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; 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 = PetscMalloc(n*sizeof(PetscInt),&order);CHKERRQ(ierr); 42 ierr = PetscMemzero(done,n*sizeof(PetscTruth));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; 69 past = 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 (*B)->ops->iludtfactor = MatILUDTFactor_SeqAIJ; 122 } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) { 123 ierr = MatSetType(*B,MATSEQSBAIJ);CHKERRQ(ierr); 124 ierr = MatSeqSBAIJSetPreallocation(*B,1,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 125 (*B)->ops->iccfactorsymbolic = MatICCFactorSymbolic_SeqAIJ; 126 (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJ; 127 } else SETERRQ(PETSC_ERR_SUP,"Factor type not supported"); 128 (*B)->factor = ftype; 129 PetscFunctionReturn(0); 130 } 131 EXTERN_C_END 132 133 #undef __FUNCT__ 134 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ" 135 PetscErrorCode MatLUFactorSymbolic_SeqAIJ(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 136 { 137 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 138 IS isicol; 139 PetscErrorCode ierr; 140 const PetscInt *r,*ic; 141 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j; 142 PetscInt *bi,*bj,*ajtmp; 143 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 144 PetscReal f; 145 PetscInt nlnk,*lnk,k,**bi_ptr; 146 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 147 PetscBT lnkbt; 148 PetscTruth newdatastruct=PETSC_FALSE; 149 150 PetscFunctionBegin; 151 ierr = PetscOptionsGetTruth(PETSC_NULL,"-lu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 152 if(newdatastruct){ 153 ierr = MatLUFactorSymbolic_SeqAIJ_newdatastruct(B,A,isrow,iscol,info);CHKERRQ(ierr); 154 PetscFunctionReturn(0); 155 } 156 157 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square"); 158 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 159 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 160 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 161 162 /* get new row pointers */ 163 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 164 bi[0] = 0; 165 166 /* bdiag is location of diagonal in factor */ 167 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 168 bdiag[0] = 0; 169 170 /* linked list for storing column indices of the active row */ 171 nlnk = n + 1; 172 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 173 174 ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr); 175 176 /* initial FreeSpace size is f*(ai[n]+1) */ 177 f = info->fill; 178 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 179 current_space = free_space; 180 181 for (i=0; i<n; i++) { 182 /* copy previous fill into linked list */ 183 nzi = 0; 184 nnz = ai[r[i]+1] - ai[r[i]]; 185 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 186 ajtmp = aj + ai[r[i]]; 187 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 188 nzi += nlnk; 189 190 /* add pivot rows into linked list */ 191 row = lnk[n]; 192 while (row < i) { 193 nzbd = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */ 194 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 195 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 196 nzi += nlnk; 197 row = lnk[row]; 198 } 199 bi[i+1] = bi[i] + nzi; 200 im[i] = nzi; 201 202 /* mark bdiag */ 203 nzbd = 0; 204 nnz = nzi; 205 k = lnk[n]; 206 while (nnz-- && k < i){ 207 nzbd++; 208 k = lnk[k]; 209 } 210 bdiag[i] = bi[i] + nzbd; 211 212 /* if free space is not available, make more free space */ 213 if (current_space->local_remaining<nzi) { 214 nnz = (n - i)*nzi; /* estimated and max additional space needed */ 215 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 216 reallocs++; 217 } 218 219 /* copy data into free space, then initialize lnk */ 220 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 221 bi_ptr[i] = current_space->array; 222 current_space->array += nzi; 223 current_space->local_used += nzi; 224 current_space->local_remaining -= nzi; 225 } 226 #if defined(PETSC_USE_INFO) 227 if (ai[n] != 0) { 228 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 229 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 230 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 231 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr); 232 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 233 } else { 234 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 235 } 236 #endif 237 238 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 239 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 240 241 /* destroy list of free space and other temporary array(s) */ 242 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 243 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); 244 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 245 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 246 247 /* put together the new matrix */ 248 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 249 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 250 b = (Mat_SeqAIJ*)(B)->data; 251 b->free_a = PETSC_TRUE; 252 b->free_ij = PETSC_TRUE; 253 b->singlemalloc = PETSC_FALSE; 254 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 255 b->j = bj; 256 b->i = bi; 257 b->diag = bdiag; 258 b->ilen = 0; 259 b->imax = 0; 260 b->row = isrow; 261 b->col = iscol; 262 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 263 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 264 b->icol = isicol; 265 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 266 267 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 268 ierr = PetscLogObjectMemory(B,(bi[n]-n)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 269 b->maxnz = b->nz = bi[n] ; 270 271 (B)->factor = MAT_FACTOR_LU; 272 (B)->info.factor_mallocs = reallocs; 273 (B)->info.fill_ratio_given = f; 274 275 if (ai[n]) { 276 (B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 277 } else { 278 (B)->info.fill_ratio_needed = 0.0; 279 } 280 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 281 (B)->ops->solve = MatSolve_SeqAIJ; 282 (B)->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 283 /* switch to inodes if appropriate */ 284 ierr = MatLUFactorSymbolic_Inode(B,A,isrow,iscol,info);CHKERRQ(ierr); 285 PetscFunctionReturn(0); 286 } 287 288 #undef __FUNCT__ 289 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ_newdatastruct" 290 PetscErrorCode MatLUFactorSymbolic_SeqAIJ_newdatastruct(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 291 { 292 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 293 IS isicol; 294 PetscErrorCode ierr; 295 const PetscInt *r,*ic; 296 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j; 297 PetscInt *bi,*bj,*ajtmp; 298 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 299 PetscReal f; 300 PetscInt nlnk,*lnk,k,**bi_ptr; 301 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 302 PetscBT lnkbt; 303 304 PetscFunctionBegin; 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 pointers */ 311 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 312 bi[0] = 0; 313 314 /* bdiag is location of diagonal in factor */ 315 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 316 bdiag[0] = 0; 317 318 /* linked list for storing column indices of the active row */ 319 nlnk = n + 1; 320 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 321 322 ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr); 323 324 /* initial FreeSpace size is f*(ai[n]+1) */ 325 f = info->fill; 326 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 327 current_space = free_space; 328 329 for (i=0; i<n; i++) { 330 /* copy previous fill into linked list */ 331 nzi = 0; 332 nnz = ai[r[i]+1] - ai[r[i]]; 333 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 334 ajtmp = aj + ai[r[i]]; 335 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 336 nzi += nlnk; 337 338 /* add pivot rows into linked list */ 339 row = lnk[n]; 340 while (row < i){ 341 nzbd = bdiag[row] + 1; /* num of entries in the row with column index <= row */ 342 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 343 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 344 nzi += nlnk; 345 row = lnk[row]; 346 } 347 bi[i+1] = bi[i] + nzi; 348 im[i] = nzi; 349 350 /* mark bdiag */ 351 nzbd = 0; 352 nnz = nzi; 353 k = lnk[n]; 354 while (nnz-- && k < i){ 355 nzbd++; 356 k = lnk[k]; 357 } 358 bdiag[i] = nzbd; /* note: bdiag[i] = nnzL as input for PetscFreeSpaceContiguous_LU() */ 359 360 /* if free space is not available, make more free space */ 361 if (current_space->local_remaining<nzi) { 362 nnz = 2*(n - i)*nzi; /* estimated and max additional space needed */ 363 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 364 reallocs++; 365 } 366 367 /* copy data into free space, then initialize lnk */ 368 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 369 bi_ptr[i] = current_space->array; 370 current_space->array += nzi; 371 current_space->local_used += nzi; 372 current_space->local_remaining -= nzi; 373 } 374 #if defined(PETSC_USE_INFO) 375 if (ai[n] != 0) { 376 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 377 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 378 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 379 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr); 380 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 381 } else { 382 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 383 } 384 #endif 385 386 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 387 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 388 389 /* destroy list of free space and other temporary array(s) */ 390 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 391 ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 392 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 393 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 394 395 /* put together the new matrix */ 396 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 397 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 398 b = (Mat_SeqAIJ*)(B)->data; 399 b->free_a = PETSC_TRUE; 400 b->free_ij = PETSC_TRUE; 401 b->singlemalloc = PETSC_FALSE; 402 ierr = PetscMalloc((bi[2*n+1])*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 403 b->j = bj; 404 b->i = bi; 405 b->diag = bdiag; 406 b->ilen = 0; 407 b->imax = 0; 408 b->row = isrow; 409 b->col = iscol; 410 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 411 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 412 b->icol = isicol; 413 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 414 415 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 416 ierr = PetscLogObjectMemory(B,bi[2*n+1]*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 417 b->maxnz = b->nz = bi[2*n+1] ; 418 419 (B)->factor = MAT_FACTOR_LU; 420 (B)->info.factor_mallocs = reallocs; 421 (B)->info.fill_ratio_given = f; 422 423 if (ai[n]) { 424 (B)->info.fill_ratio_needed = ((PetscReal)bi[2*n+1])/((PetscReal)ai[n]); 425 } else { 426 (B)->info.fill_ratio_needed = 0.0; 427 } 428 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 429 PetscFunctionReturn(0); 430 } 431 432 /* 433 Trouble in factorization, should we dump the original matrix? 434 */ 435 #undef __FUNCT__ 436 #define __FUNCT__ "MatFactorDumpMatrix" 437 PetscErrorCode MatFactorDumpMatrix(Mat A) 438 { 439 PetscErrorCode ierr; 440 PetscTruth flg = PETSC_FALSE; 441 442 PetscFunctionBegin; 443 ierr = PetscOptionsGetTruth(PETSC_NULL,"-mat_factor_dump_on_error",&flg,PETSC_NULL);CHKERRQ(ierr); 444 if (flg) { 445 PetscViewer viewer; 446 char filename[PETSC_MAX_PATH_LEN]; 447 448 ierr = PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);CHKERRQ(ierr); 449 ierr = PetscViewerBinaryOpen(((PetscObject)A)->comm,filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr); 450 ierr = MatView(A,viewer);CHKERRQ(ierr); 451 ierr = PetscViewerDestroy(viewer);CHKERRQ(ierr); 452 } 453 PetscFunctionReturn(0); 454 } 455 456 extern PetscErrorCode MatSolve_Inode(Mat,Vec,Vec); 457 458 /* ----------------------------------------------------------- */ 459 extern PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct(Mat,Vec,Vec); 460 extern PetscErrorCode MatSolve_SeqAIJ_newdatastruct(Mat,Vec,Vec); 461 462 #undef __FUNCT__ 463 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_newdatastruct" 464 PetscErrorCode MatLUFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info) 465 { 466 Mat C=B; 467 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 468 IS isrow = b->row,isicol = b->icol; 469 PetscErrorCode ierr; 470 const PetscInt *r,*ic,*ics; 471 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 472 PetscInt *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj; 473 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 474 PetscTruth row_identity,col_identity; 475 476 LUShift_Ctx sctx; 477 PetscInt *ddiag,newshift; 478 PetscReal rs; 479 MatScalar d; 480 481 PetscFunctionBegin; 482 /* ZeropivotSetUp(): initialize shift context sctx */ 483 sctx.nshift = 0; 484 sctx.nshift_max = 0; 485 sctx.shift_top = 0.0; 486 sctx.shift_lo = 0.0; 487 sctx.shift_hi = 0.0; 488 sctx.shift_fraction = 0.0; 489 sctx.shift_amount = 0.0; 490 491 /* if both shift schemes are chosen by user, only use info->shiftpd */ 492 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 493 ddiag = a->diag; 494 sctx.shift_top = info->zeropivot; 495 for (i=0; i<n; i++) { 496 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 497 d = (aa)[ddiag[i]]; 498 rs = -PetscAbsScalar(d) - PetscRealPart(d); 499 v = aa+ai[i]; 500 nz = ai[i+1] - ai[i]; 501 for (j=0; j<nz; j++) 502 rs += PetscAbsScalar(v[j]); 503 if (rs>sctx.shift_top) sctx.shift_top = rs; 504 } 505 sctx.shift_top *= 1.1; 506 sctx.nshift_max = 5; 507 sctx.shift_lo = 0.; 508 sctx.shift_hi = 1.; 509 } 510 511 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 512 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 513 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 514 ics = ic; 515 516 do { 517 sctx.lushift = PETSC_FALSE; 518 for (i=0; i<n; i++){ 519 /* zero rtmp */ 520 /* L part */ 521 nz = bi[i+1] - bi[i]; 522 bjtmp = bj + bi[i]; 523 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 524 525 /* U part */ 526 nz = bi[2*n-i+1] - bi[2*n-i]; 527 bjtmp = bj + bi[2*n-i]; 528 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 529 530 /* load in initial (unfactored row) */ 531 nz = ai[r[i]+1] - ai[r[i]]; 532 ajtmp = aj + ai[r[i]]; 533 v = aa + ai[r[i]]; 534 for (j=0; j<nz; j++) { 535 rtmp[ics[ajtmp[j]]] = v[j]; 536 } 537 /* ZeropivotApply() */ 538 rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 539 540 /* elimination */ 541 bjtmp = bj + bi[i]; 542 row = *bjtmp++; 543 nzL = bi[i+1] - bi[i]; 544 k = 0; 545 while (k < nzL) { 546 pc = rtmp + row; 547 if (*pc != 0.0) { 548 pv = b->a + bdiag[row]; 549 multiplier = *pc * (*pv); 550 *pc = multiplier; 551 pj = b->j + bi[2*n-row]; /* begining of U(row,:) */ 552 pv = b->a + bi[2*n-row]; 553 nz = bi[2*n-row+1] - bi[2*n-row] - 1; /* num of entries in U(row,:), excluding diag */ 554 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 555 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 556 } 557 row = *bjtmp++; k++; 558 } 559 560 /* finished row so stick it into b->a */ 561 rs = 0.0; 562 /* L part */ 563 pv = b->a + bi[i] ; 564 pj = b->j + bi[i] ; 565 nz = bi[i+1] - bi[i]; 566 for (j=0; j<nz; j++) { 567 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 568 } 569 570 /* U part */ 571 pv = b->a + bi[2*n-i]; 572 pj = b->j + bi[2*n-i]; 573 nz = bi[2*n-i+1] - bi[2*n-i] - 1; 574 for (j=0; j<nz; j++) { 575 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 576 } 577 578 /* ZeropivotCheck() */ 579 sctx.rs = rs; 580 sctx.pv = rtmp[i]; 581 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 582 if (newshift == 1) break; 583 584 /* Mark diagonal and invert diagonal for simplier triangular solves */ 585 pv = b->a + bdiag[i]; 586 *pv = 1.0/rtmp[i]; 587 588 } /* endof for (i=0; i<n; i++){ */ 589 590 /* ZeropivotRefine() */ 591 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max){ 592 /* 593 * if no shift in this attempt & shifting & started shifting & can refine, 594 * then try lower shift 595 */ 596 sctx.shift_hi = sctx.shift_fraction; 597 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 598 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 599 sctx.lushift = PETSC_TRUE; 600 sctx.nshift++; 601 } 602 } while (sctx.lushift); 603 604 ierr = PetscFree(rtmp);CHKERRQ(ierr); 605 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 606 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 607 608 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 609 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 610 if (row_identity && col_identity) { 611 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct; 612 } else { 613 C->ops->solve = MatSolve_SeqAIJ_newdatastruct; 614 } 615 616 C->ops->solveadd = 0; 617 C->ops->solvetranspose = 0; 618 C->ops->solvetransposeadd = 0; 619 C->ops->matsolve = 0; 620 C->assembled = PETSC_TRUE; 621 C->preallocated = PETSC_TRUE; 622 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 623 624 /* ZeropivotView() */ 625 if (sctx.nshift){ 626 if (info->shiftpd) { 627 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); 628 } else if (info->shiftnz) { 629 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 630 } 631 } 632 PetscFunctionReturn(0); 633 } 634 635 /* ----------------------------------------------------------- */ 636 extern PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct_v2(Mat,Vec,Vec); 637 /* extern PetscErrorCode MatSolve_SeqAIJ_newdatastruct(Mat,Vec,Vec); */ 638 639 #undef __FUNCT__ 640 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_newdatastruct_v2" 641 PetscErrorCode MatLUFactorNumeric_SeqAIJ_newdatastruct_v2(Mat B,Mat A,const MatFactorInfo *info) 642 { 643 Mat C=B; 644 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 645 IS isrow = b->row,isicol = b->icol; 646 PetscErrorCode ierr; 647 const PetscInt *r,*ic,*ics; 648 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 649 PetscInt *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj; 650 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 651 PetscTruth row_identity,col_identity; 652 653 LUShift_Ctx sctx; 654 PetscInt *ddiag,newshift; 655 PetscReal rs; 656 MatScalar d; 657 658 PetscFunctionBegin; 659 /* ZeropivotSetUp(): initialize shift context sctx */ 660 sctx.nshift = 0; 661 sctx.nshift_max = 0; 662 sctx.shift_top = 0.0; 663 sctx.shift_lo = 0.0; 664 sctx.shift_hi = 0.0; 665 sctx.shift_fraction = 0.0; 666 sctx.shift_amount = 0.0; 667 668 /* if both shift schemes are chosen by user, only use info->shiftpd */ 669 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 670 ddiag = a->diag; 671 sctx.shift_top = info->zeropivot; 672 for (i=0; i<n; i++) { 673 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 674 d = (aa)[ddiag[i]]; 675 rs = -PetscAbsScalar(d) - PetscRealPart(d); 676 v = aa+ai[i]; 677 nz = ai[i+1] - ai[i]; 678 for (j=0; j<nz; j++) 679 rs += PetscAbsScalar(v[j]); 680 if (rs>sctx.shift_top) sctx.shift_top = rs; 681 } 682 sctx.shift_top *= 1.1; 683 sctx.nshift_max = 5; 684 sctx.shift_lo = 0.; 685 sctx.shift_hi = 1.; 686 } 687 688 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 689 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 690 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 691 ics = ic; 692 693 do { 694 sctx.lushift = PETSC_FALSE; 695 for (i=0; i<n; i++){ 696 /* zero rtmp */ 697 /* L part */ 698 nz = bi[i+1] - bi[i]; 699 bjtmp = bj + bi[i]; 700 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 701 702 /* U part */ 703 /* nz = bi[2*n-i+1] - bi[2*n-i]; 704 bjtmp = bj + bi[2*n-i]; */ 705 nz = bdiag[i]-bdiag[i+1]; 706 bjtmp = bj + bdiag[i+1]+1; 707 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 708 709 /* load in initial (unfactored row) */ 710 nz = ai[r[i]+1] - ai[r[i]]; 711 ajtmp = aj + ai[r[i]]; 712 v = aa + ai[r[i]]; 713 for (j=0; j<nz; j++) { 714 rtmp[ics[ajtmp[j]]] = v[j]; 715 } 716 /* ZeropivotApply() */ 717 rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 718 719 /* elimination */ 720 bjtmp = bj + bi[i]; 721 row = *bjtmp++; 722 nzL = bi[i+1] - bi[i]; 723 k = 0; 724 while (k < nzL) { 725 pc = rtmp + row; 726 if (*pc != 0.0) { 727 pv = b->a + bdiag[row]; 728 multiplier = *pc * (*pv); 729 *pc = multiplier; 730 /* pj = b->j + bi[2*n-row]; */ /* begining of U(row,:) */ 731 /* pv = b->a + bi[2*n-row]; 732 nz = bi[2*n-row+1] - bi[2*n-row] - 1; */ /* num of entries in U(row,:), excluding diag */ 733 pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */ 734 pv = b->a + bdiag[row+1]+1; 735 nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */ 736 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 737 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 738 } 739 row = *bjtmp++; k++; 740 } 741 742 /* finished row so stick it into b->a */ 743 rs = 0.0; 744 /* L part */ 745 pv = b->a + bi[i] ; 746 pj = b->j + bi[i] ; 747 nz = bi[i+1] - bi[i]; 748 for (j=0; j<nz; j++) { 749 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 750 } 751 752 /* U part */ 753 /* pv = b->a + bi[2*n-i]; 754 pj = b->j + bi[2*n-i]; 755 nz = bi[2*n-i+1] - bi[2*n-i] - 1; 756 */ 757 pv = b->a + bdiag[i+1]+1; 758 pj = b->j + bdiag[i+1]+1; 759 nz = bdiag[i] - bdiag[i+1]-1; 760 for (j=0; j<nz; j++) { 761 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 762 } 763 764 /* ZeropivotCheck() */ 765 sctx.rs = rs; 766 sctx.pv = rtmp[i]; 767 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 768 if (newshift == 1) break; 769 770 /* Mark diagonal and invert diagonal for simplier triangular solves */ 771 pv = b->a + bdiag[i]; 772 *pv = 1.0/rtmp[i]; 773 774 } /* endof for (i=0; i<n; i++){ */ 775 776 /* ZeropivotRefine() */ 777 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max){ 778 /* 779 * if no shift in this attempt & shifting & started shifting & can refine, 780 * then try lower shift 781 */ 782 sctx.shift_hi = sctx.shift_fraction; 783 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 784 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 785 sctx.lushift = PETSC_TRUE; 786 sctx.nshift++; 787 } 788 } while (sctx.lushift); 789 790 ierr = PetscFree(rtmp);CHKERRQ(ierr); 791 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 792 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 793 794 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 795 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 796 if (row_identity && col_identity) { 797 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct_v2; 798 } else { 799 C->ops->solve = MatSolve_SeqAIJ_newdatastruct; 800 } 801 802 C->ops->solveadd = 0; 803 C->ops->solvetranspose = 0; 804 C->ops->solvetransposeadd = 0; 805 C->ops->matsolve = 0; 806 C->assembled = PETSC_TRUE; 807 C->preallocated = PETSC_TRUE; 808 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 809 810 /* ZeropivotView() */ 811 if (sctx.nshift){ 812 if (info->shiftpd) { 813 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); 814 } else if (info->shiftnz) { 815 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 816 } 817 } 818 PetscFunctionReturn(0); 819 } 820 821 #undef __FUNCT__ 822 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ" 823 PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 824 { 825 Mat C=B; 826 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 827 IS isrow = b->row,isicol = b->icol; 828 PetscErrorCode ierr; 829 const PetscInt *r,*ic,*ics; 830 PetscInt nz,row,i,j,n=A->rmap->n,diag; 831 const PetscInt *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 832 const PetscInt *ajtmp,*bjtmp,*diag_offset = b->diag,*pj; 833 MatScalar *pv,*rtmp,*pc,multiplier,d; 834 const MatScalar *v,*aa=a->a; 835 PetscReal rs=0.0; 836 LUShift_Ctx sctx; 837 PetscInt newshift,*ddiag; 838 839 PetscFunctionBegin; 840 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 841 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 842 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 843 ics = ic; 844 845 /* initialize shift context sctx */ 846 sctx.nshift = 0; 847 sctx.nshift_max = 0; 848 sctx.shift_top = 0.0; 849 sctx.shift_lo = 0.0; 850 sctx.shift_hi = 0.0; 851 sctx.shift_fraction = 0.0; 852 sctx.shift_amount = 0.0; 853 854 /* if both shift schemes are chosen by user, only use info->shiftpd */ 855 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 856 ddiag = a->diag; 857 sctx.shift_top = info->zeropivot; 858 for (i=0; i<n; i++) { 859 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 860 d = (aa)[ddiag[i]]; 861 rs = -PetscAbsScalar(d) - PetscRealPart(d); 862 v = aa+ai[i]; 863 nz = ai[i+1] - ai[i]; 864 for (j=0; j<nz; j++) 865 rs += PetscAbsScalar(v[j]); 866 if (rs>sctx.shift_top) sctx.shift_top = rs; 867 } 868 sctx.shift_top *= 1.1; 869 sctx.nshift_max = 5; 870 sctx.shift_lo = 0.; 871 sctx.shift_hi = 1.; 872 } 873 874 do { 875 sctx.lushift = PETSC_FALSE; 876 for (i=0; i<n; i++){ 877 nz = bi[i+1] - bi[i]; 878 bjtmp = bj + bi[i]; 879 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 880 881 /* load in initial (unfactored row) */ 882 nz = ai[r[i]+1] - ai[r[i]]; 883 ajtmp = aj + ai[r[i]]; 884 v = aa + ai[r[i]]; 885 for (j=0; j<nz; j++) { 886 rtmp[ics[ajtmp[j]]] = v[j]; 887 } 888 rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 889 /* if (sctx.shift_amount > 0.0) printf("row %d, shift %g\n",i,sctx.shift_amount); */ 890 891 row = *bjtmp++; 892 while (row < i) { 893 pc = rtmp + row; 894 if (*pc != 0.0) { 895 pv = b->a + diag_offset[row]; 896 pj = b->j + diag_offset[row] + 1; 897 multiplier = *pc / *pv++; 898 *pc = multiplier; 899 nz = bi[row+1] - diag_offset[row] - 1; 900 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 901 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 902 } 903 row = *bjtmp++; 904 } 905 /* finished row so stick it into b->a */ 906 pv = b->a + bi[i] ; 907 pj = b->j + bi[i] ; 908 nz = bi[i+1] - bi[i]; 909 diag = diag_offset[i] - bi[i]; 910 rs = 0.0; 911 for (j=0; j<nz; j++) { 912 pv[j] = rtmp[pj[j]]; 913 rs += PetscAbsScalar(pv[j]); 914 } 915 rs -= PetscAbsScalar(pv[diag]); 916 917 /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */ 918 sctx.rs = rs; 919 sctx.pv = pv[diag]; 920 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 921 if (newshift == 1) break; 922 } 923 924 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 925 /* 926 * if no shift in this attempt & shifting & started shifting & can refine, 927 * then try lower shift 928 */ 929 sctx.shift_hi = sctx.shift_fraction; 930 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 931 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 932 sctx.lushift = PETSC_TRUE; 933 sctx.nshift++; 934 } 935 } while (sctx.lushift); 936 937 /* invert diagonal entries for simplier triangular solves */ 938 for (i=0; i<n; i++) { 939 b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]]; 940 } 941 ierr = PetscFree(rtmp);CHKERRQ(ierr); 942 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 943 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 944 if (b->inode.use) { 945 C->ops->solve = MatSolve_Inode; 946 } else { 947 PetscTruth row_identity, col_identity; 948 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 949 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 950 if (row_identity && col_identity) { 951 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 952 } else { 953 C->ops->solve = MatSolve_SeqAIJ; 954 } 955 } 956 C->ops->solveadd = MatSolveAdd_SeqAIJ; 957 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 958 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 959 C->ops->matsolve = MatMatSolve_SeqAIJ; 960 C->assembled = PETSC_TRUE; 961 C->preallocated = PETSC_TRUE; 962 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 963 if (sctx.nshift){ 964 if (info->shiftpd) { 965 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); 966 } else if (info->shiftnz) { 967 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 968 } 969 } 970 PetscFunctionReturn(0); 971 } 972 973 /* 974 This routine implements inplace ILU(0) with row or/and column permutations. 975 Input: 976 A - original matrix 977 Output; 978 A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i] 979 a->j (col index) is permuted by the inverse of colperm, then sorted 980 a->a reordered accordingly with a->j 981 a->diag (ptr to diagonal elements) is updated. 