sctx.shift_amount); */ 701 702 row = *bjtmp++; 703 while (row < i) { 704 pc = rtmp + row; 705 if (*pc != 0.0) { 706 pv = b->a + diag_offset[row]; 707 pj = b->j + diag_offset[row] + 1; 708 multiplier = *pc / *pv++; 709 *pc = multiplier; 710 nz = bi[row+1] - diag_offset[row] - 1; 711 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 712 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 713 } 714 row = *bjtmp++; 715 } 716 /* finished row so stick it into b->a */ 717 pv = b->a + bi[i] ; 718 pj = b->j + bi[i] ; 719 nz = bi[i+1] - bi[i]; 720 diag = diag_offset[i] - bi[i]; 721 rs = 0.0; 722 for (j=0; j<nz; j++) { 723 pv[j] = rtmp[pj[j]]; 724 rs += PetscAbsScalar(pv[j]); 725 } 726 rs -= PetscAbsScalar(pv[diag]); 727 728 /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */ 729 sctx.rs = rs; 730 sctx.pv = pv[diag]; 731 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 732 if (newshift == 1) break; 733 } 734 735 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.useshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 736 /* 737 * if no shift in this attempt & shifting & started shifting & can refine, 738 * then try lower shift 739 */ 740 sctx.shift_hi = sctx.shift_fraction; 741 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 742 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 743 sctx.useshift = PETSC_TRUE; 744 sctx.nshift++; 745 } 746 } while (sctx.useshift); 747 748 /* invert diagonal entries for simplier triangular solves */ 749 for (i=0; i<n; i++) { 750 b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]]; 751 } 752 ierr = PetscFree(rtmp);CHKERRQ(ierr); 753 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 754 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 755 756 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 757 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 758 if (row_identity && col_identity) { 759 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_inplace; 760 } else { 761 C->ops->solve = MatSolve_SeqAIJ_inplace; 762 } 763 C->ops->solveadd = MatSolveAdd_SeqAIJ_inplace; 764 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace; 765 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace; 766 C->ops->matsolve = MatMatSolve_SeqAIJ_inplace; 767 C->assembled = PETSC_TRUE; 768 C->preallocated = PETSC_TRUE; 769 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 770 if (sctx.nshift){ 771 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 772 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); 773 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 774 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 775 } 776 } 777 (C)->ops->solve = MatSolve_SeqAIJ_inplace; 778 (C)->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace; 779 ierr = Mat_CheckInode(C,PETSC_FALSE);CHKERRQ(ierr); 780 PetscFunctionReturn(0); 781 } 782 783 /* 784 This routine implements inplace ILU(0) with row or/and column permutations. 785 Input: 786 A - original matrix 787 Output; 788 A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i] 789 a->j (col index) is permuted by the inverse of colperm, then sorted 790 a->a reordered accordingly with a->j 791 a->diag (ptr to diagonal elements) is updated. 792 */ 793 #undef __FUNCT__ 794 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_InplaceWithPerm" 795 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info) 796 { 797 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 798 IS isrow = a->row,isicol = a->icol; 799 PetscErrorCode ierr; 800 const PetscInt *r,*ic,*ics; 801 PetscInt i,j,n=A->rmap->n,*ai=a->i,*aj=a->j; 802 PetscInt *ajtmp,nz,row; 803 PetscInt *diag = a->diag,nbdiag,*pj; 804 PetscScalar *rtmp,*pc,multiplier,d; 805 MatScalar *v,*pv; 806 PetscReal rs; 807 FactorShiftCtx sctx; 808 PetscInt newshift; 809 810 PetscFunctionBegin; 811 if (A != B) SETERRQ(PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address"); 812 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 813 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 814 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&rtmp);CHKERRQ(ierr); 815 ierr = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr); 816 ics = ic; 817 818 sctx.shift_top = 0.; 819 sctx.nshift_max = 0; 820 sctx.shift_lo = 0.; 821 sctx.shift_hi = 0.; 822 sctx.shift_fraction = 0.; 823 824 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 825 sctx.shift_top = 0.; 826 for (i=0; i<n; i++) { 827 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 828 d = (a->a)[diag[i]]; 829 rs = -PetscAbsScalar(d) - PetscRealPart(d); 830 v = a->a+ai[i]; 831 nz = ai[i+1] - ai[i]; 832 for (j=0; j<nz; j++) 833 rs += PetscAbsScalar(v[j]); 834 if (rs>sctx.shift_top) sctx.shift_top = rs; 835 } 836 if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot; 837 sctx.shift_top *= 1.1; 838 sctx.nshift_max = 5; 839 sctx.shift_lo = 0.; 840 sctx.shift_hi = 1.; 841 } 842 843 sctx.shift_amount = 0.; 844 sctx.nshift = 0; 845 do { 846 sctx.useshift = PETSC_FALSE; 847 for (i=0; i<n; i++){ 848 /* load in initial unfactored row */ 849 nz = ai[r[i]+1] - ai[r[i]]; 850 ajtmp = aj + ai[r[i]]; 851 v = a->a + ai[r[i]]; 852 /* sort permuted ajtmp and values v accordingly */ 853 for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]]; 854 ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr); 855 856 diag[r[i]] = ai[r[i]]; 857 for (j=0; j<nz; j++) { 858 rtmp[ajtmp[j]] = v[j]; 859 if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */ 860 } 861 rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 862 863 row = *ajtmp++; 864 while (row < i) { 865 pc = rtmp + row; 866 if (*pc != 0.0) { 867 pv = a->a + diag[r[row]]; 868 pj = aj + diag[r[row]] + 1; 869 870 multiplier = *pc / *pv++; 871 *pc = multiplier; 872 nz = ai[r[row]+1] - diag[r[row]] - 1; 873 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 874 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 875 } 876 row = *ajtmp++; 877 } 878 /* finished row so overwrite it onto a->a */ 879 pv = a->a + ai[r[i]] ; 880 pj = aj + ai[r[i]] ; 881 nz = ai[r[i]+1] - ai[r[i]]; 882 nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */ 883 884 rs = 0.0; 885 for (j=0; j<nz; j++) { 886 pv[j] = rtmp[pj[j]]; 887 if (j != nbdiag) rs += PetscAbsScalar(pv[j]); 888 } 889 890 /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */ 891 sctx.rs = rs; 892 sctx.pv = pv[nbdiag]; 893 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 894 if (newshift == 1) break; 895 } 896 897 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.useshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 898 /* 899 * if no shift in this attempt & shifting & started shifting & can refine, 900 * then try lower shift 901 */ 902 sctx.shift_hi = sctx.shift_fraction; 903 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 904 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 905 sctx.useshift = PETSC_TRUE; 906 sctx.nshift++; 907 } 908 } while (sctx.useshift); 909 910 /* invert diagonal entries for simplier triangular solves */ 911 for (i=0; i<n; i++) { 912 a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]]; 913 } 914 915 ierr = PetscFree(rtmp);CHKERRQ(ierr); 916 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 917 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 918 A->ops->solve = MatSolve_SeqAIJ_InplaceWithPerm; 919 A->ops->solveadd = MatSolveAdd_SeqAIJ_inplace; 920 A->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace; 921 A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace; 922 A->assembled = PETSC_TRUE; 923 A->preallocated = PETSC_TRUE; 924 ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr); 925 if (sctx.nshift){ 926 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 927 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); 928 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 929 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 930 } 931 } 932 PetscFunctionReturn(0); 933 } 934 935 /* ----------------------------------------------------------- */ 936 #undef __FUNCT__ 937 #define __FUNCT__ "MatLUFactor_SeqAIJ" 938 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info) 939 { 940 PetscErrorCode ierr; 941 Mat C; 942 943 PetscFunctionBegin; 944 ierr = MatGetFactor(A,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr); 945 ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr); 946 ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr); 947 A->ops->solve = C->ops->solve; 948 A->ops->solvetranspose = C->ops->solvetranspose; 949 ierr = MatHeaderCopy(A,C);CHKERRQ(ierr); 950 ierr = PetscLogObjectParent(A,((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr); 951 PetscFunctionReturn(0); 952 } 953 /* ----------------------------------------------------------- */ 954 955 956 #undef __FUNCT__ 957 #define __FUNCT__ "MatSolve_SeqAIJ_inplace" 958 PetscErrorCode MatSolve_SeqAIJ_inplace(Mat A,Vec bb,Vec xx) 959 { 960 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 961 IS iscol = a->col,isrow = a->row; 962 PetscErrorCode ierr; 963 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 964 PetscInt nz; 965 const PetscInt *rout,*cout,*r,*c; 966 PetscScalar *x,*tmp,*tmps,sum; 967 const PetscScalar *b; 968 const MatScalar *aa = a->a,*v; 969 970 PetscFunctionBegin; 971 if (!n) PetscFunctionReturn(0); 972 973 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 974 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 975 tmp = a->solve_work; 976 977 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 978 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 979 980 /* forward solve the lower triangular */ 981 tmp[0] = b[*r++]; 982 tmps = tmp; 983 for (i=1; i<n; i++) { 984 v = aa + ai[i] ; 985 vi = aj + ai[i] ; 986 nz = a->diag[i] - ai[i]; 987 sum = b[*r++]; 988 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 989 tmp[i] = sum; 990 } 991 992 /* backward solve the upper triangular */ 993 for (i=n-1; i>=0; i--){ 994 v = aa + a->diag[i] + 1; 995 vi = aj + a->diag[i] + 1; 996 nz = ai[i+1] - a->diag[i] - 1; 997 sum = tmp[i]; 998 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 999 x[*c--] = tmp[i] = sum*aa[a->diag[i]]; 1000 } 1001 1002 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1003 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1004 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1005 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1006 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1007 PetscFunctionReturn(0); 1008 } 1009 1010 #undef __FUNCT__ 1011 #define __FUNCT__ "MatMatSolve_SeqAIJ_inplace" 1012 PetscErrorCode MatMatSolve_SeqAIJ_inplace(Mat A,Mat B,Mat X) 1013 { 1014 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1015 IS iscol = a->col,isrow = a->row; 1016 PetscErrorCode ierr; 1017 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1018 PetscInt nz,neq; 1019 const PetscInt *rout,*cout,*r,*c; 1020 PetscScalar *x,*b,*tmp,*tmps,sum; 1021 const MatScalar *aa = a->a,*v; 1022 PetscTruth bisdense,xisdense; 1023 1024 PetscFunctionBegin; 1025 if (!n) PetscFunctionReturn(0); 1026 1027 ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr); 1028 if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 1029 ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr); 1030 if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 1031 1032 ierr = MatGetArray(B,&b);CHKERRQ(ierr); 1033 ierr = MatGetArray(X,&x);CHKERRQ(ierr); 1034 1035 tmp = a->solve_work; 1036 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1037 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1038 1039 for (neq=0; neq<B->cmap->n; neq++){ 1040 /* forward solve the lower triangular */ 1041 tmp[0] = b[r[0]]; 1042 tmps = tmp; 1043 for (i=1; i<n; i++) { 1044 v = aa + ai[i] ; 1045 vi = aj + ai[i] ; 1046 nz = a->diag[i] - ai[i]; 1047 sum = b[r[i]]; 1048 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1049 tmp[i] = sum; 1050 } 1051 /* backward solve the upper triangular */ 1052 for (i=n-1; i>=0; i--){ 1053 v = aa + a->diag[i] + 1; 1054 vi = aj + a->diag[i] + 1; 1055 nz = ai[i+1] - a->diag[i] - 1; 1056 sum = tmp[i]; 1057 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1058 x[c[i]] = tmp[i] = sum*aa[a->diag[i]]; 1059 } 1060 1061 b += n; 1062 x += n; 1063 } 1064 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1065 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1066 ierr = MatRestoreArray(B,&b);CHKERRQ(ierr); 1067 ierr = MatRestoreArray(X,&x);CHKERRQ(ierr); 1068 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 1069 PetscFunctionReturn(0); 1070 } 1071 1072 #undef __FUNCT__ 