1 #define PETSCMAT_DLL 2 3 4 #include "../src/mat/impls/aij/seq/aij.h" 5 #include "../src/mat/impls/sbaij/seq/sbaij.h" 6 #include "petscbt.h" 7 #include "../src/mat/utils/freespace.h" 8 9 EXTERN_C_BEGIN 10 #undef __FUNCT__ 11 #define __FUNCT__ "MatOrdering_Flow_SeqAIJ" 12 /* 13 Computes an ordering to get most of the large numerical values in the lower triangular part of the matrix 14 */ 15 PetscErrorCode MatOrdering_Flow_SeqAIJ(Mat mat,const MatOrderingType type,IS *irow,IS *icol) 16 { 17 Mat_SeqAIJ *a = (Mat_SeqAIJ*)mat->data; 18 PetscErrorCode ierr; 19 PetscInt i,j,jj,k, kk,n = mat->rmap->n, current = 0, newcurrent = 0,*order; 20 const PetscInt *ai = a->i, *aj = a->j; 21 const PetscScalar *aa = a->a; 22 PetscTruth *done; 23 PetscReal best,past = 0,future; 24 25 PetscFunctionBegin; 26 /* pick initial row */ 27 best = -1; 28 for (i=0; i<n; i++) { 29 future = 0.0; 30 for (j=ai[i]; j<ai[i+1]; j++) { 31 if (aj[j] != i) future += PetscAbsScalar(aa[j]); else past = PetscAbsScalar(aa[j]); 32 } 33 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 34 if (past/future > best) { 35 best = past/future; 36 current = i; 37 } 38 } 39 40 ierr = PetscMalloc(n*sizeof(PetscTruth),&done);CHKERRQ(ierr); 41 ierr = PetscMemzero(done,n*sizeof(PetscTruth));CHKERRQ(ierr); 42 ierr = PetscMalloc(n*sizeof(PetscInt),&order);CHKERRQ(ierr); 43 order[0] = current; 44 for (i=0; i<n-1; i++) { 45 done[current] = PETSC_TRUE; 46 best = -1; 47 /* loop over all neighbors of current pivot */ 48 for (j=ai[current]; j<ai[current+1]; j++) { 49 jj = aj[j]; 50 if (done[jj]) continue; 51 /* loop over columns of potential next row computing weights for below and above diagonal */ 52 past = future = 0.0; 53 for (k=ai[jj]; k<ai[jj+1]; k++) { 54 kk = aj[k]; 55 if (done[kk]) past += PetscAbsScalar(aa[k]); 56 else if (kk != jj) future += PetscAbsScalar(aa[k]); 57 } 58 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 59 if (past/future > best) { 60 best = past/future; 61 newcurrent = jj; 62 } 63 } 64 if (best == -1) { /* no neighbors to select from so select best of all that remain */ 65 best = -1; 66 for (k=0; k<n; k++) { 67 if (done[k]) continue; 68 future = 0.0; 69 past = 0.0; 70 for (j=ai[k]; j<ai[k+1]; j++) { 71 kk = aj[j]; 72 if (done[kk]) past += PetscAbsScalar(aa[j]); 73 else if (kk != k) future += PetscAbsScalar(aa[j]); 74 } 75 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 76 if (past/future > best) { 77 best = past/future; 78 newcurrent = k; 79 } 80 } 81 } 82 if (current == newcurrent) SETERRQ(PETSC_ERR_PLIB,"newcurrent cannot be current"); 83 current = newcurrent; 84 order[i+1] = current; 85 } 86 ierr = ISCreateGeneral(PETSC_COMM_SELF,n,order,irow);CHKERRQ(ierr); 87 *icol = *irow; 88 ierr = PetscObjectReference((PetscObject)*irow);CHKERRQ(ierr); 89 ierr = PetscFree(done);CHKERRQ(ierr); 90 ierr = PetscFree(order);CHKERRQ(ierr); 91 PetscFunctionReturn(0); 92 } 93 EXTERN_C_END 94 95 EXTERN_C_BEGIN 96 #undef __FUNCT__ 97 #define __FUNCT__ "MatGetFactorAvailable_seqaij_petsc" 98 PetscErrorCode MatGetFactorAvailable_seqaij_petsc(Mat A,MatFactorType ftype,PetscTruth *flg) 99 { 100 PetscFunctionBegin; 101 *flg = PETSC_TRUE; 102 PetscFunctionReturn(0); 103 } 104 EXTERN_C_END 105 106 EXTERN_C_BEGIN 107 #undef __FUNCT__ 108 #define __FUNCT__ "MatGetFactor_seqaij_petsc" 109 PetscErrorCode MatGetFactor_seqaij_petsc(Mat A,MatFactorType ftype,Mat *B) 110 { 111 PetscInt n = A->rmap->n; 112 PetscErrorCode ierr; 113 114 PetscFunctionBegin; 115 ierr = MatCreate(((PetscObject)A)->comm,B);CHKERRQ(ierr); 116 ierr = MatSetSizes(*B,n,n,n,n);CHKERRQ(ierr); 117 if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT){ 118 ierr = MatSetType(*B,MATSEQAIJ);CHKERRQ(ierr); 119 (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJ; 120 (*B)->ops->lufactorsymbolic = MatLUFactorSymbolic_SeqAIJ; 121 (*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 EXTERN PetscErrorCode Mat_CheckInode(Mat,PetscTruth); 134 #undef __FUNCT__ 135 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ" 136 PetscErrorCode MatLUFactorSymbolic_SeqAIJ(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 137 { 138 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 139 IS isicol; 140 PetscErrorCode ierr; 141 const PetscInt *r,*ic; 142 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j; 143 PetscInt *bi,*bj,*ajtmp; 144 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 145 PetscReal f; 146 PetscInt nlnk,*lnk,k,**bi_ptr; 147 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 148 PetscBT lnkbt; 149 PetscTruth newdatastruct= PETSC_FALSE; 150 151 PetscFunctionBegin; 152 ierr = PetscOptionsGetTruth(PETSC_NULL,"-lu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 153 if(newdatastruct){ 154 ierr = MatLUFactorSymbolic_SeqAIJ_newdatastruct(B,A,isrow,iscol,info);CHKERRQ(ierr); 155 PetscFunctionReturn(0); 156 } 157 158 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square"); 159 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 160 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 161 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 162 163 /* get new row pointers */ 164 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 165 bi[0] = 0; 166 167 /* bdiag is location of diagonal in factor */ 168 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 169 bdiag[0] = 0; 170 171 /* linked list for storing column indices of the active row */ 172 nlnk = n + 1; 173 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 174 175 ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr); 176 177 /* initial FreeSpace size is f*(ai[n]+1) */ 178 f = info->fill; 179 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 180 current_space = free_space; 181 182 for (i=0; i<n; i++) { 183 /* copy previous fill into linked list */ 184 nzi = 0; 185 nnz = ai[r[i]+1] - ai[r[i]]; 186 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 187 ajtmp = aj + ai[r[i]]; 188 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 189 nzi += nlnk; 190 191 /* add pivot rows into linked list */ 192 row = lnk[n]; 193 while (row < i) { 194 nzbd = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */ 195 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 196 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 197 nzi += nlnk; 198 row = lnk[row]; 199 } 200 bi[i+1] = bi[i] + nzi; 201 im[i] = nzi; 202 203 /* mark bdiag */ 204 nzbd = 0; 205 nnz = nzi; 206 k = lnk[n]; 207 while (nnz-- && k < i){ 208 nzbd++; 209 k = lnk[k]; 210 } 211 bdiag[i] = bi[i] + nzbd; 212 213 /* if free space is not available, make more free space */ 214 if (current_space->local_remaining<nzi) { 215 nnz = (n - i)*nzi; /* estimated and max additional space needed */ 216 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 217 reallocs++; 218 } 219 220 /* copy data into free space, then initialize lnk */ 221 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 222 bi_ptr[i] = current_space->array; 223 current_space->array += nzi; 224 current_space->local_used += nzi; 225 current_space->local_remaining -= nzi; 226 } 227 #if defined(PETSC_USE_INFO) 228 if (ai[n] != 0) { 229 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 230 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 231 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 232 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr); 233 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 234 } else { 235 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 236 } 237 #endif 238 239 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 240 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 241 242 /* destroy list of free space and other temporary array(s) */ 243 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 244 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); 245 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 246 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 247 248 /* put together the new matrix */ 249 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 250 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 251 b = (Mat_SeqAIJ*)(B)->data; 252 b->free_a = PETSC_TRUE; 253 b->free_ij = PETSC_TRUE; 254 b->singlemalloc = PETSC_FALSE; 255 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 256 b->j = bj; 257 b->i = bi; 258 b->diag = bdiag; 259 b->ilen = 0; 260 b->imax = 0; 261 b->row = isrow; 262 b->col = iscol; 263 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 264 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 265 b->icol = isicol; 266 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 267 268 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 269 ierr = PetscLogObjectMemory(B,(bi[n]-n)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 270 b->maxnz = b->nz = bi[n] ; 271 272 (B)->factor = MAT_FACTOR_LU; 273 (B)->info.factor_mallocs = reallocs; 274 (B)->info.fill_ratio_given = f; 275 276 if (ai[n]) { 277 (B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 278 } else { 279 (B)->info.fill_ratio_needed = 0.0; 280 } 281 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 282 (B)->ops->solve = MatSolve_SeqAIJ; 283 (B)->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 284 /* switch to inodes if appropriate */ 285 ierr = MatLUFactorSymbolic_SeqAIJ_Inode(B,A,isrow,iscol,info);CHKERRQ(ierr); 286 PetscFunctionReturn(0); 287 } 288 289 #undef __FUNCT__ 290 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ_newdatastruct" 291 PetscErrorCode MatLUFactorSymbolic_SeqAIJ_newdatastruct(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 292 { 293 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 294 IS isicol; 295 PetscErrorCode ierr; 296 const PetscInt *r,*ic; 297 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j; 298 PetscInt *bi,*bj,*ajtmp; 299 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 300 PetscReal f; 301 PetscInt nlnk,*lnk,k,**bi_ptr; 302 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 303 PetscBT lnkbt; 304 305 PetscFunctionBegin; 306 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square"); 307 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 308 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 309 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 310 311 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 312 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 313 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 314 bi[0] = bdiag[0] = 0; 315 316 /* linked list for storing column indices of the active row */ 317 nlnk = n + 1; 318 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 319 320 ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr); 321 322 /* initial FreeSpace size is f*(ai[n]+1) */ 323 f = info->fill; 324 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 325 current_space = free_space; 326 327 for (i=0; i<n; i++) { 328 /* copy previous fill into linked list */ 329 nzi = 0; 330 nnz = ai[r[i]+1] - ai[r[i]]; 331 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 332 ajtmp = aj + ai[r[i]]; 333 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 334 nzi += nlnk; 335 336 /* add pivot rows into linked list */ 337 row = lnk[n]; 338 while (row < i){ 339 nzbd = bdiag[row] + 1; /* num of entries in the row with column index <= row */ 340 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 341 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 342 nzi += nlnk; 343 row = lnk[row]; 344 } 345 bi[i+1] = bi[i] + nzi; 346 im[i] = nzi; 347 348 /* mark bdiag */ 349 nzbd = 0; 350 nnz = nzi; 351 k = lnk[n]; 352 while (nnz-- && k < i){ 353 nzbd++; 354 k = lnk[k]; 355 } 356 bdiag[i] = nzbd; /* note: bdiag[i] = nnzL as input for PetscFreeSpaceContiguous_LU() */ 357 358 /* if free space is not available, make more free space */ 359 if (current_space->local_remaining<nzi) { 360 nnz = 2*(n - i)*nzi; /* estimated and max additional space needed */ 361 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 362 reallocs++; 363 } 364 365 /* copy data into free space, then initialize lnk */ 366 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 367 bi_ptr[i] = current_space->array; 368 current_space->array += nzi; 369 current_space->local_used += nzi; 370 current_space->local_remaining -= nzi; 371 } 372 #if defined(PETSC_USE_INFO) 373 if (ai[n] != 0) { 374 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 375 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 376 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 377 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr); 378 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 379 } else { 380 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 381 } 382 #endif 383 384 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 385 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 386 387 /* destroy list of free space and other temporary array(s) */ 388 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 389 ierr = PetscFreeSpaceContiguous_LU_v2(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 390 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 391 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 392 393 /* put together the new matrix */ 394 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 395 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 396 b = (Mat_SeqAIJ*)(B)->data; 397 b->free_a = PETSC_TRUE; 398 b->free_ij = PETSC_TRUE; 399 b->singlemalloc = PETSC_FALSE; 400 ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 401 b->j = bj; 402 b->i = bi; 403 b->diag = bdiag; 404 b->ilen = 0; 405 b->imax = 0; 406 b->row = isrow; 407 b->col = iscol; 408 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 409 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 410 b->icol = isicol; 411 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 412 413 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 414 ierr = PetscLogObjectMemory(B,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 415 b->maxnz = b->nz = bdiag[0]+1; 416 (B)->factor = MAT_FACTOR_LU; 417 (B)->info.factor_mallocs = reallocs; 418 (B)->info.fill_ratio_given = f; 419 420 if (ai[n]) { 421 (B)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 422 } else { 423 (B)->info.fill_ratio_needed = 0.0; 424 } 425 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 426 /* switch to inodes if appropriate */ 427 ierr = Mat_CheckInode(B,PETSC_FALSE);CHKERRQ(ierr); /* Mat_CheckInode_FactorLU(B,PETSC_FALSE) ??? */ 428 PetscFunctionReturn(0); 429 } 430 431 /* 432 Trouble in factorization, should we dump the original matrix? 