982 */ 983 #undef __FUNCT__ 984 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_InplaceWithPerm" 985 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info) 986 { 987 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 988 IS isrow = a->row,isicol = a->icol; 989 PetscErrorCode ierr; 990 const PetscInt *r,*ic,*ics; 991 PetscInt i,j,n=A->rmap->n,*ai=a->i,*aj=a->j; 992 PetscInt *ajtmp,nz,row; 993 PetscInt *diag = a->diag,nbdiag,*pj; 994 PetscScalar *rtmp,*pc,multiplier,d; 995 MatScalar *v,*pv; 996 PetscReal rs; 997 LUShift_Ctx sctx; 998 PetscInt newshift; 999 1000 PetscFunctionBegin; 1001 if (A != B) SETERRQ(PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address"); 1002 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1003 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1004 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&rtmp);CHKERRQ(ierr); 1005 ierr = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr); 1006 ics = ic; 1007 1008 sctx.shift_top = 0; 1009 sctx.nshift_max = 0; 1010 sctx.shift_lo = 0; 1011 sctx.shift_hi = 0; 1012 sctx.shift_fraction = 0; 1013 1014 /* if both shift schemes are chosen by user, only use info->shiftpd */ 1015 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 1016 sctx.shift_top = 0; 1017 for (i=0; i<n; i++) { 1018 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 1019 d = (a->a)[diag[i]]; 1020 rs = -PetscAbsScalar(d) - PetscRealPart(d); 1021 v = a->a+ai[i]; 1022 nz = ai[i+1] - ai[i]; 1023 for (j=0; j<nz; j++) 1024 rs += PetscAbsScalar(v[j]); 1025 if (rs>sctx.shift_top) sctx.shift_top = rs; 1026 } 1027 if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot; 1028 sctx.shift_top *= 1.1; 1029 sctx.nshift_max = 5; 1030 sctx.shift_lo = 0.; 1031 sctx.shift_hi = 1.; 1032 } 1033 1034 sctx.shift_amount = 0; 1035 sctx.nshift = 0; 1036 do { 1037 sctx.lushift = PETSC_FALSE; 1038 for (i=0; i<n; i++){ 1039 /* load in initial unfactored row */ 1040 nz = ai[r[i]+1] - ai[r[i]]; 1041 ajtmp = aj + ai[r[i]]; 1042 v = a->a + ai[r[i]]; 1043 /* sort permuted ajtmp and values v accordingly */ 1044 for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]]; 1045 ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr); 1046 1047 diag[r[i]] = ai[r[i]]; 1048 for (j=0; j<nz; j++) { 1049 rtmp[ajtmp[j]] = v[j]; 1050 if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */ 1051 } 1052 rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 1053 1054 row = *ajtmp++; 1055 while (row < i) { 1056 pc = rtmp + row; 1057 if (*pc != 0.0) { 1058 pv = a->a + diag[r[row]]; 1059 pj = aj + diag[r[row]] + 1; 1060 1061 multiplier = *pc / *pv++; 1062 *pc = multiplier; 1063 nz = ai[r[row]+1] - diag[r[row]] - 1; 1064 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 1065 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 1066 } 1067 row = *ajtmp++; 1068 } 1069 /* finished row so overwrite it onto a->a */ 1070 pv = a->a + ai[r[i]] ; 1071 pj = aj + ai[r[i]] ; 1072 nz = ai[r[i]+1] - ai[r[i]]; 1073 nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */ 1074 1075 rs = 0.0; 1076 for (j=0; j<nz; j++) { 1077 pv[j] = rtmp[pj[j]]; 1078 if (j != nbdiag) rs += PetscAbsScalar(pv[j]); 1079 } 1080 1081 /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */ 1082 sctx.rs = rs; 1083 sctx.pv = pv[nbdiag]; 1084 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 1085 if (newshift == 1) break; 1086 } 1087 1088 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 1089 /* 1090 * if no shift in this attempt & shifting & started shifting & can refine, 1091 * then try lower shift 1092 */ 1093 sctx.shift_hi = sctx.shift_fraction; 1094 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 1095 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 1096 sctx.lushift = PETSC_TRUE; 1097 sctx.nshift++; 1098 } 1099 } while (sctx.lushift); 1100 1101 /* invert diagonal entries for simplier triangular solves */ 1102 for (i=0; i<n; i++) { 1103 a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]]; 1104 } 1105 1106 ierr = PetscFree(rtmp);CHKERRQ(ierr); 1107 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1108 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1109 A->ops->solve = MatSolve_SeqAIJ_InplaceWithPerm; 1110 A->ops->solveadd = MatSolveAdd_SeqAIJ; 1111 A->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 1112 A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 1113 A->assembled = PETSC_TRUE; 1114 A->preallocated = PETSC_TRUE; 1115 ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr); 1116 if (sctx.nshift){ 1117 if (info->shiftpd) { 1118 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); 1119 } else if (info->shiftnz) { 1120 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 1121 } 1122 } 1123 PetscFunctionReturn(0); 1124 } 1125 1126 /* ----------------------------------------------------------- */ 1127 #undef __FUNCT__ 1128 #define __FUNCT__ "MatLUFactor_SeqAIJ" 1129 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info) 1130 { 1131 PetscErrorCode ierr; 1132 Mat C; 1133 1134 PetscFunctionBegin; 1135 ierr = MatGetFactor(A,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr); 1136 ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr); 1137 ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr); 1138 A->ops->solve = C->ops->solve; 1139 A->ops->solvetranspose = C->ops->solvetranspose; 1140 ierr = MatHeaderCopy(A,C);CHKERRQ(ierr); 1141 ierr = PetscLogObjectParent(A,((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr); 1142 PetscFunctionReturn(0); 1143 } 1144 /* ----------------------------------------------------------- */ 1145 1146 1147 #undef __FUNCT__ 1148 #define __FUNCT__ "MatSolve_SeqAIJ" 1149 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx) 1150 { 1151 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1152 IS iscol = a->col,isrow = a->row; 1153 PetscErrorCode ierr; 1154 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1155 PetscInt nz; 1156 const PetscInt *rout,*cout,*r,*c; 1157 PetscScalar *x,*tmp,*tmps,sum; 1158 const PetscScalar *b; 1159 const MatScalar *aa = a->a,*v; 1160 1161 PetscFunctionBegin; 1162 if (!n) PetscFunctionReturn(0); 1163 1164 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1165 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1166 tmp = a->solve_work; 1167 1168 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1169 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1170 1171 /* forward solve the lower triangular */ 1172 tmp[0] = b[*r++]; 1173 tmps = tmp; 1174 for (i=1; i<n; i++) { 1175 v = aa + ai[i] ; 1176 vi = aj + ai[i] ; 1177 nz = a->diag[i] - ai[i]; 1178 sum = b[*r++]; 1179 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1180 tmp[i] = sum; 1181 } 1182 1183 /* backward solve the upper triangular */ 1184 for (i=n-1; i>=0; i--){ 1185 v = aa + a->diag[i] + 1; 1186 vi = aj + a->diag[i] + 1; 1187 nz = ai[i+1] - a->diag[i] - 1; 1188 sum = tmp[i]; 1189 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1190 x[*c--] = tmp[i] = sum*aa[a->diag[i]]; 1191 } 1192 1193 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1194 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1195 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1196 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1197 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1198 PetscFunctionReturn(0); 1199 } 1200 1201 #undef __FUNCT__ 1202 #define __FUNCT__ "MatMatSolve_SeqAIJ" 1203 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X) 1204 { 1205 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1206 IS iscol = a->col,isrow = a->row; 1207 PetscErrorCode ierr; 1208 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1209 PetscInt nz,neq; 1210 const PetscInt *rout,*cout,*r,*c; 1211 PetscScalar *x,*b,*tmp,*tmps,sum; 1212 const MatScalar *aa = a->a,*v; 1213 PetscTruth bisdense,xisdense; 1214 1215 PetscFunctionBegin; 1216 if (!n) PetscFunctionReturn(0); 1217 1218 ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr); 1219 if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 1220 ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr); 1221 if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 1222 1223 ierr = MatGetArray(B,&b);CHKERRQ(ierr); 1224 ierr = MatGetArray(X,&x);CHKERRQ(ierr); 1225 1226 tmp = a->solve_work; 1227 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1228 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1229 1230 for (neq=0; neq<B->cmap->n; neq++){ 1231 /* forward solve the lower triangular */ 1232 tmp[0] = b[r[0]]; 1233 tmps = tmp; 1234 for (i=1; i<n; i++) { 1235 v = aa + ai[i] ; 1236 vi = aj + ai[i] ; 1237 nz = a->diag[i] - ai[i]; 1238 sum = b[r[i]]; 1239 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1240 tmp[i] = sum; 1241 } 1242 /* backward solve the upper triangular */ 1243 for (i=n-1; i>=0; i--){ 1244 v = aa + a->diag[i] + 1; 1245 vi = aj + a->diag[i] + 1; 1246 nz = ai[i+1] - a->diag[i] - 1; 1247 sum = tmp[i]; 1248 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1249 x[c[i]] = tmp[i] = sum*aa[a->diag[i]]; 1250 } 1251 1252 b += n; 1253 x += n; 1254 } 1255 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1256 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1257 ierr = MatRestoreArray(B,&b);CHKERRQ(ierr); 1258 ierr = MatRestoreArray(X,&x);CHKERRQ(ierr); 1259 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 1260 PetscFunctionReturn(0); 1261 } 1262 1263 #undef __FUNCT__ 1264 #define __FUNCT__ "MatSolve_SeqAIJ_InplaceWithPerm" 1265 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx) 1266 { 1267 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1268 IS iscol = a->col,isrow = a->row; 1269 PetscErrorCode ierr; 1270 const PetscInt *r,*c,*rout,*cout; 1271 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1272 PetscInt nz,row; 1273 PetscScalar *x,*b,*tmp,*tmps,sum; 1274 const MatScalar *aa = a->a,*v; 1275 1276 PetscFunctionBegin; 1277 if (!n) PetscFunctionReturn(0); 1278 1279 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1280 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1281 tmp = a->solve_work; 1282 1283 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1284 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1285 1286 /* forward solve the lower triangular */ 1287 tmp[0] = b[*r++]; 1288 tmps = tmp; 1289 for (row=1; row<n; row++) { 1290 i = rout[row]; /* permuted row */ 1291 v = aa + ai[i] ; 1292 vi = aj + ai[i] ; 1293 nz = a->diag[i] - ai[i]; 1294 sum = b[*r++]; 1295 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1296 tmp[row] = sum; 1297 } 1298 1299 /* backward solve the upper triangular */ 1300 for (row=n-1; row>=0; row--){ 1301 i = rout[row]; /* permuted row */ 1302 v = aa + a->diag[i] + 1; 1303 vi = aj + a->diag[i] + 1; 1304 nz = ai[i+1] - a->diag[i] - 1; 1305 sum = tmp[row]; 1306 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1307 x[*c--] = tmp[row] = sum*aa[a->diag[i]]; 1308 } 1309 1310 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1311 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1312 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1313 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1314 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1315 PetscFunctionReturn(0); 1316 } 1317 1318 /* ----------------------------------------------------------- */ 1319 #include "../src/mat/impls/aij/seq/ftn-kernels/fsolve.h" 1320 #undef __FUNCT__ 1321 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering" 1322 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx) 1323 { 1324 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1325 PetscErrorCode ierr; 1326 PetscInt n = A->rmap->n; 1327 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag; 1328 PetscScalar *x; 1329 const PetscScalar *b; 1330 const MatScalar *aa = a->a; 1331 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1332 PetscInt adiag_i,i,nz,ai_i; 1333 const PetscInt *vi; 1334 const MatScalar *v; 1335 PetscScalar sum; 1336 #endif 1337 1338 PetscFunctionBegin; 1339 if (!n) PetscFunctionReturn(0); 1340 1341 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1342 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1343 1344 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1345 fortransolveaij_(&n,x,ai,aj,adiag,aa,b); 1346 #else 1347 /* forward solve the lower triangular */ 1348 x[0] = b[0]; 1349 for (i=1; i<n; i++) { 1350 ai_i = ai[i]; 1351 v = aa + ai_i; 1352 vi = aj + ai_i; 1353 nz = adiag[i] - ai_i; 1354 sum = b[i]; 1355 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1356 x[i] = sum; 1357 } 1358 1359 /* backward solve the upper triangular */ 1360 for (i=n-1; i>=0; i--){ 1361 adiag_i = adiag[i]; 1362 v = aa + adiag_i + 1; 1363 vi = aj + adiag_i + 1; 1364 nz = ai[i+1] - adiag_i - 1; 1365 sum = x[i]; 1366 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1367 x[i] = sum*aa[adiag_i]; 1368 } 1369 #endif 1370 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1371 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1372 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1373 PetscFunctionReturn(0); 1374 } 1375 1376 #undef __FUNCT__ 1377 #define __FUNCT__ "MatSolveAdd_SeqAIJ" 1378 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx) 1379 { 1380 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1381 IS iscol = a->col,isrow = a->row; 1382 PetscErrorCode ierr; 1383 PetscInt i, n = A->rmap->n,j; 1384 PetscInt nz; 1385 const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j; 1386 PetscScalar *x,*tmp,sum; 1387 const PetscScalar *b; 1388 const MatScalar *aa = a->a,*v; 1389 1390 PetscFunctionBegin; 1391 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 1392 1393 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1394 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1395 tmp = a->solve_work; 1396 1397 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1398 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1399 1400 /* forward solve the lower triangular */ 1401 tmp[0] = b[*r++]; 1402 for (i=1; i<n; i++) { 1403 v = aa + ai[i] ; 1404 vi = aj + ai[i] ; 1405 nz = a->diag[i] - ai[i]; 1406 sum = b[*r++]; 1407 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1408 tmp[i] = sum; 1409 } 1410 1411 /* backward solve the upper triangular */ 1412 for (i=n-1; i>=0; i--){ 1413 v = aa + a->diag[i] + 1; 1414 vi = aj + a->diag[i] + 1; 1415 nz = ai[i+1] - a->diag[i] - 1; 1416 sum = tmp[i]; 1417 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1418 tmp[i] = sum*aa[a->diag[i]]; 1419 x[*c--] += tmp[i]; 1420 } 1421 1422 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1423 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1424 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1425 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1426 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1427 1428 PetscFunctionReturn(0); 1429 } 1430 1431 #undef __FUNCT__ 1432 #define __FUNCT__ "MatSolveTranspose_SeqAIJ" 1433 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx) 1434 { 1435 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1436 IS iscol = a->col,isrow = a->row; 1437 PetscErrorCode ierr; 1438 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1439 PetscInt i,n = A->rmap->n,j; 1440 PetscInt nz; 1441 PetscScalar *x,*tmp,s1; 1442 const MatScalar *aa = a->a,*v; 1443 const PetscScalar *b; 1444 1445 PetscFunctionBegin; 1446 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1447 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1448 tmp = a->solve_work; 1449 1450 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1451 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1452 1453 /* copy the b into temp work space according to permutation */ 1454 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1455 1456 /* forward solve the U^T */ 1457 for (i=0; i<n; i++) { 1458 v = aa + diag[i] ; 1459 vi = aj + diag[i] + 1; 1460 nz = ai[i+1] - diag[i] - 1; 1461 s1 = tmp[i]; 1462 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1463 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1464 tmp[i] = s1; 1465 } 1466 1467 /* backward solve the L^T */ 1468 for (i=n-1; i>=0; i--){ 1469 v = aa + diag[i] - 1 ; 1470 vi = aj + diag[i] - 1 ; 1471 nz = diag[i] - ai[i]; 1472 s1 = tmp[i]; 1473 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1474 } 1475 1476 /* copy tmp into x according to permutation */ 1477 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1478 1479 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1480 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1481 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1482 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1483 1484 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1485 PetscFunctionReturn(0); 1486 } 1487 1488 #undef __FUNCT__ 1489 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ" 1490 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx) 1491 { 1492 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1493 IS iscol = a->col,isrow = a->row; 1494 PetscErrorCode ierr; 1495 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1496 PetscInt i,n = A->rmap->n,j; 1497 PetscInt nz; 1498 PetscScalar *x,*tmp,s1; 1499 const MatScalar *aa = a->a,*v; 1500 const PetscScalar *b; 1501 1502 PetscFunctionBegin; 1503 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1504 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1505 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1506 tmp = a->solve_work; 1507 1508 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1509 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1510 1511 /* copy the b into temp work space according to permutation */ 1512 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1513 1514 /* forward solve the U^T */ 1515 for (i=0; i<n; i++) { 1516 v = aa + diag[i] ; 1517 vi = aj + diag[i] + 1; 1518 nz = ai[i+1] - diag[i] - 1; 1519 s1 = tmp[i]; 1520 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1521 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1522 tmp[i] = s1; 1523 } 1524 1525 /* backward solve the L^T */ 1526 for (i=n-1; i>=0; i--){ 1527 v = aa + diag[i] - 1 ; 1528 vi = aj + diag[i] - 1 ; 1529 nz = diag[i] - ai[i]; 1530 s1 = tmp[i]; 1531 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1532 } 1533 1534 /* copy tmp into x according to permutation */ 1535 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1536 1537 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1538 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1539 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1540 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1541 1542 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1543 PetscFunctionReturn(0); 1544 } 1545 1546 /* ----------------------------------------------------------------*/ 1547 EXTERN PetscErrorCode Mat_CheckInode(Mat,PetscTruth); 1548 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth); 1549 1550 /* 1551 ilu(0) with natural ordering under new data structure. 