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 PetscTruth olddatastruct=PETSC_FALSE; 1714 1715 PetscFunctionBegin; 1716 /* Uncomment the old data struct part only while testing new data structure for MatSolve() */ 1717 ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_old",&olddatastruct,PETSC_NULL);CHKERRQ(ierr); 1718 if(olddatastruct){ 1719 ierr = MatILUFactorSymbolic_SeqAIJ_inplace(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1720 PetscFunctionReturn(0); 1721 } 1722 1723 levels = (PetscInt)info->levels; 1724 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1725 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1726 1727 if (!levels && row_identity && col_identity) { 1728 /* special case: ilu(0) with natural ordering */ 1729 ierr = MatILUFactorSymbolic_SeqAIJ_ilu0(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1730 ierr = Mat_CheckInode_FactorLU(fact,PETSC_FALSE);CHKERRQ(ierr); 1731 PetscFunctionReturn(0); 1732 } 1733 1734 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); 1735 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1736 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1737 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1738 1739 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1740 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1741 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1742 bi[0] = bdiag[0] = 0; 1743 1744 ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr); 1745 1746 /* create a linked list for storing column indices of the active row */ 1747 nlnk = n + 1; 1748 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1749 1750 /* initial FreeSpace size is f*(ai[n]+1) */ 1751 f = info->fill; 1752 diagonal_fill = (PetscInt)info->diagonal_fill; 1753 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1754 current_space = free_space; 1755 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1756 current_space_lvl = free_space_lvl; 1757 1758 for (i=0; i<n; i++) { 1759 nzi = 0; 1760 /* copy current row into linked list */ 1761 nnz = ai[r[i]+1] - ai[r[i]]; 1762 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1763 cols = aj + ai[r[i]]; 1764 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1765 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1766 nzi += nlnk; 1767 1768 /* make sure diagonal entry is included */ 1769 if (diagonal_fill && lnk[i] == -1) { 1770 fm = n; 1771 while (lnk[fm] < i) fm = lnk[fm]; 1772 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1773 lnk[fm] = i; 1774 lnk_lvl[i] = 0; 1775 nzi++; dcount++; 1776 } 1777 1778 /* add pivot rows into the active row */ 1779 nzbd = 0; 1780 prow = lnk[n]; 1781 while (prow < i) { 1782 nnz = bdiag[prow]; 1783 cols = bj_ptr[prow] + nnz + 1; 1784 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1785 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1786 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1787 nzi += nlnk; 1788 prow = lnk[prow]; 1789 nzbd++; 1790 } 1791 bdiag[i] = nzbd; 1792 bi[i+1] = bi[i] + nzi; 1793 1794 /* if free space is not available, make more free space */ 1795 if (current_space->local_remaining<nzi) { 1796 nnz = 2*nzi*(n - i); /* estimated and max additional space needed */ 1797 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1798 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1799 reallocs++; 1800 } 1801 1802 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1803 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1804 bj_ptr[i] = current_space->array; 1805 bjlvl_ptr[i] = current_space_lvl->array; 1806 1807 /* make sure the active row i has diagonal entry */ 1808 if (*(bj_ptr[i]+bdiag[i]) != i) { 1809 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 1810 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1811 } 1812 1813 current_space->array += nzi; 1814 current_space->local_used += nzi; 1815 current_space->local_remaining -= nzi; 1816 current_space_lvl->array += nzi; 1817 current_space_lvl->local_used += nzi; 1818 current_space_lvl->local_remaining -= nzi; 1819 } 1820 1821 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1822 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1823 1824 /* destroy list of free space and other temporary arrays */ 1825 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 1826 1827 /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */ 1828 ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 1829 1830 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1831 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1832 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 1833 1834 #if defined(PETSC_USE_INFO) 1835 { 1836 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1837 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 1838 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1839 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 1840 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1841 if (diagonal_fill) { 1842 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 1843 } 1844 } 1845 #endif 1846 1847 /* put together the new matrix */ 1848 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 1849 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 1850 b = (Mat_SeqAIJ*)(fact)->data; 1851 b->free_a = PETSC_TRUE; 1852 b->free_ij = PETSC_TRUE; 1853 b->singlemalloc = PETSC_FALSE; 1854 ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 1855 b->j = bj; 1856 b->i = bi; 1857 b->diag = bdiag; 1858 b->ilen = 0; 1859 b->imax = 0; 1860 b->row = isrow; 1861 b->col = iscol; 1862 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1863 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1864 b->icol = isicol; 1865 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1866 /* In b structure: Free imax, ilen, old a, old j. 1867 Allocate bdiag, solve_work, new a, new j */ 1868 ierr = PetscLogObjectMemory(fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1869 b->maxnz = b->nz = bdiag[0]+1; 1870 (fact)->info.factor_mallocs = reallocs; 1871 (fact)->info.fill_ratio_given = f; 1872 (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 1873 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1874 if (a->inode.size) { 1875 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode; 1876 } 1877 PetscFunctionReturn(0); 1878 } 1879 1880 #undef __FUNCT__ 1881 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_inplace" 1882 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1883 { 1884 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1885 IS isicol; 1886 PetscErrorCode ierr; 1887 const PetscInt *r,*ic; 1888 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,d; 1889 PetscInt *bi,*cols,nnz,*cols_lvl; 1890 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1891 PetscInt i,levels,diagonal_fill; 1892 PetscTruth col_identity,row_identity; 1893 PetscReal f; 1894 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1895 PetscBT lnkbt; 1896 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1897 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1898 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1899 PetscTruth missing; 1900 1901 PetscFunctionBegin; 1902 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); 1903 f = info->fill; 1904 levels = (PetscInt)info->levels; 1905 diagonal_fill = (PetscInt)info->diagonal_fill; 1906 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1907 1908 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1909 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1910 if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */ 1911 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr); 1912 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace; 1913 if (a->inode.size) { 1914 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace; 1915 } 1916 fact->factor = MAT_FACTOR_ILU; 1917 (fact)->info.factor_mallocs = 0; 1918 (fact)->info.fill_ratio_given = info->fill; 1919 (fact)->info.fill_ratio_needed = 1.0; 1920 b = (Mat_SeqAIJ*)(fact)->data; 1921 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 1922 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 1923 b->row = isrow; 1924 b->col = iscol; 1925 b->icol = isicol; 1926 ierr = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1927 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1928 