1 2 #include <../src/mat/impls/aij/seq/aij.h> 3 #include <../src/mat/impls/sbaij/seq/sbaij.h> 4 #include <petscbt.h> 5 #include <../src/mat/utils/freespace.h> 6 7 /* 8 Computes an ordering to get most of the large numerical values in the lower triangular part of the matrix 9 10 This code does not work and is not called anywhere. It would be registered with MatOrderingRegisterAll() 11 */ 12 PetscErrorCode MatGetOrdering_Flow_SeqAIJ(Mat mat,MatOrderingType type,IS *irow,IS *icol) 13 { 14 Mat_SeqAIJ *a = (Mat_SeqAIJ*)mat->data; 15 PetscErrorCode ierr; 16 PetscInt i,j,jj,k, kk,n = mat->rmap->n, current = 0, newcurrent = 0,*order; 17 const PetscInt *ai = a->i, *aj = a->j; 18 const PetscScalar *aa = a->a; 19 PetscBool *done; 20 PetscReal best,past = 0,future; 21 22 PetscFunctionBegin; 23 /* pick initial row */ 24 best = -1; 25 for (i=0; i<n; i++) { 26 future = 0.0; 27 for (j=ai[i]; j<ai[i+1]; j++) { 28 if (aj[j] != i) future += PetscAbsScalar(aa[j]); 29 else past = PetscAbsScalar(aa[j]); 30 } 31 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 32 if (past/future > best) { 33 best = past/future; 34 current = i; 35 } 36 } 37 38 ierr = PetscMalloc1(n,&done);CHKERRQ(ierr); 39 ierr = PetscArrayzero(done,n);CHKERRQ(ierr); 40 ierr = PetscMalloc1(n,&order);CHKERRQ(ierr); 41 order[0] = current; 42 for (i=0; i<n-1; i++) { 43 done[current] = PETSC_TRUE; 44 best = -1; 45 /* loop over all neighbors of current pivot */ 46 for (j=ai[current]; j<ai[current+1]; j++) { 47 jj = aj[j]; 48 if (done[jj]) continue; 49 /* loop over columns of potential next row computing weights for below and above diagonal */ 50 past = future = 0.0; 51 for (k=ai[jj]; k<ai[jj+1]; k++) { 52 kk = aj[k]; 53 if (done[kk]) past += PetscAbsScalar(aa[k]); 54 else if (kk != jj) future += PetscAbsScalar(aa[k]); 55 } 56 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 57 if (past/future > best) { 58 best = past/future; 59 newcurrent = jj; 60 } 61 } 62 if (best == -1) { /* no neighbors to select from so select best of all that remain */ 63 best = -1; 64 for (k=0; k<n; k++) { 65 if (done[k]) continue; 66 future = 0.0; 67 past = 0.0; 68 for (j=ai[k]; j<ai[k+1]; j++) { 69 kk = aj[j]; 70 if (done[kk]) past += PetscAbsScalar(aa[j]); 71 else if (kk != k) future += PetscAbsScalar(aa[j]); 72 } 73 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 74 if (past/future > best) { 75 best = past/future; 76 newcurrent = k; 77 } 78 } 79 } 80 if (current == newcurrent) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"newcurrent cannot be current"); 81 current = newcurrent; 82 order[i+1] = current; 83 } 84 ierr = ISCreateGeneral(PETSC_COMM_SELF,n,order,PETSC_COPY_VALUES,irow);CHKERRQ(ierr); 85 *icol = *irow; 86 ierr = PetscObjectReference((PetscObject)*irow);CHKERRQ(ierr); 87 ierr = PetscFree(done);CHKERRQ(ierr); 88 ierr = PetscFree(order);CHKERRQ(ierr); 89 PetscFunctionReturn(0); 90 } 91 92 static PetscErrorCode MatFactorGetSolverType_petsc(Mat A,MatSolverType *type) 93 { 94 PetscFunctionBegin; 95 *type = MATSOLVERPETSC; 96 PetscFunctionReturn(0); 97 } 98 99 PETSC_INTERN PetscErrorCode MatGetFactor_seqaij_petsc(Mat A,MatFactorType ftype,Mat *B) 100 { 101 PetscInt n = A->rmap->n; 102 PetscErrorCode ierr; 103 104 PetscFunctionBegin; 105 #if defined(PETSC_USE_COMPLEX) 106 if (A->hermitian && !A->symmetric && (ftype == MAT_FACTOR_CHOLESKY||ftype == MAT_FACTOR_ICC)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Hermitian CHOLESKY or ICC Factor is not supported"); 107 #endif 108 ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr); 109 ierr = MatSetSizes(*B,n,n,n,n);CHKERRQ(ierr); 110 if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT) { 111 ierr = MatSetType(*B,MATSEQAIJ);CHKERRQ(ierr); 112 113 (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJ; 114 (*B)->ops->lufactorsymbolic = MatLUFactorSymbolic_SeqAIJ; 115 116 ierr = MatSetBlockSizesFromMats(*B,A,A);CHKERRQ(ierr); 117 ierr = PetscStrallocpy(MATORDERINGND,(char**)&(*B)->preferredordering[MAT_FACTOR_LU]);CHKERRQ(ierr); 118 ierr = PetscStrallocpy(MATORDERINGNATURAL,(char**)&(*B)->preferredordering[MAT_FACTOR_ILU]);CHKERRQ(ierr); 119 ierr = PetscStrallocpy(MATORDERINGNATURAL,(char**)&(*B)->preferredordering[MAT_FACTOR_ILUDT]);CHKERRQ(ierr); 120 } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) { 121 ierr = MatSetType(*B,MATSEQSBAIJ);CHKERRQ(ierr); 122 ierr = MatSeqSBAIJSetPreallocation(*B,1,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr); 123 124 (*B)->ops->iccfactorsymbolic = MatICCFactorSymbolic_SeqAIJ; 125 (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJ; 126 ierr = PetscStrallocpy(MATORDERINGND,(char**)&(*B)->preferredordering[MAT_FACTOR_CHOLESKY]);CHKERRQ(ierr); 127 ierr = PetscStrallocpy(MATORDERINGNATURAL,(char**)&(*B)->preferredordering[MAT_FACTOR_ICC]);CHKERRQ(ierr); 128 } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor type not supported"); 129 (*B)->factortype = ftype; 130 131 ierr = PetscFree((*B)->solvertype);CHKERRQ(ierr); 132 ierr = PetscStrallocpy(MATSOLVERPETSC,&(*B)->solvertype);CHKERRQ(ierr); 133 (*B)->canuseordering = PETSC_TRUE; 134 ierr = PetscObjectComposeFunction((PetscObject)*B,"MatFactorGetSolverType_C",MatFactorGetSolverType_petsc);CHKERRQ(ierr); 135 PetscFunctionReturn(0); 136 } 137 138 PetscErrorCode MatLUFactorSymbolic_SeqAIJ_inplace(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 139 { 140 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 141 IS isicol; 142 PetscErrorCode ierr; 143 const PetscInt *r,*ic; 144 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j; 145 PetscInt *bi,*bj,*ajtmp; 146 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 147 PetscReal f; 148 PetscInt nlnk,*lnk,k,**bi_ptr; 149 PetscFreeSpaceList free_space=NULL,current_space=NULL; 150 PetscBT lnkbt; 151 PetscBool missing; 152 153 PetscFunctionBegin; 154 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"matrix must be square"); 155 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 156 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 157 158 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 159 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 160 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 161 162 /* get new row pointers */ 163 ierr = PetscMalloc1(n+1,&bi);CHKERRQ(ierr); 164 bi[0] = 0; 165 166 /* bdiag is location of diagonal in factor */ 167 ierr = PetscMalloc1(n+1,&bdiag);CHKERRQ(ierr); 168 bdiag[0] = 0; 169 170 /* linked list for storing column indices of the active row */ 171 nlnk = n + 1; 172 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 173 174 ierr = PetscMalloc2(n+1,&bi_ptr,n+1,&im);CHKERRQ(ierr); 175 176 /* initial FreeSpace size is f*(ai[n]+1) */ 177 f = info->fill; 178 if (n==1) f = 1; /* prevent failure in corner case of 1x1 matrix with fill < 0.5 */ 179 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space);CHKERRQ(ierr); 180 current_space = free_space; 181 182 for (i=0; i<n; i++) { 183 /* copy previous fill into linked list */ 184 nzi = 0; 185 nnz = ai[r[i]+1] - ai[r[i]]; 186 ajtmp = aj + ai[r[i]]; 187 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 188 nzi += nlnk; 189 190 /* add pivot rows into linked list */ 191 row = lnk[n]; 192 while (row < i) { 193 nzbd = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */ 194 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 195 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 196 nzi += nlnk; 197 row = lnk[row]; 198 } 199 bi[i+1] = bi[i] + nzi; 200 im[i] = nzi; 201 202 /* mark bdiag */ 203 nzbd = 0; 204 nnz = nzi; 205 k = lnk[n]; 206 while (nnz-- && k < i) { 207 nzbd++; 208 k = lnk[k]; 209 } 210 bdiag[i] = bi[i] + nzbd; 211 212 /* if free space is not available, make more free space */ 213 if (current_space->local_remaining<nzi) { 214 nnz = PetscIntMultTruncate(n - i,nzi); /* estimated and max additional space needed */ 215 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 216 reallocs++; 217 } 218 219 /* copy data into free space, then initialize lnk */ 220 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 221 222 bi_ptr[i] = current_space->array; 223 current_space->array += nzi; 224 current_space->local_used += nzi; 225 current_space->local_remaining -= nzi; 226 } 227 #if defined(PETSC_USE_INFO) 228 if (ai[n] != 0) { 229 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 230 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);CHKERRQ(ierr); 231 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 232 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g);\n",(double)af);CHKERRQ(ierr); 233 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 234 } else { 235 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 236 } 237 #endif 238 239 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 240 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 241 242 /* destroy list of free space and other temporary array(s) */ 243 ierr = PetscMalloc1(bi[n]+1,&bj);CHKERRQ(ierr); 244 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); 245 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 246 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 247 248 /* put together the new matrix */ 249 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr); 250 ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)isicol);CHKERRQ(ierr); 251 b = (Mat_SeqAIJ*)(B)->data; 252 253 b->free_a = PETSC_TRUE; 254 b->free_ij = PETSC_TRUE; 255 b->singlemalloc = PETSC_FALSE; 256 257 ierr = PetscMalloc1(bi[n]+1,&b->a);CHKERRQ(ierr); 258 b->j = bj; 259 b->i = bi; 260 b->diag = bdiag; 261 b->ilen = NULL; 262 b->imax = NULL; 263 b->row = isrow; 264 b->col = iscol; 265 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 266 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 267 b->icol = isicol; 268 ierr = PetscMalloc1(n+1,&b->solve_work);CHKERRQ(ierr); 269 270 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 271 ierr = PetscLogObjectMemory((PetscObject)B,(bi[n]-n)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 272 b->maxnz = b->nz = bi[n]; 273 274 (B)->factortype = MAT_FACTOR_LU; 275 (B)->info.factor_mallocs = reallocs; 276 (B)->info.fill_ratio_given = f; 277 278 if (ai[n]) { 279 (B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 280 } else { 281 (B)->info.fill_ratio_needed = 0.0; 282 } 283 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace; 284 if (a->inode.size) { 285 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace; 286 } 287 PetscFunctionReturn(0); 288 } 289 290 PetscErrorCode MatLUFactorSymbolic_SeqAIJ(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 291 { 292 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 293 IS isicol; 294 PetscErrorCode ierr; 295 const PetscInt *r,*ic,*ai=a->i,*aj=a->j,*ajtmp; 296 PetscInt i,n=A->rmap->n; 297 PetscInt *bi,*bj; 298 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 299 PetscReal f; 300 PetscInt nlnk,*lnk,k,**bi_ptr; 301 PetscFreeSpaceList free_space=NULL,current_space=NULL; 302 PetscBT lnkbt; 303 PetscBool missing; 304 305 PetscFunctionBegin; 306 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"matrix must be square"); 307 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 308 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 309 310 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 311 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 312 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 313 314 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 315 ierr = PetscMalloc1(n+1,&bi);CHKERRQ(ierr); 316 ierr = PetscMalloc1(n+1,&bdiag);CHKERRQ(ierr); 317 bi[0] = bdiag[0] = 0; 318 319 /* linked list for storing column indices of the active row */ 320 nlnk = n + 1; 321 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 322 323 ierr = PetscMalloc2(n+1,&bi_ptr,n+1,&im);CHKERRQ(ierr); 324 325 /* initial FreeSpace size is f*(ai[n]+1) */ 326 f = info->fill; 327 if (n==1) f = 1; /* prevent failure in corner case of 1x1 matrix with fill < 0.5 */ 328 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space);CHKERRQ(ierr); 329 current_space = free_space; 330 331 for (i=0; i<n; i++) { 332 /* copy previous fill into linked list */ 333 nzi = 0; 334 nnz = ai[r[i]+1] - ai[r[i]]; 335 ajtmp = aj + ai[r[i]]; 336 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 337 nzi += nlnk; 338 339 /* add pivot rows into linked list */ 340 row = lnk[n]; 341 while (row < i) { 342 nzbd = bdiag[row] + 1; /* num of entries in the row with column index <= row */ 343 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 344 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 345 nzi += nlnk; 346 row = lnk[row]; 347 } 348 bi[i+1] = bi[i] + nzi; 349 im[i] = nzi; 350 351 /* mark bdiag */ 352 nzbd = 0; 353 nnz = nzi; 354 k = lnk[n]; 355 while (nnz-- && k < i) { 356 nzbd++; 357 k = lnk[k]; 358 } 359 bdiag[i] = nzbd; /* note: bdiag[i] = nnzL as input for PetscFreeSpaceContiguous_LU() */ 360 361 /* if free space is not available, make more free space */ 362 if (current_space->local_remaining<nzi) { 363 /* estimated additional space needed */ 364 nnz = PetscIntMultTruncate(2,PetscIntMultTruncate(n-1,nzi)); 365 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 366 reallocs++; 367 } 368 369 /* copy data into free space, then initialize lnk */ 370 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 371 372 bi_ptr[i] = current_space->array; 373 current_space->array += nzi; 374 current_space->local_used += nzi; 375 current_space->local_remaining -= nzi; 376 } 377 378 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 379 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 380 381 /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */ 382 ierr = PetscMalloc1(bi[n]+1,&bj);CHKERRQ(ierr); 383 ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 384 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 385 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 386 387 /* put together the new matrix */ 388 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr); 389 ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)isicol);CHKERRQ(ierr); 390 b = (Mat_SeqAIJ*)(B)->data; 391 392 b->free_a = PETSC_TRUE; 393 b->free_ij = PETSC_TRUE; 394 b->singlemalloc = PETSC_FALSE; 395 396 ierr = PetscMalloc1(bdiag[0]+1,&b->a);CHKERRQ(ierr); 397 398 b->j = bj; 399 b->i = bi; 400 b->diag = bdiag; 401 b->ilen = NULL; 402 b->imax = NULL; 403 b->row = isrow; 404 b->col = iscol; 405 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 406 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 407 b->icol = isicol; 408 ierr = PetscMalloc1(n+1,&b->solve_work);CHKERRQ(ierr); 409 410 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 411 ierr = PetscLogObjectMemory((PetscObject)B,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 412 b->maxnz = b->nz = bdiag[0]+1; 413 414 B->factortype = MAT_FACTOR_LU; 415 B->info.factor_mallocs = reallocs; 416 B->info.fill_ratio_given = f; 417 418 if (ai[n]) { 419 B->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 420 } else { 421 B->info.fill_ratio_needed = 0.0; 422 } 423 #if defined(PETSC_USE_INFO) 424 if (ai[n] != 0) { 425 PetscReal af = B->info.fill_ratio_needed; 426 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);CHKERRQ(ierr); 427 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 428 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g);\n",(double)af);CHKERRQ(ierr); 429 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 430 } else { 431 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 432 } 433 #endif 434 B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 435 if (a->inode.size) { 436 B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode; 437 } 438 ierr = MatSeqAIJCheckInode_FactorLU(B);CHKERRQ(ierr); 439 PetscFunctionReturn(0); 440 } 441 442 /* 443 Trouble in factorization, should we dump the original matrix? 