1073 #define __FUNCT__ "MatMatSolve_SeqAIJ" 1074 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X) 1075 { 1076 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1077 IS iscol = a->col,isrow = a->row; 1078 PetscErrorCode ierr; 1079 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag; 1080 PetscInt nz,neq; 1081 const PetscInt *rout,*cout,*r,*c; 1082 PetscScalar *x,*b,*tmp,sum; 1083 const MatScalar *aa = a->a,*v; 1084 PetscTruth bisdense,xisdense; 1085 1086 PetscFunctionBegin; 1087 if (!n) PetscFunctionReturn(0); 1088 1089 ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr); 1090 if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 1091 ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr); 1092 if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 1093 1094 ierr = MatGetArray(B,&b);CHKERRQ(ierr); 1095 ierr = MatGetArray(X,&x);CHKERRQ(ierr); 1096 1097 tmp = a->solve_work; 1098 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1099 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1100 1101 for (neq=0; neq<B->cmap->n; neq++){ 1102 /* forward solve the lower triangular */ 1103 tmp[0] = b[r[0]]; 1104 v = aa; 1105 vi = aj; 1106 for (i=1; i<n; i++) { 1107 nz = ai[i+1] - ai[i]; 1108 sum = b[r[i]]; 1109 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 1110 tmp[i] = sum; 1111 v += nz; vi += nz; 1112 } 1113 1114 /* backward solve the upper triangular */ 1115 for (i=n-1; i>=0; i--){ 1116 v = aa + adiag[i+1]+1; 1117 vi = aj + adiag[i+1]+1; 1118 nz = adiag[i]-adiag[i+1]-1; 1119 sum = tmp[i]; 1120 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 1121 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 1122 } 1123 1124 b += n; 1125 x += n; 1126 } 1127 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1128 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1129 ierr = MatRestoreArray(B,&b);CHKERRQ(ierr); 1130 ierr = MatRestoreArray(X,&x);CHKERRQ(ierr); 1131 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 1132 PetscFunctionReturn(0); 1133 } 1134 1135 #undef __FUNCT__ 1136 #define __FUNCT__ "MatSolve_SeqAIJ_InplaceWithPerm" 1137 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx) 1138 { 1139 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1140 IS iscol = a->col,isrow = a->row; 1141 PetscErrorCode ierr; 1142 const PetscInt *r,*c,*rout,*cout; 1143 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1144 PetscInt nz,row; 1145 PetscScalar *x,*b,*tmp,*tmps,sum; 1146 const MatScalar *aa = a->a,*v; 1147 1148 PetscFunctionBegin; 1149 if (!n) PetscFunctionReturn(0); 1150 1151 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1152 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1153 tmp = a->solve_work; 1154 1155 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1156 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1157 1158 /* forward solve the lower triangular */ 1159 tmp[0] = b[*r++]; 1160 tmps = tmp; 1161 for (row=1; row<n; row++) { 1162 i = rout[row]; /* permuted row */ 1163 v = aa + ai[i] ; 1164 vi = aj + ai[i] ; 1165 nz = a->diag[i] - ai[i]; 1166 sum = b[*r++]; 1167 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1168 tmp[row] = sum; 1169 } 1170 1171 /* backward solve the upper triangular */ 1172 for (row=n-1; row>=0; row--){ 1173 i = rout[row]; /* permuted row */ 1174 v = aa + a->diag[i] + 1; 1175 vi = aj + a->diag[i] + 1; 1176 nz = ai[i+1] - a->diag[i] - 1; 1177 sum = tmp[row]; 1178 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1179 x[*c--] = tmp[row] = sum*aa[a->diag[i]]; 1180 } 1181 1182 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1183 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1184 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1185 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1186 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1187 PetscFunctionReturn(0); 1188 } 1189 1190 /* ----------------------------------------------------------- */ 1191 #include "../src/mat/impls/aij/seq/ftn-kernels/fsolve.h" 1192 #undef __FUNCT__ 1193 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_inplace" 1194 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_inplace(Mat A,Vec bb,Vec xx) 1195 { 1196 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1197 PetscErrorCode ierr; 1198 PetscInt n = A->rmap->n; 1199 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag; 1200 PetscScalar *x; 1201 const PetscScalar *b; 1202 const MatScalar *aa = a->a; 1203 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1204 PetscInt adiag_i,i,nz,ai_i; 1205 const PetscInt *vi; 1206 const MatScalar *v; 1207 PetscScalar sum; 1208 #endif 1209 1210 PetscFunctionBegin; 1211 if (!n) PetscFunctionReturn(0); 1212 1213 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1214 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1215 1216 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1217 fortransolveaij_(&n,x,ai,aj,adiag,aa,b); 1218 #else 1219 /* forward solve the lower triangular */ 1220 x[0] = b[0]; 1221 for (i=1; i<n; i++) { 1222 ai_i = ai[i]; 1223 v = aa + ai_i; 1224 vi = aj + ai_i; 1225 nz = adiag[i] - ai_i; 1226 sum = b[i]; 1227 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1228 x[i] = sum; 1229 } 1230 1231 /* backward solve the upper triangular */ 1232 for (i=n-1; i>=0; i--){ 1233 adiag_i = adiag[i]; 1234 v = aa + adiag_i + 1; 1235 vi = aj + adiag_i + 1; 1236 nz = ai[i+1] - adiag_i - 1; 1237 sum = x[i]; 1238 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1239 x[i] = sum*aa[adiag_i]; 1240 } 1241 #endif 1242 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1243 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1244 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1245 PetscFunctionReturn(0); 1246 } 1247 1248 #undef __FUNCT__ 1249 #define __FUNCT__ "MatSolveAdd_SeqAIJ_inplace" 1250 PetscErrorCode MatSolveAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec yy,Vec xx) 1251 { 1252 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1253 IS iscol = a->col,isrow = a->row; 1254 PetscErrorCode ierr; 1255 PetscInt i, n = A->rmap->n,j; 1256 PetscInt nz; 1257 const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j; 1258 PetscScalar *x,*tmp,sum; 1259 const PetscScalar *b; 1260 const MatScalar *aa = a->a,*v; 1261 1262 PetscFunctionBegin; 1263 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 1264 1265 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1266 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1267 tmp = a->solve_work; 1268 1269 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1270 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1271 1272 /* forward solve the lower triangular */ 1273 tmp[0] = b[*r++]; 1274 for (i=1; i<n; i++) { 1275 v = aa + ai[i] ; 1276 vi = aj + ai[i] ; 1277 nz = a->diag[i] - ai[i]; 1278 sum = b[*r++]; 1279 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1280 tmp[i] = sum; 1281 } 1282 1283 /* backward solve the upper triangular */ 1284 for (i=n-1; i>=0; i--){ 1285 v = aa + a->diag[i] + 1; 1286 vi = aj + a->diag[i] + 1; 1287 nz = ai[i+1] - a->diag[i] - 1; 1288 sum = tmp[i]; 1289 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1290 tmp[i] = sum*aa[a->diag[i]]; 1291 x[*c--] += tmp[i]; 1292 } 1293 1294 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1295 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1296 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1297 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1298 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1299 1300 PetscFunctionReturn(0); 1301 } 1302 1303 #undef __FUNCT__ 1304 #define __FUNCT__ "MatSolveAdd_SeqAIJ" 1305 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx) 1306 { 1307 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1308 IS iscol = a->col,isrow = a->row; 1309 PetscErrorCode ierr; 1310 PetscInt i, n = A->rmap->n,j; 1311 PetscInt nz; 1312 const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag; 1313 PetscScalar *x,*tmp,sum; 1314 const PetscScalar *b; 1315 const MatScalar *aa = a->a,*v; 1316 1317 PetscFunctionBegin; 1318 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 1319 1320 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1321 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1322 tmp = a->solve_work; 1323 1324 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1325 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1326 1327 /* forward solve the lower triangular */ 1328 tmp[0] = b[r[0]]; 1329 v = aa; 1330 vi = aj; 1331 for (i=1; i<n; i++) { 1332 nz = ai[i+1] - ai[i]; 1333 sum = b[r[i]]; 1334 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1335 tmp[i] = sum; 1336 v += nz; vi += nz; 1337 } 1338 1339 /* backward solve the upper triangular */ 1340 v = aa + adiag[n-1]; 1341 vi = aj + adiag[n-1]; 1342 for (i=n-1; i>=0; i--){ 1343 nz = adiag[i] - adiag[i+1] - 1; 1344 sum = tmp[i]; 1345 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1346 tmp[i] = sum*v[nz]; 1347 x[c[i]] += tmp[i]; 1348 v += nz+1; vi += nz+1; 1349 } 1350 1351 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1352 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1353 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1354 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1355 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1356 1357 PetscFunctionReturn(0); 1358 } 1359 1360 #undef __FUNCT__ 1361 #define __FUNCT__ "MatSolveTranspose_SeqAIJ_inplace" 1362 PetscErrorCode MatSolveTranspose_SeqAIJ_inplace(Mat A,Vec bb,Vec xx) 1363 { 1364 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1365 IS iscol = a->col,isrow = a->row; 1366 PetscErrorCode ierr; 1367 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1368 PetscInt i,n = A->rmap->n,j; 1369 PetscInt nz; 1370 PetscScalar *x,*tmp,s1; 1371 const MatScalar *aa = a->a,*v; 1372 const PetscScalar *b; 1373 1374 PetscFunctionBegin; 1375 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1376 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1377 tmp = a->solve_work; 1378 1379 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1380 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1381 1382 /* copy the b into temp work space according to permutation */ 1383 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1384 1385 /* forward solve the U^T */ 1386 for (i=0; i<n; i++) { 1387 v = aa + diag[i] ; 1388 vi = aj + diag[i] + 1; 1389 nz = ai[i+1] - diag[i] - 1; 1390 s1 = tmp[i]; 1391 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1392 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1393 tmp[i] = s1; 1394 } 1395 1396 /* backward solve the L^T */ 1397 for (i=n-1; i>=0; i--){ 1398 v = aa + diag[i] - 1 ; 1399 vi = aj + diag[i] - 1 ; 1400 nz = diag[i] - ai[i]; 1401 s1 = tmp[i]; 1402 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1403 } 1404 1405 /* copy tmp into x according to permutation */ 1406 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1407 1408 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1409 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1410 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1411 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1412 1413 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1414 PetscFunctionReturn(0); 1415 } 1416 1417 #undef __FUNCT__ 1418 #define __FUNCT__ "MatSolveTranspose_SeqAIJ" 1419 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx) 1420 { 1421 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1422 IS iscol = a->col,isrow = a->row; 1423 PetscErrorCode ierr; 1424 const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi; 1425 PetscInt i,n = A->rmap->n,j; 1426 PetscInt nz; 1427 PetscScalar *x,*tmp,s1; 1428 const MatScalar *aa = a->a,*v; 1429 const PetscScalar *b; 1430 1431 PetscFunctionBegin; 1432 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1433 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1434 tmp = a->solve_work; 1435 1436 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1437 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1438 1439 /* copy the b into temp work space according to permutation */ 1440 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1441 1442 /* forward solve the U^T */ 1443 for (i=0; i<n; i++) { 1444 v = aa + adiag[i+1] + 1; 1445 vi = aj + adiag[i+1] + 1; 1446 nz = adiag[i] - adiag[i+1] - 1; 1447 s1 = tmp[i]; 1448 s1 *= v[nz]; /* multiply by inverse of diagonal entry */ 1449 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1450 tmp[i] = s1; 1451 } 1452 1453 /* backward solve the L^T */ 1454 for (i=n-1; i>=0; i--){ 1455 v = aa + ai[i]; 1456 vi = aj + ai[i]; 1457 nz = ai[i+1] - ai[i]; 1458 s1 = tmp[i]; 1459 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1460 } 1461 1462 /* copy tmp into x according to permutation */ 1463 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1464 1465 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1466 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1467 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1468 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1469 1470 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1471 PetscFunctionReturn(0); 1472 } 1473 1474 #undef __FUNCT__ 1475 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ_inplace" 1476 PetscErrorCode MatSolveTransposeAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec zz,Vec xx) 1477 { 1478 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1479 IS iscol = a->col,isrow = a->row; 1480 PetscErrorCode ierr; 1481 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1482 PetscInt i,n = A->rmap->n,j; 1483 PetscInt nz; 1484 PetscScalar *x,*tmp,s1; 1485 const MatScalar *aa = a->a,*v; 1486 const PetscScalar *b; 1487 1488 PetscFunctionBegin; 1489 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1490 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1491 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1492 tmp = a->solve_work; 1493 1494 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1495 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1496 1497 /* copy the b into temp work space according to permutation */ 1498 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1499 1500 /* forward solve the U^T */ 1501 for (i=0; i<n; i++) { 1502 v = aa + diag[i] ; 1503 vi = aj + diag[i] + 1; 1504 nz = ai[i+1] - diag[i] - 1; 1505 s1 = tmp[i]; 1506 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1507 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1508 tmp[i] = s1; 1509 } 1510 1511 /* backward solve the L^T */ 1512 for (i=n-1; i>=0; i--){ 1513 v = aa + diag[i] - 1 ; 1514 vi = aj + diag[i] - 1 ; 1515 nz = diag[i] - ai[i]; 1516 s1 = tmp[i]; 1517 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1518 } 1519 1520 /* copy tmp into x according to permutation */ 1521 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1522 1523 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1524 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1525 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1526 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1527 1528 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1529 PetscFunctionReturn(0); 1530 } 1531 1532 #undef __FUNCT__ 1533 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ" 1534 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx) 1535 { 1536 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1537 IS iscol = a->col,isrow = a->row; 1538 PetscErrorCode ierr; 1539 const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi; 1540 PetscInt i,n = A->rmap->n,j; 1541 PetscInt nz; 1542 PetscScalar *x,*tmp,s1; 1543 const MatScalar *aa = a->a,*v; 1544 const PetscScalar *b; 1545 1546 PetscFunctionBegin; 1547 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1548 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1549 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1550 tmp = a->solve_work; 1551 1552 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1553 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1554 1555 /* copy the b into temp work space according to permutation */ 1556 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1557 1558 /* forward solve the U^T */ 1559 for (i=0; i<n; i++) { 1560 v = aa + adiag[i+1] + 1; 1561 vi = aj + adiag[i+1] + 1; 1562 nz = adiag[i] - adiag[i+1] - 1; 1563 s1 = tmp[i]; 1564 s1 *= v[nz]; /* multiply by inverse of diagonal entry */ 1565 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1566 tmp[i] = s1; 1567 } 1568 1569 1570 /* backward solve the L^T */ 1571 for (i=n-1; i>=0; i--){ 1572 v = aa + ai[i] ; 1573 vi = aj + ai[i]; 1574 nz = ai[i+1] - ai[i]; 1575 s1 = tmp[i]; 1576 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1577 } 1578 1579 /* copy tmp into x according to permutation */ 1580 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1581 1582 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1583 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1584 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1585 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1586 1587 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1588 PetscFunctionReturn(0); 1589 } 1590 1591 /* ----------------------------------------------------------------*/ 1592 1593 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth); 1594 1595 /* 1596 ilu() under revised new data structure. 1597 Factored arrays bj and ba are stored as 1598 L(0,:), L(1,:), ...,L(n-1,:), U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:) 1599 1600 bi=fact->i is an array of size n+1, in which 1601 bi+ 1602 bi[i]: points to 1st entry of L(i,:),i=0,...,n-1 1603 bi[n]: points to L(n-1,n-1)+1 1604 1605 bdiag=fact->diag is an array of size n+1,in which 1606 bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1 1607 bdiag[n]: points to entry of U(n-1,0)-1 1608 1609 U(i,:) contains bdiag[i] as its last entry, i.e., 1610 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 1611 */ 1612 #undef __FUNCT__ 1613 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0" 1614 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1615 { 1616 1617 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1618 PetscErrorCode ierr; 1619 const PetscInt n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag; 1620 PetscInt i,j,k=0,nz,*bi,*bj,*bdiag; 1621 PetscTruth missing; 1622 IS isicol; 1623 1624 PetscFunctionBegin; 1625 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); 1626 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 1627 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 1628 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1629 1630 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr); 1631 b = (Mat_SeqAIJ*)(fact)->data; 1632 1633 /* allocate matrix arrays for new data structure */ 1634 ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,n+1,PetscInt,&b->i);CHKERRQ(ierr); 1635 ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1636 b->singlemalloc = PETSC_TRUE; 1637 if (!b->diag){ 1638 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr); 1639 ierr = PetscLogObjectMemory(fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1640 } 1641 bdiag = b->diag; 1642 1643 if (n > 0) { 1644 ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr); 1645 } 1646 1647 /* set bi and bj with new data structure */ 1648 bi = b->i; 1649 bj = b->j; 1650 1651 /* L part */ 1652 bi[0] = 0; 1653 for (i=0; i<n; i++){ 1654 nz = adiag[i] - ai[i]; 1655 bi[i+1] = bi[i] + nz; 1656 aj = a->j + ai[i]; 1657 for (j=0; j<nz; j++){ 1658 /* *bj = aj[j]; bj++; */ 1659 bj[k++] = aj[j]; 1660 } 1661 } 1662 1663 /* U part */ 1664 bdiag[n] = bi[n]-1; 1665 for (i=n-1; i>=0; i--){ 1666 nz = ai[i+1] - adiag[i] - 1; 1667 aj = a->j + adiag[i] + 1; 1668 for (j=0; j<nz; j++){ 1669 /* *bj = aj[j]; bj++; */ 1670 bj[k++] = aj[j]; 1671 } 1672 /* diag[i] */ 1673 /* *bj = i; bj++; */ 1674 bj[k++] = i; 1675 bdiag[i] = bdiag[i+1] + nz + 1; 1676 } 1677 1678 fact->factor = MAT_FACTOR_ILU; 1679 fact->info.factor_mallocs = 0; 1680 fact->info.fill_ratio_given = info->fill; 1681 fact->info.fill_ratio_needed = 1.0; 1682 fact->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1683 1684 b = (Mat_SeqAIJ*)(fact)->data; 1685 b->row = isrow; 1686 b->col = iscol; 1687 b->icol = isicol; 1688 ierr = PetscMalloc((fact->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1689 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1690 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1691 PetscFunctionReturn(0); 1692 } 1693 1694 #undef __FUNCT__ 1695 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ" 1696 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1697 { 1698 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1699 IS isicol; 1700 PetscErrorCode ierr; 1701 const PetscInt *r,*ic; 1702 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j; 1703 PetscInt *bi,*cols,nnz,*cols_lvl; 1704 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1705 PetscInt i,levels,diagonal_fill; 1706 PetscTruth col_identity,row_identity; 1707 PetscReal f; 1708 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1709 PetscBT lnkbt; 1710 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1711 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1712 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1713 1714 PetscFunctionBegin; 1715 /* Uncomment the old data struct part only while testing new data structure for MatSolve() */ 1716 /* 1717 PetscTruth olddatastruct=PETSC_FALSE; 1718 ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_old",&olddatastruct,PETSC_NULL);CHKERRQ(ierr); 1719 if(olddatastruct){ 1720 ierr = MatILUFactorSymbolic_SeqAIJ_inplace(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1721 PetscFunctionReturn(0); 1722 } 1723 */ 1724 1725 levels = (PetscInt)info->levels; 1726 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1727 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1728 1729 if (!levels && row_identity && col_identity) { 1730 /* special case: ilu(0) with natural ordering */ 1731 ierr = MatILUFactorSymbolic_SeqAIJ_ilu0(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1732 if (a->inode.size) { 1733 fact->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode; 1734 } 1735 PetscFunctionReturn(0); 1736 } 1737 1738 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); 1739 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1740 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1741 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1742 1743 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1744 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1745 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1746 bi[0] = bdiag[0] = 0; 1747 1748 ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr); 1749 1750 /* create a linked list for storing column indices of the active row */ 1751 nlnk = n + 1; 1752 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1753 1754 /* initial FreeSpace size is f*(ai[n]+1) */ 1755 f = info->fill; 1756 diagonal_fill = (PetscInt)info->diagonal_fill; 1757 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1758 current_space = free_space; 1759 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1760 current_space_lvl = free_space_lvl; 1761 1762 for (i=0; i<n; i++) { 1763 nzi = 0; 1764 /* copy current row into linked list */ 1765 nnz = ai[r[i]+1] - ai[r[i]]; 1766 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1767 cols = aj + ai[r[i]]; 1768 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1769 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1770 nzi += nlnk; 1771 1772 /* make sure diagonal entry is included */ 1773 if (diagonal_fill && lnk[i] == -1) { 1774 fm = n; 1775 while (lnk[fm] < i) fm = lnk[fm]; 1776 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1777 lnk[fm] = i; 1778 lnk_lvl[i] = 0; 1779 nzi++; dcount++; 1780 } 1781 1782 /* add pivot rows into the active row */ 1783 nzbd = 0; 1784 prow = lnk[n]; 1785 while (prow < i) { 1786 nnz = bdiag[prow]; 1787 cols = bj_ptr[prow] + nnz + 1; 1788 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1789 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1790 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1791 nzi += nlnk; 1792 prow = lnk[prow]; 1793 nzbd++; 1794 } 1795 bdiag[i] = nzbd; 1796 bi[i+1] = bi[i] + nzi; 1797 1798 /* if free space is not available, make more free space */ 1799 if (current_space->local_remaining<nzi) { 1800 nnz = 2*nzi*(n - i); /* estimated and max additional space needed */ 1801 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1802 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1803 reallocs++; 1804 } 1805 1806 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1807 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1808 bj_ptr[i] = current_space->array; 1809 bjlvl_ptr[i] = current_space_lvl->array; 1810 1811 /* make sure the active row i has diagonal entry */ 1812 if (*(bj_ptr[i]+bdiag[i]) != i) { 1813 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 1814 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1815 } 1816 1817 current_space->array += nzi; 1818 current_space->local_used += nzi; 1819 current_space->local_remaining -= nzi; 1820 current_space_lvl->array += nzi; 1821 current_space_lvl->local_used += nzi; 1822 current_space_lvl->local_remaining -= nzi; 1823 } 1824 1825 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1826 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1827 1828 /* destroy list of free space and other temporary arrays */ 1829 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 1830 1831 /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */ 1832 ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 1833 1834 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1835 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1836 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 1837 1838 #if defined(PETSC_USE_INFO) 1839 { 1840 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1841 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 1842 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1843 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 1844 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1845 if (diagonal_fill) { 1846 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 1847 } 1848 } 1849 #endif 1850 1851 /* put together the new matrix */ 1852 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 1853 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 1854 b = (Mat_SeqAIJ*)(fact)->data; 1855 b->free_a = PETSC_TRUE; 1856 b->free_ij = PETSC_TRUE; 1857 b->singlemalloc = PETSC_FALSE; 1858 ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 1859 b->j = bj; 1860 b->i = bi; 1861 b->diag = bdiag; 1862 b->ilen = 0; 1863 b->imax = 0; 1864 b->row = isrow; 1865 b->col = iscol; 1866 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1867 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1868 b->icol = isicol; 1869 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1870 /* In b structure: Free imax, ilen, old a, old j. 1871 Allocate bdiag, solve_work, new a, new j */ 1872 ierr = PetscLogObjectMemory(fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1873 b->maxnz = b->nz = bdiag[0]+1; 1874 (fact)->info.factor_mallocs = reallocs; 1875 (fact)->info.fill_ratio_given = f; 1876 (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 1877 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1878 if (a->inode.size) { 1879 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode; 1880 } 1881 PetscFunctionReturn(0); 1882 } 1883 1884 #undef __FUNCT__ 1885 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_inplace" 1886 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1887 { 1888 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1889 IS isicol; 1890 PetscErrorCode ierr; 1891 const PetscInt *r,*ic; 1892 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,d; 1893 PetscInt *bi,*cols,nnz,*cols_lvl; 1894 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1895 PetscInt i,levels,diagonal_fill; 1896 PetscTruth col_identity,row_identity; 1897 PetscReal f; 1898 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1899 PetscBT lnkbt; 1900 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1901 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1902 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1903 PetscTruth missing; 1904 1905 PetscFunctionBegin; 1906 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); 1907 f = info->fill; 1908 levels = (PetscInt)info->levels; 1909 diagonal_fill = (PetscInt)info->diagonal_fill; 1910 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1911 1912 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1913 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1914 if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */ 1915 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr); 1916 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace; 1917 if (a->inode.size) { 1918 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace; 1919 } 1920 fact->factor = MAT_FACTOR_ILU; 1921 (fact)->info.factor_mallocs = 0; 1922 (fact)->info.fill_ratio_given = info->fill; 1923 (fact)->info.fill_ratio_needed = 1.0; 1924 b = (Mat_SeqAIJ*)(fact)->data; 1925 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 1926 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 1927 b->row = isrow; 1928 b->col = iscol; 1929 b->icol = isicol; 1930 ierr = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1931 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1932 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1933 PetscFunctionReturn(0); 1934 } 1935 1936 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1937 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1938 1939 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1940 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1941 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1942 bi[0] = bdiag[0] = 0; 1943 1944 ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr); 1945 1946 /* create a linked list for storing column indices of the active row */ 1947 nlnk = n + 1; 1948 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1949 1950 /* initial FreeSpace size is f*(ai[n]+1) */ 1951 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1952 current_space = free_space; 1953 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1954 current_space_lvl = free_space_lvl; 1955 1956 for (i=0; i<n; i++) { 1957 nzi = 0; 1958 /* copy current row into linked list */ 1959 nnz = ai[r[i]+1] - ai[r[i]]; 1960 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1961 cols = aj + ai[r[i]]; 1962 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1963 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1964 nzi += nlnk; 1965 1966 /* make sure diagonal entry is included */ 1967 if (diagonal_fill && lnk[i] == -1) { 1968 fm = n; 1969 while (lnk[fm] < i) fm = lnk[fm]; 1970 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1971 lnk[fm] = i; 1972 lnk_lvl[i] = 0; 1973 nzi++; dcount++; 1974 } 1975 1976 /* add pivot rows into the active row */ 1977 nzbd = 0; 1978 prow = lnk[n]; 1979 while (prow < i) { 1980 nnz = bdiag[prow]; 1981 cols = bj_ptr[prow] + nnz + 1; 1982 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1983 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1984 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1985 nzi += nlnk; 1986 prow = lnk[prow]; 1987 nzbd++; 1988 } 1989 bdiag[i] = nzbd; 1990 bi[i+1] = bi[i] + nzi; 1991 1992 /* if free space is not available, make more free space */ 1993 if (current_space->local_remaining<nzi) { 1994 nnz = nzi*(n - i); /* estimated and max additional space needed */ 1995 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1996 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1997 reallocs++; 1998 } 1999 2000 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2001 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2002 bj_ptr[i] = current_space->array; 2003 bjlvl_ptr[i] = current_space_lvl->array; 2004 2005 /* make sure the active row i has diagonal entry */ 2006 if (*(bj_ptr[i]+bdiag[i]) != i) { 2007 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 2008 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 2009 } 2010 2011 current_space->array += nzi; 2012 current_space->local_used += nzi; 2013 current_space->local_remaining -= nzi; 2014 current_space_lvl->array += nzi; 2015 current_space_lvl->local_used += nzi; 2016 current_space_lvl->local_remaining -= nzi; 2017 } 2018 2019 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 2020 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 2021 2022 /* destroy list of free space and other temporary arrays */ 2023 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 2024 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */ 2025 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2026 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2027 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 2028 2029 #if defined(PETSC_USE_INFO) 2030 { 2031 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 2032 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 2033 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2034 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 2035 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 2036 if (diagonal_fill) { 2037 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 2038 } 2039 } 2040 #endif 2041 2042 /* put together the new matrix */ 2043 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 2044 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 2045 b = (Mat_SeqAIJ*)(fact)->data; 2046 b->free_a = PETSC_TRUE; 2047 b->free_ij = PETSC_TRUE; 2048 b->singlemalloc = PETSC_FALSE; 2049 ierr = PetscMalloc(bi[n]*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 2050 b->j = bj; 2051 b->i = bi; 2052 for (i=0; i<n; i++) bdiag[i] += bi[i]; 2053 b->diag = bdiag; 2054 b->ilen = 0; 2055 b->imax = 0; 2056 b->row = isrow; 2057 b->col = iscol; 2058 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 2059 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 2060 b->icol = isicol; 2061 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2062 /* In b structure: Free imax, ilen, old a, old j. 2063 Allocate bdiag, solve_work, new a, new j */ 2064 ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 2065 b->maxnz = b->nz = bi[n] ; 2066 (fact)->info.factor_mallocs = reallocs; 2067 (fact)->info.fill_ratio_given = f; 2068 (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 2069 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace; 2070 if (a->inode.size) { 2071 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace; 2072 } 2073 PetscFunctionReturn(0); 2074 } 2075 2076 #undef __FUNCT__ 2077 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ" 2078 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 2079 { 2080 Mat C = B; 2081 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2082 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2083 IS ip=b->row,iip = b->icol; 2084 PetscErrorCode ierr; 2085 const PetscInt *rip,*riip; 2086 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp; 2087 PetscInt *ai=a->i,*aj=a->j; 2088 PetscInt k,jmin,jmax,*c2r,*il,col,nexti,ili,nz; 2089 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2090 PetscTruth perm_identity; 2091 2092 FactorShiftCtx sctx; 2093 PetscReal rs; 2094 MatScalar d,*v; 2095 2096 PetscFunctionBegin; 2097 /* MatPivotSetUp(): initialize shift context sctx */ 2098 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 2099 2100 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 2101 sctx.shift_top = info->zeropivot; 2102 for (i=0; i<mbs; i++) { 2103 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 2104 d = (aa)[a->diag[i]]; 2105 rs = -PetscAbsScalar(d) - PetscRealPart(d); 2106 v = aa+ai[i]; 2107 nz = ai[i+1] - ai[i]; 2108 for (j=0; j<nz; j++) 2109 rs += PetscAbsScalar(v[j]); 2110 if (rs>sctx.shift_top) sctx.shift_top = rs; 2111 } 2112 sctx.shift_top *= 1.1; 2113 sctx.nshift_max = 5; 2114 sctx.shift_lo = 0.; 2115 sctx.shift_hi = 1.; 2116 } 2117 2118 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2119 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2120 2121 /* allocate working arrays 2122 c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col 2123 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 2124 */ 2125 ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&c2r);CHKERRQ(ierr); 2126 2127 do { 2128 sctx.useshift = PETSC_FALSE; 2129 2130 for (i=0; i<mbs; i++) c2r[i] = mbs; 2131 il[0] = 0; 2132 2133 for (k = 0; k<mbs; k++){ 2134 /* zero rtmp */ 2135 nz = bi[k+1] - bi[k]; 2136 bjtmp = bj + bi[k]; 2137 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2138 2139 /* load in initial unfactored row */ 2140 bval = ba + bi[k]; 2141 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2142 for (j = jmin; j < jmax; j++){ 2143 col = riip[aj[j]]; 2144 if (col >= k){ /* only take upper triangular entry */ 2145 rtmp[col] = aa[j]; 2146 *bval++ = 0.0; /* for in-place factorization */ 2147 } 2148 } 2149 /* shift the diagonal of the matrix: ZeropivotApply() */ 2150 rtmp[k] += sctx.shift_amount; /* shift the diagonal of the matrix */ 2151 2152 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2153 dk = rtmp[k]; 2154 i = c2r[k]; /* first row to be added to k_th row */ 2155 2156 while (i < k){ 2157 nexti = c2r[i]; /* next row to be added to k_th row */ 2158 2159 /* compute multiplier, update diag(k) and U(i,k) */ 2160 