433 */ 434 #undef __FUNCT__ 435 #define __FUNCT__ "MatFactorDumpMatrix" 436 PetscErrorCode MatFactorDumpMatrix(Mat A) 437 { 438 PetscErrorCode ierr; 439 PetscTruth flg = PETSC_FALSE; 440 441 PetscFunctionBegin; 442 ierr = PetscOptionsGetTruth(PETSC_NULL,"-mat_factor_dump_on_error",&flg,PETSC_NULL);CHKERRQ(ierr); 443 if (flg) { 444 PetscViewer viewer; 445 char filename[PETSC_MAX_PATH_LEN]; 446 447 ierr = PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);CHKERRQ(ierr); 448 ierr = PetscViewerBinaryOpen(((PetscObject)A)->comm,filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr); 449 ierr = MatView(A,viewer);CHKERRQ(ierr); 450 ierr = PetscViewerDestroy(viewer);CHKERRQ(ierr); 451 } 452 PetscFunctionReturn(0); 453 } 454 455 extern PetscErrorCode MatSolve_SeqAIJ_Inode(Mat,Vec,Vec); 456 457 #undef __FUNCT__ 458 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_newdatastruct" 459 PetscErrorCode MatLUFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info) 460 { 461 Mat C=B; 462 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 463 IS isrow = b->row,isicol = b->icol; 464 PetscErrorCode ierr; 465 const PetscInt *r,*ic,*ics; 466 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 467 PetscInt *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj; 468 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 469 PetscTruth row_identity,col_identity; 470 471 LUShift_Ctx sctx; 472 PetscInt *ddiag,newshift; 473 PetscReal rs; 474 MatScalar d; 475 476 PetscFunctionBegin; 477 /* MatPivotSetUp(): initialize shift context sctx */ 478 ierr = PetscMemzero(&sctx,sizeof(LUShift_Ctx));CHKERRQ(ierr); 479 480 /* if both shift schemes are chosen by user, only use info->shiftpd */ 481 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 482 ddiag = a->diag; 483 sctx.shift_top = info->zeropivot; 484 for (i=0; i<n; i++) { 485 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 486 d = (aa)[ddiag[i]]; 487 rs = -PetscAbsScalar(d) - PetscRealPart(d); 488 v = aa+ai[i]; 489 nz = ai[i+1] - ai[i]; 490 for (j=0; j<nz; j++) 491 rs += PetscAbsScalar(v[j]); 492 if (rs>sctx.shift_top) sctx.shift_top = rs; 493 } 494 sctx.shift_top *= 1.1; 495 sctx.nshift_max = 5; 496 sctx.shift_lo = 0.; 497 sctx.shift_hi = 1.; 498 } 499 500 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 501 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 502 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 503 ics = ic; 504 505 do { 506 sctx.lushift = PETSC_FALSE; 507 for (i=0; i<n; i++){ 508 /* zero rtmp */ 509 /* L part */ 510 nz = bi[i+1] - bi[i]; 511 bjtmp = bj + bi[i]; 512 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 513 514 /* U part */ 515 nz = bdiag[i]-bdiag[i+1]; 516 bjtmp = bj + bdiag[i+1]+1; 517 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 518 519 /* load in initial (unfactored row) */ 520 nz = ai[r[i]+1] - ai[r[i]]; 521 ajtmp = aj + ai[r[i]]; 522 v = aa + ai[r[i]]; 523 for (j=0; j<nz; j++) { 524 rtmp[ics[ajtmp[j]]] = v[j]; 525 } 526 /* ZeropivotApply() */ 527 rtmp[i] += sctx.shift_amount; /* shift the diagonal of the matrix */ 528 529 /* elimination */ 530 bjtmp = bj + bi[i]; 531 row = *bjtmp++; 532 nzL = bi[i+1] - bi[i]; 533 for(k=0; k < nzL;k++) { 534 pc = rtmp + row; 535 if (*pc != 0.0) { 536 pv = b->a + bdiag[row]; 537 multiplier = *pc * (*pv); 538 *pc = multiplier; 539 pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */ 540 pv = b->a + bdiag[row+1]+1; 541 nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */ 542 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 543 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 544 } 545 row = *bjtmp++; 546 } 547 548 /* finished row so stick it into b->a */ 549 rs = 0.0; 550 /* L part */ 551 pv = b->a + bi[i] ; 552 pj = b->j + bi[i] ; 553 nz = bi[i+1] - bi[i]; 554 for (j=0; j<nz; j++) { 555 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 556 } 557 558 /* U part */ 559 pv = b->a + bdiag[i+1]+1; 560 pj = b->j + bdiag[i+1]+1; 561 nz = bdiag[i] - bdiag[i+1]-1; 562 for (j=0; j<nz; j++) { 563 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 564 } 565 566 /* MatPivotCheck() */ 567 sctx.rs = rs; 568 sctx.pv = rtmp[i]; 569 /* ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); */ 570 if (info->shiftnz){ 571 ierr = MatPivotCheck_nz(info,sctx,i,newshift);CHKERRQ(ierr); 572 } else if (info->shiftpd){ 573 ierr = MatPivotCheck_pd(info,sctx,i,newshift);CHKERRQ(ierr); 574 } else if (info->shiftinblocks){ 575 ierr = MatPivotCheck_inblocks(info,sctx,i,newshift);CHKERRQ(ierr); 576 } else { 577 ierr = MatPivotCheck_none(info,sctx,i,newshift);CHKERRQ(ierr); 578 } 579 rtmp[i] = sctx.pv; 580 if (newshift == 1) break; 581 582 /* Mark diagonal and invert diagonal for simplier triangular solves */ 583 pv = b->a + bdiag[i]; 584 *pv = 1.0/rtmp[i]; 585 586 } /* endof for (i=0; i<n; i++){ */ 587 588 /* MatPivotRefine() */ 589 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max){ 590 /* 591 * if no shift in this attempt & shifting & started shifting & can refine, 592 * then try lower shift 593 */ 594 sctx.shift_hi = sctx.shift_fraction; 595 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 596 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 597 sctx.lushift = PETSC_TRUE; 598 sctx.nshift++; 599 } 600 } while (sctx.lushift); 601 602 ierr = PetscFree(rtmp);CHKERRQ(ierr); 603 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 604 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 605 if (b->inode.use){ 606 SETERRQ(1,"MatSolve_SeqAIJ_Inode_newdatastruct not done yet"); 607 /* C->ops->solve = MatSolve_SeqAIJ_Inode_newdatastruct; not done yet! */ 608 } else { 609 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 610 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 611 if (row_identity && col_identity) { 612 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct; 613 } else { 614 C->ops->solve = MatSolve_SeqAIJ_newdatastruct; 615 } 616 } 617 C->ops->solveadd = MatSolveAdd_SeqAIJ_newdatastruct; 618 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ_newdatastruct; 619 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_newdatastruct; 620 C->ops->matsolve = MatMatSolve_SeqAIJ_newdatastruct; 621 C->assembled = PETSC_TRUE; 622 C->preallocated = PETSC_TRUE; 623 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 624 625 /* MatPivotView() */ 626 if (sctx.nshift){ 627 if (info->shiftpd) { 628 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); 629 } else if (info->shiftnz) { 630 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 631 } else if (info->shiftinblocks){ 632 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftinblocks);CHKERRQ(ierr); 633 } 634 } 635 PetscFunctionReturn(0); 636 } 637 638 #undef __FUNCT__ 639 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ" 640 PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 641 { 642 Mat C=B; 643 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 644 IS isrow = b->row,isicol = b->icol; 645 PetscErrorCode ierr; 646 const PetscInt *r,*ic,*ics; 647 PetscInt nz,row,i,j,n=A->rmap->n,diag; 648 const PetscInt *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 649 const PetscInt *ajtmp,*bjtmp,*diag_offset = b->diag,*pj; 650 MatScalar *pv,*rtmp,*pc,multiplier,d; 651 const MatScalar *v,*aa=a->a; 652 PetscReal rs=0.0; 653 LUShift_Ctx sctx; 654 PetscInt newshift,*ddiag; 655 656 PetscFunctionBegin; 657 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 658 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 659 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 660 ics = ic; 661 662 /* initialize shift context sctx */ 663 sctx.nshift = 0; 664 sctx.nshift_max = 0; 665 sctx.shift_top = 0.0; 666 sctx.shift_lo = 0.0; 667 sctx.shift_hi = 0.0; 668 sctx.shift_fraction = 0.0; 669 sctx.shift_amount = 0.0; 670 671 /* if both shift schemes are chosen by user, only use info->shiftpd */ 672 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 673 ddiag = a->diag; 674 sctx.shift_top = info->zeropivot; 675 for (i=0; i<n; i++) { 676 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 677 d = (aa)[ddiag[i]]; 678 rs = -PetscAbsScalar(d) - PetscRealPart(d); 679 v = aa+ai[i]; 680 nz = ai[i+1] - ai[i]; 681 for (j=0; j<nz; j++) 682 rs += PetscAbsScalar(v[j]); 683 if (rs>sctx.shift_top) sctx.shift_top = rs; 684 } 685 sctx.shift_top *= 1.1; 686 sctx.nshift_max = 5; 687 sctx.shift_lo = 0.; 688 sctx.shift_hi = 1.; 689 } 690 691 do { 692 sctx.lushift = PETSC_FALSE; 693 for (i=0; i<n; i++){ 694 nz = bi[i+1] - bi[i]; 695 bjtmp = bj + bi[i]; 696 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 697 698 /* load in initial (unfactored row) */ 699 nz = ai[r[i]+1] - ai[r[i]]; 700 ajtmp = aj + ai[r[i]]; 701 v = aa + ai[r[i]]; 702 for (j=0; j<nz; j++) { 703 rtmp[ics[ajtmp[j]]] = v[j]; 704 } 705 rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 706 /* if (sctx.shift_amount > 0.0) printf("row %d, shift %g\n",i,sctx.shift_amount); */ 707 708 row = *bjtmp++; 709 while (row < i) { 710 pc = rtmp + row; 711 if (*pc != 0.0) { 712 pv = b->a + diag_offset[row]; 713 pj = b->j + diag_offset[row] + 1; 714 multiplier = *pc / *pv++; 715 *pc = multiplier; 716 nz = bi[row+1] - diag_offset[row] - 1; 717 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 718 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 719 } 720 row = *bjtmp++; 721 } 722 /* finished row so stick it into b->a */ 723 pv = b->a + bi[i] ; 724 pj = b->j + bi[i] ; 725 nz = bi[i+1] - bi[i]; 726 diag = diag_offset[i] - bi[i]; 727 rs = 0.0; 728 for (j=0; j<nz; j++) { 729 pv[j] = rtmp[pj[j]]; 730 rs += PetscAbsScalar(pv[j]); 731 } 732 rs -= PetscAbsScalar(pv[diag]); 733 734 /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */ 735 sctx.rs = rs; 736 sctx.pv = pv[diag]; 737 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 738 if (newshift == 1) break; 739 } 740 741 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 742 /* 743 * if no shift in this attempt & shifting & started shifting & can refine, 744 * then try lower shift 745 */ 746 sctx.shift_hi = sctx.shift_fraction; 747 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 748 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 749 sctx.lushift = PETSC_TRUE; 750 sctx.nshift++; 751 } 752 } while (sctx.lushift); 753 754 /* invert diagonal entries for simplier triangular solves */ 755 for (i=0; i<n; i++) { 756 b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]]; 757 } 758 ierr = PetscFree(rtmp);CHKERRQ(ierr); 759 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 760 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 761 if (b->inode.use) { 762 C->ops->solve = MatSolve_SeqAIJ_Inode; 763 } else { 764 PetscTruth row_identity, col_identity; 765 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 766 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 767 if (row_identity && col_identity) { 768 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 769 } else { 770 C->ops->solve = MatSolve_SeqAIJ; 771 } 772 } 773 C->ops->solveadd = MatSolveAdd_SeqAIJ; 774 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 775 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 776 C->ops->matsolve = MatMatSolve_SeqAIJ; 777 C->assembled = PETSC_TRUE; 778 C->preallocated = PETSC_TRUE; 779 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 780 if (sctx.nshift){ 781 if (info->shiftpd) { 782 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); 783 } else if (info->shiftnz) { 784 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 785 } 786 } 787 PetscFunctionReturn(0); 788 } 789 790 /* 791 This routine implements inplace ILU(0) with row or/and column permutations. 792 Input: 793 A - original matrix 794 Output; 795 A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i] 796 a->j (col index) is permuted by the inverse of colperm, then sorted 797 a->a reordered accordingly with a->j 798 a->diag (ptr to diagonal elements) is updated. 799 */ 800 #undef __FUNCT__ 801 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_InplaceWithPerm" 802 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info) 803 { 804 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 805 IS isrow = a->row,isicol = a->icol; 806 PetscErrorCode ierr; 807 const PetscInt *r,*ic,*ics; 808 PetscInt i,j,n=A->rmap->n,*ai=a->i,*aj=a->j; 809 PetscInt *ajtmp,nz,row; 810 PetscInt *diag = a->diag,nbdiag,*pj; 811 PetscScalar *rtmp,*pc,multiplier,d; 812 MatScalar *v,*pv; 813 PetscReal rs; 814 LUShift_Ctx sctx; 815 PetscInt newshift; 816 817 PetscFunctionBegin; 818 if (A != B) SETERRQ(PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address"); 819 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 820 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 821 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&rtmp);CHKERRQ(ierr); 822 ierr = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr); 823 ics = ic; 824 825 sctx.shift_top = 0.; 826 sctx.nshift_max = 0; 827 sctx.shift_lo = 0.; 828 sctx.shift_hi = 0.; 829 sctx.shift_fraction = 0.; 830 831 /* if both shift schemes are chosen by user, only use info->shiftpd */ 832 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 833 sctx.shift_top = 0.; 834 for (i=0; i<n; i++) { 835 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 836 d = (a->a)[diag[i]]; 837 rs = -PetscAbsScalar(d) - PetscRealPart(d); 838 v = a->a+ai[i]; 839 nz = ai[i+1] - ai[i]; 840 for (j=0; j<nz; j++) 841 rs += PetscAbsScalar(v[j]); 842 if (rs>sctx.shift_top) sctx.shift_top = rs; 843 } 844 if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot; 845 sctx.shift_top *= 1.1; 846 sctx.nshift_max = 5; 847 sctx.shift_lo = 0.; 848 sctx.shift_hi = 1.; 849 } 850 851 sctx.shift_amount = 0.; 852 sctx.nshift = 0; 853 do { 854 sctx.lushift = PETSC_FALSE; 855 for (i=0; i<n; i++){ 856 /* load in initial unfactored row */ 857 nz = ai[r[i]+1] - ai[r[i]]; 858 ajtmp = aj + ai[r[i]]; 859 v = a->a + ai[r[i]]; 860 /* sort permuted ajtmp and values v accordingly */ 861 for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]]; 862 ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr); 863 864 diag[r[i]] = ai[r[i]]; 865 for (j=0; j<nz; j++) { 866 rtmp[ajtmp[j]] = v[j]; 867 if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */ 868 } 869 rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 870 871 row = *ajtmp++; 872 while (row < i) { 873 pc = rtmp + row; 874 if (*pc != 0.0) { 875 pv = a->a + diag[r[row]]; 876 pj = aj + diag[r[row]] + 1; 877 878 multiplier = *pc / *pv++; 879 *pc = multiplier; 880 nz = ai[r[row]+1] - diag[r[row]] - 1; 881 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 882 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 883 } 884 row = *ajtmp++; 885 } 886 /* finished row so overwrite it onto a->a */ 887 pv = a->a + ai[r[i]] ; 888 pj = aj + ai[r[i]] ; 889 nz = ai[r[i]+1] - ai[r[i]]; 890 nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */ 891 892 rs = 0.0; 893 for (j=0; j<nz; j++) { 894 pv[j] = rtmp[pj[j]]; 895 if (j != nbdiag) rs += PetscAbsScalar(pv[j]); 896 } 897 898 /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */ 899 sctx.rs = rs; 900 sctx.pv = pv[nbdiag]; 901 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 902 if (newshift == 1) break; 903 } 904 905 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 906 /* 907 * if no shift in this attempt & shifting & started shifting & can refine, 908 * then try lower shift 909 */ 910 sctx.shift_hi = sctx.shift_fraction; 911 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 912 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 913 sctx.lushift = PETSC_TRUE; 914 sctx.nshift++; 915 } 916 } while (sctx.lushift); 917 918 /* invert diagonal entries for simplier triangular solves */ 919 for (i=0; i<n; i++) { 920 a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]]; 921 } 922 923 ierr = PetscFree(rtmp);CHKERRQ(ierr); 924 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 925 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 926 A->ops->solve = MatSolve_SeqAIJ_InplaceWithPerm; 927 A->ops->solveadd = MatSolveAdd_SeqAIJ; 928 A->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 929 A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 930 A->assembled = PETSC_TRUE; 931 A->preallocated = PETSC_TRUE; 932 ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr); 