1 #define PETSCMAT_DLL 2 3 4 #include "../src/mat/impls/aij/seq/aij.h" 5 #include "../src/mat/impls/sbaij/seq/sbaij.h" 6 #include "petscbt.h" 7 #include "../src/mat/utils/freespace.h" 8 9 EXTERN_C_BEGIN 10 #undef __FUNCT__ 11 #define __FUNCT__ "MatOrdering_Flow_SeqAIJ" 12 /* 13 Computes an ordering to get most of the large numerical values in the lower triangular part of the matrix 14 */ 15 PetscErrorCode MatOrdering_Flow_SeqAIJ(Mat mat,const MatOrderingType type,IS *irow,IS *icol) 16 { 17 Mat_SeqAIJ *a = (Mat_SeqAIJ*)mat->data; 18 PetscErrorCode ierr; 19 PetscInt i,j,jj,k, kk,n = mat->rmap->n, current = 0, newcurrent = 0,*order; 20 const PetscInt *ai = a->i, *aj = a->j; 21 const PetscScalar *aa = a->a; 22 PetscTruth *done; 23 PetscReal best,past = 0,future; 24 25 PetscFunctionBegin; 26 /* pick initial row */ 27 best = -1; 28 for (i=0; i<n; i++) { 29 future = 0.0; 30 for (j=ai[i]; j<ai[i+1]; j++) { 31 if (aj[j] != i) future += PetscAbsScalar(aa[j]); else past = PetscAbsScalar(aa[j]); 32 } 33 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 34 if (past/future > best) { 35 best = past/future; 36 current = i; 37 } 38 } 39 40 ierr = PetscMalloc(n*sizeof(PetscTruth),&done);CHKERRQ(ierr); 41 ierr = PetscMemzero(done,n*sizeof(PetscTruth));CHKERRQ(ierr); 42 ierr = PetscMalloc(n*sizeof(PetscInt),&order);CHKERRQ(ierr); 43 order[0] = current; 44 for (i=0; i<n-1; i++) { 45 done[current] = PETSC_TRUE; 46 best = -1; 47 /* loop over all neighbors of current pivot */ 48 for (j=ai[current]; j<ai[current+1]; j++) { 49 jj = aj[j]; 50 if (done[jj]) continue; 51 /* loop over columns of potential next row computing weights for below and above diagonal */ 52 past = future = 0.0; 53 for (k=ai[jj]; k<ai[jj+1]; k++) { 54 kk = aj[k]; 55 if (done[kk]) past += PetscAbsScalar(aa[k]); 56 else if (kk != jj) future += PetscAbsScalar(aa[k]); 57 } 58 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 59 if (past/future > best) { 60 best = past/future; 61 newcurrent = jj; 62 } 63 } 64 if (best == -1) { /* no neighbors to select from so select best of all that remain */ 65 best = -1; 66 for (k=0; k<n; k++) { 67 if (done[k]) continue; 68 future = 0.0; 69 past = 0.0; 70 for (j=ai[k]; j<ai[k+1]; j++) { 71 kk = aj[j]; 72 if (done[kk]) past += PetscAbsScalar(aa[j]); 73 else if (kk != k) future += PetscAbsScalar(aa[j]); 74 } 75 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 76 if (past/future > best) { 77 best = past/future; 78 newcurrent = k; 79 } 80 } 81 } 82 if (current == newcurrent) SETERRQ(PETSC_ERR_PLIB,"newcurrent cannot be current"); 83 current = newcurrent; 84 order[i+1] = current; 85 } 86 ierr = ISCreateGeneral(PETSC_COMM_SELF,n,order,irow);CHKERRQ(ierr); 87 *icol = *irow; 88 ierr = PetscObjectReference((PetscObject)*irow);CHKERRQ(ierr); 89 ierr = PetscFree(done);CHKERRQ(ierr); 90 ierr = PetscFree(order);CHKERRQ(ierr); 91 PetscFunctionReturn(0); 92 } 93 EXTERN_C_END 94 95 EXTERN_C_BEGIN 96 #undef __FUNCT__ 97 #define __FUNCT__ "MatGetFactorAvailable_seqaij_petsc" 98 PetscErrorCode MatGetFactorAvailable_seqaij_petsc(Mat A,MatFactorType ftype,PetscTruth *flg) 99 { 100 PetscFunctionBegin; 101 *flg = PETSC_TRUE; 102 PetscFunctionReturn(0); 103 } 104 EXTERN_C_END 105 106 EXTERN_C_BEGIN 107 #undef __FUNCT__ 108 #define __FUNCT__ "MatGetFactor_seqaij_petsc" 109 PetscErrorCode MatGetFactor_seqaij_petsc(Mat A,MatFactorType ftype,Mat *B) 110 { 111 PetscInt n = A->rmap->n; 112 PetscErrorCode ierr; 113 114 PetscFunctionBegin; 115 ierr = MatCreate(((PetscObject)A)->comm,B);CHKERRQ(ierr); 116 ierr = MatSetSizes(*B,n,n,n,n);CHKERRQ(ierr); 117 if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT){ 118 ierr = MatSetType(*B,MATSEQAIJ);CHKERRQ(ierr); 119 (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJ; 120 (*B)->ops->lufactorsymbolic = MatLUFactorSymbolic_SeqAIJ; 121 (*B)->ops->iludtfactor = MatILUDTFactor_SeqAIJ; 122 } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) { 123 ierr = MatSetType(*B,MATSEQSBAIJ);CHKERRQ(ierr); 124 ierr = MatSeqSBAIJSetPreallocation(*B,1,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 125 (*B)->ops->iccfactorsymbolic = MatICCFactorSymbolic_SeqAIJ; 126 (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJ; 127 } else SETERRQ(PETSC_ERR_SUP,"Factor type not supported"); 128 (*B)->factor = ftype; 129 PetscFunctionReturn(0); 130 } 131 EXTERN_C_END 132 133 #undef __FUNCT__ 134 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ" 135 PetscErrorCode MatLUFactorSymbolic_SeqAIJ(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 136 { 137 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 138 IS isicol; 139 PetscErrorCode ierr; 140 const PetscInt *r,*ic; 141 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j; 142 PetscInt *bi,*bj,*ajtmp; 143 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 144 PetscReal f; 145 PetscInt nlnk,*lnk,k,**bi_ptr; 146 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 147 PetscBT lnkbt; 148 PetscTruth newdatastruct= PETSC_FALSE; 149 150 PetscFunctionBegin; 151 ierr = PetscOptionsGetTruth(PETSC_NULL,"-lu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 152 if(newdatastruct){ 153 ierr = MatLUFactorSymbolic_SeqAIJ_newdatastruct(B,A,isrow,iscol,info);CHKERRQ(ierr); 154 PetscFunctionReturn(0); 155 } 156 157 158 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square"); 159 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 160 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 161 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 162 163 /* get new row pointers */ 164 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 165 bi[0] = 0; 166 167 /* bdiag is location of diagonal in factor */ 168 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 169 bdiag[0] = 0; 170 171 /* linked list for storing column indices of the active row */ 172 nlnk = n + 1; 173 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 174 175 ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr); 176 177 /* initial FreeSpace size is f*(ai[n]+1) */ 178 f = info->fill; 179 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 180 current_space = free_space; 181 182 for (i=0; i<n; i++) { 183 /* copy previous fill into linked list */ 184 nzi = 0; 185 nnz = ai[r[i]+1] - ai[r[i]]; 186 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 187 ajtmp = aj + ai[r[i]]; 188 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 189 nzi += nlnk; 190 191 /* add pivot rows into linked list */ 192 row = lnk[n]; 193 while (row < i) { 194 nzbd = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */ 195 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 196 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 197 nzi += nlnk; 198 row = lnk[row]; 199 } 200 bi[i+1] = bi[i] + nzi; 201 im[i] = nzi; 202 203 /* mark bdiag */ 204 nzbd = 0; 205 nnz = nzi; 206 k = lnk[n]; 207 while (nnz-- && k < i){ 208 nzbd++; 209 k = lnk[k]; 210 } 211 bdiag[i] = bi[i] + nzbd; 212 213 /* if free space is not available, make more free space */ 214 if (current_space->local_remaining<nzi) { 215 nnz = (n - i)*nzi; /* estimated and max additional space needed */ 216 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 217 reallocs++; 218 } 219 220 /* copy data into free space, then initialize lnk */ 221 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 222 bi_ptr[i] = current_space->array; 223 current_space->array += nzi; 224 current_space->local_used += nzi; 225 current_space->local_remaining -= nzi; 226 } 227 #if defined(PETSC_USE_INFO) 228 if (ai[n] != 0) { 229 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 230 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 231 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 232 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr); 233 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 234 } else { 235 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 236 } 237 #endif 238 239 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 240 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 241 242 /* destroy list of free space and other temporary array(s) */ 243 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 244 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); 245 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 246 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 247 248 /* put together the new matrix */ 249 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 250 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 251 b = (Mat_SeqAIJ*)(B)->data; 252 b->free_a = PETSC_TRUE; 253 b->free_ij = PETSC_TRUE; 254 b->singlemalloc = PETSC_FALSE; 255 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 256 b->j = bj; 257 b->i = bi; 258 b->diag = bdiag; 259 b->ilen = 0; 260 b->imax = 0; 261 b->row = isrow; 262 b->col = iscol; 263 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 264 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 265 b->icol = isicol; 266 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 267 268 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 269 ierr = PetscLogObjectMemory(B,(bi[n]-n)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 270 b->maxnz = b->nz = bi[n] ; 271 272 (B)->factor = MAT_FACTOR_LU; 273 (B)->info.factor_mallocs = reallocs; 274 (B)->info.fill_ratio_given = f; 275 276 if (ai[n]) { 277 (B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 278 } else { 279 (B)->info.fill_ratio_needed = 0.0; 280 } 281 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 282 (B)->ops->solve = MatSolve_SeqAIJ; 283 (B)->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 284 /* switch to inodes if appropriate */ 285 ierr = MatLUFactorSymbolic_SeqAIJ_Inode(B,A,isrow,iscol,info);CHKERRQ(ierr); 286 PetscFunctionReturn(0); 287 } 288 289 #undef __FUNCT__ 290 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ_newdatastruct" 291 PetscErrorCode MatLUFactorSymbolic_SeqAIJ_newdatastruct(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 292 { 293 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 294 IS isicol; 295 PetscErrorCode ierr; 296 const PetscInt *r,*ic; 297 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j; 298 PetscInt *bi,*bj,*ajtmp; 299 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 300 PetscReal f; 301 PetscInt nlnk,*lnk,k,**bi_ptr; 302 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 303 PetscBT lnkbt; 304 305 PetscFunctionBegin; 306 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square"); 307 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 308 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 309 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 310 311 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 312 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 313 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 314 bi[0] = bdiag[0] = 0; 315 316 /* linked list for storing column indices of the active row */ 317 nlnk = n + 1; 318 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 319 320 ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr); 321 322 /* initial FreeSpace size is f*(ai[n]+1) */ 323 f = info->fill; 324 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 325 current_space = free_space; 326 327 for (i=0; i<n; i++) { 328 /* copy previous fill into linked list */ 329 nzi = 0; 330 nnz = ai[r[i]+1] - ai[r[i]]; 331 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 332 ajtmp = aj + ai[r[i]]; 333 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 334 nzi += nlnk; 335 336 /* add pivot rows into linked list */ 337 row = lnk[n]; 338 while (row < i){ 339 nzbd = bdiag[row] + 1; /* num of entries in the row with column index <= row */ 340 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 341 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 342 nzi += nlnk; 343 row = lnk[row]; 344 } 345 bi[i+1] = bi[i] + nzi; 346 im[i] = nzi; 347 348 /* mark bdiag */ 349 nzbd = 0; 350 nnz = nzi; 351 k = lnk[n]; 352 while (nnz-- && k < i){ 353 nzbd++; 354 k = lnk[k]; 355 } 356 bdiag[i] = nzbd; /* note: bdiag[i] = nnzL as input for PetscFreeSpaceContiguous_LU() */ 357 358 /* if free space is not available, make more free space */ 359 if (current_space->local_remaining<nzi) { 360 nnz = 2*(n - i)*nzi; /* estimated and max additional space needed */ 361 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 362 reallocs++; 363 } 364 365 /* copy data into free space, then initialize lnk */ 366 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 367 bi_ptr[i] = current_space->array; 368 current_space->array += nzi; 369 current_space->local_used += nzi; 370 current_space->local_remaining -= nzi; 371 } 372 #if defined(PETSC_USE_INFO) 373 if (ai[n] != 0) { 374 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 375 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 376 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 377 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr); 378 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 379 } else { 380 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 381 } 382 #endif 383 384 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 385 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 386 387 /* destroy list of free space and other temporary array(s) */ 388 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 389 ierr = PetscFreeSpaceContiguous_LU_v2(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 390 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 391 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 392 393 /* put together the new matrix */ 394 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 395 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 396 b = (Mat_SeqAIJ*)(B)->data; 397 b->free_a = PETSC_TRUE; 398 b->free_ij = PETSC_TRUE; 399 b->singlemalloc = PETSC_FALSE; 400 ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 401 b->j = bj; 402 b->i = bi; 403 b->diag = bdiag; 404 b->ilen = 0; 405 b->imax = 0; 406 b->row = isrow; 407 b->col = iscol; 408 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 409 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 410 b->icol = isicol; 411 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 412 413 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 414 ierr = PetscLogObjectMemory(B,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 415 b->maxnz = b->nz = bdiag[0]+1; 416 (B)->factor = MAT_FACTOR_LU; 417 (B)->info.factor_mallocs = reallocs; 418 (B)->info.fill_ratio_given = f; 419 420 if (ai[n]) { 421 (B)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 422 } else { 423 (B)->info.fill_ratio_needed = 0.0; 424 } 425 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 426 PetscFunctionReturn(0); 427 } 428 429 /* 430 Trouble in factorization, should we dump the original matrix? 