1 #define PETSCMAT_DLL 2 3 4 #include "../src/mat/impls/aij/seq/aij.h" 5 #include "../src/mat/impls/sbaij/seq/sbaij.h" 6 #include "petscbt.h" 7 #include "../src/mat/utils/freespace.h" 8 9 EXTERN_C_BEGIN 10 #undef __FUNCT__ 11 #define __FUNCT__ "MatOrdering_Flow_SeqAIJ" 12 /* 13 Computes an ordering to get most of the large numerical values in the lower triangular part of the matrix 14 */ 15 PetscErrorCode MatOrdering_Flow_SeqAIJ(Mat mat,const MatOrderingType type,IS *irow,IS *icol) 16 { 17 Mat_SeqAIJ *a = (Mat_SeqAIJ*)mat->data; 18 PetscErrorCode ierr; 19 PetscInt i,j,jj,k, kk,n = mat->rmap->n, current = 0, newcurrent = 0,*order; 20 const PetscInt *ai = a->i, *aj = a->j; 21 const PetscScalar *aa = a->a; 22 PetscTruth *done; 23 PetscReal best,past = 0,future; 24 25 PetscFunctionBegin; 26 /* pick initial row */ 27 best = -1; 28 for (i=0; i<n; i++) { 29 future = 0.0; 30 for (j=ai[i]; j<ai[i+1]; j++) { 31 if (aj[j] != i) future += PetscAbsScalar(aa[j]); else past = PetscAbsScalar(aa[j]); 32 } 33 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 34 if (past/future > best) { 35 best = past/future; 36 current = i; 37 } 38 } 39 40 ierr = PetscMalloc(n*sizeof(PetscTruth),&done);CHKERRQ(ierr); 41 ierr = PetscMemzero(done,n*sizeof(PetscTruth));CHKERRQ(ierr); 42 ierr = PetscMalloc(n*sizeof(PetscInt),&order);CHKERRQ(ierr); 43 order[0] = current; 44 for (i=0; i<n-1; i++) { 45 done[current] = PETSC_TRUE; 46 best = -1; 47 /* loop over all neighbors of current pivot */ 48 for (j=ai[current]; j<ai[current+1]; j++) { 49 jj = aj[j]; 50 if (done[jj]) continue; 51 /* loop over columns of potential next row computing weights for below and above diagonal */ 52 past = future = 0.0; 53 for (k=ai[jj]; k<ai[jj+1]; k++) { 54 kk = aj[k]; 55 if (done[kk]) past += PetscAbsScalar(aa[k]); 56 else if (kk != jj) future += PetscAbsScalar(aa[k]); 57 } 58 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 59 if (past/future > best) { 60 best = past/future; 61 newcurrent = jj; 62 } 63 } 64 if (best == -1) { /* no neighbors to select from so select best of all that remain */ 65 best = -1; 66 for (k=0; k<n; k++) { 67 if (done[k]) continue; 68 future = 0.0; 69 past = 0.0; 70 for (j=ai[k]; j<ai[k+1]; j++) { 71 kk = aj[j]; 72 if (done[kk]) past += PetscAbsScalar(aa[j]); 73 else if (kk != k) future += PetscAbsScalar(aa[j]); 74 } 75 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 76 if (past/future > best) { 77 best = past/future; 78 newcurrent = k; 79 } 80 } 81 } 82 if (current == newcurrent) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"newcurrent cannot be current"); 83 current = newcurrent; 84 order[i+1] = current; 85 } 86 ierr = ISCreateGeneral(PETSC_COMM_SELF,n,order,irow);CHKERRQ(ierr); 87 *icol = *irow; 88 ierr = PetscObjectReference((PetscObject)*irow);CHKERRQ(ierr); 89 ierr = PetscFree(done);CHKERRQ(ierr); 90 ierr = PetscFree(order);CHKERRQ(ierr); 91 PetscFunctionReturn(0); 92 } 93 EXTERN_C_END 94 95 EXTERN_C_BEGIN 96 #undef __FUNCT__ 97 #define __FUNCT__ "MatGetFactorAvailable_seqaij_petsc" 98 PetscErrorCode MatGetFactorAvailable_seqaij_petsc(Mat A,MatFactorType ftype,PetscTruth *flg) 99 { 100 PetscFunctionBegin; 101 *flg = PETSC_TRUE; 102 PetscFunctionReturn(0); 103 } 104 EXTERN_C_END 105 106 EXTERN_C_BEGIN 107 #undef __FUNCT__ 108 #define __FUNCT__ "MatGetFactor_seqaij_petsc" 109 PetscErrorCode MatGetFactor_seqaij_petsc(Mat A,MatFactorType ftype,Mat *B) 110 { 111 PetscInt n = A->rmap->n; 112 PetscErrorCode ierr; 113 114 PetscFunctionBegin; 115 ierr = MatCreate(((PetscObject)A)->comm,B);CHKERRQ(ierr); 116 ierr = MatSetSizes(*B,n,n,n,n);CHKERRQ(ierr); 117 if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT){ 118 ierr = MatSetType(*B,MATSEQAIJ);CHKERRQ(ierr); 119 (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJ; 120 (*B)->ops->lufactorsymbolic = MatLUFactorSymbolic_SeqAIJ; 121 } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) { 122 ierr = MatSetType(*B,MATSEQSBAIJ);CHKERRQ(ierr); 123 ierr = MatSeqSBAIJSetPreallocation(*B,1,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 124 (*B)->ops->iccfactorsymbolic = MatICCFactorSymbolic_SeqAIJ; 125 (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJ; 126 } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor type not supported"); 127 (*B)->factortype = ftype; 128 PetscFunctionReturn(0); 129 } 130 EXTERN_C_END 131 132 #undef __FUNCT__ 133 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ_inplace" 134 PetscErrorCode MatLUFactorSymbolic_SeqAIJ_inplace(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 135 { 136 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 137 IS isicol; 138 PetscErrorCode ierr; 139 const PetscInt *r,*ic; 140 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j; 141 PetscInt *bi,*bj,*ajtmp; 142 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 143 PetscReal f; 144 PetscInt nlnk,*lnk,k,**bi_ptr; 145 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 146 PetscBT lnkbt; 147 148 PetscFunctionBegin; 149 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"matrix must be square"); 150 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 151 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 152 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 153 154 /* get new row pointers */ 155 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 156 bi[0] = 0; 157 158 /* bdiag is location of diagonal in factor */ 159 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 160 bdiag[0] = 0; 161 162 /* linked list for storing column indices of the active row */ 163 nlnk = n + 1; 164 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 165 166 ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr); 167 168 /* initial FreeSpace size is f*(ai[n]+1) */ 169 f = info->fill; 170 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 171 current_space = free_space; 172 173 for (i=0; i<n; i++) { 174 /* copy previous fill into linked list */ 175 nzi = 0; 176 nnz = ai[r[i]+1] - ai[r[i]]; 177 if (!nnz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 178 ajtmp = aj + ai[r[i]]; 179 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 180 nzi += nlnk; 181 182 /* add pivot rows into linked list */ 183 row = lnk[n]; 184 while (row < i) { 185 nzbd = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */ 186 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 187 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 188 nzi += nlnk; 189 row = lnk[row]; 190 } 191 bi[i+1] = bi[i] + nzi; 192 im[i] = nzi; 193 194 /* mark bdiag */ 195 nzbd = 0; 196 nnz = nzi; 197 k = lnk[n]; 198 while (nnz-- && k < i){ 199 nzbd++; 200 k = lnk[k]; 201 } 202 bdiag[i] = bi[i] + nzbd; 203 204 /* if free space is not available, make more free space */ 205 if (current_space->local_remaining<nzi) { 206 nnz = (n - i)*nzi; /* estimated and max additional space needed */ 207 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 208 reallocs++; 209 } 210 211 /* copy data into free space, then initialize lnk */ 212 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 213 bi_ptr[i] = current_space->array; 214 current_space->array += nzi; 215 current_space->local_used += nzi; 216 current_space->local_remaining -= nzi; 217 } 218 #if defined(PETSC_USE_INFO) 219 if (ai[n] != 0) { 220 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 221 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 222 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 223 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr); 224 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 225 } else { 226 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 227 } 228 #endif 229 230 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 231 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 232 233 /* destroy list of free space and other temporary array(s) */ 234 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 235 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); 236 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 237 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 238 239 /* put together the new matrix */ 240 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 241 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 242 b = (Mat_SeqAIJ*)(B)->data; 243 b->free_a = PETSC_TRUE; 244 b->free_ij = PETSC_TRUE; 245 b->singlemalloc = PETSC_FALSE; 246 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 247 b->j = bj; 248 b->i = bi; 249 b->diag = bdiag; 250 b->ilen = 0; 251 b->imax = 0; 252 b->row = isrow; 253 b->col = iscol; 254 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 255 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 256 b->icol = isicol; 257 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 258 259 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 260 ierr = PetscLogObjectMemory(B,(bi[n]-n)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 261 b->maxnz = b->nz = bi[n] ; 262 263 (B)->factortype = MAT_FACTOR_LU; 264 (B)->info.factor_mallocs = reallocs; 265 (B)->info.fill_ratio_given = f; 266 267 if (ai[n]) { 268 (B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 269 } else { 270 (B)->info.fill_ratio_needed = 0.0; 271 } 272 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace; 273 if (a->inode.size) { 274 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace; 275 } 276 PetscFunctionReturn(0); 277 } 278 279 #undef __FUNCT__ 280 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ" 281 PetscErrorCode MatLUFactorSymbolic_SeqAIJ(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 282 { 283 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 284 IS isicol; 285 PetscErrorCode ierr; 286 const PetscInt *r,*ic; 287 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j; 288 PetscInt *bi,*bj,*ajtmp; 289 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 290 PetscReal f; 291 PetscInt nlnk,*lnk,k,**bi_ptr; 292 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 293 PetscBT lnkbt; 294 PetscTruth olddatastruct=PETSC_FALSE; 295 296 PetscFunctionBegin; 297 /* Uncomment the oldatastruct part only while testing new data structure for MatSolve() */ 298 ierr = PetscOptionsGetTruth(PETSC_NULL,"-lu_old",&olddatastruct,PETSC_NULL);CHKERRQ(ierr); 299 if(olddatastruct){ 300 ierr = MatLUFactorSymbolic_SeqAIJ_inplace(B,A,isrow,iscol,info);CHKERRQ(ierr); 301 PetscFunctionReturn(0); 302 } 303 304 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"matrix must be square"); 305 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 306 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 307 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 308 309 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 310 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 311 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 312 bi[0] = bdiag[0] = 0; 313 314 /* linked list for storing column indices of the active row */ 315 nlnk = n + 1; 316 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 317 318 ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr); 319 320 /* initial FreeSpace size is f*(ai[n]+1) */ 321 f = info->fill; 322 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 323 current_space = free_space; 324 325 for (i=0; i<n; i++) { 326 /* copy previous fill into linked list */ 327 nzi = 0; 328 nnz = ai[r[i]+1] - ai[r[i]]; 329 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); 330 ajtmp = aj + ai[r[i]]; 331 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 332 nzi += nlnk; 333 334 /* add pivot rows into linked list */ 335 row = lnk[n]; 336 while (row < i){ 337 nzbd = bdiag[row] + 1; /* num of entries in the row with column index <= row */ 338 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 339 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 340 nzi += nlnk; 341 row = lnk[row]; 342 } 343 bi[i+1] = bi[i] + nzi; 344 im[i] = nzi; 345 346 /* mark bdiag */ 347 nzbd = 0; 348 nnz = nzi; 349 k = lnk[n]; 350 while (nnz-- && k < i){ 351 nzbd++; 352 k = lnk[k]; 353 } 354 bdiag[i] = nzbd; /* note: bdiag[i] = nnzL as input for PetscFreeSpaceContiguous_LU() */ 355 356 /* if free space is not available, make more free space */ 357 if (current_space->local_remaining<nzi) { 358 nnz = 2*(n - i)*nzi; /* estimated and max additional space needed */ 359 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 360 reallocs++; 361 } 362 363 /* copy data into free space, then initialize lnk */ 364 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 365 bi_ptr[i] = current_space->array; 366 current_space->array += nzi; 367 current_space->local_used += nzi; 368 current_space->local_remaining -= nzi; 369 } 370 #if defined(PETSC_USE_INFO) 371 if (ai[n] != 0) { 372 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 373 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 374 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 375 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr); 376 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 377 } else { 378 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 379 } 380 #endif 381 382 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 383 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 384 385 /* destroy list of free space and other temporary array(s) */ 386 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 387 ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 388 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 389 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 390 391 /* put together the new matrix */ 392 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 393 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 394 b = (Mat_SeqAIJ*)(B)->data; 395 b->free_a = PETSC_TRUE; 396 b->free_ij = PETSC_TRUE; 397 b->singlemalloc = PETSC_FALSE; 398 ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 399 b->j = bj; 400 b->i = bi; 401 b->diag = bdiag; 402 b->ilen = 0; 403 b->imax = 0; 404 b->row = isrow; 405 b->col = iscol; 406 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 407 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 408 b->icol = isicol; 409 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 410 411 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 412 ierr = PetscLogObjectMemory(B,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 413 b->maxnz = b->nz = bdiag[0]+1; 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 B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 424 if (a->inode.size) { 425 B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode; 426 } 427 PetscFunctionReturn(0); 428 } 429 430 /* 431 Trouble in factorization, should we dump the original matrix? 