933 if (sctx.nshift){ 934 if (info->shiftpd) { 935 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); 936 } else if (info->shiftnz) { 937 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 938 } 939 } 940 PetscFunctionReturn(0); 941 } 942 943 /* ----------------------------------------------------------- */ 944 #undef __FUNCT__ 945 #define __FUNCT__ "MatLUFactor_SeqAIJ" 946 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info) 947 { 948 PetscErrorCode ierr; 949 Mat C; 950 951 PetscFunctionBegin; 952 ierr = MatGetFactor(A,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr); 953 ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr); 954 ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr); 955 A->ops->solve = C->ops->solve; 956 A->ops->solvetranspose = C->ops->solvetranspose; 957 ierr = MatHeaderCopy(A,C);CHKERRQ(ierr); 958 ierr = PetscLogObjectParent(A,((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr); 959 PetscFunctionReturn(0); 960 } 961 /* ----------------------------------------------------------- */ 962 963 964 #undef __FUNCT__ 965 #define __FUNCT__ "MatSolve_SeqAIJ" 966 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx) 967 { 968 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 969 IS iscol = a->col,isrow = a->row; 970 PetscErrorCode ierr; 971 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 972 PetscInt nz; 973 const PetscInt *rout,*cout,*r,*c; 974 PetscScalar *x,*tmp,*tmps,sum; 975 const PetscScalar *b; 976 const MatScalar *aa = a->a,*v; 977 978 PetscFunctionBegin; 979 if (!n) PetscFunctionReturn(0); 980 981 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 982 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 983 tmp = a->solve_work; 984 985 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 986 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 987 988 /* forward solve the lower triangular */ 989 tmp[0] = b[*r++]; 990 tmps = tmp; 991 for (i=1; i<n; i++) { 992 v = aa + ai[i] ; 993 vi = aj + ai[i] ; 994 nz = a->diag[i] - ai[i]; 995 sum = b[*r++]; 996 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 997 tmp[i] = sum; 998 } 999 1000 /* backward solve the upper triangular */ 1001 for (i=n-1; i>=0; i--){ 1002 v = aa + a->diag[i] + 1; 1003 vi = aj + a->diag[i] + 1; 1004 nz = ai[i+1] - a->diag[i] - 1; 1005 sum = tmp[i]; 1006 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1007 x[*c--] = tmp[i] = sum*aa[a->diag[i]]; 1008 } 1009 1010 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1011 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1012 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1013 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1014 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1015 PetscFunctionReturn(0); 1016 } 1017 1018 #undef __FUNCT__ 1019 #define __FUNCT__ "MatMatSolve_SeqAIJ" 1020 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X) 1021 { 1022 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1023 IS iscol = a->col,isrow = a->row; 1024 PetscErrorCode ierr; 1025 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1026 PetscInt nz,neq; 1027 const PetscInt *rout,*cout,*r,*c; 1028 PetscScalar *x,*b,*tmp,*tmps,sum; 1029 const MatScalar *aa = a->a,*v; 1030 PetscTruth bisdense,xisdense; 1031 1032 PetscFunctionBegin; 1033 if (!n) PetscFunctionReturn(0); 1034 1035 ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr); 1036 if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 1037 ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr); 1038 if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 1039 1040 ierr = MatGetArray(B,&b);CHKERRQ(ierr); 1041 ierr = MatGetArray(X,&x);CHKERRQ(ierr); 1042 1043 tmp = a->solve_work; 1044 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1045 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1046 1047 for (neq=0; neq<B->cmap->n; neq++){ 1048 /* forward solve the lower triangular */ 1049 tmp[0] = b[r[0]]; 1050 tmps = tmp; 1051 for (i=1; i<n; i++) { 1052 v = aa + ai[i] ; 1053 vi = aj + ai[i] ; 1054 nz = a->diag[i] - ai[i]; 1055 sum = b[r[i]]; 1056 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1057 tmp[i] = sum; 1058 } 1059 /* backward solve the upper triangular */ 1060 for (i=n-1; i>=0; i--){ 1061 v = aa + a->diag[i] + 1; 1062 vi = aj + a->diag[i] + 1; 1063 nz = ai[i+1] - a->diag[i] - 1; 1064 sum = tmp[i]; 1065 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1066 x[c[i]] = tmp[i] = sum*aa[a->diag[i]]; 1067 } 1068 1069 b += n; 1070 x += n; 1071 } 1072 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1073 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1074 ierr = MatRestoreArray(B,&b);CHKERRQ(ierr); 1075 ierr = MatRestoreArray(X,&x);CHKERRQ(ierr); 1076 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 1077 PetscFunctionReturn(0); 1078 } 1079 1080 #undef __FUNCT__ 1081 #define __FUNCT__ "MatMatSolve_SeqAIJ_newdatastruct" 1082 PetscErrorCode MatMatSolve_SeqAIJ_newdatastruct(Mat A,Mat B,Mat X) 1083 { 1084 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1085 IS iscol = a->col,isrow = a->row; 1086 PetscErrorCode ierr; 1087 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag; 1088 PetscInt nz,neq; 1089 const PetscInt *rout,*cout,*r,*c; 1090 PetscScalar *x,*b,*tmp,sum; 1091 const MatScalar *aa = a->a,*v; 1092 PetscTruth bisdense,xisdense; 1093 1094 PetscFunctionBegin; 1095 if (!n) PetscFunctionReturn(0); 1096 1097 ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr); 1098 if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 1099 ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr); 1100 if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 1101 1102 ierr = MatGetArray(B,&b);CHKERRQ(ierr); 1103 ierr = MatGetArray(X,&x);CHKERRQ(ierr); 1104 1105 tmp = a->solve_work; 1106 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1107 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1108 1109 for (neq=0; neq<B->cmap->n; neq++){ 1110 /* forward solve the lower triangular */ 1111 tmp[0] = b[r[0]]; 1112 v = aa; 1113 vi = aj; 1114 for (i=1; i<n; i++) { 1115 nz = ai[i+1] - ai[i]; 1116 sum = b[r[i]]; 1117 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 1118 tmp[i] = sum; 1119 v += nz; vi += nz; 1120 } 1121 1122 /* backward solve the upper triangular */ 1123 for (i=n-1; i>=0; i--){ 1124 v = aa + adiag[i+1]+1; 1125 vi = aj + adiag[i+1]+1; 1126 nz = adiag[i]-adiag[i+1]-1; 1127 sum = tmp[i]; 1128 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 1129 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 1130 } 1131 1132 b += n; 1133 x += n; 1134 } 1135 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1136 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1137 ierr = MatRestoreArray(B,&b);CHKERRQ(ierr); 1138 ierr = MatRestoreArray(X,&x);CHKERRQ(ierr); 1139 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 1140 PetscFunctionReturn(0); 1141 } 1142 1143 #undef __FUNCT__ 1144 #define __FUNCT__ "MatSolve_SeqAIJ_InplaceWithPerm" 1145 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx) 1146 { 1147 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1148 IS iscol = a->col,isrow = a->row; 1149 PetscErrorCode ierr; 1150 const PetscInt *r,*c,*rout,*cout; 1151 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1152 PetscInt nz,row; 1153 PetscScalar *x,*b,*tmp,*tmps,sum; 1154 const MatScalar *aa = a->a,*v; 1155 1156 PetscFunctionBegin; 1157 if (!n) PetscFunctionReturn(0); 1158 1159 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1160 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1161 tmp = a->solve_work; 1162 1163 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1164 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1165 1166 /* forward solve the lower triangular */ 1167 tmp[0] = b[*r++]; 1168 tmps = tmp; 1169 for (row=1; row<n; row++) { 1170 i = rout[row]; /* permuted row */ 1171 v = aa + ai[i] ; 1172 vi = aj + ai[i] ; 1173 nz = a->diag[i] - ai[i]; 1174 sum = b[*r++]; 1175 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1176 tmp[row] = sum; 1177 } 1178 1179 /* backward solve the upper triangular */ 1180 for (row=n-1; row>=0; row--){ 1181 i = rout[row]; /* permuted row */ 1182 v = aa + a->diag[i] + 1; 1183 vi = aj + a->diag[i] + 1; 1184 nz = ai[i+1] - a->diag[i] - 1; 1185 sum = tmp[row]; 1186 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1187 x[*c--] = tmp[row] = sum*aa[a->diag[i]]; 1188 } 1189 1190 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1191 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1192 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1193 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1194 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1195 PetscFunctionReturn(0); 1196 } 1197 1198 /* ----------------------------------------------------------- */ 1199 #include "../src/mat/impls/aij/seq/ftn-kernels/fsolve.h" 1200 #undef __FUNCT__ 1201 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering" 1202 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx) 1203 { 1204 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1205 PetscErrorCode ierr; 1206 PetscInt n = A->rmap->n; 1207 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag; 1208 PetscScalar *x; 1209 const PetscScalar *b; 1210 const MatScalar *aa = a->a; 1211 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1212 PetscInt adiag_i,i,nz,ai_i; 1213 const PetscInt *vi; 1214 const MatScalar *v; 1215 PetscScalar sum; 1216 #endif 1217 1218 PetscFunctionBegin; 1219 if (!n) PetscFunctionReturn(0); 1220 1221 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1222 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1223 1224 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1225 fortransolveaij_(&n,x,ai,aj,adiag,aa,b); 1226 #else 1227 /* forward solve the lower triangular */ 1228 x[0] = b[0]; 1229 for (i=1; i<n; i++) { 1230 ai_i = ai[i]; 1231 v = aa + ai_i; 1232 vi = aj + ai_i; 1233 nz = adiag[i] - ai_i; 1234 sum = b[i]; 1235 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1236 x[i] = sum; 1237 } 1238 1239 /* backward solve the upper triangular */ 1240 for (i=n-1; i>=0; i--){ 1241 adiag_i = adiag[i]; 1242 v = aa + adiag_i + 1; 1243 vi = aj + adiag_i + 1; 1244 nz = ai[i+1] - adiag_i - 1; 1245 sum = x[i]; 1246 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1247 x[i] = sum*aa[adiag_i]; 1248 } 1249 #endif 1250 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1251 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1252 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1253 PetscFunctionReturn(0); 1254 } 1255 1256 #undef __FUNCT__ 1257 #define __FUNCT__ "MatSolveAdd_SeqAIJ" 1258 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx) 1259 { 1260 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1261 IS iscol = a->col,isrow = a->row; 1262 PetscErrorCode ierr; 1263 PetscInt i, n = A->rmap->n,j; 1264 PetscInt nz; 1265 const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j; 1266 PetscScalar *x,*tmp,sum; 1267 const PetscScalar *b; 1268 const MatScalar *aa = a->a,*v; 1269 1270 PetscFunctionBegin; 1271 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 1272 1273 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1274 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1275 tmp = a->solve_work; 1276 1277 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1278 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1279 1280 /* forward solve the lower triangular */ 1281 tmp[0] = b[*r++]; 1282 for (i=1; i<n; i++) { 1283 v = aa + ai[i] ; 1284 vi = aj + ai[i] ; 1285 nz = a->diag[i] - ai[i]; 1286 sum = b[*r++]; 1287 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1288 tmp[i] = sum; 1289 } 1290 1291 /* backward solve the upper triangular */ 1292 for (i=n-1; i>=0; i--){ 1293 v = aa + a->diag[i] + 1; 1294 vi = aj + a->diag[i] + 1; 1295 nz = ai[i+1] - a->diag[i] - 1; 1296 sum = tmp[i]; 1297 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1298 tmp[i] = sum*aa[a->diag[i]]; 1299 x[*c--] += tmp[i]; 1300 } 1301 1302 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1303 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1304 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1305 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1306 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1307 1308 PetscFunctionReturn(0); 1309 } 1310 1311 #undef __FUNCT__ 1312 #define __FUNCT__ "MatSolveAdd_SeqAIJ_newdatastruct" 1313 PetscErrorCode MatSolveAdd_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec yy,Vec xx) 1314 { 1315 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1316 IS iscol = a->col,isrow = a->row; 1317 PetscErrorCode ierr; 1318 PetscInt i, n = A->rmap->n,j; 1319 PetscInt nz; 1320 const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag; 1321 PetscScalar *x,*tmp,sum; 1322 const PetscScalar *b; 1323 const MatScalar *aa = a->a,*v; 1324 1325 PetscFunctionBegin; 1326 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 1327 1328 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1329 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1330 tmp = a->solve_work; 1331 1332 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1333 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1334 1335 /* forward solve the lower triangular */ 1336 tmp[0] = b[r[0]]; 1337 v = aa; 1338 vi = aj; 1339 for (i=1; i<n; i++) { 1340 nz = ai[i+1] - ai[i]; 1341 sum = b[r[i]]; 1342 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1343 tmp[i] = sum; 1344 v += nz; vi += nz; 1345 } 1346 1347 /* backward solve the upper triangular */ 1348 v = aa + adiag[n-1]; 1349 vi = aj + adiag[n-1]; 1350 for (i=n-1; i>=0; i--){ 1351 nz = adiag[i] - adiag[i+1] - 1; 1352 sum = tmp[i]; 1353 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1354 tmp[i] = sum*v[nz]; 1355 x[c[i]] += tmp[i]; 1356 v += nz+1; vi += nz+1; 1357 } 1358 1359 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1360 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1361 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1362 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1363 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1364 1365 PetscFunctionReturn(0); 1366 } 1367 1368 #undef __FUNCT__ 1369 #define __FUNCT__ "MatSolveTranspose_SeqAIJ" 1370 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx) 1371 { 1372 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1373 IS iscol = a->col,isrow = a->row; 1374 PetscErrorCode ierr; 1375 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1376 PetscInt i,n = A->rmap->n,j; 1377 PetscInt nz; 1378 PetscScalar *x,*tmp,s1; 1379 const MatScalar *aa = a->a,*v; 1380 const PetscScalar *b; 1381 1382 PetscFunctionBegin; 1383 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1384 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1385 tmp = a->solve_work; 1386 1387 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1388 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1389 1390 /* copy the b into temp work space according to permutation */ 1391 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1392 1393 /* forward solve the U^T */ 1394 for (i=0; i<n; i++) { 1395 v = aa + diag[i] ; 1396 vi = aj + diag[i] + 1; 1397 nz = ai[i+1] - diag[i] - 1; 1398 s1 = tmp[i]; 1399 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1400 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1401 tmp[i] = s1; 1402 } 1403 1404 /* backward