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_v2; 608 } else { 609 C->ops->solve = MatSolve_SeqAIJ_newdatastruct_v2; 610 } 611 612 C->ops->solveadd = 0; 613 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ_newdatastruct_v2; 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 1301 #undef __FUNCT__ 1302 #define __FUNCT__ "MatSolveTranspose_SeqAIJ_newdatastruct_v2" 1303 PetscErrorCode MatSolveTranspose_SeqAIJ_newdatastruct_v2(Mat A,Vec bb,Vec xx) 1304 { 1305 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1306 IS iscol = a->col,isrow = a->row; 1307 PetscErrorCode ierr; 1308 const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi; 1309 PetscInt i,n = A->rmap->n,j; 1310 PetscInt nz; 1311 PetscScalar *x,*tmp,s1; 1312 const MatScalar *aa = a->a,*v; 1313 const PetscScalar *b; 1314 1315 PetscFunctionBegin; 1316 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1317 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1318 tmp = a->solve_work; 1319 1320 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1321 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1322 1323 /* copy the b into temp work space according to permutation */ 1324 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1325 1326 /* forward solve the U^T */ 1327 for (i=0; i<n; i++) { 1328 v = aa + adiag[i+1] + 1; 1329 vi = aj + adiag[i+1] + 1; 1330 nz = adiag[i] - adiag[i+1] - 1; 1331 s1 = tmp[i]; 1332 s1 *= v[nz]; /* multiply by inverse of diagonal entry */ 1333 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1334 tmp[i] = s1; 1335 } 1336 1337 /* backward solve the L^T */ 1338 for (i=n-1; i>=0; i--){ 1339 v = aa + ai[i]; 1340 vi = aj + ai[i]; 1341 nz = ai[i+1] - ai[i]; 1342 s1 = tmp[i]; 1343 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1344 } 1345 1346 /* copy tmp into x according to permutation */ 1347 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1348 1349 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1350 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1351 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1352 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1353 1354 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1355 PetscFunctionReturn(0); 1356 } 1357 1358 #undef __FUNCT__ 1359 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ" 1360 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx) 1361 { 1362 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1363 IS iscol = a->col,isrow = a->row; 1364 PetscErrorCode ierr; 1365 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1366 PetscInt i,n = A->rmap->n,j; 1367 PetscInt nz; 1368 PetscScalar *x,*tmp,s1; 1369 const MatScalar *aa = a->a,*v; 1370 const PetscScalar *b; 1371 1372 PetscFunctionBegin; 1373 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1374 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1375 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1376 tmp = a->solve_work; 1377 1378 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1379 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1380 1381 /* copy the b into temp work space according to permutation */ 1382 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1383 1384 /* forward solve the U^T */ 1385 for (i=0; i<n; i++) { 1386 v = aa + diag[i] ; 1387 vi = aj + diag[i] + 1; 1388 nz = ai[i+1] - diag[i] - 1; 1389 s1 = tmp[i]; 1390 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1391 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1392 tmp[i] = s1; 1393 } 1394 1395 /* backward solve the L^T */ 1396 for (i=n-1; i>=0; i--){ 1397 v = aa + diag[i] - 1 ; 1398 vi = aj + diag[i] - 1 ; 1399 nz = diag[i] - ai[i]; 1400 s1 = tmp[i]; 1401 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1402 } 1403 1404 /* copy tmp into x according to permutation */ 1405 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1406 1407 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1408 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1409 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1410 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1411 1412 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1413 PetscFunctionReturn(0); 1414 } 1415 1416 /* ----------------------------------------------------------------*/ 1417 EXTERN PetscErrorCode Mat_CheckInode(Mat,PetscTruth); 1418 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth); 1419 1420 /* 1421 ilu() under revised new data structure. 1422 Factored arrays bj and ba are stored as 1423 L(0,:), L(1,:), ...,L(n-1,:), U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:) 1424 1425 bi=fact->i is an array of size n+1, in which 1426 bi+ 1427 bi[i]: points to 1st entry of L(i,:),i=0,...,n-1 1428 bi[n]: points to L(n-1,n-1)+1 1429 1430 bdiag=fact->diag is an array of size n+1,in which 1431 bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1 1432 bdiag[n]: points to entry of U(n-1,0)-1 1433 1434 U(i,:) contains bdiag[i] as its last entry, i.e., 1435 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 1436 */ 1437 #undef __FUNCT__ 1438 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct" 1439 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1440 { 1441 1442 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1443 PetscErrorCode ierr; 1444 PetscInt n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag; 1445 PetscInt i,j,nz,*bi,*bj,*bdiag; 1446 PetscTruth missing; 1447 IS isicol; 1448 1449 PetscFunctionBegin; 1450 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); 1451 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 1452 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 1453 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1454 1455 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr); 1456 b = (Mat_SeqAIJ*)(fact)->data; 1457 1458 /* allocate matrix arrays for new data structure */ 1459 ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,n+1,PetscInt,&b->i);CHKERRQ(ierr); 1460 ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1461 b->singlemalloc = PETSC_TRUE; 1462 if (!b->diag){ 1463 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr); 1464 ierr = PetscLogObjectMemory(fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1465 } 1466 bdiag = b->diag; 1467 