432 */ 433 #undef __FUNCT__ 434 #define __FUNCT__ "MatFactorDumpMatrix" 435 PetscErrorCode MatFactorDumpMatrix(Mat A) 436 { 437 PetscErrorCode ierr; 438 PetscTruth flg = PETSC_FALSE; 439 440 PetscFunctionBegin; 441 ierr = PetscOptionsGetTruth(PETSC_NULL,"-mat_factor_dump_on_error",&flg,PETSC_NULL);CHKERRQ(ierr); 442 if (flg) { 443 PetscViewer viewer; 444 char filename[PETSC_MAX_PATH_LEN]; 445 446 ierr = PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);CHKERRQ(ierr); 447 ierr = PetscViewerBinaryOpen(((PetscObject)A)->comm,filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr); 448 ierr = MatView(A,viewer);CHKERRQ(ierr); 449 ierr = PetscViewerDestroy(viewer);CHKERRQ(ierr); 450 } 451 PetscFunctionReturn(0); 452 } 453 454 #undef __FUNCT__ 455 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ" 456 PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 457 { 458 Mat C=B; 459 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 460 IS isrow = b->row,isicol = b->icol; 461 PetscErrorCode ierr; 462 const PetscInt *r,*ic,*ics; 463 const PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bdiag=b->diag; 464 PetscInt i,j,k,nz,nzL,row,*pj; 465 const PetscInt *ajtmp,*bjtmp; 466 MatScalar *rtmp,*pc,multiplier,*pv; 467 const MatScalar *aa=a->a,*v; 468 PetscTruth row_identity,col_identity; 469 FactorShiftCtx sctx; 470 const PetscInt *ddiag; 471 PetscReal rs; 472 MatScalar d; 473 PetscInt newshift = 0; 474 475 PetscFunctionBegin; 476 /* MatPivotSetUp(): initialize shift context sctx */ 477 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 478 479 if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 480 ddiag = a->diag; 481 sctx.shift_top = info->zeropivot; 482 for (i=0; i<n; i++) { 483 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 484 d = (aa)[ddiag[i]]; 485 rs = -PetscAbsScalar(d) - PetscRealPart(d); 486 v = aa+ai[i]; 487 nz = ai[i+1] - ai[i]; 488 for (j=0; j<nz; j++) 489 rs += PetscAbsScalar(v[j]); 490 if (rs>sctx.shift_top) sctx.shift_top = rs; 491 } 492 sctx.shift_top *= 1.1; 493 sctx.nshift_max = 5; 494 sctx.shift_lo = 0.; 495 sctx.shift_hi = 1.; 496 } 497 498 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 499 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 500 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 501 ics = ic; 502 503 do { 504 sctx.useshift = PETSC_FALSE; 505 for (i=0; i<n; i++){ 506 /* zero rtmp */ 507 /* L part */ 508 nz = bi[i+1] - bi[i]; 509 bjtmp = bj + bi[i]; 510 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 511 512 /* U part */ 513 nz = bdiag[i]-bdiag[i+1]; 514 bjtmp = bj + bdiag[i+1]+1; 515 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 516 517 /* load in initial (unfactored row) */ 518 nz = ai[r[i]+1] - ai[r[i]]; 519 ajtmp = aj + ai[r[i]]; 520 v = aa + ai[r[i]]; 521 for (j=0; j<nz; j++) { 522 rtmp[ics[ajtmp[j]]] = v[j]; 523 } 524 /* ZeropivotApply() */ 525 rtmp[i] += sctx.shift_amount; /* shift the diagonal of the matrix */ 526 527 /* elimination */ 528 bjtmp = bj + bi[i]; 529 row = *bjtmp++; 530 nzL = bi[i+1] - bi[i]; 531 for(k=0; k < nzL;k++) { 532 pc = rtmp + row; 533 if (*pc != 0.0) { 534 pv = b->a + bdiag[row]; 535 multiplier = *pc * (*pv); 536 *pc = multiplier; 537 pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */ 538 pv = b->a + bdiag[row+1]+1; 539 nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */ 540 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 541 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 542 } 543 row = *bjtmp++; 544 } 545 546 /* finished row so stick it into b->a */ 547 rs = 0.0; 548 /* L part */ 549 pv = b->a + bi[i] ; 550 pj = b->j + bi[i] ; 551 nz = bi[i+1] - bi[i]; 552 for (j=0; j<nz; j++) { 553 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 554 } 555 556 /* U part */ 557 pv = b->a + bdiag[i+1]+1; 558 pj = b->j + bdiag[i+1]+1; 559 nz = bdiag[i] - bdiag[i+1]-1; 560 for (j=0; j<nz; j++) { 561 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 562 } 563 564 sctx.rs = rs; 565 sctx.pv = rtmp[i]; 566 ierr = MatPivotCheck(info,&sctx,i,&newshift);CHKERRQ(ierr); 567 if(newshift == 1) break; 568 rtmp[i] = sctx.pv; 569 570 /* Mark diagonal and invert diagonal for simplier triangular solves */ 571 pv = b->a + bdiag[i]; 572 *pv = 1.0/rtmp[i]; 573 574 } /* endof for (i=0; i<n; i++){ */ 575 576 /* MatPivotRefine() */ 577 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.useshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max){ 578 /* 579 * if no shift in this attempt & shifting & started shifting & can refine, 580 * then try lower shift 581 */ 582 sctx.shift_hi = sctx.shift_fraction; 583 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 584 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 585 sctx.useshift = PETSC_TRUE; 586 sctx.nshift++; 587 } 588 } while (sctx.useshift); 589 590 ierr = PetscFree(rtmp);CHKERRQ(ierr); 591 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 592 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 593 594 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 595 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 596 if (row_identity && col_identity) { 597 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 598 } else { 599 C->ops->solve = MatSolve_SeqAIJ; 600 } 601 C->ops->solveadd = MatSolveAdd_SeqAIJ; 602 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 603 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 604 C->ops->matsolve = MatMatSolve_SeqAIJ; 605 C->assembled = PETSC_TRUE; 606 C->preallocated = PETSC_TRUE; 607 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 608 609 /* MatShiftView(A,info,&sctx) */ 610 if (sctx.nshift){ 611 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 612 ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %G, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,sctx.shift_amount,sctx.shift_fraction,sctx.shift_top);CHKERRQ(ierr); 613 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 614 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 615 } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS){ 616 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftamount);CHKERRQ(ierr); 617 } 618 } 619 ierr = Mat_CheckInode_FactorLU(C,PETSC_FALSE);CHKERRQ(ierr); 620 PetscFunctionReturn(0); 621 } 622 623 #undef __FUNCT__ 624 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_inplace" 625 PetscErrorCode MatLUFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info) 626 { 627 Mat C=B; 628 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 629 IS isrow = b->row,isicol = b->icol; 630 PetscErrorCode ierr; 631 const PetscInt *r,*ic,*ics; 632 PetscInt nz,row,i,j,n=A->rmap->n,diag; 633 const PetscInt *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 634 const PetscInt *ajtmp,*bjtmp,*diag_offset = b->diag,*pj; 635 MatScalar *pv,*rtmp,*pc,multiplier,d; 636 const MatScalar *v,*aa=a->a; 637 PetscReal rs=0.0; 638 FactorShiftCtx sctx; 639 PetscInt newshift; 640 const PetscInt *ddiag; 641 PetscTruth row_identity, col_identity; 642 643 PetscFunctionBegin; 644 printf("MatLUFactorNumeric_SeqAIJ_inplace ...\n"); 645 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 646 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 647 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 648 ics = ic; 649 650 /* initialize shift context sctx */ 651 sctx.nshift = 0; 652 sctx.nshift_max = 0; 653 sctx.shift_top = 0.0; 654 sctx.shift_lo = 0.0; 655 sctx.shift_hi = 0.0; 656 sctx.shift_fraction = 0.0; 657 sctx.shift_amount = 0.0; 658 659 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 660 ddiag = a->diag; 661 sctx.shift_top = info->zeropivot; 662 for (i=0; i<n; i++) { 663 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 664 d = (aa)[ddiag[i]]; 665 rs = -PetscAbsScalar(d) - PetscRealPart(d); 666 v = aa+ai[i]; 667 nz = ai[i+1] - ai[i]; 668 for (j=0; j<nz; j++) 669 rs += PetscAbsScalar(v[j]); 670 if (rs>sctx.shift_top) sctx.shift_top = rs; 671 } 672 sctx.shift_top *= 1.1; 673 sctx.nshift_max = 5; 674 sctx.shift_lo = 0.; 675 sctx.shift_hi = 1.; 676 } 677 678 do { 679 sctx.useshift = PETSC_FALSE; 680 for (i=0; i<n; i++){ 681 nz = bi[i+1] - bi[i]; 682 bjtmp = bj + bi[i]; 683 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 684 685 /* load in initial (unfactored row) */ 686 nz = ai[r[i]+1] - ai[r[i]]; 687 ajtmp = aj + ai[r[i]]; 688 v = aa + ai[r[i]]; 689 for (j=0; j<nz; j++) { 690 rtmp[ics[ajtmp[j]]] = v[j]; 691 } 692 rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 693 /* if (sctx.shift_amount > 0.0) printf("row %d, shift %g\n",i,sctx.shift_amount); */ 694 695 row = *bjtmp++; 696 while (row < i) { 697 pc = rtmp + row; 698 if (*pc != 0.0) { 699 pv = b->a + diag_offset[row]; 700 pj = b->j + diag_offset[row] + 1; 701 multiplier = *pc / *pv++; 702 *pc = multiplier; 703 nz = bi[row+1] - diag_offset[row] - 1; 704 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 705 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 706 } 707 row = *bjtmp++; 708 } 709 /* finished row so stick it into b->a */ 710 pv = b->a + bi[i] ; 711 pj = b->j + bi[i] ; 712 nz = bi[i+1] - bi[i]; 713 diag = diag_offset[i] - bi[i]; 714 rs = 0.0; 715 for (j=0; j<nz; j++) { 716 pv[j] = rtmp[pj[j]]; 717 rs += PetscAbsScalar(pv[j]); 718 } 719 rs -= PetscAbsScalar(pv[diag]); 720 721 /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */ 722 sctx.rs = rs; 723 sctx.pv = pv[diag]; 724 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 725 if (newshift == 1) break; 726 } 727 728 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.useshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 729 /* 730 * if no shift in this attempt & shifting & started shifting & can refine, 731 * then try lower shift 732 */ 733 sctx.shift_hi = sctx.shift_fraction; 734 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 735 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 736 sctx.useshift = PETSC_TRUE; 737 sctx.nshift++; 738 } 739 } while (sctx.useshift); 740 741 /* invert diagonal entries for simplier triangular solves */ 742 for (i=0; i<n; i++) { 743 b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]]; 744 } 745 ierr = PetscFree(rtmp);CHKERRQ(ierr); 746 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 747 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 748 749 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 750 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 751 if (row_identity && col_identity) { 752 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_inplace; 753 } else { 754 C->ops->solve = MatSolve_SeqAIJ_inplace; 755 } 756 C->ops->solveadd = MatSolveAdd_SeqAIJ_inplace; 757 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace; 758 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace; 759 C->ops->matsolve = MatMatSolve_SeqAIJ_inplace; 760 C->assembled = PETSC_TRUE; 761 C->preallocated = PETSC_TRUE; 762 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 763 if (sctx.nshift){ 764 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 765 ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %G, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,sctx.shift_amount,sctx.shift_fraction,sctx.shift_top);CHKERRQ(ierr); 766 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 767 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 768 } 769 } 770 (C)->ops->solve = MatSolve_SeqAIJ_inplace; 771 (C)->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace; 772 ierr = Mat_CheckInode(C,PETSC_FALSE);CHKERRQ(ierr); 773 PetscFunctionReturn(0); 774 } 775 776 /* 777 This routine implements inplace ILU(0) with row or/and column permutations. 778 Input: 779 A - original matrix 780 Output; 781 A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i] 782 a->j (col index) is permuted by the inverse of colperm, then sorted 783 a->a reordered accordingly with a->j 784 a->diag (ptr to diagonal elements) is updated. 785 */ 786 #undef __FUNCT__ 787 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_InplaceWithPerm" 788 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info) 789 { 790 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 791 IS isrow = a->row,isicol = a->icol; 792 PetscErrorCode ierr; 793 const PetscInt *r,*ic,*ics; 794 PetscInt i,j,n=A->rmap->n,*ai=a->i,*aj=a->j; 795 PetscInt *ajtmp,nz,row; 796 PetscInt *diag = a->diag,nbdiag,*pj; 797 PetscScalar *rtmp,*pc,multiplier,d; 798 MatScalar *v,*pv; 799 PetscReal rs; 800 FactorShiftCtx sctx; 801 PetscInt newshift = 0; 802 803 PetscFunctionBegin; 804 if (A != B) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address"); 805 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 806 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 807 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&rtmp);CHKERRQ(ierr); 808 ierr = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr); 809 ics = ic; 810 811 sctx.shift_top = 0.; 812 sctx.nshift_max = 0; 813 sctx.shift_lo = 0.; 814 sctx.shift_hi = 0.; 815 sctx.shift_fraction = 0.; 816 817 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 818 sctx.shift_top = 0.; 819 for (i=0; i<n; i++) { 820 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 821 d = (a->a)[diag[i]]; 822 rs = -PetscAbsScalar(d) - PetscRealPart(d); 823 v = a->a+ai[i]; 824 nz = ai[i+1] - ai[i]; 825 for (j=0; j<nz; j++) 826 rs += PetscAbsScalar(v[j]); 827 if (rs>sctx.shift_top) sctx.shift_top = rs; 828 } 829 if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot; 830 sctx.shift_top *= 1.1; 831 sctx.nshift_max = 5; 832 sctx.shift_lo = 0.; 833 sctx.shift_hi = 1.; 834 } 835 836 sctx.shift_amount = 0.; 837 sctx.nshift = 0; 838 do { 839 sctx.useshift = PETSC_FALSE; 840 for (i=0; i<n; i++){ 841 /* load in initial unfactored row */ 842 nz = ai[r[i]+1] - ai[r[i]]; 843 ajtmp = aj + ai[r[i]]; 844 v = a->a + ai[r[i]]; 845 /* sort permuted ajtmp and values v accordingly */ 846 for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]]; 847 ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr); 848 849 diag[r[i]] = ai[r[i]]; 850 for (j=0; j<nz; j++) { 851 rtmp[ajtmp[j]] = v[j]; 852 if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */ 853 } 854 rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 855 856 row = *ajtmp++; 857 while (row < i) { 858 pc = rtmp + row; 859 if (*pc != 0.0) { 860 pv = a->a + diag[r[row]]; 861 pj = aj + diag[r[row]] + 1; 862 863 multiplier = *pc / *pv++; 864 *pc = multiplier; 865 nz = ai[r[row]+1] - diag[r[row]] - 1; 866 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 867 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 868 } 869 row = *ajtmp++; 870 } 871 /* finished row so overwrite it onto a->a */ 872 pv = a->a + ai[r[i]] ; 873 pj = aj + ai[r[i]] ; 874 nz = ai[r[i]+1] - ai[r[i]]; 875 nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */ 876 877 rs = 0.0; 878 for (j=0; j<nz; j++) { 879 pv[j] = rtmp[pj[j]]; 880 if (j != nbdiag) rs += PetscAbsScalar(pv[j]); 881 } 882 883 /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */ 884 sctx.rs = rs; 885 sctx.pv = pv[nbdiag]; 886 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 887 if (newshift == 1) break; 888 } 889 890 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.useshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 891 /* 892 * if no shift in this attempt & shifting & started shifting & can refine, 893 * then try lower shift 894 */ 895 sctx.shift_hi = sctx.shift_fraction; 896 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 897 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 898 sctx.useshift = PETSC_TRUE; 899 sctx.nshift++; 900 } 901 } while (sctx.useshift); 902 903 /* invert diagonal entries for simplier triangular solves */ 904 for (i=0; i<n; i++) { 905 a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]]; 906 } 907 908 ierr = PetscFree(rtmp);CHKERRQ(ierr); 909 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 910 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 911 A->ops->solve = MatSolve_SeqAIJ_InplaceWithPerm; 912 A->ops->solveadd = MatSolveAdd_SeqAIJ_inplace; 913 A->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace; 914 A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace; 915 A->assembled = PETSC_TRUE; 916 A->preallocated = PETSC_TRUE; 917 ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr); 