solve the L^T */ 1405 for (i=n-1; i>=0; i--){ 1406 v = aa + diag[i] - 1 ; 1407 vi = aj + diag[i] - 1 ; 1408 nz = diag[i] - ai[i]; 1409 s1 = tmp[i]; 1410 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1411 } 1412 1413 /* copy tmp into x according to permutation */ 1414 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1415 1416 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1417 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1418 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1419 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1420 1421 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1422 PetscFunctionReturn(0); 1423 } 1424 1425 #undef __FUNCT__ 1426 #define __FUNCT__ "MatSolveTranspose_SeqAIJ_newdatastruct" 1427 PetscErrorCode MatSolveTranspose_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx) 1428 { 1429 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1430 IS iscol = a->col,isrow = a->row; 1431 PetscErrorCode ierr; 1432 const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi; 1433 PetscInt i,n = A->rmap->n,j; 1434 PetscInt nz; 1435 PetscScalar *x,*tmp,s1; 1436 const MatScalar *aa = a->a,*v; 1437 const PetscScalar *b; 1438 1439 PetscFunctionBegin; 1440 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1441 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1442 tmp = a->solve_work; 1443 1444 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1445 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1446 1447 /* copy the b into temp work space according to permutation */ 1448 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1449 1450 /* forward solve the U^T */ 1451 for (i=0; i<n; i++) { 1452 v = aa + adiag[i+1] + 1; 1453 vi = aj + adiag[i+1] + 1; 1454 nz = adiag[i] - adiag[i+1] - 1; 1455 s1 = tmp[i]; 1456 s1 *= v[nz]; /* multiply by inverse of diagonal entry */ 1457 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1458 tmp[i] = s1; 1459 } 1460 1461 /* backward solve the L^T */ 1462 for (i=n-1; i>=0; i--){ 1463 v = aa + ai[i]; 1464 vi = aj + ai[i]; 1465 nz = ai[i+1] - ai[i]; 1466 s1 = tmp[i]; 1467 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1468 } 1469 1470 /* copy tmp into x according to permutation */ 1471 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1472 1473 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1474 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1475 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1476 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1477 1478 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1479 PetscFunctionReturn(0); 1480 } 1481 1482 #undef __FUNCT__ 1483 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ" 1484 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx) 1485 { 1486 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1487 IS iscol = a->col,isrow = a->row; 1488 PetscErrorCode ierr; 1489 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1490 PetscInt i,n = A->rmap->n,j; 1491 PetscInt nz; 1492 PetscScalar *x,*tmp,s1; 1493 const MatScalar *aa = a->a,*v; 1494 const PetscScalar *b; 1495 1496 PetscFunctionBegin; 1497 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1498 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1499 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1500 tmp = a->solve_work; 1501 1502 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1503 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1504 1505 /* copy the b into temp work space according to permutation */ 1506 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1507 1508 /* forward solve the U^T */ 1509 for (i=0; i<n; i++) { 1510 v = aa + diag[i] ; 1511 vi = aj + diag[i] + 1; 1512 nz = ai[i+1] - diag[i] - 1; 1513 s1 = tmp[i]; 1514 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1515 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1516 tmp[i] = s1; 1517 } 1518 1519 /* backward solve the L^T */ 1520 for (i=n-1; i>=0; i--){ 1521 v = aa + diag[i] - 1 ; 1522 vi = aj + diag[i] - 1 ; 1523 nz = diag[i] - ai[i]; 1524 s1 = tmp[i]; 1525 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1526 } 1527 1528 /* copy tmp into x according to permutation */ 1529 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1530 1531 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1532 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1533 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1534 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1535 1536 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1537 PetscFunctionReturn(0); 1538 } 1539 1540 #undef __FUNCT__ 1541 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ_newdatastruct" 1542 PetscErrorCode MatSolveTransposeAdd_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec zz,Vec xx) 1543 { 1544 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1545 IS iscol = a->col,isrow = a->row; 1546 PetscErrorCode ierr; 1547 const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi; 1548 PetscInt i,n = A->rmap->n,j; 1549 PetscInt nz; 1550 PetscScalar *x,*tmp,s1; 1551 const MatScalar *aa = a->a,*v; 1552 const PetscScalar *b; 1553 1554 PetscFunctionBegin; 1555 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1556 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1557 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1558 tmp = a->solve_work; 1559 1560 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1561 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1562 1563 /* copy the b into temp work space according to permutation */ 1564 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1565 1566 /* forward solve the U^T */ 1567 for (i=0; i<n; i++) { 1568 v = aa + adiag[i+1] + 1; 1569 vi = aj + adiag[i+1] + 1; 1570 nz = adiag[i] - adiag[i+1] - 1; 1571 s1 = tmp[i]; 1572 s1 *= v[nz]; /* multiply by inverse of diagonal entry */ 1573 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1574 tmp[i] = s1; 1575 } 1576 1577 1578 /* backward solve the L^T */ 1579 for (i=n-1; i>=0; i--){ 1580 v = aa + ai[i] ; 1581 vi = aj + ai[i]; 1582 nz = ai[i+1] - ai[i]; 1583 s1 = tmp[i]; 1584 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1585 } 1586 1587 /* copy tmp into x according to permutation */ 1588 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1589 1590 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1591 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1592 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1593 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1594 1595 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1596 PetscFunctionReturn(0); 1597 } 1598 1599 /* ----------------------------------------------------------------*/ 1600 1601 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth); 1602 1603 /* 1604 ilu() under revised new data structure. 1605 Factored arrays bj and ba are stored as 1606 L(0,:), L(1,:), ...,L(n-1,:), U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:) 1607 1608 bi=fact->i is an array of size n+1, in which 1609 bi+ 1610 bi[i]: points to 1st entry of L(i,:),i=0,...,n-1 1611 bi[n]: points to L(n-1,n-1)+1 1612 1613 bdiag=fact->diag is an array of size n+1,in which 1614 bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1 1615 bdiag[n]: points to entry of U(n-1,0)-1 1616 1617 U(i,:) contains bdiag[i] as its last entry, i.e., 1618 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 1619 */ 1620 #undef __FUNCT__ 1621 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct" 1622 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1623 { 1624 1625 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1626 PetscErrorCode ierr; 1627 PetscInt n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag; 1628 PetscInt i,j,nz,*bi,*bj,*bdiag; 1629 PetscTruth missing; 1630 IS isicol; 1631 1632 PetscFunctionBegin; 1633 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); 1634 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 1635 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 1636 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1637 1638 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr); 1639 b = (Mat_SeqAIJ*)(fact)->data; 1640 1641 /* allocate matrix arrays for new data structure */ 1642 ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,n+1,PetscInt,&b->i);CHKERRQ(ierr); 1643 ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1644 b->singlemalloc = PETSC_TRUE; 1645 if (!b->diag){ 1646 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr); 1647 ierr = PetscLogObjectMemory(fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1648 } 1649 bdiag = b->diag; 1650 1651 if (n > 0) { 1652 ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr); 1653 } 1654 1655 /* set bi and bj with new data structure */ 1656 bi = b->i; 1657 bj = b->j; 1658 1659 /* L part */ 1660 bi[0] = 0; 1661 for (i=0; i<n; i++){ 1662 nz = adiag[i] - ai[i]; 1663 bi[i+1] = bi[i] + nz; 1664 aj = a->j + ai[i]; 1665 for (j=0; j<nz; j++){ 1666 *bj = aj[j]; bj++; 1667 } 1668 } 1669 1670 /* U part */ 1671 bdiag[n] = bi[n]-1; 1672 for (i=n-1; i>=0; i--){ 1673 nz = ai[i+1] - adiag[i] - 1; 1674 aj = a->j + adiag[i] + 1; 1675 for (j=0; j<nz; j++){ 1676 *bj = aj[j]; bj++; 1677 } 1678 /* diag[i] */ 1679 *bj = i; bj++; 1680 bdiag[i] = bdiag[i+1] + nz + 1; 1681 } 1682 1683 fact->factor = MAT_FACTOR_ILU; 1684 fact->info.factor_mallocs = 0; 1685 fact->info.fill_ratio_given = info->fill; 1686 fact->info.fill_ratio_needed = 1.0; 1687 fact->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 1688 1689 b = (Mat_SeqAIJ*)(fact)->data; 1690 b->row = isrow; 1691 b->col = iscol; 1692 b->icol = isicol; 1693 ierr = PetscMalloc((fact->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1694 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1695 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1696 PetscFunctionReturn(0); 1697 } 1698 1699 #undef __FUNCT__ 1700 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_newdatastruct" 1701 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1702 { 1703 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1704 IS isicol; 1705 PetscErrorCode ierr; 1706 const PetscInt *r,*ic; 1707 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j; 1708 PetscInt *bi,*cols,nnz,*cols_lvl; 1709 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1710 PetscInt i,levels,diagonal_fill; 1711 PetscTruth col_identity,row_identity; 1712 PetscReal f; 1713 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1714 PetscBT lnkbt; 1715 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1716 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1717 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1718 1719 PetscFunctionBegin; 1720 /* printf("MatILUFactorSymbolic_SeqAIJ_newdatastruct ...\n"); */ 1721 levels = (PetscInt)info->levels; 1722 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1723 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1724 1725 if (!levels && row_identity && col_identity) { 1726 /* special case: ilu(0) with natural ordering */ 1727 ierr = MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1728 ierr = Mat_CheckInode(fact,PETSC_FALSE);CHKERRQ(ierr); /* Mat_CheckInode_FactorLU(fact,PETSC_FALSE) ??? */ 1729 PetscFunctionReturn(0); 1730 } 1731 1732 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); 1733 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1734 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1735 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1736 1737 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1738 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1739 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1740 bi[0] = bdiag[0] = 0; 1741 1742 ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr); 1743 1744 /* create a linked list for storing column indices of the active row */ 1745 nlnk = n + 1; 1746 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1747 1748 /* initial FreeSpace size is f*(ai[n]+1) */ 1749 f = info->fill; 1750 diagonal_fill = (PetscInt)info->diagonal_fill; 1751 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1752 current_space = free_space; 1753 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1754 current_space_lvl = free_space_lvl; 1755 1756 for (i=0; i<n; i++) { 1757 nzi = 0; 1758 /* copy current row into linked list */ 1759 nnz = ai[r[i]+1] - ai[r[i]]; 1760 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1761 cols = aj + ai[r[i]]; 1762 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1763 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1764 nzi += nlnk; 1765 1766 /* make sure diagonal entry is included */ 1767 if (diagonal_fill && lnk[i] == -1) { 1768 fm = n; 1769 while (lnk[fm] < i) fm = lnk[fm]; 1770 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1771 lnk[fm] = i; 1772 lnk_lvl[i] = 0; 1773 nzi++; dcount++; 1774 } 1775 1776 /* add pivot rows into the active row */ 1777 nzbd = 0; 1778 prow = lnk[n]; 1779 while (prow < i) { 1780 nnz = bdiag[prow]; 1781 cols = bj_ptr[prow] + nnz + 1; 1782 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1783 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1784 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1785 nzi += nlnk; 1786 prow = lnk[prow]; 1787 nzbd++; 1788 } 1789 bdiag[i] = nzbd; 1790 bi[i+1] = bi[i] + nzi; 1791 1792 /* if free space is not available, make more free space */ 1793 if (current_space->local_remaining<nzi) { 1794 nnz = 2*nzi*(n - i); /* estimated and max additional space needed */ 1795 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1796 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1797 reallocs++; 1798 } 1799 1800 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1801 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1802 bj_ptr[i] = current_space->array; 1803 bjlvl_ptr[i] = current_space_lvl->array; 1804 1805 /* make sure the active row i has diagonal entry */ 1806 if (*(bj_ptr[i]+bdiag[i]) != i) { 1807 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 1808 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1809 } 1810 1811 current_space->array += nzi; 1812 current_space->local_used += nzi; 1813 current_space->local_remaining -= nzi; 1814 current_space_lvl->array += nzi; 1815 current_space_lvl->local_used += nzi; 1816 current_space_lvl->local_remaining -= nzi; 1817 } 1818 1819 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1820 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1821 1822 /* destroy list of free space and other temporary arrays */ 1823 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 1824 1825 /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */ 1826 ierr = PetscFreeSpaceContiguous_LU_v2(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 1827 1828 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1829 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1830 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 1831 1832 #if defined(PETSC_USE_INFO) 1833 { 1834 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1835 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 1836 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1837 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 1838 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1839 if (diagonal_fill) { 1840 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 1841 } 1842 } 1843 #endif 1844 1845 /* put together the