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1929 PetscFunctionReturn(0); 1930 } 1931 1932 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1933 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1934 1935 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1936 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1937 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1938 bi[0] = bdiag[0] = 0; 1939 1940 ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr); 1941 1942 /* create a linked list for storing column indices of the active row */ 1943 nlnk = n + 1; 1944 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1945 1946 /* initial FreeSpace size is f*(ai[n]+1) */ 1947 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1948 current_space = free_space; 1949 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1950 current_space_lvl = free_space_lvl; 1951 1952 for (i=0; i<n; i++) { 1953 nzi = 0; 1954 /* copy current row into linked list */ 1955 nnz = ai[r[i]+1] - ai[r[i]]; 1956 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1957 cols = aj + ai[r[i]]; 1958 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1959 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1960 nzi += nlnk; 1961 1962 /* make sure diagonal entry is included */ 1963 if (diagonal_fill && lnk[i] == -1) { 1964 fm = n; 1965 while (lnk[fm] < i) fm = lnk[fm]; 1966 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1967 lnk[fm] = i; 1968 lnk_lvl[i] = 0; 1969 nzi++; dcount++; 1970 } 1971 1972 /* add pivot rows into the active row */ 1973 nzbd = 0; 1974 prow = lnk[n]; 1975 while (prow < i) { 1976 nnz = bdiag[prow]; 1977 cols = bj_ptr[prow] + nnz + 1; 1978 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1979 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1980 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1981 nzi += nlnk; 1982 prow = lnk[prow]; 1983 nzbd++; 1984 } 1985 bdiag[i] = nzbd; 1986 bi[i+1] = bi[i] + nzi; 1987 1988 /* if free space is not available, make more free space */ 1989 if (current_space->local_remaining<nzi) { 1990 nnz = nzi*(n - i); /* estimated and max additional space needed */ 1991 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1992 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1993 reallocs++; 1994 } 1995 1996 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1997 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1998 bj_ptr[i] = current_space->array; 1999 bjlvl_ptr[i] = current_space_lvl->array; 2000 2001 /* make sure the active row i has diagonal entry */ 2002 if (*(bj_ptr[i]+bdiag[i]) != i) { 2003 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 2004 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 2005 } 2006 2007 current_space->array += nzi; 2008 current_space->local_used += nzi; 2009 current_space->local_remaining -= nzi; 2010 current_space_lvl->array += nzi; 2011 current_space_lvl->local_used += nzi; 2012 current_space_lvl->local_remaining -= nzi; 2013 } 2014 2015 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 2016 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 2017 2018 /* destroy list of free space and other temporary arrays */ 2019 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 2020 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */ 2021 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2022 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2023 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 2024 2025 #if defined(PETSC_USE_INFO) 2026 { 2027 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 2028 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 2029 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2030 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 2031 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 2032 if (diagonal_fill) { 2033 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 2034 } 2035 } 2036 #endif 2037 2038 /* put together the new matrix */ 2039 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 2040 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 2041 b = (Mat_SeqAIJ*)(fact)->data; 2042 b->free_a = PETSC_TRUE; 2043 b->free_ij = PETSC_TRUE; 2044 b->singlemalloc = PETSC_FALSE; 2045 ierr = PetscMalloc(bi[n]*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 2046 b->j = bj; 2047 b->i = bi; 2048 for (i=0; i<n; i++) bdiag[i] += bi[i]; 2049 b->diag = bdiag; 2050 b->ilen = 0; 2051 b->imax = 0; 2052 b->row = isrow; 2053 b->col = iscol; 2054 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 2055 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 2056 b->icol = isicol; 2057 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2058 /* In b structure: Free imax, ilen, old a, old j. 2059 Allocate bdiag, solve_work, new a, new j */ 2060 ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 2061 b->maxnz = b->nz = bi[n] ; 2062 (fact)->info.factor_mallocs = reallocs; 2063 (fact)->info.fill_ratio_given = f; 2064 (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 2065 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace; 2066 if (a->inode.size) { 2067 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace; 2068 } 2069 PetscFunctionReturn(0); 2070 } 2071 2072 #undef __FUNCT__ 2073 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ" 2074 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 2075 { 2076 Mat C = B; 2077 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2078 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2079 IS ip=b->row,iip = b->icol; 2080 PetscErrorCode ierr; 2081 const PetscInt *rip,*riip; 2082 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp; 2083 PetscInt *ai=a->i,*aj=a->j; 2084 PetscInt k,jmin,jmax,*c2r,*il,col,nexti,ili,nz; 2085 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2086 PetscTruth perm_identity; 2087 2088 FactorShiftCtx sctx; 2089 PetscReal rs; 2090 MatScalar d,*v; 2091 2092 PetscFunctionBegin; 2093 /* MatPivotSetUp(): initialize shift context sctx */ 2094 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 2095 2096 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 2097 sctx.shift_top = info->zeropivot; 2098 for (i=0; i<mbs; i++) { 2099 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 2100 d = (aa)[a->diag[i]]; 2101 rs = -PetscAbsScalar(d) - PetscRealPart(d); 2102 v = aa+ai[i]; 2103 nz = ai[i+1] - ai[i]; 2104 for (j=0; j<nz; j++) 2105 rs += PetscAbsScalar(v[j]); 2106 if (rs>sctx.shift_top) sctx.shift_top = rs; 2107 } 2108 sctx.shift_top *= 1.1; 2109 sctx.nshift_max = 5; 2110 sctx.shift_lo = 0.; 2111 sctx.shift_hi = 1.; 2112 } 2113 2114 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2115 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2116 2117 /* allocate working arrays 2118 c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col 2119 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 2120 */ 2121 ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&c2r);CHKERRQ(ierr); 2122 2123 do { 2124 sctx.useshift = PETSC_FALSE; 2125 2126 for (i=0; i<mbs; i++) c2r[i] = mbs; 2127 il[0] = 0; 2128 2129 for (k = 0; k<mbs; k++){ 2130 /* zero rtmp */ 2131 nz = bi[k+1] - bi[k]; 2132 bjtmp = bj + bi[k]; 2133 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2134 2135 /* load in initial unfactored row */ 2136 bval = ba + bi[k]; 2137 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2138 for (j = jmin; j < jmax; j++){ 2139 col = riip[aj[j]]; 2140 if (col >= k){ /* only take upper triangular entry */ 2141 rtmp[col] = aa[j]; 2142 *bval++ = 0.0; /* for in-place factorization */ 2143 } 2144 } 2145 /* shift the diagonal of the matrix: ZeropivotApply() */ 2146 rtmp[k] += sctx.shift_amount; /* shift the diagonal of the matrix */ 2147 2148 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2149 dk = rtmp[k]; 2150 i = c2r[k]; /* first row to be added to k_th row */ 2151 2152 while (i < k){ 2153 nexti = c2r[i]; /* next row to be added to k_th row */ 2154 2155 /* compute multiplier, update diag(k) and U(i,k) */ 2156 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2157 uikdi = - ba[ili]*ba[bdiag[i]]; /* diagonal(k) */ 2158 dk += uikdi*ba[ili]; /* update diag[k] */ 2159 ba[ili] = uikdi; /* -U(i,k) */ 2160 2161 /* add multiple of row i to k-th row */ 2162 jmin = ili + 1; jmax = bi[i+1]; 2163 if (jmin < jmax){ 2164 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2165 /* update il and c2r for row i */ 2166 il[i] = jmin; 2167 j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i; 2168 } 2169 i = nexti; 2170 } 2171 2172 /* copy data into U(k,:) */ 2173 rs = 0.0; 2174 jmin = bi[k]; jmax = bi[k+1]-1; 2175 if (jmin < jmax) { 2176 for (j=jmin; j<jmax; j++){ 2177 col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]); 2178 } 2179 /* add the k-th row into il and c2r */ 2180 il[k] = jmin; 2181 i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k; 2182 } 2183 2184 /* MatPivotCheck() */ 2185 sctx.rs = rs; 2186 sctx.pv = dk; 2187 if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO){ 2188 ierr = MatPivotCheck_nz(info,sctx,k);CHKERRQ(ierr); 2189 } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE){ 2190 ierr = MatPivotCheck_pd(info,sctx,k);CHKERRQ(ierr); 2191 } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS){ 2192 ierr = MatPivotCheck_inblocks(info,sctx,k);CHKERRQ(ierr); 2193 } else { 2194 ierr = MatPivotCheck_none(info,sctx,k);CHKERRQ(ierr); 2195 } 2196 dk = sctx.pv; 2197 2198 ba[bdiag[k]] = 1.0/dk; /* U(k,k) */ 2199 } 2200 } while (sctx.useshift); 2201 2202 ierr = PetscFree3(rtmp,il,c2r);CHKERRQ(ierr); 2203 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2204 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2205 2206 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2207 if (perm_identity){ 2208 B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2209 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2210 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering; 2211 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering; 2212 } else { 2213 B->ops->solve = MatSolve_SeqSBAIJ_1; 2214 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1; 2215 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1; 2216 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1; 2217 } 2218 2219 C->assembled = PETSC_TRUE; 2220 C->preallocated = PETSC_TRUE; 2221 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2222 2223 /* MatPivotView() */ 2224 if (sctx.nshift){ 2225 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 2226 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); 2227 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 2228 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2229 } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS){ 2230 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftamount);CHKERRQ(ierr); 2231 } 2232 } 2233 PetscFunctionReturn(0); 2234 } 2235 2236 #undef __FUNCT__ 2237 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ_inplace" 2238 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info) 2239 { 2240 Mat C = B; 2241 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2242 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2243 IS ip=b->row,iip = b->icol; 2244 PetscErrorCode ierr; 2245 const PetscInt *rip,*riip; 2246 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol,*bjtmp; 2247 PetscInt *ai=a->i,*aj=a->j; 2248 PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz; 2249 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2250 PetscReal zeropivot,rs; 2251 ChShift_Ctx sctx; 2252 PetscInt newshift; 2253 PetscTruth perm_identity; 2254 2255 PetscFunctionBegin; 2256 zeropivot = info->zeropivot; 2257 2258 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2259 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2260 2261 /* initialization */ 2262 ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr); 2263 sctx.shift_amount = 0; 2264 sctx.nshift = 0; 2265 do { 2266 sctx.chshift = PETSC_FALSE; 2267 for (i=0; i<mbs; i++) jl[i] = mbs; 2268 il[0] = 0; 2269 2270 for (k = 0; k<mbs; k++){ 2271 /* zero rtmp */ 2272 nz = bi[k+1] - bi[k]; 2273 bjtmp = bj + bi[k]; 2274 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2275 2276 bval = ba + bi[k]; 2277 /* initialize k-th row by the perm[k]-th row of A */ 2278 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2279 for (j = jmin; j < jmax; j++){ 2280 col = riip[aj[j]]; 2281 if (col >= k){ /* only take upper triangular entry */ 2282 rtmp[col] = aa[j]; 2283 *bval++ = 0.0; /* for in-place factorization */ 2284 } 2285 } 2286 /* shift the diagonal of the matrix */ 2287 if (sctx.nshift) rtmp[k] += sctx.shift_amount; 2288 2289 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2290 dk = rtmp[k]; 2291 i = jl[k]; /* first row to be added to k_th row */ 2292 2293 while (i < k){ 2294 nexti = jl[i]; /* next row to be added to k_th row */ 2295 2296 /* compute multiplier, update diag(k) and U(i,k) */ 2297 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2298 uikdi = - ba[ili]*ba[bi[i]]; /* diagonal(k) */ 2299 dk += uikdi*ba[ili]; 2300 ba[ili] = uikdi; /* -U(i,k) */ 2301 2302 /* add multiple of row i to k-th row */ 2303 jmin = ili + 1; jmax = bi[i+1]; 2304 if (jmin < jmax){ 2305 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2306 /* update il and jl for row i */ 2307 il[i] = jmin; 2308 j = bj[jmin]; jl[i] = jl[j]; jl[j] = i; 2309 } 2310 i = nexti; 2311 } 2312 2313 /* shift the diagonals when zero pivot is detected */ 2314 /* compute rs=sum of abs(off-diagonal) */ 2315 rs = 0.0; 2316 jmin = bi[k]+1; 2317 nz = bi[k+1] - jmin; 2318 bcol = bj + jmin; 2319 for (j=0; j<nz; j++) { 2320 rs += PetscAbsScalar(rtmp[bcol[j]]); 2321 } 2322 2323 sctx.rs = rs; 2324 sctx.pv = dk; 2325 ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr); 2326 2327 if (newshift == 1) { 2328 if (!sctx.shift_amount) { 2329 sctx.shift_amount = 1e-5; 2330 } 2331 break; 2332 } 2333 2334 /* copy data into U(k,:) */ 2335 ba[bi[k]] = 1.0/dk; /* U(k,k) */ 2336 jmin = bi[k]+1; jmax = bi[k+1]; 2337 if (jmin < jmax) { 2338 for (j=jmin; j<jmax; j++){ 2339 col = bj[j]; ba[j] = rtmp[col]; 2340 } 2341 /* add the k-th row into il and jl */ 2342 il[k] = jmin; 2343 i = bj[jmin]; jl[k] = jl[i]; jl[i] = k; 2344 } 2345 } 2346 } while (sctx.chshift); 2347 ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr); 2348 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2349 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2350 2351 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2352 if (perm_identity){ 2353 B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2354 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2355 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2356 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2357 } else { 2358 B->ops->solve = MatSolve_SeqSBAIJ_1_inplace; 2359 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_inplace; 2360 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_inplace; 2361 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_inplace; 2362 } 2363 2364 C->assembled = PETSC_TRUE; 2365 C->preallocated = PETSC_TRUE; 2366 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2367 if (sctx.nshift){ 2368 if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 2369 ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2370 } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 2371 ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2372 } 2373 } 2374 PetscFunctionReturn(0); 2375 } 2376 2377 /* 2378 icc() under revised new data structure. 