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