431 */ 432 #undef __FUNCT__ 433 #define __FUNCT__ "MatFactorDumpMatrix" 434 PetscErrorCode MatFactorDumpMatrix(Mat A) 435 { 436 PetscErrorCode ierr; 437 PetscTruth flg = PETSC_FALSE; 438 439 PetscFunctionBegin; 440 ierr = PetscOptionsGetTruth(PETSC_NULL,"-mat_factor_dump_on_error",&flg,PETSC_NULL);CHKERRQ(ierr); 441 if (flg) { 442 PetscViewer viewer; 443 char filename[PETSC_MAX_PATH_LEN]; 444 445 ierr = PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);CHKERRQ(ierr); 446 ierr = PetscViewerBinaryOpen(((PetscObject)A)->comm,filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr); 447 ierr = MatView(A,viewer);CHKERRQ(ierr); 448 ierr = PetscViewerDestroy(viewer);CHKERRQ(ierr); 449 } 450 PetscFunctionReturn(0); 451 } 452 453 extern PetscErrorCode MatSolve_SeqAIJ_Inode(Mat,Vec,Vec); 454 455 #undef __FUNCT__ 456 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_newdatastruct" 457 PetscErrorCode MatLUFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info) 458 { 459 Mat C=B; 460 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 461 IS isrow = b->row,isicol = b->icol; 462 PetscErrorCode ierr; 463 const PetscInt *r,*ic,*ics; 464 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 465 PetscInt *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj; 466 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 467 PetscTruth row_identity,col_identity; 468 469 LUShift_Ctx sctx; 470 PetscInt *ddiag,newshift; 471 PetscReal rs; 472 MatScalar d; 473 474 PetscFunctionBegin; 475 /* MatPivotSetUp(): initialize shift context sctx */ 476 ierr = PetscMemzero(&sctx,sizeof(LUShift_Ctx));CHKERRQ(ierr); 477 478 /* if both shift schemes are chosen by user, only use info->shiftpd */ 479 if (info->shiftpd) { /* 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.lushift = 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 /* MatPivotCheck() */ 565 sctx.rs = rs; 566 sctx.pv = rtmp[i]; 567 /* ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); */ 568 if (info->shiftnz){ 569 ierr = MatPivotCheck_nz(info,sctx,i,newshift);CHKERRQ(ierr); 570 } else if (info->shiftpd){ 571 ierr = MatPivotCheck_pd(info,sctx,i,newshift);CHKERRQ(ierr); 572 } else if (info->shiftinblocks){ 573 ierr = MatPivotCheck_inblocks(info,sctx,i,newshift);CHKERRQ(ierr); 574 } else { 575 ierr = MatPivotCheck_none(info,sctx,i,newshift);CHKERRQ(ierr); 576 } 577 rtmp[i] = sctx.pv; 578 if (newshift == 1) break; 579 580 /* Mark diagonal and invert diagonal for simplier triangular solves */ 581 pv = b->a + bdiag[i]; 582 *pv = 1.0/rtmp[i]; 583 584 } /* endof for (i=0; i<n; i++){ */ 585 586 /* MatPivotRefine() */ 587 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max){ 588 /* 589 * if no shift in this attempt & shifting & started shifting & can refine, 590 * then try lower shift 591 */ 592 sctx.shift_hi = sctx.shift_fraction; 593 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 594 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 595 sctx.lushift = PETSC_TRUE; 596 sctx.nshift++; 597 } 598 } while (sctx.lushift); 599 600 ierr = PetscFree(rtmp);CHKERRQ(ierr); 601 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 602 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 603 604 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 605 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 606 if (row_identity && col_identity) { 607 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct; 608 } else { 609 C->ops->solve = MatSolve_SeqAIJ_newdatastruct; 610 } 611 612 C->ops->solveadd = MatSolveAdd_SeqAIJ_newdatastruct; 613 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ_newdatastruct; 614 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_newdatastruct; 615 C->ops->matsolve = 0; 616 C->assembled = PETSC_TRUE; 617 C->preallocated = PETSC_TRUE; 618 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 619 620 /* MatPivotView() */ 621 if (sctx.nshift){ 622 if (info->shiftpd) { 623 ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %G, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,sctx.shift_amount,sctx.shift_fraction,sctx.shift_top);CHKERRQ(ierr); 624 } else if (info->shiftnz) { 625 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 626 } else if (info->shiftinblocks){ 627 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftinblocks);CHKERRQ(ierr); 628 } 629 } 630 PetscFunctionReturn(0); 631 } 632 633 #undef __FUNCT__ 634 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ" 635 PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 636 { 637 Mat C=B; 638 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 639 IS isrow = b->row,isicol = b->icol; 640 PetscErrorCode ierr; 641 const PetscInt *r,*ic,*ics; 642 PetscInt nz,row,i,j,n=A->rmap->n,diag; 643 const PetscInt *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 644 const PetscInt *ajtmp,*bjtmp,*diag_offset = b->diag,*pj; 645 MatScalar *pv,*rtmp,*pc,multiplier,d; 646 const MatScalar *v,*aa=a->a; 647 PetscReal rs=0.0; 648 LUShift_Ctx sctx; 649 PetscInt newshift,*ddiag; 650 651 PetscFunctionBegin; 652 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 653 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 654 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 655 ics = ic; 656 657 /* initialize shift context sctx */ 658 sctx.nshift = 0; 659 sctx.nshift_max = 0; 660 sctx.shift_top = 0.0; 661 sctx.shift_lo = 0.0; 662 sctx.shift_hi = 0.0; 663 sctx.shift_fraction = 0.0; 664 sctx.shift_amount = 0.0; 665 666 /* if both shift schemes are chosen by user, only use info->shiftpd */ 667 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 668 ddiag = a->diag; 669 sctx.shift_top = info->zeropivot; 670 for (i=0; i<n; i++) { 671 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 672 d = (aa)[ddiag[i]]; 673 rs = -PetscAbsScalar(d) - PetscRealPart(d); 674 v = aa+ai[i]; 675 nz = ai[i+1] - ai[i]; 676 for (j=0; j<nz; j++) 677 rs += PetscAbsScalar(v[j]); 678 if (rs>sctx.shift_top) sctx.shift_top = rs; 679 } 680 sctx.shift_top *= 1.1; 681 sctx.nshift_max = 5; 682 sctx.shift_lo = 0.; 683 sctx.shift_hi = 1.; 684 } 685 686 do { 687 sctx.lushift = PETSC_FALSE; 688 for (i=0; i<n; i++){ 689 nz = bi[i+1] - bi[i]; 690 bjtmp = bj + bi[i]; 691 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 692 693 /* load in initial (unfactored row) */ 694 nz = ai[r[i]+1] - ai[r[i]]; 695 ajtmp = aj + ai[r[i]]; 696 v = aa + ai[r[i]]; 697 for (j=0; j<nz; j++) { 698 rtmp[ics[ajtmp[j]]] = v[j]; 699 } 700 rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 701 /* if (sctx.shift_amount > 0.0) printf("row %d, shift %g\n",i,sctx.shift_amount); */ 702 703 row = *bjtmp++; 704 while (row < i) { 705 pc = rtmp + row; 706 if (*pc != 0.0) { 707 pv = b->a + diag_offset[row]; 708 pj = b->j + diag_offset[row] + 1; 709 multiplier = *pc / *pv++; 710 *pc = multiplier; 711 nz = bi[row+1] - diag_offset[row] - 1; 712 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 713 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 714 } 715 row = *bjtmp++; 716 } 717 /* finished row so stick it into b->a */ 718 pv = b->a + bi[i] ; 719 pj = b->j + bi[i] ; 720 nz = bi[i+1] - bi[i]; 721 diag = diag_offset[i] - bi[i]; 722 rs = 0.0; 723 for (j=0; j<nz; j++) { 724 pv[j] = rtmp[pj[j]]; 725 rs += PetscAbsScalar(pv[j]); 726 } 727 rs -= PetscAbsScalar(pv[diag]); 728 729 /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */ 730 sctx.rs = rs; 731 sctx.pv = pv[diag]; 732 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 733 if (newshift == 1) break; 734 } 735 736 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 737 /* 738 * if no shift in this attempt & shifting & started shifting & can refine, 739 * then try lower shift 740 */ 741 sctx.shift_hi = sctx.shift_fraction; 742 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 743 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 744 sctx.lushift = PETSC_TRUE; 745 sctx.nshift++; 746 } 747 } while (sctx.lushift); 748 749 /* invert diagonal entries for simplier triangular solves */ 750 for (i=0; i<n; i++) { 751 b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]]; 752 } 753 ierr = PetscFree(rtmp);CHKERRQ(ierr); 754 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 755 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 756 if (b->inode.use) { 757 C->ops->solve = MatSolve_SeqAIJ_Inode; 758 } else { 759 PetscTruth row_identity, col_identity; 760 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 761 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 762 if (row_identity && col_identity) { 763 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 764 } else { 765 C->ops->solve = MatSolve_SeqAIJ; 766 } 767 } 768 C->ops->solveadd = MatSolveAdd_SeqAIJ; 769 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 770 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 771 C->ops->matsolve = MatMatSolve_SeqAIJ; 772 C->assembled = PETSC_TRUE; 773 C->preallocated = PETSC_TRUE; 774 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 775 if (sctx.nshift){ 776 if (info->shiftpd) { 777 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); 778 } else if (info->shiftnz) { 779 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 780 } 781 } 782 PetscFunctionReturn(0); 783 } 784 785 /* 786 This routine implements inplace ILU(0) with row or/and column permutations. 787 Input: 788 A - original matrix 789 Output; 790 A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i] 791 a->j (col index) is permuted by the inverse of colperm, then sorted 792 a->a reordered accordingly with a->j 793 a->diag (ptr to diagonal elements) is updated. 794 */ 795 #undef __FUNCT__ 796 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_InplaceWithPerm" 797 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info) 798 { 799 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 800 IS isrow = a->row,isicol = a->icol; 801 PetscErrorCode ierr; 802 const PetscInt *r,*ic,*ics; 803 PetscInt i,j,n=A->rmap->n,*ai=a->i,*aj=a->j; 804 PetscInt *ajtmp,nz,row; 805 PetscInt *diag = a->diag,nbdiag,*pj; 806 PetscScalar *rtmp,*pc,multiplier,d; 807 MatScalar *v,*pv; 808 PetscReal rs; 809 LUShift_Ctx sctx; 810 PetscInt newshift; 811 812 PetscFunctionBegin; 813 if (A != B) SETERRQ(PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address"); 814 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 815 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 816 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&rtmp);CHKERRQ(ierr); 817 ierr = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr); 818 ics = ic; 819 820 sctx.shift_top = 0.; 821 sctx.nshift_max = 0.; 822 sctx.shift_lo = 0.; 823 sctx.shift_hi = 0.; 824 sctx.shift_fraction = 0.; 825 826 /* if both shift schemes are chosen by user, only use info->shiftpd */ 827 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 828 sctx.shift_top = 0.; 829 for (i=0; i<n; i++) { 830 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 831 d = (a->a)[diag[i]]; 832 rs = -PetscAbsScalar(d) - PetscRealPart(d); 833 v = a->a+ai[i]; 834 nz = ai[i+1] - ai[i]; 835 for (j=0; j<nz; j++) 836 rs += PetscAbsScalar(v[j]); 837 if (rs>sctx.shift_top) sctx.shift_top = rs; 838 } 839 if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot; 840 sctx.shift_top *= 1.1; 841 sctx.nshift_max = 5; 842 sctx.shift_lo = 0.; 843 sctx.shift_hi = 1.; 844 } 845 846 sctx.shift_amount = 0.; 847 sctx.nshift = 0; 848 do { 849 sctx.lushift = PETSC_FALSE; 850 for (i=0; i<n; i++){ 851 /* load in initial unfactored row */ 852 nz = ai[r[i]+1] - ai[r[i]]; 853 ajtmp = aj + ai[r[i]]; 854 v = a->a + ai[r[i]]; 855 /* sort permuted ajtmp and values v accordingly */ 856 for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]]; 857 ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr); 858 859 diag[r[i]] = ai[r[i]]; 860 for (j=0; j<nz; j++) { 861 rtmp[ajtmp[j]] = v[j]; 862 if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */ 863 } 864 rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 865 866 row = *ajtmp++; 867 while (row < i) { 868 pc = rtmp + row; 869 if (*pc != 0.0) { 870 pv = a->a + diag[r[row]]; 871 pj = aj + diag[r[row]] + 1; 872 873 multiplier = *pc / *pv++; 874 *pc = multiplier; 875 nz = ai[r[row]+1] - diag[r[row]] - 1; 876 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 877 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 878 } 879 row = *ajtmp++; 880 } 881 /* finished row so overwrite it onto a->a */ 882 pv = a->a + ai[r[i]] ; 883 pj = aj + ai[r[i]] ; 884 nz = ai[r[i]+1] - ai[r[i]]; 885 nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */ 886 887 rs = 0.0; 888 for (j=0; j<nz; j++) { 889 pv[j] = rtmp[pj[j]]; 890 if (j != nbdiag) rs += PetscAbsScalar(pv[j]); 891 } 892 893 /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */ 894 sctx.rs = rs; 895 sctx.pv = pv[nbdiag]; 896 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 897 if (newshift == 1) break; 898 } 899 900 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 901 /* 902 * if no shift in this attempt & shifting & started shifting & can refine, 903 * then try lower shift 904 */ 905 sctx.shift_hi = sctx.shift_fraction; 906 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 907 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 908 sctx.lushift = PETSC_TRUE; 909 sctx.nshift++; 910 } 911 } while (sctx.lushift); 912 913 /* invert diagonal entries for simplier triangular solves */ 914 for (i=0; i<n; i++) { 915 a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]]; 916 } 917 918 ierr = PetscFree(rtmp);CHKERRQ(ierr); 919 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 920 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 921 A->ops->solve = MatSolve_SeqAIJ_InplaceWithPerm; 922 A->ops->solveadd = MatSolveAdd_SeqAIJ; 923 A->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 924 A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 925 A->assembled = PETSC_TRUE; 926 A->preallocated = PETSC_TRUE; 927 ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr); 928 if (sctx.nshift){ 929 if (info->shiftpd) { 930 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); 931 } else if (info->shiftnz) { 932 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 933 } 934 } 935 PetscFunctionReturn(0); 936 } 937 938 /* ----------------------------------------------------------- */ 939 #undef __FUNCT__ 940 #define __FUNCT__ "MatLUFactor_SeqAIJ" 941 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info) 942 { 943 PetscErrorCode ierr; 944 Mat C; 945 946 PetscFunctionBegin; 947 ierr = MatGetFactor(A,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr); 948 ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr); 949 ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr); 950 A->ops->solve = C->ops->solve; 951 A->ops->solvetranspose = C->ops->solvetranspose; 952 ierr = MatHeaderCopy(A,C);CHKERRQ(ierr); 953 ierr = PetscLogObjectParent(A,((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr); 954 PetscFunctionReturn(0); 955 } 956 /* ----------------------------------------------------------- */ 957 958 959 #undef __FUNCT__ 960 #define __FUNCT__ "MatSolve_SeqAIJ" 961 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx) 962 { 963 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 964 IS iscol = a->col,isrow = a->row; 965 PetscErrorCode ierr; 966 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 967 PetscInt nz; 968 const PetscInt *rout,*cout,*r,*c; 969 PetscScalar *x,*tmp,*tmps,sum; 970 const PetscScalar *b; 971 const MatScalar *aa = a->a,*v; 972 973 PetscFunctionBegin; 974 if (!n) PetscFunctionReturn(0); 975 976 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 977 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 978 tmp = a->solve_work; 979 980 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 981 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 982 983 /* forward solve the lower triangular */ 984 tmp[0] = b[*r++]; 985 tmps = tmp; 986 for (i=1; i<n; i++) { 987 v = aa + ai[i] ; 988 vi = aj + ai[i] ; 989 nz = a->diag[i] - ai[i]; 990 sum = b[*r++]; 991 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 992 tmp[i] = sum; 993 } 994 995 /* backward solve the upper triangular */ 996 for (i=n-1; i>=0; i--){ 997 v = aa + a->diag[i] + 1; 998 vi = aj + a->diag[i] + 1; 999 nz = ai[i+1] - a->diag[i] - 1; 1000 sum = tmp[i]; 1001 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1002 x[*c--] = tmp[i] = sum*aa[a->diag[i]]; 1003 } 1004 1005 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1006 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1007 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1008 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1009 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1010 PetscFunctionReturn(0); 1011 } 1012 1013 #undef __FUNCT__ 1014 #define __FUNCT__ "MatMatSolve_SeqAIJ" 1015 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X) 1016 { 1017 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1018 IS iscol = a->col,isrow = a->row; 1019 PetscErrorCode ierr; 1020 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1021 PetscInt nz,neq; 1022 const PetscInt *rout,*cout,*r,*c; 1023 PetscScalar *x,*b,*tmp,*tmps,sum; 1024 const MatScalar *aa = a->a,*v; 1025 PetscTruth bisdense,xisdense; 1026 1027 PetscFunctionBegin; 1028 if (!n) PetscFunctionReturn(0); 1029 1030 ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr); 1031 if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 1032 ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr); 1033 if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 1034 1035 ierr = MatGetArray(B,&b);CHKERRQ(ierr); 1036 ierr = MatGetArray(X,&x);CHKERRQ(ierr); 1037 1038 tmp = a->solve_work; 1039 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1040 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1041 1042 for (neq=0; neq<B->cmap->n; neq++){ 1043 /* forward solve the lower triangular */ 1044 tmp[0] = b[r[0]]; 1045 tmps = tmp; 1046 for (i=1; i<n; i++) { 1047 v = aa + ai[i] ; 1048 vi = aj + ai[i] ; 1049 nz = a->diag[i] - ai[i]; 1050 sum = b[r[i]]; 1051 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1052 tmp[i] = sum; 1053 } 1054 /* backward solve the upper triangular */ 1055 for (i=n-1; i>=0; i--){ 1056 v = aa + a->diag[i] + 1; 1057 vi = aj + a->diag[i] + 1; 1058 nz = ai[i+1] - a->diag[i] - 1; 1059 sum = tmp[i]; 1060 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1061 x[c[i]] = tmp[i] = sum*aa[a->diag[i]]; 1062 } 1063 1064 b += n; 1065 x += n; 1066 } 1067 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1068 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1069 ierr = MatRestoreArray(B,&b);CHKERRQ(ierr); 1070 ierr = MatRestoreArray(X,&x);CHKERRQ(ierr); 1071 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 1072 PetscFunctionReturn(0); 1073 } 1074 1075 #undef __FUNCT__ 1076 #define __FUNCT__ "MatSolve_SeqAIJ_InplaceWithPerm" 1077 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx) 1078 { 1079 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1080 IS iscol = a->col,isrow = a->row; 1081 PetscErrorCode ierr; 1082 const PetscInt *r,*c,*rout,*cout; 1083 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1084 PetscInt nz,row; 1085 PetscScalar *x,*b,*tmp,*tmps,sum; 1086 const MatScalar *aa = a->a,*v; 1087 1088 PetscFunctionBegin; 1089 if (!n) PetscFunctionReturn(0); 1090 1091 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1092 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1093 tmp = a->solve_work; 1094 1095 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1096 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1097 1098 /* forward solve the lower triangular */ 1099 tmp[0] = b[*r++]; 1100 tmps = tmp; 1101 for (row=1; row<n; row++) { 1102 i = rout[row]; /* permuted row */ 1103 v = aa + ai[i] ; 1104 vi = aj + ai[i] ; 1105 nz = a->diag[i] - ai[i]; 1106 sum = b[*r++]; 1107 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1108 tmp[row] = sum; 1109 } 1110 1111 /* backward solve the upper triangular */ 1112 for (row=n-1; row>=0; row--){ 1113 i = rout[row]; /* permuted row */ 1114 v = aa + a->diag[i] + 1; 1115 vi = aj + a->diag[i] + 1; 1116 nz = ai[i+1] - a->diag[i] - 1; 1117 sum = tmp[row]; 1118 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1119 x[*c--] = tmp[row] = sum*aa[a->diag[i]]; 1120 } 1121 1122 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1123 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1124 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1125 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1126 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1127 PetscFunctionReturn(0); 1128 } 1129 1130 /* ----------------------------------------------------------- */ 1131 #include "../src/mat/impls/aij/seq/ftn-kernels/fsolve.h" 1132 #undef __FUNCT__ 1133 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering" 1134 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx) 1135 { 1136 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1137 PetscErrorCode ierr; 1138 PetscInt n = A->rmap->n; 1139 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag; 1140 PetscScalar *x; 1141 const PetscScalar *b; 1142 const MatScalar *aa = a->a; 1143 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1144 PetscInt adiag_i,i,nz,ai_i; 1145 const PetscInt *vi; 1146 const MatScalar *v; 1147 PetscScalar sum; 1148 #endif 1149 1150 PetscFunctionBegin; 1151 if (!n) PetscFunctionReturn(0); 1152 1153 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1154 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1155 1156 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1157 fortransolveaij_(&n,x,ai,aj,adiag,aa,b); 1158 #else 1159 /* forward solve the lower triangular */ 1160 x[0] = b[0]; 1161 for (i=1; i<n; i++) { 1162 ai_i = ai[i]; 1163 v = aa + ai_i; 1164 vi = aj + ai_i; 1165 nz = adiag[i] - ai_i; 1166 sum = b[i]; 1167 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1168 x[i] = sum; 1169 } 1170 1171 /* backward solve the upper triangular */ 1172 for (i=n-1; i>=0; i--){ 1173 adiag_i = adiag[i]; 1174 v = aa + adiag_i + 1; 1175 vi = aj + adiag_i + 1; 1176 nz = ai[i+1] - adiag_i - 1; 1177 sum = x[i]; 1178 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1179 x[i] = sum*aa[adiag_i]; 1180 } 1181 #endif 1182 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1183 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1184 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1185 PetscFunctionReturn(0); 1186 } 1187 1188 #undef __FUNCT__ 1189 #define __FUNCT__ "MatSolveAdd_SeqAIJ" 1190 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx) 1191 { 1192 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1193 IS iscol = a->col,isrow = a->row; 1194 PetscErrorCode ierr; 1195 PetscInt i, n = A->rmap->n,j; 1196 PetscInt nz; 1197 const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j; 1198 PetscScalar *x,*tmp,sum; 1199 const PetscScalar *b; 1200 const MatScalar *aa = a->a,*v; 1201 1202 PetscFunctionBegin; 1203 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 1204 1205 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1206 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1207 tmp = a->solve_work; 1208 1209 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1210 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1211 1212 /* forward solve the lower triangular */ 1213 tmp[0] = b[*r++]; 1214 for (i=1; i<n; i++) { 1215 v = aa + ai[i] ; 1216 vi = aj + ai[i] ; 1217 nz = a->diag[i] - ai[i]; 1218 sum = b[*r++]; 1219 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1220 tmp[i] = sum; 1221 } 1222 1223 /* backward solve the upper triangular */ 1224 for (i=n-1; i>=0; i--){ 1225 v = aa + a->diag[i] + 1; 1226 vi = aj + a->diag[i] + 1; 1227 nz = ai[i+1] - a->diag[i] - 1; 1228 sum = tmp[i]; 1229 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1230 tmp[i] = sum*aa[a->diag[i]]; 1231 x[*c--] += tmp[i]; 1232 } 1233 1234 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1235 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1236 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1237 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1238 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1239 1240 PetscFunctionReturn(0); 1241 } 1242 1243 #undef __FUNCT__ 1244 #define __FUNCT__ "MatSolveAdd_SeqAIJ_newdatastruct" 1245 PetscErrorCode MatSolveAdd_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec yy,Vec xx) 1246 { 1247 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1248 IS iscol = a->col,isrow = a->row; 1249 PetscErrorCode ierr; 1250 PetscInt i, n = A->rmap->n,j; 1251 PetscInt nz; 1252 const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag; 1253 PetscScalar *x,*tmp,sum; 1254 const PetscScalar *b; 1255 const MatScalar *aa = a->a,*v; 1256 1257 PetscFunctionBegin; 1258 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 1259 1260 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1261 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1262 tmp = a->solve_work; 1263 1264 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1265 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1266 1267 /* forward solve the lower triangular */ 1268 tmp[0] = b[r[0]]; 1269 v = aa; 1270 vi = aj; 1271 for (i=1; i<n; i++) { 1272 nz = ai[i+1] - ai[i]; 1273 sum = b[r[i]]; 1274 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1275 tmp[i] = sum; 1276 v += nz; vi += nz; 1277 } 1278 1279 /* backward solve the upper triangular */ 1280 v = aa + adiag[n-1]; 1281 vi = aj + adiag[n-1]; 1282 for (i=n-1; i>=0; i--){ 1283 nz = adiag[i] - adiag[i+1] - 1; 1284 sum = tmp[i]; 1285 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1286 tmp[i] = sum*v[nz]; 1287 x[c[i]] += tmp[i]; 1288 v += nz+1; vi += nz+1; 1289 } 1290 1291 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1292 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1293 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1294 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1295 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1296 1297 PetscFunctionReturn(0); 1298 } 1299 1300 #undef __FUNCT__ 1301 #define __FUNCT__ "MatSolveTranspose_SeqAIJ" 1302 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx) 1303 { 1304 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1305 IS iscol = a->col,isrow = a->row; 1306 PetscErrorCode ierr; 1307 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1308 PetscInt i,n = A->rmap->n,j; 1309 PetscInt nz; 1310 PetscScalar *x,*tmp,s1; 1311 const MatScalar *aa = a->a,*v; 1312 const PetscScalar *b; 1313 1314 PetscFunctionBegin; 1315 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1316 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1317 tmp = a->solve_work; 1318 1319 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1320 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1321 1322 /* copy the b into temp work space according to permutation */ 1323 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1324 1325 /* forward solve the U^T */ 1326 for (i=0; i<n; i++) { 1327 v = aa + diag[i] ; 1328 vi = aj + diag[i] + 1; 1329 nz = ai[i+1] - diag[i] - 1; 1330 s1 = tmp[i]; 1331 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1332 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1333 tmp[i] = s1; 1334 } 1335 1336 /* backward solve the L^T */ 1337 for (i=n-1; i>=0; i--){ 1338 v = aa + diag[i] - 1 ; 1339 vi = aj + diag[i] - 1 ; 1340 nz = diag[i] - ai[i]; 1341 s1 = tmp[i]; 1342 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1343 } 1344 1345 /* copy tmp into x according to permutation */ 1346 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1347 1348 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1349 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1350 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1351 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1352 1353 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1354 PetscFunctionReturn(0); 1355 } 1356 1357 #undef __FUNCT__ 1358 #define __FUNCT__ "MatSolveTranspose_SeqAIJ_newdatastruct" 1359 PetscErrorCode MatSolveTranspose_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx) 1360 { 1361 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1362 IS iscol = a->col,isrow = a->row; 1363 PetscErrorCode ierr; 1364 const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi; 1365 PetscInt i,n = A->rmap->n,j; 1366 PetscInt nz; 1367 PetscScalar *x,*tmp,s1; 1368 const MatScalar *aa = a->a,*v; 1369 const PetscScalar *b; 1370 1371 PetscFunctionBegin; 1372 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1373 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1374 tmp = a->solve_work; 1375 1376 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1377 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1378 1379 /* copy the b into temp work space according to permutation */ 1380 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1381 1382 /* forward solve the U^T */ 1383 for (i=0; i<n; i++) { 1384 v = aa + adiag[i+1] + 1; 1385 vi = aj + adiag[i+1] + 1; 1386 nz = adiag[i] - adiag[i+1] - 1; 1387 s1 = tmp[i]; 1388 s1 *= v[nz]; /* multiply by inverse of diagonal entry */ 1389 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1390 tmp[i] = s1; 1391 } 1392 1393 /* backward solve the L^T */ 1394 for (i=n-1; i>=0; i--){ 1395 v = aa + ai[i]; 1396 vi = aj + ai[i]; 1397 nz = ai[i+1] - ai[i]; 1398 s1 = tmp[i]; 1399 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1400 } 1401 1402 /* copy tmp into x according to permutation */ 1403 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1404 1405 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1406 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1407 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1408 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1409 1410 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1411 PetscFunctionReturn(0); 1412 } 1413 1414 #undef __FUNCT__ 1415 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ" 