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; 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; 69 past = 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 = 0; 613 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ_newdatastruct; 614 C->ops->solvetransposeadd = 0; 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__ "MatSolveTranspose_SeqAIJ" 1245 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx) 1246 { 1247 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1248 IS iscol = a->col,isrow = a->row; 1249 PetscErrorCode ierr; 1250 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1251 PetscInt i,n = A->rmap->n,j; 1252 PetscInt nz; 1253 PetscScalar *x,*tmp,s1; 1254 const MatScalar *aa = a->a,*v; 1255 const PetscScalar *b; 1256 1257 PetscFunctionBegin; 1258 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1259 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1260 tmp = a->solve_work; 1261 1262 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1263 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1264 1265 /* copy the b into temp work space according to permutation */ 1266 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1267 1268 /* forward solve the U^T */ 1269 for (i=0; i<n; i++) { 1270 v = aa + diag[i] ; 1271 vi = aj + diag[i] + 1; 1272 nz = ai[i+1] - diag[i] - 1; 1273 s1 = tmp[i]; 1274 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1275 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1276 tmp[i] = s1; 1277 } 1278 1279 /* backward solve the L^T */ 1280 for (i=n-1; i>=0; i--){ 1281 v = aa + diag[i] - 1 ; 1282 vi = aj + diag[i] - 1 ; 1283 nz = diag[i] - ai[i]; 1284 s1 = tmp[i]; 1285 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1286 } 1287 1288 /* copy tmp into x according to permutation */ 1289 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 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 1296 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1297 PetscFunctionReturn(0); 1298 } 1299 1300 #undef __FUNCT__ 1301 #define __FUNCT__ "MatSolveTranspose_SeqAIJ_newdatastruct" 1302 PetscErrorCode MatSolveTranspose_SeqAIJ_newdatastruct(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,*adiag = 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 + adiag[i+1] + 1; 1328 vi = aj + adiag[i+1] + 1; 1329 nz = adiag[i] - adiag[i+1] - 1; 1330 s1 = tmp[i]; 1331 s1 *= v[nz]; /* 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 + ai[i]; 1339 vi = aj + ai[i]; 1340 nz = ai[i+1] - 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__ "MatSolveTransposeAdd_SeqAIJ" 1359 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,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,*diag = 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 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1373 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1374 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1375 tmp = a->solve_work; 1376 1377 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1378 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1379 1380 /* copy the b into temp work space according to permutation */ 1381 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1382 1383 /* forward solve the U^T */ 1384 for (i=0; i<n; i++) { 1385 v = aa + diag[i] ; 1386 vi = aj + diag[i] + 1; 1387 nz = ai[i+1] - diag[i] - 1; 1388 s1 = tmp[i]; 1389 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1390 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1391 tmp[i] = s1; 1392 } 1393 1394 /* backward solve the L^T */ 1395 for (i=n-1; i>=0; i--){ 1396 v = aa + diag[i] - 1 ; 1397 vi = aj + diag[i] - 1 ; 1398 nz = diag[i] - ai[i]; 1399 s1 = tmp[i]; 1400 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1401 } 1402 1403 /* copy tmp into x according to permutation */ 1404 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1405 1406 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1407 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1408 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1409 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1410 1411 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1412 PetscFunctionReturn(0); 1413 } 1414 1415 /* ----------------------------------------------------------------*/ 1416 EXTERN PetscErrorCode Mat_CheckInode(Mat,PetscTruth); 1417 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth); 1418 1419 /* 1420 ilu() under revised new data structure. 1421 Factored arrays bj and ba are stored as 1422 L(0,:), L(1,:), ...,L(n-1,:), U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:) 1423 1424 bi=fact->i is an array of size n+1, in which 1425 bi+ 1426 bi[i]: points to 1st entry of L(i,:),i=0,...,n-1 1427 bi[n]: points to L(n-1,n-1)+1 1428 1429 bdiag=fact->diag is an array of size n+1,in which 1430 bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1 1431 bdiag[n]: points to entry of U(n-1,0)-1 1432 1433 U(i,:) contains bdiag[i] as its last entry, i.e., 1434 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 1435 */ 1436 #undef __FUNCT__ 1437 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct" 1438 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1439 { 1440 1441 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1442 PetscErrorCode ierr; 1443 PetscInt n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag; 1444 PetscInt i,j,nz,*bi,*bj,*bdiag; 1445 PetscTruth missing; 1446 IS isicol; 1447 1448 PetscFunctionBegin; 1449 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); 1450 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 1451 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 1452 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1453 1454 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr); 1455 b = (Mat_SeqAIJ*)(fact)->data; 1456 1457 /* allocate matrix arrays for new data structure */ 1458 ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,n+1,PetscInt,&b->i);CHKERRQ(ierr); 1459 ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1460 b->singlemalloc = PETSC_TRUE; 1461 if (!b->diag){ 1462 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr); 1463 ierr = PetscLogObjectMemory(fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1464 } 1465 bdiag = b->diag; 1466 1467 if (n > 0) { 1468 ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr); 1469 } 1470 1471 /* set bi and bj with new data structure */ 1472 bi = b->i; 1473 bj = b->j; 1474 1475 /* L part */ 1476 bi[0] = 0; 1477 for (i=0; i<n; i++){ 1478 nz = adiag[i] - ai[i]; 1479 bi[i+1] = bi[i] + nz; 1480 aj = a->j + ai[i]; 1481 for (j=0; j<nz; j++){ 1482 *bj = aj[j]; bj++; 1483 } 1484 } 1485 1486 /* U part */ 1487 bdiag[n] = bi[n]-1; 1488 for (i=n-1; i>=0; i--){ 1489 nz = ai[i+1] - adiag[i] - 1; 1490 aj = a->j + adiag[i] + 1; 1491 for (j=0; j<nz; j++){ 1492 *bj = aj[j]; bj++; 1493 } 1494 /* diag[i] */ 1495 *bj = i; bj++; 1496 bdiag[i] = bdiag[i+1] + nz + 1; 1497 } 1498 1499 fact->factor = MAT_FACTOR_ILU; 1500 fact->info.factor_mallocs = 0; 1501 fact->info.fill_ratio_given = info->fill; 1502 fact->info.fill_ratio_needed = 1.0; 1503 fact->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 1504 1505 b = (Mat_SeqAIJ*)(fact)->data; 1506 b->row = isrow; 1507 b->col = iscol; 1508 b->icol = isicol; 1509 ierr = PetscMalloc((fact->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1510 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1511 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1512 PetscFunctionReturn(0); 1513 } 1514 1515 #undef __FUNCT__ 1516 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_newdatastruct" 1517 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1518 { 1519 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1520 IS isicol; 1521 PetscErrorCode ierr; 1522 const PetscInt *r,*ic; 1523 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j; 1524 PetscInt *bi,*cols,nnz,*cols_lvl; 1525 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1526 PetscInt i,levels,diagonal_fill; 1527 PetscTruth col_identity,row_identity; 1528 PetscReal f; 1529 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1530 PetscBT lnkbt; 1531 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1532 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1533 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1534 1535 PetscFunctionBegin; 1536 /* printf("MatILUFactorSymbolic_SeqAIJ_newdatastruct ...