918 if (sctx.nshift){ 919 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 920 ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %G, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,sctx.shift_amount,sctx.shift_fraction,sctx.shift_top);CHKERRQ(ierr); 921 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 922 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 923 } 924 } 925 PetscFunctionReturn(0); 926 } 927 928 /* ----------------------------------------------------------- */ 929 #undef __FUNCT__ 930 #define __FUNCT__ "MatLUFactor_SeqAIJ" 931 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info) 932 { 933 PetscErrorCode ierr; 934 Mat C; 935 936 PetscFunctionBegin; 937 ierr = MatGetFactor(A,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr); 938 ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr); 939 ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr); 940 A->ops->solve = C->ops->solve; 941 A->ops->solvetranspose = C->ops->solvetranspose; 942 ierr = MatHeaderCopy(A,C);CHKERRQ(ierr); 943 ierr = PetscLogObjectParent(A,((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr); 944 PetscFunctionReturn(0); 945 } 946 /* ----------------------------------------------------------- */ 947 948 949 #undef __FUNCT__ 950 #define __FUNCT__ "MatSolve_SeqAIJ_inplace" 951 PetscErrorCode MatSolve_SeqAIJ_inplace(Mat A,Vec bb,Vec xx) 952 { 953 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 954 IS iscol = a->col,isrow = a->row; 955 PetscErrorCode ierr; 956 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 957 PetscInt nz; 958 const PetscInt *rout,*cout,*r,*c; 959 PetscScalar *x,*tmp,*tmps,sum; 960 const PetscScalar *b; 961 const MatScalar *aa = a->a,*v; 962 963 PetscFunctionBegin; 964 if (!n) PetscFunctionReturn(0); 965 966 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 967 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 968 tmp = a->solve_work; 969 970 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 971 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 972 973 /* forward solve the lower triangular */ 974 tmp[0] = b[*r++]; 975 tmps = tmp; 976 for (i=1; i<n; i++) { 977 v = aa + ai[i] ; 978 vi = aj + ai[i] ; 979 nz = a->diag[i] - ai[i]; 980 sum = b[*r++]; 981 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 982 tmp[i] = sum; 983 } 984 985 /* backward solve the upper triangular */ 986 for (i=n-1; i>=0; i--){ 987 v = aa + a->diag[i] + 1; 988 vi = aj + a->diag[i] + 1; 989 nz = ai[i+1] - a->diag[i] - 1; 990 sum = tmp[i]; 991 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 992 x[*c--] = tmp[i] = sum*aa[a->diag[i]]; 993 } 994 995 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 996 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 997 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 998 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 999 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1000 PetscFunctionReturn(0); 1001 } 1002 1003 #undef __FUNCT__ 1004 #define __FUNCT__ "MatMatSolve_SeqAIJ_inplace" 1005 PetscErrorCode MatMatSolve_SeqAIJ_inplace(Mat A,Mat B,Mat X) 1006 { 1007 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1008 IS iscol = a->col,isrow = a->row; 1009 PetscErrorCode ierr; 1010 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1011 PetscInt nz,neq; 1012 const PetscInt *rout,*cout,*r,*c; 1013 PetscScalar *x,*b,*tmp,*tmps,sum; 1014 const MatScalar *aa = a->a,*v; 1015 PetscTruth bisdense,xisdense; 1016 1017 PetscFunctionBegin; 1018 if (!n) PetscFunctionReturn(0); 1019 1020 ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr); 1021 if (!bisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 1022 ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr); 1023 if (!xisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 1024 1025 ierr = MatGetArray(B,&b);CHKERRQ(ierr); 1026 ierr = MatGetArray(X,&x);CHKERRQ(ierr); 1027 1028 tmp = a->solve_work; 1029 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1030 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1031 1032 for (neq=0; neq<B->cmap->n; neq++){ 1033 /* forward solve the lower triangular */ 1034 tmp[0] = b[r[0]]; 1035 tmps = tmp; 1036 for (i=1; i<n; i++) { 1037 v = aa + ai[i] ; 1038 vi = aj + ai[i] ; 1039 nz = a->diag[i] - ai[i]; 1040 sum = b[r[i]]; 1041 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1042 tmp[i] = sum; 1043 } 1044 /* backward solve the upper triangular */ 1045 for (i=n-1; i>=0; i--){ 1046 v = aa + a->diag[i] + 1; 1047 vi = aj + a->diag[i] + 1; 1048 nz = ai[i+1] - a->diag[i] - 1; 1049 sum = tmp[i]; 1050 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1051 x[c[i]] = tmp[i] = sum*aa[a->diag[i]]; 1052 } 1053 1054 b += n; 1055 x += n; 1056 } 1057 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1058 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1059 ierr = MatRestoreArray(B,&b);CHKERRQ(ierr); 1060 ierr = MatRestoreArray(X,&x);CHKERRQ(ierr); 1061 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 1062 PetscFunctionReturn(0); 1063 } 1064 1065 #undef __FUNCT__ 1066 #define __FUNCT__ "MatMatSolve_SeqAIJ" 1067 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X) 1068 { 1069 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1070 IS iscol = a->col,isrow = a->row; 1071 PetscErrorCode ierr; 1072 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag; 1073 PetscInt nz,neq; 1074 const PetscInt *rout,*cout,*r,*c; 1075 PetscScalar *x,*b,*tmp,sum; 1076 const MatScalar *aa = a->a,*v; 1077 PetscTruth bisdense,xisdense; 1078 1079 PetscFunctionBegin; 1080 if (!n) PetscFunctionReturn(0); 1081 1082 ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr); 1083 if (!bisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 1084 ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr); 1085 if (!xisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 1086 1087 ierr = MatGetArray(B,&b);CHKERRQ(ierr); 1088 ierr = MatGetArray(X,&x);CHKERRQ(ierr); 1089 1090 tmp = a->solve_work; 1091 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1092 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1093 1094 for (neq=0; neq<B->cmap->n; neq++){ 1095 /* forward solve the lower triangular */ 1096 tmp[0] = b[r[0]]; 1097 v = aa; 1098 vi = aj; 1099 for (i=1; i<n; i++) { 1100 nz = ai[i+1] - ai[i]; 1101 sum = b[r[i]]; 1102 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 1103 tmp[i] = sum; 1104 v += nz; vi += nz; 1105 } 1106 1107 /* backward solve the upper triangular */ 1108 for (i=n-1; i>=0; i--){ 1109 v = aa + adiag[i+1]+1; 1110 vi = aj + adiag[i+1]+1; 1111 nz = adiag[i]-adiag[i+1]-1; 1112 sum = tmp[i]; 1113 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 1114 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 1115 } 1116 1117 b += n; 1118 x += n; 1119 } 1120 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1121 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1122 ierr = MatRestoreArray(B,&b);CHKERRQ(ierr); 1123 ierr = MatRestoreArray(X,&x);CHKERRQ(ierr); 1124 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 1125 PetscFunctionReturn(0); 1126 } 1127 1128 #undef __FUNCT__ 1129 #define __FUNCT__ "MatSolve_SeqAIJ_InplaceWithPerm" 1130 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx) 1131 { 1132 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1133 IS iscol = a->col,isrow = a->row; 1134 PetscErrorCode ierr; 1135 const PetscInt *r,*c,*rout,*cout; 1136 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1137 PetscInt nz,row; 1138 PetscScalar *x,*b,*tmp,*tmps,sum; 1139 const MatScalar *aa = a->a,*v; 1140 1141 PetscFunctionBegin; 1142 if (!n) PetscFunctionReturn(0); 1143 1144 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1145 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1146 tmp = a->solve_work; 1147 1148 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1149 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1150 1151 /* forward solve the lower triangular */ 1152 tmp[0] = b[*r++]; 1153 tmps = tmp; 1154 for (row=1; row<n; row++) { 1155 i = rout[row]; /* permuted row */ 1156 v = aa + ai[i] ; 1157 vi = aj + ai[i] ; 1158 nz = a->diag[i] - ai[i]; 1159 sum = b[*r++]; 1160 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1161 tmp[row] = sum; 1162 } 1163 1164 /* backward solve the upper triangular */ 1165 for (row=n-1; row>=0; row--){ 1166 i = rout[row]; /* permuted row */ 1167 v = aa + a->diag[i] + 1; 1168 vi = aj + a->diag[i] + 1; 1169 nz = ai[i+1] - a->diag[i] - 1; 1170 sum = tmp[row]; 1171 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1172 x[*c--] = tmp[row] = sum*aa[a->diag[i]]; 1173 } 1174 1175 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1176 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1177 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1178 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1179 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1180 PetscFunctionReturn(0); 1181 } 1182 1183 /* ----------------------------------------------------------- */ 1184 #include "../src/mat/impls/aij/seq/ftn-kernels/fsolve.h" 1185 #undef __FUNCT__ 1186 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_inplace" 1187 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_inplace(Mat A,Vec bb,Vec xx) 1188 { 1189 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1190 PetscErrorCode ierr; 1191 PetscInt n = A->rmap->n; 1192 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag; 1193 PetscScalar *x; 1194 const PetscScalar *b; 1195 const MatScalar *aa = a->a; 1196 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1197 PetscInt adiag_i,i,nz,ai_i; 1198 const PetscInt *vi; 1199 const MatScalar *v; 1200 PetscScalar sum; 1201 #endif 1202 1203 PetscFunctionBegin; 1204 if (!n) PetscFunctionReturn(0); 1205 1206 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1207 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1208 1209 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1210 fortransolveaij_(&n,x,ai,aj,adiag,aa,b); 1211 #else 1212 /* forward solve the lower triangular */ 1213 x[0] = b[0]; 1214 for (i=1; i<n; i++) { 1215 ai_i = ai[i]; 1216 v = aa + ai_i; 1217 vi = aj + ai_i; 1218 nz = adiag[i] - ai_i; 1219 sum = b[i]; 1220 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1221 x[i] = sum; 1222 } 1223 1224 /* backward solve the upper triangular */ 1225 for (i=n-1; i>=0; i--){ 1226 adiag_i = adiag[i]; 1227 v = aa + adiag_i + 1; 1228 vi = aj + adiag_i + 1; 1229 nz = ai[i+1] - adiag_i - 1; 1230 sum = x[i]; 1231 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1232 x[i] = sum*aa[adiag_i]; 1233 } 1234 #endif 1235 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1236 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1237 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1238 PetscFunctionReturn(0); 1239 } 1240 1241 #undef __FUNCT__ 1242 #define __FUNCT__ "MatSolveAdd_SeqAIJ_inplace" 1243 PetscErrorCode MatSolveAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec yy,Vec xx) 1244 { 1245 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1246 IS iscol = a->col,isrow = a->row; 1247 PetscErrorCode ierr; 1248 PetscInt i, n = A->rmap->n,j; 1249 PetscInt nz; 1250 const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j; 1251 PetscScalar *x,*tmp,sum; 1252 const PetscScalar *b; 1253 const MatScalar *aa = a->a,*v; 1254 1255 PetscFunctionBegin; 1256 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 1257 1258 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1259 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1260 tmp = a->solve_work; 1261 1262 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1263 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1264 1265 /* forward solve the lower triangular */ 1266 tmp[0] = b[*r++]; 1267 for (i=1; i<n; i++) { 1268 v = aa + ai[i] ; 1269 vi = aj + ai[i] ; 1270 nz = a->diag[i] - ai[i]; 1271 sum = b[*r++]; 1272 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1273 tmp[i] = sum; 1274 } 1275 1276 /* backward solve the upper triangular */ 1277 for (i=n-1; i>=0; i--){ 1278 v = aa + a->diag[i] + 1; 1279 vi = aj + a->diag[i] + 1; 1280 nz = ai[i+1] - a->diag[i] - 1; 1281 sum = tmp[i]; 1282 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1283 tmp[i] = sum*aa[a->diag[i]]; 1284 x[*c--] += tmp[i]; 1285 } 1286 1287 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1288 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1289 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1290 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1291 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1292 1293 PetscFunctionReturn(0); 1294 } 1295 1296 #undef __FUNCT__ 1297 #define __FUNCT__ "MatSolveAdd_SeqAIJ" 1298 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx) 1299 { 1300 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1301 IS iscol = a->col,isrow = a->row; 1302 PetscErrorCode ierr; 1303 PetscInt i, n = A->rmap->n,j; 1304 PetscInt nz; 1305 const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag; 1306 PetscScalar *x,*tmp,sum; 1307 const PetscScalar *b; 1308 const MatScalar *aa = a->a,*v; 1309 1310 PetscFunctionBegin; 1311 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 1312 1313 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1314 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1315 tmp = a->solve_work; 1316 1317 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1318 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1319 1320 /* forward solve the lower triangular */ 1321 tmp[0] = b[r[0]]; 1322 v = aa; 1323 vi = aj; 1324 for (i=1; i<n; i++) { 1325 nz = ai[i+1] - ai[i]; 1326 sum = b[r[i]]; 1327 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1328 tmp[i] = sum; 1329 v += nz; vi += nz; 1330 } 1331 1332 /* backward solve the upper triangular */ 1333 v = aa + adiag[n-1]; 1334 vi = aj + adiag[n-1]; 1335 for (i=n-1; i>=0; i--){ 1336 nz = adiag[i] - adiag[i+1] - 1; 1337 sum = tmp[i]; 1338 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1339 tmp[i] = sum*v[nz]; 1340 x[c[i]] += tmp[i]; 1341 v += nz+1; vi += nz+1; 1342 } 1343 1344 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1345 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1346 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1347 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1348 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1349 1350 PetscFunctionReturn(0); 1351 } 1352 1353 #undef __FUNCT__ 1354 #define __FUNCT__ "MatSolveTranspose_SeqAIJ_inplace" 1355 PetscErrorCode MatSolveTranspose_SeqAIJ_inplace(Mat A,Vec bb,Vec xx) 1356 { 1357 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1358 IS iscol = a->col,isrow = a->row; 1359 PetscErrorCode ierr; 1360 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1361 PetscInt i,n = A->rmap->n,j; 1362 PetscInt nz; 1363 PetscScalar *x,*tmp,s1; 1364 const MatScalar *aa = a->a,*v; 1365 const PetscScalar *b; 1366 1367 PetscFunctionBegin; 1368 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1369 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1370 tmp = a->solve_work; 1371 1372 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1373 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1374 1375 /* copy the b into temp work space according to permutation */ 1376 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1377 1378 /* forward solve the U^T */ 1379 for (i=0; i<n; i++) { 1380 v = aa + diag[i] ; 1381 vi = aj + diag[i] + 1; 1382 nz = ai[i+1] - diag[i] - 