1416 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx) 1417 { 1418 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1419 IS iscol = a->col,isrow = a->row; 1420 PetscErrorCode ierr; 1421 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1422 PetscInt i,n = A->rmap->n,j; 1423 PetscInt nz; 1424 PetscScalar *x,*tmp,s1; 1425 const MatScalar *aa = a->a,*v; 1426 const PetscScalar *b; 1427 1428 PetscFunctionBegin; 1429 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1430 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1431 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1432 tmp = a->solve_work; 1433 1434 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1435 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1436 1437 /* copy the b into temp work space according to permutation */ 1438 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1439 1440 /* forward solve the U^T */ 1441 for (i=0; i<n; i++) { 1442 v = aa + diag[i] ; 1443 vi = aj + diag[i] + 1; 1444 nz = ai[i+1] - diag[i] - 1; 1445 s1 = tmp[i]; 1446 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1447 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1448 tmp[i] = s1; 1449 } 1450 1451 /* backward solve the L^T */ 1452 for (i=n-1; i>=0; i--){ 1453 v = aa + diag[i] - 1 ; 1454 vi = aj + diag[i] - 1 ; 1455 nz = diag[i] - ai[i]; 1456 s1 = tmp[i]; 1457 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1458 } 1459 1460 /* copy tmp into x according to permutation */ 1461 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1462 1463 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1464 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1465 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1466 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1467 1468 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1469 PetscFunctionReturn(0); 1470 } 1471 1472 #undef __FUNCT__ 1473 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ_newdatastruct" 1474 PetscErrorCode MatSolveTransposeAdd_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec zz,Vec xx) 1475 { 1476 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1477 IS iscol = a->col,isrow = a->row; 1478 PetscErrorCode ierr; 1479 const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi; 1480 PetscInt i,n = A->rmap->n,j; 1481 PetscInt nz; 1482 PetscScalar *x,*tmp,s1; 1483 const MatScalar *aa = a->a,*v; 1484 const PetscScalar *b; 1485 1486 PetscFunctionBegin; 1487 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1488 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1489 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1490 tmp = a->solve_work; 1491 1492 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1493 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1494 1495 /* copy the b into temp work space according to permutation */ 1496 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1497 1498 /* forward solve the U^T */ 1499 for (i=0; i<n; i++) { 1500 v = aa + adiag[i+1] + 1; 1501 vi = aj + adiag[i+1] + 1; 1502 nz = adiag[i] - adiag[i+1] - 1; 1503 s1 = tmp[i]; 1504 s1 *= v[nz]; /* multiply by inverse of diagonal entry */ 1505 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1506 tmp[i] = s1; 1507 } 1508 1509 1510 /* backward solve the L^T */ 1511 for (i=n-1; i>=0; i--){ 1512 v = aa + ai[i] ; 1513 vi = aj + ai[i]; 1514 nz = ai[i+1] - ai[i]; 1515 s1 = tmp[i]; 1516 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1517 } 1518 1519 /* copy tmp into x according to permutation */ 1520 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1521 1522 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1523 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1524 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1525 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1526 1527 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1528 PetscFunctionReturn(0); 1529 } 1530 1531 /* ----------------------------------------------------------------*/ 1532 EXTERN PetscErrorCode Mat_CheckInode(Mat,PetscTruth); 1533 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth); 1534 1535 /* 1536 ilu() under revised new data structure. 1537 Factored arrays bj and ba are stored as 1538 L(0,:), L(1,:), ...,L(n-1,:), U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:) 1539 1540 bi=fact->i is an array of size n+1, in which 1541 bi+ 1542 bi[i]: points to 1st entry of L(i,:),i=0,...,n-1 1543 bi[n]: points to L(n-1,n-1)+1 1544 1545 bdiag=fact->diag is an array of size n+1,in which 1546 bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1 1547 bdiag[n]: points to entry of U(n-1,0)-1 1548 1549 U(i,:) contains bdiag[i] as its last entry, i.e., 1550 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 1551 */ 1552 #undef __FUNCT__ 1553 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct" 1554 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1555 { 1556 1557 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1558 PetscErrorCode ierr; 1559 PetscInt n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag; 1560 PetscInt i,j,nz,*bi,*bj,*bdiag; 1561 PetscTruth missing; 1562 IS isicol; 1563 1564 PetscFunctionBegin; 1565 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 1566 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 1567 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 1568 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1569 1570 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr); 1571 b = (Mat_SeqAIJ*)(fact)->data; 1572 1573 /* allocate matrix arrays for new data structure */ 1574 ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,n+1,PetscInt,&b->i);CHKERRQ(ierr); 1575 ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1576 b->singlemalloc = PETSC_TRUE; 1577 if (!b->diag){ 1578 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr); 1579 ierr = PetscLogObjectMemory(fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1580 } 1581 bdiag = b->diag; 1582 1583 if (n > 0) { 1584 ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr); 1585 } 1586 1587 /* set bi and bj with new data structure */ 1588 bi = b->i; 1589 bj = b->j; 1590 1591 /* L part */ 1592 bi[0] = 0.; 1593 for (i=0; i<n; i++){ 1594 nz = adiag[i] - ai[i]; 1595 bi[i+1] = bi[i] + nz; 1596 aj = a->j + ai[i]; 1597 for (j=0; j<nz; j++){ 1598 *bj = aj[j]; bj++; 1599 } 1600 } 1601 1602 /* U part */ 1603 bdiag[n] = bi[n]-1; 1604 for (i=n-1; i>=0; i--){ 1605 nz = ai[i+1] - adiag[i] - 1; 1606 aj = a->j + adiag[i] + 1; 1607 for (j=0; j<nz; j++){ 1608 *bj = aj[j]; bj++; 1609 } 1610 /* diag[i] */ 1611 *bj = i; bj++; 1612 bdiag[i] = bdiag[i+1] + nz + 1; 1613 } 1614 1615 fact->factor = MAT_FACTOR_ILU; 1616 fact->info.factor_mallocs = 0; 1617 fact->info.fill_ratio_given = info->fill; 1618 fact->info.fill_ratio_needed = 1.0; 1619 fact->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 1620 1621 b = (Mat_SeqAIJ*)(fact)->data; 1622 b->row = isrow; 1623 b->col = iscol; 1624 b->icol = isicol; 1625 ierr = PetscMalloc((fact->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1626 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1627 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1628 PetscFunctionReturn(0); 1629 } 1630 1631 #undef __FUNCT__ 1632 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_newdatastruct" 1633 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1634 { 1635 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1636 IS isicol; 1637 PetscErrorCode ierr; 1638 const PetscInt *r,*ic; 1639 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j; 1640 PetscInt *bi,*cols,nnz,*cols_lvl; 1641 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1642 PetscInt i,levels,diagonal_fill; 1643 PetscTruth col_identity,row_identity; 1644 PetscReal f; 1645 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1646 PetscBT lnkbt; 1647 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1648 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1649 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1650 1651 PetscFunctionBegin; 1652 /* printf("MatILUFactorSymbolic_SeqAIJ_newdatastruct ...\n"); */ 1653 levels = (PetscInt)info->levels; 1654 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1655 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1656 1657 if (!levels && row_identity && col_identity) { 1658 /* special case: ilu(0) with natural ordering */ 1659 ierr = MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1660 PetscFunctionReturn(0); 1661 } 1662 1663 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 1664 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1665 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1666 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1667 1668 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1669 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1670 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1671 bi[0] = bdiag[0] = 0.; 1672 1673 ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr); 1674 1675 /* create a linked list for storing column indices of the active row */ 1676 nlnk = n + 1; 1677 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1678 1679 /* initial FreeSpace size is f*(ai[n]+1) */ 1680 f = info->fill; 1681 diagonal_fill = (PetscInt)info->diagonal_fill; 1682 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1683 current_space = free_space; 1684 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1685 current_space_lvl = free_space_lvl; 1686 1687 for (i=0; i<n; i++) { 1688 nzi = 0; 1689 /* copy current row into linked list */ 1690 nnz = ai[r[i]+1] - ai[r[i]]; 1691 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1692 cols = aj + ai[r[i]]; 1693 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1694 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1695 nzi += nlnk; 1696 1697 /* make sure diagonal entry is included */ 1698 if (diagonal_fill && lnk[i] == -1) { 1699 fm = n; 1700 while (lnk[fm] < i) fm = lnk[fm]; 1701 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1702 lnk[fm] = i; 1703 lnk_lvl[i] = 0; 1704 nzi++; dcount++; 1705 } 1706 1707 /* add pivot rows into the active row */ 1708 nzbd = 0; 1709 prow = lnk[n]; 1710 while (prow < i) { 1711 nnz = bdiag[prow]; 1712 cols = bj_ptr[prow] + nnz + 1; 1713 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1714 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1715 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1716 nzi += nlnk; 1717 prow = lnk[prow]; 1718 nzbd++; 1719 } 1720 bdiag[i] = nzbd; 1721 bi[i+1] = bi[i] + nzi; 1722 1723 /* if free space is not available, make more free space */ 1724 if (current_space->local_remaining<nzi) { 1725 nnz = 2*nzi*(n - i); /* estimated and max additional space needed */ 1726 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1727 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1728 reallocs++; 1729 } 1730 1731 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1732 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1733 bj_ptr[i] = current_space->array; 1734 bjlvl_ptr[i] = current_space_lvl->array; 1735 1736 /* make sure the active row i has diagonal entry */ 1737 if (*(bj_ptr[i]+bdiag[i]) != i) { 1738 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 1739 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1740 } 1741 1742 current_space->array += nzi; 1743 current_space->local_used += nzi; 1744 current_space->local_remaining -= nzi; 1745 current_space_lvl->array += nzi; 1746 current_space_lvl->local_used += nzi; 1747 current_space_lvl->local_remaining -= nzi; 1748 } 1749 1750 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1751 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1752 1753 /* destroy list of free space and other temporary arrays */ 1754 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 1755 1756 /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */ 1757 ierr = PetscFreeSpaceContiguous_LU_v2(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 1758 1759 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1760 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1761 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 1762 1763 #if defined(PETSC_USE_INFO) 1764 { 1765 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1766 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 1767 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1768 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 1769 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1770 if (diagonal_fill) { 1771 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 1772 } 1773 } 1774 #endif 1775 1776 /* put together the new matrix */ 1777 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 1778 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 1779 b = (Mat_SeqAIJ*)(fact)->data; 1780 b->free_a = PETSC_TRUE; 1781 b->free_ij = PETSC_TRUE; 1782 b->singlemalloc = PETSC_FALSE; 1783 ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 1784 b->j = bj; 1785 b->i = bi; 1786 b->diag = bdiag; 1787 b->ilen = 0; 1788 b->imax = 0; 1789 b->row = isrow; 1790 b->col = iscol; 1791 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1792 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1793 b->icol = isicol; 1794 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1795 /* In b structure: Free imax, ilen, old a, old j. 1796 Allocate bdiag, solve_work, new a, new j */ 1797 ierr = PetscLogObjectMemory(fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1798 b->maxnz = b->nz = bdiag[0]+1; 1799 (fact)->info.factor_mallocs = reallocs; 1800 (fact)->info.fill_ratio_given = f; 1801 (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 1802 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 1803 /* ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */ 1804 PetscFunctionReturn(0); 1805 } 1806 1807 #undef __FUNCT__ 1808 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ" 1809 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1810 { 1811 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1812 IS isicol; 1813 PetscErrorCode ierr; 1814 const PetscInt *r,*ic; 1815 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,d; 1816 PetscInt *bi,*cols,nnz,*cols_lvl; 1817 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1818 PetscInt i,levels,diagonal_fill; 1819 PetscTruth col_identity,row_identity; 1820 PetscReal f; 1821 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1822 PetscBT lnkbt; 1823 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1824 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1825 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1826 PetscTruth missing; 1827 PetscTruth newdatastruct=PETSC_FALSE; 1828 1829 PetscFunctionBegin; 1830 ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 1831 if(newdatastruct){ 1832 ierr = MatILUFactorSymbolic_SeqAIJ_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1833 PetscFunctionReturn(0); 