new matrix */ 1846 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 1847 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 1848 b = (Mat_SeqAIJ*)(fact)->data; 1849 b->free_a = PETSC_TRUE; 1850 b->free_ij = PETSC_TRUE; 1851 b->singlemalloc = PETSC_FALSE; 1852 ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 1853 b->j = bj; 1854 b->i = bi; 1855 b->diag = bdiag; 1856 b->ilen = 0; 1857 b->imax = 0; 1858 b->row = isrow; 1859 b->col = iscol; 1860 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1861 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1862 b->icol = isicol; 1863 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1864 /* In b structure: Free imax, ilen, old a, old j. 1865 Allocate bdiag, solve_work, new a, new j */ 1866 ierr = PetscLogObjectMemory(fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1867 b->maxnz = b->nz = bdiag[0]+1; 1868 (fact)->info.factor_mallocs = reallocs; 1869 (fact)->info.fill_ratio_given = f; 1870 (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 1871 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 1872 ierr = Mat_CheckInode(fact,PETSC_FALSE);CHKERRQ(ierr); /* Mat_CheckInode_FactorLU(fact,PETSC_FALSE) ??? */ 1873 PetscFunctionReturn(0); 1874 } 1875 1876 #undef __FUNCT__ 1877 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ" 1878 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1879 { 1880 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1881 IS isicol; 1882 PetscErrorCode ierr; 1883 const PetscInt *r,*ic; 1884 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,d; 1885 PetscInt *bi,*cols,nnz,*cols_lvl; 1886 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1887 PetscInt i,levels,diagonal_fill; 1888 PetscTruth col_identity,row_identity; 1889 PetscReal f; 1890 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1891 PetscBT lnkbt; 1892 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1893 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1894 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1895 PetscTruth missing; 1896 PetscTruth newdatastruct=PETSC_FALSE; 1897 1898 PetscFunctionBegin; 1899 ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 1900 if(newdatastruct){ 1901 ierr = MatILUFactorSymbolic_SeqAIJ_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1902 PetscFunctionReturn(0); 1903 } 1904 1905 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); 1906 f = info->fill; 1907 levels = (PetscInt)info->levels; 1908 diagonal_fill = (PetscInt)info->diagonal_fill; 1909 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1910 1911 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1912 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1913 if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */ 1914 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr); 1915 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1916 1917 fact->factor = MAT_FACTOR_ILU; 1918 (fact)->info.factor_mallocs = 0; 1919 (fact)->info.fill_ratio_given = info->fill; 1920 (fact)->info.fill_ratio_needed = 1.0; 1921 b = (Mat_SeqAIJ*)(fact)->data; 1922 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 1923 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 1924 b->row = isrow; 1925 b->col = iscol; 1926 b->icol = isicol; 1927 ierr = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1928 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1929 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1930 ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1931 PetscFunctionReturn(0); 1932 } 1933 1934 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1935 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1936 1937 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1938 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1939 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1940 bi[0] = bdiag[0] = 0; 1941 1942 ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr); 1943 1944 /* create a linked list for storing column indices of the active row */ 1945 nlnk = n + 1; 1946 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1947 1948 /* initial FreeSpace size is f*(ai[n]+1) */ 1949 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1950 current_space = free_space; 1951 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1952 current_space_lvl = free_space_lvl; 1953 1954 for (i=0; i<n; i++) { 1955 nzi = 0; 1956 /* copy current row into linked list */ 1957 nnz = ai[r[i]+1] - ai[r[i]]; 1958 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1959 cols = aj + ai[r[i]]; 1960 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1961 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1962 nzi += nlnk; 1963 1964 /* make sure diagonal entry is included */ 1965 if (diagonal_fill && lnk[i] == -1) { 1966 fm = n; 1967 while (lnk[fm] < i) fm = lnk[fm]; 1968 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1969 lnk[fm] = i; 1970 lnk_lvl[i] = 0; 1971 nzi++; dcount++; 1972 } 1973 1974 /* add pivot rows into the active row */ 1975 nzbd = 0; 1976 prow = lnk[n]; 1977 while (prow < i) { 1978 nnz = bdiag[prow]; 1979 cols = bj_ptr[prow] + nnz + 1; 1980 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1981 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1982 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1983 nzi += nlnk; 1984 prow = lnk[prow]; 1985 nzbd++; 1986 } 1987 bdiag[i] = nzbd; 1988 bi[i+1] = bi[i] + nzi; 1989 1990 /* if free space is not available, make more free space */ 1991 if (current_space->local_remaining<nzi) { 1992 nnz = nzi*(n - i); /* estimated and max additional space needed */ 1993 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1994 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1995 reallocs++; 1996 } 1997 1998 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1999 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2000 bj_ptr[i] = current_space->array; 2001 bjlvl_ptr[i] = current_space_lvl->array; 2002 2003 /* make sure the active row i has diagonal entry */ 2004 if (*(bj_ptr[i]+bdiag[i]) != i) { 2005 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 2006 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 2007 } 2008 2009 current_space->array += nzi; 2010 current_space->local_used += nzi; 2011 current_space->local_remaining -= nzi; 2012 current_space_lvl->array += nzi; 2013 current_space_lvl->local_used += nzi; 2014 current_space_lvl->local_remaining -= nzi; 2015 } 2016 2017 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 2018 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 2019 2020 /* destroy list of free space and other temporary arrays */ 2021 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 2022 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */ 2023 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2024 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2025 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 2026 2027 #if defined(PETSC_USE_INFO) 2028 { 2029 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 2030 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 2031 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2032 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 2033 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 2034 if (diagonal_fill) { 2035 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 2036 } 2037 } 2038 #endif 2039 2040 /* put together the new matrix */ 2041 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 2042 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 2043 b = (Mat_SeqAIJ*)(fact)->data; 2044 b->free_a = PETSC_TRUE; 2045 b->free_ij = PETSC_TRUE; 2046 b->singlemalloc = PETSC_FALSE; 2047 ierr = PetscMalloc(bi[n]*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 2048 b->j = bj; 2049 b->i = bi; 2050 for (i=0; i<n; i++) bdiag[i] += bi[i]; 2051 b->diag = bdiag; 2052 b->ilen = 0; 2053 b->imax = 0; 2054 b->row = isrow; 2055 b->col = iscol; 2056 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 2057 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 2058 b->icol = isicol; 2059 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2060 /* In b structure: Free imax, ilen, old a, old j. 2061 Allocate bdiag, solve_work, new a, new j */ 2062 ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 2063 b->maxnz = b->nz = bi[n] ; 2064 (fact)->info.factor_mallocs = reallocs; 2065 (fact)->info.fill_ratio_given = f; 2066 (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 2067 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 2068 ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); 2069 PetscFunctionReturn(0); 2070 } 2071 2072 #undef __FUNCT__ 2073 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ_newdatastruct" 2074 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info) 2075 { 2076 Mat C = B; 2077 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2078 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2079 IS ip=b->row,iip = b->icol; 2080 PetscErrorCode ierr; 2081 const PetscInt *rip,*riip; 2082 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp; 2083 PetscInt *ai=a->i,*aj=a->j; 2084 PetscInt k,jmin,jmax,*c2r,*il,col,nexti,ili,nz; 2085 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2086 PetscTruth perm_identity; 2087 2088 LUShift_Ctx sctx; 2089 PetscInt newshift; 2090 PetscReal rs; 2091 MatScalar d,*v; 2092 2093 PetscFunctionBegin; 2094 /* MatPivotSetUp(): initialize shift context sctx */ 2095 ierr = PetscMemzero(&sctx,sizeof(LUShift_Ctx));CHKERRQ(ierr); 2096 2097 /* if both shift schemes are chosen by user, only use info->shiftpd */ 2098 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 2099 sctx.shift_top = info->zeropivot; 2100 for (i=0; i<mbs; i++) { 2101 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 2102 d = (aa)[a->diag[i]]; 2103 rs = -PetscAbsScalar(d) - PetscRealPart(d); 2104 v = aa+ai[i]; 2105 nz = ai[i+1] - ai[i]; 2106 for (j=0; j<nz; j++) 2107 rs += PetscAbsScalar(v[j]); 2108 if (rs>sctx.shift_top) sctx.shift_top = rs; 2109 } 2110 sctx.shift_top *= 1.1; 2111 sctx.nshift_max = 5; 2112 sctx.shift_lo = 0.; 2113 sctx.shift_hi = 1.; 2114 } 2115 2116 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2117 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2118 2119 /* allocate working arrays 2120 c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col 2121 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 2122 */ 2123 ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&c2r);CHKERRQ(ierr); 2124 2125 do { 2126 sctx.lushift = PETSC_FALSE; 2127 2128 for (i=0; i<mbs; i++) c2r[i] = mbs; 2129 il[0] = 0; 2130 2131 for (k = 0; k<mbs; k++){ 2132 /* zero rtmp */ 2133 nz = bi[k+1] - bi[k]; 2134 bjtmp = bj + bi[k]; 2135 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2136 2137 /* load in initial unfactored row */ 2138 bval = ba + bi[k]; 2139 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2140 for (j = jmin; j < jmax; j++){ 2141 col = riip[aj[j]]; 2142 if (col >= k){ /* only take upper triangular entry */ 2143 rtmp[col] = aa[j]; 2144 *bval++ = 0.0; /* for in-place factorization */ 2145 } 2146 } 2147 /* shift the diagonal of the matrix: ZeropivotApply() */ 2148 rtmp[k] += sctx.shift_amount; /* shift the diagonal of the matrix */ 2149 2150 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2151 dk = rtmp[k]; 2152 i = c2r[k]; /* first row to be added to k_th row */ 2153 2154 while (i < k){ 2155 nexti = c2r[i]; /* next row to be added to k_th row */ 2156 2157 /* compute multiplier, update diag(k) and U(i,k) */ 2158 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2159 uikdi = - ba[ili]*ba[bdiag[i]]; /* diagonal(k) */ 2160 dk += uikdi*ba[ili]; /* update diag[k] */ 2161 ba[ili] = uikdi; /* -U(i,k) */ 2162 2163 /* add multiple of row i to k-th row */ 2164 jmin = ili + 1; jmax = bi[i+1]; 2165 if (jmin < jmax){ 2166 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2167 /* update il and c2r for row i */ 2168 il[i] = jmin; 2169 j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i; 2170 } 2171 i = nexti; 2172 } 2173 2174 /* copy data into U(k,:) */ 2175 rs = 0.0; 2176 jmin = bi[k]; jmax = bi[k+1]-1; 2177 if (jmin < jmax) { 2178 for (j=jmin; j<jmax; j++){ 2179 col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]); 2180 } 2181 /* add the k-th row into il and c2r */ 2182 il[k] = jmin; 2183 i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k; 2184 } 2185 2186 /* MatPivotCheck() */ 2187 sctx.rs = rs; 2188 sctx.pv = dk; 2189 if (info->shiftnz){ 2190 ierr = MatPivotCheck_nz(info,sctx,k,newshift);CHKERRQ(ierr); 2191 } else if (info->shiftpd){ 2192 ierr = MatPivotCheck_pd(info,sctx,k,newshift);CHKERRQ(ierr); 2193 } else if (info->shiftinblocks){ 2194 ierr = MatPivotCheck_inblocks(info,sctx,k,newshift);CHKERRQ(ierr); 2195 } else { 2196 ierr = MatPivotCheck_none(info,sctx,k,newshift);CHKERRQ(ierr); 2197 } 2198 dk = sctx.pv; 2199 if (newshift == 1) break; 2200 2201 ba[bdiag[k]] = 1.0/dk; /* U(k,k) */ 2202 } 2203 } while (sctx.lushift); 2204 2205 ierr = PetscFree3(rtmp,il,c2r);CHKERRQ(ierr); 2206 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2207 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2208 2209 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2210 if (perm_identity){ 2211 (B)->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_newdatastruct; 2212 (B)->ops->solvetranspose = 0; 2213 (B)->ops->forwardsolve = 0; 2214 (B)->ops->backwardsolve = 0; 2215 } else { 2216 (B)->ops->solve = MatSolve_SeqSBAIJ_1_newdatastruct; 2217 (B)->ops->solvetranspose = 0; 2218 (B)->ops->forwardsolve = 0; 2219 (B)->ops->backwardsolve = 0; 2220 } 2221 2222 C->assembled = PETSC_TRUE; 2223 C->preallocated = PETSC_TRUE; 2224 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2225 2226 /* MatPivotView() */ 2227 if (sctx.nshift){ 2228 if (info->shiftpd) { 2229 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); 2230 } else if (info->shiftnz) { 2231 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2232 } else if (info->shiftinblocks){ 2233 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftinblocks);CHKERRQ(ierr); 2234 } 2235 } 2236 PetscFunctionReturn(0); 2237 } 2238 2239 #undef __FUNCT__ 2240 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ" 2241 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 2242 { 2243 Mat C = B; 2244 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2245 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2246 IS ip=b->row,iip = b->icol; 2247 PetscErrorCode ierr; 2248 const PetscInt *rip,*riip; 2249 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol,*bjtmp; 2250 PetscInt *ai=a->i,*aj=a->j; 2251 PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz; 2252 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2253 PetscReal zeropivot,rs,shiftnz; 2254 PetscReal shiftpd; 2255 ChShift_Ctx sctx; 2256 PetscInt newshift; 2257 PetscTruth perm_identity; 2258 2259 PetscFunctionBegin; 2260 shiftnz = info->shiftnz; 2261 shiftpd = info->shiftpd; 2262 zeropivot = info->zeropivot; 2263 2264 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2265 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2266 2267 /* initialization */ 2268 ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr); 2269 sctx.shift_amount = 0; 2270 sctx.nshift = 0; 2271 do { 2272 sctx.chshift = PETSC_FALSE; 2273 for (i=0; i<mbs; i++) jl[i] = mbs; 2274 il[0] = 0; 2275 2276 for (k = 0; k<mbs; k++){ 