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