\n"); */ 1537 levels = (PetscInt)info->levels; 1538 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1539 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1540 1541 if (!levels && row_identity && col_identity) { 1542 /* special case: ilu(0) with natural ordering */ 1543 ierr = MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1544 PetscFunctionReturn(0); 1545 } 1546 1547 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); 1548 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1549 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1550 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1551 1552 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1553 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1554 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1555 bi[0] = bdiag[0] = 0; 1556 1557 ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr); 1558 1559 /* create a linked list for storing column indices of the active row */ 1560 nlnk = n + 1; 1561 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1562 1563 /* initial FreeSpace size is f*(ai[n]+1) */ 1564 f = info->fill; 1565 diagonal_fill = (PetscInt)info->diagonal_fill; 1566 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1567 current_space = free_space; 1568 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1569 current_space_lvl = free_space_lvl; 1570 1571 for (i=0; i<n; i++) { 1572 nzi = 0; 1573 /* copy current row into linked list */ 1574 nnz = ai[r[i]+1] - ai[r[i]]; 1575 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1576 cols = aj + ai[r[i]]; 1577 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1578 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1579 nzi += nlnk; 1580 1581 /* make sure diagonal entry is included */ 1582 if (diagonal_fill && lnk[i] == -1) { 1583 fm = n; 1584 while (lnk[fm] < i) fm = lnk[fm]; 1585 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1586 lnk[fm] = i; 1587 lnk_lvl[i] = 0; 1588 nzi++; dcount++; 1589 } 1590 1591 /* add pivot rows into the active row */ 1592 nzbd = 0; 1593 prow = lnk[n]; 1594 while (prow < i) { 1595 nnz = bdiag[prow]; 1596 cols = bj_ptr[prow] + nnz + 1; 1597 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1598 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1599 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1600 nzi += nlnk; 1601 prow = lnk[prow]; 1602 nzbd++; 1603 } 1604 bdiag[i] = nzbd; 1605 bi[i+1] = bi[i] + nzi; 1606 1607 /* if free space is not available, make more free space */ 1608 if (current_space->local_remaining<nzi) { 1609 nnz = 2*nzi*(n - i); /* estimated and max additional space needed */ 1610 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1611 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1612 reallocs++; 1613 } 1614 1615 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1616 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1617 bj_ptr[i] = current_space->array; 1618 bjlvl_ptr[i] = current_space_lvl->array; 1619 1620 /* make sure the active row i has diagonal entry */ 1621 if (*(bj_ptr[i]+bdiag[i]) != i) { 1622 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 1623 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1624 } 1625 1626 current_space->array += nzi; 1627 current_space->local_used += nzi; 1628 current_space->local_remaining -= nzi; 1629 current_space_lvl->array += nzi; 1630 current_space_lvl->local_used += nzi; 1631 current_space_lvl->local_remaining -= nzi; 1632 } 1633 1634 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1635 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1636 1637 /* destroy list of free space and other temporary arrays */ 1638 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 1639 1640 /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */ 1641 ierr = PetscFreeSpaceContiguous_LU_v2(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 1642 1643 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1644 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1645 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 1646 1647 #if defined(PETSC_USE_INFO) 1648 { 1649 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1650 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 1651 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1652 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 1653 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1654 if (diagonal_fill) { 1655 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 1656 } 1657 } 1658 #endif 1659 1660 /* put together the new matrix */ 1661 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 1662 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 1663 b = (Mat_SeqAIJ*)(fact)->data; 1664 b->free_a = PETSC_TRUE; 1665 b->free_ij = PETSC_TRUE; 1666 b->singlemalloc = PETSC_FALSE; 1667 ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 1668 b->j = bj; 1669 b->i = bi; 1670 b->diag = bdiag; 1671 b->ilen = 0; 1672 b->imax = 0; 1673 b->row = isrow; 1674 b->col = iscol; 1675 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1676 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1677 b->icol = isicol; 1678 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1679 /* In b structure: Free imax, ilen, old a, old j. 1680 Allocate bdiag, solve_work, new a, new j */ 1681 ierr = PetscLogObjectMemory(fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1682 b->maxnz = b->nz = bdiag[0]+1; 1683 (fact)->info.factor_mallocs = reallocs; 1684 (fact)->info.fill_ratio_given = f; 1685 (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 1686 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 1687 /* ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */ 1688 PetscFunctionReturn(0); 1689 } 1690 1691 #undef __FUNCT__ 1692 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ" 1693 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1694 { 1695 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1696 IS isicol; 1697 PetscErrorCode ierr; 1698 const PetscInt *r,*ic; 1699 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,d; 1700 PetscInt *bi,*cols,nnz,*cols_lvl; 1701 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1702 PetscInt i,levels,diagonal_fill; 1703 PetscTruth col_identity,row_identity; 1704 PetscReal f; 1705 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1706 PetscBT lnkbt; 1707 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1708 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1709 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1710 PetscTruth missing; 1711 PetscTruth newdatastruct=PETSC_FALSE; 1712 1713 PetscFunctionBegin; 1714 ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 1715 if(newdatastruct){ 1716 ierr = MatILUFactorSymbolic_SeqAIJ_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1717 PetscFunctionReturn(0); 1718 } 1719 1720 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); 1721 f = info->fill; 1722 levels = (PetscInt)info->levels; 1723 diagonal_fill = (PetscInt)info->diagonal_fill; 1724 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1725 1726 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1727 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1728 if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */ 1729 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr); 1730 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1731 1732 fact->factor = MAT_FACTOR_ILU; 1733 (fact)->info.factor_mallocs = 0; 1734 (fact)->info.fill_ratio_given = info->fill; 1735 (fact)->info.fill_ratio_needed = 1.0; 1736 b = (Mat_SeqAIJ*)(fact)->data; 1737 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 1738 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 1739 b->row = isrow; 1740 b->col = iscol; 1741 b->icol = isicol; 1742 ierr = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1743 