1834 } 1835 1836 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 1837 f = info->fill; 1838 levels = (PetscInt)info->levels; 1839 diagonal_fill = (PetscInt)info->diagonal_fill; 1840 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1841 1842 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1843 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1844 if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */ 1845 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr); 1846 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1847 1848 fact->factor = MAT_FACTOR_ILU; 1849 (fact)->info.factor_mallocs = 0; 1850 (fact)->info.fill_ratio_given = info->fill; 1851 (fact)->info.fill_ratio_needed = 1.0; 1852 b = (Mat_SeqAIJ*)(fact)->data; 1853 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 1854 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 1855 b->row = isrow; 1856 b->col = iscol; 1857 b->icol = isicol; 1858 ierr = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1859 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1860 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1861 ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1862 PetscFunctionReturn(0); 1863 } 1864 1865 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1866 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1867 1868 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1869 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1870 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1871 bi[0] = bdiag[0] = 0; 1872 1873 ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr); 1874 1875 /* create a linked list for storing column indices of the active row */ 1876 nlnk = n + 1; 1877 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1878 1879 /* initial FreeSpace size is f*(ai[n]+1) */ 1880 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1881 current_space = free_space; 1882 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1883 current_space_lvl = free_space_lvl; 1884 1885 for (i=0; i<n; i++) { 1886 nzi = 0; 1887 /* copy current row into linked list */ 1888 nnz = ai[r[i]+1] - ai[r[i]]; 1889 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1890 cols = aj + ai[r[i]]; 1891 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1892 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1893 nzi += nlnk; 1894 1895 /* make sure diagonal entry is included */ 1896 if (diagonal_fill && lnk[i] == -1) { 1897 fm = n; 1898 while (lnk[fm] < i) fm = lnk[fm]; 1899 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1900 lnk[fm] = i; 1901 lnk_lvl[i] = 0; 1902 nzi++; dcount++; 1903 } 1904 1905 /* add pivot rows into the active row */ 1906 nzbd = 0; 1907 prow = lnk[n]; 1908 while (prow < i) { 1909 nnz = bdiag[prow]; 1910 cols = bj_ptr[prow] + nnz + 1; 1911 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1912 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1913 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1914 nzi += nlnk; 1915 prow = lnk[prow]; 1916 nzbd++; 1917 } 1918 bdiag[i] = nzbd; 1919 bi[i+1] = bi[i] + nzi; 1920 1921 /* if free space is not available, make more free space */ 1922 if (current_space->local_remaining<nzi) { 1923 nnz = nzi*(n - i); /* estimated and max additional space needed */ 1924 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1925 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1926 reallocs++; 1927 } 1928 1929 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1930 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1931 bj_ptr[i] = current_space->array; 1932 bjlvl_ptr[i] = current_space_lvl->array; 1933 1934 /* make sure the active row i has diagonal entry */ 1935 if (*(bj_ptr[i]+bdiag[i]) != i) { 1936 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 1937 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1938 } 1939 1940 current_space->array += nzi; 1941 current_space->local_used += nzi; 1942 current_space->local_remaining -= nzi; 1943 current_space_lvl->array += nzi; 1944 current_space_lvl->local_used += nzi; 1945 current_space_lvl->local_remaining -= nzi; 1946 } 1947 1948 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1949 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1950 1951 /* destroy list of free space and other temporary arrays */ 1952 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 1953 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */ 1954 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1955 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1956 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 1957 1958 #if defined(PETSC_USE_INFO) 1959 { 1960 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1961 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 1962 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1963 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 1964 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1965 if (diagonal_fill) { 1966 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 1967 } 1968 } 1969 #endif 1970 1971 /* put together the new matrix */ 1972 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 1973 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 1974 b = (Mat_SeqAIJ*)(fact)->data; 1975 b->free_a = PETSC_TRUE; 1976 b->free_ij = PETSC_TRUE; 1977 b->singlemalloc = PETSC_FALSE; 1978 ierr = PetscMalloc(bi[n]*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 1979 b->j = bj; 1980 b->i = bi; 1981 for (i=0; i<n; i++) bdiag[i] += bi[i]; 1982 b->diag = bdiag; 1983 b->ilen = 0; 1984 b->imax = 0; 1985 b->row = isrow; 1986 b->col = iscol; 1987 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1988 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1989 b->icol = isicol; 1990 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1991 /* In b structure: Free imax, ilen, old a, old j. 1992 Allocate bdiag, solve_work, new a, new j */ 1993 ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1994 b->maxnz = b->nz = bi[n] ; 1995 (fact)->info.factor_mallocs = reallocs; 1996 (fact)->info.fill_ratio_given = f; 1997 (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1998 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1999 ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); 2000 PetscFunctionReturn(0); 2001 } 2002 2003 #undef __FUNCT__ 2004 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ_newdatastruct" 2005 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info) 2006 { 2007 Mat C = B; 2008 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2009 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2010 IS ip=b->row,iip = b->icol; 2011 PetscErrorCode ierr; 2012 const PetscInt *rip,*riip; 2013 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp; 2014 PetscInt *ai=a->i,*aj=a->j; 2015 PetscInt k,jmin,jmax,*c2r,*il,col,nexti,ili,nz; 2016 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2017 PetscTruth perm_identity; 2018 2019 LUShift_Ctx sctx; 2020 PetscInt newshift; 2021 PetscReal rs; 2022 MatScalar d,*v; 2023 2024 PetscFunctionBegin; 2025 /* MatPivotSetUp(): initialize shift context sctx */ 2026 ierr = PetscMemzero(&sctx,sizeof(LUShift_Ctx));CHKERRQ(ierr); 2027 2028 /* if both shift schemes are chosen by user, only use info->shiftpd */ 2029 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 2030 sctx.shift_top = info->zeropivot; 2031 for (i=0; i<mbs; i++) { 2032 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 2033 d = (aa)[a->diag[i]]; 2034 rs = -PetscAbsScalar(d) - PetscRealPart(d); 2035 v = aa+ai[i]; 2036 nz = ai[i+1] - ai[i]; 2037 for (j=0; j<nz; j++) 2038 rs += PetscAbsScalar(v[j]); 2039 if (rs>sctx.shift_top) sctx.shift_top = rs; 2040 } 2041 sctx.shift_top *= 1.1; 2042 sctx.nshift_max = 5; 2043 sctx.shift_lo = 0.; 2044 sctx.shift_hi = 1.; 2045 } 2046 2047 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2048 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2049 2050 /* allocate working arrays 2051 c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col 2052 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 2053 */ 2054 ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&c2r);CHKERRQ(ierr); 2055 2056 do { 2057 sctx.lushift = PETSC_FALSE; 2058 2059 for (i=0; i<mbs; i++) c2r[i] = mbs; 2060 il[0] = 0; 2061 2062 for (k = 0; k<mbs; k++){ 2063 /* zero rtmp */ 2064 nz = bi[k+1] - bi[k]; 2065 bjtmp = bj + bi[k]; 2066 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2067 2068 /* load in initial unfactored row */ 2069 bval = ba + bi[k]; 2070 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2071 for (j = jmin; j < jmax; j++){ 2072 col = riip[aj[j]]; 2073 if (col >= k){ /* only take upper triangular entry */ 2074 rtmp[col] = aa[j]; 2075 *bval++ = 0.0; /* for in-place factorization */ 2076 } 2077 } 2078 /* shift the diagonal of the matrix: ZeropivotApply() */ 2079 rtmp[k] += sctx.shift_amount; /* shift the diagonal of the matrix */ 2080 2081 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2082 dk = rtmp[k]; 2083 i = c2r[k]; /* first row to be added to k_th row */ 2084 2085 while (i < k){ 2086 nexti = c2r[i]; /* next row to be added to k_th row */ 2087 2088 /* compute multiplier, update diag(k) and U(i,k) */ 2089 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2090 uikdi = - ba[ili]*ba[bdiag[i]]; /* diagonal(k) */ 2091 dk += uikdi*ba[ili]; /* update diag[k] */ 2092 ba[ili] = uikdi; /* -U(i,k) */ 2093 2094 /* add multiple of row i to k-th row */ 2095 jmin = ili + 1; jmax = bi[i+1]; 2096 if (jmin < jmax){ 2097 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2098 /* update il and c2r for row i */ 2099 il[i] = jmin; 2100 j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i; 2101 } 2102 i = nexti; 2103 } 2104 2105 /* copy data into U(k,:) */ 2106 rs = 0.0; 2107 jmin = bi[k]; jmax = bi[k+1]-1; 2108 if (jmin < jmax) { 2109 for (j=jmin; j<jmax; j++){ 2110 col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]); 2111 } 2112 /* add the k-th row into il and c2r */ 2113 il[k] = jmin; 2114 i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k; 2115 } 2116 2117 /* MatPivotCheck() */ 2118 sctx.rs = rs; 2119 sctx.pv = dk; 2120 if (info->shiftnz){ 2121 ierr = MatPivotCheck_nz(info,sctx,k,newshift);CHKERRQ(ierr); 2122 } else if (info->shiftpd){ 2123 ierr = MatPivotCheck_pd(info,sctx,k,newshift);CHKERRQ(ierr); 2124 } else if (info->shiftinblocks){ 2125 ierr = MatPivotCheck_inblocks(info,sctx,k,newshift);CHKERRQ(ierr); 2126 } else { 2127 ierr = MatPivotCheck_none(info,sctx,k,newshift);CHKERRQ(ierr); 2128 } 2129 dk = sctx.pv; 2130 if (newshift == 1) break; 2131 2132 ba[bdiag[k]] = 1.0/dk; /* U(k,k) */ 2133 } 2134 } while (sctx.lushift); 2135 2136 ierr = PetscFree3(rtmp,il,c2r);CHKERRQ(ierr); 2137 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2138 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2139 2140 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2141 if (perm_identity){ 2142 (B)->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_newdatastruct; 2143 (B)->ops->solvetranspose = 0; 2144 (B)->ops->forwardsolve = 0; 2145 (B)->ops->backwardsolve = 0; 2146 } else { 2147 (B)->ops->solve = MatSolve_SeqSBAIJ_1_newdatastruct; 2148 (B)->ops->solvetranspose = 0; 2149 (B)->ops->forwardsolve = 0; 2150 (B)->ops->backwardsolve = 0; 2151 } 2152 2153 C->assembled = PETSC_TRUE; 2154 C->preallocated = PETSC_TRUE; 2155 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2156 2157 /* MatPivotView() */ 2158 if (sctx.nshift){ 2159 if (info->shiftpd) { 2160 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); 2161 } else if (info->shiftnz) { 2162 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2163 } else if (info->shiftinblocks){ 2164 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftinblocks);CHKERRQ(ierr); 2165 } 2166 } 2167 PetscFunctionReturn(0); 2168 } 2169 2170 #undef __FUNCT__ 2171 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ" 2172 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 2173 { 2174 Mat C = B; 2175 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2176 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2177 IS ip=b->row,iip = b->icol; 2178 PetscErrorCode ierr; 2179 const PetscInt *rip,*riip; 2180 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol,*bjtmp; 2181 PetscInt *ai=a->i,*aj=a->j; 2182 PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz; 2183 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2184 PetscReal zeropivot,rs,shiftnz; 2185 PetscReal shiftpd; 2186 ChShift_Ctx sctx; 2187 PetscInt newshift; 2188 PetscTruth perm_identity; 2189 2190 PetscFunctionBegin; 2191 shiftnz = info->shiftnz; 2192 shiftpd = info->shiftpd; 2193 zeropivot = info->zeropivot; 2194 2195 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2196 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2197 2198 /* initialization */ 2199 ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr); 2200 sctx.shift_amount = 0; 2201 sctx.nshift = 0; 2202 do { 2203 sctx.chshift = PETSC_FALSE; 2204 for (i=0; i<mbs; i++) jl[i] = mbs; 2205 il[0] = 0; 2206 2207 for (k = 0; k<mbs; k++){ 2208 /* zero rtmp */ 2209 nz = bi[k+1] - bi[k]; 2210 bjtmp = bj + bi[k]; 2211 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2212 2213 bval = ba + bi[k]; 2214 /* initialize k-th row by the perm[k]-th row of A */ 2215 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2216 for (j = jmin; j < jmax; j++){ 2217 col = riip[aj[j]]; 2218 if (col >= k){ /* only take upper triangular entry */ 2219 rtmp[col] = aa[j]; 2220 *bval++ = 0.0; /* for in-place factorization */ 2221 } 2222 } 2223 /* shift the diagonal of the matrix */ 2224 if (sctx.nshift) rtmp[k] += sctx.shift_amount; 2225 2226 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2227 dk = rtmp[k]; 2228 i = jl[k]; /* first row to be added to k_th row */ 2229 2230 while (i < k){ 2231 nexti = jl[i]; /* next row to be added to k_th row */ 2232 2233 /* compute multiplier, update diag(k) and U(i,k) */ 2234 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2235 uikdi = - ba[ili]*ba[bi[i]]; /* diagonal(k) */ 2236 dk += uikdi*ba[ili]; 2237 ba[ili] = uikdi; /* -U(i,k) */ 2238 2239 /* add multiple of row i to k-th row */ 2240 jmin = ili + 1; jmax = bi[i+1]; 2241 if (jmin < jmax){ 2242 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2243 /* update il and jl for row i */ 2244 il[i] = jmin; 2245 j = bj[jmin]; jl[i] = jl[j]; jl[j] = i; 2246 } 2247 i = nexti; 2248 } 2249 2250 /* shift the diagonals when zero pivot is detected */ 2251 /* compute rs=sum of abs(off-diagonal) */ 2252 rs = 0.0; 2253 jmin = bi[k]+1; 2254 nz = bi[k+1] - jmin; 2255 bcol = bj + jmin; 2256 for (j=0; j<nz; j++) { 2257 rs += PetscAbsScalar(rtmp[bcol[j]]); 2258 } 2259 2260 sctx.rs = rs; 2261 sctx.pv = dk; 2262 ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr); 2263 2264 if (newshift == 1) { 2265 if (!sctx.shift_amount) { 2266 sctx.shift_amount = 1e-5; 2267 } 2268 break; 2269 } 2270 2271 /* copy data into U(k,:) */ 2272 ba[bi[k]] = 1.0/dk; /* U(k,k) */ 2273 jmin = bi[k]+1; jmax = bi[k+1]; 2274 if (jmin < jmax) { 2275 for (j=jmin; j<jmax; j++){ 2276 col = bj[j]; ba[j] = rtmp[col]; 2277 } 2278 /* add the k-th row into il and jl */ 2279 il[k] = jmin; 2280 i = bj[jmin]; jl[k] = jl[i]; jl[i] = k; 2281 } 2282 } 2283 } while (sctx.chshift); 2284 ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr); 2285 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2286 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2287 2288 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2289 if (perm_identity){ 2290 (B)->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2291 (B)->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2292 (B)->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering; 2293 (B)->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering; 2294 } else { 2295 (B)->ops->solve = MatSolve_SeqSBAIJ_1; 2296 (B)->ops->solvetranspose = MatSolve_SeqSBAIJ_1; 2297 (B)->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1; 2298 (B)->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1; 2299 } 2300 2301 C->assembled = PETSC_TRUE; 2302 C->preallocated = PETSC_TRUE; 2303 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2304 if (sctx.nshift){ 2305 if (shiftnz) { 2306 ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2307 } else if (shiftpd) { 2308 ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2309 } 2310 } 2311 PetscFunctionReturn(0); 2312 } 2313 2314 /* 2315 icc() under revised new data structure. 