1552 Factored arrays bj and ba are stored as 1553 L(0,:), L(1,:), ...,L(n-1,:), U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:) 1554 1555 bi=fact->i is an array of size 2n+2, in which 1556 bi+ 1557 bi[i] -> 1st entry of L(i,:),i=0,...,i-1 1558 bi[n] -> points to L(n-1,:)+1 1559 bi[n+1] -> 1st entry of U(n-1,:) 1560 bi[2n-i] -> 1st entry of U(i,:) 1561 bi[2n-i+1] -> end of U(i,:)+1, the 1st entry of U(i-1,:) 1562 bi[2n] -> 1st entry of U(0,:) 1563 bi[2n+1] -> points to U(0,:)+1 1564 1565 U(i,:) contains diag[i] as its last entry, i.e., 1566 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 1567 */ 1568 #undef __FUNCT__ 1569 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct" 1570 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1571 { 1572 1573 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1574 PetscErrorCode ierr; 1575 PetscInt n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag; 1576 PetscInt i,j,nz,*bi,*bj,*bdiag; 1577 1578 PetscFunctionBegin; 1579 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr); 1580 b = (Mat_SeqAIJ*)(fact)->data; 1581 1582 /* allocate matrix arrays for new data structure */ 1583 ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,2*n+2,PetscInt,&b->i);CHKERRQ(ierr); 1584 ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(2*n+2)*sizeof(PetscInt));CHKERRQ(ierr); 1585 b->singlemalloc = PETSC_TRUE; 1586 if (!b->diag){ 1587 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr); 1588 } 1589 bdiag = b->diag; 1590 1591 if (n > 0) { 1592 ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr); 1593 } 1594 1595 /* set bi and bj with new data structure */ 1596 bi = b->i; 1597 bj = b->j; 1598 1599 /* L part */ 1600 bi[0] = 0; 1601 for (i=0; i<n; i++){ 1602 nz = adiag[i] - ai[i]; 1603 bi[i+1] = bi[i] + nz; 1604 aj = a->j + ai[i]; 1605 for (j=0; j<nz; j++){ 1606 *bj = aj[j]; bj++; 1607 } 1608 } 1609 1610 /* U part */ 1611 bi[n+1] = bi[n]; 1612 for (i=n-1; i>=0; i--){ 1613 nz = ai[i+1] - adiag[i] - 1; 1614 bi[2*n-i+1] = bi[2*n-i] + nz + 1; 1615 aj = a->j + adiag[i] + 1; 1616 for (j=0; j<nz; j++){ 1617 *bj = aj[j]; bj++; 1618 } 1619 /* diag[i] */ 1620 *bj = i; bj++; 1621 bdiag[i] = bi[2*n-i+1]-1; 1622 } 1623 PetscFunctionReturn(0); 1624 } 1625 1626 #undef __FUNCT__ 1627 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_newdatastruct" 1628 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1629 { 1630 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1631 IS isicol; 1632 PetscErrorCode ierr; 1633 const PetscInt *r,*ic; 1634 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,d; 1635 PetscInt *bi,*cols,nnz,*cols_lvl; 1636 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1637 PetscInt i,levels,diagonal_fill; 1638 PetscTruth col_identity,row_identity; 1639 PetscReal f; 1640 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1641 PetscBT lnkbt; 1642 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1643 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1644 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1645 PetscTruth missing; 1646 1647 PetscFunctionBegin; 1648 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); 1649 f = info->fill; 1650 levels = (PetscInt)info->levels; 1651 diagonal_fill = (PetscInt)info->diagonal_fill; 1652 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1653 1654 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1655 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1656 1657 if (!levels && row_identity && col_identity) { 1658 /* special case: ilu(0) with natural ordering */ 1659 ierr = MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1660 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 1661 1662 fact->factor = MAT_FACTOR_ILU; 1663 (fact)->info.factor_mallocs = 0; 1664 (fact)->info.fill_ratio_given = info->fill; 1665 (fact)->info.fill_ratio_needed = 1.0; 1666 b = (Mat_SeqAIJ*)(fact)->data; 1667 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 1668 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 1669 b->row = isrow; 1670 b->col = iscol; 1671 b->icol = isicol; 1672 ierr = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1673 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1674 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1675 /* ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */ 1676 PetscFunctionReturn(0); 1677 } 1678 1679 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1680 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1681 1682 /* get new row pointers */ 1683 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1684 bi[0] = 0; 1685 /* bdiag is location of diagonal in factor */ 1686 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1687 bdiag[0] = 0; 1688 1689 ierr = PetscMalloc((2*n+1)*sizeof(PetscInt**),&bj_ptr);CHKERRQ(ierr); 1690 bjlvl_ptr = (PetscInt**)(bj_ptr + n); 1691 1692 /* create a linked list for storing column indices of the active row */ 1693 nlnk = n + 1; 1694 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1695 1696 /* initial FreeSpace size is f*(ai[n]+1) */ 1697 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1698 current_space = free_space; 1699 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1700 current_space_lvl = free_space_lvl; 1701 1702 for (i=0; i<n; i++) { 1703 nzi = 0; 1704 /* copy current row into linked list */ 1705 nnz = ai[r[i]+1] - ai[r[i]]; 1706 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1707 cols = aj + ai[r[i]]; 1708 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1709 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1710 nzi += nlnk; 1711 1712 /* make sure diagonal entry is included */ 1713 if (diagonal_fill && lnk[i] == -1) { 1714 fm = n; 1715 while (lnk[fm] < i) fm = lnk[fm]; 1716 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1717 lnk[fm] = i; 1718 lnk_lvl[i] = 0; 1719 nzi++; dcount++; 1720 } 1721 1722 /* add pivot rows into the active row */ 1723 nzbd = 0; 1724 prow = lnk[n]; 1725 while (prow < i) { 1726 nnz = bdiag[prow]; 1727 cols = bj_ptr[prow] + nnz + 1; 1728 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1729 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1730 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1731 nzi += nlnk; 1732 prow = lnk[prow]; 1733 nzbd++; 1734 } 1735 bdiag[i] = nzbd; 1736 bi[i+1] = bi[i] + nzi; 1737 1738 /* if free space is not available, make more free space */ 1739 if (current_space->local_remaining<nzi) { 1740 nnz = 2*nzi*(n - i); /* estimated and max additional space needed */ 1741 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1742 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1743 reallocs++; 1744 } 1745 1746 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1747 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1748 bj_ptr[i] = current_space->array; 1749 bjlvl_ptr[i] = current_space_lvl->array; 1750 1751 /* make sure the active row i has diagonal entry */ 1752 if (*(bj_ptr[i]+bdiag[i]) != i) { 1753 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 1754 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1755 } 1756 1757 current_space->array += nzi; 1758 current_space->local_used += nzi; 1759 current_space->local_remaining -= nzi; 1760 current_space_lvl->array += nzi; 1761 current_space_lvl->local_used += nzi; 1762 current_space_lvl->local_remaining -= nzi; 1763 } 1764 1765 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1766 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1767 1768 /* destroy list of free space and other temporary arrays */ 1769 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 1770 1771 /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */ 1772 ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 1773 1774 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1775 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1776 ierr = PetscFree(bj_ptr);CHKERRQ(ierr); 1777 1778 #if defined(PETSC_USE_INFO) 1779 { 1780 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1781 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 1782 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1783 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 1784 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1785 if (diagonal_fill) { 1786 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 1787 } 1788 } 1789 #endif 1790 1791 /* put together the new matrix */ 1792 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 1793 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 1794 b = (Mat_SeqAIJ*)(fact)->data; 1795 b->free_a = PETSC_TRUE; 1796 b->free_ij = PETSC_TRUE; 1797 b->singlemalloc = PETSC_FALSE; 1798 ierr = PetscMalloc( (bi[2*n+1] )*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 1799 b->j = bj; 1800 b->i = bi; 1801 b->diag = bdiag; 1802 b->ilen = 0; 1803 b->imax = 0; 1804 b->row = isrow; 1805 b->col = iscol; 1806 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1807 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1808 b->icol = isicol; 1809 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1810 /* In b structure: Free imax, ilen, old a, old j. 1811 Allocate bdiag, solve_work, new a, new j */ 1812 ierr = PetscLogObjectMemory(fact,bi[2*n+1] * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1813 b->maxnz = b->nz = bi[2*n+1] ; 1814 (fact)->info.factor_mallocs = reallocs; 1815 (fact)->info.fill_ratio_given = f; 1816 (fact)->info.fill_ratio_needed = ((PetscReal)bi[2*n+1])/((PetscReal)ai[n]); 1817 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 1818 /* ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */ 1819 PetscFunctionReturn(0); 1820 } 1821 1822 1823 /* 1824 ilu(0) with natural ordering under revised new data structure. 1825 Factored arrays bj and ba are stored as 1826 L(0,:), L(1,:), ...,L(n-1,:), U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:) 1827 1828 bi=fact->i is an array of size n+1, in which 1829 bi+ 1830 bi[i] -> 1st entry of L(i,:),i=0,...,i-1 1831 bi[n] -> points to L(n-1,:)+1 1832 bi[n+1] -> 1st entry of U(n-1,:) 1833 bdiag=fact->diag is an array of size n+1,in which 1834 bdiag[0] -> points to diagonal of U(n-1,:) 1835 bdiag[n-1] -> points to diagonal of U(0,:) 1836 1837 U(i,:) contains bdiag[i] as its last entry, i.e., 1838 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 1839 */ 1840 #undef __FUNCT__ 1841 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct_v2" 1842 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct_v2(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1843 { 1844 1845 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1846 PetscErrorCode ierr; 1847 PetscInt n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag; 1848 PetscInt i,j,nz,*bi,*bj,*bdiag,bi_temp; 1849 1850 PetscFunctionBegin; 1851 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr); 1852 b = (Mat_SeqAIJ*)(fact)->data; 1853 1854 /* allocate matrix arrays for new data structure */ 1855 ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,n+1,PetscInt,&b->i);CHKERRQ(ierr); 1856 ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1857 b->singlemalloc = PETSC_TRUE; 1858 if (!b->diag){ 1859 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr); 1860 ierr = PetscLogObjectMemory(fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1861 } 1862 bdiag = b->diag; 1863 1864 if (n > 0) { 1865 ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr); 1866 } 1867 1868 /* set bi and bj with new data structure */ 1869 bi = b->i; 1870 bj = b->j; 1871 1872 /* L part */ 1873 bi[0] = 0; 1874 for (i=0; i<n; i++){ 1875 nz = adiag[i] - ai[i]; 1876 bi[i+1] = bi[i] + nz; 1877 aj = a->j + ai[i]; 1878 for (j=0; j<nz; j++){ 1879 *bj = aj[j]; bj++; 1880 } 1881 } 1882 1883 /* U part */ 1884 /* bi[n+1] = bi[n]; */ 1885 bi_temp = bi[n]; 1886 bdiag[n] = bi[n]-1; 1887 for (i=n-1; i>=0; i--){ 1888 nz = ai[i+1] - adiag[i] - 1; 1889 /* bi[2*n-i+1] = bi[2*n-i] + nz + 1; */ 1890 bi_temp = bi_temp + nz + 1; 1891 aj = a->j + adiag[i] + 1; 1892 for (j=0; j<nz; j++){ 1893 *bj = aj[j]; bj++; 1894 } 1895 /* diag[i] */ 1896 *bj = i; bj++; 1897 /* bdiag[i] = bi[2*n-i+1]-1; */ 1898 bdiag[i] = bi_temp - 1; 1899 } 1900 PetscFunctionReturn(0); 1901 } 1902 1903 #undef __FUNCT__ 1904 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_newdatastruct_v2" 1905 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_newdatastruct_v2(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1906 { 1907 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1908 IS isicol; 1909 PetscErrorCode ierr; 1910 const PetscInt *r,*ic; 1911 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,d; 1912 PetscInt *bi,*cols,nnz,*cols_lvl; 1913 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1914 PetscInt i,levels,diagonal_fill; 1915 PetscTruth col_identity,row_identity; 1916 PetscReal f; 1917 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1918 PetscBT lnkbt; 1919 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1920 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1921 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1922 PetscTruth missing; 1923 1924 PetscFunctionBegin; 1925 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); 1926 f = info->fill; 1927 levels = (PetscInt)info->levels; 1928 diagonal_fill = (PetscInt)info->diagonal_fill; 1929 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1930 1931 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1932 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1933 1934 if (!levels && row_identity && col_identity) { 1935 /* special case: ilu(0) with natural ordering */ 1936 ierr = MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct_v2(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1937 