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1744 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1745 ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1746 PetscFunctionReturn(0); 1747 } 1748 1749 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1750 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1751 1752 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1753 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1754 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1755 bi[0] = bdiag[0] = 0; 1756 1757 ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr); 1758 1759 /* create a linked list for storing column indices of the active row */ 1760 nlnk = n + 1; 1761 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1762 1763 /* initial FreeSpace size is f*(ai[n]+1) */ 1764 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1765 current_space = free_space; 1766 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1767 current_space_lvl = free_space_lvl; 1768 1769 for (i=0; i<n; i++) { 1770 nzi = 0; 1771 /* copy current row into linked list */ 1772 nnz = ai[r[i]+1] - ai[r[i]]; 1773 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1774 cols = aj + ai[r[i]]; 1775 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1776 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1777 nzi += nlnk; 1778 1779 /* make sure diagonal entry is included */ 1780 if (diagonal_fill && lnk[i] == -1) { 1781 fm = n; 1782 while (lnk[fm] < i) fm = lnk[fm]; 1783 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1784 lnk[fm] = i; 1785 lnk_lvl[i] = 0; 1786 nzi++; dcount++; 1787 } 1788 1789 /* add pivot rows into the active row */ 1790 nzbd = 0; 1791 prow = lnk[n]; 1792 while (prow < i) { 1793 nnz = bdiag[prow]; 1794 cols = bj_ptr[prow] + nnz + 1; 1795 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1796 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1797 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1798 nzi += nlnk; 1799 prow = lnk[prow]; 1800 nzbd++; 1801 } 1802 bdiag[i] = nzbd; 1803 bi[i+1] = bi[i] + nzi; 1804 1805 /* if free space is not available, make more free space */ 1806 if (current_space->local_remaining<nzi) { 1807 nnz = nzi*(n - i); /* estimated and max additional space needed */ 1808 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1809 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1810 reallocs++; 1811 } 1812 1813 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1814 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1815 bj_ptr[i] = current_space->array; 1816 bjlvl_ptr[i] = current_space_lvl->array; 1817 1818 /* make sure the active row i has diagonal entry */ 1819 if (*(bj_ptr[i]+bdiag[i]) != i) { 1820 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 1821 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1822 } 1823 1824 current_space->array += nzi; 1825 current_space->local_used += nzi; 1826 current_space->local_remaining -= nzi; 1827 current_space_lvl->array += nzi; 1828 current_space_lvl->local_used += nzi; 1829 current_space_lvl->local_remaining -= nzi; 1830 } 1831 1832 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1833 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1834 1835 /* destroy list of free space and other temporary arrays */ 1836 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 1837 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */ 1838 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1839 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1840 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 1841 1842 #if defined(PETSC_USE_INFO) 1843 { 1844 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1845 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 1846 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1847 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 1848 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1849 if (diagonal_fill) { 1850 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 1851 } 1852 } 1853 #endif 1854 1855 /* put together the new matrix */ 1856 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 1857 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 1858 b = (Mat_SeqAIJ*)(fact)->data; 1859 b->free_a = PETSC_TRUE; 1860 b->free_ij = PETSC_TRUE; 1861 b->singlemalloc = PETSC_FALSE; 1862 ierr = PetscMalloc(bi[n]*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 1863 b->j = bj; 1864 b->i = bi; 1865 for (i=0; i<n; i++) bdiag[i] += bi[i]; 1866 b->diag = bdiag; 1867 b->ilen = 0; 1868 b->imax = 0; 1869 b->row = isrow; 1870 b->col = iscol; 1871 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1872 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1873 b->icol = isicol; 1874 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1875 /* In b structure: Free imax, ilen, old a, old j. 1876 Allocate bdiag, solve_work, new a, new j */ 1877 ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1878 b->maxnz = b->nz = bi[n] ; 1879 (fact)->info.factor_mallocs = reallocs; 1880 (fact)->info.fill_ratio_given = f; 1881 (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1882 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1883 ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1884 PetscFunctionReturn(0); 1885 } 1886 1887 #undef __FUNCT__ 1888 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ_newdatastruct" 1889 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info) 1890 { 1891 Mat C = B; 1892 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 1893 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 1894 IS ip=b->row,iip = b->icol; 1895 PetscErrorCode ierr; 1896 const PetscInt *rip,*riip; 1897 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp; 1898 PetscInt *ai=a->i,*aj=a->j; 1899 PetscInt k,jmin,jmax,*c2r,*il,col,nexti,ili,nz; 1900 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 1901 PetscTruth perm_identity; 1902 1903 LUShift_Ctx sctx; 1904 PetscInt newshift; 1905 PetscReal rs; 1906 MatScalar d,*v; 1907 1908 PetscFunctionBegin; 1909 /* MatPivotSetUp(): initialize shift context sctx */ 1910 ierr = PetscMemzero(&sctx,sizeof(LUShift_Ctx));CHKERRQ(ierr); 1911 1912 /* if both shift schemes are chosen by user, only use info->shiftpd */ 1913 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 1914 sctx.shift_top = info->zeropivot; 1915 for (i=0; i<mbs; i++) { 1916 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 1917 d = (aa)[a->diag[i]]; 1918 rs = -PetscAbsScalar(d) - PetscRealPart(d); 1919 v = aa+ai[i]; 1920 nz = ai[i+1] - ai[i]; 1921 for (j=0; j<nz; j++) 1922 rs += PetscAbsScalar(v[j]); 1923 if (rs>sctx.shift_top) sctx.shift_top = rs; 1924 } 1925 sctx.shift_top *= 1.1; 1926 sctx.nshift_max = 5; 1927 sctx.shift_lo = 0.; 1928 sctx.shift_hi = 1.; 1929 } 1930 1931 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 1932 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 1933 1934 /* allocate working arrays 1935 c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col 1936 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 1937 */ 1938 ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&c2r);CHKERRQ(ierr); 1939 1940 do { 1941 sctx.lushift = PETSC_FALSE; 1942 1943 for (i=0; i<mbs; i++) c2r[i] = mbs; 1944 il[0] = 0; 1945 1946 for (k = 0; k<mbs; k++){ 1947 /* zero rtmp */ 1948 nz = bi[k+1] - bi[k]; 1949 bjtmp = bj + bi[k]; 1950 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 1951 1952 /* load in initial unfactored row */ 1953 bval = ba + bi[k]; 1954 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 1955 for (j = jmin; j < jmax; j++){ 1956 col = riip[aj[j]]; 1957 if (col >= k){ /* only take upper triangular entry */ 1958 rtmp[col] = aa[j]; 1959 *bval++ = 0.0; /* for in-place factorization */ 1960 } 1961 } 1962 /* shift the diagonal of the matrix: ZeropivotApply() */ 1963 rtmp[k] += sctx.shift_amount; /* shift the diagonal of the matrix */ 1964 1965 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 1966 dk = rtmp[k]; 1967 i = c2r[k]; /* first row to be added to k_th row */ 1968 1969 while (i < k){ 1970 nexti = c2r[i]; /* next row to