444 */ 445 PetscErrorCode MatFactorDumpMatrix(Mat A) 446 { 447 PetscErrorCode ierr; 448 PetscBool flg = PETSC_FALSE; 449 450 PetscFunctionBegin; 451 ierr = PetscOptionsGetBool(((PetscObject)A)->options,NULL,"-mat_factor_dump_on_error",&flg,NULL);CHKERRQ(ierr); 452 if (flg) { 453 PetscViewer viewer; 454 char filename[PETSC_MAX_PATH_LEN]; 455 456 ierr = PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);CHKERRQ(ierr); 457 ierr = PetscViewerBinaryOpen(PetscObjectComm((PetscObject)A),filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr); 458 ierr = MatView(A,viewer);CHKERRQ(ierr); 459 ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr); 460 } 461 PetscFunctionReturn(0); 462 } 463 464 PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 465 { 466 Mat C =B; 467 Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)C->data; 468 IS isrow = b->row,isicol = b->icol; 469 PetscErrorCode ierr; 470 const PetscInt *r,*ic,*ics; 471 const PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bdiag=b->diag; 472 PetscInt i,j,k,nz,nzL,row,*pj; 473 const PetscInt *ajtmp,*bjtmp; 474 MatScalar *rtmp,*pc,multiplier,*pv; 475 const MatScalar *aa=a->a,*v; 476 PetscBool row_identity,col_identity; 477 FactorShiftCtx sctx; 478 const PetscInt *ddiag; 479 PetscReal rs; 480 MatScalar d; 481 482 PetscFunctionBegin; 483 /* MatPivotSetUp(): initialize shift context sctx */ 484 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 485 486 if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 487 ddiag = a->diag; 488 sctx.shift_top = info->zeropivot; 489 for (i=0; i<n; i++) { 490 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 491 d = (aa)[ddiag[i]]; 492 rs = -PetscAbsScalar(d) - PetscRealPart(d); 493 v = aa+ai[i]; 494 nz = ai[i+1] - ai[i]; 495 for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]); 496 if (rs>sctx.shift_top) sctx.shift_top = rs; 497 } 498 sctx.shift_top *= 1.1; 499 sctx.nshift_max = 5; 500 sctx.shift_lo = 0.; 501 sctx.shift_hi = 1.; 502 } 503 504 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 505 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 506 ierr = PetscMalloc1(n+1,&rtmp);CHKERRQ(ierr); 507 ics = ic; 508 509 do { 510 sctx.newshift = PETSC_FALSE; 511 for (i=0; i<n; i++) { 512 /* zero rtmp */ 513 /* L part */ 514 nz = bi[i+1] - bi[i]; 515 bjtmp = bj + bi[i]; 516 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 517 518 /* U part */ 519 nz = bdiag[i]-bdiag[i+1]; 520 bjtmp = bj + bdiag[i+1]+1; 521 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 522 523 /* load in initial (unfactored row) */ 524 nz = ai[r[i]+1] - ai[r[i]]; 525 ajtmp = aj + ai[r[i]]; 526 v = aa + ai[r[i]]; 527 for (j=0; j<nz; j++) { 528 rtmp[ics[ajtmp[j]]] = v[j]; 529 } 530 /* ZeropivotApply() */ 531 rtmp[i] += sctx.shift_amount; /* shift the diagonal of the matrix */ 532 533 /* elimination */ 534 bjtmp = bj + bi[i]; 535 row = *bjtmp++; 536 nzL = bi[i+1] - bi[i]; 537 for (k=0; k < nzL; k++) { 538 pc = rtmp + row; 539 if (*pc != 0.0) { 540 pv = b->a + bdiag[row]; 541 multiplier = *pc * (*pv); 542 *pc = multiplier; 543 544 pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */ 545 pv = b->a + bdiag[row+1]+1; 546 nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */ 547 548 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 549 ierr = PetscLogFlops(1+2.0*nz);CHKERRQ(ierr); 550 } 551 row = *bjtmp++; 552 } 553 554 /* finished row so stick it into b->a */ 555 rs = 0.0; 556 /* L part */ 557 pv = b->a + bi[i]; 558 pj = b->j + bi[i]; 559 nz = bi[i+1] - bi[i]; 560 for (j=0; j<nz; j++) { 561 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 562 } 563 564 /* U part */ 565 pv = b->a + bdiag[i+1]+1; 566 pj = b->j + bdiag[i+1]+1; 567 nz = bdiag[i] - bdiag[i+1]-1; 568 for (j=0; j<nz; j++) { 569 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 570 } 571 572 sctx.rs = rs; 573 sctx.pv = rtmp[i]; 574 ierr = MatPivotCheck(B,A,info,&sctx,i);CHKERRQ(ierr); 575 if (sctx.newshift) break; /* break for-loop */ 576 rtmp[i] = sctx.pv; /* sctx.pv might be updated in the case of MAT_SHIFT_INBLOCKS */ 577 578 /* Mark diagonal and invert diagonal for simplier triangular solves */ 579 pv = b->a + bdiag[i]; 580 *pv = 1.0/rtmp[i]; 581 582 } /* endof for (i=0; i<n; i++) { */ 583 584 /* MatPivotRefine() */ 585 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 586 /* 587 * if no shift in this attempt & shifting & started shifting & can refine, 588 * then try lower shift 589 */ 590 sctx.shift_hi = sctx.shift_fraction; 591 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 592 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 593 sctx.newshift = PETSC_TRUE; 594 sctx.nshift++; 595 } 596 } while (sctx.newshift); 597 598 ierr = PetscFree(rtmp);CHKERRQ(ierr); 599 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 600 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 601 602 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 603 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 604 if (b->inode.size) { 605 C->ops->solve = MatSolve_SeqAIJ_Inode; 606 } else if (row_identity && col_identity) { 607 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 608 } else { 609 C->ops->solve = MatSolve_SeqAIJ; 610 } 611 C->ops->solveadd = MatSolveAdd_SeqAIJ; 612 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 613 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 614 C->ops->matsolve = MatMatSolve_SeqAIJ; 615 C->assembled = PETSC_TRUE; 616 C->preallocated = PETSC_TRUE; 617 618 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 619 620 /* MatShiftView(A,info,&sctx) */ 621 if (sctx.nshift) { 622 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 623 ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %g, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,(double)sctx.shift_amount,(double)sctx.shift_fraction,(double)sctx.shift_top);CHKERRQ(ierr); 624 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 625 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 626 } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS) { 627 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %g\n",sctx.nshift,(double)info->shiftamount);CHKERRQ(ierr); 628 } 629 } 630 PetscFunctionReturn(0); 631 } 632 633 PetscErrorCode MatLUFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info) 634 { 635 Mat C =B; 636 Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)C->data; 637 IS isrow = b->row,isicol = b->icol; 638 PetscErrorCode ierr; 639 const PetscInt *r,*ic,*ics; 640 PetscInt nz,row,i,j,n=A->rmap->n,diag; 641 const PetscInt *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 642 const PetscInt *ajtmp,*bjtmp,*diag_offset = b->diag,*pj; 643 MatScalar *pv,*rtmp,*pc,multiplier,d; 644 const MatScalar *v,*aa=a->a; 645 PetscReal rs=0.0; 646 FactorShiftCtx sctx; 647 const PetscInt *ddiag; 648 PetscBool row_identity, col_identity; 649 650 PetscFunctionBegin; 651 /* MatPivotSetUp(): initialize shift context sctx */ 652 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 653 654 if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 655 ddiag = a->diag; 656 sctx.shift_top = info->zeropivot; 657 for (i=0; i<n; i++) { 658 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 659 d = (aa)[ddiag[i]]; 660 rs = -PetscAbsScalar(d) - PetscRealPart(d); 661 v = aa+ai[i]; 662 nz = ai[i+1] - ai[i]; 663 for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]); 664 if (rs>sctx.shift_top) sctx.shift_top = rs; 665 } 666 sctx.shift_top *= 1.1; 667 sctx.nshift_max = 5; 668 sctx.shift_lo = 0.; 669 sctx.shift_hi = 1.; 670 } 671 672 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 673 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 674 ierr = PetscMalloc1(n+1,&rtmp);CHKERRQ(ierr); 675 ics = ic; 676 677 do { 678 sctx.newshift = PETSC_FALSE; 679 for (i=0; i<n; i++) { 680 nz = bi[i+1] - bi[i]; 681 bjtmp = bj + bi[i]; 682 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 683 684 /* load in initial (unfactored row) */ 685 nz = ai[r[i]+1] - ai[r[i]]; 686 ajtmp = aj + ai[r[i]]; 687 v = aa + ai[r[i]]; 688 for (j=0; j<nz; j++) { 689 rtmp[ics[ajtmp[j]]] = v[j]; 690 } 691 rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 692 693 row = *bjtmp++; 694 while (row < i) { 695 pc = rtmp + row; 696 if (*pc != 0.0) { 697 pv = b->a + diag_offset[row]; 698 pj = b->j + diag_offset[row] + 1; 699 multiplier = *pc / *pv++; 700 *pc = multiplier; 701 nz = bi[row+1] - diag_offset[row] - 1; 702 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 703 ierr = PetscLogFlops(1+2.0*nz);CHKERRQ(ierr); 704 } 705 row = *bjtmp++; 706 } 707 /* finished row so stick it into b->a */ 708 pv = b->a + bi[i]; 709 pj = b->j + bi[i]; 710 nz = bi[i+1] - bi[i]; 711 diag = diag_offset[i] - bi[i]; 712 rs = 0.0; 713 for (j=0; j<nz; j++) { 714 pv[j] = rtmp[pj[j]]; 715 rs += PetscAbsScalar(pv[j]); 716 } 717 rs -= PetscAbsScalar(pv[diag]); 718 719 sctx.rs = rs; 720 sctx.pv = pv[diag]; 721 ierr = MatPivotCheck(B,A,info,&sctx,i);CHKERRQ(ierr); 722 if (sctx.newshift) break; 723 pv[diag] = sctx.pv; 724 } 725 726 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 727 /* 728 * if no shift in this attempt & shifting & started shifting & can refine, 729 * then try lower shift 730 */ 731 sctx.shift_hi = sctx.shift_fraction; 732 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 733 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 734 sctx.newshift = PETSC_TRUE; 735 sctx.nshift++; 736 } 737 } while (sctx.newshift); 738 739 /* invert diagonal entries for simplier triangular solves */ 740 for (i=0; i<n; i++) { 741 b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]]; 742 } 743 ierr = PetscFree(rtmp);CHKERRQ(ierr); 744 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 745 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 746 747 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 748 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 749 if (row_identity && col_identity) { 750 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_inplace; 751 } else { 752 C->ops->solve = MatSolve_SeqAIJ_inplace; 753 } 754 C->ops->solveadd = MatSolveAdd_SeqAIJ_inplace; 755 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace; 756 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace; 757 C->ops->matsolve = MatMatSolve_SeqAIJ_inplace; 758 759 C->assembled = PETSC_TRUE; 760 C->preallocated = PETSC_TRUE; 761 762 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,(double)sctx.shift_amount,(double)sctx.shift_fraction,(double)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,(double)sctx.shift_amount);CHKERRQ(ierr); 768 } 769 } 770 (C)->ops->solve = MatSolve_SeqAIJ_inplace; 771 (C)->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace; 772 773 ierr = MatSeqAIJCheckInode(C);CHKERRQ(ierr); 774 PetscFunctionReturn(0); 775 } 776 777 /* 778 This routine implements inplace ILU(0) with row or/and column permutations. 779 Input: 780 A - original matrix 781 Output; 782 A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i] 783 a->j (col index) is permuted by the inverse of colperm, then sorted 784 a->a reordered accordingly with a->j 785 a->diag (ptr to diagonal elements) is updated. 786 */ 787 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info) 788 { 789 Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data; 790 IS isrow = a->row,isicol = a->icol; 791 PetscErrorCode ierr; 792 const PetscInt *r,*ic,*ics; 793 PetscInt i,j,n=A->rmap->n,*ai=a->i,*aj=a->j; 794 PetscInt *ajtmp,nz,row; 795 PetscInt *diag = a->diag,nbdiag,*pj; 796 PetscScalar *rtmp,*pc,multiplier,d; 797 MatScalar *pv,*v; 798 PetscReal rs; 799 FactorShiftCtx sctx; 800 const MatScalar *aa=a->a,*vtmp; 801 802 PetscFunctionBegin; 803 if (A != B) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address"); 804 805 /* MatPivotSetUp(): initialize shift context sctx */ 806 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 807 808 if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 809 const PetscInt *ddiag = a->diag; 810 sctx.shift_top = info->zeropivot; 811 for (i=0; i<n; i++) { 812 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 813 d = (aa)[ddiag[i]]; 814 rs = -PetscAbsScalar(d) - PetscRealPart(d); 815 vtmp = aa+ai[i]; 816 nz = ai[i+1] - ai[i]; 817 for (j=0; j<nz; j++) rs += PetscAbsScalar(vtmp[j]); 818 if (rs>sctx.shift_top) sctx.shift_top = rs; 819 } 820 sctx.shift_top *= 1.1; 821 sctx.nshift_max = 5; 822 sctx.shift_lo = 0.; 823 sctx.shift_hi = 1.; 824 } 825 826 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 827 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 828 ierr = PetscMalloc1(n+1,&rtmp);CHKERRQ(ierr); 829 ierr = PetscArrayzero(rtmp,n+1);CHKERRQ(ierr); 830 ics = ic; 831 832 #if defined(MV) 833 sctx.shift_top = 0.; 834 sctx.nshift_max = 0; 835 sctx.shift_lo = 0.; 836 sctx.shift_hi = 0.; 837 sctx.shift_fraction = 0.; 838 839 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 840 sctx.shift_top = 0.; 841 for (i=0; i<n; i++) { 842 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 843 d = (a->a)[diag[i]]; 844 rs = -PetscAbsScalar(d) - PetscRealPart(d); 845 v = a->a+ai[i]; 846 nz = ai[i+1] - ai[i]; 847 for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]); 848 if (rs>sctx.shift_top) sctx.shift_top = rs; 849 } 850 if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot; 851 sctx.shift_top *= 1.1; 852 sctx.nshift_max = 5; 853 sctx.shift_lo = 0.; 854 sctx.shift_hi = 1.; 855 } 856 857 sctx.shift_amount = 0.; 858 sctx.nshift = 0; 859 #endif 860 861 do { 862 sctx.newshift = PETSC_FALSE; 863 for (i=0; i<n; i++) { 864 /* load in initial unfactored row */ 865 nz = ai[r[i]+1] - ai[r[i]]; 866 ajtmp = aj + ai[r[i]]; 867 v = a->a + ai[r[i]]; 868 /* sort permuted ajtmp and values v accordingly */ 869 for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]]; 870 ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr); 871 872 diag[r[i]] = ai[r[i]]; 873 for (j=0; j<nz; j++) { 874 rtmp[ajtmp[j]] = v[j]; 875 if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */ 876 } 877 rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 878 879 row = *ajtmp++; 880 while (row < i) { 881 pc = rtmp + row; 882 if (*pc != 0.0) { 883 pv = a->a + diag[r[row]]; 884 pj = aj + diag[r[row]] + 1; 885 886 multiplier = *pc / *pv++; 887 *pc = multiplier; 888 nz = ai[r[row]+1] - diag[r[row]] - 1; 889 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 890 ierr = PetscLogFlops(1+2.0*nz);CHKERRQ(ierr); 891 } 892 row = *ajtmp++; 893 } 894 /* finished row so overwrite it onto a->a */ 895 pv = a->a + ai[r[i]]; 896 pj = aj + ai[r[i]]; 897 nz = ai[r[i]+1] - ai[r[i]]; 898 nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */ 899 900 rs = 0.0; 901 for (j=0; j<nz; j++) { 902 pv[j] = rtmp[pj[j]]; 903 if (j != nbdiag) rs += PetscAbsScalar(pv[j]); 904 } 905 906 sctx.rs = rs; 907 sctx.pv = pv[nbdiag]; 908 ierr = MatPivotCheck(B,A,info,&sctx,i);CHKERRQ(ierr); 909 if (sctx.newshift) break; 910 pv[nbdiag] = sctx.pv; 911 } 912 913 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 914 /* 915 * if no shift in this attempt & shifting & started shifting & can refine, 916 * then try lower shift 917 */ 918 sctx.shift_hi = sctx.shift_fraction; 919 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 920 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 921 sctx.newshift = PETSC_TRUE; 922 sctx.nshift++; 923 } 924 } while (sctx.newshift); 925 926 /* invert diagonal entries for simplier triangular solves */ 927 for (i=0; i<n; i++) { 928 a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]]; 929 } 930 931 ierr = PetscFree(rtmp);CHKERRQ(ierr); 932 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 933 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 934 935 A->ops->solve = MatSolve_SeqAIJ_InplaceWithPerm; 936 A->ops->solveadd = MatSolveAdd_SeqAIJ_inplace; 937 A->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace; 938 A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace; 939 940 A->assembled = PETSC_TRUE; 941 A->preallocated = PETSC_TRUE; 942 943 ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr); 944 if (sctx.nshift) { 945 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 946 ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %g, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,(double)sctx.shift_amount,(double)sctx.shift_fraction,(double)sctx.shift_top);CHKERRQ(ierr); 947 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 948 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 949 } 950 } 951 PetscFunctionReturn(0); 952 } 953 954 /* ----------------------------------------------------------- */ 955 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info) 956 { 957 PetscErrorCode ierr; 958 Mat C; 959 960 PetscFunctionBegin; 961 ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr); 962 ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr); 963 ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr); 964 965 A->ops->solve = C->ops->solve; 966 A->ops->solvetranspose = C->ops->solvetranspose; 967 968 ierr = MatHeaderMerge(A,&C);CHKERRQ(ierr); 969 ierr = PetscLogObjectParent((PetscObject)A,(PetscObject)((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr); 970 PetscFunctionReturn(0); 971 } 972 /* ----------------------------------------------------------- */ 973 974 975 PetscErrorCode MatSolve_SeqAIJ_inplace(Mat A,Vec bb,Vec xx) 976 { 977 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 978 IS iscol = a->col,isrow = a->row; 979 PetscErrorCode ierr; 980 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 981 PetscInt nz; 982 const PetscInt *rout,*cout,*r,*c; 983 PetscScalar *x,*tmp,*tmps,sum; 984 const PetscScalar *b; 985 const MatScalar *aa = a->a,*v; 986 987 PetscFunctionBegin; 988 if (!n) PetscFunctionReturn(0); 989 990 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 991 ierr = VecGetArrayWrite(xx,&x);CHKERRQ(ierr); 992 tmp = a->solve_work; 993 994 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 995 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 996 997 /* forward solve the lower triangular */ 998 tmp[0] = b[*r++]; 999 tmps = tmp; 1000 for (i=1; i<n; i++) { 1001 v = aa + ai[i]; 1002 vi = aj + ai[i]; 1003 nz = a->diag[i] - ai[i]; 1004 sum = b[*r++]; 1005 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1006 tmp[i] = sum; 1007 } 1008 1009 /* backward solve the upper triangular */ 1010 for (i=n-1; i>=0; i--) { 1011 v = aa + a->diag[i] + 1; 1012 vi = aj + a->diag[i] + 1; 1013 nz = ai[i+1] - a->diag[i] - 1; 1014 sum = tmp[i]; 1015 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1016 x[*c--] = tmp[i] = sum*aa[a->diag[i]]; 1017 } 1018 1019 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1020 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1021 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1022 ierr = VecRestoreArrayWrite(xx,&x);CHKERRQ(ierr); 1023 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1024 PetscFunctionReturn(0); 1025 } 1026 1027 PetscErrorCode MatMatSolve_SeqAIJ_inplace(Mat A,Mat B,Mat X) 1028 { 1029 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1030 IS iscol = a->col,isrow = a->row; 1031 PetscErrorCode ierr; 1032 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1033 PetscInt nz,neq,ldb,ldx; 1034 const PetscInt *rout,*cout,*r,*c; 1035 PetscScalar *x,*tmp = a->solve_work,*tmps,sum; 1036 const PetscScalar *b,*aa = a->a,*v; 1037 PetscBool isdense; 1038 1039 PetscFunctionBegin; 1040 if (!n) PetscFunctionReturn(0); 1041 ierr = PetscObjectTypeCompare((PetscObject)B,MATSEQDENSE,&isdense);CHKERRQ(ierr); 1042 if (!isdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 1043 if (X != B) { 1044 ierr = PetscObjectTypeCompare((PetscObject)X,MATSEQDENSE,&isdense);CHKERRQ(ierr); 1045 if (!isdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 1046 } 1047 ierr = MatDenseGetArrayRead(B,&b);CHKERRQ(ierr); 1048 ierr = MatDenseGetLDA(B,&ldb);CHKERRQ(ierr); 1049 ierr = MatDenseGetArray(X,&x);CHKERRQ(ierr); 1050 ierr = MatDenseGetLDA(X,&ldx);CHKERRQ(ierr); 1051 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1052 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1053 for (neq=0; neq<B->cmap->n; neq++) { 1054 /* forward solve the lower triangular */ 1055 tmp[0] = b[r[0]]; 1056 tmps = tmp; 1057 for (i=1; i<n; i++) { 1058 v = aa + ai[i]; 1059 vi = aj + ai[i]; 1060 nz = a->diag[i] - ai[i]; 1061 sum = b[r[i]]; 1062 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1063 tmp[i] = sum; 1064 } 1065 /* backward solve the upper triangular */ 1066 for (i=n-1; i>=0; i--) { 1067 v = aa + a->diag[i] + 1; 1068 vi = aj + a->diag[i] + 1; 1069 nz = ai[i+1] - a->diag[i] - 1; 1070 sum = tmp[i]; 1071 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1072 x[c[i]] = tmp[i] = sum*aa[a->diag[i]]; 1073 } 1074 b += ldb; 1075 x += ldx; 1076 } 1077 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1078 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1079 ierr = MatDenseRestoreArrayRead(B,&b);CHKERRQ(ierr); 1080 ierr = MatDenseRestoreArray(X,&x);CHKERRQ(ierr); 1081 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 1082 PetscFunctionReturn(0); 1083 } 1084 1085 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X) 1086 { 1087 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1088 IS iscol = a->col,isrow = a->row; 1089 PetscErrorCode ierr; 1090 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag; 1091 PetscInt nz,neq,ldb,ldx; 1092 const PetscInt *rout,*cout,*r,*c; 1093 PetscScalar *x,*tmp = a->solve_work,sum; 1094 const PetscScalar *b,*aa = a->a,*v; 1095 PetscBool isdense; 1096 1097 PetscFunctionBegin; 1098 if (!n) PetscFunctionReturn(0); 1099 ierr = PetscObjectTypeCompare((PetscObject)B,MATSEQDENSE,&isdense);CHKERRQ(ierr); 1100 if (!isdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 1101 if (X != B) { 1102 ierr = PetscObjectTypeCompare((PetscObject)X,MATSEQDENSE,&isdense);CHKERRQ(ierr); 1103 if (!isdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 1104 } 1105 ierr = MatDenseGetArrayRead(B,&b);CHKERRQ(ierr); 1106 ierr = MatDenseGetLDA(B,&ldb);CHKERRQ(ierr); 1107 ierr = MatDenseGetArray(X,&x);CHKERRQ(ierr); 1108 ierr = MatDenseGetLDA(X,&ldx);CHKERRQ(ierr); 1109 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1110 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1111 for (neq=0; neq<B->cmap->n; neq++) { 1112 /* forward solve the lower triangular */ 1113 tmp[0] = b[r[0]]; 1114 v = aa; 1115 vi = aj; 1116 for (i=1; i<n; i++) { 1117 nz = ai[i+1] - ai[i]; 1118 sum = b[r[i]]; 1119 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 1120 tmp[i] = sum; 1121 v += nz; vi += nz; 1122 } 1123 /* backward solve the upper triangular */ 1124 for (i=n-1; i>=0; i--) { 1125 v = aa + adiag[i+1]+1; 1126 vi = aj + adiag[i+1]+1; 1127 nz = adiag[i]-adiag[i+1]-1; 1128 sum = tmp[i]; 1129 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 1130 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 1131 } 1132 b += ldb; 1133 x += ldx; 1134 } 1135 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1136 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1137 ierr = MatDenseRestoreArrayRead(B,&b);CHKERRQ(ierr); 1138 ierr = MatDenseRestoreArray(X,&x);CHKERRQ(ierr); 1139 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 1140 PetscFunctionReturn(0); 1141 } 1142 1143 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx) 1144 { 1145 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1146 IS iscol = a->col,isrow = a->row; 1147 PetscErrorCode ierr; 1148 const PetscInt *r,*c,*rout,*cout; 1149 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1150 PetscInt nz,row; 1151 PetscScalar *x,*tmp,*tmps,sum; 1152 const PetscScalar *b; 1153 const MatScalar *aa = a->a,*v; 1154 1155 PetscFunctionBegin; 1156 if (!n) PetscFunctionReturn(0); 1157 1158 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1159 ierr = VecGetArrayWrite(xx,&x);CHKERRQ(ierr); 1160 tmp = a->solve_work; 1161 1162 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1163 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1164 1165 /* forward solve the lower triangular */ 1166 tmp[0] = b[*r++]; 1167 tmps = tmp; 1168 for (row=1; row<n; row++) { 1169 i = rout[row]; /* permuted row */ 1170 v = aa + ai[i]; 1171 vi = aj + ai[i]; 1172 nz = a->diag[i] - ai[i]; 1173 sum = b[*r++]; 1174 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1175 tmp[row] = sum; 1176 } 1177 1178 /* backward solve the upper triangular */ 1179 for (row=n-1; row>=0; row--) { 1180 i = rout[row]; /* permuted row */ 1181 v = aa + a->diag[i] + 1; 1182 vi = aj + a->diag[i] + 1; 1183 nz = ai[i+1] - a->diag[i] - 1; 1184 sum = tmp[row]; 1185 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1186 x[*c--] = tmp[row] = sum*aa[a->diag[i]]; 1187 } 1188 1189 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1190 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1191 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1192 ierr = VecRestoreArrayWrite(xx,&x);CHKERRQ(ierr); 1193 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1194 PetscFunctionReturn(0); 1195 } 1196 1197 /* ----------------------------------------------------------- */ 1198 #include <../src/mat/impls/aij/seq/ftn-kernels/fsolve.h> 1199 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_inplace(Mat A,Vec bb,Vec xx) 1200 { 1201 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1202 PetscErrorCode ierr; 1203 PetscInt n = A->rmap->n; 1204 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag; 1205 PetscScalar *x; 1206 const PetscScalar *b; 1207 const MatScalar *aa = a->a; 1208 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1209 PetscInt adiag_i,i,nz,ai_i; 1210 const PetscInt *vi; 1211 const MatScalar *v; 1212 PetscScalar sum; 1213 #endif 1214 1215 PetscFunctionBegin; 1216 if (!n) PetscFunctionReturn(0); 1217 1218 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1219 ierr = VecGetArrayWrite(xx,&x);CHKERRQ(ierr); 1220 1221 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1222 fortransolveaij_(&n,x,ai,aj,adiag,aa,b); 1223 #else 1224 /* forward solve the lower triangular */ 1225 x[0] = b[0]; 1226 for (i=1; i<n; i++) { 1227 ai_i = ai[i]; 1228 v = aa + ai_i; 1229 vi = aj + ai_i; 1230 nz = adiag[i] - ai_i; 1231 sum = b[i]; 1232 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1233 x[i] = sum; 1234 } 1235 1236 /* backward solve the upper triangular */ 1237 for (i=n-1; i>=0; i--) { 1238 adiag_i = adiag[i]; 1239 v = aa + adiag_i + 1; 1240 vi = aj + adiag_i + 1; 1241 nz = ai[i+1] - adiag_i - 1; 1242 sum = x[i]; 1243 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1244 x[i] = sum*aa[adiag_i]; 1245 } 1246 #endif 1247 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1248 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1249 ierr = VecRestoreArrayWrite(xx,&x);CHKERRQ(ierr); 1250 PetscFunctionReturn(0); 1251 } 1252 1253 PetscErrorCode MatSolveAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec yy,Vec xx) 1254 { 1255 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1256 IS iscol = a->col,isrow = a->row; 1257 PetscErrorCode ierr; 1258 PetscInt i, n = A->rmap->n,j; 1259 PetscInt nz; 1260 const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j; 1261 PetscScalar *x,*tmp,sum; 1262 const PetscScalar *b; 1263 const MatScalar *aa = a->a,*v; 1264 1265 PetscFunctionBegin; 1266 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 1267 1268 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1269 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1270 tmp = a->solve_work; 1271 1272 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1273 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1274 1275 /* forward solve the lower triangular */ 1276 tmp[0] = b[*r++]; 1277 for (i=1; i<n; i++) { 1278 v = aa + ai[i]; 1279 vi = aj + ai[i]; 1280 nz = a->diag[i] - ai[i]; 1281 sum = b[*r++]; 1282 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1283 tmp[i] = sum; 1284 } 1285 1286 /* backward solve the upper triangular */ 1287 for (i=n-1; i>=0; i--) { 1288 v = aa + a->diag[i] + 1; 1289 vi = aj + a->diag[i] + 1; 1290 nz = ai[i+1] - a->diag[i] - 1; 1291 sum = tmp[i]; 1292 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1293 tmp[i] = sum*aa[a->diag[i]]; 1294 x[*c--] += tmp[i]; 1295 } 1296 1297 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1298 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1299 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1300 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1301 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1302 PetscFunctionReturn(0); 1303 } 1304 1305 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx) 1306 { 1307 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1308 IS iscol = a->col,isrow = a->row; 1309 PetscErrorCode ierr; 1310 PetscInt i, n = A->rmap->n,j; 1311 PetscInt nz; 1312 const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag; 1313 PetscScalar *x,*tmp,sum; 1314 const PetscScalar *b; 1315 const MatScalar *aa = a->a,*v; 1316 1317 PetscFunctionBegin; 1318 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 1319 1320 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1321 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1322 tmp = a->solve_work; 1323 1324 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1325 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1326 1327 /* forward solve the lower triangular */ 1328 tmp[0] = b[r[0]]; 1329 v = aa; 1330 vi = aj; 1331 for (i=1; i<n; i++) { 1332 nz = ai[i+1] - ai[i]; 1333 sum = b[r[i]]; 1334 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1335 tmp[i] = sum; 1336 v += nz; 1337 vi += nz; 1338 } 1339 1340 /* backward solve the upper triangular */ 1341 v = aa + adiag[n-1]; 1342 vi = aj + adiag[n-1]; 1343 for (i=n-1; i>=0; i--) { 1344 nz = adiag[i] - adiag[i+1] - 1; 1345 sum = tmp[i]; 1346 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1347 tmp[i] = sum*v[nz]; 1348 x[c[i]] += tmp[i]; 1349 v += nz+1; vi += nz+1; 1350 } 1351 1352 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1353 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1354 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1355 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1356 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1357 PetscFunctionReturn(0); 1358 } 1359 1360 PetscErrorCode MatSolveTranspose_SeqAIJ_inplace(Mat A,Vec bb,Vec xx) 1361 { 1362 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1363 IS iscol = a->col,isrow = a->row; 1364 PetscErrorCode ierr; 1365 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1366 PetscInt i,n = A->rmap->n,j; 1367 PetscInt nz; 1368 PetscScalar *x,*tmp,s1; 1369 const MatScalar *aa = a->a,*v; 1370 const PetscScalar *b; 1371 1372 PetscFunctionBegin; 1373 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1374 ierr = VecGetArrayWrite(xx,&x);CHKERRQ(ierr); 1375 tmp = a->solve_work; 1376 1377 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1378 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1379 1380 /* copy the b into temp work space according to permutation */ 1381 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1382 1383 /* forward solve the U^T */ 1384 for (i=0; i<n; i++) { 1385 v = aa + diag[i]; 1386 vi = aj + diag[i] + 1; 1387 nz = ai[i+1] - diag[i] - 1; 1388 s1 = tmp[i]; 1389 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1390 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1391 tmp[i] = s1; 1392 } 1393 1394 /* backward solve the L^T */ 1395 for (i=n-1; i>=0; i--) { 1396 v = aa + diag[i] - 1; 1397 vi = aj + diag[i] - 1; 1398 nz = diag[i] - ai[i]; 1399 s1 = tmp[i]; 1400 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1401 } 1402 1403 /* copy tmp into x according to permutation */ 1404 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1405 1406 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1407 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1408 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1409 ierr = VecRestoreArrayWrite(xx,&x);CHKERRQ(ierr); 1410 1411 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1412 PetscFunctionReturn(0); 1413 } 1414 1415 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx) 1416 { 1417 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1418 IS iscol = a->col,isrow = a->row; 1419 PetscErrorCode ierr; 1420 const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi; 1421 PetscInt i,n = A->rmap->n,j; 1422 PetscInt nz; 1423 PetscScalar *x,*tmp,s1; 1424 const MatScalar *aa = a->a,*v; 1425 const PetscScalar *b; 1426 1427 PetscFunctionBegin; 1428 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1429 ierr = VecGetArrayWrite(xx,&x);CHKERRQ(ierr); 1430 tmp = a->solve_work; 1431 1432 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1433 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1434 1435 /* copy the b into temp work space according to permutation */ 1436 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1437 1438 /* forward solve the U^T */ 1439 for (i=0; i<n; i++) { 1440 v = aa + adiag[i+1] + 1; 1441 vi = aj + adiag[i+1] + 1; 1442 nz = adiag[i] - adiag[i+1] - 1; 1443 s1 = tmp[i]; 1444 s1 *= v[nz]; /* multiply by inverse of diagonal entry */ 1445 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1446 tmp[i] = s1; 1447 } 1448 1449 /* backward solve the L^T */ 1450 for (i=n-1; i>=0; i--) { 1451 v = aa + ai[i]; 1452 vi = aj + ai[i]; 1453 nz = ai[i+1] - ai[i]; 1454 s1 = tmp[i]; 1455 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1456 } 1457 1458 /* copy tmp into x according to permutation */ 1459 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1460 1461 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1462 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1463 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1464 ierr = VecRestoreArrayWrite(xx,&x);CHKERRQ(ierr); 1465 1466 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1467 PetscFunctionReturn(0); 1468 } 1469 1470 PetscErrorCode MatSolveTransposeAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec zz,Vec xx) 1471 { 1472 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1473 IS iscol = a->col,isrow = a->row; 1474 PetscErrorCode ierr; 1475 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1476 PetscInt i,n = A->rmap->n,j; 1477 PetscInt nz; 1478 PetscScalar *x,*tmp,s1; 1479 const MatScalar *aa = a->a,*v; 1480 const PetscScalar *b; 1481 1482 PetscFunctionBegin; 1483 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1484 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1485 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1486 tmp = a->solve_work; 1487 1488 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1489 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1490 1491 /* copy the b into temp work space according to permutation */ 1492 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1493 1494 /* forward solve the U^T */ 1495 for (i=0; i<n; i++) { 1496 v = aa + diag[i]; 1497 vi = aj + diag[i] + 1; 1498 nz = ai[i+1] - diag[i] - 1; 1499 s1 = tmp[i]; 1500 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1501 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1502 tmp[i] = s1; 1503 } 1504 1505 /* backward solve the L^T */ 1506 for (i=n-1; i>=0; i--) { 1507 v = aa + diag[i] - 1; 1508 vi = aj + diag[i] - 1; 1509 nz = diag[i] - ai[i]; 1510 s1 = tmp[i]; 1511 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1512 } 1513 1514 /* copy tmp into x according to permutation */ 1515 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1516 1517 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1518 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1519 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1520 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1521 1522 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1523 PetscFunctionReturn(0); 1524 } 1525 1526 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx) 1527 { 1528 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1529 IS iscol = a->col,isrow = a->row; 1530 PetscErrorCode ierr; 1531 const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi; 1532 PetscInt i,n = A->rmap->n,j; 1533 PetscInt nz; 1534 PetscScalar *x,*tmp,s1; 1535 const MatScalar *aa = a->a,*v; 1536 const PetscScalar *b; 1537 1538 PetscFunctionBegin; 1539 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1540 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1541 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1542 tmp = a->solve_work; 1543 1544 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1545 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1546 1547 /* copy the b into temp work space according to permutation */ 1548 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1549 1550 /* forward solve the U^T */ 1551 for (i=0; i<n; i++) { 1552 v = aa + adiag[i+1] + 1; 1553 vi = aj + adiag[i+1] + 1; 1554 nz = adiag[i] - adiag[i+1] - 1; 1555 s1 = tmp[i]; 1556 s1 *= v[nz]; /* multiply by inverse of diagonal entry */ 1557 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1558 tmp[i] = s1; 1559 } 1560 1561 1562 /* backward solve the L^T */ 1563 for (i=n-1; i>=0; i--) { 1564 v = aa + ai[i]; 1565 vi = aj + ai[i]; 1566 nz = ai[i+1] - ai[i]; 1567 s1 = tmp[i]; 1568 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1569 } 1570 1571 /* copy tmp into x according to permutation */ 1572 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1573 1574 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1575 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1576 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1577 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1578 1579 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1580 PetscFunctionReturn(0); 1581 } 1582 1583 /* ----------------------------------------------------------------*/ 1584 1585 /* 1586 ilu() under revised new data structure. 1587 Factored arrays bj and ba are stored as 1588 L(0,:), L(1,:), ...,L(n-1,:), U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:) 1589 1590 bi=fact->i is an array of size n+1, in which 1591 bi+ 1592 bi[i]: points to 1st entry of L(i,:),i=0,...,n-1 1593 bi[n]: points to L(n-1,n-1)+1 1594 1595 bdiag=fact->diag is an array of size n+1,in which 1596 bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1 1597 bdiag[n]: points to entry of U(n-1,0)-1 1598 1599 U(i,:) contains bdiag[i] as its last entry, i.e., 1600 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 1601 */ 1602 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1603 { 1604 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1605 PetscErrorCode ierr; 1606 const PetscInt n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag; 1607 PetscInt i,j,k=0,nz,*bi,*bj,*bdiag; 1608 IS isicol; 1609 1610 PetscFunctionBegin; 1611 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1612 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr); 1613 b = (Mat_SeqAIJ*)(fact)->data; 1614 1615 /* allocate matrix arrays for new data structure */ 1616 ierr = PetscMalloc3(ai[n]+1,&b->a,ai[n]+1,&b->j,n+1,&b->i);CHKERRQ(ierr); 1617 ierr = PetscLogObjectMemory((PetscObject)fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1618 1619 b->singlemalloc = PETSC_TRUE; 1620 if (!b->diag) { 1621 ierr = PetscMalloc1(n+1,&b->diag);CHKERRQ(ierr); 1622 ierr = PetscLogObjectMemory((PetscObject)fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1623 } 1624 bdiag = b->diag; 1625 1626 if (n > 0) { 1627 ierr = PetscArrayzero(b->a,ai[n]);CHKERRQ(ierr); 1628 } 1629 1630 /* set bi and bj with new data structure */ 1631 bi = b->i; 1632 bj = b->j; 1633 1634 /* L part */ 1635 bi[0] = 0; 1636 for (i=0; i<n; i++) { 1637 nz = adiag[i] - ai[i]; 1638 bi[i+1] = bi[i] + nz; 1639 aj = a->j + ai[i]; 1640 for (j=0; j<nz; j++) { 1641 /* *bj = aj[j]; bj++; */ 1642 bj[k++] = aj[j]; 1643 } 1644 } 1645 1646 /* U part */ 1647 bdiag[n] = bi[n]-1; 1648 for (i=n-1; i>=0; i--) { 1649 nz = ai[i+1] - adiag[i] - 1; 1650 aj = a->j + adiag[i] + 1; 1651 for (j=0; j<nz; j++) { 1652 /* *bj = aj[j]; bj++; */ 1653 bj[k++] = aj[j]; 1654 } 1655 /* diag[i] */ 1656 /* *bj = i; bj++; */ 1657 bj[k++] = i; 1658 bdiag[i] = bdiag[i+1] + nz + 1; 1659 } 1660 1661 fact->factortype = MAT_FACTOR_ILU; 1662 fact->info.factor_mallocs = 0; 1663 fact->info.fill_ratio_given = info->fill; 1664 fact->info.fill_ratio_needed = 1.0; 1665 fact->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1666 ierr = MatSeqAIJCheckInode_FactorLU(fact);CHKERRQ(ierr); 1667 1668 b = (Mat_SeqAIJ*)(fact)->data; 1669 b->row = isrow; 1670 b->col = iscol; 1671 b->icol = isicol; 1672 ierr = PetscMalloc1(fact->rmap->n+1,&b->solve_work);CHKERRQ(ierr); 1673 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1674 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1675 PetscFunctionReturn(0); 1676 } 1677 1678 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1679 { 1680 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1681 IS isicol; 1682 PetscErrorCode ierr; 1683 const PetscInt *r,*ic; 1684 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j; 1685 PetscInt *bi,*cols,nnz,*cols_lvl; 1686 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1687 PetscInt i,levels,diagonal_fill; 1688 PetscBool col_identity,row_identity,missing; 1689 PetscReal f; 1690 PetscInt nlnk,*lnk,*lnk_lvl=NULL; 1691 PetscBT lnkbt; 1692 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1693 PetscFreeSpaceList free_space =NULL,current_space=NULL; 1694 PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL; 1695 1696 PetscFunctionBegin; 1697 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 1698 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 1699 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 1700 1701 levels = (PetscInt)info->levels; 1702 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1703 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1704 if (!levels && row_identity && col_identity) { 1705 /* special case: ilu(0) with natural ordering */ 1706 ierr = MatILUFactorSymbolic_SeqAIJ_ilu0(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1707 if (a->inode.size) { 1708 fact->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode; 1709 } 1710 PetscFunctionReturn(0); 1711 } 1712 1713 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1714 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1715 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1716 1717 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1718 ierr = PetscMalloc1(n+1,&bi);CHKERRQ(ierr); 1719 ierr = PetscMalloc1(n+1,&bdiag);CHKERRQ(ierr); 1720 bi[0] = bdiag[0] = 0; 1721 ierr = PetscMalloc2(n,&bj_ptr,n,&bjlvl_ptr);CHKERRQ(ierr); 1722 1723 /* create a linked list for storing column indices of the active row */ 1724 nlnk = n + 1; 1725 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1726 1727 /* initial FreeSpace size is f*(ai[n]+1) */ 1728 f = info->fill; 1729 diagonal_fill = (PetscInt)info->diagonal_fill; 1730 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space);CHKERRQ(ierr); 1731 current_space = free_space; 1732 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space_lvl);CHKERRQ(ierr); 1733 current_space_lvl = free_space_lvl; 1734 for (i=0; i<n; i++) { 1735 nzi = 0; 1736 /* copy current row into linked list */ 1737 nnz = ai[r[i]+1] - ai[r[i]]; 1738 if (!nnz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1739 cols = aj + ai[r[i]]; 1740 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1741 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1742 nzi += nlnk; 1743 1744 /* make sure diagonal entry is included */ 1745 if (diagonal_fill && lnk[i] == -1) { 1746 fm = n; 1747 while (lnk[fm] < i) fm = lnk[fm]; 1748 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1749 lnk[fm] = i; 1750 lnk_lvl[i] = 0; 1751 nzi++; dcount++; 1752 } 1753 1754 /* add pivot rows into the active row */ 1755 nzbd = 0; 1756 prow = lnk[n]; 1757 while (prow < i) { 1758 nnz = bdiag[prow]; 1759 cols = bj_ptr[prow] + nnz + 1; 1760 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1761 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1762 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1763 nzi += nlnk; 1764 prow = lnk[prow]; 1765 nzbd++; 1766 } 1767 bdiag[i] = nzbd; 1768 bi[i+1] = bi[i] + nzi; 1769 /* if free space is not available, make more free space */ 1770 if (current_space->local_remaining<nzi) { 1771 nnz = PetscIntMultTruncate(2,PetscIntMultTruncate(nzi,n - i)); /* estimated and max additional space needed */ 1772 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1773 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1774 reallocs++; 1775 } 1776 1777 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1778 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1779 bj_ptr[i] = current_space->array; 1780 bjlvl_ptr[i] = current_space_lvl->array; 1781 1782 /* make sure the active row i has diagonal entry */ 1783 if (*(bj_ptr[i]+bdiag[i]) != i) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\ntry running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1784 1785 current_space->array += nzi; 1786 current_space->local_used += nzi; 1787 current_space->local_remaining -= nzi; 1788 current_space_lvl->array += nzi; 1789 current_space_lvl->local_used += nzi; 1790 current_space_lvl->local_remaining -= nzi; 1791 } 1792 1793 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1794 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1795 /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */ 1796 ierr = PetscMalloc1(bi[n]+1,&bj);CHKERRQ(ierr); 1797 ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 1798 1799 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1800 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1801 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 1802 1803 #if defined(PETSC_USE_INFO) 1804 { 1805 PetscReal af = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 1806 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);CHKERRQ(ierr); 1807 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 1808 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%g);\n",(double)af);CHKERRQ(ierr); 1809 