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct_v2; 1938 1939 fact->factor = MAT_FACTOR_ILU; 1940 (fact)->info.factor_mallocs = 0; 1941 (fact)->info.fill_ratio_given = info->fill; 1942 (fact)->info.fill_ratio_needed = 1.0; 1943 b = (Mat_SeqAIJ*)(fact)->data; 1944 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 1945 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 1946 b->row = isrow; 1947 b->col = iscol; 1948 b->icol = isicol; 1949 ierr = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1950 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1951 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1952 /* ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */ 1953 PetscFunctionReturn(0); 1954 } 1955 1956 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1957 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1958 1959 /* get new row pointers */ 1960 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1961 bi[0] = 0; 1962 /* bdiag is location of diagonal in factor */ 1963 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1964 bdiag[0] = 0; 1965 1966 ierr = PetscMalloc((2*n+1)*sizeof(PetscInt**),&bj_ptr);CHKERRQ(ierr); 1967 bjlvl_ptr = (PetscInt**)(bj_ptr + n); 1968 1969 /* create a linked list for storing column indices of the active row */ 1970 nlnk = n + 1; 1971 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1972 1973 /* initial FreeSpace size is f*(ai[n]+1) */ 1974 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1975 current_space = free_space; 1976 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1977 current_space_lvl = free_space_lvl; 1978 1979 for (i=0; i<n; i++) { 1980 nzi = 0; 1981 /* copy current row into linked list */ 1982 nnz = ai[r[i]+1] - ai[r[i]]; 1983 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1984 cols = aj + ai[r[i]]; 1985 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1986 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1987 nzi += nlnk; 1988 1989 /* make sure diagonal entry is included */ 1990 if (diagonal_fill && lnk[i] == -1) { 1991 fm = n; 1992 while (lnk[fm] < i) fm = lnk[fm]; 1993 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1994 lnk[fm] = i; 1995 lnk_lvl[i] = 0; 1996 nzi++; dcount++; 1997 } 1998 1999 /* add pivot rows into the active row */ 2000 nzbd = 0; 2001 prow = lnk[n]; 2002 while (prow < i) { 2003 nnz = bdiag[prow]; 2004 cols = bj_ptr[prow] + nnz + 1; 2005 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 2006 nnz = bi[prow+1] - bi[prow] - nnz - 1; 2007 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 2008 nzi += nlnk; 2009 prow = lnk[prow]; 2010 nzbd++; 2011 } 2012 bdiag[i] = nzbd; 2013 bi[i+1] = bi[i] + nzi; 2014 2015 /* if free space is not available, make more free space */ 2016 if (current_space->local_remaining<nzi) { 2017 nnz = 2*nzi*(n - i); /* estimated and max additional space needed */ 2018 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 2019 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 2020 reallocs++; 2021 } 2022 2023 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2024 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2025 bj_ptr[i] = current_space->array; 2026 bjlvl_ptr[i] = current_space_lvl->array; 2027 2028 /* make sure the active row i has diagonal entry */ 2029 if (*(bj_ptr[i]+bdiag[i]) != i) { 2030 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 2031 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 2032 } 2033 2034 current_space->array += nzi; 2035 current_space->local_used += nzi; 2036 current_space->local_remaining -= nzi; 2037 current_space_lvl->array += nzi; 2038 current_space_lvl->local_used += nzi; 2039 current_space_lvl->local_remaining -= nzi; 2040 } 2041 2042 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 2043 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 2044 2045 /* destroy list of free space and other temporary arrays */ 2046 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 2047 2048 /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */ 2049 ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 2050 2051 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2052 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2053 ierr = PetscFree(bj_ptr);CHKERRQ(ierr); 2054 2055 #if defined(PETSC_USE_INFO) 2056 { 2057 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 2058 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 2059 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2060 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 2061 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 2062 if (diagonal_fill) { 2063 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 2064 } 2065 } 2066 #endif 2067 2068 /* put together the new matrix */ 2069 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 2070 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 2071 b = (Mat_SeqAIJ*)(fact)->data; 2072 b->free_a = PETSC_TRUE; 2073 b->free_ij = PETSC_TRUE; 2074 b->singlemalloc = PETSC_FALSE; 2075 ierr = PetscMalloc( (bi[2*n+1] )*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 2076 b->j = bj; 2077 b->i = bi; 2078 b->diag = bdiag; 2079 b->ilen = 0; 2080 b->imax = 0; 2081 b->row = isrow; 2082 b->col = iscol; 2083 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 2084 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 2085 b->icol = isicol; 2086 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2087 /* In b structure: Free imax, ilen, old a, old j. 2088 Allocate bdiag, solve_work, new a, new j */ 2089 ierr = PetscLogObjectMemory(fact,bi[2*n+1] * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 2090 b->maxnz = b->nz = bi[2*n+1] ; 2091 (fact)->info.factor_mallocs = reallocs; 2092 (fact)->info.fill_ratio_given = f; 2093 (fact)->info.fill_ratio_needed = ((PetscReal)bi[2*n+1])/((PetscReal)ai[n]); 2094 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 2095 /* ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */ 2096 PetscFunctionReturn(0); 2097 } 2098 2099 #undef __FUNCT__ 2100 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ" 2101 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 2102 { 2103 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 2104 IS isicol; 2105 PetscErrorCode ierr; 2106 const PetscInt *r,*ic; 2107 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,d; 2108 PetscInt *bi,*cols,nnz,*cols_lvl; 2109 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 2110 PetscInt i,levels,diagonal_fill; 2111 PetscTruth col_identity,row_identity; 2112 PetscReal f; 2113 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 2114 PetscBT lnkbt; 2115 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 2116 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2117 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2118 PetscTruth missing; 2119 PetscTruth newdatastruct=PETSC_FALSE,newdatastruct_v2=PETSC_FALSE; 2120 2121 PetscFunctionBegin; 2122 ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 2123 if (newdatastruct){ 2124 ierr = MatILUFactorSymbolic_SeqAIJ_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr); 2125 PetscFunctionReturn(0); 2126 } 2127 ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_new_v2",&newdatastruct_v2,PETSC_NULL);CHKERRQ(ierr); 2128 if(newdatastruct_v2){ 2129 ierr = MatILUFactorSymbolic_SeqAIJ_newdatastruct_v2(fact,A,isrow,iscol,info);CHKERRQ(ierr); 2130 PetscFunctionReturn(0); 2131 } 2132 2133 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); 2134 f = info->fill; 2135 levels = (PetscInt)info->levels; 2136 diagonal_fill = (PetscInt)info->diagonal_fill; 2137 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 2138 2139 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 2140 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 2141 if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */ 2142 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr); 2143 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 2144 2145 fact->factor = MAT_FACTOR_ILU; 2146 (fact)->info.factor_mallocs = 0; 2147 (fact)->info.fill_ratio_given = info->fill; 2148 (fact)->info.fill_ratio_needed = 1.0; 2149 b = (Mat_SeqAIJ*)(fact)->data; 2150 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2151 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2152 b->row = isrow; 2153 b->col = iscol; 2154 b->icol = isicol; 2155 ierr = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2156 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 2157 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 2158 ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); 2159 PetscFunctionReturn(0); 2160 } 2161 2162 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 2163 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 2164 2165 /* get new row pointers */ 2166 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 2167 bi[0] = 0; 2168 /* bdiag is location of diagonal in factor */ 2169 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 2170 bdiag[0] = 0; 2171 2172 ierr = PetscMalloc((2*n+1)*sizeof(PetscInt**),&bj_ptr);CHKERRQ(ierr); 2173 bjlvl_ptr = (PetscInt**)(bj_ptr + n); 2174 2175 /* create a linked list for storing column indices of the active row */ 2176 nlnk = n + 1; 2177 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2178 2179 /* initial FreeSpace size is f*(ai[n]+1) */ 2180 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 2181 current_space = free_space; 2182 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 2183 current_space_lvl = free_space_lvl; 2184 2185 for (i=0; i<n; i++) { 2186 nzi = 0; 2187 /* copy current row into linked list */ 2188 nnz = ai[r[i]+1] - ai[r[i]]; 2189 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 2190 cols = aj + ai[r[i]]; 2191 lnk[i] = -1; /* marker to indicate if diagonal exists */ 2192 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2193 nzi += nlnk; 2194 2195 /* make sure diagonal entry is included */ 2196 if (diagonal_fill && lnk[i] == -1) { 2197 fm = n; 2198 while (lnk[fm] < i) fm = lnk[fm]; 2199 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 2200 lnk[fm] = i; 2201 lnk_lvl[i] = 0; 2202 nzi++; dcount++; 2203 } 2204 2205 /* add pivot rows into the active row */ 2206 nzbd = 0; 2207 prow = lnk[n]; 2208 while (prow < i) { 2209 nnz = bdiag[prow]; 2210 cols = bj_ptr[prow] + nnz + 1; 2211 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 2212 nnz = bi[prow+1] - bi[prow] - nnz - 1; 2213 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 2214 nzi += nlnk; 2215 prow = lnk[prow]; 2216 nzbd++; 2217 } 2218 bdiag[i] = nzbd; 2219 bi[i+1] = bi[i] + nzi; 2220 2221 /* if free space is not available, make more free space */ 2222 if (current_space->local_remaining<nzi) { 2223 nnz = nzi*(n - i); /* estimated and max additional space needed */ 2224 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 2225 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 2226 reallocs++; 2227 } 2228 2229 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2230 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2231 bj_ptr[i] = current_space->array; 2232 bjlvl_ptr[i] = current_space_lvl->array; 2233 2234 /* make sure the active row i has diagonal entry */ 2235 if (*(bj_ptr[i]+bdiag[i]) != i) { 2236 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 2237 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 2238 } 2239 2240 current_space->array += nzi; 2241 current_space->local_used += nzi; 2242 current_space->local_remaining -= nzi; 2243 current_space_lvl->array += nzi; 2244 current_space_lvl->local_used += nzi; 2245 current_space_lvl->local_remaining -= nzi; 2246 } 2247 2248 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 2249 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 2250 2251 /* destroy list of free space and other temporary arrays */ 2252 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 2253 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */ 2254 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2255 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2256 ierr = PetscFree(bj_ptr);CHKERRQ(ierr); 2257 2258 #if defined(PETSC_USE_INFO) 2259 { 2260 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 2261 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 2262 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2263 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 2264 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 2265 if (diagonal_fill) { 2266 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 2267 } 2268 } 2269 #endif 2270 2271 /* put together the new matrix */ 2272 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 2273 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 2274 b = (Mat_SeqAIJ*)(fact)->data; 2275 b->free_a = PETSC_TRUE; 2276 b->free_ij = PETSC_TRUE; 2277 b->singlemalloc = PETSC_FALSE; 2278 ierr = PetscMalloc( (bi[n] )*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 2279 b->j = bj; 2280 b->i = bi; 2281 for (i=0; i<n; i++) bdiag[i] += bi[i]; 2282 b->diag = bdiag; 2283 b->ilen = 0; 2284 b->imax = 0; 2285 b->row = isrow; 2286 b->col = iscol; 2287 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 2288 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 2289 b->icol = isicol; 2290 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2291 /* In b structure: Free imax, ilen, old a, old j. 2292 Allocate bdiag, solve_work, new a, new j */ 2293 ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 2294 b->maxnz = b->nz = bi[n] ; 2295 (fact)->info.factor_mallocs = reallocs; 2296 (fact)->info.fill_ratio_given = f; 2297 (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 2298 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 2299 ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); 2300 PetscFunctionReturn(0); 2301 } 2302 2303 #undef __FUNCT__ 2304 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ_newdatastruct" 2305 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info) 2306 { 2307 Mat C = B; 2308 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2309 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2310 IS ip=b->row,iip = b->icol; 2311 PetscErrorCode ierr; 2312 const PetscInt *rip,*riip; 2313 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp; 2314 PetscInt *ai=a->i,*aj=a->j; 2315 PetscInt k,jmin,jmax,*c2r,*il,col,nexti,ili,nz; 2316 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2317 PetscReal zeropivot,shiftnz; 2318 PetscReal shiftpd; 2319 PetscTruth perm_identity; 2320 2321 PetscFunctionBegin; 2322 2323 shiftnz = info->shiftnz; 2324 shiftpd = info->shiftpd; 2325 zeropivot = info->zeropivot; 2326 2327 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2328 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2329 2330 /* allocate working arrays 2331 c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col 2332 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 2333 */ 2334 nz = (2*mbs+1)*sizeof(PetscInt)+mbs*sizeof(MatScalar); 2335 ierr = PetscMalloc(nz,&il);CHKERRQ(ierr); 2336 c2r = il + mbs; 2337 rtmp = (MatScalar*)(c2r + mbs); 2338 2339 for (i=0; i<mbs; i++) { 2340 c2r[i] = mbs; 2341 } 2342 il[0] = 0; 2343 2344 for (k = 0; k<mbs; k++){ 2345 /* zero rtmp */ 