be added to k_th row */ 1971 1972 /* compute multiplier, update diag(k) and U(i,k) */ 1973 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 1974 uikdi = - ba[ili]*ba[bdiag[i]]; /* diagonal(k) */ 1975 dk += uikdi*ba[ili]; /* update diag[k] */ 1976 ba[ili] = uikdi; /* -U(i,k) */ 1977 1978 /* add multiple of row i to k-th row */ 1979 jmin = ili + 1; jmax = bi[i+1]; 1980 if (jmin < jmax){ 1981 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 1982 /* update il and c2r for row i */ 1983 il[i] = jmin; 1984 j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i; 1985 } 1986 i = nexti; 1987 } 1988 1989 /* copy data into U(k,:) */ 1990 rs = 0.0; 1991 jmin = bi[k]; jmax = bi[k+1]-1; 1992 if (jmin < jmax) { 1993 for (j=jmin; j<jmax; j++){ 1994 col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]); 1995 } 1996 /* add the k-th row into il and c2r */ 1997 il[k] = jmin; 1998 i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k; 1999 } 2000 2001 /* MatPivotCheck() */ 2002 sctx.rs = rs; 2003 sctx.pv = dk; 2004 if (info->shiftnz){ 2005 ierr = MatPivotCheck_nz(info,sctx,k,newshift);CHKERRQ(ierr); 2006 } else if (info->shiftpd){ 2007 ierr = MatPivotCheck_pd(info,sctx,k,newshift);CHKERRQ(ierr); 2008 } else if (info->shiftinblocks){ 2009 ierr = MatPivotCheck_inblocks(info,sctx,k,newshift);CHKERRQ(ierr); 2010 } else { 2011 ierr = MatPivotCheck_none(info,sctx,k,newshift);CHKERRQ(ierr); 2012 } 2013 dk = sctx.pv; 2014 if (newshift == 1) break; 2015 2016 ba[bdiag[k]] = 1.0/dk; /* U(k,k) */ 2017 } 2018 } while (sctx.lushift); 2019 2020 ierr = PetscFree3(rtmp,il,c2r);CHKERRQ(ierr); 2021 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2022 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2023 2024 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2025 if (perm_identity){ 2026 (B)->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_newdatastruct; 2027 (B)->ops->solvetranspose = 0; 2028 (B)->ops->forwardsolve = 0; 2029 (B)->ops->backwardsolve = 0; 2030 } else { 2031 (B)->ops->solve = MatSolve_SeqSBAIJ_1_newdatastruct; 2032 (B)->ops->solvetranspose = 0; 2033 (B)->ops->forwardsolve = 0; 2034 (B)->ops->backwardsolve = 0; 2035 } 2036 2037 C->assembled = PETSC_TRUE; 2038 C->preallocated = PETSC_TRUE; 2039 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2040 2041 /* MatPivotView() */ 2042 if (sctx.nshift){ 2043 if (info->shiftpd) { 2044 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); 2045 } else if (info->shiftnz) { 2046 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2047 } else if (info->shiftinblocks){ 2048 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftinblocks);CHKERRQ(ierr); 2049 } 2050 } 2051 PetscFunctionReturn(0); 2052 } 2053 2054 #undef __FUNCT__ 2055 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ" 2056 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 2057 { 2058 Mat C = B; 2059 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2060 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2061 IS ip=b->row,iip = b->icol; 2062 PetscErrorCode ierr; 2063 const PetscInt *rip,*riip; 2064 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol,*bjtmp; 2065 PetscInt *ai=a->i,*aj=a->j; 2066 PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz; 2067 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2068 PetscReal zeropivot,rs,shiftnz; 2069 PetscReal shiftpd; 2070 ChShift_Ctx sctx; 2071 PetscInt newshift; 2072 PetscTruth perm_identity; 2073 2074 PetscFunctionBegin; 2075 shiftnz = info->shiftnz; 2076 shiftpd = info->shiftpd; 2077 zeropivot = info->zeropivot; 2078 2079 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2080 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2081 2082 /* initialization */ 2083 ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr); 2084 sctx.shift_amount = 0; 2085 sctx.nshift = 0; 2086 do { 2087 sctx.chshift = PETSC_FALSE; 2088 for (i=0; i<mbs; i++) jl[i] = mbs; 2089 il[0] = 0; 2090 2091 for (k = 0; k<mbs; k++){ 2092 /* zero rtmp */ 2093 nz = bi[k+1] - bi[k]; 2094 bjtmp = bj + bi[k]; 2095 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2096 2097 bval = ba + bi[k]; 2098 /* initialize k-th row by the perm[k]-th row of A */ 2099 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2100 for (j = jmin; j < jmax; j++){ 2101 col = riip[aj[j]]; 2102 if (col >= k){ /* only take upper triangular entry */ 2103 rtmp[col] = aa[j]; 2104 *bval++ = 0.0; /* for in-place factorization */ 2105 } 2106 } 2107 /* shift the diagonal of the matrix */ 2108 if (sctx.nshift) rtmp[k] += sctx.shift_amount; 2109 2110 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2111 dk = rtmp[k]; 2112 i = jl[k]; /* first row to be added to k_th row */ 2113 2114 while (i < k){ 2115 nexti = jl[i]; /* next row to be added to k_th row */ 2116 2117 /* compute multiplier, update diag(k) and U(i,k) */ 2118 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2119 uikdi = - ba[ili]*ba[bi[i]]; /* diagonal(k) */ 2120 dk += uikdi*ba[ili]; 2121 ba[ili] = uikdi; /* -U(i,k) */ 2122 2123 /* add multiple of row i to k-th row */ 2124 jmin = ili + 1; jmax = bi[i+1]; 2125 if (jmin < jmax){ 2126 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2127 /* update il and jl for row i */ 2128 il[i] = jmin; 2129 j = bj[jmin]; jl[i] = jl[j]; jl[j] = i; 2130 } 2131 i = nexti; 2132 } 2133 2134 /* shift the diagonals when zero pivot is detected */ 2135 /* compute rs=sum of abs(off-diagonal) */ 2136 rs = 0.0; 2137 jmin = bi[k]+1; 2138 nz = bi[k+1] - jmin; 2139 bcol = bj + jmin; 2140 for (j=0; j<nz; j++) { 2141 rs += PetscAbsScalar(rtmp[bcol[j]]); 2142 } 2143 2144 sctx.rs = rs; 2145 sctx.pv = dk; 2146 ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr); 2147 2148 if (newshift == 1) { 2149 if (!sctx.shift_amount) { 2150 sctx.shift_amount = 1e-5; 2151 } 2152 break; 2153 } 2154 2155 /* copy data into U(k,:) */ 2156 ba[bi[k]] = 1.0/dk; /* U(k,k) */ 2157 jmin = bi[k]+1; jmax = bi[k+1]; 2158 if (jmin < jmax) { 2159 for (j=jmin; j<jmax; j++){ 2160 col = bj[j]; ba[j] = rtmp[col]; 2161 } 2162 /* add the k-th row into il and jl */ 2163 il[k] = jmin; 2164 i = bj[jmin]; jl[k] = jl[i]; jl[i] = k; 2165 } 2166 } 2167 } while (sctx.chshift); 2168 ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr); 2169 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2170 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2171 2172 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2173 if (perm_identity){ 2174 (B)->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2175 (B)->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2176 (B)->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering; 2177 (B)->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering; 2178 } else { 2179 (B)->ops->solve = MatSolve_SeqSBAIJ_1; 2180 (B)->ops->solvetranspose = MatSolve_SeqSBAIJ_1; 2181 (B)->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1; 2182 (B)->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1; 2183 } 2184 2185 C->assembled = PETSC_TRUE; 2186 C->preallocated = PETSC_TRUE; 2187 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2188 if (sctx.nshift){ 2189 if (shiftnz) { 2190 ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2191 } else if (shiftpd) { 2192 ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2193 } 2194 } 2195 PetscFunctionReturn(0); 2196 } 2197 2198 /* 2199 icc() under revised new data structure. 