2316 Factored arrays bj and ba are stored as 2317 U(0,:),...,U(i,:),U(n-1,:) 2318 2319 ui=fact->i is an array of size n+1, in which 2320 ui+ 2321 ui[i]: points to 1st entry of U(i,:),i=0,...,n-1 2322 ui[n]: points to U(n-1,n-1)+1 2323 2324 udiag=fact->diag is an array of size n,in which 2325 udiag[i]: points to diagonal of U(i,:), i=0,...,n-1 2326 2327 U(i,:) contains udiag[i] as its last entry, i.e., 2328 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 2329 */ 2330 2331 #undef __FUNCT__ 2332 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ_newdatastruct" 2333 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2334 { 2335 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2336 Mat_SeqSBAIJ *b; 2337 PetscErrorCode ierr; 2338 PetscTruth perm_identity,missing; 2339 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2340 const PetscInt *rip,*riip; 2341 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2342 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2343 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2344 PetscReal fill=info->fill,levels=info->levels; 2345 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2346 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2347 PetscBT lnkbt; 2348 IS iperm; 2349 2350 PetscFunctionBegin; 2351 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 2352 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2353 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2354 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2355 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2356 2357 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2358 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2359 ui[0] = 0; 2360 2361 /* ICC(0) without matrix ordering: simply rearrange column indices */ 2362 if (!levels && perm_identity) { 2363 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2364 cols = uj; 2365 for (i=0; i<am; i++) { 2366 ncols = ai[i+1] - a->diag[i]; 2367 ui[i+1] = ui[i] + ncols; 2368 udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */ 2369 2370 aj = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */ 2371 ncols--; /* exclude diagonal */ 2372 for (j=0; j<ncols; j++) *cols++ = aj[j]; 2373 *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */ 2374 } 2375 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2376 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2377 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2378 2379 /* initialization */ 2380 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2381 2382 /* jl: linked list for storing indices of the pivot rows 2383 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2384 ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr); 2385 for (i=0; i<am; i++){ 2386 jl[i] = am; il[i] = 0; 2387 } 2388 2389 /* create and initialize a linked list for storing column indices of the active row k */ 2390 nlnk = am + 1; 2391 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2392 2393 /* initial FreeSpace size is fill*(ai[am]+1) */ 2394 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2395 current_space = free_space; 2396 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2397 current_space_lvl = free_space_lvl; 2398 2399 for (k=0; k<am; k++){ /* for each active row k */ 2400 /* initialize lnk by the column indices of row rip[k] of A */ 2401 nzk = 0; 2402 ncols = ai[rip[k]+1] - ai[rip[k]]; 2403 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2404 ncols_upper = 0; 2405 for (j=0; j<ncols; j++){ 2406 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2407 if (riip[i] >= k){ /* only take upper triangular entry */ 2408 ajtmp[ncols_upper] = i; 2409 ncols_upper++; 2410 } 2411 } 2412 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2413 nzk += nlnk; 2414 2415 /* update lnk by computing fill-in for each pivot row to be merged in */ 2416 prow = jl[k]; /* 1st pivot row */ 2417 2418 while (prow < k){ 2419 nextprow = jl[prow]; 2420 2421 /* merge prow into k-th row */ 2422 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2423 jmax = ui[prow+1]; 2424 ncols = jmax-jmin; 2425 i = jmin - ui[prow]; 2426 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2427 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2428 j = *(uj - 1); 2429 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2430 nzk += nlnk; 2431 2432 /* update il and jl for prow */ 2433 if (jmin < jmax){ 2434 il[prow] = jmin; 2435 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2436 } 2437 prow = nextprow; 2438 } 2439 2440 /* if free space is not available, make more free space */ 2441 if (current_space->local_remaining<nzk) { 2442 i = am - k + 1; /* num of unfactored rows */ 2443 i *= PetscMin(nzk, i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2444 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2445 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2446 reallocs++; 2447 } 2448 2449 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2450 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2451 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2452 2453 /* add the k-th row into il and jl */ 2454 if (nzk > 1){ 2455 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2456 jl[k] = jl[i]; jl[i] = k; 2457 il[k] = ui[k] + 1; 2458 } 2459 uj_ptr[k] = current_space->array; 2460 uj_lvl_ptr[k] = current_space_lvl->array; 2461 2462 current_space->array += nzk; 2463 current_space->local_used += nzk; 2464 current_space->local_remaining -= nzk; 2465 2466 current_space_lvl->array += nzk; 2467 current_space_lvl->local_used += nzk; 2468 current_space_lvl->local_remaining -= nzk; 2469 2470 ui[k+1] = ui[k] + nzk; 2471 } 2472 2473 #if defined(PETSC_USE_INFO) 2474 if (ai[am] != 0) { 2475 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2476 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2477 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2478 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2479 } else { 2480 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2481 } 2482 #endif 2483 2484 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2485 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2486 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2487 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2488 2489 /* destroy list of free space and other temporary array(s) */ 2490 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2491 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor in newdatastruct */ 2492 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2493 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2494 2495 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2496 2497 /* put together the new matrix in MATSEQSBAIJ format */ 2498 2499 b = (Mat_SeqSBAIJ*)(fact)->data; 2500 b->singlemalloc = PETSC_FALSE; 2501 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2502 b->j = uj; 2503 b->i = ui; 2504 b->diag = udiag; 2505 b->free_diag = PETSC_TRUE; 2506 b->ilen = 0; 2507 b->imax = 0; 2508 b->row = perm; 2509 b->col = perm; 2510 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2511 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2512 b->icol = iperm; 2513 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2514 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2515 ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2516 b->maxnz = b->nz = ui[am]; 2517 b->free_a = PETSC_TRUE; 2518 b->free_ij = PETSC_TRUE; 2519 2520 (fact)->info.factor_mallocs = reallocs; 2521 (fact)->info.fill_ratio_given = fill; 2522 if (ai[am] != 0) { 2523 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2524 } else { 2525 (fact)->info.fill_ratio_needed = 0.0; 2526 } 2527 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct; 2528 PetscFunctionReturn(0); 2529 } 2530 2531 #undef __FUNCT__ 2532 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ" 2533 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2534 { 2535 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2536 Mat_SeqSBAIJ *b; 2537 PetscErrorCode ierr; 2538 PetscTruth perm_identity,missing; 2539 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2540 const PetscInt *rip,*riip; 2541 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2542 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2543 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2544 PetscReal fill=info->fill,levels=info->levels; 2545 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2546 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2547 PetscBT lnkbt; 2548 IS iperm; 2549 PetscTruth newdatastruct=PETSC_FALSE; 2550 2551 PetscFunctionBegin; 2552 ierr = PetscOptionsGetTruth(PETSC_NULL,"-icc_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 2553 if(newdatastruct){ 2554 ierr = MatICCFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr); 2555 PetscFunctionReturn(0); 2556 } 2557 2558 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 2559 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2560 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2561 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2562 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2563 2564 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2565 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2566 ui[0] = 0; 2567 2568 /* ICC(0) without matrix ordering: simply copies fill pattern */ 2569 if (!levels && perm_identity) { 2570 2571 for (i=0; i<am; i++) { 2572 ui[i+1] = ui[i] + ai[i+1] - a->diag[i]; 2573 udiag[i] = ui[i]; 2574 } 2575 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2576 cols = uj; 2577 for (i=0; i<am; i++) { 2578 aj = a->j + a->diag[i]; 2579 ncols = ui[i+1] - ui[i]; 2580 for (j=0; j<ncols; j++) *cols++ = *aj++; 2581 } 2582 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2583 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2584 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2585 2586 /* initialization */ 2587 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2588 2589 /* jl: linked list for storing indices of the pivot rows 2590 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2591 ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr); 2592 for (i=0; i<am; i++){ 2593 jl[i] = am; il[i] = 0; 2594 } 2595 2596 /* create and initialize a linked list for storing column indices of the active row k */ 2597 nlnk = am + 1; 2598 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2599 2600 /* initial FreeSpace size is fill*(ai[am]+1) */ 2601 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2602 current_space = free_space; 2603 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2604 current_space_lvl = free_space_lvl; 2605 2606 for (k=0; k<am; k++){ /* for each active row k */ 2607 /* initialize lnk by the column indices of row rip[k] of A */ 2608 nzk = 0; 2609 ncols = ai[rip[k]+1] - ai[rip[k]]; 2610 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2611 ncols_upper = 0; 2612 for (j=0; j<ncols; j++){ 2613 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2614 if (riip[i] >= k){ /* only take upper triangular entry */ 2615 ajtmp[ncols_upper] = i; 2616 ncols_upper++; 2617 } 2618 } 2619 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2620 nzk += nlnk; 2621 2622 /* update lnk by computing fill-in for each pivot row to be merged in */ 2623 prow = jl[k]; /* 1st pivot row */ 2624 2625 while (prow < k){ 2626 nextprow = jl[prow]; 2627 2628 /* merge prow into k-th row */ 2629 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2630 jmax = ui[prow+1]; 2631 ncols = jmax-jmin; 2632 i = jmin - ui[prow]; 2633 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2634 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2635 j = *(uj - 1); 2636 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2637 nzk += nlnk; 2638 2639 /* update il and jl for prow */ 2640 if (jmin < jmax){ 2641 il[prow] = jmin; 2642 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2643 } 2644 prow = nextprow; 2645 } 2646 2647 /* if free space is not available, make more free space */ 2648 if (current_space->local_remaining<nzk) { 2649 i = am - k + 1; /* num of unfactored rows */ 2650 i *= PetscMin(nzk, (i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2651 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2652 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2653 reallocs++; 2654 } 2655 2656 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2657 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2658 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2659 2660 /* add the k-th row into il and jl */ 2661 if (nzk > 1){ 2662 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2663 jl[k] = jl[i]; jl[i] = k; 2664 il[k] = ui[k] + 1; 2665 } 2666 uj_ptr[k] = current_space->array; 2667 uj_lvl_ptr[k] = current_space_lvl->array; 2668 2669 current_space->array += nzk; 2670 current_space->local_used += nzk; 2671 current_space->local_remaining -= nzk; 2672 2673 current_space_lvl->array += nzk; 2674 current_space_lvl->local_used += nzk; 2675 current_space_lvl->local_remaining -= nzk; 2676 2677 ui[k+1] = ui[k] + nzk; 2678 } 2679 2680 #if defined(PETSC_USE_INFO) 2681 if (ai[am] != 0) { 2682 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2683 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2684 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2685 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2686 } else { 2687 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2688 } 2689 #endif 2690 2691 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2692 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2693 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2694 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2695 2696 /* destroy list of free space and other temporary array(s) */ 2697 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2698 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 2699 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2700 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2701 2702 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2703 2704 /* put together the new matrix in MATSEQSBAIJ format */ 2705 2706 b = (Mat_SeqSBAIJ*)(fact)->data; 2707 b->singlemalloc = PETSC_FALSE; 2708 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2709 b->j = uj; 2710 b->i = ui; 2711 b->diag = udiag; 2712 b->free_diag = PETSC_TRUE; 2713 b->ilen = 0; 2714 b->imax = 0; 2715 b->row = perm; 2716 b->col = perm; 2717 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2718 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2719 b->icol = iperm; 2720 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2721 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2722 ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2723 b->maxnz = b->nz = ui[am]; 2724 b->free_a = PETSC_TRUE; 2725 b->free_ij = PETSC_TRUE; 2726 2727 (fact)->info.factor_mallocs = reallocs; 2728 (fact)->info.fill_ratio_given = fill; 2729 if (ai[am] != 0) { 2730 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2731 } else { 2732 (fact)->info.fill_ratio_needed = 0.0; 2733 } 2734 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2735 PetscFunctionReturn(0); 2736 } 2737 2738 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2739 { 2740 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2741 Mat_SeqSBAIJ *b; 2742 PetscErrorCode ierr; 2743 PetscTruth perm_identity; 2744 PetscReal fill = info->fill; 2745 const PetscInt *rip,*riip; 2746 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2747 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2748 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr,*udiag; 2749 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2750 PetscBT lnkbt; 2751 IS iperm; 2752 2753 PetscFunctionBegin; 2754 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 2755 /* check whether perm is the identity mapping */ 2756 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2757 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2758 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2759 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2760 2761 /* initialization */ 2762 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2763 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2764 ui[0] = 0; 2765 2766 /* jl: linked list for storing indices of the pivot rows 2767 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2768 ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr); 2769 for (i=0; i<am; i++){ 2770 jl[i] = am; il[i] = 0; 2771 } 2772 2773 /* create and initialize a linked list for storing column indices of the active row k */ 2774 nlnk = am + 1; 2775 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2776 2777 /* initial FreeSpace size is fill*(ai[am]+1) */ 2778 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2779 current_space = free_space; 2780 2781 for (k=0; k<am; k++){ /* for each active row k */ 2782 /* initialize lnk by the column indices of row rip[k] of A */ 2783 nzk = 0; 2784 ncols = ai[rip[k]+1] - ai[rip[k]]; 2785 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2786 ncols_upper = 0; 2787 for (j=0; j<ncols; j++){ 2788 i = riip[*(aj + ai[rip[k]] + j)]; 2789 if (i >= k){ /* only take upper triangular entry */ 2790 cols[ncols_upper] = i; 2791 ncols_upper++; 2792 } 2793 } 2794 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2795 nzk += nlnk; 2796 2797 /* update lnk by computing fill-in for each pivot row to be merged in */ 2798 prow = jl[k]; /* 1st pivot row */ 2799 2800 while (prow < k){ 2801 nextprow = jl[prow]; 2802 /* merge prow into k-th row */ 2803 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2804 jmax = ui[prow+1]; 2805 ncols = jmax-jmin; 2806 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2807 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2808 nzk += nlnk; 2809 2810 /* update il and jl for prow */ 2811 if (jmin < jmax){ 2812 il[prow] = jmin; 2813 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 2814 } 2815 prow = nextprow; 2816 } 2817 2818 /* if free space is not available, make more free space */ 2819 if (current_space->local_remaining<nzk) { 2820 i = am - k + 1; /* num of unfactored rows */ 2821 i *= PetscMin(nzk,i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2822 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2823 reallocs++; 2824 } 2825 2826 /* copy data into free space, then initialize lnk */ 2827 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 2828 2829 /* add the k-th row into il and jl */ 2830 if (nzk-1 > 0){ 2831 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2832 jl[k] = jl[i]; jl[i] = k; 2833 il[k] = ui[k] + 1; 2834 } 2835 ui_ptr[k] = current_space->array; 2836 current_space->array += nzk; 2837 current_space->local_used += nzk; 2838 current_space->local_remaining -= nzk; 2839 2840 ui[k+1] = ui[k] + nzk; 2841 } 2842 2843 #if defined(PETSC_USE_INFO) 2844 if (ai[am] != 0) { 2845 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 2846 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2847 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2848 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2849 } else { 2850 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2851 } 2852 #endif 2853 2854 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2855 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2856 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 2857 2858 /* destroy list of free space and other temporary array(s) */ 2859 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2860 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor in newdatastruct */ 2861 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2862 2863 /* put together the new matrix in MATSEQSBAIJ format */ 2864 2865 b = (Mat_SeqSBAIJ*)(fact)->data; 2866 b->singlemalloc = PETSC_FALSE; 2867 b->free_a = PETSC_TRUE; 2868 b->free_ij = PETSC_TRUE; 2869 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2870 b->j = uj; 2871 b->i = ui; 2872 b->diag = udiag; 2873 b->free_diag = PETSC_TRUE; 2874 b->ilen = 0; 2875 b->imax = 0; 2876 b->row = perm; 2877 b->col = perm; 2878 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2879 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2880 b->icol = iperm; 2881 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2882 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2883 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2884 b->maxnz = b->nz = ui[am]; 2885 2886 (fact)->info.factor_mallocs = reallocs; 2887 (fact)->info.fill_ratio_given = fill; 2888 if (ai[am] != 0) { 2889 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2890 } else { 2891 (fact)->info.fill_ratio_needed = 0.0; 2892 } 2893 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct; 2894 PetscFunctionReturn(0); 2895 } 2896 2897 #undef __FUNCT__ 2898 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ" 2899 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2900 { 2901 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2902 Mat_SeqSBAIJ *b; 2903 PetscErrorCode ierr; 2904 PetscTruth perm_identity; 2905 PetscReal fill = info->fill; 2906 const PetscInt *rip,*riip; 2907 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2908 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2909 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr; 2910 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2911 PetscBT lnkbt; 2912 IS iperm; 2913 PetscTruth newdatastruct=PETSC_FALSE; 2914 2915 PetscFunctionBegin; 2916 ierr = PetscOptionsGetTruth(PETSC_NULL,"-cholesky_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 2917 if(newdatastruct){ 2918 ierr = MatCholeskyFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr); 2919 PetscFunctionReturn(0); 2920 } 2921 2922 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 2923 /* check whether perm is the identity mapping */ 2924 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2925 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2926 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2927 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2928 2929 /* initialization */ 2930 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2931 ui[0] = 0; 2932 2933 /* jl: linked list for storing indices of the pivot rows 2934 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2935 ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr); 2936 for (i=0; i<am; i++){ 2937 jl[i] = am; il[i] = 0; 2938 } 2939 2940 /* create and initialize a linked list for storing column indices of the active row k */ 2941 nlnk = am + 1; 2942 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2943 2944 /* initial FreeSpace size is fill*(ai[am]+1) */ 2945 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2946 current_space = free_space; 2947 2948 for (k=0; k<am; k++){ /* for each active row k */ 2949 /* initialize lnk by the column indices of row rip[k] of A */ 2950 nzk = 0; 2951 ncols = ai[rip[k]+1] - ai[rip[k]]; 2952 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2953 ncols_upper = 0; 2954 for (j=0; j<ncols; j++){ 2955 i = riip[*(aj + ai[rip[k]] + j)]; 2956 if (i >= k){ /* only take upper triangular entry */ 2957 cols[ncols_upper] = i; 2958 ncols_upper++; 2959 } 2960 } 2961 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2962 nzk += nlnk; 2963 2964 /* update lnk by computing fill-in for each pivot row to be merged in */ 2965 prow = jl[k]; /* 1st pivot row */ 2966 2967 while (prow < k){ 2968 nextprow = jl[prow]; 2969 /* merge prow into k-th row */ 2970 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2971 jmax = ui[prow+1]; 2972 ncols = jmax-jmin; 2973 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2974 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2975 nzk += nlnk; 2976 2977 /* update il and jl for prow */ 2978 if (jmin < jmax){ 2979 il[prow] = jmin; 2980 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 2981 } 2982 prow = nextprow; 2983 } 2984 2985 /* if free space is not available, make more free space */ 2986 if (current_space->local_remaining<nzk) { 2987 i = am - k + 1; /* num of unfactored rows */ 2988 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2989 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2990 reallocs++; 2991 } 2992 2993 /* copy data into free space, then initialize lnk */ 2994 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 2995 2996 /* add the k-th row into il and jl */ 2997 if (nzk-1 > 0){ 2998 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2999 jl[k] = jl[i]; jl[i] = k; 3000 il[k] = ui[k] + 1; 3001 } 3002 ui_ptr[k] = current_space->array; 3003 current_space->array += nzk; 3004 current_space->local_used += nzk; 3005 current_space->local_remaining -= nzk; 3006 3007 ui[k+1] = ui[k] + nzk; 3008 } 3009 3010 #if defined(PETSC_USE_INFO) 3011 if (ai[am] != 0) { 3012 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 3013 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 3014 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 3015 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 3016 } else { 3017 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 3018 } 3019 #endif 3020 3021 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 3022 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 3023 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 3024 3025 /* destroy list of free space and other temporary array(s) */ 3026 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 3027 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 3028 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3029 3030 /* put together the new matrix in MATSEQSBAIJ format */ 3031 3032 b = (Mat_SeqSBAIJ*)(fact)->data; 3033 b->singlemalloc = PETSC_FALSE; 3034 b->free_a = PETSC_TRUE; 3035 b->free_ij = PETSC_TRUE; 3036 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 3037 b->j = uj; 3038 b->i = ui; 3039 b->diag = 0; 3040 b->ilen = 0; 3041 b->imax = 0; 3042 b->row = perm; 3043 b->col = perm; 3044 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3045 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3046 b->icol = iperm; 3047 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 3048 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 3049 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3050 b->maxnz = b->nz = ui[am]; 3051 3052 (fact)->info.factor_mallocs = reallocs; 3053 (fact)->info.fill_ratio_given = fill; 3054 if (ai[am] != 0) { 3055 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 3056 } else { 3057 (fact)->info.fill_ratio_needed = 0.0; 3058 } 3059 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 3060 PetscFunctionReturn(0); 3061 } 3062 3063 #undef __FUNCT__ 3064 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct" 3065 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx) 3066 { 3067 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3068 PetscErrorCode ierr; 3069 PetscInt n = A->rmap->n; 3070 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag,*vi; 3071 PetscScalar *x,sum; 3072 const PetscScalar *b; 3073 const MatScalar *aa = a->a,*v; 3074 PetscInt i,nz; 3075 3076 PetscFunctionBegin; 3077 if (!n) PetscFunctionReturn(0); 3078 3079 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3080 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3081 3082 /* forward solve the lower triangular */ 3083 x[0] = b[0]; 3084 v = aa; 3085 vi = aj; 3086 for (i=1; i<n; i++) { 3087 nz = ai[i+1] - ai[i]; 3088 sum = b[i]; 3089 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3090 v += nz; 3091 vi += nz; 3092 x[i] = sum; 3093 } 3094 3095 /* backward solve the upper triangular */ 3096 for (i=n-1; i>=0; i--){ 3097 v = aa + adiag[i+1] + 1; 3098 vi = aj + adiag[i+1] + 1; 3099 nz = adiag[i] - adiag[i+1]-1; 3100 sum = x[i]; 3101 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3102 x[i] = sum*v[nz]; /* x[i]=aa[adiag[i]]*sum; v++; */ 3103 } 3104 3105 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 3106 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3107 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3108 PetscFunctionReturn(0); 3109 } 3110 3111 #undef __FUNCT__ 3112 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct" 3113 PetscErrorCode MatSolve_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx) 3114 { 3115 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3116 