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2161 uikdi = - ba[ili]*ba[bdiag[i]]; /* diagonal(k) */ 2162 dk += uikdi*ba[ili]; /* update diag[k] */ 2163 ba[ili] = uikdi; /* -U(i,k) */ 2164 2165 /* add multiple of row i to k-th row */ 2166 jmin = ili + 1; jmax = bi[i+1]; 2167 if (jmin < jmax){ 2168 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2169 /* update il and c2r for row i */ 2170 il[i] = jmin; 2171 j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i; 2172 } 2173 i = nexti; 2174 } 2175 2176 /* copy data into U(k,:) */ 2177 rs = 0.0; 2178 jmin = bi[k]; jmax = bi[k+1]-1; 2179 if (jmin < jmax) { 2180 for (j=jmin; j<jmax; j++){ 2181 col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]); 2182 } 2183 /* add the k-th row into il and c2r */ 2184 il[k] = jmin; 2185 i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k; 2186 } 2187 2188 /* MatPivotCheck() */ 2189 sctx.rs = rs; 2190 sctx.pv = dk; 2191 if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO){ 2192 ierr = MatPivotCheck_nz(info,sctx,k);CHKERRQ(ierr); 2193 } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE){ 2194 ierr = MatPivotCheck_pd(info,sctx,k);CHKERRQ(ierr); 2195 } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS){ 2196 ierr = MatPivotCheck_inblocks(info,sctx,k);CHKERRQ(ierr); 2197 } else { 2198 ierr = MatPivotCheck_none(info,sctx,k);CHKERRQ(ierr); 2199 } 2200 dk = sctx.pv; 2201 2202 ba[bdiag[k]] = 1.0/dk; /* U(k,k) */ 2203 } 2204 } while (sctx.useshift); 2205 2206 ierr = PetscFree3(rtmp,il,c2r);CHKERRQ(ierr); 2207 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2208 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2209 2210 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2211 if (perm_identity){ 2212 B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2213 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2214 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering; 2215 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering; 2216 } else { 2217 B->ops->solve = MatSolve_SeqSBAIJ_1; 2218 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1; 2219 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1; 2220 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1; 2221 } 2222 2223 C->assembled = PETSC_TRUE; 2224 C->preallocated = PETSC_TRUE; 2225 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2226 2227 /* MatPivotView() */ 2228 if (sctx.nshift){ 2229 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 2230 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); 2231 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 2232 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2233 } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS){ 2234 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftamount);CHKERRQ(ierr); 2235 } 2236 } 2237 PetscFunctionReturn(0); 2238 } 2239 2240 #undef __FUNCT__ 2241 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ_inplace" 2242 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info) 2243 { 2244 Mat C = B; 2245 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2246 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2247 IS ip=b->row,iip = b->icol; 2248 PetscErrorCode ierr; 2249 const PetscInt *rip,*riip; 2250 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol,*bjtmp; 2251 PetscInt *ai=a->i,*aj=a->j; 2252 PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz; 2253 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2254 PetscReal zeropivot,rs; 2255 ChShift_Ctx sctx; 2256 PetscInt newshift; 2257 PetscTruth perm_identity; 2258 2259 PetscFunctionBegin; 2260 zeropivot = info->zeropivot; 2261 2262 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2263 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2264 2265 /* initialization */ 2266 ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr); 2267 sctx.shift_amount = 0; 2268 sctx.nshift = 0; 2269 do { 2270 sctx.chshift = PETSC_FALSE; 2271 for (i=0; i<mbs; i++) jl[i] = mbs; 2272 il[0] = 0; 2273 2274 for (k = 0; k<mbs; k++){ 2275 /* zero rtmp */ 2276 nz = bi[k+1] - bi[k]; 2277 bjtmp = bj + bi[k]; 2278 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2279 2280 bval = ba + bi[k]; 2281 /* initialize k-th row by the perm[k]-th row of A */ 2282 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2283 for (j = jmin; j < jmax; j++){ 2284 col = riip[aj[j]]; 2285 if (col >= k){ /* only take upper triangular entry */ 2286 rtmp[col] = aa[j]; 2287 *bval++ = 0.0; /* for in-place factorization */ 2288 } 2289 } 2290 /* shift the diagonal of the matrix */ 2291 if (sctx.nshift) rtmp[k] += sctx.shift_amount; 2292 2293 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2294 dk = rtmp[k]; 2295 i = jl[k]; /* first row to be added to k_th row */ 2296 2297 while (i < k){ 2298 nexti = jl[i]; /* next row to be added to k_th row */ 2299 2300 /* compute multiplier, update diag(k) and U(i,k) */ 2301 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2302 uikdi = - ba[ili]*ba[bi[i]]; /* diagonal(k) */ 2303 dk += uikdi*ba[ili]; 2304 ba[ili] = uikdi; /* -U(i,k) */ 2305 2306 /* add multiple of row i to k-th row */ 2307 jmin = ili + 1; jmax = bi[i+1]; 2308 if (jmin < jmax){ 2309 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2310 /* update il and jl for row i */ 2311 il[i] = jmin; 2312 j = bj[jmin]; jl[i] = jl[j]; jl[j] = i; 2313 } 2314 i = nexti; 2315 } 2316 2317 /* shift the diagonals when zero pivot is detected */ 2318 /* compute rs=sum of abs(off-diagonal) */ 2319 rs = 0.0; 2320 jmin = bi[k]+1; 2321 nz = bi[k+1] - jmin; 2322 bcol = bj + jmin; 2323 for (j=0; j<nz; j++) { 2324 rs += PetscAbsScalar(rtmp[bcol[j]]); 2325 } 2326 2327 sctx.rs = rs; 2328 sctx.pv = dk; 2329 ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr); 2330 2331 if (newshift == 1) { 2332 if (!sctx.shift_amount) { 2333 sctx.shift_amount = 1e-5; 2334 } 2335 break; 2336 } 2337 2338 /* copy data into U(k,:) */ 2339 ba[bi[k]] = 1.0/dk; /* U(k,k) */ 2340 jmin = bi[k]+1; jmax = bi[k+1]; 2341 if (jmin < jmax) { 2342 for (j=jmin; j<jmax; j++){ 2343 col = bj[j]; ba[j] = rtmp[col]; 2344 } 2345 /* add the k-th row into il and jl */ 2346 il[k] = jmin; 2347 i = bj[jmin]; jl[k] = jl[i]; jl[i] = k; 2348 } 2349 } 2350 } while (sctx.chshift); 2351 ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr); 2352 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2353 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2354 2355 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2356 if (perm_identity){ 2357 B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2358 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2359 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2360 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2361 } else { 2362 B->ops->solve = MatSolve_SeqSBAIJ_1_inplace; 2363 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_inplace; 2364 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_inplace; 2365 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_inplace; 2366 } 2367 2368 C->assembled = PETSC_TRUE; 2369 C->preallocated = PETSC_TRUE; 2370 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2371 if (sctx.nshift){ 2372 if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 2373 ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2374 } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 2375 ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2376 } 2377 } 2378 PetscFunctionReturn(0); 2379 } 2380 2381 /* 2382 icc() under revised new data structure. 2383 Factored arrays bj and ba are stored as 2384 U(0,:),...,U(i,:),U(n-1,:) 2385 2386 ui=fact->i is an array of size n+1, in which 2387 ui+ 2388 ui[i]: points to 1st entry of U(i,:),i=0,...,n-1 2389 ui[n]: points to U(n-1,n-1)+1 2390 2391 udiag=fact->diag is an array of size n,in which 2392 udiag[i]: points to diagonal of U(i,:), i=0,...,n-1 2393 2394 U(i,:) contains udiag[i] as its last entry, i.e., 2395 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 2396 */ 2397 2398 #undef __FUNCT__ 2399 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ" 2400 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2401 { 2402 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2403 Mat_SeqSBAIJ *b; 2404 PetscErrorCode ierr; 2405 PetscTruth perm_identity,missing; 2406 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2407 const PetscInt *rip,*riip; 2408 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2409 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2410 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2411 PetscReal fill=info->fill,levels=info->levels; 2412 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2413 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2414 PetscBT lnkbt; 2415 IS iperm; 2416 2417 PetscFunctionBegin; 2418 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); 2419 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2420 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2421 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2422 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2423 2424 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2425 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2426 ui[0] = 0; 2427 2428 /* ICC(0) without matrix ordering: simply rearrange column indices */ 2429 if (!levels && perm_identity) { 2430 for (i=0; i<am; i++) { 2431 ncols = ai[i+1] - a->diag[i]; 2432 ui[i+1] = ui[i] + ncols; 2433 udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */ 2434 } 2435 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2436 cols = uj; 2437 for (i=0; i<am; i++) { 2438 aj = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */ 2439 ncols = ai[i+1] - a->diag[i] -1; 2440 for (j=0; j<ncols; j++) *cols++ = aj[j]; 2441 *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */ 2442 } 2443 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2444 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2445 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2446 2447 /* initialization */ 2448 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2449 2450 /* jl: linked list for storing indices of the pivot rows 2451 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2452 ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr); 2453 for (i=0; i<am; i++){ 2454 jl[i] = am; il[i] = 0; 2455 } 2456 2457 /* create and initialize a linked list for storing column indices of the active row k */ 2458 nlnk = am + 1; 2459 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2460 2461 /* initial FreeSpace size is fill*(ai[am]+1) */ 2462 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2463 current_space = free_space; 2464 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2465 current_space_lvl = free_space_lvl; 2466 2467 for (k=0; k<am; k++){ /* for each active row k */ 2468 /* initialize lnk by the column indices of row rip[k] of A */ 2469 nzk = 0; 2470 ncols = ai[rip[k]+1] - ai[rip[k]]; 2471 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2472 ncols_upper = 0; 2473 for (j=0; j<ncols; j++){ 2474 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2475 if (riip[i] >= k){ /* only take upper triangular entry */ 2476 ajtmp[ncols_upper] = i; 2477 ncols_upper++; 2478 } 2479 } 2480 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2481 nzk += nlnk; 2482 2483 /* update lnk by computing fill-in for each pivot row to be merged in */ 2484 prow = jl[k]; /* 1st pivot row */ 2485 2486 while (prow < k){ 2487 nextprow = jl[prow]; 2488 2489 /* merge prow into k-th row */ 2490 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2491 jmax = ui[prow+1]; 2492 ncols = jmax-jmin; 2493 i = jmin - ui[prow]; 2494 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2495 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2496 j = *(uj - 1); 2497 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2498 nzk += nlnk; 2499 2500 /* update il and jl for prow */ 2501 if (jmin < jmax){ 2502 il[prow] = jmin; 2503 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2504 } 2505 prow = nextprow; 2506 } 2507 2508 /* if free space is not available, make more free space */ 2509 if (current_space->local_remaining<nzk) { 2510 i = am - k + 1; /* num of unfactored rows */ 2511 i *= PetscMin(nzk, i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2512 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2513 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2514 reallocs++; 2515 } 2516 2517 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2518 