2200 Factored arrays bj and ba are stored as 2201 U(0,:),...,U(i,:),U(n-1,:) 2202 2203 ui=fact->i is an array of size n+1, in which 2204 ui+ 2205 ui[i]: points to 1st entry of U(i,:),i=0,...,n-1 2206 ui[n]: points to U(n-1,n-1)+1 2207 2208 udiag=fact->diag is an array of size n,in which 2209 udiag[i]: points to diagonal of U(i,:), i=0,...,n-1 2210 2211 U(i,:) contains udiag[i] as its last entry, i.e., 2212 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 2213 */ 2214 2215 #undef __FUNCT__ 2216 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ_newdatastruct" 2217 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2218 { 2219 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2220 Mat_SeqSBAIJ *b; 2221 PetscErrorCode ierr; 2222 PetscTruth perm_identity,missing; 2223 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2224 const PetscInt *rip,*riip; 2225 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2226 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2227 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2228 PetscReal fill=info->fill,levels=info->levels; 2229 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2230 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2231 PetscBT lnkbt; 2232 IS iperm; 2233 2234 PetscFunctionBegin; 2235 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); 2236 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2237 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2238 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2239 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2240 2241 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2242 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2243 ui[0] = 0; 2244 2245 /* ICC(0) without matrix ordering: simply rearrange column indices */ 2246 if (!levels && perm_identity) { 2247 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2248 cols = uj; 2249 for (i=0; i<am; i++) { 2250 ncols = ai[i+1] - a->diag[i]; 2251 ui[i+1] = ui[i] + ncols; 2252 udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */ 2253 2254 aj = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */ 2255 ncols--; /* exclude diagonal */ 2256 for (j=0; j<ncols; j++) *cols++ = aj[j]; 2257 *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */ 2258 } 2259 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2260 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2261 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2262 2263 /* initialization */ 2264 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2265 2266 /* jl: linked list for storing indices of the pivot rows 2267 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2268 ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr); 2269 for (i=0; i<am; i++){ 2270 jl[i] = am; il[i] = 0; 2271 } 2272 2273 /* create and initialize a linked list for storing column indices of the active row k */ 2274 nlnk = am + 1; 2275 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2276 2277 /* initial FreeSpace size is fill*(ai[am]+1) */ 2278 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2279 current_space = free_space; 2280 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2281 current_space_lvl = free_space_lvl; 2282 2283 for (k=0; k<am; k++){ /* for each active row k */ 2284 /* initialize lnk by the column indices of row rip[k] of A */ 2285 nzk = 0; 2286 ncols = ai[rip[k]+1] - ai[rip[k]]; 2287 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2288 ncols_upper = 0; 2289 for (j=0; j<ncols; j++){ 2290 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2291 if (riip[i] >= k){ /* only take upper triangular entry */ 2292 ajtmp[ncols_upper] = i; 2293 ncols_upper++; 2294 } 2295 } 2296 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2297 nzk += nlnk; 2298 2299 /* update lnk by computing fill-in for each pivot row to be merged in */ 2300 prow = jl[k]; /* 1st pivot row */ 2301 2302 while (prow < k){ 2303 nextprow = jl[prow]; 2304 2305 /* merge prow into k-th row */ 2306 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2307 jmax = ui[prow+1]; 2308 ncols = jmax-jmin; 2309 i = jmin - ui[prow]; 2310 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2311 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2312 j = *(uj - 1); 2313 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2314 nzk += nlnk; 2315 2316 /* update il and jl for prow */ 2317 if (jmin < jmax){ 2318 il[prow] = jmin; 2319 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2320 } 2321 prow = nextprow; 2322 } 2323 2324 /* if free space is not available, make more free space */ 2325 if (current_space->local_remaining<nzk) { 2326 i = am - k + 1; /* num of unfactored rows */ 2327 i *= PetscMin(nzk, i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2328 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2329 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2330 reallocs++; 2331 } 2332 2333 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2334 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2335 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2336 2337 /* add the k-th row into il and jl */ 2338 if (nzk > 1){ 2339 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2340 jl[k] = jl[i]; jl[i] = k; 2341 il[k] = ui[k] + 1; 2342 } 2343 uj_ptr[k] = current_space->array; 2344 uj_lvl_ptr[k] = current_space_lvl->array; 2345 2346 current_space->array += nzk; 2347 current_space->local_used += nzk; 2348 current_space->local_remaining -= nzk; 2349 2350 current_space_lvl->array += nzk; 2351 current_space_lvl->local_used += nzk; 2352 current_space_lvl->local_remaining -= nzk; 2353 2354 ui[k+1] = ui[k] + nzk; 2355 } 2356 2357 #if defined(PETSC_USE_INFO) 2358 if (ai[am] != 0) { 2359 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2360 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2361 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2362 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2363 } else { 2364 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2365 } 2366 #endif 2367 2368 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2369 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2370 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2371 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2372 2373 /* destroy list of free space and other temporary array(s) */ 2374 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2375 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor in newdatastruct */ 2376 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2377 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2378 2379 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2380 2381 /* put together the new matrix in MATSEQSBAIJ format */ 2382 2383 b = (Mat_SeqSBAIJ*)(fact)->data; 2384 b->singlemalloc = PETSC_FALSE; 2385 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2386 b->j = uj; 2387 b->i = ui; 2388 b->diag = udiag; 2389 b->free_diag = PETSC_TRUE; 2390 b->ilen = 0; 2391 b->imax = 0; 2392 b->row = perm; 2393 b->col = perm; 2394 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2395 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2396 b->icol = iperm; 2397 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2398 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2399 ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2400 b->maxnz = b->nz = ui[am]; 2401 b->free_a = PETSC_TRUE; 2402 b->free_ij = PETSC_TRUE; 2403 2404 (fact)->info.factor_mallocs = reallocs; 2405 (fact)->info.fill_ratio_given = fill; 2406 if (ai[am] != 0) { 2407 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2408 } else { 2409 (fact)->info.fill_ratio_needed = 0.0; 2410 } 2411 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct; 2412 PetscFunctionReturn(0); 2413 } 2414 2415 #undef __FUNCT__ 2416 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ" 2417 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2418 { 2419 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2420 Mat_SeqSBAIJ *b; 2421 PetscErrorCode ierr; 2422 PetscTruth perm_identity,missing; 2423 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2424 const PetscInt *rip,*riip; 2425 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2426 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2427 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2428 PetscReal fill=info->fill,levels=info->levels; 2429 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2430 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2431 PetscBT lnkbt; 2432 IS iperm; 2433 PetscTruth newdatastruct=PETSC_FALSE; 2434 2435 PetscFunctionBegin; 2436 ierr = PetscOptionsGetTruth(PETSC_NULL,"-icc_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 2437 if(newdatastruct){ 2438 ierr = MatICCFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr); 2439 PetscFunctionReturn(0); 