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