2379 Factored arrays bj and ba are stored as 2380 U(0,:),...,U(i,:),U(n-1,:) 2381 2382 ui=fact->i is an array of size n+1, in which 2383 ui+ 2384 ui[i]: points to 1st entry of U(i,:),i=0,...,n-1 2385 ui[n]: points to U(n-1,n-1)+1 2386 2387 udiag=fact->diag is an array of size n,in which 2388 udiag[i]: points to diagonal of U(i,:), i=0,...,n-1 2389 2390 U(i,:) contains udiag[i] as its last entry, i.e., 2391 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 2392 */ 2393 2394 #undef __FUNCT__ 2395 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ" 2396 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2397 { 2398 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2399 Mat_SeqSBAIJ *b; 2400 PetscErrorCode ierr; 2401 PetscTruth perm_identity,missing; 2402 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2403 const PetscInt *rip,*riip; 2404 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2405 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2406 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2407 PetscReal fill=info->fill,levels=info->levels; 2408 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2409 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2410 PetscBT lnkbt; 2411 IS iperm; 2412 2413 PetscFunctionBegin; 2414 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); 2415 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2416 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2417 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2418 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2419 2420 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2421 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2422 ui[0] = 0; 2423 2424 /* ICC(0) without matrix ordering: simply rearrange column indices */ 2425 if (!levels && perm_identity) { 2426 for (i=0; i<am; i++) { 2427 ncols = ai[i+1] - a->diag[i]; 2428 ui[i+1] = ui[i] + ncols; 2429 udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */ 2430 } 2431 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2432 cols = uj; 2433 for (i=0; i<am; i++) { 2434 aj = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */ 2435 ncols = ai[i+1] - a->diag[i] -1; 2436 for (j=0; j<ncols; j++) *cols++ = aj[j]; 2437 *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */ 2438 } 2439 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2440 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2441 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2442 2443 /* initialization */ 2444 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2445 2446 /* jl: linked list for storing indices of the pivot rows 2447 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2448 ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr); 2449 for (i=0; i<am; i++){ 2450 jl[i] = am; il[i] = 0; 2451 } 2452 2453 /* create and initialize a linked list for storing column indices of the active row k */ 2454 nlnk = am + 1; 2455 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2456 2457 /* initial FreeSpace size is fill*(ai[am]+1) */ 2458 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2459 current_space = free_space; 2460 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2461 current_space_lvl = free_space_lvl; 2462 2463 for (k=0; k<am; k++){ /* for each active row k */ 2464 /* initialize lnk by the column indices of row rip[k] of A */ 2465 nzk = 0; 2466 ncols = ai[rip[k]+1] - ai[rip[k]]; 2467 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2468 ncols_upper = 0; 2469 for (j=0; j<ncols; j++){ 2470 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2471 if (riip[i] >= k){ /* only take upper triangular entry */ 2472 ajtmp[ncols_upper] = i; 2473 ncols_upper++; 2474 } 2475 } 2476 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2477 nzk += nlnk; 2478 2479 /* update lnk by computing fill-in for each pivot row to be merged in */ 2480 prow = jl[k]; /* 1st pivot row */ 2481 2482 while (prow < k){ 2483 nextprow = jl[prow]; 2484 2485 /* merge prow into k-th row */ 2486 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2487 jmax = ui[prow+1]; 2488 ncols = jmax-jmin; 2489 i = jmin - ui[prow]; 2490 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2491 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2492 j = *(uj - 1); 2493 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2494 nzk += nlnk; 2495 2496 /* update il and jl for prow */ 2497 if (jmin < jmax){ 2498 il[prow] = jmin; 2499 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2500 } 2501 prow = nextprow; 2502 } 2503 2504 /* if free space is not available, make more free space */ 2505 if (current_space->local_remaining<nzk) { 2506 i = am - k + 1; /* num of unfactored rows */ 2507 i *= PetscMin(nzk, i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2508 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2509 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2510 reallocs++; 2511 } 2512 2513 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2514 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2515 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2516 2517 /* add the k-th row into il and jl */ 2518 if (nzk > 1){ 2519 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2520 jl[k] = jl[i]; jl[i] = k; 2521 il[k] = ui[k] + 1; 2522 } 2523 uj_ptr[k] = current_space->array; 2524 uj_lvl_ptr[k] = current_space_lvl->array; 2525 2526 current_space->array += nzk; 2527 current_space->local_used += nzk; 2528 current_space->local_remaining -= nzk; 2529 2530 current_space_lvl->array += nzk; 2531 current_space_lvl->local_used += nzk; 2532 current_space_lvl->local_remaining -= nzk; 2533 2534 ui[k+1] = ui[k] + nzk; 2535 } 2536 2537 #if defined(PETSC_USE_INFO) 2538 if (ai[am] != 0) { 2539 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2540 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2541 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2542 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2543 } else { 2544 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2545 } 2546 #endif 2547 2548 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2549 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2550 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2551 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2552 2553 /* destroy list of free space and other temporary array(s) */ 2554 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2555 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor */ 2556 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2557 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2558 2559 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2560 2561 /* put together the new matrix in MATSEQSBAIJ format */ 2562 b = (Mat_SeqSBAIJ*)(fact)->data; 2563 b->singlemalloc = PETSC_FALSE; 2564 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2565 b->j = uj; 2566 b->i = ui; 2567 b->diag = udiag; 2568 b->free_diag = PETSC_TRUE; 2569 b->ilen = 0; 2570 b->imax = 0; 2571 b->row = perm; 2572 b->col = perm; 2573 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2574 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2575 b->icol = iperm; 2576 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2577 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2578 ierr = PetscLogObjectMemory(fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2579 b->maxnz = b->nz = ui[am]; 2580 b->free_a = PETSC_TRUE; 2581 b->free_ij = PETSC_TRUE; 2582 2583 fact->info.factor_mallocs = reallocs; 2584 fact->info.fill_ratio_given = fill; 2585 if (ai[am] != 0) { 2586 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2587 } else { 2588 fact->info.fill_ratio_needed = 0.0; 2589 } 2590 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2591 PetscFunctionReturn(0); 2592 } 2593 2594 #undef __FUNCT__ 2595 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ_inplace" 2596 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2597 { 2598 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2599 Mat_SeqSBAIJ *b; 2600 PetscErrorCode ierr; 2601 PetscTruth perm_identity,missing; 2602 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2603 const PetscInt *rip,*riip; 2604 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2605 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2606 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2607 PetscReal fill=info->fill,levels=info->levels; 2608 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2609 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2610 PetscBT lnkbt; 2611 IS iperm; 2612 2613 PetscFunctionBegin; 2614 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); 2615 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2616 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2617 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2618 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2619 2620 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2621 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2622 ui[0] = 0; 2623 2624 /* ICC(0) without matrix ordering: simply copies fill pattern */ 2625 if (!levels && perm_identity) { 2626 2627 for (i=0; i<am; i++) { 2628 ui[i+1] = ui[i] + ai[i+1] - a->diag[i]; 2629 udiag[i] = ui[i]; 2630 } 2631 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2632 cols = uj; 2633 for (i=0; i<am; i++) { 2634 aj = a->j + a->diag[i]; 2635 