2440 } 2441 2442 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); 2443 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2444 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2445 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2446 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2447 2448 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2449 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2450 ui[0] = 0; 2451 2452 /* ICC(0) without matrix ordering: simply copies fill pattern */ 2453 if (!levels && perm_identity) { 2454 2455 for (i=0; i<am; i++) { 2456 ui[i+1] = ui[i] + ai[i+1] - a->diag[i]; 2457 udiag[i] = ui[i]; 2458 } 2459 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2460 cols = uj; 2461 for (i=0; i<am; i++) { 2462 aj = a->j + a->diag[i]; 2463 ncols = ui[i+1] - ui[i]; 2464 for (j=0; j<ncols; j++) *cols++ = *aj++; 2465 } 2466 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2467 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2468 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2469 2470 /* initialization */ 2471 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2472 2473 /* jl: linked list for storing indices of the pivot rows 2474 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2475 ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr); 2476 for (i=0; i<am; i++){ 2477 jl[i] = am; il[i] = 0; 2478 } 2479 2480 /* create and initialize a linked list for storing column indices of the active row k */ 2481 nlnk = am + 1; 2482 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2483 2484 /* initial FreeSpace size is fill*(ai[am]+1) */ 2485 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2486 current_space = free_space; 2487 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2488 current_space_lvl = free_space_lvl; 2489 2490 for (k=0; k<am; k++){ /* for each active row k */ 2491 /* initialize lnk by the column indices of row rip[k] of A */ 2492 nzk = 0; 2493 ncols = ai[rip[k]+1] - ai[rip[k]]; 2494 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2495 ncols_upper = 0; 2496 for (j=0; j<ncols; j++){ 2497 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2498 if (riip[i] >= k){ /* only take upper triangular entry */ 2499 ajtmp[ncols_upper] = i; 2500 ncols_upper++; 2501 } 2502 } 2503 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2504 nzk += nlnk; 2505 2506 /* update lnk by computing fill-in for each pivot row to be merged in */ 2507 prow = jl[k]; /* 1st pivot row */ 2508 2509 while (prow < k){ 2510 nextprow = jl[prow]; 2511 2512 /* merge prow into k-th row */ 2513 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2514 jmax = ui[prow+1]; 2515 ncols = jmax-jmin; 2516 i = jmin - ui[prow]; 2517 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2518 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2519 j = *(uj - 1); 2520 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2521 nzk += nlnk; 2522 2523 /* update il and jl for prow */ 2524 if (jmin < jmax){ 2525 il[prow] = jmin; 2526 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2527 } 2528 prow = nextprow; 2529 } 2530 2531 /* if free space is not available, make more free space */ 2532 if (current_space->local_remaining<nzk) { 2533 i = am - k + 1; /* num of unfactored rows */ 2534 i *= PetscMin(nzk, (i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2535 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2536 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2537 reallocs++; 2538 } 2539 2540 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2541 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2542 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2543 2544 /* add the k-th row into il and jl */ 2545 if (nzk > 1){ 2546 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2547 jl[k] = jl[i]; jl[i] = k; 2548 il[k] = ui[k] + 1; 2549 } 2550 uj_ptr[k] = current_space->array; 2551 uj_lvl_ptr[k] = current_space_lvl->array; 2552 2553 current_space->array += nzk; 2554 current_space->local_used += nzk; 2555 current_space->local_remaining -= nzk; 2556 2557 current_space_lvl->array += nzk; 2558 current_space_lvl->local_used += nzk; 2559 current_space_lvl->local_remaining -= nzk; 2560 2561 ui[k+1] = ui[k] + nzk; 2562 } 2563 2564 #if defined(PETSC_USE_INFO) 2565 if (ai[am] != 0) { 2566 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2567 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2568 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2569 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2570 } else { 2571 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2572 } 2573 #endif 2574 2575 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2576 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2577 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2578 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2579 2580 /* destroy list of free space and other temporary array(s) */ 2581 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2582 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 2583 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2584 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2585 2586 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2587 2588 /* put together the new matrix in MATSEQSBAIJ format */ 2589 2590 b = (Mat_SeqSBAIJ*)(fact)->data; 2591 b->singlemalloc = PETSC_FALSE; 2592 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2593 b->j = uj; 2594 b->i = ui; 2595 b->diag = udiag; 2596 b->free_diag = PETSC_TRUE; 2597 b->ilen = 0; 2598 b->imax = 0; 2599 b->row = perm; 2600 b->col = perm; 2601 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2602 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2603 b->icol = iperm; 2604 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2605 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2606 ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2607 b->maxnz = b->nz = ui[am]; 2608 b->free_a = PETSC_TRUE; 2609 b->free_ij = PETSC_TRUE; 2610 2611 (fact)->info.factor_mallocs = reallocs; 2612 (fact)->info.fill_ratio_given = fill; 2613 if (ai[am] != 0) { 2614 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2615 } else { 2616 (fact)->info.fill_ratio_needed = 0.0; 2617 } 2618 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2619 PetscFunctionReturn(0); 2620 } 2621 2622 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2623 { 2624 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2625 Mat_SeqSBAIJ *b; 2626 PetscErrorCode ierr; 2627 PetscTruth perm_identity; 2628 PetscReal fill = info->fill; 2629 const PetscInt *rip,*riip; 2630 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2631 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2632 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr,*udiag; 2633 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2634 PetscBT lnkbt; 2635 IS iperm; 2636 2637 PetscFunctionBegin; 2638 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); 2639 /* check whether perm is the identity mapping */ 2640 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2641 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2642 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2643 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2644 2645 /* initialization */ 2646 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2647 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2648 ui[0] = 0; 2649 2650 /* jl: linked list for storing indices of the pivot rows 2651 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2652 ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr); 2653 for (i=0; i<am; i++){ 2654 jl[i] = am; il[i] = 0; 2655 } 2656 2657 /* create and initialize a linked list for storing column indices of the active row k */ 2658 nlnk = am + 1; 2659 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2660 2661 /* initial FreeSpace size is fill*(ai[am]+1) */ 2662 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2663 current_space = free_space; 2664 2665 for (k=0; k<am; k++){ /* for each active row k */ 2666 /* initialize lnk by