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2519 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2520 2521 /* add the k-th row into il and jl */ 2522 if (nzk > 1){ 2523 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2524 jl[k] = jl[i]; jl[i] = k; 2525 il[k] = ui[k] + 1; 2526 } 2527 uj_ptr[k] = current_space->array; 2528 uj_lvl_ptr[k] = current_space_lvl->array; 2529 2530 current_space->array += nzk; 2531 current_space->local_used += nzk; 2532 current_space->local_remaining -= nzk; 2533 2534 current_space_lvl->array += nzk; 2535 current_space_lvl->local_used += nzk; 2536 current_space_lvl->local_remaining -= nzk; 2537 2538 ui[k+1] = ui[k] + nzk; 2539 } 2540 2541 #if defined(PETSC_USE_INFO) 2542 if (ai[am] != 0) { 2543 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2544 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2545 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2546 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2547 } else { 2548 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2549 } 2550 #endif 2551 2552 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2553 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2554 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2555 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2556 2557 /* destroy list of free space and other temporary array(s) */ 2558 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2559 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor */ 2560 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2561 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2562 2563 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2564 2565 /* put together the new matrix in MATSEQSBAIJ format */ 2566 b = (Mat_SeqSBAIJ*)(fact)->data; 2567 b->singlemalloc = PETSC_FALSE; 2568 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2569 b->j = uj; 2570 b->i = ui; 2571 b->diag = udiag; 2572 b->free_diag = PETSC_TRUE; 2573 b->ilen = 0; 2574 b->imax = 0; 2575 b->row = perm; 2576 b->col = perm; 2577 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2578 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2579 b->icol = iperm; 2580 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2581 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2582 ierr = PetscLogObjectMemory(fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2583 b->maxnz = b->nz = ui[am]; 2584 b->free_a = PETSC_TRUE; 2585 b->free_ij = PETSC_TRUE; 2586 2587 fact->info.factor_mallocs = reallocs; 2588 fact->info.fill_ratio_given = fill; 2589 if (ai[am] != 0) { 2590 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2591 } else { 2592 fact->info.fill_ratio_needed = 0.0; 2593 } 2594 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2595 PetscFunctionReturn(0); 2596 } 2597 2598 #undef __FUNCT__ 2599 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ_inplace" 2600 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2601 { 2602 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2603 Mat_SeqSBAIJ *b; 2604 PetscErrorCode ierr; 2605 PetscTruth perm_identity,missing; 2606 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2607 const PetscInt *rip,*riip; 2608 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2609 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2610 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2611 PetscReal fill=info->fill,levels=info->levels; 2612 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2613 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2614 PetscBT lnkbt; 2615 IS iperm; 2616 2617 PetscFunctionBegin; 2618 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); 2619 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2620 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2621 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2622 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2623 2624 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2625 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2626 ui[0] = 0; 2627 2628 /* ICC(0) without matrix ordering: simply copies fill pattern */ 2629 if (!levels && perm_identity) { 2630 2631 for (i=0; i<am; i++) { 2632 ui[i+1] = ui[i] + ai[i+1] - a->diag[i]; 2633 udiag[i] = ui[i]; 2634 } 2635 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2636 cols = uj; 2637 for (i=0; i<am; i++) { 2638 aj = a->j + a->diag[i]; 2639 ncols = ui[i+1] - ui[i]; 2640 for (j=0; j<ncols; j++) *cols++ = *aj++; 2641 } 2642 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2643 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2644 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2645 2646 /* initialization */ 2647 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2648 2649 /* jl: linked list for storing indices of the pivot rows 2650 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2651 ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr); 2652 for (i=0; i<am; i++){ 2653 jl[i] = am; il[i] = 0; 2654 } 2655 2656 /* create and initialize a linked list for storing column indices of the active row k */ 2657 nlnk = am + 1; 2658 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2659 2660 /* initial FreeSpace size is fill*(ai[am]+1) */ 2661 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2662 current_space = free_space; 2663 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2664 current_space_lvl = free_space_lvl; 2665 2666 for (k=0; k<am; k++){ /* for each active row k */ 2667 /* initialize lnk by the column indices of row rip[k] of A */ 2668 nzk = 0; 2669 ncols = ai[rip[k]+1] - ai[rip[k]]; 2670 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2671 ncols_upper = 0; 2672 for (j=0; j<ncols; j++){ 2673 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2674 if (riip[i] >= k){ /* only take upper triangular entry */ 2675 ajtmp[ncols_upper] = i; 2676 ncols_upper++; 2677 } 2678 } 2679 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2680 nzk += nlnk; 2681 2682 /* update lnk by computing fill-in for each pivot row to be merged in */ 2683 prow = jl[k]; /* 1st pivot row */ 2684 2685 while (prow < k){ 2686 nextprow = jl[prow]; 2687 2688 /* merge prow into k-th row */ 2689 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2690 jmax = ui[prow+1]; 2691 ncols = jmax-jmin; 2692 i = jmin - ui[prow]; 2693 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2694 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2695 j = *(uj - 1); 2696 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2697 nzk += nlnk; 2698 2699 /* update il and jl for prow */ 2700 if (jmin < jmax){ 2701 il[prow] = jmin; 2702 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2703 } 2704 prow = nextprow; 2705 } 2706 2707 /* if free space is not available, make more free space */ 2708 if (current_space->local_remaining<nzk) { 2709 i = am - k + 1; /* num of unfactored rows */ 2710 i *= PetscMin(nzk, (i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2711 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2712 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2713 reallocs++; 2714 } 2715 2716 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2717 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2718 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2719 2720 /* add the k-th row into il and jl */ 2721 if (nzk > 1){ 2722 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2723 jl[k] = jl[i]; jl[i] = k; 2724 il[k] = ui[k] + 1; 2725 } 2726 uj_ptr[k] = current_space->array; 2727 uj_lvl_ptr[k] = current_space_lvl->array; 2728 2729 current_space->array += nzk; 2730 current_space->local_used += nzk; 2731 current_space->local_remaining -= nzk; 2732 2733 current_space_lvl->array += nzk; 2734 current_space_lvl->local_used += nzk; 2735 current_space_lvl->local_remaining -= nzk; 2736 2737 ui[k+1] = ui[k] + nzk; 2738 } 2739 2740 #if defined(PETSC_USE_INFO) 2741 if (ai[am] != 0) { 2742 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2743 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2744 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2745 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2746 } else { 2747 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2748 } 2749 #endif 2750 2751 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2752 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2753 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2754 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2755 2756 /* destroy list of free space and other temporary array(s) */ 2757 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2758 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 2759 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2760 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2761 2762 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2763 2764 /* put together the new matrix in MATSEQSBAIJ format */ 2765 2766 b = (Mat_SeqSBAIJ*)fact->data; 2767 b->singlemalloc = PETSC_FALSE; 2768 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2769 b->j = uj; 2770 b->i = ui; 2771 b->diag = udiag; 2772 b->free_diag = PETSC_TRUE; 2773 b->ilen = 0; 2774 b->imax = 0; 2775 b->row = perm; 2776 b->col = perm; 2777 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2778 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2779 b->icol = iperm; 2780 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2781 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2782 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2783 b->maxnz = b->nz = ui[am]; 2784 b->free_a = PETSC_TRUE; 2785 b->free_ij = PETSC_TRUE; 2786 2787 fact->info.factor_mallocs = reallocs; 2788 fact->info.fill_ratio_given = fill; 2789 if (ai[am] != 0) { 2790 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2791 } else { 2792 fact->info.fill_ratio_needed = 0.0; 2793 } 2794 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace; 2795 PetscFunctionReturn(0); 2796 } 2797 2798 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2799 { 2800 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2801 Mat_SeqSBAIJ *b; 2802 PetscErrorCode ierr; 2803 PetscTruth perm_identity; 2804 PetscReal fill = info->fill; 2805 const PetscInt *rip,*riip; 2806 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2807 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2808 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr,*udiag; 2809 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2810 PetscBT lnkbt; 2811 IS iperm; 2812 2813 PetscFunctionBegin; 2814 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); 2815 /* check whether perm is the identity mapping */ 2816 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2817 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2818 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2819 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2820 2821 /* initialization */ 2822 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2823 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2824 ui[0] = 0; 2825 2826 /* jl: linked list for storing indices of the pivot rows 2827 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2828 ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr); 2829 for (i=0; i<am; i++){ 2830 jl[i] = am; il[i] = 0; 2831 } 2832 2833 /* create and initialize a linked list for storing column indices of the active row k */ 2834 nlnk = am + 1; 2835 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2836 2837 /* initial FreeSpace size is fill*(ai[am]+1) */ 2838 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2839 current_space = free_space; 2840 2841 for (k=0; k<am; k++){ /* for each active row k */ 2842 /* initialize lnk by the column indices of row rip[k] of A */ 2843 nzk = 0; 2844 ncols = ai[rip[k]+1] - ai[rip[k]]; 2845 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2846 ncols_upper = 0; 2847 for (j=0; j<ncols; j++){ 2848 i = riip[*(aj + ai[rip[k]] + j)]; 2849 if (i >= k){ /* only take upper triangular entry */ 2850 cols[ncols_upper] = i; 2851 ncols_upper++; 2852 } 2853 } 2854 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2855 nzk += nlnk; 2856 2857 /* update lnk by computing fill-in for each pivot row to be merged in */ 2858 prow = jl[k]; /* 1st pivot row */ 2859 2860 while (prow < k){ 2861 nextprow = jl[prow]; 2862 /* merge prow into k-th row */ 2863 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2864 jmax = ui[prow+1]; 2865 ncols = jmax-jmin; 2866 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2867 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2868 