ncols = ui[i+1] - ui[i]; 2636 for (j=0; j<ncols; j++) *cols++ = *aj++; 2637 } 2638 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2639 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2640 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2641 2642 /* initialization */ 2643 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2644 2645 /* jl: linked list for storing indices of the pivot rows 2646 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2647 ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr); 2648 for (i=0; i<am; i++){ 2649 jl[i] = am; il[i] = 0; 2650 } 2651 2652 /* create and initialize a linked list for storing column indices of the active row k */ 2653 nlnk = am + 1; 2654 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2655 2656 /* initial FreeSpace size is fill*(ai[am]+1) */ 2657 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2658 current_space = free_space; 2659 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2660 current_space_lvl = free_space_lvl; 2661 2662 for (k=0; k<am; k++){ /* for each active row k */ 2663 /* initialize lnk by the column indices of row rip[k] of A */ 2664 nzk = 0; 2665 ncols = ai[rip[k]+1] - ai[rip[k]]; 2666 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2667 ncols_upper = 0; 2668 for (j=0; j<ncols; j++){ 2669 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2670 if (riip[i] >= k){ /* only take upper triangular entry */ 2671 ajtmp[ncols_upper] = i; 2672 ncols_upper++; 2673 } 2674 } 2675 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2676 nzk += nlnk; 2677 2678 /* update lnk by computing fill-in for each pivot row to be merged in */ 2679 prow = jl[k]; /* 1st pivot row */ 2680 2681 while (prow < k){ 2682 nextprow = jl[prow]; 2683 2684 /* merge prow into k-th row */ 2685 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2686 jmax = ui[prow+1]; 2687 ncols = jmax-jmin; 2688 i = jmin - ui[prow]; 2689 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2690 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2691 j = *(uj - 1); 2692 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2693 nzk += nlnk; 2694 2695 /* update il and jl for prow */ 2696 if (jmin < jmax){ 2697 il[prow] = jmin; 2698 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2699 } 2700 prow = nextprow; 2701 } 2702 2703 /* if free space is not available, make more free space */ 2704 if (current_space->local_remaining<nzk) { 2705 i = am - k + 1; /* num of unfactored rows */ 2706 i *= PetscMin(nzk, (i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2707 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2708 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2709 reallocs++; 2710 } 2711 2712 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2713 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2714 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2715 2716 /* add the k-th row into il and jl */ 2717 if (nzk > 1){ 2718 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2719 jl[k] = jl[i]; jl[i] = k; 2720 il[k] = ui[k] + 1; 2721 } 2722 uj_ptr[k] = current_space->array; 2723 uj_lvl_ptr[k] = current_space_lvl->array; 2724 2725 current_space->array += nzk; 2726 current_space->local_used += nzk; 2727 current_space->local_remaining -= nzk; 2728 2729 current_space_lvl->array += nzk; 2730 current_space_lvl->local_used += nzk; 2731 current_space_lvl->local_remaining -= nzk; 2732 2733 ui[k+1] = ui[k] + nzk; 2734 } 2735 2736 #if defined(PETSC_USE_INFO) 2737 if (ai[am] != 0) { 2738 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2739 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2740 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2741 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2742 } else { 2743 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2744 } 2745 #endif 2746 2747 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2748 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2749 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2750 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2751 2752 /* destroy list of free space and other temporary array(s) */ 2753 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2754 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 2755 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2756 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2757 2758 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2759 2760 /* put together the new matrix in MATSEQSBAIJ format */ 2761 2762 b = (Mat_SeqSBAIJ*)fact->data; 2763 b->singlemalloc = PETSC_FALSE; 2764 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2765 b->j = uj; 2766 b->i = ui; 2767 b->diag = udiag; 2768 b->free_diag = PETSC_TRUE; 2769 b->ilen = 0; 2770 b->imax = 0; 2771 b->row = perm; 2772 b->col = perm; 2773 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2774 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2775 b->icol = iperm; 2776 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2777 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2778 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2779 b->maxnz = b->nz = ui[am]; 2780 b->free_a = PETSC_TRUE; 2781 b->free_ij = PETSC_TRUE; 2782 2783 fact->info.factor_mallocs = reallocs; 2784 fact->info.fill_ratio_given = fill; 2785 if (ai[am] != 0) { 2786 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2787 } else { 2788 fact->info.fill_ratio_needed = 0.0; 2789 } 2790 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace; 2791 PetscFunctionReturn(0); 2792 } 2793 2794 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2795 { 2796 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2797 Mat_SeqSBAIJ *b; 2798 PetscErrorCode ierr; 2799 PetscTruth perm_identity; 2800 PetscReal fill = info->fill; 2801 const PetscInt *rip,*riip; 2802 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2803 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2804 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr,*udiag; 2805 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2806 PetscBT lnkbt; 2807 IS iperm; 2808 2809 PetscFunctionBegin; 2810 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); 2811 /* check whether perm is the identity mapping */ 2812 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2813 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2814 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2815 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2816 2817 /* initialization */ 2818 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2819 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2820 ui[0] = 0; 2821 2822 /* jl: linked list for storing indices of the pivot rows 2823 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2824 ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr); 2825 for (i=0; i<am; i++){ 2826 jl[i] = am; il[i] = 0; 2827 } 2828 2829 /* create and initialize a linked list for storing column indices of the active row k */ 2830 nlnk = am + 1; 2831 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2832 2833 /* initial FreeSpace size is fill*(ai[am]+1) */ 2834 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2835 current_space = free_space; 2836 2837 for (k=0; k<am; k++){ /* for each active row k */ 2838 /* initialize lnk by the column indices of row rip[k] of A */ 2839 nzk = 0; 2840 ncols = ai[rip[k]+1] - ai[rip[k]]; 2841 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2842 ncols_upper = 0; 2843 for (j=0; j<ncols; j++){ 2844 i = riip[*(aj + ai[rip[k]] + j)]; 2845 if (i >= k){ /* only take upper triangular entry */ 2846 cols[ncols_upper] = i; 2847 ncols_upper++; 2848 } 2849 } 2850 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2851 nzk += nlnk; 2852 2853 /* update lnk by computing fill-in for each pivot row to be merged in */ 2854 prow = jl[k]; /* 1st pivot row */ 2855 2856 while (prow < k){ 2857 nextprow = jl[prow]; 2858 /* merge prow into k-th row */ 2859 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2860 jmax = ui[prow+1]; 2861 ncols = jmax-jmin; 2862 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2863 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2864 nzk += nlnk; 2865 2866 /* update il and jl for prow */ 2867 if (jmin < jmax){ 2868 il[prow] = jmin; 2869 