IS iscol = a->col,isrow = a->row; 3117 PetscErrorCode ierr; 3118 PetscInt i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz; 3119 const PetscInt *rout,*cout,*r,*c; 3120 PetscScalar *x,*tmp,sum; 3121 const PetscScalar *b; 3122 const MatScalar *aa = a->a,*v; 3123 3124 PetscFunctionBegin; 3125 if (!n) PetscFunctionReturn(0); 3126 3127 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3128 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3129 tmp = a->solve_work; 3130 3131 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 3132 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 3133 3134 /* forward solve the lower triangular */ 3135 tmp[0] = b[r[0]]; 3136 v = aa; 3137 vi = aj; 3138 for (i=1; i<n; i++) { 3139 nz = ai[i+1] - ai[i]; 3140 sum = b[r[i]]; 3141 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3142 tmp[i] = sum; 3143 v += nz; vi += nz; 3144 } 3145 3146 /* backward solve the upper triangular */ 3147 for (i=n-1; i>=0; i--){ 3148 v = aa + adiag[i+1]+1; 3149 vi = aj + adiag[i+1]+1; 3150 nz = adiag[i]-adiag[i+1]-1; 3151 sum = tmp[i]; 3152 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3153 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 3154 } 3155 3156 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 3157 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 3158 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3159 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3160 ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr); 3161 PetscFunctionReturn(0); 3162 } 3163 3164 #undef __FUNCT__ 3165 #define __FUNCT__ "MatILUDTFactor_SeqAIJ" 3166 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact) 3167 { 3168 Mat B = *fact; 3169 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b; 3170 IS isicol; 3171 PetscErrorCode ierr; 3172 const PetscInt *r,*ic; 3173 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag; 3174 PetscInt *bi,*bj,*bdiag,*bdiag_rev; 3175 PetscInt row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au; 3176 PetscInt nlnk,*lnk; 3177 PetscBT lnkbt; 3178 PetscTruth row_identity,icol_identity,both_identity; 3179 MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp; 3180 const PetscInt *ics; 3181 PetscInt j,nz,*pj,*bjtmp,k,ncut,*jtmp; 3182 PetscReal dt=info->dt,dtcol=info->dtcol,shift=info->shiftinblocks; 3183 PetscInt dtcount=(PetscInt)info->dtcount,nnz_max; 3184 PetscTruth missing; 3185 3186 PetscFunctionBegin; 3187 3188 if (dt == PETSC_DEFAULT) dt = 0.005; 3189 if (dtcol == PETSC_DEFAULT) dtcol = 0.01; /* XXX unused! */ 3190 if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax); 3191 3192 /* ------- symbolic factorization, can be reused ---------*/ 3193 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 3194 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 3195 adiag=a->diag; 3196 3197 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 3198 3199 /* bdiag is location of diagonal in factor */ 3200 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); /* becomes b->diag */ 3201 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag_rev);CHKERRQ(ierr); /* temporary */ 3202 3203 /* allocate row pointers bi */ 3204 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 3205 3206 /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */ 3207 if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */ 3208 nnz_max = ai[n]+2*n*dtcount+2; 3209 3210 ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 3211 ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr); 3212 3213 /* put together the new matrix */ 3214 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 3215 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 3216 b = (Mat_SeqAIJ*)(B)->data; 3217 b->free_a = PETSC_TRUE; 3218 b->free_ij = PETSC_TRUE; 3219 b->singlemalloc = PETSC_FALSE; 3220 b->a = ba; 3221 b->j = bj; 3222 b->i = bi; 3223 b->diag = bdiag; 3224 b->ilen = 0; 3225 b->imax = 0; 3226 b->row = isrow; 3227 b->col = iscol; 3228 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 3229 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 3230 b->icol = isicol; 3231 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 3232 3233 ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3234 b->maxnz = nnz_max; 3235 3236 (B)->factor = MAT_FACTOR_ILUDT; 3237 (B)->info.factor_mallocs = 0; 3238 (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]); 3239 CHKMEMQ; 3240 /* ------- end of symbolic factorization ---------*/ 3241 3242 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3243 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3244 ics = ic; 3245 3246 /* linked list for storing column indices of the active row */ 3247 nlnk = n + 1; 3248 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3249 3250 /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */ 3251 ierr = PetscMalloc2(n,PetscInt,&im,n,PetscInt,&jtmp);CHKERRQ(ierr); 3252 /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */ 3253 ierr = PetscMalloc2(n,MatScalar,&rtmp,n,MatScalar,&vtmp);CHKERRQ(ierr); 3254 ierr = PetscMemzero(rtmp,n*sizeof(MatScalar));CHKERRQ(ierr); 3255 3256 bi[0] = 0; 3257 bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */ 3258 bdiag_rev[n] = bdiag[0]; 3259 bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */ 3260 for (i=0; i<n; i++) { 3261 /* copy initial fill into linked list */ 3262 nzi = 0; /* nonzeros for active row i */ 3263 nzi = ai[r[i]+1] - ai[r[i]]; 3264 if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 3265 nzi_al = adiag[r[i]] - ai[r[i]]; 3266 nzi_au = ai[r[i]+1] - adiag[r[i]] -1; 3267 ajtmp = aj + ai[r[i]]; 3268 ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3269 3270 /* load in initial (unfactored row) */ 3271 aatmp = a->a + ai[r[i]]; 3272 for (j=0; j<nzi; j++) { 3273 rtmp[ics[*ajtmp++]] = *aatmp++; 3274 } 3275 3276 /* add pivot rows into linked list */ 3277 row = lnk[n]; 3278 while (row < i ) { 3279 nzi_bl = bi[row+1] - bi[row] + 1; 3280 bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */ 3281 ierr = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr); 3282 nzi += nlnk; 3283 row = lnk[row]; 3284 } 3285 3286 /* copy data from lnk into jtmp, then initialize lnk */ 3287 ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr); 3288 3289 /* numerical factorization */ 3290 bjtmp = jtmp; 3291 row = *bjtmp++; /* 1st pivot row */ 3292 while ( row < i ) { 3293 pc = rtmp + row; 3294 pv = ba + bdiag[row]; /* 1./(diag of the pivot row) */ 3295 multiplier = (*pc) * (*pv); 3296 *pc = multiplier; 3297 if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */ 3298 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3299 pv = ba + bdiag[row+1] + 1; 3300 /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */ 3301 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3302 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3303 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 3304 } 3305 row = *bjtmp++; 3306 } 3307 3308 /* copy sparse rtmp into contiguous vtmp; separate L and U part */ 3309 diag_tmp = rtmp[i]; /* save diagonal value - may not needed?? */ 3310 nzi_bl = 0; j = 0; 3311 while (jtmp[j] < i){ /* Note: jtmp is sorted */ 3312 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3313 nzi_bl++; j++; 3314 } 3315 nzi_bu = nzi - nzi_bl -1; 3316 while (j < nzi){ 3317 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3318 j++; 3319 } 3320 3321 bjtmp = bj + bi[i]; 3322 batmp = ba + bi[i]; 3323 /* apply level dropping rule to L part */ 3324 ncut = nzi_al + dtcount; 3325 if (ncut < nzi_bl){ 3326 ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr); 3327 ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr); 3328 } else { 3329 ncut = nzi_bl; 3330 } 3331 for (j=0; j<ncut; j++){ 3332 bjtmp[j] = jtmp[j]; 3333 batmp[j] = vtmp[j]; 3334 /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */ 3335 } 3336 bi[i+1] = bi[i] + ncut; 3337 nzi = ncut + 1; 3338 3339 /* apply level dropping rule to U part */ 3340 ncut = nzi_au + dtcount; 3341 if (ncut < nzi_bu){ 3342 ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr); 3343 ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr); 3344 } else { 3345 ncut = nzi_bu; 3346 } 3347 nzi += ncut; 3348 3349 /* mark bdiagonal */ 3350 bdiag[i+1] = bdiag[i] - (ncut + 1); 3351 bdiag_rev[n-i-1] = bdiag[i+1]; 3352 bi[2*n - i] = bi[2*n - i +1] - (ncut + 1); 3353 bjtmp = bj + bdiag[i]; 3354 batmp = ba + bdiag[i]; 3355 *bjtmp = i; 3356 *batmp = diag_tmp; /* rtmp[i]; */ 3357 if (*batmp == 0.0) { 3358 *batmp = dt+shift; 3359 /* printf(" row %d add shift %g\n",i,shift); */ 3360 } 3361 *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */ 3362 /* printf(" (%d,%g),",*bjtmp,*batmp); */ 3363 3364 bjtmp = bj + bdiag[i+1]+1; 3365 batmp = ba + bdiag[i+1]+1; 3366 for (k=0; k<ncut; k++){ 3367 bjtmp[k] = jtmp[nzi_bl+1+k]; 3368 batmp[k] = vtmp[nzi_bl+1+k]; 3369 /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */ 3370 } 3371 /* printf("\n"); */ 3372 3373 im[i] = nzi; /* used by PetscLLAddSortedLU() */ 3374 /* 3375 printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]); 3376 printf(" ----------------------------\n"); 3377 */ 3378 } /* for (i=0; i<n; i++) */ 3379 /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */ 3380 if (bi[n] >= bdiag[n]) SETERRQ2(PETSC_ERR_ARG_SIZ,"end of L array %d cannot >= the beginning of U array %d",bi[n],bdiag[n]); 3381 3382 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3383 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3384 3385 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3386 ierr = PetscFree2(im,jtmp);CHKERRQ(ierr); 3387 ierr = PetscFree2(rtmp,vtmp);CHKERRQ(ierr); 3388 ierr = PetscFree(bdiag_rev);CHKERRQ(ierr); 3389 3390 ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr); 3391 b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n]; 3392 3393 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3394 ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr); 3395 both_identity = (PetscTruth) (row_identity && icol_identity); 3396 if (row_identity && icol_identity) { 3397 B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct; 3398 } else { 3399 B->ops->solve = MatSolve_SeqAIJ_newdatastruct; 3400 } 3401 3402 B->ops->lufactorsymbolic = MatILUDTFactorSymbolic_SeqAIJ; 3403 B->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ; 3404 B->ops->solveadd = 0; 3405 B->ops->solvetranspose = 0; 3406 B->ops->solvetransposeadd = 0; 3407 B->ops->matsolve = 0; 3408 B->assembled = PETSC_TRUE; 3409 B->preallocated = PETSC_TRUE; 3410 PetscFunctionReturn(0); 3411 } 3412 3413 /* a wraper of MatILUDTFactor_SeqAIJ() */ 3414 #undef __FUNCT__ 3415 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ" 3416 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info) 3417 { 3418 PetscErrorCode ierr; 3419 3420 PetscFunctionBegin; 3421 ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr); 3422 3423 fact->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ; 3424 PetscFunctionReturn(0); 3425 } 3426 3427 /* 3428 same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors 3429 - intend to replace existing MatLUFactorNumeric_SeqAIJ() 3430 */ 3431 #undef __FUNCT__ 3432 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ" 3433 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info) 3434 { 3435 Mat C=fact; 3436 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 3437 IS isrow = b->row,isicol = b->icol; 3438 PetscErrorCode ierr; 3439 const PetscInt *r,*ic,*ics; 3440 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 3441 PetscInt *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj; 3442 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 3443 PetscReal dt=info->dt,shift=info->shiftinblocks; 3444 PetscTruth row_identity, col_identity; 3445 3446 PetscFunctionBegin; 3447 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3448 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3449 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 3450 ics = ic; 3451 3452 for (i=0; i<n; i++){ 3453 /* initialize rtmp array */ 3454 nzl = bi[i+1] - bi[i]; /* num of nozeros in L(i,:) */ 3455 bjtmp = bj + bi[i]; 3456 for (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0; 3457 rtmp[i] = 0.0; 3458 nzu = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */ 3459 bjtmp = bj + bdiag[i+1] + 1; 3460 for (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0; 3461 3462 /* load in initial unfactored row of A */ 3463 /* printf("row %d\n",i); */ 3464 nz = ai[r[i]+1] - ai[r[i]]; 3465 ajtmp = aj + ai[r[i]]; 3466 v = aa + ai[r[i]]; 3467 for (j=0; j<nz; j++) { 3468 rtmp[ics[*ajtmp++]] = v[j]; 3469 /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */ 3470 } 3471 /* printf("\n"); */ 3472 3473 /* numerical factorization */ 3474 bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */ 3475 nzl = bi[i+1] - bi[i]; /* num of entries in L(i,:) */ 3476 k = 0; 3477 while (k < nzl){ 3478 row = *bjtmp++; 3479 /* printf(" prow %d\n",row); */ 3480 pc = rtmp + row; 3481 pv = b->a + bdiag[row]; /* 1./(diag of the pivot row) */ 3482 multiplier = (*pc) * (*pv); 3483 *pc = multiplier; 3484 if (PetscAbsScalar(multiplier) > dt){ 3485 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3486 pv = b->a + bdiag[row+1] + 1; 3487 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3488 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3489 /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */ 3490 } 3491 k++; 3492 } 3493 3494 /* finished row so stick it into b->a */ 3495 /* L-part */ 3496 pv = b->a + bi[i] ; 3497 pj = bj + bi[i] ; 3498 nzl = bi[i+1] - bi[i]; 3499 for (j=0; j<nzl; j++) { 3500 pv[j] = rtmp[pj[j]]; 3501 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3502 } 3503 3504 /* diagonal: invert diagonal entries for simplier triangular solves */ 3505 if (rtmp[i] == 0.0) rtmp[i] = dt+shift; 3506 b->a[bdiag[i]] = 1.0/rtmp[i]; 3507 /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */ 3508 3509 /* U-part */ 3510 pv = b->a + bdiag[i+1] + 1; 3511 pj = bj + bdiag[i+1] + 1; 3512 nzu = bdiag[i] - bdiag[i+1] - 1; 3513 for (j=0; j<nzu; j++) { 3514 pv[j] = rtmp[pj[j]]; 3515 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3516 } 3517 /* printf("\n"); */ 3518 } 3519 3520 ierr = PetscFree(rtmp);CHKERRQ(ierr); 3521 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3522 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3523 3524 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3525 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 3526 if (row_identity && col_identity) { 3527 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct; 3528 } else { 3529 C->ops->solve = MatSolve_SeqAIJ_newdatastruct; 3530 } 3531 C->ops->solveadd = 0; 3532 C->ops->solvetranspose = 0; 3533 C->ops->solvetransposeadd = 0; 3534 C->ops->matsolve = 0; 3535 C->assembled = PETSC_TRUE; 3536 C->preallocated = PETSC_TRUE; 3537 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 3538 PetscFunctionReturn(0); 3539 } 3540