2277 /* zero rtmp */ 2278 nz = bi[k+1] - bi[k]; 2279 bjtmp = bj + bi[k]; 2280 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2281 2282 bval = ba + bi[k]; 2283 /* initialize k-th row by the perm[k]-th row of A */ 2284 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2285 for (j = jmin; j < jmax; j++){ 2286 col = riip[aj[j]]; 2287 if (col >= k){ /* only take upper triangular entry */ 2288 rtmp[col] = aa[j]; 2289 *bval++ = 0.0; /* for in-place factorization */ 2290 } 2291 } 2292 /* shift the diagonal of the matrix */ 2293 if (sctx.nshift) rtmp[k] += sctx.shift_amount; 2294 2295 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2296 dk = rtmp[k]; 2297 i = jl[k]; /* first row to be added to k_th row */ 2298 2299 while (i < k){ 2300 nexti = jl[i]; /* next row to be added to k_th row */ 2301 2302 /* compute multiplier, update diag(k) and U(i,k) */ 2303 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2304 uikdi = - ba[ili]*ba[bi[i]]; /* diagonal(k) */ 2305 dk += uikdi*ba[ili]; 2306 ba[ili] = uikdi; /* -U(i,k) */ 2307 2308 /* add multiple of row i to k-th row */ 2309 jmin = ili + 1; jmax = bi[i+1]; 2310 if (jmin < jmax){ 2311 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2312 /* update il and jl for row i */ 2313 il[i] = jmin; 2314 j = bj[jmin]; jl[i] = jl[j]; jl[j] = i; 2315 } 2316 i = nexti; 2317 } 2318 2319 /* shift the diagonals when zero pivot is detected */ 2320 /* compute rs=sum of abs(off-diagonal) */ 2321 rs = 0.0; 2322 jmin = bi[k]+1; 2323 nz = bi[k+1] - jmin; 2324 bcol = bj + jmin; 2325 for (j=0; j<nz; j++) { 2326 rs += PetscAbsScalar(rtmp[bcol[j]]); 2327 } 2328 2329 sctx.rs = rs; 2330 sctx.pv = dk; 2331 ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr); 2332 2333 if (newshift == 1) { 2334 if (!sctx.shift_amount) { 2335 sctx.shift_amount = 1e-5; 2336 } 2337 break; 2338 } 2339 2340 /* copy data into U(k,:) */ 2341 ba[bi[k]] = 1.0/dk; /* U(k,k) */ 2342 jmin = bi[k]+1; jmax = bi[k+1]; 2343 if (jmin < jmax) { 2344 for (j=jmin; j<jmax; j++){ 2345 col = bj[j]; ba[j] = rtmp[col]; 2346 } 2347 /* add the k-th row into il and jl */ 2348 il[k] = jmin; 2349 i = bj[jmin]; jl[k] = jl[i]; jl[i] = k; 2350 } 2351 } 2352 } while (sctx.chshift); 2353 ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr); 2354 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2355 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2356 2357 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2358 if (perm_identity){ 2359 (B)->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2360 (B)->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2361 (B)->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering; 2362 (B)->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering; 2363 } else { 2364 (B)->ops->solve = MatSolve_SeqSBAIJ_1; 2365 (B)->ops->solvetranspose = MatSolve_SeqSBAIJ_1; 2366 (B)->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1; 2367 (B)->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1; 2368 } 2369 2370 C->assembled = PETSC_TRUE; 2371 C->preallocated = PETSC_TRUE; 2372 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2373 if (sctx.nshift){ 2374 if (shiftnz) { 2375 ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2376 } else if (shiftpd) { 2377 ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2378 } 2379 } 2380 PetscFunctionReturn(0); 2381 } 2382 2383 /* 2384 icc() under revised new data structure. 2385 Factored arrays bj and ba are stored as 2386 U(0,:),...,U(i,:),U(n-1,:) 2387 2388 ui=fact->i is an array of size n+1, in which 2389 ui+ 2390 ui[i]: points to 1st entry of U(i,:),i=0,...,n-1 2391 ui[n]: points to U(n-1,n-1)+1 2392 2393 udiag=fact->diag is an array of size n,in which 2394 udiag[i]: points to diagonal of U(i,:), i=0,...,n-1 2395 2396 U(i,:) contains udiag[i] as its last entry, i.e., 2397 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 2398 */ 2399 2400 #undef __FUNCT__ 2401 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ_newdatastruct" 2402 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2403 { 2404 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2405 Mat_SeqSBAIJ *b; 2406 PetscErrorCode ierr; 2407 PetscTruth perm_identity,missing; 2408 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2409 const PetscInt *rip,*riip; 2410 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2411 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2412 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2413 PetscReal fill=info->fill,levels=info->levels; 2414 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2415 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2416 PetscBT lnkbt; 2417 IS iperm; 2418 2419 PetscFunctionBegin; 2420 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); 2421 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2422 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2423 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2424 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2425 2426 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2427 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2428 ui[0] = 0; 2429 2430 /* ICC(0) without matrix ordering: simply rearrange column indices */ 2431 if (!levels && perm_identity) { 2432 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2433 cols = uj; 2434 for (i=0; i<am; i++) { 2435 ncols = ai[i+1] - a->diag[i]; 2436 ui[i+1] = ui[i] + ncols; 2437 udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */ 2438 2439 aj = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */ 2440 ncols--; /* exclude diagonal */ 2441 for (j=0; j<ncols; j++) *cols++ = aj[j]; 2442 *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */ 2443 } 2444 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2445 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2446 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2447 2448 /* initialization */ 2449 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2450 2451 /* jl: linked list for storing indices of the pivot rows 2452 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2453 ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr); 2454 for (i=0; i<am; i++){ 2455 jl[i] = am; il[i] = 0; 2456 } 2457 2458 /* create and initialize a linked list for storing column indices of the active row k */ 2459 nlnk = am + 1; 2460 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2461 2462 /* initial FreeSpace size is fill*(ai[am]+1) */ 2463 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2464 current_space = free_space; 2465 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2466 current_space_lvl = free_space_lvl; 2467 2468 for (k=0; k<am; k++){ /* for each active row k */ 2469 /* initialize lnk by the column indices of row rip[k] of A */ 2470 nzk = 0; 2471 ncols = ai[rip[k]+1] - ai[rip[k]]; 2472 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2473 ncols_upper = 0; 2474 for (j=0; j<ncols; j++){ 2475 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2476 if (riip[i] >= k){ /* only take upper triangular entry */ 2477 ajtmp[ncols_upper] = i; 2478 ncols_upper++; 2479 } 2480 } 2481 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2482 nzk += nlnk; 2483 2484 /* update lnk by computing fill-in for each pivot row to be merged in */ 2485 prow = jl[k]; /* 1st pivot row */ 2486 2487 while (prow < k){ 2488 nextprow = jl[prow]; 2489 2490 /* merge prow into k-th row */ 2491 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2492 jmax = ui[prow+1]; 2493 ncols = jmax-jmin; 2494 i = jmin - ui[prow]; 2495 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2496 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2497 j = *(uj - 1); 2498 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2499 nzk += nlnk; 2500 2501 /* update il and jl for prow */ 2502 if (jmin < jmax){ 2503 il[prow] = jmin; 2504 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2505 } 2506 prow = nextprow; 2507 } 2508 2509 /* if free space is not available, make more free space */ 2510 if (current_space->local_remaining<nzk) { 2511 i = am - k + 1; /* num of unfactored rows */ 2512 i *= PetscMin(nzk, i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2513 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2514 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2515 reallocs++; 2516 } 2517 2518 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2519 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2520 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2521 2522 /* add the k-th row into il and jl */ 2523 if (nzk > 1){ 2524 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2525 jl[k] = jl[i]; jl[i] = k; 2526 il[k] = ui[k] + 1; 2527 } 2528 uj_ptr[k] = current_space->array; 2529 uj_lvl_ptr[k] = current_space_lvl->array; 2530 2531 current_space->array += nzk; 2532 current_space->local_used += nzk; 2533 current_space->local_remaining -= nzk; 2534 2535 current_space_lvl->array += nzk; 2536 current_space_lvl->local_used += nzk; 2537 current_space_lvl->local_remaining -= nzk; 2538 2539 ui[k+1] = ui[k] + nzk; 2540 } 2541 2542 #if defined(PETSC_USE_INFO) 2543 if (ai[am] != 0) { 2544 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2545 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2546 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2547 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2548 } else { 2549 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2550 } 2551 #endif 2552 2553 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2554 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2555 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2556 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2557 2558 /* destroy list of free space and other temporary array(s) */ 2559 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2560 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor in newdatastruct */ 2561 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2562 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2563 2564 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2565 2566 /* put together the new matrix in MATSEQSBAIJ format */ 2567 2568 b = (Mat_SeqSBAIJ*)(fact)->data; 2569 b->singlemalloc = PETSC_FALSE; 2570 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2571 b->j = uj; 2572 b->i = ui; 2573 b->diag = udiag; 2574 b->free_diag = PETSC_TRUE; 2575 b->ilen = 0; 2576 b->imax = 0; 2577 b->row = perm; 2578 b->col = perm; 2579 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2580 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2581 b->icol = iperm; 2582 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2583 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2584 ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2585 b->maxnz = b->nz = ui[am]; 2586 b->free_a = PETSC_TRUE; 2587 b->free_ij = PETSC_TRUE; 2588 2589 (fact)->info.factor_mallocs = reallocs; 2590 (fact)->info.fill_ratio_given = fill; 2591 if (ai[am] != 0) { 2592 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2593 } else { 2594 (fact)->info.fill_ratio_needed = 0.0; 2595 } 2596 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct; 2597 PetscFunctionReturn(0); 2598 } 2599 2600 #undef __FUNCT__ 2601 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ" 2602 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2603 { 2604 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2605 Mat_SeqSBAIJ *b; 2606 PetscErrorCode ierr; 2607 PetscTruth perm_identity,missing; 2608 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2609 const PetscInt *rip,*riip; 2610 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2611 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2612 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2613 PetscReal fill=info->fill,levels=info->levels; 2614 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2615 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2616 PetscBT lnkbt; 2617 IS iperm; 2618 PetscTruth newdatastruct=PETSC_FALSE; 2619 2620 PetscFunctionBegin; 2621 ierr = PetscOptionsGetTruth(PETSC_NULL,"-icc_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 2622 if(newdatastruct){ 2623 ierr = MatICCFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr); 2624 PetscFunctionReturn(0); 2625 } 2626 2627 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); 2628 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2629 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2630 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2631 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2632 2633 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2634 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2635 ui[0] = 0; 2636 2637 /* ICC(0) without matrix ordering: simply copies fill pattern */ 2638 if (!levels && perm_identity) { 2639 2640 for (i=0; i<am; i++) { 2641 ui[i+1] = ui[i] + ai[i+1] - a->diag[i]; 2642 udiag[i] = ui[i]; 2643 } 2644 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2645 cols = uj; 2646 for (i=0; i<am; i++) { 2647 aj = a->j + a->diag[i]; 2648 ncols = ui[i+1] - ui[i]; 2649 for (j=0; j<ncols; j++) *cols++ = *aj++; 2650 } 2651 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2652 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2653 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2654 2655 /* initialization */ 2656 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2657 2658 /* jl: linked list for storing indices of the pivot rows 2659 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2660 ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr); 2661 for (i=0; i<am; i++){ 2662 jl[i] = am; il[i] = 0; 2663 } 2664 2665 /* create and initialize a linked list for storing column indices of the active row k */ 2666 nlnk = am + 1; 2667 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2668 2669 /* initial FreeSpace size is fill*(ai[am]+1) */ 2670 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2671 current_space = free_space; 2672 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2673 current_space_lvl = free_space_lvl; 2674 2675 for (k=0; k<am; k++){ /* for each active row k */ 2676 /* initialize lnk by the column indices of row rip[k] of A */ 2677 nzk = 0; 2678 ncols = ai[rip[k]+1] - ai[rip[k]]; 2679 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2680 ncols_upper = 0; 2681 for (j=0; j<ncols; j++){ 2682 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2683 if (riip[i] >= k){ /* only take upper triangular entry */ 2684 ajtmp[ncols_upper] = i; 2685 ncols_upper++; 2686 } 2687 } 2688 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2689 nzk += nlnk; 2690 2691 /* update lnk by computing fill-in for each pivot row to be merged in */ 2692 prow = jl[k]; /* 1st pivot row */ 2693 2694 while (prow < k){ 2695 nextprow = jl[prow]; 2696 2697 /* merge prow into k-th row */ 2698 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2699 jmax = ui[prow+1]; 2700 ncols = jmax-jmin; 2701 i = jmin - ui[prow]; 2702 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2703 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2704 j = *(uj - 1); 2705 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2706 nzk += nlnk; 2707 2708 /* update il and jl for prow */ 2709 if (jmin < jmax){ 2710 il[prow] = jmin; 2711 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2712 } 2713 prow = nextprow; 2714 } 2715 2716 /* if free space is not