1468 if (n > 0) { 1469 ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr); 1470 } 1471 1472 /* set bi and bj with new data structure */ 1473 bi = b->i; 1474 bj = b->j; 1475 1476 /* L part */ 1477 bi[0] = 0; 1478 for (i=0; i<n; i++){ 1479 nz = adiag[i] - ai[i]; 1480 bi[i+1] = bi[i] + nz; 1481 aj = a->j + ai[i]; 1482 for (j=0; j<nz; j++){ 1483 *bj = aj[j]; bj++; 1484 } 1485 } 1486 1487 /* U part */ 1488 bdiag[n] = bi[n]-1; 1489 for (i=n-1; i>=0; i--){ 1490 nz = ai[i+1] - adiag[i] - 1; 1491 aj = a->j + adiag[i] + 1; 1492 for (j=0; j<nz; j++){ 1493 *bj = aj[j]; bj++; 1494 } 1495 /* diag[i] */ 1496 *bj = i; bj++; 1497 bdiag[i] = bdiag[i+1] + nz + 1; 1498 } 1499 1500 fact->factor = MAT_FACTOR_ILU; 1501 fact->info.factor_mallocs = 0; 1502 fact->info.fill_ratio_given = info->fill; 1503 fact->info.fill_ratio_needed = 1.0; 1504 fact->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 1505 1506 b = (Mat_SeqAIJ*)(fact)->data; 1507 b->row = isrow; 1508 b->col = iscol; 1509 b->icol = isicol; 1510 ierr = PetscMalloc((fact->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1511 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1512 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1513 PetscFunctionReturn(0); 1514 } 1515 1516 #undef __FUNCT__ 1517 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_newdatastruct" 1518 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1519 { 1520 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1521 IS isicol; 1522 PetscErrorCode ierr; 1523 const PetscInt *r,*ic; 1524 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j; 1525 PetscInt *bi,*cols,nnz,*cols_lvl; 1526 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1527 PetscInt i,levels,diagonal_fill; 1528 PetscTruth col_identity,row_identity; 1529 PetscReal f; 1530 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1531 PetscBT lnkbt; 1532 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1533 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1534 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1535 1536 PetscFunctionBegin; 1537 /* printf("MatILUFactorSymbolic_SeqAIJ_newdatastruct ...\n"); */ 1538 levels = (PetscInt)info->levels; 1539 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1540 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1541 1542 if (!levels && row_identity && col_identity) { 1543 /* special case: ilu(0) with natural ordering */ 1544 ierr = MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1545 PetscFunctionReturn(0); 1546 } 1547 1548 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); 1549 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1550 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1551 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1552 1553 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1554 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1555 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1556 bi[0] = bdiag[0] = 0; 1557 1558 ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr); 1559 1560 /* create a linked list for storing column indices of the active row */ 1561 nlnk = n + 1; 1562 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1563 1564 /* initial FreeSpace size is f*(ai[n]+1) */ 1565 f = info->fill; 1566 diagonal_fill = (PetscInt)info->diagonal_fill; 1567 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1568 current_space = free_space; 1569 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1570 current_space_lvl = free_space_lvl; 1571 1572 for (i=0; i<n; i++) { 1573 nzi = 0; 1574 /* copy current row into linked list */ 1575 nnz = ai[r[i]+1] - ai[r[i]]; 1576 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1577 cols = aj + ai[r[i]]; 1578 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1579 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1580 nzi += nlnk; 1581 1582 /* make sure diagonal entry is included */ 1583 if (diagonal_fill && lnk[i] == -1) { 1584 fm = n; 1585 while (lnk[fm] < i) fm = lnk[fm]; 1586 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1587 lnk[fm] = i; 1588 lnk_lvl[i] = 0; 1589 nzi++; dcount++; 1590 } 1591 1592 /* add pivot rows into the active row */ 1593 nzbd = 0; 1594 prow = lnk[n]; 1595 while (prow < i) { 1596 nnz = bdiag[prow]; 1597 cols = bj_ptr[prow] + nnz + 1; 1598 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1599 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1600 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1601 nzi += nlnk; 1602 prow = lnk[prow]; 1603 nzbd++; 1604 } 1605 bdiag[i] = nzbd; 1606 bi[i+1] = bi[i] + nzi; 1607 1608 /* if free space is not available, make more free space */ 1609 if (current_space->local_remaining<nzi) { 1610 nnz = 2*nzi*(n - i); /* estimated and max additional space needed */ 1611 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1612 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1613 reallocs++; 1614 } 1615 1616 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1617 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1618 bj_ptr[i] = current_space->array; 1619 bjlvl_ptr[i] = current_space_lvl->array; 1620 1621 /* make sure the active row i has diagonal entry */ 1622 if (*(bj_ptr[i]+bdiag[i]) != i) { 1623 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 1624 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1625 } 1626 1627 current_space->array += nzi; 1628 current_space->local_used += nzi; 1629 current_space->local_remaining -= nzi; 1630 current_space_lvl->array += nzi; 1631 current_space_lvl->local_used += nzi; 1632 current_space_lvl->local_remaining -= nzi; 1633 } 1634 1635 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1636 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1637 1638 /* destroy list of free space and other temporary arrays */ 1639 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 1640 1641 /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */ 1642 ierr = PetscFreeSpaceContiguous_LU_v2(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 1643 1644 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1645 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1646 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 1647 1648 #if defined(PETSC_USE_INFO) 1649 { 1650 