1; 1383 s1 = tmp[i]; 1384 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1385 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1386 tmp[i] = s1; 1387 } 1388 1389 /* backward solve the L^T */ 1390 for (i=n-1; i>=0; i--){ 1391 v = aa + diag[i] - 1 ; 1392 vi = aj + diag[i] - 1 ; 1393 nz = diag[i] - ai[i]; 1394 s1 = tmp[i]; 1395 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1396 } 1397 1398 /* copy tmp into x according to permutation */ 1399 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1400 1401 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1402 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1403 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1404 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1405 1406 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1407 PetscFunctionReturn(0); 1408 } 1409 1410 #undef __FUNCT__ 1411 #define __FUNCT__ "MatSolveTranspose_SeqAIJ" 1412 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx) 1413 { 1414 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1415 IS iscol = a->col,isrow = a->row; 1416 PetscErrorCode ierr; 1417 const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi; 1418 PetscInt i,n = A->rmap->n,j; 1419 PetscInt nz; 1420 PetscScalar *x,*tmp,s1; 1421 const MatScalar *aa = a->a,*v; 1422 const PetscScalar *b; 1423 1424 PetscFunctionBegin; 1425 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1426 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1427 tmp = a->solve_work; 1428 1429 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1430 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1431 1432 /* copy the b into temp work space according to permutation */ 1433 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1434 1435 /* forward solve the U^T */ 1436 for (i=0; i<n; i++) { 1437 v = aa + adiag[i+1] + 1; 1438 vi = aj + adiag[i+1] + 1; 1439 nz = adiag[i] - adiag[i+1] - 1; 1440 s1 = tmp[i]; 1441 s1 *= v[nz]; /* multiply by inverse of diagonal entry */ 1442 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1443 tmp[i] = s1; 1444 } 1445 1446 /* backward solve the L^T */ 1447 for (i=n-1; i>=0; i--){ 1448 v = aa + ai[i]; 1449 vi = aj + ai[i]; 1450 nz = ai[i+1] - ai[i]; 1451 s1 = tmp[i]; 1452 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1453 } 1454 1455 /* copy tmp into x according to permutation */ 1456 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1457 1458 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1459 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1460 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1461 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1462 1463 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1464 PetscFunctionReturn(0); 1465 } 1466 1467 #undef __FUNCT__ 1468 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ_inplace" 1469 PetscErrorCode MatSolveTransposeAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec zz,Vec xx) 1470 { 1471 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1472 IS iscol = a->col,isrow = a->row; 1473 PetscErrorCode ierr; 1474 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1475 PetscInt i,n = A->rmap->n,j; 1476 PetscInt nz; 1477 PetscScalar *x,*tmp,s1; 1478 const MatScalar *aa = a->a,*v; 1479 const PetscScalar *b; 1480 1481 PetscFunctionBegin; 1482 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1483 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1484 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1485 tmp = a->solve_work; 1486 1487 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1488 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1489 1490 /* copy the b into temp work space according to permutation */ 1491 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1492 1493 /* forward solve the U^T */ 1494 for (i=0; i<n; i++) { 1495 v = aa + diag[i] ; 1496 vi = aj + diag[i] + 1; 1497 nz = ai[i+1] - diag[i] - 1; 1498 s1 = tmp[i]; 1499 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1500 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1501 tmp[i] = s1; 1502 } 1503 1504 /* backward solve the L^T */ 1505 for (i=n-1; i>=0; i--){ 1506 v = aa + diag[i] - 1 ; 1507 vi = aj + diag[i] - 1 ; 1508 nz = diag[i] - ai[i]; 1509 s1 = tmp[i]; 1510 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1511 } 1512 1513 /* copy tmp into x according to permutation */ 1514 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1515 1516 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1517 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1518 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1519 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1520 1521 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1522 PetscFunctionReturn(0); 1523 } 1524 1525 #undef __FUNCT__ 1526 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ" 1527 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx) 1528 { 1529 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1530 IS iscol = a->col,isrow = a->row; 1531 PetscErrorCode ierr; 1532 const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi; 1533 PetscInt i,n = A->rmap->n,j; 1534 PetscInt nz; 1535 PetscScalar *x,*tmp,s1; 1536 const MatScalar *aa = a->a,*v; 1537 const PetscScalar *b; 1538 1539 PetscFunctionBegin; 1540 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1541 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1542 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1543 tmp = a->solve_work; 1544 1545 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1546 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1547 1548 /* copy the b into temp work space according to permutation */ 1549 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1550 1551 /* forward solve the U^T */ 1552 for (i=0; i<n; i++) { 1553 v = aa + adiag[i+1] + 1; 1554 vi = aj + adiag[i+1] + 1; 1555 nz = adiag[i] - adiag[i+1] - 1; 1556 s1 = tmp[i]; 1557 s1 *= v[nz]; /* multiply by inverse of diagonal entry */ 1558 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1559 tmp[i] = s1; 1560 } 1561 1562 1563 /* backward solve the L^T */ 1564 for (i=n-1; i>=0; i--){ 1565 v = aa + ai[i] ; 1566 vi = aj + ai[i]; 1567 nz = ai[i+1] - ai[i]; 1568 s1 = tmp[i]; 1569 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1570 } 1571 1572 /* copy tmp into x according to permutation */ 1573 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1574 1575 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1576 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1577 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1578 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1579 1580 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1581 PetscFunctionReturn(0); 1582 } 1583 1584 /* ----------------------------------------------------------------*/ 1585 1586 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth); 1587 1588 /* 1589 ilu() under revised new data structure. 1590 Factored arrays bj and ba are stored as 1591 L(0,:), L(1,:), ...,L(n-1,:), U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:) 1592 1593 bi=fact->i is an array of size n+1, in which 1594 bi+ 1595 bi[i]: points to 1st entry of L(i,:),i=0,...,n-1 1596 bi[n]: points to L(n-1,n-1)+1 1597 1598 bdiag=fact->diag is an array of size n+1,in which 1599 bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1 1600 bdiag[n]: points to entry of U(n-1,0)-1 1601 1602 U(i,:) contains bdiag[i] as its last entry, i.e., 1603 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 1604 */ 1605 #undef __FUNCT__ 1606 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0" 1607 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1608 { 1609 1610 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1611 PetscErrorCode ierr; 1612 const PetscInt n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag; 1613 PetscInt i,j,k=0,nz,*bi,*bj,*bdiag; 1614 PetscTruth missing; 1615 IS isicol; 1616 1617 PetscFunctionBegin; 1618 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 1619 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 1620 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 1621 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1622 1623 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr); 1624 b = (Mat_SeqAIJ*)(fact)->data; 1625 1626 /* allocate matrix arrays for new data structure */ 1627 ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,n+1,PetscInt,&b->i);CHKERRQ(ierr); 1628 ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1629 b->singlemalloc = PETSC_TRUE; 1630 if (!b->diag){ 1631 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr); 1632 ierr = PetscLogObjectMemory(fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1633 } 1634 bdiag = b->diag; 1635 1636 if (n > 0) { 1637 ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr); 1638 } 1639 1640 /* set bi and bj with new data structure */ 1641 bi = b->i; 1642 bj = b->j; 1643 1644 /* L part */ 1645 bi[0] = 0; 1646 for (i=0; i<n; i++){ 1647 nz = adiag[i] - ai[i]; 1648 bi[i+1] = bi[i] + nz; 1649 aj = a->j + ai[i]; 1650 for (j=0; j<nz; j++){ 1651 /* *bj = aj[j]; bj++; */ 1652 bj[k++] = aj[j]; 1653 } 1654 } 1655 1656 /* U part */ 1657 bdiag[n] = bi[n]-1; 1658 for (i=n-1; i>=0; i--){ 1659 nz = ai[i+1] - adiag[i] - 1; 1660 aj = a->j + adiag[i] + 1; 1661 for (j=0; j<nz; j++){ 1662 /* *bj = aj[j]; bj++; */ 1663 bj[k++] = aj[j]; 1664 } 1665 /* diag[i] */ 1666 /* *bj = i; bj++; */ 1667 bj[k++] = i; 1668 bdiag[i] = bdiag[i+1] + nz + 1; 1669 } 1670 1671 fact->factortype = MAT_FACTOR_ILU; 1672 fact->info.factor_mallocs = 0; 1673 fact->info.fill_ratio_given = info->fill; 1674 fact->info.fill_ratio_needed = 1.0; 1675 fact->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1676 1677 b = (Mat_SeqAIJ*)(fact)->data; 1678 b->row = isrow; 1679 b->col = iscol; 1680 b->icol = isicol; 1681 ierr = PetscMalloc((fact->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1682 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1683 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1684 PetscFunctionReturn(0); 1685 } 1686 1687 #undef __FUNCT__ 1688 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ" 1689 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1690 { 1691 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1692 IS isicol; 1693 PetscErrorCode ierr; 1694 const PetscInt *r,*ic; 1695 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j; 1696 PetscInt *bi,*cols,nnz,*cols_lvl; 1697 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1698 PetscInt i,levels,diagonal_fill; 1699 PetscTruth col_identity,row_identity; 1700 PetscReal f; 1701 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1702 PetscBT lnkbt; 1703 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1704 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1705 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1706 1707 PetscFunctionBegin; 1708 /* Uncomment the old data struct part only while testing new data structure for MatSolve() */ 1709 /* 1710 PetscTruth olddatastruct=PETSC_FALSE; 1711 ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_old",&olddatastruct,PETSC_NULL);CHKERRQ(ierr); 1712 if(olddatastruct){ 1713 ierr = MatILUFactorSymbolic_SeqAIJ_inplace(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1714 PetscFunctionReturn(0); 1715 } 1716 */ 1717 1718 levels = (PetscInt)info->levels; 1719 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1720 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1721 1722 if (!levels && row_identity && col_identity) { 1723 /* special case: ilu(0) with natural ordering */ 1724 ierr = MatILUFactorSymbolic_SeqAIJ_ilu0(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1725 if (a->inode.size) { 1726 fact->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode; 1727 } 1728 PetscFunctionReturn(0); 1729 } 1730 1731 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 1732 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1733 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1734 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1735 1736 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1737 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1738 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1739 bi[0] = bdiag[0] = 0; 1740 1741 ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr); 1742 1743 /* create a linked list for storing column indices of the active row */ 1744 nlnk = n + 1; 1745 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1746 1747 /* initial FreeSpace size is f*(ai[n]+1) */ 1748 f = info->fill; 1749 diagonal_fill = (PetscInt)info->diagonal_fill; 1750 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1751 current_space = free_space; 1752 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1753 current_space_lvl = free_space_lvl; 1754 1755 for (i=0; i<n; i++) { 1756 nzi = 0; 1757 /* copy current row into linked list */ 1758 nnz = ai[r[i]+1] - ai[r[i]]; 1759 if (!nnz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1760 cols = aj + ai[r[i]]; 1761 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1762 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1763 nzi += nlnk; 1764 1765 /* make sure diagonal entry is included */ 1766 if (diagonal_fill && lnk[i] == -1) { 1767 fm = n; 1768 while (lnk[fm] < i) fm = lnk[fm]; 1769 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1770 lnk[fm] = i; 1771 lnk_lvl[i] = 0; 1772 nzi++; dcount++; 1773 } 1774 1775 /* add pivot rows into the active row */ 1776 nzbd = 0; 1777 prow = lnk[n]; 1778 while (prow < i) { 1779 nnz = bdiag[prow]; 1780 cols = bj_ptr[prow] + nnz + 1; 1781 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1782 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1783 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1784 nzi += nlnk; 1785 prow = lnk[prow]; 1786 nzbd++; 1787 } 1788 bdiag[i] = nzbd; 1789 bi[i+1] = bi[i] + nzi; 1790 1791 /* if free space is not available, make more free space */ 1792 if (current_space->local_remaining<nzi) { 1793 nnz = 2*nzi*(n - i); /* estimated and max additional space needed */ 1794 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1795 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1796 reallocs++; 1797 } 1798 1799 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1800 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1801 bj_ptr[i] = current_space->array; 1802 bjlvl_ptr[i] = current_space_lvl->array; 1803 1804 /* make sure the active row i has diagonal entry */ 1805 if (*(bj_ptr[i]+bdiag[i]) != i) 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); 1806 1807 current_space->array += nzi; 1808 current_space->local_used += nzi; 1809 current_space->local_remaining -= nzi; 1810 current_space_lvl->array += nzi; 1811 current_space_lvl->local_used += nzi; 1812 current_space_lvl->local_remaining -= nzi; 1813 } 1814 1815 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1816 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1817 1818 /* destroy list of free space and other temporary arrays */ 1819 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 1820 1821 /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */ 1822 ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 1823 1824 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1825 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1826 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 1827 1828 #if defined(PETSC_USE_INFO) 