2346 nz = bi[k+1] - bi[k]; 2347 bjtmp = bj + bi[k]; 2348 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2349 2350 /* load in initial unfactored row */ 2351 bval = ba + bi[k]; 2352 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2353 for (j = jmin; j < jmax; j++){ 2354 col = riip[aj[j]]; 2355 if (col >= k){ /* only take upper triangular entry */ 2356 rtmp[col] = aa[j]; 2357 *bval++ = 0.0; /* for in-place factorization */ 2358 } 2359 } 2360 /* shift the diagonal of the matrix */ 2361 2362 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2363 dk = rtmp[k]; 2364 i = c2r[k]; /* first row to be added to k_th row */ 2365 2366 while (i < k){ 2367 nexti = c2r[i]; /* next row to be added to k_th row */ 2368 2369 /* compute multiplier, update diag(k) and U(i,k) */ 2370 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2371 uikdi = - ba[ili]*ba[bdiag[i]]; /* diagonal(k) */ 2372 dk += uikdi*ba[ili]; /* update diag[k] */ 2373 ba[ili] = uikdi; /* -U(i,k) */ 2374 2375 /* add multiple of row i to k-th row */ 2376 jmin = ili + 1; jmax = bi[i+1]; 2377 if (jmin < jmax){ 2378 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2379 /* update il and c2r for row i */ 2380 il[i] = jmin; 2381 j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i; 2382 } 2383 i = nexti; 2384 } 2385 2386 /* copy data into U(k,:) */ 2387 ba[bdiag[k]] = 1.0/dk; /* U(k,k) */ 2388 jmin = bi[k]; jmax = bi[k+1]-1; 2389 if (jmin < jmax) { 2390 for (j=jmin; j<jmax; j++){ 2391 col = bj[j]; ba[j] = rtmp[col]; 2392 } 2393 /* add the k-th row into il and c2r */ 2394 il[k] = jmin; 2395 i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k; 2396 } 2397 } 2398 2399 ierr = PetscFree(il);CHKERRQ(ierr); 2400 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2401 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2402 2403 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2404 if (perm_identity){ 2405 (B)->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_newdatastruct; 2406 (B)->ops->solvetranspose = 0; 2407 (B)->ops->forwardsolve = 0; 2408 (B)->ops->backwardsolve = 0; 2409 } else { 2410 (B)->ops->solve = MatSolve_SeqSBAIJ_1_newdatastruct; 2411 (B)->ops->solvetranspose = 0; 2412 (B)->ops->forwardsolve = 0; 2413 (B)->ops->backwardsolve = 0; 2414 } 2415 2416 C->assembled = PETSC_TRUE; 2417 C->preallocated = PETSC_TRUE; 2418 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2419 PetscFunctionReturn(0); 2420 } 2421 2422 #undef __FUNCT__ 2423 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ" 2424 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 2425 { 2426 Mat C = B; 2427 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2428 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2429 IS ip=b->row,iip = b->icol; 2430 PetscErrorCode ierr; 2431 const PetscInt *rip,*riip; 2432 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol; 2433 PetscInt *ai=a->i,*aj=a->j; 2434 PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz; 2435 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2436 PetscReal zeropivot,rs,shiftnz; 2437 PetscReal shiftpd; 2438 ChShift_Ctx sctx; 2439 PetscInt newshift; 2440 PetscTruth perm_identity; 2441 2442 PetscFunctionBegin; 2443 shiftnz = info->shiftnz; 2444 shiftpd = info->shiftpd; 2445 zeropivot = info->zeropivot; 2446 2447 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2448 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2449 2450 /* initialization */ 2451 nz = (2*mbs+1)*sizeof(PetscInt)+mbs*sizeof(MatScalar); 2452 ierr = PetscMalloc(nz,&il);CHKERRQ(ierr); 2453 jl = il + mbs; 2454 rtmp = (MatScalar*)(jl + mbs); 2455 2456 sctx.shift_amount = 0; 2457 sctx.nshift = 0; 2458 do { 2459 sctx.chshift = PETSC_FALSE; 2460 for (i=0; i<mbs; i++) { 2461 rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0; 2462 } 2463 2464 for (k = 0; k<mbs; k++){ 2465 bval = ba + bi[k]; 2466 /* initialize k-th row by the perm[k]-th row of A */ 2467 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2468 for (j = jmin; j < jmax; j++){ 2469 col = riip[aj[j]]; 2470 if (col >= k){ /* only take upper triangular entry */ 2471 rtmp[col] = aa[j]; 2472 *bval++ = 0.0; /* for in-place factorization */ 2473 } 2474 } 2475 /* shift the diagonal of the matrix */ 2476 if (sctx.nshift) rtmp[k] += sctx.shift_amount; 2477 2478 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2479 dk = rtmp[k]; 2480 i = jl[k]; /* first row to be added to k_th row */ 2481 2482 while (i < k){ 2483 nexti = jl[i]; /* next row to be added to k_th row */ 2484 2485 /* compute multiplier, update diag(k) and U(i,k) */ 2486 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2487 uikdi = - ba[ili]*ba[bi[i]]; /* diagonal(k) */ 2488 dk += uikdi*ba[ili]; 2489 ba[ili] = uikdi; /* -U(i,k) */ 2490 2491 /* add multiple of row i to k-th row */ 2492 jmin = ili + 1; jmax = bi[i+1]; 2493 if (jmin < jmax){ 2494 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2495 /* update il and jl for row i */ 2496 il[i] = jmin; 2497 j = bj[jmin]; jl[i] = jl[j]; jl[j] = i; 2498 } 2499 i = nexti; 2500 } 2501 2502 /* shift the diagonals when zero pivot is detected */ 2503 /* compute rs=sum of abs(off-diagonal) */ 2504 rs = 0.0; 2505 jmin = bi[k]+1; 2506 nz = bi[k+1] - jmin; 2507 bcol = bj + jmin; 2508 for (j=0; j<nz; j++) { 2509 rs += PetscAbsScalar(rtmp[bcol[j]]); 2510 } 2511 2512 sctx.rs = rs; 2513 sctx.pv = dk; 2514 ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr); 2515 2516 if (newshift == 1) { 2517 if (!sctx.shift_amount) { 2518 sctx.shift_amount = 1e-5; 2519 } 2520 break; 2521 } 2522 2523 /* copy data into U(k,:) */ 2524 ba[bi[k]] = 1.0/dk; /* U(k,k) */ 2525 jmin = bi[k]+1; jmax = bi[k+1]; 2526 if (jmin < jmax) { 2527 for (j=jmin; j<jmax; j++){ 2528 col = bj[j]; ba[j] = rtmp[col]; rtmp[col] = 0.0; 2529 } 2530 /* add the k-th row into il and jl */ 2531 il[k] = jmin; 2532 i = bj[jmin]; jl[k] = jl[i]; jl[i] = k; 2533 } 2534 } 2535 } while (sctx.chshift); 2536 ierr = PetscFree(il);CHKERRQ(ierr); 2537 2538 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2539 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2540 2541 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2542 if (perm_identity){ 2543 (B)->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2544 (B)->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2545 (B)->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering; 2546 (B)->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering; 2547 } else { 2548 (B)->ops->solve = MatSolve_SeqSBAIJ_1; 2549 (B)->ops->solvetranspose = MatSolve_SeqSBAIJ_1; 2550 (B)->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1; 2551 (B)->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1; 2552 } 2553 2554 C->assembled = PETSC_TRUE; 2555 C->preallocated = PETSC_TRUE; 2556 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2557 if (sctx.nshift){ 2558 if (shiftnz) { 2559 ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2560 } else if (shiftpd) { 2561 ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2562 } 2563 } 2564 PetscFunctionReturn(0); 2565 } 2566 2567 #undef __FUNCT__ 2568 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ_newdatastruct" 2569 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2570 { 2571 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2572 Mat_SeqSBAIJ *b; 2573 PetscErrorCode ierr; 2574 PetscTruth perm_identity,missing; 2575 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2576 const PetscInt *rip,*riip; 2577 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2578 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2579 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2580 PetscReal fill=info->fill,levels=info->levels; 2581 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2582 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2583 PetscBT lnkbt; 2584 IS iperm; 2585 2586 PetscFunctionBegin; 2587 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); 2588 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2589 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2590 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2591 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2592 2593 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2594 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2595 ui[0] = 0; 2596 2597 /* ICC(0) without matrix ordering: simply copies fill pattern */ 2598 if (!levels && perm_identity) { 2599 2600 for (i=0; i<am; i++) { 2601 ui[i+1] = ui[i] + ai[i+1] - a->diag[i]; 2602 udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */ 2603 } 2604 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2605 cols = uj; 2606 for (i=0; i<am; i++) { 2607 aj = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */ 2608 ncols = ui[i+1] - ui[i] - 1; 2609 for (j=0; j<ncols; j++) *cols++ = aj[j]; 2610 *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */ 2611 } 2612 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2613 2614 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2615 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2616 2617 /* initialization */ 2618 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2619 2620 /* jl: linked list for storing indices of the pivot rows 2621 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2622 ierr = PetscMalloc((2*am+1)*sizeof(PetscInt)+2*am*sizeof(PetscInt**),&jl);CHKERRQ(ierr); 2623 il = jl + am; 2624 uj_ptr = (PetscInt**)(il + am); 2625 uj_lvl_ptr = (PetscInt**)(uj_ptr + am); 2626 for (i=0; i<am; i++){ 2627 jl[i] = am; il[i] = 0; 2628 } 2629 2630 /* create and initialize a linked list for storing column indices of the active row k */ 2631 nlnk = am + 1; 2632 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2633 2634 /* initial FreeSpace size is fill*(ai[am]+1) */ 2635 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2636 current_space = free_space; 2637 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2638 current_space_lvl = free_space_lvl; 2639 2640 for (k=0; k<am; k++){ /* for each active row k */ 2641 /* initialize lnk by the column indices of row rip[k] of A */ 2642 nzk = 0; 2643 ncols = ai[rip[k]+1] - ai[rip[k]]; 2644 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2645 ncols_upper = 0; 2646 for (j=0; j<ncols; j++){ 2647 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2648 if (riip[i] >= k){ /* only take upper triangular entry */ 2649 ajtmp[ncols_upper] = i; 2650 ncols_upper++; 2651 } 2652 } 2653 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2654 nzk += nlnk; 2655 2656 /* update lnk by computing fill-in for each pivot row to be merged in */ 2657 prow = jl[k]; /* 1st pivot row */ 2658 2659 while (prow < k){ 2660 nextprow = jl[prow]; 2661 2662 /* merge prow into k-th row */ 2663 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2664 jmax = ui[prow+1]; 2665 ncols = jmax-jmin; 2666 i = jmin - ui[prow]; 2667 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2668 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2669 j = *(uj - 1); 2670 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2671 nzk += nlnk; 2672 2673 /* update il and jl for prow */ 2674 if (jmin < jmax){ 2675 il[prow] = jmin; 2676 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2677 } 2678 prow = nextprow; 2679 } 2680 2681 /* if free space is not available, make more free space */ 2682 if (current_space->local_remaining<nzk) { 2683 i = am - k + 1; /* num of unfactored rows */ 2684 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2685 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2686 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2687 reallocs++; 2688 } 2689 2690 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2691 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2692 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2693 2694 /* add the k-th row into il and jl */ 2695 if (nzk > 1){ 2696 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2697 jl[k] = jl[i]; jl[i] = k; 2698 il[k] = ui[k] + 1; 2699 } 2700 uj_ptr[k] = current_space->array; 2701 uj_lvl_ptr[k] = current_space_lvl->array; 2702 2703 current_space->array += nzk; 2704 current_space->local_used += nzk; 2705 current_space->local_remaining -= nzk; 2706 2707 current_space_lvl->array += nzk; 2708 current_space_lvl->local_used += nzk; 2709 current_space_lvl->local_remaining -= nzk; 2710 2711 ui[k+1] = ui[k] + nzk; 2712 } 2713 2714 #if defined(PETSC_USE_INFO) 2715 if (ai[am] != 0) { 2716 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2717 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2718 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2719 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2720 } else { 2721 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2722 } 2723 #endif 2724 2725 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2726 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2727 ierr = PetscFree(jl);CHKERRQ(ierr); 2728 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2729 2730 /* destroy list of free space and other temporary array(s) */ 2731 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2732 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); 2733 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2734 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2735 2736 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2737 2738 /* put together the new matrix in MATSEQSBAIJ format */ 2739 2740 b = (Mat_SeqSBAIJ*)(fact)->data; 2741 b->singlemalloc = PETSC_FALSE; 2742 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2743 b->j = uj; 2744 b->i = ui; 2745 b->diag = udiag; 2746 b->free_diag = PETSC_TRUE; 2747 b->ilen = 0; 2748 b->imax = 0; 2749 b->row = perm; 2750 b->col = perm; 2751 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2752 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2753 b->icol = iperm; 2754 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2755 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2756 ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2757 b->maxnz = b->nz = ui[am]; 2758 b->free_a = PETSC_TRUE; 2759 b->free_ij = PETSC_TRUE; 2760 2761 (fact)->info.factor_mallocs = reallocs; 2762 (fact)->info.fill_ratio_given = fill; 2763 if (ai[am] != 0) { 2764 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2765 } else { 2766 (fact)->info.fill_ratio_needed = 0.0; 2767 } 2768 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct; 2769 PetscFunctionReturn(0); 2770 } 2771 2772 #undef __FUNCT__ 2773 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ" 2774 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2775 { 2776 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2777 Mat_SeqSBAIJ *b; 2778 PetscErrorCode ierr; 2779 PetscTruth perm_identity,missing; 2780 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2781 const PetscInt *rip,*riip; 2782 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2783 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2784 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2785 PetscReal fill=info->fill,levels=info->levels; 2786 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2787 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2788 PetscBT lnkbt; 2789 IS iperm; 2790 PetscTruth