nzk += nlnk; 2869 2870 /* update il and jl for prow */ 2871 if (jmin < jmax){ 2872 il[prow] = jmin; 2873 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 2874 } 2875 prow = nextprow; 2876 } 2877 2878 /* if free space is not available, make more free space */ 2879 if (current_space->local_remaining<nzk) { 2880 i = am - k + 1; /* num of unfactored rows */ 2881 i *= PetscMin(nzk,i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2882 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2883 reallocs++; 2884 } 2885 2886 /* copy data into free space, then initialize lnk */ 2887 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 2888 2889 /* add the k-th row into il and jl */ 2890 if (nzk > 1){ 2891 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2892 jl[k] = jl[i]; jl[i] = k; 2893 il[k] = ui[k] + 1; 2894 } 2895 ui_ptr[k] = current_space->array; 2896 current_space->array += nzk; 2897 current_space->local_used += nzk; 2898 current_space->local_remaining -= nzk; 2899 2900 ui[k+1] = ui[k] + nzk; 2901 } 2902 2903 #if defined(PETSC_USE_INFO) 2904 if (ai[am] != 0) { 2905 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 2906 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2907 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2908 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2909 } else { 2910 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2911 } 2912 #endif 2913 2914 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2915 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2916 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 2917 2918 /* destroy list of free space and other temporary array(s) */ 2919 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2920 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor */ 2921 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2922 2923 /* put together the new matrix in MATSEQSBAIJ format */ 2924 2925 b = (Mat_SeqSBAIJ*)fact->data; 2926 b->singlemalloc = PETSC_FALSE; 2927 b->free_a = PETSC_TRUE; 2928 b->free_ij = PETSC_TRUE; 2929 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2930 b->j = uj; 2931 b->i = ui; 2932 b->diag = udiag; 2933 b->free_diag = PETSC_TRUE; 2934 b->ilen = 0; 2935 b->imax = 0; 2936 b->row = perm; 2937 b->col = perm; 2938 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2939 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2940 b->icol = iperm; 2941 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2942 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2943 ierr = PetscLogObjectMemory(fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2944 b->maxnz = b->nz = ui[am]; 2945 2946 fact->info.factor_mallocs = reallocs; 2947 fact->info.fill_ratio_given = fill; 2948 if (ai[am] != 0) { 2949 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2950 } else { 2951 fact->info.fill_ratio_needed = 0.0; 2952 } 2953 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2954 PetscFunctionReturn(0); 2955 } 2956 2957 #undef __FUNCT__ 2958 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ_inplace" 2959 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2960 { 2961 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2962 Mat_SeqSBAIJ *b; 2963 PetscErrorCode ierr; 2964 PetscTruth perm_identity; 2965 PetscReal fill = info->fill; 2966 const PetscInt *rip,*riip; 2967 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2968 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2969 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr; 2970 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2971 PetscBT lnkbt; 2972 IS iperm; 2973 2974 PetscFunctionBegin; 2975 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); 2976 /* check whether perm is the identity mapping */ 2977 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2978 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2979 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2980 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2981 2982 /* initialization */ 2983 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2984 ui[0] = 0; 2985 2986 /* jl: linked list for storing indices of the pivot rows 2987 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2988 ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr); 2989 for (i=0; i<am; i++){ 2990 jl[i] = am; il[i] = 0; 2991 } 2992 2993 /* create and initialize a linked list for storing column indices of the active row k */ 2994 nlnk = am + 1; 2995 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2996 2997 /* initial FreeSpace size is fill*(ai[am]+1) */ 2998 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2999 current_space = free_space; 3000 3001 for (k=0; k<am; k++){ /* for each active row k */ 3002 /* initialize lnk by the column indices of row rip[k] of A */ 3003 nzk = 0; 3004 ncols = ai[rip[k]+1] - ai[rip[k]]; 3005 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 3006 ncols_upper = 0; 3007 for (j=0; j<ncols; j++){ 3008 i = riip[*(aj + ai[rip[k]] + j)]; 3009 if (i >= k){ /* only take upper triangular entry */ 3010 cols[ncols_upper] = i; 3011 ncols_upper++; 3012 } 3013 } 3014 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3015 nzk += nlnk; 3016 3017 /* update lnk by computing fill-in for each pivot row to be merged in */ 3018 prow = jl[k]; /* 1st pivot row */ 3019 3020 while (prow < k){ 3021 nextprow = jl[prow]; 3022 /* merge prow into k-th row */ 3023 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 3024 jmax = ui[prow+1]; 3025 ncols = jmax-jmin; 3026 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 3027 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3028 nzk += nlnk; 3029 3030 /* update il and jl for prow */ 3031 if (jmin < jmax){ 3032 il[prow] = jmin; 3033 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 3034 } 3035 prow = nextprow; 3036 } 3037 3038 /* if free space is not available, make more free space */ 3039 if (current_space->local_remaining<nzk) { 3040 i = am - k + 1; /* num of unfactored rows */ 3041 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 3042 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 3043 reallocs++; 3044 } 3045 3046 /* copy data into free space, then initialize lnk */ 3047 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 3048 3049 /* add the k-th row into il and jl */ 3050 if (nzk-1 > 0){ 3051 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 3052 jl[k] = jl[i]; jl[i] = k; 3053 il[k] = ui[k] + 1; 3054 } 3055 ui_ptr[k] = current_space->array; 3056 current_space->array += nzk; 3057 current_space->local_used += nzk; 3058 current_space->local_remaining -= nzk; 3059 3060 ui[k+1] = ui[k] + nzk; 3061 } 3062 3063 #if defined(PETSC_USE_INFO) 3064 if (ai[am] != 0) { 3065 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 3066 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 3067 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 3068 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 3069 } else { 3070 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 3071 } 3072 #endif 3073 3074 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 3075 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 3076 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 3077 3078 /* destroy list of free space and other temporary array(s) */ 3079 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 3080 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 3081 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3082 3083 /* put together the new matrix in MATSEQSBAIJ format */ 3084 3085 b = (Mat_SeqSBAIJ*)fact->data; 3086 b->singlemalloc = PETSC_FALSE; 3087 b->free_a = PETSC_TRUE; 3088 b->free_ij = PETSC_TRUE; 3089 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 3090 b->j = uj; 3091 b->i = ui; 3092 b->diag = 0; 3093 b->ilen = 0; 3094 b->imax = 0; 3095 b->row = perm; 3096 b->col = perm; 3097 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3098 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3099 b->icol = iperm; 3100 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 3101 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 3102 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3103 b->maxnz = b->nz = ui[am]; 3104 3105 fact->info.factor_mallocs = reallocs; 3106 fact->info.fill_ratio_given = fill; 3107 if (ai[am] != 0) { 3108 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 3109 } else { 3110 fact->info.fill_ratio_needed = 0.0; 3111 } 3112 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace; 3113 PetscFunctionReturn(0); 3114 } 3115 3116 #undef __FUNCT__ 3117 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering" 3118 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx) 3119 { 3120 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3121 PetscErrorCode ierr; 3122 PetscInt n = A->rmap->n; 3123 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag,*vi; 3124 PetscScalar *x,sum; 3125 const PetscScalar *b; 3126 const MatScalar *aa = a->a,*v; 3127 PetscInt i,nz; 3128 3129 PetscFunctionBegin; 3130 if (!n) PetscFunctionReturn(0); 3131 3132 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3133 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3134 3135 /* forward solve the lower triangular */ 3136 x[0] = b[0]; 3137 v = aa; 3138 vi = aj; 3139 for (i=1; i<n; i++) { 3140 nz = ai[i+1] - ai[i]; 3141 sum = b[i]; 3142 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3143 v += nz; 3144 vi += nz; 3145 x[i] = sum; 3146 } 3147 3148 /* backward solve the upper triangular */ 3149 for (i=n-1; i>=0; i--){ 3150 v = aa + adiag[i+1] + 1; 3151 vi = aj + adiag[i+1] + 1; 3152 nz = adiag[i] - adiag[i+1]-1; 3153 sum = x[i]; 3154 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3155 x[i] = sum*v[nz]; /* x[i]=aa[adiag[i]]*sum; v++; */ 3156 } 3157 3158 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 3159 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3160 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3161 PetscFunctionReturn(0); 3162 } 3163 3164 #undef __FUNCT__ 3165 #define __FUNCT__ "MatSolve_SeqAIJ" 3166 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx) 3167 { 3168 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3169 IS iscol = a->col,isrow = a->row; 3170 PetscErrorCode ierr; 3171 PetscInt i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz; 3172 const PetscInt *rout,*cout,*r,*c; 3173 PetscScalar *x,*tmp,sum; 3174 const PetscScalar *b; 3175 const MatScalar *aa = a->a,*v; 3176 3177 PetscFunctionBegin; 3178 if (!n) PetscFunctionReturn(0); 3179 3180 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3181 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3182 tmp = a->solve_work; 3183 3184 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 3185 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 3186 3187 /* forward solve the lower triangular */ 3188 tmp[0] = b[r[0]]; 3189 v = aa; 3190 vi = aj; 3191 for (i=1; i<n; i++) { 3192 nz = ai[i+1] - ai[i]; 3193 sum = b[r[i]]; 3194 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3195 tmp[i] = sum; 3196 v += nz; vi += nz; 3197 } 3198 3199 /* backward solve the upper triangular */ 3200 for (i=n-1; i>=0; i--){ 3201 v = aa + adiag[i+1]+1; 3202 vi = aj + adiag[i+1]+1; 3203 nz = adiag[i]-adiag[i+1]-1; 3204 sum = tmp[i]; 3205 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3206 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 3207 } 3208 3209 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 3210 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 3211 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3212 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3213 ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr); 3214 PetscFunctionReturn(0); 3215 } 3216 3217 #undef __FUNCT__ 3218 #define __FUNCT__ "MatILUDTFactor_SeqAIJ" 3219 /* 3220 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 3221 */ 3222 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact) 3223 { 3224 Mat B = *fact; 3225 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b; 3226 IS isicol; 3227 PetscErrorCode ierr; 3228 const PetscInt *r,*ic; 3229 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag; 3230 PetscInt *bi,*bj,*bdiag,*bdiag_rev; 3231 PetscInt row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au; 3232 PetscInt nlnk,*lnk; 3233 PetscBT lnkbt; 3234 PetscTruth row_identity,icol_identity,both_identity; 3235 MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp; 3236 const PetscInt *ics; 3237 PetscInt j,nz,*pj,*bjtmp,k,ncut,*jtmp; 