1829 { 1830 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1831 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 1832 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1833 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 1834 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1835 if (diagonal_fill) { 1836 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 1837 } 1838 } 1839 #endif 1840 1841 /* put together the new matrix */ 1842 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 1843 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 1844 b = (Mat_SeqAIJ*)(fact)->data; 1845 b->free_a = PETSC_TRUE; 1846 b->free_ij = PETSC_TRUE; 1847 b->singlemalloc = PETSC_FALSE; 1848 ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 1849 b->j = bj; 1850 b->i = bi; 1851 b->diag = bdiag; 1852 b->ilen = 0; 1853 b->imax = 0; 1854 b->row = isrow; 1855 b->col = iscol; 1856 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1857 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1858 b->icol = isicol; 1859 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1860 /* In b structure: Free imax, ilen, old a, old j. 1861 Allocate bdiag, solve_work, new a, new j */ 1862 ierr = PetscLogObjectMemory(fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1863 b->maxnz = b->nz = bdiag[0]+1; 1864 (fact)->info.factor_mallocs = reallocs; 1865 (fact)->info.fill_ratio_given = f; 1866 (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 1867 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1868 if (a->inode.size) { 1869 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode; 1870 } 1871 PetscFunctionReturn(0); 1872 } 1873 1874 #undef __FUNCT__ 1875 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_inplace" 1876 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1877 { 1878 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1879 IS isicol; 1880 PetscErrorCode ierr; 1881 const PetscInt *r,*ic; 1882 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,d; 1883 PetscInt *bi,*cols,nnz,*cols_lvl; 1884 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1885 PetscInt i,levels,diagonal_fill; 1886 PetscTruth col_identity,row_identity; 1887 PetscReal f; 1888 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1889 PetscBT lnkbt; 1890 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1891 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1892 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1893 PetscTruth missing; 1894 1895 PetscFunctionBegin; 1896 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); 1897 f = info->fill; 1898 levels = (PetscInt)info->levels; 1899 diagonal_fill = (PetscInt)info->diagonal_fill; 1900 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1901 1902 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1903 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1904 if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */ 1905 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr); 1906 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace; 1907 if (a->inode.size) { 1908 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace; 1909 } 1910 fact->factortype = MAT_FACTOR_ILU; 1911 (fact)->info.factor_mallocs = 0; 1912 (fact)->info.fill_ratio_given = info->fill; 1913 (fact)->info.fill_ratio_needed = 1.0; 1914 b = (Mat_SeqAIJ*)(fact)->data; 1915 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 1916 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 1917 b->row = isrow; 1918 b->col = iscol; 1919 b->icol = isicol; 1920 ierr = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1921 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1922 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1923 PetscFunctionReturn(0); 1924 } 1925 1926 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1927 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1928 1929 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1930 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1931 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1932 bi[0] = bdiag[0] = 0; 1933 1934 ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr); 1935 1936 /* create a linked list for storing column indices of the active row */ 1937 nlnk = n + 1; 1938 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1939 1940 /* initial FreeSpace size is f*(ai[n]+1) */ 1941 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1942 current_space = free_space; 1943 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1944 current_space_lvl = free_space_lvl; 1945 1946 for (i=0; i<n; i++) { 1947 nzi = 0; 1948 /* copy current row into linked list */ 1949 nnz = ai[r[i]+1] - ai[r[i]]; 1950 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); 1951 cols = aj + ai[r[i]]; 1952 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1953 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1954 nzi += nlnk; 1955 1956 /* make sure diagonal entry is included */ 1957 if (diagonal_fill && lnk[i] == -1) { 1958 fm = n; 1959 while (lnk[fm] < i) fm = lnk[fm]; 1960 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1961 lnk[fm] = i; 1962 lnk_lvl[i] = 0; 1963 nzi++; dcount++; 1964 } 1965 1966 /* add pivot rows into the active row */ 1967 nzbd = 0; 1968 prow = lnk[n]; 1969 while (prow < i) { 1970 nnz = bdiag[prow]; 1971 cols = bj_ptr[prow] + nnz + 1; 1972 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1973 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1974 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1975 nzi += nlnk; 1976 prow = lnk[prow]; 1977 nzbd++; 1978 } 1979 bdiag[i] = nzbd; 1980 bi[i+1] = bi[i] + nzi; 1981 1982 /* if free space is not available, make more free space */ 1983 if (current_space->local_remaining<nzi) { 1984 nnz = nzi*(n - i); /* estimated and max additional space needed */ 1985 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1986 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1987 reallocs++; 1988 } 1989 1990 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1991 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1992 bj_ptr[i] = current_space->array; 1993 bjlvl_ptr[i] = current_space_lvl->array; 1994 1995 /* make sure the active row i has diagonal entry */ 1996 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); 1997 1998 current_space->array += nzi; 1999 current_space->local_used += nzi; 2000 current_space->local_remaining -= nzi; 2001 current_space_lvl->array += nzi; 2002 current_space_lvl->local_used += nzi; 2003 current_space_lvl->local_remaining -= nzi; 2004 } 2005 2006 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 2007 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 2008 2009 /* destroy list of free space and other temporary arrays */ 2010 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 2011 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */ 2012 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2013 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2014 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 2015 2016 #if defined(PETSC_USE_INFO) 2017 { 2018 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 2019 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 2020 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2021 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 2022 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 2023 if (diagonal_fill) { 2024 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 2025 } 2026 } 2027 #endif 2028 2029 /* put together the new matrix */ 2030 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 2031 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 2032 b = (Mat_SeqAIJ*)(fact)->data; 2033 b->free_a = PETSC_TRUE; 2034 b->free_ij = PETSC_TRUE; 2035 b->singlemalloc = PETSC_FALSE; 2036 ierr = PetscMalloc(bi[n]*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 2037 b->j = bj; 2038 b->i = bi; 2039 for (i=0; i<n; i++) bdiag[i] += bi[i]; 2040 b->diag = bdiag; 2041 b->ilen = 0; 2042 b->imax = 0; 2043 b->row = isrow; 2044 b->col = iscol; 2045 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 2046 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 2047 b->icol = isicol; 2048 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2049 /* In b structure: Free imax, ilen, old a, old j. 2050 Allocate bdiag, solve_work, new a, new j */ 2051 ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 2052 b->maxnz = b->nz = bi[n] ; 2053 (fact)->info.factor_mallocs = reallocs; 2054 (fact)->info.fill_ratio_given = f; 2055 (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 2056 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace; 2057 if (a->inode.size) { 2058 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace; 2059 } 2060 PetscFunctionReturn(0); 2061 } 2062 2063 #undef __FUNCT__ 2064 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ" 2065 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 2066 { 2067 Mat C = B; 2068 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2069 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2070 IS ip=b->row,iip = b->icol; 2071 PetscErrorCode ierr; 2072 const PetscInt *rip,*riip; 2073 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp; 2074 PetscInt *ai=a->i,*aj=a->j; 2075 PetscInt k,jmin,jmax,*c2r,*il,col,nexti,ili,nz; 2076 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2077 PetscTruth perm_identity; 2078 PetscInt newshift = 0; 2079 2080 FactorShiftCtx sctx; 2081 PetscReal rs; 2082 MatScalar d,*v; 2083 2084 PetscFunctionBegin; 2085 /* MatPivotSetUp(): initialize shift context sctx */ 2086 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 2087 2088 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 2089 sctx.shift_top = info->zeropivot; 2090 for (i=0; i<mbs; i++) { 2091 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 2092 d = (aa)[a->diag[i]]; 2093 rs = -PetscAbsScalar(d) - PetscRealPart(d); 2094 v = aa+ai[i]; 2095 nz = ai[i+1] - ai[i]; 2096 for (j=0; j<nz; j++) 2097 rs += PetscAbsScalar(v[j]); 2098 if (rs>sctx.shift_top) sctx.shift_top = rs; 2099 } 2100 sctx.shift_top *= 1.1; 2101 sctx.nshift_max = 5; 2102 sctx.shift_lo = 0.; 2103 sctx.shift_hi = 1.; 2104 } 2105 2106 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2107 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2108 2109 /* allocate working arrays 2110 c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col 2111 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 2112 */ 2113 ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&c2r);CHKERRQ(ierr); 2114 2115 do { 2116 sctx.useshift = PETSC_FALSE; 2117 2118 for (i=0; i<mbs; i++) c2r[i] = mbs; 2119 il[0] = 0; 2120 2121 for (k = 0; k<mbs; k++){ 2122 /* zero rtmp */ 2123 nz = bi[k+1] - bi[k]; 2124 bjtmp = bj + bi[k]; 2125 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2126 2127 /* load in initial unfactored row */ 2128 bval = ba + bi[k]; 2129 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2130 for (j = jmin; j < jmax; j++){ 2131 col = riip[aj[j]]; 2132 if (col >= k){ /* only take upper triangular entry */ 2133 rtmp[col] = aa[j]; 2134 *bval++ = 0.0; /* for in-place factorization */ 2135 } 2136 } 2137 /* shift the diagonal of the matrix: ZeropivotApply() */ 2138 rtmp[k] += sctx.shift_amount; /* shift the diagonal of the matrix */ 2139 2140 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2141 dk = rtmp[k]; 2142 i = c2r[k]; /* first row to be added to k_th row */ 2143 2144 while (i < k){ 2145 nexti = c2r[i]; /* next row to be added to k_th row */ 2146 2147 /* compute multiplier, update diag(k) and U(i,k) */ 2148 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2149 uikdi = - ba[ili]*ba[bdiag[i]]; /* diagonal(k) */ 2150 dk += uikdi*ba[ili]; /* update diag[k] */ 2151 ba[ili] = uikdi; /* -U(i,k) */ 2152 2153 /* add multiple of row i to k-th row */ 2154 jmin = ili + 1; jmax = bi[i+1]; 2155 if (jmin < jmax){ 2156 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2157 /* update il and c2r for row i */ 2158 il[i] = jmin; 2159 j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i; 2160 } 2161 i = nexti; 2162 } 2163 2164 /* copy data into U(k,:) */ 2165 rs = 0.0; 2166 jmin = bi[k]; jmax = bi[k+1]-1; 2167 if (jmin < jmax) { 2168 for (j=jmin; j<jmax; j++){ 2169 col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]); 2170 } 2171 /* add the k-th row into il and c2r */ 2172 il[k] = jmin; 2173 i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k; 2174 } 2175 2176 /* MatPivotCheck() */ 2177 sctx.rs = rs; 2178 sctx.pv = dk; 2179 ierr = MatPivotCheck(info,&sctx,i,&newshift);CHKERRQ(ierr); 2180 if(newshift == 1) break; 2181 dk = sctx.pv; 2182 2183 ba[bdiag[k]] = 1.0/dk; /* U(k,k) */ 2184 } 2185 } while (sctx.useshift); 2186 2187 ierr = PetscFree3(rtmp,il,c2r);CHKERRQ(ierr); 2188 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2189 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2190 2191 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2192 if (perm_identity){ 2193 B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2194 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2195 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering; 2196 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering; 2197 } else { 2198 B->ops->solve = MatSolve_SeqSBAIJ_1; 2199 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1; 2200 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1; 2201 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1; 2202 } 2203 2204 C->assembled = PETSC_TRUE; 2205 C->preallocated = PETSC_TRUE; 2206 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2207 2208 /* MatPivotView() */ 2209 if (sctx.nshift){ 2210 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 2211 ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %G, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,sctx.shift_amount,sctx.shift_fraction,sctx.shift_top);CHKERRQ(ierr); 2212 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 2213 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2214 } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS){ 2215 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftamount);CHKERRQ(ierr); 2216 } 2217 } 2218 PetscFunctionReturn(0); 2219 } 2220 2221 #undef __FUNCT__ 2222 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ_inplace" 2223 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info) 2224 { 2225 Mat C = B; 2226 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2227 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2228 IS ip=b->row,iip = b->icol; 2229 PetscErrorCode ierr; 2230 const PetscInt *rip,*riip; 2231 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol,*bjtmp; 2232 PetscInt *ai=a->i,*aj=a->j; 2233 PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz; 2234 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2235 PetscReal zeropivot,rs; 2236 ChShift_Ctx sctx; 2237 PetscInt newshift; 2238 PetscTruth perm_identity; 2239 2240 PetscFunctionBegin; 2241 zeropivot = info->zeropivot; 2242 2243 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2244 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2245 2246 /* initialization */ 2247 ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr); 2248 sctx.shift_amount = 0; 2249 sctx.nshift = 0; 2250 do { 2251 sctx.chshift = PETSC_FALSE; 2252 for (i=0; i<mbs; i++) jl[i] = mbs; 2253 il[0] = 0; 2254 2255 for (k = 0; k<mbs; k++){ 2256 /* zero rtmp */ 2257 nz = bi[k+1] - bi[k]; 