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 2870 } 2871 prow = nextprow; 2872 } 2873 2874 /* if free space is not available, make more free space */ 2875 if (current_space->local_remaining<nzk) { 2876 i = am - k + 1; /* num of unfactored rows */ 2877 i *= PetscMin(nzk,i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2878 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2879 reallocs++; 2880 } 2881 2882 /* copy data into free space, then initialize lnk */ 2883 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 2884 2885 /* add the k-th row into il and jl */ 2886 if (nzk > 1){ 2887 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2888 jl[k] = jl[i]; jl[i] = k; 2889 il[k] = ui[k] + 1; 2890 } 2891 ui_ptr[k] = current_space->array; 2892 current_space->array += nzk; 2893 current_space->local_used += nzk; 2894 current_space->local_remaining -= nzk; 2895 2896 ui[k+1] = ui[k] + nzk; 2897 } 2898 2899 #if defined(PETSC_USE_INFO) 2900 if (ai[am] != 0) { 2901 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 2902 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2903 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2904 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2905 } else { 2906 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2907 } 2908 #endif 2909 2910 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2911 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2912 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 2913 2914 /* destroy list of free space and other temporary array(s) */ 2915 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2916 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor */ 2917 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2918 2919 /* put together the new matrix in MATSEQSBAIJ format */ 2920 2921 b = (Mat_SeqSBAIJ*)fact->data; 2922 b->singlemalloc = PETSC_FALSE; 2923 b->free_a = PETSC_TRUE; 2924 b->free_ij = PETSC_TRUE; 2925 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2926 b->j = uj; 2927 b->i = ui; 2928 b->diag = udiag; 2929 b->free_diag = PETSC_TRUE; 2930 b->ilen = 0; 2931 b->imax = 0; 2932 b->row = perm; 2933 b->col = perm; 2934 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2935 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2936 b->icol = iperm; 2937 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2938 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2939 ierr = PetscLogObjectMemory(fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2940 b->maxnz = b->nz = ui[am]; 2941 2942 fact->info.factor_mallocs = reallocs; 2943 fact->info.fill_ratio_given = fill; 2944 if (ai[am] != 0) { 2945 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2946 } else { 2947 fact->info.fill_ratio_needed = 0.0; 2948 } 2949 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2950 PetscFunctionReturn(0); 2951 } 2952 2953 #undef __FUNCT__ 2954 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ_inplace" 2955 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2956 { 2957 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2958 Mat_SeqSBAIJ *b; 2959 PetscErrorCode ierr; 2960 PetscTruth perm_identity; 2961 PetscReal fill = info->fill; 2962 const PetscInt *rip,*riip; 2963 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2964 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2965 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr; 2966 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2967 PetscBT lnkbt; 2968 IS iperm; 2969 2970 PetscFunctionBegin; 2971 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); 2972 /* check whether perm is the identity mapping */ 2973 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2974 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2975 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2976 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2977 2978 /* initialization */ 2979 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2980 ui[0] = 0; 2981 2982 /* jl: linked list for storing indices of the pivot rows 2983 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2984 ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr); 2985 for (i=0; i<am; i++){ 2986 jl[i] = am; il[i] = 0; 2987 } 2988 2989 /* create and initialize a linked list for storing column indices of the active row k */ 2990 nlnk = am + 1; 2991 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2992 2993 /* initial FreeSpace size is fill*(ai[am]+1) */ 2994 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2995 current_space = free_space; 2996 2997 for (k=0; k<am; k++){ /* for each active row k */ 2998 /* initialize lnk by the column indices of row rip[k] of A */ 2999 nzk = 0; 3000 ncols = ai[rip[k]+1] - ai[rip[k]]; 3001 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 3002 ncols_upper = 0; 3003 for (j=0; j<ncols; j++){ 3004 i = riip[*(aj + ai[rip[k]] + j)]; 3005 if (i >= k){ /* only take upper triangular entry */ 3006 cols[ncols_upper] = i; 3007 ncols_upper++; 3008 } 3009 } 3010 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3011 nzk += nlnk; 3012 3013 /* update lnk by computing fill-in for each pivot row to be merged in */ 3014 prow = jl[k]; /* 1st pivot row */ 3015 3016 while (prow < k){ 3017 nextprow = jl[prow]; 3018 /* merge prow into k-th row */ 3019 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 3020 jmax = ui[prow+1]; 3021 ncols = jmax-jmin; 3022 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 3023 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3024 nzk += nlnk; 3025 3026 /* update il and jl for prow */ 3027 if (jmin < jmax){ 3028 il[prow] = jmin; 3029 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 3030 } 3031 prow = nextprow; 3032 } 3033 3034 /* if free space is not available, make more free space */ 3035 if (current_space->local_remaining<nzk) { 3036 i = am - k + 1; /* num of unfactored rows */ 3037 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 3038 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 3039 reallocs++; 3040 } 3041 3042 /* copy data into free space, then initialize lnk */ 3043 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 3044 3045 /* add the k-th row into il and jl */ 3046 if (nzk-1 > 0){ 3047 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 3048 jl[k] = jl[i]; jl[i] = k; 3049 il[k] = ui[k] + 1; 3050 } 3051 ui_ptr[k] = current_space->array; 3052 current_space->array += nzk; 3053 current_space->local_used += nzk; 3054 current_space->local_remaining -= nzk; 3055 3056 ui[k+1] = ui[k] + nzk; 3057 } 3058 3059 #if defined(PETSC_USE_INFO) 3060 if (ai[am] != 0) { 3061 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 3062 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 3063 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 3064 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 3065 } else { 3066 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 3067 } 3068 #endif 3069 3070 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 3071 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 3072 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 3073 3074 /* destroy list of free space and other temporary array(s) */ 3075 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 3076 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 3077 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3078 3079 /* put together the new matrix in MATSEQSBAIJ format */ 3080 3081 b = (Mat_SeqSBAIJ*)fact->data; 3082 b->singlemalloc = PETSC_FALSE; 3083 b->free_a = PETSC_TRUE; 3084 b->free_ij = PETSC_TRUE; 3085 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 3086 b->j = uj; 3087 b->i = ui; 3088 b->diag = 0; 3089 b->ilen = 0; 3090 b->imax = 0; 3091 b->row = perm; 3092 b->col = perm; 3093 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3094 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3095 b->icol = iperm; 3096 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 3097 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 3098 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3099 b->maxnz = b->nz = ui[am]; 3100 3101 fact->info.factor_mallocs = reallocs; 3102 fact->info.fill_ratio_given = fill; 3103 if (ai[am] != 0) { 3104 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 3105 } else { 3106 fact->info.fill_ratio_needed = 