the column indices of row rip[k] of A */ 2667 nzk = 0; 2668 ncols = ai[rip[k]+1] - ai[rip[k]]; 2669 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2670 ncols_upper = 0; 2671 for (j=0; j<ncols; j++){ 2672 i = riip[*(aj + ai[rip[k]] + j)]; 2673 if (i >= k){ /* only take upper triangular entry */ 2674 cols[ncols_upper] = i; 2675 ncols_upper++; 2676 } 2677 } 2678 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2679 nzk += nlnk; 2680 2681 /* update lnk by computing fill-in for each pivot row to be merged in */ 2682 prow = jl[k]; /* 1st pivot row */ 2683 2684 while (prow < k){ 2685 nextprow = jl[prow]; 2686 /* merge prow into k-th row */ 2687 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2688 jmax = ui[prow+1]; 2689 ncols = jmax-jmin; 2690 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2691 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2692 nzk += nlnk; 2693 2694 /* update il and jl for prow */ 2695 if (jmin < jmax){ 2696 il[prow] = jmin; 2697 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 2698 } 2699 prow = nextprow; 2700 } 2701 2702 /* if free space is not available, make more free space */ 2703 if (current_space->local_remaining<nzk) { 2704 i = am - k + 1; /* num of unfactored rows */ 2705 i *= PetscMin(nzk,i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2706 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2707 reallocs++; 2708 } 2709 2710 /* copy data into free space, then initialize lnk */ 2711 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 2712 2713 /* add the k-th row into il and jl */ 2714 if (nzk-1 > 0){ 2715 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2716 jl[k] = jl[i]; jl[i] = k; 2717 il[k] = ui[k] + 1; 2718 } 2719 ui_ptr[k] = current_space->array; 2720 current_space->array += nzk; 2721 current_space->local_used += nzk; 2722 current_space->local_remaining -= nzk; 2723 2724 ui[k+1] = ui[k] + nzk; 2725 } 2726 2727 #if defined(PETSC_USE_INFO) 2728 if (ai[am] != 0) { 2729 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 2730 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2731 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2732 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2733 } else { 2734 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2735 } 2736 #endif 2737 2738 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2739 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2740 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 2741 2742 /* destroy list of free space and other temporary array(s) */ 2743 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2744 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor in newdatastruct */ 2745 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2746 2747 /* put together the new matrix in MATSEQSBAIJ format */ 2748 2749 b = (Mat_SeqSBAIJ*)(fact)->data; 2750 b->singlemalloc = PETSC_FALSE; 2751 b->free_a = PETSC_TRUE; 2752 b->free_ij = PETSC_TRUE; 2753 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2754 b->j = uj; 2755 b->i = ui; 2756 b->diag = udiag; 2757 b->free_diag = PETSC_TRUE; 2758 b->ilen = 0; 2759 b->imax = 0; 2760 b->row = perm; 2761 b->col = perm; 2762 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2763 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2764 b->icol = iperm; 2765 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2766 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2767 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2768 b->maxnz = b->nz = ui[am]; 2769 2770 (fact)->info.factor_mallocs = reallocs; 2771 (fact)->info.fill_ratio_given = fill; 2772 if (ai[am] != 0) { 2773 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2774 } else { 2775 (fact)->info.fill_ratio_needed = 0.0; 2776 } 2777 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct; 2778 PetscFunctionReturn(0); 2779 } 2780 2781 #undef __FUNCT__ 2782 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ" 2783 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2784 { 2785 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2786 Mat_SeqSBAIJ *b; 2787 PetscErrorCode ierr; 2788 PetscTruth perm_identity; 2789 PetscReal fill = info->fill; 2790 const PetscInt *rip,*riip; 2791 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2792 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2793 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr; 2794 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2795 PetscBT lnkbt; 2796 IS iperm; 2797 PetscTruth newdatastruct=PETSC_FALSE; 2798 2799 PetscFunctionBegin; 2800 ierr = PetscOptionsGetTruth(PETSC_NULL,"-cholesky_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 2801 if(newdatastruct){ 2802 ierr = MatCholeskyFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr); 2803 PetscFunctionReturn(0); 2804 } 2805 2806 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); 2807 /* check whether perm is the identity mapping */ 2808 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2809 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2810 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2811 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2812 2813 /* initialization */ 2814 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2815 ui[0] = 0; 2816 2817 /* jl: linked list for storing indices of the pivot rows 2818 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2819 ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr); 2820 for (i=0; i<am; i++){ 2821 jl[i] = am; il[i] = 0; 2822 } 2823 2824 /* create and initialize a linked list for storing column indices of the active row k */ 2825 nlnk = am + 1; 2826 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2827 2828 /* initial FreeSpace size is fill*(ai[am]+1) */ 2829 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2830 current_space = free_space; 2831 2832 for (k=0; k<am; k++){ /* for each active row k */ 2833 /* initialize lnk by the column indices of row rip[k] of A */ 2834 nzk = 0; 2835 ncols = ai[rip[k]+1] - ai[rip[k]]; 2836 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2837 ncols_upper = 0; 2838 for (j=0; j<ncols; j++){ 2839 i = riip[*(aj + ai[rip[k]] + j)]; 2840 if (i >= k){ /* only take upper triangular entry */ 2841 cols[ncols_upper] = i; 2842 ncols_upper++; 2843 } 2844 } 2845 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2846 nzk += nlnk; 2847 2848 /* update lnk by computing fill-in for each pivot row to be merged in */ 2849 prow = jl[k]; /* 1st pivot row */ 2850 2851 while (prow < k){ 2852 nextprow = jl[prow]; 2853 /* merge prow into k-th row */ 2854 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2855 jmax = ui[prow+1]; 2856 ncols = jmax-jmin; 2857 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2858 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2859 nzk += nlnk; 2860 2861 /* update il and jl for prow */ 2862 if (jmin < jmax){ 2863 il[prow] = jmin; 2864 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 2865 } 2866 prow = nextprow; 2867 } 2868 2869 /* if free space is not available, make more free space */ 2870 if (current_space->local_remaining<nzk) { 2871 i = am - k + 1; /* num of unfactored rows */ 2872 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2873 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2874 reallocs++; 2875 } 2876 2877 /* copy data into free space, then initialize lnk */ 2878 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 2879 2880 /* add the k-th row into il and jl */ 2881 if (nzk-1 > 0){ 2882 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2883 jl[k] = jl[i]; jl[i] = k; 2884 il[k] = ui[k] + 1; 2885 } 2886 ui_ptr[k] = current_space->array; 2887 current_space->array += nzk; 2888 current_space->local_used += nzk; 2889 current_space->local_remaining -= nzk; 2890 2891 ui[k+1] = ui[k] + nzk; 2892 } 2893 2894 #if defined(PETSC_USE_INFO) 2895 if (ai[am] != 0) { 2896 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 2897 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2898 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2899 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2900 } else { 2901 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2902 } 2903 #endif 2904 2905 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2906 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2907 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 2908 2909 /* destroy list of free space and other temporary array(s) */ 2910 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2911 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 2912 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2913 2914 /* put together the new matrix in MATSEQSBAIJ format */ 2915 2916 b = (Mat_SeqSBAIJ*)(fact)->data; 2917 b->singlemalloc = PETSC_FALSE; 2918 b->free_a = PETSC_TRUE; 2919 b->free_ij = PETSC_TRUE; 2920 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2921 b->j = uj; 2922 b->i = ui; 2923 b->diag = 0; 2924 b->ilen = 0; 2925 b->imax = 0; 2926 b->row = perm; 2927 b->col = perm; 2928 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2929 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2930 b->icol = iperm; 2931 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2932 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2933 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2934 b->maxnz = b->nz = ui[am]; 2935 2936 (fact)->info.factor_mallocs = reallocs; 2937 (fact)->info.fill_ratio_given = fill; 2938 if (ai[am] != 0) { 2939 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2940 } else { 2941 (fact)->info.fill_ratio_needed = 0.0; 2942 } 2943 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2944 PetscFunctionReturn(0); 2945 } 2946 2947 #if defined(OLD_ROUTINE_TO_BE_REPLACED) 2948 #undef __FUNCT__ 2949 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct" 2950 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx) 2951 { 2952 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2953 PetscErrorCode ierr; 2954 PetscInt n = A->rmap->n; 2955 const PetscInt *ai = a->i,*aj = a->j,*vi; 2956 PetscScalar *x,sum; 2957 const PetscScalar *b; 2958 const MatScalar *aa = a->a,*v; 2959 PetscInt i,nz; 2960 2961 PetscFunctionBegin; 2962 if (!n) PetscFunctionReturn(0); 2963 2964 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 2965 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 2966 2967 /* forward solve the lower triangular */ 2968 x[0] = b[0]; 2969 v = aa; 2970 vi = aj; 2971 for (i=1; i<n; i++) { 2972 nz = ai[i+1] - ai[i]; 2973 sum = b[i]; 2974 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 2975 v += nz; 2976 vi += nz; 2977 x[i] = sum; 2978 } 2979 2980 /* backward solve the upper triangular */ 2981 v = aa + ai[n+1]; 2982 vi = aj + ai[n+1]; 2983 for (i=n-1; i>=0; i--){ 2984 nz = ai[2*n-i +1] - ai[2*n-i]-1; 2985 sum = x[i]; 2986 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 2987 v += nz; 2988 vi += nz; vi++; 2989 x[i] = *v++ *sum; /* x[i]=aa[adiag[i]]*sum; v++; */ 2990 } 2991 2992 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 2993 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 2994 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 2995 PetscFunctionReturn(0); 2996 } 2997 #endif 2998 2999 #undef __FUNCT__ 3000 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct" 3001 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx) 3002 { 3003 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3004 PetscErrorCode ierr; 3005 PetscInt n = A->rmap->n; 3006 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag,*vi; 3007 PetscScalar *x,sum; 3008 const PetscScalar *b; 3009 const MatScalar *aa = a->a,*v; 3010 PetscInt i,nz; 3011 3012 PetscFunctionBegin; 3013 if (!n) PetscFunctionReturn(0); 3014 3015 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3016 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3017 3018 /* forward solve the lower triangular */ 3019 x[0] = b[0]; 3020 v = aa; 3021 vi = aj; 3022 for (i=1; i<n; i++) { 3023 nz = ai[i+1] - ai[i]; 3024 sum = b[i]; 3025 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3026 v += nz; 3027 vi += nz; 3028 x[i] = sum; 3029 } 3030 3031 /* backward solve the upper triangular */ 3032 /* v = aa + ai[n+1]; 3033 vi = aj + ai[n+1]; */ 3034 v = aa + adiag[n-1]; 3035 vi = aj + adiag[n-1]; 3036 for (i=n-1; i>=0; i--){ 3037 nz = adiag[i] - adiag[i+1]-1; 3038 sum = x[i]; 3039 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3040 v += nz; 3041 vi += nz; vi++; 3042 x[i] = *v++ *sum; /* x[i]=aa[adiag[i]]*sum; v++; */ 3043 } 3044 3045 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 3046 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3047 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3048 PetscFunctionReturn(0); 3049 } 3050 3051 #if defined(OLD_ROUTINE_TO_BE_REPLACED) 3052 #undef __FUNCT__ 3053 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct" 3054 PetscErrorCode MatSolve_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx) 3055 { 3056 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3057 IS iscol = a->col,isrow = a->row; 3058 PetscErrorCode ierr; 3059 PetscInt i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,nz,k; 3060 const PetscInt *rout,*cout,*r,*c; 3061 PetscScalar *x,*tmp,*tmps,sum; 3062 const PetscScalar *b; 3063 const MatScalar *aa = a->a,*v; 3064 3065 PetscFunctionBegin; 3066 if (!n) PetscFunctionReturn(0); 3067 3068 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3069 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3070 tmp = a->solve_work; 3071 3072 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 3073 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 3074 3075 /* forward solve the lower triangular */ 3076 tmp[0] = b[*r++]; 3077 tmps = tmp; 3078 v = aa; 3079 vi = aj; 3080 for (i=1; i<n; i++) { 3081 nz = ai[i+1] - ai[i]; 3082 sum = b[*r++]; 3083 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 3084 tmp[i] = sum; 3085 v += nz; vi += nz; 3086 } 3087 3088 /* backward solve the upper triangular */ 3089 k = n+1; 3090 v = aa + ai[k]; /* 1st entry of U(n-1,:) */ 3091 vi = aj + ai[k]; 3092 for (i=n-1; i>=0; i--){ 3093 k = 2*n-i; 3094 nz = ai[k +1] - ai[k] - 1; 3095 sum = tmp[i]; 3096 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 3097 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 3098 v += nz+1; vi += nz+1; 3099 } 3100 3101 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 3102 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 3103 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3104 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3105 ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr); 3106 PetscFunctionReturn(0); 3107 } 3108 #endif 3109 3110 #undef __FUNCT__ 3111 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct" 3112 PetscErrorCode MatSolve_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx) 3113 { 3114 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3115 IS iscol = a->col,isrow = a->row; 3116 PetscErrorCode ierr; 3117 PetscInt i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz; 3118 const PetscInt *rout,*cout,*r,*c; 3119 PetscScalar *x,*tmp,sum; 3120 const PetscScalar *b; 3121 const MatScalar *aa = a->a,*v; 3122 3123 PetscFunctionBegin; 3124 if (!n) PetscFunctionReturn(0); 3125 3126 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3127 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3128 tmp = a->solve_work; 3129 3130 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 3131 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 3132 3133 /* forward solve the lower triangular */ 3134 tmp[0] = b[r[0]]; 3135 v = aa; 3136 vi = aj; 3137 for (i=1; i<n; i++) { 3138 nz = ai[i+1] - ai[i]; 3139 sum = b[r[i]]; 3140 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3141 tmp[i] = sum; 3142 v += nz; vi += nz; 3143 } 3144 3145 /* backward solve the upper triangular */ 3146 v = aa + adiag[n-1]; /* 1st entry of U(n-1,:) */ 3147 vi = aj + adiag[n-1]; 3148 for (i=n-1; i>=0; i--){ 3149 nz = adiag[i]-adiag[i+1]-1; 3150 sum = tmp[i]; 3151 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3152 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 3153 v += nz+1; vi += nz+1; 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