2258 bjtmp = bj + bi[k]; 2259 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2260 2261 bval = ba + bi[k]; 2262 /* initialize k-th row by the perm[k]-th row of A */ 2263 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2264 for (j = jmin; j < jmax; j++){ 2265 col = riip[aj[j]]; 2266 if (col >= k){ /* only take upper triangular entry */ 2267 rtmp[col] = aa[j]; 2268 *bval++ = 0.0; /* for in-place factorization */ 2269 } 2270 } 2271 /* shift the diagonal of the matrix */ 2272 if (sctx.nshift) rtmp[k] += sctx.shift_amount; 2273 2274 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2275 dk = rtmp[k]; 2276 i = jl[k]; /* first row to be added to k_th row */ 2277 2278 while (i < k){ 2279 nexti = jl[i]; /* next row to be added to k_th row */ 2280 2281 /* compute multiplier, update diag(k) and U(i,k) */ 2282 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2283 uikdi = - ba[ili]*ba[bi[i]]; /* diagonal(k) */ 2284 dk += uikdi*ba[ili]; 2285 ba[ili] = uikdi; /* -U(i,k) */ 2286 2287 /* add multiple of row i to k-th row */ 2288 jmin = ili + 1; jmax = bi[i+1]; 2289 if (jmin < jmax){ 2290 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2291 /* update il and jl for row i */ 2292 il[i] = jmin; 2293 j = bj[jmin]; jl[i] = jl[j]; jl[j] = i; 2294 } 2295 i = nexti; 2296 } 2297 2298 /* shift the diagonals when zero pivot is detected */ 2299 /* compute rs=sum of abs(off-diagonal) */ 2300 rs = 0.0; 2301 jmin = bi[k]+1; 2302 nz = bi[k+1] - jmin; 2303 bcol = bj + jmin; 2304 for (j=0; j<nz; j++) { 2305 rs += PetscAbsScalar(rtmp[bcol[j]]); 2306 } 2307 2308 sctx.rs = rs; 2309 sctx.pv = dk; 2310 ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr); 2311 2312 if (newshift == 1) { 2313 if (!sctx.shift_amount) { 2314 sctx.shift_amount = 1e-5; 2315 } 2316 break; 2317 } 2318 2319 /* copy data into U(k,:) */ 2320 ba[bi[k]] = 1.0/dk; /* U(k,k) */ 2321 jmin = bi[k]+1; jmax = bi[k+1]; 2322 if (jmin < jmax) { 2323 for (j=jmin; j<jmax; j++){ 2324 col = bj[j]; ba[j] = rtmp[col]; 2325 } 2326 /* add the k-th row into il and jl */ 2327 il[k] = jmin; 2328 i = bj[jmin]; jl[k] = jl[i]; jl[i] = k; 2329 } 2330 } 2331 } while (sctx.chshift); 2332 ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr); 2333 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2334 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2335 2336 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2337 if (perm_identity){ 2338 B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2339 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2340 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2341 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2342 } else { 2343 B->ops->solve = MatSolve_SeqSBAIJ_1_inplace; 2344 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_inplace; 2345 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_inplace; 2346 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_inplace; 2347 } 2348 2349 C->assembled = PETSC_TRUE; 2350 C->preallocated = PETSC_TRUE; 2351 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2352 if (sctx.nshift){ 2353 if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 2354 ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2355 } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 2356 ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2357 } 2358 } 2359 PetscFunctionReturn(0); 2360 } 2361 2362 /* 2363 icc() under revised new data structure. 2364 Factored arrays bj and ba are stored as 2365 U(0,:),...,U(i,:),U(n-1,:) 2366 2367 ui=fact->i is an array of size n+1, in which 2368 ui+ 2369 ui[i]: points to 1st entry of U(i,:),i=0,...,n-1 2370 ui[n]: points to U(n-1,n-1)+1 2371 2372 udiag=fact->diag is an array of size n,in which 2373 udiag[i]: points to diagonal of U(i,:), i=0,...,n-1 2374 2375 U(i,:) contains udiag[i] as its last entry, i.e., 2376 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 2377 */ 2378 2379 #undef __FUNCT__ 2380 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ" 2381 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2382 { 2383 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2384 Mat_SeqSBAIJ *b; 2385 PetscErrorCode ierr; 2386 PetscTruth perm_identity,missing; 2387 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2388 const PetscInt *rip,*riip; 2389 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2390 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2391 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2392 PetscReal fill=info->fill,levels=info->levels; 2393 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2394 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2395 PetscBT lnkbt; 2396 IS iperm; 2397 2398 PetscFunctionBegin; 2399 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); 2400 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2401 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2402 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2403 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2404 2405 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2406 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2407 ui[0] = 0; 2408 2409 /* ICC(0) without matrix ordering: simply rearrange column indices */ 2410 if (!levels && perm_identity) { 2411 for (i=0; i<am; i++) { 2412 ncols = ai[i+1] - a->diag[i]; 2413 ui[i+1] = ui[i] + ncols; 2414 udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */ 2415 } 2416 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2417 cols = uj; 2418 for (i=0; i<am; i++) { 2419 aj = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */ 2420 ncols = ai[i+1] - a->diag[i] -1; 2421 for (j=0; j<ncols; j++) *cols++ = aj[j]; 2422 *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */ 2423 } 2424 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2425 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2426 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2427 2428 /* initialization */ 2429 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2430 2431 /* jl: linked list for storing indices of the pivot rows 2432 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2433 ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr); 2434 for (i=0; i<am; i++){ 2435 jl[i] = am; il[i] = 0; 2436 } 2437 2438 /* create and initialize a linked list for storing column indices of the active row k */ 2439 nlnk = am + 1; 2440 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2441 2442 /* initial FreeSpace size is fill*(ai[am]+1) */ 2443 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2444 current_space = free_space; 2445 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2446 current_space_lvl = free_space_lvl; 2447 2448 for (k=0; k<am; k++){ /* for each active row k */ 2449 /* initialize lnk by the column indices of row rip[k] of A */ 2450 nzk = 0; 2451 ncols = ai[rip[k]+1] - ai[rip[k]]; 2452 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); 2453 ncols_upper = 0; 2454 for (j=0; j<ncols; j++){ 2455 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2456 if (riip[i] >= k){ /* only take upper triangular entry */ 2457 ajtmp[ncols_upper] = i; 2458 ncols_upper++; 2459 } 2460 } 2461 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2462 nzk += nlnk; 2463 2464 /* update lnk by computing fill-in for each pivot row to be merged in */ 2465 prow = jl[k]; /* 1st pivot row */ 2466 2467 while (prow < k){ 2468 nextprow = jl[prow]; 2469 2470 /* merge prow into k-th row */ 2471 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2472 jmax = ui[prow+1]; 2473 ncols = jmax-jmin; 2474 i = jmin - ui[prow]; 2475 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2476 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2477 j = *(uj - 1); 2478 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2479 nzk += nlnk; 2480 2481 /* update il and jl for prow */ 2482 if (jmin < jmax){ 2483 il[prow] = jmin; 2484 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2485 } 2486 prow = nextprow; 2487 } 2488 2489 /* if free space is not available, make more free space */ 2490 if (current_space->local_remaining<nzk) { 2491 i = am - k + 1; /* num of unfactored rows */ 2492 i *= PetscMin(nzk, i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2493 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2494 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2495 reallocs++; 2496 } 2497 2498 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2499 if (nzk == 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2500 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2501 2502 /* add the k-th row into il and jl */ 2503 if (nzk > 1){ 2504 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2505 jl[k] = jl[i]; jl[i] = k; 2506 il[k] = ui[k] + 1; 2507 } 2508 uj_ptr[k] = current_space->array; 2509 uj_lvl_ptr[k] = current_space_lvl->array; 2510 2511 current_space->array += nzk; 2512 current_space->local_used += nzk; 2513 current_space->local_remaining -= nzk; 2514 2515 current_space_lvl->array += nzk; 2516 current_space_lvl->local_used += nzk; 2517 current_space_lvl->local_remaining -= nzk; 2518 2519 ui[k+1] = ui[k] + nzk; 2520 } 2521 2522 #if defined(PETSC_USE_INFO) 2523 if (ai[am] != 0) { 2524 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2525 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2526 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2527 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2528 } else { 2529 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2530 } 2531 #endif 2532 2533 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2534 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2535 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2536 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2537 2538 /* destroy list of free space and other temporary array(s) */ 2539 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2540 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor */ 2541 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2542 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2543 2544 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2545 2546 /* put together the new matrix in MATSEQSBAIJ format */ 2547 b = (Mat_SeqSBAIJ*)(fact)->data; 2548 b->singlemalloc = PETSC_FALSE; 2549 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2550 b->j = uj; 2551 b->i = ui; 2552 b->diag = udiag; 2553 b->free_diag = PETSC_TRUE; 2554 b->ilen = 0; 2555 b->imax = 0; 2556 b->row = perm; 2557 b->col = perm; 2558 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2559 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2560 b->icol = iperm; 2561 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2562 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2563 ierr = PetscLogObjectMemory(fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2564 b->maxnz = b->nz = ui[am]; 2565 b->free_a = PETSC_TRUE; 2566 b->free_ij = PETSC_TRUE; 2567 2568 fact->info.factor_mallocs = reallocs; 2569 fact->info.fill_ratio_given = fill; 2570 if (ai[am] != 0) { 2571 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2572 } else { 2573 fact->info.fill_ratio_needed = 0.0; 2574 } 2575 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2576 PetscFunctionReturn(0); 2577 } 2578 2579 #undef __FUNCT__ 2580 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ_inplace" 2581 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2582 { 2583 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2584 Mat_SeqSBAIJ *b; 2585 PetscErrorCode ierr; 2586 PetscTruth perm_identity,missing; 2587 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2588 const PetscInt *rip,*riip; 2589 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2590 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2591 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2592 PetscReal fill=info->fill,levels=info->levels; 2593 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2594 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2595 PetscBT lnkbt; 2596 IS iperm; 2597 2598 PetscFunctionBegin; 2599 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); 2600 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2601 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2602 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2603 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2604 2605 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2606 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2607 ui[0] = 0; 2608 2609 /* ICC(0) without matrix ordering: simply copies fill pattern */ 2610 if (!levels && perm_identity) { 2611 2612 for (i=0; i<am; i++) { 2613 ui[i+1] = ui[i] + ai[i+1] - a->diag[i]; 2614 udiag[i] = ui[i]; 2615 } 2616 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2617 cols = uj; 2618 for (i=0; i<am; i++) { 2619 aj = a->j + a->diag[i]; 2620 ncols = ui[i+1] - ui[i]; 2621 for (j=0; j<ncols; j++) *cols++ = *aj++; 2622 } 2623 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2624 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2625 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2626 2627 /* initialization */ 2628 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2629 2630 /* jl: linked list for storing indices of the pivot rows 2631 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2632 ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr); 2633 for (i=0; i<am; i++){ 2634 jl[i] = am; il[i] = 0; 2635 } 2636 2637 /* create and initialize a linked list for storing column indices of the active row k */ 2638 nlnk = am + 1; 2639 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2640 2641 /* initial FreeSpace size is fill*(ai[am]+1) */ 2642 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2643 current_space = free_space; 2644 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2645 current_space_lvl = free_space_lvl; 2646 2647 for (k=0; k<am; k++){ /* for each active row k */ 2648 /* initialize lnk by the column indices of row rip[k] of A */ 2649 nzk = 0; 2650 ncols = ai[rip[k]+1] - ai[rip[k]]; 2651 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); 2652 ncols_upper = 0; 2653 for (j=0; j<ncols; j++){ 2654 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2655 if (riip[i] >= k){ /* only take upper triangular entry */ 2656 ajtmp[ncols_upper] = i; 2657 ncols_upper++; 2658 } 2659 } 2660 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2661 nzk += nlnk; 2662 2663 /* update lnk by computing fill-in for each pivot row to be merged in */ 2664 prow = jl[k]; /* 1st pivot row */ 2665 2666 while (prow < k){ 2667 nextprow = jl[prow]; 2668 2669 /* merge prow into k-th row */ 2670 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2671 jmax = ui[prow+1]; 2672 ncols = jmax-jmin; 2673 i = jmin - ui[prow]; 2674 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2675 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2676 j = *(uj - 1); 2677 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2678 nzk += nlnk; 2679 2680 /* update il and jl for prow */ 2681 if (jmin < jmax){ 2682 il[prow] = jmin; 2683 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2684 } 2685 prow = nextprow; 2686 } 2687 2688 /* if free space is not available, make more free space */ 2689 if (current_space->local_remaining<nzk) { 2690 i = am - k + 1; /* num of unfactored rows */ 2691 i *= PetscMin(nzk, (i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2692 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2693 