newdatastruct=PETSC_FALSE; 2791 2792 PetscFunctionBegin; 2793 ierr = PetscOptionsGetTruth(PETSC_NULL,"-icc_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 2794 if(newdatastruct){ 2795 ierr = MatICCFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr); 2796 PetscFunctionReturn(0); 2797 } 2798 2799 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 2800 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2801 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2802 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2803 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2804 2805 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2806 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2807 ui[0] = 0; 2808 2809 /* ICC(0) without matrix ordering: simply copies fill pattern */ 2810 if (!levels && perm_identity) { 2811 2812 for (i=0; i<am; i++) { 2813 ui[i+1] = ui[i] + ai[i+1] - a->diag[i]; 2814 udiag[i] = ui[i]; 2815 } 2816 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2817 cols = uj; 2818 for (i=0; i<am; i++) { 2819 aj = a->j + a->diag[i]; 2820 ncols = ui[i+1] - ui[i]; 2821 for (j=0; j<ncols; j++) *cols++ = *aj++; 2822 } 2823 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2824 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2825 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2826 2827 /* initialization */ 2828 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2829 2830 /* jl: linked list for storing indices of the pivot rows 2831 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2832 ierr = PetscMalloc((2*am+1)*sizeof(PetscInt)+2*am*sizeof(PetscInt**),&jl);CHKERRQ(ierr); 2833 il = jl + am; 2834 uj_ptr = (PetscInt**)(il + am); 2835 uj_lvl_ptr = (PetscInt**)(uj_ptr + am); 2836 for (i=0; i<am; i++){ 2837 jl[i] = am; il[i] = 0; 2838 } 2839 2840 /* create and initialize a linked list for storing column indices of the active row k */ 2841 nlnk = am + 1; 2842 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2843 2844 /* initial FreeSpace size is fill*(ai[am]+1) */ 2845 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2846 current_space = free_space; 2847 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2848 current_space_lvl = free_space_lvl; 2849 2850 for (k=0; k<am; k++){ /* for each active row k */ 2851 /* initialize lnk by the column indices of row rip[k] of A */ 2852 nzk = 0; 2853 ncols = ai[rip[k]+1] - ai[rip[k]]; 2854 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2855 ncols_upper = 0; 2856 for (j=0; j<ncols; j++){ 2857 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2858 if (riip[i] >= k){ /* only take upper triangular entry */ 2859 ajtmp[ncols_upper] = i; 2860 ncols_upper++; 2861 } 2862 } 2863 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2864 nzk += nlnk; 2865 2866 /* update lnk by computing fill-in for each pivot row to be merged in */ 2867 prow = jl[k]; /* 1st pivot row */ 2868 2869 while (prow < k){ 2870 nextprow = jl[prow]; 2871 2872 /* merge prow into k-th row */ 2873 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2874 jmax = ui[prow+1]; 2875 ncols = jmax-jmin; 2876 i = jmin - ui[prow]; 2877 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2878 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2879 j = *(uj - 1); 2880 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2881 nzk += nlnk; 2882 2883 /* update il and jl for prow */ 2884 if (jmin < jmax){ 2885 il[prow] = jmin; 2886 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2887 } 2888 prow = nextprow; 2889 } 2890 2891 /* if free space is not available, make more free space */ 2892 if (current_space->local_remaining<nzk) { 2893 i = am - k + 1; /* num of unfactored rows */ 2894 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2895 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2896 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2897 reallocs++; 2898 } 2899 2900 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2901 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2902 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2903 2904 /* add the k-th row into il and jl */ 2905 if (nzk > 1){ 2906 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2907 jl[k] = jl[i]; jl[i] = k; 2908 il[k] = ui[k] + 1; 2909 } 2910 uj_ptr[k] = current_space->array; 2911 uj_lvl_ptr[k] = current_space_lvl->array; 2912 2913 current_space->array += nzk; 2914 current_space->local_used += nzk; 2915 current_space->local_remaining -= nzk; 2916 2917 current_space_lvl->array += nzk; 2918 current_space_lvl->local_used += nzk; 2919 current_space_lvl->local_remaining -= nzk; 2920 2921 ui[k+1] = ui[k] + nzk; 2922 } 2923 2924 #if defined(PETSC_USE_INFO) 2925 if (ai[am] != 0) { 2926 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2927 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2928 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2929 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2930 } else { 2931 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2932 } 2933 #endif 2934 2935 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2936 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2937 ierr = PetscFree(jl);CHKERRQ(ierr); 2938 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2939 2940 /* destroy list of free space and other temporary array(s) */ 2941 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2942 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 2943 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2944 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2945 2946 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2947 2948 /* put together the new matrix in MATSEQSBAIJ format */ 2949 2950 b = (Mat_SeqSBAIJ*)(fact)->data; 2951 b->singlemalloc = PETSC_FALSE; 2952 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2953 b->j = uj; 2954 b->i = ui; 2955 b->diag = udiag; 2956 b->free_diag = PETSC_TRUE; 2957 b->ilen = 0; 2958 b->imax = 0; 2959 b->row = perm; 2960 b->col = perm; 2961 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2962 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2963 b->icol = iperm; 2964 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2965 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2966 ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2967 b->maxnz = b->nz = ui[am]; 2968 b->free_a = PETSC_TRUE; 2969 b->free_ij = PETSC_TRUE; 2970 2971 (fact)->info.factor_mallocs = reallocs; 2972 (fact)->info.fill_ratio_given = fill; 2973 if (ai[am] != 0) { 2974 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2975 } else { 2976 (fact)->info.fill_ratio_needed = 0.0; 2977 } 2978 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2979 PetscFunctionReturn(0); 2980 } 2981 2982 #undef __FUNCT__ 2983 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ" 2984 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2985 { 2986 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2987 Mat_SeqSBAIJ *b; 2988 PetscErrorCode ierr; 2989 PetscTruth perm_identity; 2990 PetscReal fill = info->fill; 2991 const PetscInt *rip,*riip; 2992 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2993 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2994 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr; 2995 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2996 PetscBT lnkbt; 2997 IS iperm; 2998 2999 PetscFunctionBegin; 3000 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); 3001 /* check whether perm is the identity mapping */ 3002 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 3003 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 3004 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 3005 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 3006 3007 /* initialization */ 3008 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 3009 ui[0] = 0; 3010 3011 /* jl: linked list for storing indices of the pivot rows 3012 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 3013 ierr = PetscMalloc((3*am+1)*sizeof(PetscInt)+am*sizeof(PetscInt**),&jl);CHKERRQ(ierr); 3014 il = jl + am; 3015 cols = il + am; 3016 ui_ptr = (PetscInt**)(cols + am); 3017 for (i=0; i<am; i++){ 3018 jl[i] = am; il[i] = 0; 3019 } 3020 3021 /* create and initialize a linked list for storing column indices of the active row k */ 3022 nlnk = am + 1; 3023 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3024 3025 /* initial FreeSpace size is fill*(ai[am]+1) */ 3026 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 3027 current_space = free_space; 3028 3029 for (k=0; k<am; k++){ /* for each active row k */ 3030 /* initialize lnk by the column indices of row rip[k] of A */ 3031 nzk = 0; 3032 ncols = ai[rip[k]+1] - ai[rip[k]]; 3033 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 3034 ncols_upper = 0; 3035 for (j=0; j<ncols; j++){ 3036 i = riip[*(aj + ai[rip[k]] + j)]; 3037 if (i >= k){ /* only take upper triangular entry */ 3038 cols[ncols_upper] = i; 3039 ncols_upper++; 3040 } 3041 } 3042 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3043 nzk += nlnk; 3044 3045 /* update lnk by computing fill-in for each pivot row to be merged in */ 3046 prow = jl[k]; /* 1st pivot row */ 3047 3048 while (prow < k){ 3049 nextprow = jl[prow]; 3050 /* merge prow into k-th row */ 3051 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 3052 jmax = ui[prow+1]; 3053 ncols = jmax-jmin; 3054 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 3055 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3056 nzk += nlnk; 3057 3058 /* update il and jl for prow */ 3059 if (jmin < jmax){ 3060 il[prow] = jmin; 3061 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 3062 } 3063 prow = nextprow; 3064 } 3065 3066 /* if free space is not available, make more free space */ 3067 if (current_space->local_remaining<nzk) { 3068 i = am - k + 1; /* num of unfactored rows */ 3069 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 3070 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 3071 reallocs++; 3072 } 3073 3074 /* copy data into free space, then initialize lnk */ 3075 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 3076 3077 /* add the k-th row into il and jl */ 3078 if (nzk-1 > 0){ 3079 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 3080 jl[k] = jl[i]; jl[i] = k; 3081 il[k] = ui[k] + 1; 3082 } 3083 ui_ptr[k] = current_space->array; 3084 current_space->array += nzk; 3085 current_space->local_used += nzk; 3086 current_space->local_remaining -= nzk; 3087 3088 ui[k+1] = ui[k] + nzk; 3089 } 3090 3091 #if defined(PETSC_USE_INFO) 3092 if (ai[am] != 0) { 3093 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 3094 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 3095 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 3096 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 3097 } else { 3098 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 3099 } 3100 #endif 3101 3102 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 3103 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 3104 ierr = PetscFree(jl);CHKERRQ(ierr); 3105 3106 /* destroy list of free space and other temporary array(s) */ 3107 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 3108 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 3109 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3110 3111 /* put together the new matrix in MATSEQSBAIJ format */ 3112 3113 b = (Mat_SeqSBAIJ*)(fact)->data; 3114 b->singlemalloc = PETSC_FALSE; 3115 b->free_a = PETSC_TRUE; 3116 b->free_ij = PETSC_TRUE; 3117 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 3118 b->j = uj; 3119 b->i = ui; 3120 b->diag = 0; 3121 b->ilen = 0; 3122 b->imax = 0; 3123 b->row = perm; 3124 b->col = perm; 3125 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3126 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3127 b->icol = iperm; 3128 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 3129 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 3130 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3131 b->maxnz = b->nz = ui[am]; 3132 3133 (fact)->info.factor_mallocs = reallocs; 3134 (fact)->info.fill_ratio_given = fill; 3135 if (ai[am] != 0) { 3136 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 3137 } else { 3138 (fact)->info.fill_ratio_needed = 0.0; 3139 } 3140 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 3141 PetscFunctionReturn(0); 3142 } 3143 3144 #undef __FUNCT__ 3145 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct" 3146 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx) 3147 { 3148 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3149 PetscErrorCode ierr; 3150 PetscInt n = A->rmap->n; 3151 const PetscInt *ai = a->i,*aj = a->j,*vi; 3152 PetscScalar *x,sum; 3153 const PetscScalar *b; 3154 const MatScalar *aa = a->a,*v; 3155 PetscInt i,nz; 3156 3157 PetscFunctionBegin; 3158 if (!n) PetscFunctionReturn(0); 3159 3160 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3161 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3162 3163 /* forward solve the lower triangular */ 3164 x[0] = b[0]; 3165 v = aa; 3166 vi = aj; 3167 for (i=1; i<n; i++) { 3168 nz = ai[i+1] - ai[i]; 3169 sum = b[i]; 3170 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3171 v += nz; 3172 vi += nz; 3173 x[i] = sum; 3174 } 3175 3176 /* backward solve the upper triangular */ 3177 v = aa + ai[n+1]; 3178 vi = aj + ai[n+1]; 3179 for (i=n-1; i>=0; i--){ 3180 nz = ai[2*n-i +1] - ai[2*n-i]-1; 3181 sum = x[i]; 3182 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3183 v += nz; 3184 vi += nz; vi++; 3185 x[i] = *v++ *sum; /* x[i]=aa[adiag[i]]*sum; v++; */ 3186 } 3187 3188 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 3189 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3190 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3191 PetscFunctionReturn(0); 3192 } 3193 3194 #undef __FUNCT__ 3195 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct_v2" 3196 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct_v2(Mat A,Vec bb,Vec xx) 3197 { 3198 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3199 PetscErrorCode ierr; 3200 PetscInt n = A->rmap->n; 3201 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag,*vi; 3202 PetscScalar *x,sum; 3203 const PetscScalar *b; 3204 const MatScalar *aa = a->a,*v; 3205 PetscInt i,nz; 3206 3207 PetscFunctionBegin; 3208 if (!n) PetscFunctionReturn(0); 3209 3210 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3211 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3212 3213 /* forward solve the lower triangular */ 3214 x[0] = b[0]; 3215 v = aa; 3216 vi = aj; 3217 for (i=1; i<n; i++) { 3218 nz = ai[i+1] - ai[i]; 3219 sum = b[i]; 3220 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3221 v += nz; 3222 vi += nz; 3223 x[i] = sum; 3224 } 3225 3226 /* backward solve the upper triangular */ 3227 /* v = aa + ai[n+1]; 3228 vi = aj + ai[n+1]; */ 3229 v = aa + adiag[n-1]; 3230 vi = aj + adiag[n-1]; 3231 for (i=n-1; i>=0; i--){ 3232 nz = adiag[i] - adiag[i+1]-1; 3233 sum = x[i]; 3234 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3235 v += nz; 3236 vi += nz; vi++; 3237 x[i] = *v++ *sum; /* x[i]=aa[adiag[i]]*sum; v++; */ 3238 } 3239 3240 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 