available, make more free space */ 2717 if (current_space->local_remaining<nzk) { 2718 i = am - k + 1; /* num of unfactored rows */ 2719 i *= PetscMin(nzk, (i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2720 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2721 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2722 reallocs++; 2723 } 2724 2725 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2726 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2727 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2728 2729 /* add the k-th row into il and jl */ 2730 if (nzk > 1){ 2731 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2732 jl[k] = jl[i]; jl[i] = k; 2733 il[k] = ui[k] + 1; 2734 } 2735 uj_ptr[k] = current_space->array; 2736 uj_lvl_ptr[k] = current_space_lvl->array; 2737 2738 current_space->array += nzk; 2739 current_space->local_used += nzk; 2740 current_space->local_remaining -= nzk; 2741 2742 current_space_lvl->array += nzk; 2743 current_space_lvl->local_used += nzk; 2744 current_space_lvl->local_remaining -= nzk; 2745 2746 ui[k+1] = ui[k] + nzk; 2747 } 2748 2749 #if defined(PETSC_USE_INFO) 2750 if (ai[am] != 0) { 2751 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2752 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2753 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2754 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2755 } else { 2756 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2757 } 2758 #endif 2759 2760 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2761 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2762 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2763 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2764 2765 /* destroy list of free space and other temporary array(s) */ 2766 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2767 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 2768 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2769 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2770 2771 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2772 2773 /* put together the new matrix in MATSEQSBAIJ format */ 2774 2775 b = (Mat_SeqSBAIJ*)(fact)->data; 2776 b->singlemalloc = PETSC_FALSE; 2777 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2778 b->j = uj; 2779 b->i = ui; 2780 b->diag = udiag; 2781 b->free_diag = PETSC_TRUE; 2782 b->ilen = 0; 2783 b->imax = 0; 2784 b->row = perm; 2785 b->col = perm; 2786 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2787 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2788 b->icol = iperm; 2789 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2790 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2791 ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2792 b->maxnz = b->nz = ui[am]; 2793 b->free_a = PETSC_TRUE; 2794 b->free_ij = PETSC_TRUE; 2795 2796 (fact)->info.factor_mallocs = reallocs; 2797 (fact)->info.fill_ratio_given = fill; 2798 if (ai[am] != 0) { 2799 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2800 } else { 2801 (fact)->info.fill_ratio_needed = 0.0; 2802 } 2803 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2804 PetscFunctionReturn(0); 2805 } 2806 2807 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2808 { 2809 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2810 Mat_SeqSBAIJ *b; 2811 PetscErrorCode ierr; 2812 PetscTruth perm_identity; 2813 PetscReal fill = info->fill; 2814 const PetscInt *rip,*riip; 2815 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2816 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2817 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr,*udiag; 2818 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2819 PetscBT lnkbt; 2820 IS iperm; 2821 2822 PetscFunctionBegin; 2823 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); 2824 /* check whether perm is the identity mapping */ 2825 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2826 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2827 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2828 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2829 2830 /* initialization */ 2831 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2832 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2833 ui[0] = 0; 2834 2835 /* jl: linked list for storing indices of the pivot rows 2836 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2837 ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr); 2838 for (i=0; i<am; i++){ 2839 jl[i] = am; il[i] = 0; 2840 } 2841 2842 /* create and initialize a linked list for storing column indices of the active row k */ 2843 nlnk = am + 1; 2844 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2845 2846 /* initial FreeSpace size is fill*(ai[am]+1) */ 2847 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2848 current_space = free_space; 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 = riip[*(aj + ai[rip[k]] + j)]; 2858 if (i >= k){ /* only take upper triangular entry */ 2859 cols[ncols_upper] = i; 2860 ncols_upper++; 2861 } 2862 } 2863 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,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 /* merge prow into k-th row */ 2872 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2873 jmax = ui[prow+1]; 2874 ncols = jmax-jmin; 2875 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2876 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2877 nzk += nlnk; 2878 2879 /* update il and jl for prow */ 2880 if (jmin < jmax){ 2881 il[prow] = jmin; 2882 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 2883 } 2884 prow = nextprow; 2885 } 2886 2887 /* if free space is not available, make more free space */ 2888 if (current_space->local_remaining<nzk) { 2889 i = am - k + 1; /* num of unfactored rows */ 2890 i *= PetscMin(nzk,i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2891 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2892 reallocs++; 2893 } 2894 2895 /* copy data into free space, then initialize lnk */ 2896 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 2897 2898 /* add the k-th row into il and jl */ 2899 if (nzk-1 > 0){ 2900 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2901 jl[k] = jl[i]; jl[i] = k; 2902 il[k] = ui[k] + 1; 2903 } 2904 ui_ptr[k] = current_space->array; 2905 current_space->array += nzk; 2906 current_space->local_used += nzk; 2907 current_space->local_remaining -= nzk; 2908 2909 ui[k+1] = ui[k] + nzk; 2910 } 2911 2912 #if defined(PETSC_USE_INFO) 2913 if (ai[am] != 0) { 2914 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 2915 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2916 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2917 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2918 } else { 2919 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2920 } 2921 #endif 2922 2923 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2924 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2925 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 2926 2927 /* destroy list of free space and other temporary array(s) */ 2928 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2929 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor in newdatastruct */ 2930 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2931 2932 /* put together the new matrix in MATSEQSBAIJ format */ 2933 2934 b = (Mat_SeqSBAIJ*)(fact)->data; 2935 b->singlemalloc = PETSC_FALSE; 2936 b->free_a = PETSC_TRUE; 2937 b->free_ij = PETSC_TRUE; 2938 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2939 b->j = uj; 2940 b->i = ui; 2941 b->diag = udiag; 2942 b->free_diag = PETSC_TRUE; 2943 b->ilen = 0; 2944 b->imax = 0; 2945 b->row = perm; 2946 b->col = perm; 2947 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2948 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2949 b->icol = iperm; 2950 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2951 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2952 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2953 b->maxnz = b->nz = ui[am]; 2954 2955 (fact)->info.factor_mallocs = reallocs; 2956 (fact)->info.fill_ratio_given = fill; 2957 if (ai[am] != 0) { 2958 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2959 } else { 2960 (fact)->info.fill_ratio_needed = 0.0; 2961 } 2962 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct; 2963 PetscFunctionReturn(0); 2964 } 2965 2966 #undef __FUNCT__ 2967 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ" 2968 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2969 { 2970 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2971 Mat_SeqSBAIJ *b; 2972 PetscErrorCode ierr; 2973 PetscTruth perm_identity; 2974 PetscReal fill = info->fill; 2975 const PetscInt *rip,*riip; 2976 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2977 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2978 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr; 2979 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2980 PetscBT lnkbt; 2981 IS iperm; 2982 PetscTruth newdatastruct=PETSC_FALSE; 2983 2984 PetscFunctionBegin; 2985 ierr = PetscOptionsGetTruth(PETSC_NULL,"-cholesky_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 2986 if(newdatastruct){ 2987 ierr = MatCholeskyFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr); 2988 PetscFunctionReturn(0); 2989 } 2990 2991 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); 2992 /* check whether perm is the identity mapping */ 2993 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2994 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2995 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2996 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2997 2998 /* initialization */ 2999 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 3000 ui[0] = 0; 3001 3002 /* jl: linked list for storing indices of the pivot rows 3003 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 3004 ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr); 3005 for (i=0; i<am; i++){ 3006 jl[i] = am; il[i] = 0; 3007 } 3008 3009 /* create and initialize a linked list for storing column indices of the active row k */ 3010 nlnk = am + 1; 3011 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3012 3013 /* initial FreeSpace size is fill*(ai[am]+1) */ 3014 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 3015 current_space = free_space; 3016 3017 for (k=0; k<am; k++){ /* for each active row k */ 3018 /* initialize lnk by the column indices of row rip[k] of A */ 3019 nzk = 0; 3020 ncols = ai[rip[k]+1] - ai[rip[k]]; 3021 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 3022 ncols_upper = 0; 3023 for (j=0; j<ncols; j++){ 3024 i = riip[*(aj + ai[rip[k]] + j)]; 3025 if (i >= k){ /* only take upper triangular entry */ 3026 cols[ncols_upper] = i; 3027 ncols_upper++; 3028 } 3029 } 3030 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3031 nzk += nlnk; 3032 3033 /* update lnk by computing fill-in for each pivot row to be merged in */ 3034 prow = jl[k]; /* 1st pivot row */ 3035 3036 while (prow < k){ 3037 nextprow = jl[prow]; 3038 /* merge prow into k-th row */ 3039 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 3040 jmax = ui[prow+1]; 3041 ncols = jmax-jmin; 3042 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 3043 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3044 nzk += nlnk; 3045 3046 /* update il and jl for prow */ 3047 if (jmin < jmax){ 3048 il[prow] = jmin; 3049 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 3050 } 3051 prow = nextprow; 3052 } 3053 3054 /* if free space is not available, make more free space */ 3055 if (current_space->local_remaining<nzk) { 3056 i = am - k + 1; /* num of unfactored rows */ 3057 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 3058 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 3059 reallocs++; 3060 } 3061 3062 /* copy data into free space, then initialize lnk */ 3063 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 3064 3065 /* add the k-th row into il and jl */ 3066 if (nzk-1 > 0){ 3067 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 3068 jl[k] = jl[i]; jl[i] = k; 3069 il[k] = ui[k] + 1; 3070 } 3071 ui_ptr[k] = current_space->array; 3072 current_space->array += nzk; 3073 current_space->local_used += nzk; 3074 current_space->local_remaining -= nzk; 3075 3076 ui[k+1] = ui[k] + nzk; 3077 } 3078 3079 #if defined(PETSC_USE_INFO) 3080 if (ai[am] != 0) { 3081 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 3082 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 3083 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 3084 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 3085 } else { 3086 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 3087 } 3088 #endif 3089 3090 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 3091 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 3092 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 3093 3094 /* destroy list of free space and other temporary array(s) */ 3095 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 3096 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 3097 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3098 3099 /* put together the new matrix in MATSEQSBAIJ format */ 3100 3101 b = (Mat_SeqSBAIJ*)(fact)->data; 3102 b->singlemalloc = PETSC_FALSE; 3103 b->free_a = PETSC_TRUE; 3104 b->free_ij = PETSC_TRUE; 3105 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 3106 b->j = uj; 3107 b->i = ui; 3108 b->diag = 0; 3109 b->ilen = 0; 3110 b->imax = 0; 3111 b->row = perm; 3112 b->col = perm; 3113 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3114 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3115 b->icol = iperm; 3116 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 3117 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 3118 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3119 b->maxnz = b->nz = ui[am]; 3120 3121 (fact)->info.factor_mallocs = reallocs; 3122 (fact)->info.fill_ratio_given = fill; 3123 if (ai[am] != 0) { 3124 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 3125 } else { 3126 (fact)->info.fill_ratio_needed = 0.0; 3127 } 3128 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 3129 PetscFunctionReturn(0); 3130 } 3131 3132 #undef __FUNCT__ 3133 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct" 3134 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx) 3135 { 3136 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3137 PetscErrorCode ierr; 3138 PetscInt n = A->rmap->n; 3139 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag,*vi; 3140 PetscScalar *x,sum; 3141 const PetscScalar *b; 3142 const MatScalar *aa = a->a,*v; 3143 PetscInt i,nz; 3144 3145 PetscFunctionBegin; 3146 if (!n) PetscFunctionReturn(0); 3147 3148 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3149 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3150 3151 /* forward solve the lower triangular */ 3152 x[0] = b[0]; 3153 v = aa; 3154 vi = aj; 3155 for (i=1; i<n; i++) { 3156 nz = ai[i+1] - ai[i]; 3157 sum = b[i]; 3158 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3159 v += nz; 3160 vi += nz; 3161 x[i] = sum; 3162 } 3163 3164 /* backward solve the upper triangular */ 3165 for (i=n-1; i>=0; i--){ 3166 v = aa + adiag[i+1] + 1; 3167 vi = aj + adiag[i+1] + 1; 3168 nz = adiag[i] - adiag[i+1]-1; 3169 sum = x[i]; 3170 