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2694 reallocs++; 2695 } 2696 2697 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2698 if (!nzk) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2699 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2700 2701 /* add the k-th row into il and jl */ 2702 if (nzk > 1){ 2703 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2704 jl[k] = jl[i]; jl[i] = k; 2705 il[k] = ui[k] + 1; 2706 } 2707 uj_ptr[k] = current_space->array; 2708 uj_lvl_ptr[k] = current_space_lvl->array; 2709 2710 current_space->array += nzk; 2711 current_space->local_used += nzk; 2712 current_space->local_remaining -= nzk; 2713 2714 current_space_lvl->array += nzk; 2715 current_space_lvl->local_used += nzk; 2716 current_space_lvl->local_remaining -= nzk; 2717 2718 ui[k+1] = ui[k] + nzk; 2719 } 2720 2721 #if defined(PETSC_USE_INFO) 2722 if (ai[am] != 0) { 2723 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2724 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2725 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2726 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2727 } else { 2728 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2729 } 2730 #endif 2731 2732 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2733 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2734 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2735 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2736 2737 /* destroy list of free space and other temporary array(s) */ 2738 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2739 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 2740 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2741 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2742 2743 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2744 2745 /* put together the new matrix in MATSEQSBAIJ format */ 2746 2747 b = (Mat_SeqSBAIJ*)fact->data; 2748 b->singlemalloc = PETSC_FALSE; 2749 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2750 b->j = uj; 2751 b->i = ui; 2752 b->diag = udiag; 2753 b->free_diag = PETSC_TRUE; 2754 b->ilen = 0; 2755 b->imax = 0; 2756 b->row = perm; 2757 b->col = perm; 2758 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2759 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2760 b->icol = iperm; 2761 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2762 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2763 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2764 b->maxnz = b->nz = ui[am]; 2765 b->free_a = PETSC_TRUE; 2766 b->free_ij = PETSC_TRUE; 2767 2768 fact->info.factor_mallocs = reallocs; 2769 fact->info.fill_ratio_given = fill; 2770 if (ai[am] != 0) { 2771 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2772 } else { 2773 fact->info.fill_ratio_needed = 0.0; 2774 } 2775 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace; 2776 PetscFunctionReturn(0); 2777 } 2778 2779 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2780 { 2781 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2782 Mat_SeqSBAIJ *b; 2783 PetscErrorCode ierr; 2784 PetscTruth perm_identity; 2785 PetscReal fill = info->fill; 2786 const PetscInt *rip,*riip; 2787 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2788 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2789 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr,*udiag; 2790 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2791 PetscBT lnkbt; 2792 IS iperm; 2793 2794 PetscFunctionBegin; 2795 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); 2796 /* check whether perm is the identity mapping */ 2797 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2798 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2799 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2800 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2801 2802 /* initialization */ 2803 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2804 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2805 ui[0] = 0; 2806 2807 /* jl: linked list for storing indices of the pivot rows 2808 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2809 ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr); 2810 for (i=0; i<am; i++){ 2811 jl[i] = am; il[i] = 0; 2812 } 2813 2814 /* create and initialize a linked list for storing column indices of the active row k */ 2815 nlnk = am + 1; 2816 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2817 2818 /* initial FreeSpace size is fill*(ai[am]+1) */ 2819 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2820 current_space = free_space; 2821 2822 for (k=0; k<am; k++){ /* for each active row k */ 2823 /* initialize lnk by the column indices of row rip[k] of A */ 2824 nzk = 0; 2825 ncols = ai[rip[k]+1] - ai[rip[k]]; 2826 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); 2827 ncols_upper = 0; 2828 for (j=0; j<ncols; j++){ 2829 i = riip[*(aj + ai[rip[k]] + j)]; 2830 if (i >= k){ /* only take upper triangular entry */ 2831 cols[ncols_upper] = i; 2832 ncols_upper++; 2833 } 2834 } 2835 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2836 nzk += nlnk; 2837 2838 /* update lnk by computing fill-in for each pivot row to be merged in */ 2839 prow = jl[k]; /* 1st pivot row */ 2840 2841 while (prow < k){ 2842 nextprow = jl[prow]; 2843 /* merge prow into k-th row */ 2844 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2845 jmax = ui[prow+1]; 2846 ncols = jmax-jmin; 2847 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2848 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2849 nzk += nlnk; 2850 2851 /* update il and jl for prow */ 2852 if (jmin < jmax){ 2853 il[prow] = jmin; 2854 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 2855 } 2856 prow = nextprow; 2857 } 2858 2859 /* if free space is not available, make more free space */ 2860 if (current_space->local_remaining<nzk) { 2861 i = am - k + 1; /* num of unfactored rows */ 2862 i *= PetscMin(nzk,i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2863 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2864 reallocs++; 2865 } 2866 2867 /* copy data into free space, then initialize lnk */ 2868 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 2869 2870 /* add the k-th row into il and jl */ 2871 if (nzk > 1){ 2872 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2873 jl[k] = jl[i]; jl[i] = k; 2874 il[k] = ui[k] + 1; 2875 } 2876 ui_ptr[k] = current_space->array; 2877 current_space->array += nzk; 2878 current_space->local_used += nzk; 2879 current_space->local_remaining -= nzk; 2880 2881 ui[k+1] = ui[k] + nzk; 2882 } 2883 2884 #if defined(PETSC_USE_INFO) 2885 if (ai[am] != 0) { 2886 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 2887 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2888 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2889 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2890 } else { 2891 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2892 } 2893 #endif 2894 2895 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2896 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2897 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 2898 2899 /* destroy list of free space and other temporary array(s) */ 2900 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2901 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor */ 2902 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2903 2904 /* put together the new matrix in MATSEQSBAIJ format */ 2905 2906 b = (Mat_SeqSBAIJ*)fact->data; 2907 b->singlemalloc = PETSC_FALSE; 2908 b->free_a = PETSC_TRUE; 2909 b->free_ij = PETSC_TRUE; 2910 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2911 b->j = uj; 2912 b->i = ui; 2913 b->diag = udiag; 2914 b->free_diag = PETSC_TRUE; 2915 b->ilen = 0; 2916 b->imax = 0; 2917 b->row = perm; 2918 b->col = perm; 2919 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2920 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2921 b->icol = iperm; 2922 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2923 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2924 ierr = PetscLogObjectMemory(fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2925 b->maxnz = b->nz = ui[am]; 2926 2927 fact->info.factor_mallocs = reallocs; 2928 fact->info.fill_ratio_given = fill; 2929 if (ai[am] != 0) { 2930 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2931 } else { 2932 fact->info.fill_ratio_needed = 0.0; 2933 } 2934 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2935 PetscFunctionReturn(0); 2936 } 2937 2938 #undef __FUNCT__ 2939 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ_inplace" 2940 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2941 { 2942 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2943 Mat_SeqSBAIJ *b; 2944 PetscErrorCode ierr; 2945 PetscTruth perm_identity; 2946 PetscReal fill = info->fill; 2947 const PetscInt *rip,*riip; 2948 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2949 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2950 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr; 2951 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2952 PetscBT lnkbt; 2953 IS iperm; 2954 2955 PetscFunctionBegin; 2956 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); 2957 /* check whether perm is the identity mapping */ 2958 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2959 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2960 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2961 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2962 2963 /* initialization */ 2964 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2965 ui[0] = 0; 2966 2967 /* jl: linked list for storing indices of the pivot rows 2968 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2969 ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr); 2970 for (i=0; i<am; i++){ 2971 jl[i] = am; il[i] = 0; 2972 } 2973 2974 /* create and initialize a linked list for storing column indices of the active row k */ 2975 nlnk = am + 1; 2976 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2977 2978 /* initial FreeSpace size is fill*(ai[am]+1) */ 2979 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2980 current_space = free_space; 2981 2982 for (k=0; k<am; k++){ /* for each active row k */ 2983 /* initialize lnk by the column indices of row rip[k] of A */ 2984 nzk = 0; 2985 ncols = ai[rip[k]+1] - ai[rip[k]]; 2986 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); 2987 ncols_upper = 0; 2988 for (j=0; j<ncols; j++){ 2989 i = riip[*(aj + ai[rip[k]] + j)]; 2990 if (i >= k){ /* only take upper triangular entry */ 2991 cols[ncols_upper] = i; 2992 ncols_upper++; 2993 } 2994 } 2995 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2996 nzk += nlnk; 2997 2998 /* update lnk by computing fill-in for each pivot row to be merged in */ 2999 prow = jl[k]; /* 1st pivot row */ 3000 3001 while (prow < k){ 3002 nextprow = jl[prow]; 3003 /* merge prow into k-th row */ 3004 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 3005 jmax = ui[prow+1]; 3006 ncols = jmax-jmin; 3007 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 3008 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3009 nzk += nlnk; 3010 3011 /* update il and jl for prow */ 3012 if (jmin < jmax){ 3013 il[prow] = jmin; 3014 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 3015 } 3016 prow = nextprow; 3017 } 3018 3019 /* if free space is not available, make more free space */ 3020 if (current_space->local_remaining<nzk) { 3021 i = am - k + 1; /* num of unfactored rows */ 3022 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 3023 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 3024 reallocs++; 3025 } 3026 3027 /* copy data into free space, then initialize lnk */ 3028 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 3029 3030 /* add the k-th row into il and jl */ 3031 if (nzk-1 > 0){ 3032 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 3033 jl[k] = jl[i]; jl[i] = k; 3034 il[k] = ui[k] + 1; 3035 } 3036 ui_ptr[k] = current_space->array; 3037 current_space->array += nzk; 3038 current_space->local_used += nzk; 3039 current_space->local_remaining -= nzk; 3040 3041 ui[k+1] = ui[k] + nzk; 3042 } 3043 3044 #if defined(PETSC_USE_INFO) 3045 if (ai[am] != 0) { 3046 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 3047 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 3048 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 3049 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 3050 } else { 3051 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 3052 } 3053 #endif 3054 3055 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 3056 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 3057 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 3058 3059 /* destroy list of free space and other temporary array(s) */ 3060 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 3061 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 3062 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3063 3064 /* put together the new matrix in MATSEQSBAIJ format */ 3065 3066 b = (Mat_SeqSBAIJ*)fact->data; 3067 b->singlemalloc = PETSC_FALSE; 3068 b->free_a = PETSC_TRUE; 3069 b->free_ij = PETSC_TRUE; 3070 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 3071 b->j = uj; 3072 b->i = ui; 3073 b->diag = 0; 3074 b->ilen = 0; 3075 b->imax = 0; 3076 b->row = perm; 3077 b->col = perm; 3078 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3079 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3080 b->icol = iperm; 3081 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 3082 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 3083 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3084 b->maxnz = b->nz = ui[am]; 3085 3086 fact->info.factor_mallocs = reallocs; 3087 fact->info.fill_ratio_given = fill; 3088 if (ai[am] != 0) { 3089 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 3090 } else { 3091 fact->info.fill_ratio_needed = 0.0; 3092 } 3093 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace; 3094 PetscFunctionReturn(0); 3095 } 3096 3097 #undef __FUNCT__ 3098 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering" 3099 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx) 3100 { 3101 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3102 PetscErrorCode ierr; 3103 PetscInt n = A->rmap->n; 3104 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag,*vi; 3105 PetscScalar *x,sum; 3106 const PetscScalar *b; 3107 const MatScalar *aa = a->a,*v; 3108 PetscInt i,nz; 3109 3110 PetscFunctionBegin; 3111 if (!n) PetscFunctionReturn(0); 3112 3113 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3114 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3115 3116 /* forward solve the lower triangular */ 3117 x[0] = b[0]; 3118 v = aa; 3119 vi = aj; 3120 for (i=1; i<n; i++) { 3121 nz = ai[i+1] - ai[i]; 3122 sum = b[i]; 3123 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3124 v += nz; 3125 vi += nz; 3126 x[i] = sum; 3127 } 3128 3129 /* backward solve the upper triangular */ 3130 for (i=n-1; i>=0; i--){ 3131 v = aa + adiag[i+1] + 1; 3132 vi = aj + adiag[i+1] + 1; 3133 nz = adiag[i] - adiag[i+1]-1; 3134 sum = x[i]; 3135 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3136 x[i] = sum*v[nz]; /* x[i]=aa[adiag[i]]*sum; v++; */ 3137 } 3138 3139 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 3140 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3141 