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1810 if (diagonal_fill) { 1811 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals\n",dcount);CHKERRQ(ierr); 1812 } 1813 } 1814 #endif 1815 /* put together the new matrix */ 1816 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr); 1817 ierr = PetscLogObjectParent((PetscObject)fact,(PetscObject)isicol);CHKERRQ(ierr); 1818 b = (Mat_SeqAIJ*)(fact)->data; 1819 1820 b->free_a = PETSC_TRUE; 1821 b->free_ij = PETSC_TRUE; 1822 b->singlemalloc = PETSC_FALSE; 1823 1824 ierr = PetscMalloc1(bdiag[0]+1,&b->a);CHKERRQ(ierr); 1825 1826 b->j = bj; 1827 b->i = bi; 1828 b->diag = bdiag; 1829 b->ilen = NULL; 1830 b->imax = NULL; 1831 b->row = isrow; 1832 b->col = iscol; 1833 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1834 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1835 b->icol = isicol; 1836 1837 ierr = PetscMalloc1(n+1,&b->solve_work);CHKERRQ(ierr); 1838 /* In b structure: Free imax, ilen, old a, old j. 1839 Allocate bdiag, solve_work, new a, new j */ 1840 ierr = PetscLogObjectMemory((PetscObject)fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1841 b->maxnz = b->nz = bdiag[0]+1; 1842 1843 (fact)->info.factor_mallocs = reallocs; 1844 (fact)->info.fill_ratio_given = f; 1845 (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 1846 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1847 if (a->inode.size) { 1848 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode; 1849 } 1850 ierr = MatSeqAIJCheckInode_FactorLU(fact);CHKERRQ(ierr); 1851 PetscFunctionReturn(0); 1852 } 1853 1854 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1855 { 1856 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1857 IS isicol; 1858 PetscErrorCode ierr; 1859 const PetscInt *r,*ic; 1860 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j; 1861 PetscInt *bi,*cols,nnz,*cols_lvl; 1862 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1863 PetscInt i,levels,diagonal_fill; 1864 PetscBool col_identity,row_identity; 1865 PetscReal f; 1866 PetscInt nlnk,*lnk,*lnk_lvl=NULL; 1867 PetscBT lnkbt; 1868 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1869 PetscFreeSpaceList free_space =NULL,current_space=NULL; 1870 PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL; 1871 PetscBool missing; 1872 1873 PetscFunctionBegin; 1874 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 1875 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 1876 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 1877 1878 f = info->fill; 1879 levels = (PetscInt)info->levels; 1880 diagonal_fill = (PetscInt)info->diagonal_fill; 1881 1882 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1883 1884 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1885 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1886 if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */ 1887 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr); 1888 1889 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace; 1890 if (a->inode.size) { 1891 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace; 1892 } 1893 fact->factortype = MAT_FACTOR_ILU; 1894 (fact)->info.factor_mallocs = 0; 1895 (fact)->info.fill_ratio_given = info->fill; 1896 (fact)->info.fill_ratio_needed = 1.0; 1897 1898 b = (Mat_SeqAIJ*)(fact)->data; 1899 b->row = isrow; 1900 b->col = iscol; 1901 b->icol = isicol; 1902 ierr = PetscMalloc1((fact)->rmap->n+1,&b->solve_work);CHKERRQ(ierr); 1903 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1904 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1905 PetscFunctionReturn(0); 1906 } 1907 1908 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1909 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1910 1911 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1912 ierr = PetscMalloc1(n+1,&bi);CHKERRQ(ierr); 1913 ierr = PetscMalloc1(n+1,&bdiag);CHKERRQ(ierr); 1914 bi[0] = bdiag[0] = 0; 1915 1916 ierr = PetscMalloc2(n,&bj_ptr,n,&bjlvl_ptr);CHKERRQ(ierr); 1917 1918 /* create a linked list for storing column indices of the active row */ 1919 nlnk = n + 1; 1920 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1921 1922 /* initial FreeSpace size is f*(ai[n]+1) */ 1923 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space);CHKERRQ(ierr); 1924 current_space = free_space; 1925 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space_lvl);CHKERRQ(ierr); 1926 current_space_lvl = free_space_lvl; 1927 1928 for (i=0; i<n; i++) { 1929 nzi = 0; 1930 /* copy current row into linked list */ 1931 nnz = ai[r[i]+1] - ai[r[i]]; 1932 if (!nnz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1933 cols = aj + ai[r[i]]; 1934 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1935 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1936 nzi += nlnk; 1937 1938 /* make sure diagonal entry is included */ 1939 if (diagonal_fill && lnk[i] == -1) { 1940 fm = n; 1941 while (lnk[fm] < i) fm = lnk[fm]; 1942 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1943 lnk[fm] = i; 1944 lnk_lvl[i] = 0; 1945 nzi++; dcount++; 1946 } 1947 1948 /* add pivot rows into the active row */ 1949 nzbd = 0; 1950 prow = lnk[n]; 1951 while (prow < i) { 1952 nnz = bdiag[prow]; 1953 cols = bj_ptr[prow] + nnz + 1; 1954 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1955 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1956 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1957 nzi += nlnk; 1958 prow = lnk[prow]; 1959 nzbd++; 1960 } 1961 bdiag[i] = nzbd; 1962 bi[i+1] = bi[i] + nzi; 1963 1964 /* if free space is not available, make more free space */ 1965 if (current_space->local_remaining<nzi) { 1966 nnz = PetscIntMultTruncate(nzi,n - i); /* estimated and max additional space needed */ 1967 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1968 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1969 reallocs++; 1970 } 1971 1972 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1973 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1974 bj_ptr[i] = current_space->array; 1975 bjlvl_ptr[i] = current_space_lvl->array; 1976 1977 /* make sure the active row i has diagonal entry */ 1978 if (*(bj_ptr[i]+bdiag[i]) != i) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\ntry running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1979 1980 current_space->array += nzi; 1981 current_space->local_used += nzi; 1982 current_space->local_remaining -= nzi; 1983 current_space_lvl->array += nzi; 1984 current_space_lvl->local_used += nzi; 1985 current_space_lvl->local_remaining -= nzi; 1986 } 1987 1988 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1989 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1990 1991 /* destroy list of free space and other temporary arrays */ 1992 ierr = PetscMalloc1(bi[n]+1,&bj);CHKERRQ(ierr); 1993 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */ 1994 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1995 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1996 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 1997 1998 #if defined(PETSC_USE_INFO) 1999 { 2000 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 2001 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);CHKERRQ(ierr); 2002 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 2003 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%g);\n",(double)af);CHKERRQ(ierr); 2004 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 2005 if (diagonal_fill) { 2006 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals\n",dcount);CHKERRQ(ierr); 2007 } 2008 } 2009 #endif 2010 2011 /* put together the new matrix */ 2012 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr); 2013 ierr = PetscLogObjectParent((PetscObject)fact,(PetscObject)isicol);CHKERRQ(ierr); 2014 b = (Mat_SeqAIJ*)(fact)->data; 2015 2016 b->free_a = PETSC_TRUE; 2017 b->free_ij = PETSC_TRUE; 2018 b->singlemalloc = PETSC_FALSE; 2019 2020 ierr = PetscMalloc1(bi[n],&b->a);CHKERRQ(ierr); 2021 b->j = bj; 2022 b->i = bi; 2023 for (i=0; i<n; i++) bdiag[i] += bi[i]; 2024 b->diag = bdiag; 2025 b->ilen = NULL; 2026 b->imax = NULL; 2027 b->row = isrow; 2028 b->col = iscol; 2029 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 2030 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 2031 b->icol = isicol; 2032 ierr = PetscMalloc1(n+1,&b->solve_work);CHKERRQ(ierr); 2033 /* In b structure: Free imax, ilen, old a, old j. 2034 Allocate bdiag, solve_work, new a, new j */ 2035 ierr = PetscLogObjectMemory((PetscObject)fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 2036 b->maxnz = b->nz = bi[n]; 2037 2038 (fact)->info.factor_mallocs = reallocs; 2039 (fact)->info.fill_ratio_given = f; 2040 (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 2041 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace; 2042 if (a->inode.size) { 2043 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace; 2044 } 2045 PetscFunctionReturn(0); 2046 } 2047 2048 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 2049 { 2050 Mat C = B; 2051 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2052 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2053 IS ip=b->row,iip = b->icol; 2054 PetscErrorCode ierr; 2055 const PetscInt *rip,*riip; 2056 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp; 2057 PetscInt *ai=a->i,*aj=a->j; 2058 PetscInt k,jmin,jmax,*c2r,*il,col,nexti,ili,nz; 2059 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2060 PetscBool perm_identity; 2061 FactorShiftCtx sctx; 2062 PetscReal rs; 2063 MatScalar d,*v; 2064 2065 PetscFunctionBegin; 2066 /* MatPivotSetUp(): initialize shift context sctx */ 2067 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 2068 2069 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 2070 sctx.shift_top = info->zeropivot; 2071 for (i=0; i<mbs; i++) { 2072 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 2073 d = (aa)[a->diag[i]]; 2074 rs = -PetscAbsScalar(d) - PetscRealPart(d); 2075 v = aa+ai[i]; 2076 nz = ai[i+1] - ai[i]; 2077 for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]); 2078 if (rs>sctx.shift_top) sctx.shift_top = rs; 2079 } 2080 sctx.shift_top *= 1.1; 2081 sctx.nshift_max = 5; 2082 sctx.shift_lo = 0.; 2083 sctx.shift_hi = 1.; 2084 } 2085 2086 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2087 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2088 2089 /* allocate working arrays 2090 c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col 2091 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 2092 */ 2093 ierr = PetscMalloc3(mbs,&rtmp,mbs,&il,mbs,&c2r);CHKERRQ(ierr); 2094 2095 do { 2096 sctx.newshift = PETSC_FALSE; 2097 2098 for (i=0; i<mbs; i++) c2r[i] = mbs; 2099 if (mbs) il[0] = 0; 2100 2101 for (k = 0; k<mbs; k++) { 2102 /* zero rtmp */ 2103 nz = bi[k+1] - bi[k]; 2104 bjtmp = bj + bi[k]; 2105 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2106 2107 /* load in initial unfactored row */ 2108 bval = ba + bi[k]; 2109 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2110 for (j = jmin; j < jmax; j++) { 2111 col = riip[aj[j]]; 2112 if (col >= k) { /* only take upper triangular entry */ 2113 rtmp[col] = aa[j]; 2114 *bval++ = 0.0; /* for in-place factorization */ 2115 } 2116 } 2117 /* shift the diagonal of the matrix: ZeropivotApply() */ 2118 rtmp[k] += sctx.shift_amount; /* shift the diagonal of the matrix */ 2119 2120 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2121 dk = rtmp[k]; 2122 i = c2r[k]; /* first row to be added to k_th row */ 2123 2124 while (i < k) { 2125 nexti = c2r[i]; /* next row to be added to k_th row */ 2126 2127 /* compute multiplier, update diag(k) and U(i,k) */ 2128 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2129 uikdi = -ba[ili]*ba[bdiag[i]]; /* diagonal(k) */ 2130 dk += uikdi*ba[ili]; /* update diag[k] */ 2131 ba[ili] = uikdi; /* -U(i,k) */ 2132 2133 /* add multiple of row i to k-th row */ 2134 jmin = ili + 1; jmax = bi[i+1]; 2135 if (jmin < jmax) { 2136 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2137 /* update il and c2r for row i */ 2138 il[i] = jmin; 2139 j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i; 2140 } 2141 i = nexti; 2142 } 2143 2144 /* copy data into U(k,:) */ 2145 rs = 0.0; 2146 jmin = bi[k]; jmax = bi[k+1]-1; 2147 if (jmin < jmax) { 2148 for (j=jmin; j<jmax; j++) { 2149 col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]); 2150 } 2151 /* add the k-th row into il and c2r */ 2152 il[k] = jmin; 2153 i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k; 2154 } 2155 2156 /* MatPivotCheck() */ 2157 sctx.rs = rs; 2158 sctx.pv = dk; 2159 ierr = MatPivotCheck(B,A,info,&sctx,i);CHKERRQ(ierr); 2160 if (sctx.newshift) break; 2161 dk = sctx.pv; 2162 2163 ba[bdiag[k]] = 1.0/dk; /* U(k,k) */ 2164 } 2165 } while (sctx.newshift); 2166 2167 ierr = PetscFree3(rtmp,il,c2r);CHKERRQ(ierr); 2168 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2169 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2170 2171 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2172 if (perm_identity) { 2173 B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2174 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2175 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering; 2176 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering; 2177 } else { 2178 B->ops->solve = MatSolve_SeqSBAIJ_1; 2179 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1; 2180 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1; 2181 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1; 2182 } 2183 2184 C->assembled = PETSC_TRUE; 2185 C->preallocated = PETSC_TRUE; 2186 2187 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2188 2189 /* MatPivotView() */ 2190 if (sctx.nshift) { 2191 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 2192 ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %g, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,(double)sctx.shift_amount,(double)sctx.shift_fraction,(double)sctx.shift_top);CHKERRQ(ierr); 2193 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 2194 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 2195 } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS) { 2196 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %g\n",sctx.nshift,(double)info->shiftamount);CHKERRQ(ierr); 2197 } 2198 } 2199 PetscFunctionReturn(0); 2200 } 2201 2202 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info) 2203 { 2204 Mat C = B; 2205 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2206 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2207 IS ip=b->row,iip = b->icol; 2208 PetscErrorCode ierr; 2209 const PetscInt *rip,*riip; 2210 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol,*bjtmp; 2211 PetscInt *ai=a->i,*aj=a->j; 2212 PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz; 2213 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2214 PetscBool perm_identity; 2215 FactorShiftCtx sctx; 2216 PetscReal rs; 2217 MatScalar d,*v; 2218 2219 PetscFunctionBegin; 2220 /* MatPivotSetUp(): initialize shift context sctx */ 2221 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 2222 2223 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 2224 sctx.shift_top = info->zeropivot; 2225 for (i=0; i<mbs; i++) { 2226 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 2227 d = (aa)[a->diag[i]]; 2228 rs = -PetscAbsScalar(d) - PetscRealPart(d); 2229 v = aa+ai[i]; 2230 nz = ai[i+1] - ai[i]; 2231 for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]); 2232 if (rs>sctx.shift_top) sctx.shift_top = rs; 2233 } 2234 sctx.shift_top *= 1.1; 2235 sctx.nshift_max = 5; 2236 sctx.shift_lo = 0.; 2237 sctx.shift_hi = 1.; 2238 } 2239 2240 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2241 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2242 2243 /* initialization */ 2244 ierr = PetscMalloc3(mbs,&rtmp,mbs,&il,mbs,&jl);CHKERRQ(ierr); 2245 2246 do { 2247 sctx.newshift = PETSC_FALSE; 2248 2249 for (i=0; i<mbs; i++) jl[i] = mbs; 2250 il[0] = 0; 2251 2252 for (k = 0; k<mbs; k++) { 2253 /* zero rtmp */ 2254 nz = bi[k+1] - bi[k]; 2255 bjtmp = bj + bi[k]; 2256 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2257 2258 bval = ba + bi[k]; 2259 /* initialize k-th row by the perm[k]-th row of A */ 2260 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2261 for (j = jmin; j < jmax; j++) { 2262 col = riip[aj[j]]; 2263 if (col >= k) { /* only take upper triangular entry */ 2264 rtmp[col] = aa[j]; 2265 *bval++ = 0.0; /* for in-place factorization */ 2266 } 2267 } 2268 /* shift the diagonal of the matrix */ 2269 if (sctx.nshift) rtmp[k] += sctx.shift_amount; 2270 2271 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2272 dk = rtmp[k]; 2273 i = jl[k]; /* first row to be added to k_th row */ 2274 2275 while (i < k) { 2276 nexti = jl[i]; /* next row to be added to k_th row */ 2277 2278 /* compute multiplier, update diag(k) and U(i,k) */ 2279 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2280 uikdi = -ba[ili]*ba[bi[i]]; /* diagonal(k) */ 2281 dk += uikdi*ba[ili]; 2282 ba[ili] = uikdi; /* -U(i,k) */ 2283 2284 /* add multiple of row i to k-th row */ 2285 jmin = ili + 1; jmax = bi[i+1]; 2286 if (jmin < jmax) { 2287 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2288 /* update il and jl for row i */ 2289 il[i] = jmin; 2290 j = bj[jmin]; jl[i] = jl[j]; jl[j] = i; 2291 } 2292 i = nexti; 2293 } 2294 2295 /* shift the diagonals when zero pivot is detected */ 2296 /* compute rs=sum of abs(off-diagonal) */ 2297 rs = 0.0; 2298 jmin = bi[k]+1; 2299 nz = bi[k+1] - jmin; 2300 bcol = bj + jmin; 2301 for (j=0; j<nz; j++) { 2302 rs += PetscAbsScalar(rtmp[bcol[j]]); 2303 } 2304 2305 sctx.rs = rs; 2306 sctx.pv = dk; 2307 ierr = MatPivotCheck(B,A,info,&sctx,k);CHKERRQ(ierr); 2308 if (sctx.newshift) break; 2309 dk = sctx.pv; 2310 2311 /* copy data into U(k,:) */ 2312 ba[bi[k]] = 1.0/dk; /* U(k,k) */ 2313 jmin = bi[k]+1; jmax = bi[k+1]; 2314 if (jmin < jmax) { 2315 for (j=jmin; j<jmax; j++) { 2316 col = bj[j]; ba[j] = rtmp[col]; 2317 } 2318 /* add the k-th row into il and jl */ 2319 il[k] = jmin; 2320 i = bj[jmin]; jl[k] = jl[i]; jl[i] = k; 2321 } 2322 } 2323 } while (sctx.newshift); 2324 2325 ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr); 2326 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2327 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2328 2329 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2330 if (perm_identity) { 2331 B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2332 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2333 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2334 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2335 } else { 2336 B->ops->solve = MatSolve_SeqSBAIJ_1_inplace; 2337 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_inplace; 2338 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_inplace; 2339 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_inplace; 2340 } 2341 2342 C->assembled = PETSC_TRUE; 2343 C->preallocated = PETSC_TRUE; 2344 2345 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2346 if (sctx.nshift) { 2347 if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 2348 ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 2349 } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 2350 ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 2351 } 2352 } 2353 PetscFunctionReturn(0); 2354 } 2355 2356 /* 2357 icc() under revised new data structure. 2358 Factored arrays bj and ba are stored as 2359 U(0,:),...,U(i,:),U(n-1,:) 2360 2361 ui=fact->i is an array of size n+1, in which 2362 ui+ 2363 ui[i]: points to 1st entry of U(i,:),i=0,...,n-1 2364 ui[n]: points to U(n-1,n-1)+1 2365 2366 udiag=fact->diag is an array of size n,in which 2367 udiag[i]: points to diagonal of U(i,:), i=0,...,n-1 2368 2369 U(i,:) contains udiag[i] as its last entry, i.e., 2370 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 2371 */ 2372 2373 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2374 { 2375 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2376 Mat_SeqSBAIJ *b; 2377 PetscErrorCode ierr; 2378 PetscBool perm_identity,missing; 2379 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2380 const PetscInt *rip,*riip; 2381 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2382 PetscInt nlnk,*lnk,*lnk_lvl=NULL,d; 2383 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2384 PetscReal fill =info->fill,levels=info->levels; 2385 PetscFreeSpaceList free_space =NULL,current_space=NULL; 2386 PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL; 2387 PetscBT lnkbt; 2388 IS iperm; 2389 2390 PetscFunctionBegin; 2391 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 2392 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2393 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2394 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2395 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2396 2397 ierr = PetscMalloc1(am+1,&ui);CHKERRQ(ierr); 2398 ierr = PetscMalloc1(am+1,&udiag);CHKERRQ(ierr); 2399 ui[0] = 0; 2400 2401 /* ICC(0) without matrix ordering: simply rearrange column indices */ 2402 if (!levels && perm_identity) { 2403 for (i=0; i<am; i++) { 2404 ncols = ai[i+1] - a->diag[i]; 2405 ui[i+1] = ui[i] + ncols; 2406 udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */ 2407 } 2408 ierr = PetscMalloc1(ui[am]+1,&uj);CHKERRQ(ierr); 2409 cols = uj; 2410 for (i=0; i<am; i++) { 2411 aj = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */ 2412 ncols = ai[i+1] - a->diag[i] -1; 2413 for (j=0; j<ncols; j++) *cols++ = aj[j]; 2414 *cols++ = i; /* diagonal is located as the last entry of U(i,:) */ 2415 } 2416 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2417 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2418 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2419 2420 /* initialization */ 2421 ierr = PetscMalloc1(am+1,&ajtmp);CHKERRQ(ierr); 2422 2423 /* jl: linked list for storing indices of the pivot rows 2424 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2425 ierr = PetscMalloc4(am,&uj_ptr,am,&uj_lvl_ptr,am,&jl,am,&il);CHKERRQ(ierr); 2426 for (i=0; i<am; i++) { 2427 jl[i] = am; il[i] = 0; 2428 } 2429 2430 /* create and initialize a linked list for storing column indices of the active row k */ 2431 nlnk = am + 1; 2432 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2433 2434 /* initial FreeSpace size is fill*(ai[am]+am)/2 */ 2435 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,(ai[am]+am)/2),&free_space);CHKERRQ(ierr); 2436 current_space = free_space; 2437 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,(ai[am]+am)/2),&free_space_lvl);CHKERRQ(ierr); 2438 current_space_lvl = free_space_lvl; 2439 2440 for (k=0; k<am; k++) { /* for each active row k */ 2441 /* initialize lnk by the column indices of row rip[k] of A */ 2442 nzk = 0; 2443 ncols = ai[rip[k]+1] - ai[rip[k]]; 2444 if (!ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2445 ncols_upper = 0; 2446 for (j=0; j<ncols; j++) { 2447 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2448 if (riip[i] >= k) { /* only take upper triangular entry */ 2449 ajtmp[ncols_upper] = i; 2450 ncols_upper++; 2451 } 2452 } 2453 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2454 nzk += nlnk; 2455 2456 /* update lnk by computing fill-in for each pivot row to be merged in */ 2457 prow = jl[k]; /* 1st pivot row */ 2458 2459 while (prow < k) { 2460 nextprow = jl[prow]; 2461 2462 /* merge prow into k-th row */ 2463 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2464 jmax = ui[prow+1]; 2465 ncols = jmax-jmin; 2466 i = jmin - ui[prow]; 2467 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2468 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2469 j = *(uj - 1); 2470 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2471 nzk += nlnk; 2472 2473 /* update il and jl for prow */ 2474 if (jmin < jmax) { 2475 il[prow] = jmin; 2476 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2477 } 2478 prow = nextprow; 2479 } 2480 2481 /* if free space is not available, make more free space */ 2482 if (current_space->local_remaining<nzk) { 2483 i = am - k + 1; /* num of unfactored rows */ 2484 i = PetscIntMultTruncate(i,PetscMin(nzk, i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2485 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2486 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2487 reallocs++; 2488 } 2489 2490 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2491 if (nzk == 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2492 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2493 2494 /* add the k-th row into il and jl */ 2495 if (nzk > 1) { 2496 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2497 jl[k] = jl[i]; jl[i] = k; 2498 il[k] = ui[k] + 1; 2499 } 2500 uj_ptr[k] = current_space->array; 2501 uj_lvl_ptr[k] = current_space_lvl->array; 2502 2503 current_space->array += nzk; 2504 current_space->local_used += nzk; 2505 current_space->local_remaining -= nzk; 2506 2507 current_space_lvl->array += nzk; 2508 current_space_lvl->local_used += nzk; 2509 current_space_lvl->local_remaining -= nzk; 2510 2511 ui[k+1] = ui[k] + nzk; 2512 } 2513 2514 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2515 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2516 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2517 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2518 2519 /* copy free_space into uj and free free_space; set ui, uj, udiag in new datastructure; */ 2520 ierr = PetscMalloc1(ui[am]+1,&uj);CHKERRQ(ierr); 2521 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor */ 2522 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2523 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2524 2525 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2526 2527 /* put together the new matrix in MATSEQSBAIJ format */ 2528 b = (Mat_SeqSBAIJ*)(fact)->data; 2529 b->singlemalloc = PETSC_FALSE; 2530 2531 ierr = PetscMalloc1(ui[am]+1,&b->a);CHKERRQ(ierr); 2532 2533 b->j = uj; 2534 b->i = ui; 2535 b->diag = udiag; 2536 b->free_diag = PETSC_TRUE; 2537 b->ilen = NULL; 2538 b->imax = NULL; 2539 b->row = perm; 2540 b->col = perm; 2541 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2542 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2543 b->icol = iperm; 2544 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2545 2546 ierr = PetscMalloc1(am+1,&b->solve_work);CHKERRQ(ierr); 2547 ierr = PetscLogObjectMemory((PetscObject)fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2548 2549 b->maxnz = b->nz = ui[am]; 2550 b->free_a = PETSC_TRUE; 2551 b->free_ij = PETSC_TRUE; 2552 2553 fact->info.factor_mallocs = reallocs; 2554 fact->info.fill_ratio_given = fill; 2555 if (ai[am] != 0) { 2556 /* nonzeros in lower triangular part of A (including diagonals) = (ai[am]+am)/2 */ 2557 fact->info.fill_ratio_needed = ((PetscReal)2*ui[am])/(ai[am]+am); 2558 } else { 2559 fact->info.fill_ratio_needed = 0.0; 2560 } 2561 #if defined(PETSC_USE_INFO) 2562 if (ai[am] != 0) { 2563 PetscReal af = fact->info.fill_ratio_needed; 2564 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);CHKERRQ(ierr); 2565 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 2566 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);CHKERRQ(ierr); 2567 } else { 2568 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 2569 } 2570 #endif 2571 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2572 PetscFunctionReturn(0); 2573 } 2574 2575 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2576 { 2577 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2578 Mat_SeqSBAIJ *b; 2579 PetscErrorCode ierr; 2580 PetscBool perm_identity,missing; 2581 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2582 const PetscInt *rip,*riip; 2583 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2584 PetscInt nlnk,*lnk,*lnk_lvl=NULL,d; 2585 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2586 PetscReal fill =info->fill,levels=info->levels; 2587 PetscFreeSpaceList free_space =NULL,current_space=NULL; 2588 PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL; 2589 PetscBT lnkbt; 2590 IS iperm; 2591 2592 PetscFunctionBegin; 2593 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 2594 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2595 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2596 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2597 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2598 2599 ierr = PetscMalloc1(am+1,&ui);CHKERRQ(ierr); 2600 ierr = PetscMalloc1(am+1,&udiag);CHKERRQ(ierr); 2601 ui[0] = 0; 2602 2603 /* ICC(0) without matrix ordering: simply copies fill pattern */ 2604 if (!levels && perm_identity) { 2605 2606 for (i=0; i<am; i++) { 2607 ui[i+1] = ui[i] + ai[i+1] - a->diag[i]; 2608 udiag[i] = ui[i]; 2609 } 2610 ierr = PetscMalloc1(ui[am]+1,&uj);CHKERRQ(ierr); 2611 cols = uj; 2612 for (i=0; i<am; i++) { 2613 aj = a->j + a->diag[i]; 2614 ncols = ui[i+1] - ui[i]; 2615 for (j=0; j<ncols; j++) *cols++ = *aj++; 2616 } 2617 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2618 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2619 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2620 2621 /* initialization */ 2622 ierr = PetscMalloc1(am+1,&ajtmp);CHKERRQ(ierr); 2623 2624 /* jl: linked list for storing indices of the pivot rows 2625 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2626 ierr = PetscMalloc4(am,&uj_ptr,am,&uj_lvl_ptr,am,&jl,am,&il);CHKERRQ(ierr); 2627 for (i=0; i<am; i++) { 2628 jl[i] = am; il[i] = 0; 2629 } 2630 2631 /* create and initialize a linked list for storing column indices of the active row k */ 2632 nlnk = am + 1; 2633 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2634 2635 /* initial FreeSpace size is fill*(ai[am]+1) */ 2636 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,ai[am]+1),&free_space);CHKERRQ(ierr); 2637 current_space = free_space; 2638 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,ai[am]+1),&free_space_lvl);CHKERRQ(ierr); 2639 current_space_lvl = free_space_lvl; 2640 2641 for (k=0; k<am; k++) { /* for each active row k */ 2642 /* initialize lnk by the column indices of row rip[k] of A */ 2643 nzk = 0; 2644 ncols = ai[rip[k]+1] - ai[rip[k]]; 2645 if (!ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2646 ncols_upper = 0; 2647 for (j=0; j<ncols; j++) { 2648 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2649 if (riip[i] >= k) { /* only take upper triangular entry */ 2650 ajtmp[ncols_upper] = i; 2651 ncols_upper++; 2652 } 2653 } 2654 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2655 nzk += nlnk; 2656 2657 /* update lnk by computing fill-in for each pivot row to be merged in */ 2658 prow = jl[k]; /* 1st pivot row */ 2659 2660 while (prow < k) { 2661 nextprow = jl[prow]; 2662 2663 /* merge prow into k-th row */ 2664 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2665 jmax = ui[prow+1]; 2666 ncols = jmax-jmin; 2667 i = jmin - ui[prow]; 2668 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2669 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2670 j = *(uj - 1); 2671 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2672 nzk += nlnk; 2673 2674 /* update il and jl for prow */ 2675 if (jmin < jmax) { 2676 il[prow] = jmin; 2677 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2678 } 2679 prow = nextprow; 2680 } 2681 2682 /* if free space is not available, make more free space */ 2683 if (current_space->local_remaining<nzk) { 2684 i = am - k + 1; /* num of unfactored rows */ 2685 i = PetscIntMultTruncate(i,PetscMin(nzk, i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2686 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2687 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2688 reallocs++; 2689 } 2690 2691 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2692 if (!nzk) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2693 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2694 2695 /* add the k-th row into il and jl */ 2696 if (nzk > 1) { 2697 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2698 jl[k] = jl[i]; jl[i] = k; 2699 il[k] = ui[k] + 1; 2700 } 2701 uj_ptr[k] = current_space->array; 2702 uj_lvl_ptr[k] = current_space_lvl->array; 2703 2704 current_space->array += nzk; 2705 current_space->local_used += nzk; 2706 current_space->local_remaining -= nzk; 2707 2708 current_space_lvl->array += nzk; 2709 current_space_lvl->local_used += nzk; 2710 current_space_lvl->local_remaining -= nzk; 2711 2712 ui[k+1] = ui[k] + nzk; 2713 } 2714 2715 #if defined(PETSC_USE_INFO) 2716 if (ai[am] != 0) { 2717 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2718 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);CHKERRQ(ierr); 2719 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 2720 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);CHKERRQ(ierr); 2721 } else { 2722 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 2723 } 2724 #endif 2725 2726 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2727 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2728 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2729 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2730 2731 /* destroy list of free space and other temporary array(s) */ 2732 ierr = PetscMalloc1(ui[am]+1,&uj);CHKERRQ(ierr); 2733 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 2734 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2735 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2736 2737 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2738 2739 /* put together the new matrix in MATSEQSBAIJ format */ 2740 2741 b = (Mat_SeqSBAIJ*)fact->data; 2742 b->singlemalloc = PETSC_FALSE; 2743 2744 ierr = PetscMalloc1(ui[am]+1,&b->a);CHKERRQ(ierr); 2745 2746 b->j = uj; 2747 b->i = ui; 2748 b->diag = udiag; 2749 b->free_diag = PETSC_TRUE; 2750 b->ilen = NULL; 2751 b->imax = NULL; 2752 b->row = perm; 2753 b->col = perm; 2754 2755 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2756 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2757 2758 b->icol = iperm; 2759 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2760 ierr = PetscMalloc1(am+1,&b->solve_work);CHKERRQ(ierr); 2761 ierr = PetscLogObjectMemory((PetscObject)fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2762 b->maxnz = b->nz = ui[am]; 2763 b->free_a = PETSC_TRUE; 2764 b->free_ij = PETSC_TRUE; 2765 2766 fact->info.factor_mallocs = reallocs; 2767 fact->info.fill_ratio_given = fill; 2768 if (ai[am] != 0) { 2769 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2770 } else { 2771 fact->info.fill_ratio_needed = 0.0; 2772 } 2773 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace; 2774 PetscFunctionReturn(0); 2775 } 2776 2777 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2778 { 2779 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2780 Mat_SeqSBAIJ *b; 2781 PetscErrorCode ierr; 2782 PetscBool perm_identity,missing; 2783 PetscReal fill = info->fill; 2784 const PetscInt *rip,*riip; 2785 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2786 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2787 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr,*udiag; 2788 PetscFreeSpaceList free_space=NULL,current_space=NULL; 2789 PetscBT lnkbt; 2790 IS iperm; 2791 2792 PetscFunctionBegin; 2793 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 2794 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 2795 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 2796 2797 /* check whether perm is the identity mapping */ 2798 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2799 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2800 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2801 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2802 2803 /* initialization */ 2804 ierr = PetscMalloc1(am+1,&ui);CHKERRQ(ierr); 2805 ierr = PetscMalloc1(am+1,&udiag);CHKERRQ(ierr); 2806 ui[0] = 0; 2807 2808 /* jl: linked list for storing indices of the pivot rows 2809 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2810 ierr = PetscMalloc4(am,&ui_ptr,am,&jl,am,&il,am,&cols);CHKERRQ(ierr); 2811 for (i=0; i<am; i++) { 2812 jl[i] = am; il[i] = 0; 2813 } 2814 2815 /* create and initialize a linked list for storing column indices of the active row k */ 2816 nlnk = am + 1; 2817 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2818 2819 /* initial FreeSpace size is fill*(ai[am]+am)/2 */ 2820 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,(ai[am]+am)/2),&free_space);CHKERRQ(ierr); 2821 current_space = free_space; 2822 2823 for (k=0; k<am; k++) { /* for each active row k */ 2824 /* initialize lnk by the column indices of row rip[k] of A */ 2825 nzk = 0; 2826 ncols = ai[rip[k]+1] - ai[rip[k]]; 2827 if (!ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2828 ncols_upper = 0; 2829 for (j=0; j<ncols; j++) { 2830 i = riip[*(aj + ai[rip[k]] + j)]; 2831 if (i >= k) { /* only take upper triangular entry */ 2832 cols[ncols_upper] = i; 2833 ncols_upper++; 2834 } 2835 } 2836 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2837 nzk += nlnk; 2838 2839 /* update lnk by computing fill-in for each pivot row to be merged in */ 2840 prow = jl[k]; /* 1st pivot row */ 2841 2842 while (prow < k) { 2843 nextprow = jl[prow]; 2844 /* merge prow into k-th row */ 2845 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2846 jmax = ui[prow+1]; 2847 ncols = jmax-jmin; 2848 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2849 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2850 nzk += nlnk; 2851 2852 /* update il and jl for prow */ 2853 if (jmin < jmax) { 2854 il[prow] = jmin; 2855 j = *uj_ptr; 2856 jl[prow] = jl[j]; 2857 jl[j] = prow; 2858 } 2859 prow = nextprow; 2860 } 2861 2862 /* if free space is not available, make more free space */ 2863 if (current_space->local_remaining<nzk) { 2864 i = am - k + 1; /* num of unfactored rows */ 2865 i = PetscIntMultTruncate(i,PetscMin(nzk,i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2866 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2867 reallocs++; 2868 } 2869 2870 /* copy data into free space, then initialize lnk */ 2871 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 2872 2873 /* add the k-th row into il and jl */ 2874 if (nzk > 1) { 2875 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2876 jl[k] = jl[i]; jl[i] = k; 2877 il[k] = ui[k] + 1; 2878 } 2879 ui_ptr[k] = current_space->array; 2880 2881 current_space->array += nzk; 2882 current_space->local_used += nzk; 2883 current_space->local_remaining -= nzk; 2884 2885 ui[k+1] = ui[k] + nzk; 2886 } 2887 2888 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2889 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2890 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 2891 2892 /* copy free_space into uj and free free_space; set ui, uj, udiag in new datastructure; */ 2893 ierr = PetscMalloc1(ui[am]+1,&uj);CHKERRQ(ierr); 2894 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor */ 2895 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2896 2897 /* put together the new matrix in MATSEQSBAIJ format */ 2898 2899 b = (Mat_SeqSBAIJ*)fact->data; 2900 b->singlemalloc = PETSC_FALSE; 2901 b->free_a = PETSC_TRUE; 2902 b->free_ij = PETSC_TRUE; 2903 2904 ierr = PetscMalloc1(ui[am]+1,&b->a);CHKERRQ(ierr); 2905 2906 b->j = uj; 2907 b->i = ui; 2908 b->diag = udiag; 2909 b->free_diag = PETSC_TRUE; 2910 b->ilen = NULL; 2911 b->imax = NULL; 2912 b->row = perm; 2913 b->col = perm; 2914 2915 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2916 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2917 2918 b->icol = iperm; 2919 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2920 2921 ierr = PetscMalloc1(am+1,&b->solve_work);CHKERRQ(ierr); 2922 ierr = PetscLogObjectMemory((PetscObject)fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2923 2924 b->maxnz = b->nz = ui[am]; 2925 2926 fact->info.factor_mallocs = reallocs; 2927 fact->info.fill_ratio_given = fill; 2928 if (ai[am] != 0) { 2929 /* nonzeros in lower triangular part of A (including diagonals) = (ai[am]+am)/2 */ 2930 fact->info.fill_ratio_needed = ((PetscReal)2*ui[am])/(ai[am]+am); 2931 } else { 2932 fact->info.fill_ratio_needed = 0.0; 2933 } 2934 #if defined(PETSC_USE_INFO) 2935 if (ai[am] != 0) { 2936 PetscReal af = fact->info.fill_ratio_needed; 2937 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);CHKERRQ(ierr); 2938 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 2939 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);CHKERRQ(ierr); 2940 } else { 2941 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 2942 } 2943 #endif 2944 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2945 PetscFunctionReturn(0); 2946 } 2947 2948 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2949 { 2950 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2951 Mat_SeqSBAIJ *b; 2952 PetscErrorCode ierr; 2953 PetscBool perm_identity,missing; 2954 PetscReal fill = info->fill; 2955 const PetscInt *rip,*riip; 2956 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2957 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2958 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr; 2959 PetscFreeSpaceList free_space=NULL,current_space=NULL; 2960 PetscBT lnkbt; 2961 IS iperm; 2962 2963 PetscFunctionBegin; 2964 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 2965 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 2966 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 2967 2968 /* check whether perm is the identity mapping */ 2969 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2970 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2971 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2972 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2973 2974 /* initialization */ 2975 ierr = PetscMalloc1(am+1,&ui);CHKERRQ(ierr); 2976 ui[0] = 0; 2977 2978 /* jl: linked list for storing indices of the pivot rows 2979 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2980 ierr = PetscMalloc4(am,&ui_ptr,am,&jl,am,&il,am,&cols);CHKERRQ(ierr); 2981 for (i=0; i<am; i++) { 2982 jl[i] = am; il[i] = 0; 2983 } 2984 2985 /* create and initialize a linked list for storing column indices of the active row k */ 2986 nlnk = am + 1; 2987 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2988 2989 /* initial FreeSpace size is fill*(ai[am]+1) */ 2990 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,ai[am]+1),&free_space);CHKERRQ(ierr); 2991 current_space = free_space; 2992 2993 for (k=0; k<am; k++) { /* for each active row k */ 2994 /* initialize lnk by the column indices of row rip[k] of A */ 2995 nzk = 0; 2996 ncols = ai[rip[k]+1] - ai[rip[k]]; 2997 if (!ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2998 ncols_upper = 0; 2999 for (j=0; j<ncols; j++) { 3000 i = riip[*(aj + ai[rip[k]] + j)]; 3001 if (i >= k) { /* only take upper triangular entry */ 3002 cols[ncols_upper] = i; 3003 ncols_upper++; 3004 } 3005 } 3006 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3007 nzk += nlnk; 3008 3009 /* update lnk by computing fill-in for each pivot row to be merged in */ 3010 prow = jl[k]; /* 1st pivot row */ 3011 3012 while (prow < k) { 3013 nextprow = jl[prow]; 3014 /* merge prow into k-th row */ 3015 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 3016 jmax = ui[prow+1]; 3017 ncols = jmax-jmin; 3018 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 3019 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3020 nzk += nlnk; 3021 3022 /* update il and jl for prow */ 3023 if (jmin < jmax) { 3024 il[prow] = jmin; 3025 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 3026 } 3027 prow = nextprow; 3028 } 3029 3030 /* if free space is not available, make more free space */ 3031 if (current_space->local_remaining<nzk) { 3032 i = am - k + 1; /* num of unfactored rows */ 3033 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 3034 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 3035 reallocs++; 3036 } 3037 3038 /* copy data into free space, then initialize lnk */ 3039 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 3040 3041 /* add the k-th row into il and jl */ 3042 if (nzk-1 > 0) { 3043 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 3044 jl[k] = jl[i]; jl[i] = k; 3045 il[k] = ui[k] + 1; 3046 } 3047 ui_ptr[k] = current_space->array; 3048 3049 current_space->array += nzk; 3050 current_space->local_used += nzk; 3051 current_space->local_remaining -= nzk; 3052 3053 ui[k+1] = ui[k] + nzk; 3054 } 3055 3056 #if defined(PETSC_USE_INFO) 3057 if (ai[am] != 0) { 3058 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 3059 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);CHKERRQ(ierr); 3060 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 3061 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);CHKERRQ(ierr); 3062 } else { 3063 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 3064 } 3065 #endif 3066 3067 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 3068 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 3069 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 3070 3071 /* destroy list of free space and other temporary array(s) */ 3072 ierr = PetscMalloc1(ui[am]+1,&uj);CHKERRQ(ierr); 3073 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 3074 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3075 3076 /* put together the new matrix in MATSEQSBAIJ format */ 3077 3078 b = (Mat_SeqSBAIJ*)fact->data; 3079 b->singlemalloc = PETSC_FALSE; 3080 b->free_a = PETSC_TRUE; 3081 b->free_ij = PETSC_TRUE; 3082 3083 ierr = PetscMalloc1(ui[am]+1,&b->a);CHKERRQ(ierr); 3084 3085 b->j = uj; 3086 b->i = ui; 3087 b->diag = NULL; 3088 b->ilen = NULL; 3089 b->imax = NULL; 3090 b->row = perm; 3091 b->col = perm; 3092 3093 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3094 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3095 3096 b->icol = iperm; 3097 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 3098 3099 ierr = PetscMalloc1(am+1,&b->solve_work);CHKERRQ(ierr); 3100 ierr = PetscLogObjectMemory((PetscObject)fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3101 b->maxnz = b->nz = ui[am]; 3102 3103 fact->info.factor_mallocs = reallocs; 3104 fact->info.fill_ratio_given = fill; 3105 if (ai[am] != 0) { 3106 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 3107 } else { 3108 fact->info.fill_ratio_needed = 0.0; 3109 } 3110 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace; 