3241 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3242 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3243 PetscFunctionReturn(0); 3244 } 3245 3246 #undef __FUNCT__ 3247 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct" 3248 PetscErrorCode MatSolve_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx) 3249 { 3250 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3251 IS iscol = a->col,isrow = a->row; 3252 PetscErrorCode ierr; 3253 PetscInt i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,nz,k; 3254 const PetscInt *rout,*cout,*r,*c; 3255 PetscScalar *x,*tmp,*tmps,sum; 3256 const PetscScalar *b; 3257 const MatScalar *aa = a->a,*v; 3258 3259 PetscFunctionBegin; 3260 if (!n) PetscFunctionReturn(0); 3261 3262 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3263 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3264 tmp = a->solve_work; 3265 3266 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 3267 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 3268 3269 /* forward solve the lower triangular */ 3270 tmp[0] = b[*r++]; 3271 tmps = tmp; 3272 v = aa; 3273 vi = aj; 3274 for (i=1; i<n; i++) { 3275 nz = ai[i+1] - ai[i]; 3276 sum = b[*r++]; 3277 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 3278 tmp[i] = sum; 3279 v += nz; vi += nz; 3280 } 3281 3282 /* backward solve the upper triangular */ 3283 k = n+1; 3284 v = aa + ai[k]; /* 1st entry of U(n-1,:) */ 3285 vi = aj + ai[k]; 3286 for (i=n-1; i>=0; i--){ 3287 k = 2*n-i; 3288 nz = ai[k +1] - ai[k] - 1; 3289 sum = tmp[i]; 3290 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 3291 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 3292 v += nz+1; vi += nz+1; 3293 } 3294 3295 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 3296 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 3297 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3298 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3299 ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr); 3300 PetscFunctionReturn(0); 3301 } 3302 3303 #undef __FUNCT__ 3304 #define __FUNCT__ "MatILUDTFactor_SeqAIJ" 3305 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact) 3306 { 3307 Mat B = *fact; 3308 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b; 3309 IS isicol; 3310 PetscErrorCode ierr; 3311 const PetscInt *r,*ic; 3312 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag; 3313 PetscInt *bi,*bj,*bdiag,*bdiag_rev; 3314 PetscInt row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au; 3315 PetscInt nlnk,*lnk; 3316 PetscBT lnkbt; 3317 PetscTruth row_identity,icol_identity,both_identity; 3318 MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp; 3319 const PetscInt *ics; 3320 PetscInt j,nz,*pj,*bjtmp,k,ncut,*jtmp; 3321 PetscReal dt=info->dt,dtcol=info->dtcol,shift=info->shiftinblocks; 3322 PetscInt dtcount=(PetscInt)info->dtcount,nnz_max; 3323 PetscTruth missing; 3324 3325 PetscFunctionBegin; 3326 3327 if (dt == PETSC_DEFAULT) dt = 0.005; 3328 if (dtcol == PETSC_DEFAULT) dtcol = 0.01; /* XXX unused! */ 3329 if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax); 3330 3331 /* ------- symbolic factorization, can be reused ---------*/ 3332 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 3333 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 3334 adiag=a->diag; 3335 3336 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 3337 3338 /* bdiag is location of diagonal in factor */ 3339 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 3340 bdiag_rev = bdiag + n+1; 3341 3342 /* allocate row pointers bi */ 3343 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 3344 3345 /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */ 3346 if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */ 3347 nnz_max = ai[n]+2*n*dtcount+2; 3348 3349 ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 3350 ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr); 3351 3352 /* put together the new matrix */ 3353 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 3354 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 3355 b = (Mat_SeqAIJ*)(B)->data; 3356 b->free_a = PETSC_TRUE; 3357 b->free_ij = PETSC_TRUE; 3358 b->singlemalloc = PETSC_FALSE; 3359 b->a = ba; 3360 b->j = bj; 3361 b->i = bi; 3362 b->diag = bdiag; 3363 b->ilen = 0; 3364 b->imax = 0; 3365 b->row = isrow; 3366 b->col = iscol; 3367 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 3368 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 3369 b->icol = isicol; 3370 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 3371 3372 ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3373 b->maxnz = nnz_max; 3374 3375 (B)->factor = MAT_FACTOR_ILUDT; 3376 (B)->info.factor_mallocs = 0; 3377 (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]); 3378 CHKMEMQ; 3379 /* ------- end of symbolic factorization ---------*/ 3380 3381 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3382 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3383 ics = ic; 3384 3385 /* linked list for storing column indices of the active row */ 3386 nlnk = n + 1; 3387 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3388 3389 /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */ 3390 ierr = PetscMalloc((2*n+1)*sizeof(PetscInt),&im);CHKERRQ(ierr); 3391 jtmp = im + n; 3392 /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */ 3393 ierr = PetscMalloc((2*n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 3394 ierr = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr); 3395 vtmp = rtmp + n; 3396 3397 bi[0] = 0; 3398 bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */ 3399 bdiag_rev[n] = bdiag[0]; 3400 bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */ 3401 for (i=0; i<n; i++) { 3402 /* copy initial fill into linked list */ 3403 nzi = 0; /* nonzeros for active row i */ 3404 nzi = ai[r[i]+1] - ai[r[i]]; 3405 if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 3406 nzi_al = adiag[r[i]] - ai[r[i]]; 3407 nzi_au = ai[r[i]+1] - adiag[r[i]] -1; 3408 ajtmp = aj + ai[r[i]]; 3409 ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3410 3411 /* load in initial (unfactored row) */ 3412 aatmp = a->a + ai[r[i]]; 3413 for (j=0; j<nzi; j++) { 3414 rtmp[ics[*ajtmp++]] = *aatmp++; 3415 } 3416 3417 /* add pivot rows into linked list */ 3418 row = lnk[n]; 3419 while (row < i ) { 3420 nzi_bl = bi[row+1] - bi[row] + 1; 3421 bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */ 3422 ierr = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr); 3423 nzi += nlnk; 3424 row = lnk[row]; 3425 } 3426 3427 /* copy data from lnk into jtmp, then initialize lnk */ 3428 ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr); 3429 3430 /* numerical factorization */ 3431 bjtmp = jtmp; 3432 row = *bjtmp++; /* 1st pivot row */ 3433 while ( row < i ) { 3434 pc = rtmp + row; 3435 pv = ba + bdiag[row]; /* 1./(diag of the pivot row) */ 3436 multiplier = (*pc) * (*pv); 3437 *pc = multiplier; 3438 if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */ 3439 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3440 pv = ba + bdiag[row+1] + 1; 3441 /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */ 3442 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3443 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3444 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 3445 } 3446 row = *bjtmp++; 3447 } 3448 3449 /* copy sparse rtmp into contiguous vtmp; separate L and U part */ 3450 diag_tmp = rtmp[i]; /* save diagonal value - may not needed?? */ 3451 nzi_bl = 0; j = 0; 3452 while (jtmp[j] < i){ /* Note: jtmp is sorted */ 3453 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3454 nzi_bl++; j++; 3455 } 3456 nzi_bu = nzi - nzi_bl -1; 3457 while (j < nzi){ 3458 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3459 j++; 3460 } 3461 3462 bjtmp = bj + bi[i]; 3463 batmp = ba + bi[i]; 3464 /* apply level dropping rule to L part */ 3465 ncut = nzi_al + dtcount; 3466 if (ncut < nzi_bl){ 3467 ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr); 3468 ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr); 3469 } else { 3470 ncut = nzi_bl; 3471 } 3472 for (j=0; j<ncut; j++){ 3473 bjtmp[j] = jtmp[j]; 3474 batmp[j] = vtmp[j]; 3475 /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */ 3476 } 3477 bi[i+1] = bi[i] + ncut; 3478 nzi = ncut + 1; 3479 3480 /* apply level dropping rule to U part */ 3481 ncut = nzi_au + dtcount; 3482 if (ncut < nzi_bu){ 3483 ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr); 3484 ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr); 3485 } else { 3486 ncut = nzi_bu; 3487 } 3488 nzi += ncut; 3489 3490 /* mark bdiagonal */ 3491 bdiag[i+1] = bdiag[i] - (ncut + 1); 3492 bdiag_rev[n-i-1] = bdiag[i+1]; 3493 bi[2*n - i] = bi[2*n - i +1] - (ncut + 1); 3494 bjtmp = bj + bdiag[i]; 3495 batmp = ba + bdiag[i]; 3496 *bjtmp = i; 3497 *batmp = diag_tmp; /* rtmp[i]; */ 3498 if (*batmp == 0.0) { 3499 *batmp = dt+shift; 3500 /* printf(" row %d add shift %g\n",i,shift); */ 3501 } 3502 *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */ 3503 /* printf(" (%d,%g),",*bjtmp,*batmp); */ 3504 3505 bjtmp = bj + bdiag[i+1]+1; 3506 batmp = ba + bdiag[i+1]+1; 3507 for (k=0; k<ncut; k++){ 3508 bjtmp[k] = jtmp[nzi_bl+1+k]; 3509 batmp[k] = vtmp[nzi_bl+1+k]; 3510 /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */ 3511 } 3512 /* printf("\n"); */ 3513 3514 im[i] = nzi; /* used by PetscLLAddSortedLU() */ 3515 /* 3516 printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]); 3517 printf(" ----------------------------\n"); 3518 */ 3519 } /* for (i=0; i<n; i++) */ 3520 /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */ 3521 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]); 3522 3523 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3524 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3525 3526 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3527 ierr = PetscFree(im);CHKERRQ(ierr); 3528 ierr = PetscFree(rtmp);CHKERRQ(ierr); 3529 3530 ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr); 3531 b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n]; 3532 3533 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3534 ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr); 3535 both_identity = (PetscTruth) (row_identity && icol_identity); 3536 if (row_identity && icol_identity) { 3537 B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct; 3538 } else { 3539 B->ops->solve = MatSolve_SeqAIJ_newdatastruct; 3540 } 3541 3542 B->ops->lufactorsymbolic = MatILUDTFactorSymbolic_SeqAIJ; 3543 B->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ; 3544 B->ops->solveadd = 0; 3545 B->ops->solvetranspose = 0; 3546 B->ops->solvetransposeadd = 0; 3547 B->ops->matsolve = 0; 3548 B->assembled = PETSC_TRUE; 3549 B->preallocated = PETSC_TRUE; 3550 PetscFunctionReturn(0); 3551 } 3552 3553 /* a wraper of MatILUDTFactor_SeqAIJ() */ 3554 #undef __FUNCT__ 3555 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ" 3556 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info) 3557 { 3558 PetscErrorCode ierr; 3559 3560 PetscFunctionBegin; 3561 ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr); 3562 3563 fact->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ; 3564 PetscFunctionReturn(0); 3565 } 3566 3567 /* 3568 same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors 3569 - intend to replace existing MatLUFactorNumeric_SeqAIJ() 3570 */ 3571 #undef __FUNCT__ 3572 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ" 3573 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info) 3574 { 3575 Mat C=fact; 3576 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 3577 IS isrow = b->row,isicol = b->icol; 3578 PetscErrorCode ierr; 3579 const PetscInt *r,*ic,*ics; 3580 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 3581 PetscInt *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj; 3582 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 3583 PetscReal dt=info->dt,shift=info->shiftinblocks; 3584 PetscTruth row_identity, col_identity; 3585 3586 PetscFunctionBegin; 3587 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3588 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3589 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 3590 ics = ic; 3591 3592 for (i=0; i<n; i++){ 3593 /* initialize rtmp array */ 3594 nzl = bi[i+1] - bi[i]; /* num of nozeros in L(i,:) */ 3595 bjtmp = bj + bi[i]; 3596 for (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0; 3597 rtmp[i] = 0.0; 3598 nzu = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */ 3599 bjtmp = bj + bdiag[i+1] + 1; 3600 for (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0; 3601 3602 /* load in initial unfactored row of A */ 3603 /* printf("row %d\n",i); */ 3604 nz = ai[r[i]+1] - ai[r[i]]; 3605 ajtmp = aj + ai[r[i]]; 3606 v = aa + ai[r[i]]; 3607 for (j=0; j<nz; j++) { 3608 rtmp[ics[*ajtmp++]] = v[j]; 3609 /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */ 3610 } 3611 /* printf("\n"); */ 3612 3613 /* numerical factorization */ 3614 bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */ 3615 nzl = bi[i+1] - bi[i]; /* num of entries in L(i,:) */ 3616 k = 0; 3617 while (k < nzl){ 3618 row = *bjtmp++; 3619 /* printf(" prow %d\n",row); */ 3620 pc = rtmp + row; 3621 pv = b->a + bdiag[row]; /* 1./(diag of the pivot row) */ 3622 multiplier = (*pc) * (*pv); 3623 *pc = multiplier; 3624 if (PetscAbsScalar(multiplier) > dt){ 3625 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3626 pv = b->a + bdiag[row+1] + 1; 3627 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3628 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3629 /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */ 3630 } 3631 k++; 3632 } 3633 3634 /* finished row so stick it into b->a */ 3635 /* L-part */ 3636 pv = b->a + bi[i] ; 3637 pj = bj + bi[i] ; 3638 nzl = bi[i+1] - bi[i]; 3639 for (j=0; j<nzl; j++) { 3640 pv[j] = rtmp[pj[j]]; 3641 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3642 } 3643 3644 /* diagonal: invert diagonal entries for simplier triangular solves */ 3645 if (rtmp[i] == 0.0) rtmp[i] = dt+shift; 3646 b->a[bdiag[i]] = 1.0/rtmp[i]; 3647 /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */ 3648 3649 /* U-part */ 3650 pv = b->a + bdiag[i+1] + 1; 3651 pj = bj + bdiag[i+1] + 1; 3652 nzu = bdiag[i] - bdiag[i+1] - 1; 3653 for (j=0; j<nzu; j++) { 3654 pv[j] = rtmp[pj[j]]; 3655 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3656 } 3657 /* printf("\n"); */ 3658 } 3659 3660 ierr = PetscFree(rtmp);CHKERRQ(ierr); 3661 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3662 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3663 3664 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3665 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 3666 if (row_identity && col_identity) { 3667 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct; 3668 } else { 3669 C->ops->solve = MatSolve_SeqAIJ_newdatastruct; 3670 } 3671 C->ops->solveadd = 0; 3672 C->ops->solvetranspose = 0; 3673 C->ops->solvetransposeadd = 0; 3674 C->ops->matsolve = 0; 3675 C->assembled = PETSC_TRUE; 3676 C->preallocated = PETSC_TRUE; 3677 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 3678 PetscFunctionReturn(0); 3679 } 3680