3238 PetscReal dt=info->dt,dtcol=info->dtcol,shift=info->shiftamount; 3239 PetscInt dtcount=(PetscInt)info->dtcount,nnz_max; 3240 PetscTruth missing; 3241 3242 PetscFunctionBegin; 3243 3244 if (dt == PETSC_DEFAULT) dt = 0.005; 3245 if (dtcol == PETSC_DEFAULT) dtcol = 0.01; /* XXX unused! */ 3246 if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax); 3247 3248 /* ------- symbolic factorization, can be reused ---------*/ 3249 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 3250 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 3251 adiag=a->diag; 3252 3253 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 3254 3255 /* bdiag is location of diagonal in factor */ 3256 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); /* becomes b->diag */ 3257 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag_rev);CHKERRQ(ierr); /* temporary */ 3258 3259 /* allocate row pointers bi */ 3260 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 3261 3262 /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */ 3263 if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */ 3264 nnz_max = ai[n]+2*n*dtcount+2; 3265 3266 ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 3267 ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr); 3268 3269 /* put together the new matrix */ 3270 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 3271 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 3272 b = (Mat_SeqAIJ*)B->data; 3273 b->free_a = PETSC_TRUE; 3274 b->free_ij = PETSC_TRUE; 3275 b->singlemalloc = PETSC_FALSE; 3276 b->a = ba; 3277 b->j = bj; 3278 b->i = bi; 3279 b->diag = bdiag; 3280 b->ilen = 0; 3281 b->imax = 0; 3282 b->row = isrow; 3283 b->col = iscol; 3284 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 3285 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 3286 b->icol = isicol; 3287 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 3288 3289 ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3290 b->maxnz = nnz_max; 3291 3292 B->factor = MAT_FACTOR_ILUDT; 3293 B->info.factor_mallocs = 0; 3294 B->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]); 3295 CHKMEMQ; 3296 /* ------- end of symbolic factorization ---------*/ 3297 3298 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3299 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3300 ics = ic; 3301 3302 /* linked list for storing column indices of the active row */ 3303 nlnk = n + 1; 3304 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3305 3306 /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */ 3307 ierr = PetscMalloc2(n,PetscInt,&im,n,PetscInt,&jtmp);CHKERRQ(ierr); 3308 /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */ 3309 ierr = PetscMalloc2(n,MatScalar,&rtmp,n,MatScalar,&vtmp);CHKERRQ(ierr); 3310 ierr = PetscMemzero(rtmp,n*sizeof(MatScalar));CHKERRQ(ierr); 3311 3312 bi[0] = 0; 3313 bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */ 3314 bdiag_rev[n] = bdiag[0]; 3315 bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */ 3316 for (i=0; i<n; i++) { 3317 /* copy initial fill into linked list */ 3318 nzi = 0; /* nonzeros for active row i */ 3319 nzi = ai[r[i]+1] - ai[r[i]]; 3320 if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 3321 nzi_al = adiag[r[i]] - ai[r[i]]; 3322 nzi_au = ai[r[i]+1] - adiag[r[i]] -1; 3323 ajtmp = aj + ai[r[i]]; 3324 ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3325 3326 /* load in initial (unfactored row) */ 3327 aatmp = a->a + ai[r[i]]; 3328 for (j=0; j<nzi; j++) { 3329 rtmp[ics[*ajtmp++]] = *aatmp++; 3330 } 3331 3332 /* add pivot rows into linked list */ 3333 row = lnk[n]; 3334 while (row < i ) { 3335 nzi_bl = bi[row+1] - bi[row] + 1; 3336 bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */ 3337 ierr = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr); 3338 nzi += nlnk; 3339 row = lnk[row]; 3340 } 3341 3342 /* copy data from lnk into jtmp, then initialize lnk */ 3343 ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr); 3344 3345 /* numerical factorization */ 3346 bjtmp = jtmp; 3347 row = *bjtmp++; /* 1st pivot row */ 3348 while ( row < i ) { 3349 pc = rtmp + row; 3350 pv = ba + bdiag[row]; /* 1./(diag of the pivot row) */ 3351 multiplier = (*pc) * (*pv); 3352 *pc = multiplier; 3353 if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */ 3354 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3355 pv = ba + bdiag[row+1] + 1; 3356 /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */ 3357 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3358 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3359 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 3360 } 3361 row = *bjtmp++; 3362 } 3363 3364 /* copy sparse rtmp into contiguous vtmp; separate L and U part */ 3365 diag_tmp = rtmp[i]; /* save diagonal value - may not needed?? */ 3366 nzi_bl = 0; j = 0; 3367 while (jtmp[j] < i){ /* Note: jtmp is sorted */ 3368 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3369 nzi_bl++; j++; 3370 } 3371 nzi_bu = nzi - nzi_bl -1; 3372 while (j < nzi){ 3373 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3374 j++; 3375 } 3376 3377 bjtmp = bj + bi[i]; 3378 batmp = ba + bi[i]; 3379 /* apply level dropping rule to L part */ 3380 ncut = nzi_al + dtcount; 3381 if (ncut < nzi_bl){ 3382 ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr); 3383 ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr); 3384 } else { 3385 ncut = nzi_bl; 3386 } 3387 for (j=0; j<ncut; j++){ 3388 bjtmp[j] = jtmp[j]; 3389 batmp[j] = vtmp[j]; 3390 /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */ 3391 } 3392 bi[i+1] = bi[i] + ncut; 3393 nzi = ncut + 1; 3394 3395 /* apply level dropping rule to U part */ 3396 ncut = nzi_au + dtcount; 3397 if (ncut < nzi_bu){ 3398 ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr); 3399 ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr); 3400 } else { 3401 ncut = nzi_bu; 3402 } 3403 nzi += ncut; 3404 3405 /* mark bdiagonal */ 3406 bdiag[i+1] = bdiag[i] - (ncut + 1); 3407 bdiag_rev[n-i-1] = bdiag[i+1]; 3408 bi[2*n - i] = bi[2*n - i +1] - (ncut + 1); 3409 bjtmp = bj + bdiag[i]; 3410 batmp = ba + bdiag[i]; 3411 *bjtmp = i; 3412 *batmp = diag_tmp; /* rtmp[i]; */ 3413 if (*batmp == 0.0) { 3414 *batmp = dt+shift; 3415 /* printf(" row %d add shift %g\n",i,shift); */ 3416 } 3417 *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */ 3418 /* printf(" (%d,%g),",*bjtmp,*batmp); */ 3419 3420 bjtmp = bj + bdiag[i+1]+1; 3421 batmp = ba + bdiag[i+1]+1; 3422 for (k=0; k<ncut; k++){ 3423 bjtmp[k] = jtmp[nzi_bl+1+k]; 3424 batmp[k] = vtmp[nzi_bl+1+k]; 3425 /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */ 3426 } 3427 /* printf("\n"); */ 3428 3429 im[i] = nzi; /* used by PetscLLAddSortedLU() */ 3430 /* 3431 printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]); 3432 printf(" ----------------------------\n"); 3433 */ 3434 } /* for (i=0; i<n; i++) */ 3435 /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */ 3436 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]); 3437 3438 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3439 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3440 3441 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3442 ierr = PetscFree2(im,jtmp);CHKERRQ(ierr); 3443 ierr = PetscFree2(rtmp,vtmp);CHKERRQ(ierr); 3444 ierr = PetscFree(bdiag_rev);CHKERRQ(ierr); 3445 3446 ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr); 3447 b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n]; 3448 3449 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3450 ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr); 3451 both_identity = (PetscTruth) (row_identity && icol_identity); 3452 if (row_identity && icol_identity) { 3453 B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 3454 } else { 3455 B->ops->solve = MatSolve_SeqAIJ; 3456 } 3457 3458 B->ops->solveadd = 0; 3459 B->ops->solvetranspose = 0; 3460 B->ops->solvetransposeadd = 0; 3461 B->ops->matsolve = 0; 3462 B->assembled = PETSC_TRUE; 3463 B->preallocated = PETSC_TRUE; 3464 PetscFunctionReturn(0); 3465 } 3466 3467 /* a wraper of MatILUDTFactor_SeqAIJ() */ 3468 #undef __FUNCT__ 3469 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ" 3470 /* 3471 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 3472 */ 3473 3474 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info) 3475 { 3476 PetscErrorCode ierr; 3477 3478 PetscFunctionBegin; 3479 ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr); 3480 PetscFunctionReturn(0); 3481 } 3482 3483 /* 3484 same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors 3485 - intend to replace existing MatLUFactorNumeric_SeqAIJ() 3486 */ 3487 #undef __FUNCT__ 3488 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ" 3489 /* 3490 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 3491 */ 3492 3493 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info) 3494 { 3495 Mat C=fact; 3496 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 3497 IS isrow = b->row,isicol = b->icol; 3498 PetscErrorCode ierr; 3499 const PetscInt *r,*ic,*ics; 3500 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 3501 PetscInt *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj; 3502 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 3503 PetscReal dt=info->dt,shift=info->shiftamount; 3504 PetscTruth row_identity, col_identity; 3505 3506 PetscFunctionBegin; 3507 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3508 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3509 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 3510 ics = ic; 3511 3512 for (i=0; i<n; i++){ 3513 /* initialize rtmp array */ 3514 nzl = bi[i+1] - bi[i]; /* num of nozeros in L(i,:) */ 3515 bjtmp = bj + bi[i]; 3516 for (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0; 3517 rtmp[i] = 0.0; 3518 nzu = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */ 3519 bjtmp = bj + bdiag[i+1] + 1; 3520 for (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0; 3521 3522 /* load in initial unfactored row of A */ 3523 /* printf("row %d\n",i); */ 3524 nz = ai[r[i]+1] - ai[r[i]]; 3525 ajtmp = aj + ai[r[i]]; 3526 v = aa + ai[r[i]]; 3527 for (j=0; j<nz; j++) { 3528 rtmp[ics[*ajtmp++]] = v[j]; 3529 /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */ 3530 } 3531 /* printf("\n"); */ 3532 3533 /* numerical factorization */ 3534 bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */ 3535 nzl = bi[i+1] - bi[i]; /* num of entries in L(i,:) */ 3536 k = 0; 3537 while (k < nzl){ 3538 row = *bjtmp++; 3539 /* printf(" prow %d\n",row); */ 3540 pc = rtmp + row; 3541 pv = b->a + bdiag[row]; /* 1./(diag of the pivot row) */ 3542 multiplier = (*pc) * (*pv); 3543 *pc = multiplier; 3544 if (PetscAbsScalar(multiplier) > dt){ 3545 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3546 pv = b->a + bdiag[row+1] + 1; 3547 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3548 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3549 /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */ 3550 } 3551 k++; 3552 } 3553 3554 /* finished row so stick it into b->a */ 3555 /* L-part */ 3556 pv = b->a + bi[i] ; 3557 pj = bj + bi[i] ; 3558 nzl = bi[i+1] - bi[i]; 3559 for (j=0; j<nzl; j++) { 3560 pv[j] = rtmp[pj[j]]; 3561 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3562 } 3563 3564 /* diagonal: invert diagonal entries for simplier triangular solves */ 3565 if (rtmp[i] == 0.0) rtmp[i] = dt+shift; 3566 b->a[bdiag[i]] = 1.0/rtmp[i]; 3567 /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */ 3568 3569 /* U-part */ 3570 pv = b->a + bdiag[i+1] + 1; 3571 pj = bj + bdiag[i+1] + 1; 3572 nzu = bdiag[i] - bdiag[i+1] - 1; 3573 for (j=0; j<nzu; j++) { 3574 pv[j] = rtmp[pj[j]]; 3575 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3576 } 3577 /* printf("\n"); */ 3578 } 3579 3580 ierr = PetscFree(rtmp);CHKERRQ(ierr); 3581 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3582 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3583 3584 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3585 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 3586 if (row_identity && col_identity) { 3587 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 3588 } else { 3589 C->ops->solve = MatSolve_SeqAIJ; 3590 } 3591 C->ops->solveadd = 0; 3592 C->ops->solvetranspose = 0; 3593 C->ops->solvetransposeadd = 0; 3594 C->ops->matsolve = 0; 3595 C->assembled = PETSC_TRUE; 3596 C->preallocated = PETSC_TRUE; 3597 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 3598 PetscFunctionReturn(0); 3599 } 3600