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3171 x[i] = sum*v[nz]; /* x[i]=aa[adiag[i]]*sum; v++; */ 3172 } 3173 3174 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 3175 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3176 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3177 PetscFunctionReturn(0); 3178 } 3179 3180 #undef __FUNCT__ 3181 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct" 3182 PetscErrorCode MatSolve_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx) 3183 { 3184 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3185 IS iscol = a->col,isrow = a->row; 3186 PetscErrorCode ierr; 3187 PetscInt i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz; 3188 const PetscInt *rout,*cout,*r,*c; 3189 PetscScalar *x,*tmp,sum; 3190 const PetscScalar *b; 3191 const MatScalar *aa = a->a,*v; 3192 3193 PetscFunctionBegin; 3194 if (!n) PetscFunctionReturn(0); 3195 3196 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3197 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3198 tmp = a->solve_work; 3199 3200 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 3201 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 3202 3203 /* forward solve the lower triangular */ 3204 tmp[0] = b[r[0]]; 3205 v = aa; 3206 vi = aj; 3207 for (i=1; i<n; i++) { 3208 nz = ai[i+1] - ai[i]; 3209 sum = b[r[i]]; 3210 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3211 tmp[i] = sum; 3212 v += nz; vi += nz; 3213 } 3214 3215 /* backward solve the upper triangular */ 3216 for (i=n-1; i>=0; i--){ 3217 v = aa + adiag[i+1]+1; 3218 vi = aj + adiag[i+1]+1; 3219 nz = adiag[i]-adiag[i+1]-1; 3220 sum = tmp[i]; 3221 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3222 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 3223 } 3224 3225 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 3226 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 3227 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3228 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3229 ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr); 3230 PetscFunctionReturn(0); 3231 } 3232 3233 #undef __FUNCT__ 3234 #define __FUNCT__ "MatILUDTFactor_SeqAIJ" 3235 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact) 3236 { 3237 Mat B = *fact; 3238 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b; 3239 IS isicol; 3240 PetscErrorCode ierr; 3241 const PetscInt *r,*ic; 3242 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag; 3243 PetscInt *bi,*bj,*bdiag,*bdiag_rev; 3244 PetscInt row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au; 3245 PetscInt nlnk,*lnk; 3246 PetscBT lnkbt; 3247 PetscTruth row_identity,icol_identity,both_identity; 3248 MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp; 3249 const PetscInt *ics; 3250 PetscInt j,nz,*pj,*bjtmp,k,ncut,*jtmp; 3251 PetscReal dt=info->dt,dtcol=info->dtcol,shift=info->shiftinblocks; 3252 PetscInt dtcount=(PetscInt)info->dtcount,nnz_max; 3253 PetscTruth missing; 3254 3255 PetscFunctionBegin; 3256 3257 if (dt == PETSC_DEFAULT) dt = 0.005; 3258 if (dtcol == PETSC_DEFAULT) dtcol = 0.01; /* XXX unused! */ 3259 if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax); 3260 3261 /* ------- symbolic factorization, can be reused ---------*/ 3262 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 3263 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 3264 adiag=a->diag; 3265 3266 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 3267 3268 /* bdiag is location of diagonal in factor */ 3269 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); /* becomes b->diag */ 3270 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag_rev);CHKERRQ(ierr); /* temporary */ 3271 3272 /* allocate row pointers bi */ 3273 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 3274 3275 /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */ 3276 if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */ 3277 nnz_max = ai[n]+2*n*dtcount+2; 3278 3279 ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 3280 ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr); 3281 3282 /* put together the new matrix */ 3283 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 3284 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 3285 b = (Mat_SeqAIJ*)(B)->data; 3286 b->free_a = PETSC_TRUE; 3287 b->free_ij = PETSC_TRUE; 3288 b->singlemalloc = PETSC_FALSE; 3289 b->a = ba; 3290 b->j = bj; 3291 b->i = bi; 3292 b->diag = bdiag; 3293 b->ilen = 0; 3294 b->imax = 0; 3295 b->row = isrow; 3296 b->col = iscol; 3297 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 3298 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 3299 b->icol = isicol; 3300 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 3301 3302 ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3303 b->maxnz = nnz_max; 3304 3305 (B)->factor = MAT_FACTOR_ILUDT; 3306 (B)->info.factor_mallocs = 0; 3307 (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]); 3308 CHKMEMQ; 3309 /* ------- end of symbolic factorization ---------*/ 3310 3311 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3312 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3313 ics = ic; 3314 3315 /* linked list for storing column indices of the active row */ 3316 nlnk = n + 1; 3317 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3318 3319 /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */ 3320 ierr = PetscMalloc2(n,PetscInt,&im,n,PetscInt,&jtmp);CHKERRQ(ierr); 3321 /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */ 3322 ierr = PetscMalloc2(n,MatScalar,&rtmp,n,MatScalar,&vtmp);CHKERRQ(ierr); 3323 ierr = PetscMemzero(rtmp,n*sizeof(MatScalar));CHKERRQ(ierr); 3324 3325 bi[0] = 0; 3326 bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */ 3327 bdiag_rev[n] = bdiag[0]; 3328 bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */ 3329 for (i=0; i<n; i++) { 3330 /* copy initial fill into linked list */ 3331 nzi = 0; /* nonzeros for active row i */ 3332 nzi = ai[r[i]+1] - ai[r[i]]; 3333 if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 3334 nzi_al = adiag[r[i]] - ai[r[i]]; 3335 nzi_au = ai[r[i]+1] - adiag[r[i]] -1; 3336 ajtmp = aj + ai[r[i]]; 3337 ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3338 3339 /* load in initial (unfactored row) */ 3340 aatmp = a->a + ai[r[i]]; 3341 for (j=0; j<nzi; j++) { 3342 rtmp[ics[*ajtmp++]] = *aatmp++; 3343 } 3344 3345 /* add pivot rows into linked list */ 3346 row = lnk[n]; 3347 while (row < i ) { 3348 nzi_bl = bi[row+1] - bi[row] + 1; 3349 bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */ 3350 ierr = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr); 3351 nzi += nlnk; 3352 row = lnk[row]; 3353 } 3354 3355 /* copy data from lnk into jtmp, then initialize lnk */ 3356 ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr); 3357 3358 /* numerical factorization */ 3359 bjtmp = jtmp; 3360 row = *bjtmp++; /* 1st pivot row */ 3361 while ( row < i ) { 3362 pc = rtmp + row; 3363 pv = ba + bdiag[row]; /* 1./(diag of the pivot row) */ 3364 multiplier = (*pc) * (*pv); 3365 *pc = multiplier; 3366 if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */ 3367 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3368 pv = ba + bdiag[row+1] + 1; 3369 /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */ 3370 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3371 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3372 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 3373 } 3374 row = *bjtmp++; 3375 } 3376 3377 /* copy sparse rtmp into contiguous vtmp; separate L and U part */ 3378 diag_tmp = rtmp[i]; /* save diagonal value - may not needed?? */ 3379 nzi_bl = 0; j = 0; 3380 while (jtmp[j] < i){ /* Note: jtmp is sorted */ 3381 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3382 nzi_bl++; j++; 3383 } 3384 nzi_bu = nzi - nzi_bl -1; 3385 while (j < nzi){ 3386 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3387 j++; 3388 } 3389 3390 bjtmp = bj + bi[i]; 3391 batmp = ba + bi[i]; 3392 /* apply level dropping rule to L part */ 3393 ncut = nzi_al + dtcount; 3394 if (ncut < nzi_bl){ 3395 ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr); 3396 ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr); 3397 } else { 3398 ncut = nzi_bl; 3399 } 3400 for (j=0; j<ncut; j++){ 3401 bjtmp[j] = jtmp[j]; 3402 batmp[j] = vtmp[j]; 3403 /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */ 3404 } 3405 bi[i+1] = bi[i] + ncut; 3406 nzi = ncut + 1; 3407 3408 /* apply level dropping rule to U part */ 3409 ncut = nzi_au + dtcount; 3410 if (ncut < nzi_bu){ 3411 ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr); 3412 ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr); 3413 } else { 3414 ncut = nzi_bu; 3415 } 3416 nzi += ncut; 3417 3418 /* mark bdiagonal */ 3419 bdiag[i+1] = bdiag[i] - (ncut + 1); 3420 bdiag_rev[n-i-1] = bdiag[i+1]; 3421 bi[2*n - i] = bi[2*n - i +1] - (ncut + 1); 3422 bjtmp = bj + bdiag[i]; 3423 batmp = ba + bdiag[i]; 3424 *bjtmp = i; 3425 *batmp = diag_tmp; /* rtmp[i]; */ 3426 if (*batmp == 0.0) { 3427 *batmp = dt+shift; 3428 /* printf(" row %d add shift %g\n",i,shift); */ 3429 } 3430 *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */ 3431 /* printf(" (%d,%g),",*bjtmp,*batmp); */ 3432 3433 bjtmp = bj + bdiag[i+1]+1; 3434 batmp = ba + bdiag[i+1]+1; 3435 for (k=0; k<ncut; k++){ 3436 bjtmp[k] = jtmp[nzi_bl+1+k]; 3437 batmp[k] = vtmp[nzi_bl+1+k]; 3438 /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */ 3439 } 3440 /* printf("\n"); */ 3441 3442 im[i] = nzi; /* used by PetscLLAddSortedLU() */ 3443 /* 3444 printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]); 3445 printf(" ----------------------------\n"); 3446 */ 3447 } /* for (i=0; i<n; i++) */ 3448 /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */ 3449 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]); 3450 3451 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3452 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3453 3454 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3455 ierr = PetscFree2(im,jtmp);CHKERRQ(ierr); 3456 ierr = PetscFree2(rtmp,vtmp);CHKERRQ(ierr); 3457 ierr = PetscFree(bdiag_rev);CHKERRQ(ierr); 3458 3459 ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr); 3460 b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n]; 3461 3462 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3463 ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr); 3464 both_identity = (PetscTruth) (row_identity && icol_identity); 3465 if (row_identity && icol_identity) { 3466 B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct; 3467 } else { 3468 B->ops->solve = MatSolve_SeqAIJ_newdatastruct; 3469 } 3470 3471 B->ops->lufactorsymbolic = MatILUDTFactorSymbolic_SeqAIJ; 3472 B->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ; 3473 B->ops->solveadd = 0; 3474 B->ops->solvetranspose = 0; 3475 B->ops->solvetransposeadd = 0; 3476 B->ops->matsolve = 0; 3477 B->assembled = PETSC_TRUE; 3478 B->preallocated = PETSC_TRUE; 3479 PetscFunctionReturn(0); 3480 } 3481 3482 /* a wraper of MatILUDTFactor_SeqAIJ() */ 3483 #undef __FUNCT__ 3484 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ" 3485 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info) 3486 { 3487 PetscErrorCode ierr; 3488 3489 PetscFunctionBegin; 3490 ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr); 3491 3492 fact->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ; 3493 PetscFunctionReturn(0); 3494 } 3495 3496 /* 3497 same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors 3498 - intend to replace existing MatLUFactorNumeric_SeqAIJ() 3499 */ 3500 #undef __FUNCT__ 3501 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ" 3502 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info) 3503 { 3504 Mat C=fact; 3505 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 3506 IS isrow = b->row,isicol = b->icol; 3507 PetscErrorCode ierr; 3508 const PetscInt *r,*ic,*ics; 3509 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 3510 PetscInt *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj; 3511 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 3512 PetscReal dt=info->dt,shift=info->shiftinblocks; 3513 PetscTruth row_identity, col_identity; 3514 3515 PetscFunctionBegin; 3516 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3517 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3518 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 3519 ics = ic; 3520 3521 for (i=0; i<n; i++){ 3522 /* initialize rtmp array */ 3523 nzl = bi[i+1] - bi[i]; /* num of nozeros in L(i,:) */ 3524 bjtmp = bj + bi[i]; 3525 for (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0; 3526 rtmp[i] = 0.0; 3527 nzu = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */ 3528 bjtmp = bj + bdiag[i+1] + 1; 3529 for (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0; 3530 3531 /* load in initial unfactored row of A */ 3532 /* printf("row %d\n",i); */ 3533 nz = ai[r[i]+1] - ai[r[i]]; 3534 ajtmp = aj + ai[r[i]]; 3535 v = aa + ai[r[i]]; 3536 for (j=0; j<nz; j++) { 3537 rtmp[ics[*ajtmp++]] = v[j]; 3538 /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */ 3539 } 3540 /* printf("\n"); */ 3541 3542 /* numerical factorization */ 3543 bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */ 3544 nzl = bi[i+1] - bi[i]; /* num of entries in L(i,:) */ 3545 k = 0; 3546 while (k < nzl){ 3547 row = *bjtmp++; 3548 /* printf(" prow %d\n",row); */ 3549 pc = rtmp + row; 3550 pv = b->a + bdiag[row]; /* 1./(diag of the pivot row) */ 3551 multiplier = (*pc) * (*pv); 3552 *pc = multiplier; 3553 if (PetscAbsScalar(multiplier) > dt){ 3554 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3555 pv = b->a + bdiag[row+1] + 1; 3556 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3557 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3558 /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */ 3559 } 3560 k++; 3561 } 3562 3563 /* finished row so stick it into b->a */ 3564 /* L-part */ 3565 pv = b->a + bi[i] ; 3566 pj = bj + bi[i] ; 3567 nzl = bi[i+1] - bi[i]; 3568 for (j=0; j<nzl; j++) { 3569 pv[j] = rtmp[pj[j]]; 3570 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3571 } 3572 3573 /* diagonal: invert diagonal entries for simplier triangular solves */ 3574 if (rtmp[i] == 0.0) rtmp[i] = dt+shift; 3575 b->a[bdiag[i]] = 1.0/rtmp[i]; 3576 /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */ 3577 3578 /* U-part */ 3579 pv = b->a + bdiag[i+1] + 1; 3580 pj = bj + bdiag[i+1] + 1; 3581 nzu = bdiag[i] - bdiag[i+1] - 1; 3582 for (j=0; j<nzu; j++) { 3583 pv[j] = rtmp[pj[j]]; 3584 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3585 } 3586 /* printf("\n"); */ 3587 } 3588 3589 ierr = PetscFree(rtmp);CHKERRQ(ierr); 3590 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3591 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3592 3593 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3594 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 3595 if (row_identity && col_identity) { 3596 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct; 3597 } else { 3598 C->ops->solve = MatSolve_SeqAIJ_newdatastruct; 3599 } 3600 C->ops->solveadd = 0; 3601 C->ops->solvetranspose = 0; 3602 C->ops->solvetransposeadd = 0; 3603 C->ops->matsolve = 0; 3604 C->assembled = PETSC_TRUE; 3605 C->preallocated = PETSC_TRUE; 3606 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 3607 PetscFunctionReturn(0); 3608 } 3609