3111 PetscFunctionReturn(0); 3112 } 3113 3114 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx) 3115 { 3116 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3117 PetscErrorCode ierr; 3118 PetscInt n = A->rmap->n; 3119 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag,*vi; 3120 PetscScalar *x,sum; 3121 const PetscScalar *b; 3122 const MatScalar *aa = a->a,*v; 3123 PetscInt i,nz; 3124 3125 PetscFunctionBegin; 3126 if (!n) PetscFunctionReturn(0); 3127 3128 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 3129 ierr = VecGetArrayWrite(xx,&x);CHKERRQ(ierr); 3130 3131 /* forward solve the lower triangular */ 3132 x[0] = b[0]; 3133 v = aa; 3134 vi = aj; 3135 for (i=1; i<n; i++) { 3136 nz = ai[i+1] - ai[i]; 3137 sum = b[i]; 3138 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3139 v += nz; 3140 vi += nz; 3141 x[i] = sum; 3142 } 3143 3144 /* backward solve the upper triangular */ 3145 for (i=n-1; i>=0; i--) { 3146 v = aa + adiag[i+1] + 1; 3147 vi = aj + adiag[i+1] + 1; 3148 nz = adiag[i] - adiag[i+1]-1; 3149 sum = x[i]; 3150 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3151 x[i] = sum*v[nz]; /* x[i]=aa[adiag[i]]*sum; v++; */ 3152 } 3153 3154 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 3155 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 3156 ierr = VecRestoreArrayWrite(xx,&x);CHKERRQ(ierr); 3157 PetscFunctionReturn(0); 3158 } 3159 3160 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx) 3161 { 3162 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3163 IS iscol = a->col,isrow = a->row; 3164 PetscErrorCode ierr; 3165 PetscInt i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz; 3166 const PetscInt *rout,*cout,*r,*c; 3167 PetscScalar *x,*tmp,sum; 3168 const PetscScalar *b; 3169 const MatScalar *aa = a->a,*v; 3170 3171 PetscFunctionBegin; 3172 if (!n) PetscFunctionReturn(0); 3173 3174 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 3175 ierr = VecGetArrayWrite(xx,&x);CHKERRQ(ierr); 3176 tmp = a->solve_work; 3177 3178 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 3179 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 3180 3181 /* forward solve the lower triangular */ 3182 tmp[0] = b[r[0]]; 3183 v = aa; 3184 vi = aj; 3185 for (i=1; i<n; i++) { 3186 nz = ai[i+1] - ai[i]; 3187 sum = b[r[i]]; 3188 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3189 tmp[i] = sum; 3190 v += nz; vi += nz; 3191 } 3192 3193 /* backward solve the upper triangular */ 3194 for (i=n-1; i>=0; i--) { 3195 v = aa + adiag[i+1]+1; 3196 vi = aj + adiag[i+1]+1; 3197 nz = adiag[i]-adiag[i+1]-1; 3198 sum = tmp[i]; 3199 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3200 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 3201 } 3202 3203 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 3204 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 3205 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 3206 ierr = VecRestoreArrayWrite(xx,&x);CHKERRQ(ierr); 3207 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 3208 PetscFunctionReturn(0); 3209 } 3210 3211 /* 3212 This will get a new name and become a varient of MatILUFactor_SeqAIJ() there is no longer separate functions in the matrix function table for dt factors 3213 */ 3214 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact) 3215 { 3216 Mat B = *fact; 3217 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b; 3218 IS isicol; 3219 PetscErrorCode ierr; 3220 const PetscInt *r,*ic; 3221 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag; 3222 PetscInt *bi,*bj,*bdiag,*bdiag_rev; 3223 PetscInt row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au; 3224 PetscInt nlnk,*lnk; 3225 PetscBT lnkbt; 3226 PetscBool row_identity,icol_identity; 3227 MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp; 3228 const PetscInt *ics; 3229 PetscInt j,nz,*pj,*bjtmp,k,ncut,*jtmp; 3230 PetscReal dt =info->dt,shift=info->shiftamount; 3231 PetscInt dtcount=(PetscInt)info->dtcount,nnz_max; 3232 PetscBool missing; 3233 3234 PetscFunctionBegin; 3235 if (dt == PETSC_DEFAULT) dt = 0.005; 3236 if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax); 3237 3238 /* ------- symbolic factorization, can be reused ---------*/ 3239 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 3240 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 3241 adiag=a->diag; 3242 3243 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 3244 3245 /* bdiag is location of diagonal in factor */ 3246 ierr = PetscMalloc1(n+1,&bdiag);CHKERRQ(ierr); /* becomes b->diag */ 3247 ierr = PetscMalloc1(n+1,&bdiag_rev);CHKERRQ(ierr); /* temporary */ 3248 3249 /* allocate row pointers bi */ 3250 ierr = PetscMalloc1(2*n+2,&bi);CHKERRQ(ierr); 3251 3252 /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */ 3253 if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */ 3254 nnz_max = ai[n]+2*n*dtcount+2; 3255 3256 ierr = PetscMalloc1(nnz_max+1,&bj);CHKERRQ(ierr); 3257 ierr = PetscMalloc1(nnz_max+1,&ba);CHKERRQ(ierr); 3258 3259 /* put together the new matrix */ 3260 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr); 3261 ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)isicol);CHKERRQ(ierr); 3262 b = (Mat_SeqAIJ*)B->data; 3263 3264 b->free_a = PETSC_TRUE; 3265 b->free_ij = PETSC_TRUE; 3266 b->singlemalloc = PETSC_FALSE; 3267 3268 b->a = ba; 3269 b->j = bj; 3270 b->i = bi; 3271 b->diag = bdiag; 3272 b->ilen = NULL; 3273 b->imax = NULL; 3274 b->row = isrow; 3275 b->col = iscol; 3276 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 3277 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 3278 b->icol = isicol; 3279 3280 ierr = PetscMalloc1(n+1,&b->solve_work);CHKERRQ(ierr); 3281 ierr = PetscLogObjectMemory((PetscObject)B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3282 b->maxnz = nnz_max; 3283 3284 B->factortype = MAT_FACTOR_ILUDT; 3285 B->info.factor_mallocs = 0; 3286 B->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]); 3287 /* ------- end of symbolic factorization ---------*/ 3288 3289 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3290 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3291 ics = ic; 3292 3293 /* linked list for storing column indices of the active row */ 3294 nlnk = n + 1; 3295 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3296 3297 /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */ 3298 ierr = PetscMalloc2(n,&im,n,&jtmp);CHKERRQ(ierr); 3299 /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */ 3300 ierr = PetscMalloc2(n,&rtmp,n,&vtmp);CHKERRQ(ierr); 3301 ierr = PetscArrayzero(rtmp,n);CHKERRQ(ierr); 3302 3303 bi[0] = 0; 3304 bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */ 3305 bdiag_rev[n] = bdiag[0]; 3306 bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */ 3307 for (i=0; i<n; i++) { 3308 /* copy initial fill into linked list */ 3309 nzi = ai[r[i]+1] - ai[r[i]]; 3310 if (!nzi) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 3311 nzi_al = adiag[r[i]] - ai[r[i]]; 3312 nzi_au = ai[r[i]+1] - adiag[r[i]] -1; 3313 ajtmp = aj + ai[r[i]]; 3314 ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3315 3316 /* load in initial (unfactored row) */ 3317 aatmp = a->a + ai[r[i]]; 3318 for (j=0; j<nzi; j++) { 3319 rtmp[ics[*ajtmp++]] = *aatmp++; 3320 } 3321 3322 /* add pivot rows into linked list */ 3323 row = lnk[n]; 3324 while (row < i) { 3325 nzi_bl = bi[row+1] - bi[row] + 1; 3326 bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */ 3327 ierr = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr); 3328 nzi += nlnk; 3329 row = lnk[row]; 3330 } 3331 3332 /* copy data from lnk into jtmp, then initialize lnk */ 3333 ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr); 3334 3335 /* numerical factorization */ 3336 bjtmp = jtmp; 3337 row = *bjtmp++; /* 1st pivot row */ 3338 while (row < i) { 3339 pc = rtmp + row; 3340 pv = ba + bdiag[row]; /* 1./(diag of the pivot row) */ 3341 multiplier = (*pc) * (*pv); 3342 *pc = multiplier; 3343 if (PetscAbsScalar(*pc) > dt) { /* apply tolerance dropping rule */ 3344 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3345 pv = ba + bdiag[row+1] + 1; 3346 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3347 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3348 ierr = PetscLogFlops(1+2.0*nz);CHKERRQ(ierr); 3349 } 3350 row = *bjtmp++; 3351 } 3352 3353 /* copy sparse rtmp into contiguous vtmp; separate L and U part */ 3354 diag_tmp = rtmp[i]; /* save diagonal value - may not needed?? */ 3355 nzi_bl = 0; j = 0; 3356 while (jtmp[j] < i) { /* Note: jtmp is sorted */ 3357 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3358 nzi_bl++; j++; 3359 } 3360 nzi_bu = nzi - nzi_bl -1; 3361 while (j < nzi) { 3362 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3363 j++; 3364 } 3365 3366 bjtmp = bj + bi[i]; 3367 batmp = ba + bi[i]; 3368 /* apply level dropping rule to L part */ 3369 ncut = nzi_al + dtcount; 3370 if (ncut < nzi_bl) { 3371 ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr); 3372 ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr); 3373 } else { 3374 ncut = nzi_bl; 3375 } 3376 for (j=0; j<ncut; j++) { 3377 bjtmp[j] = jtmp[j]; 3378 batmp[j] = vtmp[j]; 3379 } 3380 bi[i+1] = bi[i] + ncut; 3381 nzi = ncut + 1; 3382 3383 /* apply level dropping rule to U part */ 3384 ncut = nzi_au + dtcount; 3385 if (ncut < nzi_bu) { 3386 ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr); 3387 ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr); 3388 } else { 3389 ncut = nzi_bu; 3390 } 3391 nzi += ncut; 3392 3393 /* mark bdiagonal */ 3394 bdiag[i+1] = bdiag[i] - (ncut + 1); 3395 bdiag_rev[n-i-1] = bdiag[i+1]; 3396 bi[2*n - i] = bi[2*n - i +1] - (ncut + 1); 3397 bjtmp = bj + bdiag[i]; 3398 batmp = ba + bdiag[i]; 3399 *bjtmp = i; 3400 *batmp = diag_tmp; /* rtmp[i]; */ 3401 if (*batmp == 0.0) { 3402 *batmp = dt+shift; 3403 } 3404 *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */ 3405 3406 bjtmp = bj + bdiag[i+1]+1; 3407 batmp = ba + bdiag[i+1]+1; 3408 for (k=0; k<ncut; k++) { 3409 bjtmp[k] = jtmp[nzi_bl+1+k]; 3410 batmp[k] = vtmp[nzi_bl+1+k]; 3411 } 3412 3413 im[i] = nzi; /* used by PetscLLAddSortedLU() */ 3414 } /* for (i=0; i<n; i++) */ 3415 if (bi[n] >= bdiag[n]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"end of L array %d cannot >= the beginning of U array %d",bi[n],bdiag[n]); 3416 3417 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3418 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3419 3420 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3421 ierr = PetscFree2(im,jtmp);CHKERRQ(ierr); 3422 ierr = PetscFree2(rtmp,vtmp);CHKERRQ(ierr); 3423 ierr = PetscFree(bdiag_rev);CHKERRQ(ierr); 3424 3425 ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr); 3426 b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n]; 3427 3428 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3429 ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr); 3430 if (row_identity && icol_identity) { 3431 B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 3432 } else { 3433 B->ops->solve = MatSolve_SeqAIJ; 3434 } 3435 3436 B->ops->solveadd = NULL; 3437 B->ops->solvetranspose = NULL; 3438 B->ops->solvetransposeadd = NULL; 3439 B->ops->matsolve = NULL; 3440 B->assembled = PETSC_TRUE; 3441 B->preallocated = PETSC_TRUE; 3442 PetscFunctionReturn(0); 3443 } 3444 3445 /* a wraper of MatILUDTFactor_SeqAIJ() */ 3446 /* 3447 This will get a new name and become a varient of MatILUFactor_SeqAIJ() there is no longer separate functions in the matrix function table for dt factors 3448 */ 3449 3450 PetscErrorCode MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info) 3451 { 3452 PetscErrorCode ierr; 3453 3454 PetscFunctionBegin; 3455 ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr); 3456 PetscFunctionReturn(0); 3457 } 3458 3459 /* 3460 same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors 3461 - intend to replace existing MatLUFactorNumeric_SeqAIJ() 3462 */ 3463 /* 3464 This will get a new name and become a varient of MatILUFactor_SeqAIJ() there is no longer separate functions in the matrix function table for dt factors 3465 */ 3466 3467 PetscErrorCode MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info) 3468 { 3469 Mat C =fact; 3470 Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)C->data; 3471 IS isrow = b->row,isicol = b->icol; 3472 PetscErrorCode ierr; 3473 const PetscInt *r,*ic,*ics; 3474 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 3475 PetscInt *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj; 3476 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 3477 PetscReal dt=info->dt,shift=info->shiftamount; 3478 PetscBool row_identity, col_identity; 3479 3480 PetscFunctionBegin; 3481 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3482 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3483 ierr = PetscMalloc1(n+1,&rtmp);CHKERRQ(ierr); 3484 ics = ic; 3485 3486 for (i=0; i<n; i++) { 3487 /* initialize rtmp array */ 3488 nzl = bi[i+1] - bi[i]; /* num of nozeros in L(i,:) */ 3489 bjtmp = bj + bi[i]; 3490 for (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0; 3491 rtmp[i] = 0.0; 3492 nzu = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */ 3493 bjtmp = bj + bdiag[i+1] + 1; 3494 for (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0; 3495 3496 /* load in initial unfactored row of A */ 3497 nz = ai[r[i]+1] - ai[r[i]]; 3498 ajtmp = aj + ai[r[i]]; 3499 v = aa + ai[r[i]]; 3500 for (j=0; j<nz; j++) { 3501 rtmp[ics[*ajtmp++]] = v[j]; 3502 } 3503 3504 /* numerical factorization */ 3505 bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */ 3506 nzl = bi[i+1] - bi[i]; /* num of entries in L(i,:) */ 3507 k = 0; 3508 while (k < nzl) { 3509 row = *bjtmp++; 3510 pc = rtmp + row; 3511 pv = b->a + bdiag[row]; /* 1./(diag of the pivot row) */ 3512 multiplier = (*pc) * (*pv); 3513 *pc = multiplier; 3514 if (PetscAbsScalar(multiplier) > dt) { 3515 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3516 pv = b->a + bdiag[row+1] + 1; 3517 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3518 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3519 ierr = PetscLogFlops(1+2.0*nz);CHKERRQ(ierr); 3520 } 3521 k++; 3522 } 3523 3524 /* finished row so stick it into b->a */ 3525 /* L-part */ 3526 pv = b->a + bi[i]; 3527 pj = bj + bi[i]; 3528 nzl = bi[i+1] - bi[i]; 3529 for (j=0; j<nzl; j++) { 3530 pv[j] = rtmp[pj[j]]; 3531 } 3532 3533 /* diagonal: invert diagonal entries for simplier triangular solves */ 3534 if (rtmp[i] == 0.0) rtmp[i] = dt+shift; 3535 b->a[bdiag[i]] = 1.0/rtmp[i]; 3536 3537 /* U-part */ 3538 pv = b->a + bdiag[i+1] + 1; 3539 pj = bj + bdiag[i+1] + 1; 3540 nzu = bdiag[i] - bdiag[i+1] - 1; 3541 for (j=0; j<nzu; j++) { 3542 pv[j] = rtmp[pj[j]]; 3543 } 3544 } 3545 3546 ierr = PetscFree(rtmp);CHKERRQ(ierr); 3547 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3548 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3549 3550 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3551 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 3552 if (row_identity && col_identity) { 3553 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 3554 } else { 3555 C->ops->solve = MatSolve_SeqAIJ; 3556 } 3557 C->ops->solveadd = NULL; 3558 C->ops->solvetranspose = NULL; 3559 C->ops->solvetransposeadd = NULL; 3560 C->ops->matsolve = NULL; 3561 C->assembled = PETSC_TRUE; 3562 C->preallocated = PETSC_TRUE; 3563 3564 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 3565 PetscFunctionReturn(0); 3566 } 3567