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3142 PetscFunctionReturn(0); 3143 } 3144 3145 #undef __FUNCT__ 3146 #define __FUNCT__ "MatSolve_SeqAIJ" 3147 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx) 3148 { 3149 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3150 IS iscol = a->col,isrow = a->row; 3151 PetscErrorCode ierr; 3152 PetscInt i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz; 3153 const PetscInt *rout,*cout,*r,*c; 3154 PetscScalar *x,*tmp,sum; 3155 const PetscScalar *b; 3156 const MatScalar *aa = a->a,*v; 3157 3158 PetscFunctionBegin; 3159 if (!n) PetscFunctionReturn(0); 3160 3161 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3162 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3163 tmp = a->solve_work; 3164 3165 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 3166 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 3167 3168 /* forward solve the lower triangular */ 3169 tmp[0] = b[r[0]]; 3170 v = aa; 3171 vi = aj; 3172 for (i=1; i<n; i++) { 3173 nz = ai[i+1] - ai[i]; 3174 sum = b[r[i]]; 3175 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3176 tmp[i] = sum; 3177 v += nz; vi += nz; 3178 } 3179 3180 /* backward solve the upper triangular */ 3181 for (i=n-1; i>=0; i--){ 3182 v = aa + adiag[i+1]+1; 3183 vi = aj + adiag[i+1]+1; 3184 nz = adiag[i]-adiag[i+1]-1; 3185 sum = tmp[i]; 3186 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3187 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 3188 } 3189 3190 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 3191 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 3192 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3193 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3194 ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr); 3195 PetscFunctionReturn(0); 3196 } 3197 3198 #undef __FUNCT__ 3199 #define __FUNCT__ "MatILUDTFactor_SeqAIJ" 3200 /* 3201 This will get a new name and become a varient of MatILUFactor_SeqAIJ() there is no longer seperate functions in the matrix function table for dt factors 3202 */ 3203 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact) 3204 { 3205 Mat B = *fact; 3206 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b; 3207 IS isicol; 3208 PetscErrorCode ierr; 3209 const PetscInt *r,*ic; 3210 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag; 3211 PetscInt *bi,*bj,*bdiag,*bdiag_rev; 3212 PetscInt row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au; 3213 PetscInt nlnk,*lnk; 3214 PetscBT lnkbt; 3215 PetscTruth row_identity,icol_identity,both_identity; 3216 MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp; 3217 const PetscInt *ics; 3218 PetscInt j,nz,*pj,*bjtmp,k,ncut,*jtmp; 3219 PetscReal dt=info->dt,dtcol=info->dtcol,shift=info->shiftamount; 3220 PetscInt dtcount=(PetscInt)info->dtcount,nnz_max; 3221 PetscTruth missing; 3222 3223 PetscFunctionBegin; 3224 3225 if (dt == PETSC_DEFAULT) dt = 0.005; 3226 if (dtcol == PETSC_DEFAULT) dtcol = 0.01; /* XXX unused! */ 3227 if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax); 3228 3229 /* ------- symbolic factorization, can be reused ---------*/ 3230 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 3231 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 3232 adiag=a->diag; 3233 3234 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 3235 3236 /* bdiag is location of diagonal in factor */ 3237 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); /* becomes b->diag */ 3238 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag_rev);CHKERRQ(ierr); /* temporary */ 3239 3240 /* allocate row pointers bi */ 3241 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 3242 3243 /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */ 3244 if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */ 3245 nnz_max = ai[n]+2*n*dtcount+2; 3246 3247 ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 3248 ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr); 3249 3250 /* put together the new matrix */ 3251 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 3252 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 3253 b = (Mat_SeqAIJ*)B->data; 3254 b->free_a = PETSC_TRUE; 3255 b->free_ij = PETSC_TRUE; 3256 b->singlemalloc = PETSC_FALSE; 3257 b->a = ba; 3258 b->j = bj; 3259 b->i = bi; 3260 b->diag = bdiag; 3261 b->ilen = 0; 3262 b->imax = 0; 3263 b->row = isrow; 3264 b->col = iscol; 3265 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 3266 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 3267 b->icol = isicol; 3268 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 3269 3270 ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3271 b->maxnz = nnz_max; 3272 3273 B->factortype = MAT_FACTOR_ILUDT; 3274 B->info.factor_mallocs = 0; 3275 B->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]); 3276 CHKMEMQ; 3277 /* ------- end of symbolic factorization ---------*/ 3278 3279 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3280 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3281 ics = ic; 3282 3283 /* linked list for storing column indices of the active row */ 3284 nlnk = n + 1; 3285 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3286 3287 /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */ 3288 ierr = PetscMalloc2(n,PetscInt,&im,n,PetscInt,&jtmp);CHKERRQ(ierr); 3289 /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */ 3290 ierr = PetscMalloc2(n,MatScalar,&rtmp,n,MatScalar,&vtmp);CHKERRQ(ierr); 3291 ierr = PetscMemzero(rtmp,n*sizeof(MatScalar));CHKERRQ(ierr); 3292 3293 bi[0] = 0; 3294 bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */ 3295 bdiag_rev[n] = bdiag[0]; 3296 bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */ 3297 for (i=0; i<n; i++) { 3298 /* copy initial fill into linked list */ 3299 nzi = 0; /* nonzeros for active row i */ 3300 nzi = ai[r[i]+1] - ai[r[i]]; 3301 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); 3302 nzi_al = adiag[r[i]] - ai[r[i]]; 3303 nzi_au = ai[r[i]+1] - adiag[r[i]] -1; 3304 ajtmp = aj + ai[r[i]]; 3305 ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3306 3307 /* load in initial (unfactored row) */ 3308 aatmp = a->a + ai[r[i]]; 3309 for (j=0; j<nzi; j++) { 3310 rtmp[ics[*ajtmp++]] = *aatmp++; 3311 } 3312 3313 /* add pivot rows into linked list */ 3314 row = lnk[n]; 3315 while (row < i ) { 3316 nzi_bl = bi[row+1] - bi[row] + 1; 3317 bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */ 3318 ierr = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr); 3319 nzi += nlnk; 3320 row = lnk[row]; 3321 } 3322 3323 /* copy data from lnk into jtmp, then initialize lnk */ 3324 ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr); 3325 3326 /* numerical factorization */ 3327 bjtmp = jtmp; 3328 row = *bjtmp++; /* 1st pivot row */ 3329 while ( row < i ) { 3330 pc = rtmp + row; 3331 pv = ba + bdiag[row]; /* 1./(diag of the pivot row) */ 3332 multiplier = (*pc) * (*pv); 3333 *pc = multiplier; 3334 if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */ 3335 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3336 pv = ba + bdiag[row+1] + 1; 3337 /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */ 3338 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3339 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3340 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 3341 } 3342 row = *bjtmp++; 3343 } 3344 3345 /* copy sparse rtmp into contiguous vtmp; separate L and U part */ 3346 diag_tmp = rtmp[i]; /* save diagonal value - may not needed?? */ 3347 nzi_bl = 0; j = 0; 3348 while (jtmp[j] < i){ /* Note: jtmp is sorted */ 3349 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3350 nzi_bl++; j++; 3351 } 3352 nzi_bu = nzi - nzi_bl -1; 3353 while (j < nzi){ 3354 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3355 j++; 3356 } 3357 3358 bjtmp = bj + bi[i]; 3359 batmp = ba + bi[i]; 3360 /* apply level dropping rule to L part */ 3361 ncut = nzi_al + dtcount; 3362 if (ncut < nzi_bl){ 3363 ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr); 3364 ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr); 3365 } else { 3366 ncut = nzi_bl; 3367 } 3368 for (j=0; j<ncut; j++){ 3369 bjtmp[j] = jtmp[j]; 3370 batmp[j] = vtmp[j]; 3371 /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */ 3372 } 3373 bi[i+1] = bi[i] + ncut; 3374 nzi = ncut + 1; 3375 3376 /* apply level dropping rule to U part */ 3377 ncut = nzi_au + dtcount; 3378 if (ncut < nzi_bu){ 3379 ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr); 3380 ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr); 3381 } else { 3382 ncut = nzi_bu; 3383 } 3384 nzi += ncut; 3385 3386 /* mark bdiagonal */ 3387 bdiag[i+1] = bdiag[i] - (ncut + 1); 3388 bdiag_rev[n-i-1] = bdiag[i+1]; 3389 bi[2*n - i] = bi[2*n - i +1] - (ncut + 1); 3390 bjtmp = bj + bdiag[i]; 3391 batmp = ba + bdiag[i]; 3392 *bjtmp = i; 3393 *batmp = diag_tmp; /* rtmp[i]; */ 3394 if (*batmp == 0.0) { 3395 *batmp = dt+shift; 3396 /* printf(" row %d add shift %g\n",i,shift); */ 3397 } 3398 *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */ 3399 /* printf(" (%d,%g),",*bjtmp,*batmp); */ 3400 3401 bjtmp = bj + bdiag[i+1]+1; 3402 batmp = ba + bdiag[i+1]+1; 3403 for (k=0; k<ncut; k++){ 3404 bjtmp[k] = jtmp[nzi_bl+1+k]; 3405 batmp[k] = vtmp[nzi_bl+1+k]; 3406 /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */ 3407 } 3408 /* printf("\n"); */ 3409 3410 im[i] = nzi; /* used by PetscLLAddSortedLU() */ 3411 /* 3412 printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]); 3413 printf(" ----------------------------\n"); 3414 */ 3415 } /* for (i=0; i<n; i++) */ 3416 /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */ 3417 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]); 3418 3419 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3420 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3421 3422 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3423 ierr = PetscFree2(im,jtmp);CHKERRQ(ierr); 3424 ierr = PetscFree2(rtmp,vtmp);CHKERRQ(ierr); 3425 ierr = PetscFree(bdiag_rev);CHKERRQ(ierr); 3426 3427 ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr); 3428 b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n]; 3429 3430 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3431 ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr); 3432 both_identity = (PetscTruth) (row_identity && icol_identity); 3433 if (row_identity && icol_identity) { 3434 B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 3435 } else { 3436 B->ops->solve = MatSolve_SeqAIJ; 3437 } 3438 3439 B->ops->solveadd = 0; 3440 B->ops->solvetranspose = 0; 3441 B->ops->solvetransposeadd = 0; 3442 B->ops->matsolve = 0; 3443 B->assembled = PETSC_TRUE; 3444 B->preallocated = PETSC_TRUE; 3445 PetscFunctionReturn(0); 3446 } 3447 3448 /* a wraper of MatILUDTFactor_SeqAIJ() */ 3449 #undef __FUNCT__ 3450 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ" 3451 /* 3452 This will get a new name and become a varient of MatILUFactor_SeqAIJ() there is no longer seperate functions in the matrix function table for dt factors 3453 */ 3454 3455 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info) 3456 { 3457 PetscErrorCode ierr; 3458 3459 PetscFunctionBegin; 3460 ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr); 3461 PetscFunctionReturn(0); 3462 } 3463 3464 /* 3465 same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors 3466 - intend to replace existing MatLUFactorNumeric_SeqAIJ() 3467 */ 3468 #undef __FUNCT__ 3469 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ" 3470 /* 3471 This will get a new name and become a varient of MatILUFactor_SeqAIJ() there is no longer seperate functions in the matrix function table for dt factors 3472 */ 3473 3474 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info) 3475 { 3476 Mat C=fact; 3477 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 3478 IS isrow = b->row,isicol = b->icol; 3479 PetscErrorCode ierr; 3480 const PetscInt *r,*ic,*ics; 3481 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 3482 PetscInt *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj; 3483 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 3484 PetscReal dt=info->dt,shift=info->shiftamount; 3485 PetscTruth row_identity, col_identity; 3486 3487 PetscFunctionBegin; 3488 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3489 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3490 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 3491 ics = ic; 3492 3493 for (i=0; i<n; i++){ 3494 /* initialize rtmp array */ 3495 nzl = bi[i+1] - bi[i]; /* num of nozeros in L(i,:) */ 3496 bjtmp = bj + bi[i]; 3497 for (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0; 3498 rtmp[i] = 0.0; 3499 nzu = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */ 3500 bjtmp = bj + bdiag[i+1] + 1; 3501 for (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0; 3502 3503 /* load in initial unfactored row of A */ 3504 /* printf("row %d\n",i); */ 3505 nz = ai[r[i]+1] - ai[r[i]]; 3506 ajtmp = aj + ai[r[i]]; 3507 v = aa + ai[r[i]]; 3508 for (j=0; j<nz; j++) { 3509 rtmp[ics[*ajtmp++]] = v[j]; 3510 /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */ 3511 } 3512 /* printf("\n"); */ 3513 3514 /* numerical factorization */ 3515 bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */ 3516 nzl = bi[i+1] - bi[i]; /* num of entries in L(i,:) */ 3517 k = 0; 3518 while (k < nzl){ 3519 row = *bjtmp++; 3520 /* printf(" prow %d\n",row); */ 3521 pc = rtmp + row; 3522 pv = b->a + bdiag[row]; /* 1./(diag of the pivot row) */ 3523 multiplier = (*pc) * (*pv); 3524 *pc = multiplier; 3525 if (PetscAbsScalar(multiplier) > dt){ 3526 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3527 pv = b->a + bdiag[row+1] + 1; 3528 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3529 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3530 /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */ 3531 } 3532 k++; 3533 } 3534 3535 /* finished row so stick it into b->a */ 3536 /* L-part */ 3537 pv = b->a + bi[i] ; 3538 pj = bj + bi[i] ; 3539 nzl = bi[i+1] - bi[i]; 3540 for (j=0; j<nzl; j++) { 3541 pv[j] = rtmp[pj[j]]; 3542 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3543 } 3544 3545 /* diagonal: invert diagonal entries for simplier triangular solves */ 3546 if (rtmp[i] == 0.0) rtmp[i] = dt+shift; 3547 b->a[bdiag[i]] = 1.0/rtmp[i]; 3548 /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */ 3549 3550 /* U-part */ 3551 pv = b->a + bdiag[i+1] + 1; 3552 pj = bj + bdiag[i+1] + 1; 3553 nzu = bdiag[i] - bdiag[i+1] - 1; 3554 for (j=0; j<nzu; j++) { 3555 pv[j] = rtmp[pj[j]]; 3556 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3557 } 3558 /* printf("\n"); */ 3559 } 3560 3561 ierr = PetscFree(rtmp);CHKERRQ(ierr); 3562 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3563 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3564 3565 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3566 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 3567 if (row_identity && col_identity) { 3568 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 3569 } else { 3570 C->ops->solve = MatSolve_SeqAIJ; 3571 } 3572 C->ops->solveadd = 0; 3573 C->ops->solvetranspose = 0; 3574 C->ops->solvetransposeadd = 0; 3575 C->ops->matsolve = 0; 3576 C->assembled = PETSC_TRUE; 3577 C->preallocated = PETSC_TRUE; 3578 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 3579 PetscFunctionReturn(0); 3580 } 3581