0.0; 3107 } 3108 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace; 3109 PetscFunctionReturn(0); 3110 } 3111 3112 #undef __FUNCT__ 3113 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering" 3114 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx) 3115 { 3116 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3117 PetscErrorCode ierr; 3118 PetscInt n = A->rmap->n; 3119 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag,*vi; 3120 PetscScalar *x,sum; 3121 const PetscScalar *b; 3122 const MatScalar *aa = a->a,*v; 3123 PetscInt i,nz; 3124 3125 PetscFunctionBegin; 3126 if (!n) PetscFunctionReturn(0); 3127 3128 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3129 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3130 3131 /* forward solve the lower triangular */ 3132 x[0] = b[0]; 3133 v = aa; 3134 vi = aj; 3135 for (i=1; i<n; i++) { 3136 nz = ai[i+1] - ai[i]; 3137 sum = b[i]; 3138 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3139 v += nz; 3140 vi += nz; 3141 x[i] = sum; 3142 } 3143 3144 /* backward solve the upper triangular */ 3145 for (i=n-1; i>=0; i--){ 3146 v = aa + adiag[i+1] + 1; 3147 vi = aj + adiag[i+1] + 1; 3148 nz = adiag[i] - adiag[i+1]-1; 3149 sum = x[i]; 3150 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3151 x[i] = sum*v[nz]; /* x[i]=aa[adiag[i]]*sum; v++; */ 3152 } 3153 3154 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 3155 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3156 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3157 PetscFunctionReturn(0); 3158 } 3159 3160 #undef __FUNCT__ 3161 #define __FUNCT__ "MatSolve_SeqAIJ" 3162 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx) 3163 { 3164 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3165 IS iscol = a->col,isrow = a->row; 3166 PetscErrorCode ierr; 3167 PetscInt i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz; 3168 const PetscInt *rout,*cout,*r,*c; 3169 PetscScalar *x,*tmp,sum; 3170 const PetscScalar *b; 3171 const MatScalar *aa = a->a,*v; 3172 3173 PetscFunctionBegin; 3174 if (!n) PetscFunctionReturn(0); 3175 3176 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3177 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3178 tmp = a->solve_work; 3179 3180 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 3181 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 3182 3183 /* forward solve the lower triangular */ 3184 tmp[0] = b[r[0]]; 3185 v = aa; 3186 vi = aj; 3187 for (i=1; i<n; i++) { 3188 nz = ai[i+1] - ai[i]; 3189 sum = b[r[i]]; 3190 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3191 tmp[i] = sum; 3192 v += nz; vi += nz; 3193 } 3194 3195 /* backward solve the upper triangular */ 3196 for (i=n-1; i>=0; i--){ 3197 v = aa + adiag[i+1]+1; 3198 vi = aj + adiag[i+1]+1; 3199 nz = adiag[i]-adiag[i+1]-1; 3200 sum = tmp[i]; 3201 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3202 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 3203 } 3204 3205 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 3206 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 3207 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3208 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3209 ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr); 3210 PetscFunctionReturn(0); 3211 } 3212 3213 #undef __FUNCT__ 3214 #define __FUNCT__ "MatILUDTFactor_SeqAIJ" 3215 /* 3216 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 3217 */ 3218 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact) 3219 { 3220 Mat B = *fact; 3221 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b; 3222 IS isicol; 3223 PetscErrorCode ierr; 3224 const PetscInt *r,*ic; 3225 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag; 3226 PetscInt *bi,*bj,*bdiag,*bdiag_rev; 3227 PetscInt row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au; 3228 PetscInt nlnk,*lnk; 3229 PetscBT lnkbt; 3230 PetscTruth row_identity,icol_identity,both_identity; 3231 MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp; 3232 const PetscInt *ics; 3233 PetscInt j,nz,*pj,*bjtmp,k,ncut,*jtmp; 3234 PetscReal dt=info->dt,dtcol=info->dtcol,shift=info->shiftamount; 3235 PetscInt dtcount=(PetscInt)info->dtcount,nnz_max; 3236 PetscTruth missing; 3237 3238 PetscFunctionBegin; 3239 3240 if (dt == PETSC_DEFAULT) dt = 0.005; 3241 if (dtcol == PETSC_DEFAULT) dtcol = 0.01; /* XXX unused! */ 3242 if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax); 3243 3244 /* ------- symbolic factorization, can be reused ---------*/ 3245 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 3246 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 3247 adiag=a->diag; 3248 3249 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 3250 3251 /* bdiag is location of diagonal in factor */ 3252 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); /* becomes b->diag */ 3253 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag_rev);CHKERRQ(ierr); /* temporary */ 3254 3255 /* allocate row pointers bi */ 3256 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 3257 3258 /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */ 3259 if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */ 3260 nnz_max = ai[n]+2*n*dtcount+2; 3261 3262 ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 3263 ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr); 3264 3265 /* put together the new matrix */ 3266 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 3267 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 3268 b = (Mat_SeqAIJ*)B->data; 3269 b->free_a = PETSC_TRUE; 3270 b->free_ij = PETSC_TRUE; 3271 b->singlemalloc = PETSC_FALSE; 3272 b->a = ba; 3273 b->j = bj; 3274 b->i = bi; 3275 b->diag = bdiag; 3276 b->ilen = 0; 3277 b->imax = 0; 3278 b->row = isrow; 3279 b->col = iscol; 3280 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 3281 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 3282 b->icol = isicol; 3283 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 3284 3285 ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3286 b->maxnz = nnz_max; 3287 3288 B->factor = MAT_FACTOR_ILUDT; 3289 B->info.factor_mallocs = 0; 3290 B->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]); 3291 CHKMEMQ; 3292 /* ------- end of symbolic factorization ---------*/ 3293 3294 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3295 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3296 ics = ic; 3297 3298 /* linked list for storing column indices of the active row */ 3299 nlnk = n + 1; 3300 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3301 3302 /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */ 3303 ierr = PetscMalloc2(n,PetscInt,&im,n,PetscInt,&jtmp);CHKERRQ(ierr); 3304 /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */ 3305 ierr = PetscMalloc2(n,MatScalar,&rtmp,n,MatScalar,&vtmp);CHKERRQ(ierr); 3306 ierr = PetscMemzero(rtmp,n*sizeof(MatScalar));CHKERRQ(ierr); 3307 3308 bi[0] = 0; 3309 bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */ 3310 bdiag_rev[n] = bdiag[0]; 3311 bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */ 3312 for (i=0; i<n; i++) { 3313 /* copy initial fill into linked list */ 3314 nzi = 0; /* nonzeros for active row i */ 3315 nzi = ai[r[i]+1] - ai[r[i]]; 3316 if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 3317 nzi_al = adiag[r[i]] - ai[r[i]]; 3318 nzi_au = ai[r[i]+1] - adiag[r[i]] -1; 3319 ajtmp = aj + ai[r[i]]; 3320 ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3321 3322 /* load in initial (unfactored row) */ 3323 aatmp = a->a + ai[r[i]]; 3324 for (j=0; j<nzi; j++) { 3325 rtmp[ics[*ajtmp++]] = *aatmp++; 3326 } 3327 3328 /* add pivot rows into linked list */ 3329 row = lnk[n]; 3330 while (row < i ) { 3331 nzi_bl = bi[row+1] - bi[row] + 1; 3332 bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */ 3333 ierr = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr); 3334 nzi += nlnk; 3335 row = lnk[row]; 3336 } 3337 3338 /* copy data from lnk into jtmp, then initialize lnk */ 3339 ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr); 3340 3341 /* numerical factorization */ 3342 bjtmp = jtmp; 3343 row = *bjtmp++; /* 1st pivot row */ 3344 while ( row < i ) { 3345 pc = rtmp + row; 3346 pv = ba + bdiag[row]; /* 1./(diag of the pivot row) */ 3347 multiplier = (*pc) * (*pv); 3348 *pc = multiplier; 3349 if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */ 3350 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3351 pv = ba + bdiag[row+1] + 1; 3352 /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */ 3353 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3354 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3355 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 3356 } 3357 row = *bjtmp++; 3358 } 3359 3360 /* copy sparse rtmp into contiguous vtmp; separate L and U part */ 3361 diag_tmp = rtmp[i]; /* save diagonal value - may not needed?? */ 3362 nzi_bl = 0; j = 0; 3363 while (jtmp[j] < i){ /* Note: jtmp is sorted */ 3364 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3365 nzi_bl++; j++; 3366 } 3367 nzi_bu = nzi - nzi_bl -1; 3368 while (j < nzi){ 3369 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3370 j++; 3371 } 3372 3373 bjtmp = bj + bi[i]; 3374 batmp = ba + bi[i]; 3375 /* apply level dropping rule to L part */ 3376 ncut = nzi_al + dtcount; 3377 if (ncut < nzi_bl){ 3378 ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr); 3379 ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr); 3380 } else { 3381 ncut = nzi_bl; 3382 } 3383 for (j=0; j<ncut; j++){ 3384 bjtmp[j] = jtmp[j]; 3385 batmp[j] = vtmp[j]; 3386 /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */ 3387 } 3388 bi[i+1] = bi[i] + ncut; 3389 nzi = ncut + 1; 3390 3391 /* apply level dropping rule to U part */ 3392 ncut = nzi_au + dtcount; 3393 if (ncut < nzi_bu){ 3394 ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr); 3395 ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr); 3396 } else { 3397 ncut = nzi_bu; 3398 } 3399 nzi += ncut; 3400 3401 /* mark bdiagonal */ 3402 bdiag[i+1] = bdiag[i] - (ncut + 1); 3403 bdiag_rev[n-i-1] = bdiag[i+1]; 3404 bi[2*n - i] = bi[2*n - i +1] - (ncut + 1); 3405 bjtmp = bj + bdiag[i]; 3406 batmp = ba + bdiag[i]; 3407 *bjtmp = i; 3408 *batmp = diag_tmp; /* rtmp[i]; */ 3409 if (*batmp == 0.0) { 3410 *batmp = dt+shift; 3411 /* printf(" row %d add shift %g\n",i,shift); */ 3412 } 3413 *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */ 3414 /* printf(" (%d,%g),",*bjtmp,*batmp); */ 3415 3416 bjtmp = bj + bdiag[i+1]+1; 3417 batmp = ba + bdiag[i+1]+1; 3418 for (k=0; k<ncut; k++){ 3419 bjtmp[k] = jtmp[nzi_bl+1+k]; 3420 batmp[k] = vtmp[nzi_bl+1+k]; 3421 /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */ 3422 } 3423 /* printf("\n"); */ 3424 3425 im[i] = nzi; /* used by PetscLLAddSortedLU() */ 3426 /* 3427 printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]); 3428 printf(" ----------------------------\n"); 3429 */ 3430 } /* for (i=0; i<n; i++) */ 3431 /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */ 3432 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]); 3433 3434 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3435 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3436 3437 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3438 ierr = PetscFree2(im,jtmp);CHKERRQ(ierr); 3439 ierr = PetscFree2(rtmp,vtmp);CHKERRQ(ierr); 3440 ierr = PetscFree(bdiag_rev);CHKERRQ(ierr); 3441 3442 ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr); 3443 b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n]; 3444 3445 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3446 ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr); 3447 both_identity = (PetscTruth) (row_identity && icol_identity); 3448 if (row_identity && icol_identity) { 3449 B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 3450 } else { 3451 B->ops->solve = MatSolve_SeqAIJ; 3452 } 3453 3454 B->ops->solveadd = 0; 3455 B->ops->solvetranspose = 0; 3456 B->ops->solvetransposeadd = 0; 3457 B->ops->matsolve = 0; 3458 B->assembled = PETSC_TRUE; 3459 B->preallocated = PETSC_TRUE; 3460 PetscFunctionReturn(0); 3461 } 3462 3463 /* a wraper of MatILUDTFactor_SeqAIJ() */ 3464 #undef __FUNCT__ 3465 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ" 3466 /* 3467 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 3468 */ 3469 3470 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info) 3471 { 3472 PetscErrorCode ierr; 3473 3474 PetscFunctionBegin; 3475 ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr); 3476 PetscFunctionReturn(0); 3477 } 3478 3479 /* 3480 same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors 3481 - intend to replace existing MatLUFactorNumeric_SeqAIJ() 3482 */ 3483 #undef __FUNCT__ 3484 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ" 3485 /* 3486 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 3487 */ 3488 3489 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info) 3490 { 3491 Mat C=fact; 3492 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 3493 IS isrow = b->row,isicol = b->icol; 3494 PetscErrorCode ierr; 3495 const PetscInt *r,*ic,*ics; 3496 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 3497 PetscInt *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj; 3498 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 3499 PetscReal dt=info->dt,shift=info->shiftamount; 3500 PetscTruth row_identity, col_identity; 3501 3502 PetscFunctionBegin; 3503 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3504 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3505 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 3506 ics = ic; 3507 3508 for (i=0; i<n; i++){ 3509 /* initialize rtmp array */ 3510 nzl = bi[i+1] - bi[i]; /* num of nozeros in L(i,:) */ 3511 bjtmp = bj + bi[i]; 3512 for (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0; 3513 rtmp[i] = 0.0; 3514 nzu = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */ 3515 bjtmp = bj + bdiag[i+1] + 1; 3516 for (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0; 3517 3518 /* load in initial unfactored row of A */ 3519 /* printf("row %d\n",i); */ 3520 nz = ai[r[i]+1] - ai[r[i]]; 3521 ajtmp = aj + ai[r[i]]; 3522 v = aa + ai[r[i]]; 3523 for (j=0; j<nz; j++) { 3524 rtmp[ics[*ajtmp++]] = v[j]; 3525 /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */ 3526 } 3527 /* printf("\n"); */ 3528 3529 /* numerical factorization */ 3530 bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */ 3531 nzl = bi[i+1] - bi[i]; /* num of entries in L(i,:) */ 3532 k = 0; 3533 while (k < nzl){ 3534 row = *bjtmp++; 3535 /* printf(" prow %d\n",row); */ 3536 pc = rtmp + row; 3537 pv = b->a + bdiag[row]; /* 1./(diag of the pivot row) */ 3538 multiplier = (*pc) * (*pv); 3539 *pc = multiplier; 3540 if (PetscAbsScalar(multiplier) > dt){ 3541 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3542 pv = b->a + bdiag[row+1] + 1; 3543 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3544 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3545 /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */ 3546 } 3547 k++; 3548 } 3549 3550 /* finished row so stick it into b->a */ 3551 /* L-part */ 3552 pv = b->a + bi[i] ; 3553 pj = bj + bi[i] ; 3554 nzl = bi[i+1] - bi[i]; 3555 for (j=0; j<nzl; j++) { 3556 pv[j] = rtmp[pj[j]]; 3557 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3558 } 3559 3560 /* diagonal: invert diagonal entries for simplier triangular solves */ 3561 if (rtmp[i] == 0.0) rtmp[i] = dt+shift; 3562 b->a[bdiag[i]] = 1.0/rtmp[i]; 3563 /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */ 3564 3565 /* U-part */ 3566 pv = b->a + bdiag[i+1] + 1; 3567 pj = bj + bdiag[i+1] + 1; 3568 nzu = bdiag[i] - bdiag[i+1] - 1; 3569 for (j=0; j<nzu; j++) { 3570 pv[j] = rtmp[pj[j]]; 3571 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3572 } 3573 /* printf("\n"); */ 3574 } 3575 3576 ierr = PetscFree(rtmp);CHKERRQ(ierr); 3577 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3578 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3579 3580 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3581 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 3582 if (row_identity && col_identity) { 3583 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 3584 } else { 3585 C->ops->solve = MatSolve_SeqAIJ; 3586 } 3587 C->ops->solveadd = 0; 3588 C->ops->solvetranspose = 0; 3589 C->ops->solvetransposeadd = 0; 3590 C->ops->matsolve = 0; 3591 C->assembled = PETSC_TRUE; 3592 C->preallocated = PETSC_TRUE; 3593 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 3594 PetscFunctionReturn(0); 3595 } 3596