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1651 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 1652 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1653 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 1654 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1655 if (diagonal_fill) { 1656 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 1657 } 1658 } 1659 #endif 1660 1661 /* put together the new matrix */ 1662 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 1663 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 1664 b = (Mat_SeqAIJ*)(fact)->data; 1665 b->free_a = PETSC_TRUE; 1666 b->free_ij = PETSC_TRUE; 1667 b->singlemalloc = PETSC_FALSE; 1668 ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 1669 b->j = bj; 1670 b->i = bi; 1671 b->diag = bdiag; 1672 b->ilen = 0; 1673 b->imax = 0; 1674 b->row = isrow; 1675 b->col = iscol; 1676 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1677 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1678 b->icol = isicol; 1679 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1680 /* In b structure: Free imax, ilen, old a, old j. 1681 Allocate bdiag, solve_work, new a, new j */ 1682 ierr = PetscLogObjectMemory(fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1683 b->maxnz = b->nz = bdiag[0]+1; 1684 (fact)->info.factor_mallocs = reallocs; 1685 (fact)->info.fill_ratio_given = f; 1686 (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 1687 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 1688 /* ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */ 1689 PetscFunctionReturn(0); 1690 } 1691 1692 #undef __FUNCT__ 1693 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ" 1694 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1695 { 1696 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1697 IS isicol; 1698 PetscErrorCode ierr; 1699 const PetscInt *r,*ic; 1700 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,d; 1701 PetscInt *bi,*cols,nnz,*cols_lvl; 1702 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1703 PetscInt i,levels,diagonal_fill; 1704 PetscTruth col_identity,row_identity; 1705 PetscReal f; 1706 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1707 PetscBT lnkbt; 1708 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1709 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1710 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1711 PetscTruth missing; 1712 PetscTruth newdatastruct=PETSC_FALSE; 1713 1714 PetscFunctionBegin; 1715 ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 1716 if(newdatastruct){ 1717 ierr = MatILUFactorSymbolic_SeqAIJ_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1718 PetscFunctionReturn(0); 1719 } 1720 1721 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); 1722 f = info->fill; 1723 levels = (PetscInt)info->levels; 1724 diagonal_fill = (PetscInt)info->diagonal_fill; 1725 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1726 1727 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1728 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1729 if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */ 1730 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr); 1731 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1732 1733 fact->factor = MAT_FACTOR_ILU; 1734 (fact)->info.factor_mallocs = 0; 1735 (fact)->info.fill_ratio_given = info->fill; 1736 (fact)->info.fill_ratio_needed = 1.0; 1737 b = (Mat_SeqAIJ*)(fact)->data; 1738 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 1739 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 1740 b->row = isrow; 1741 b->col = iscol; 1742 b->icol = isicol; 1743 ierr = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1744 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1745 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1746 ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1747 PetscFunctionReturn(0); 1748 } 1749 1750 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1751 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1752 1753 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1754 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1755 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1756 bi[0] = bdiag[0] = 0; 1757 1758 ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr); 1759 1760 /* create a linked list for storing column indices of the active row */ 1761 nlnk = n + 1; 1762 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1763 1764 /* initial FreeSpace size is f*(ai[n]+1) */ 1765 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1766 current_space = free_space; 1767 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1768 current_space_lvl = free_space_lvl; 1769 1770 for (i=0; i<n; i++) { 1771 nzi = 0; 1772 /* copy current row into linked list */ 1773 nnz = ai[r[i]+1] - ai[r[i]]; 1774 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1775 cols = aj + ai[r[i]]; 1776 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1777 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1778 nzi += nlnk; 1779 1780 /* make sure diagonal entry is included */ 1781 if (diagonal_fill && lnk[i] == -1) { 1782 fm = n; 1783 while (lnk[fm] < i) fm = lnk[fm]; 1784 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1785 lnk[fm] = i; 1786 lnk_lvl[i] = 0; 1787 nzi++; dcount++; 1788 } 1789 1790 /* add pivot rows into the active row */ 1791 nzbd = 0; 1792 prow = lnk[n]; 1793 while (prow < i) { 1794 nnz = bdiag[prow]; 1795 cols = bj_ptr[prow] + nnz + 1; 1796 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1797 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1798 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1799 nzi += nlnk; 1800 prow = lnk[prow]; 1801 nzbd++; 1802 } 1803 bdiag[i] = nzbd; 1804 bi[i+1] = bi[i] + nzi; 1805 1806 /* if free space is not available, make more free space */ 1807 if (current_space->local_remaining<nzi) { 1808 nnz = nzi*(n - i); /* estimated and max additional space needed */ 1809 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1810 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1811 reallocs++; 1812 } 1813 1814 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1815 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1816 bj_ptr[i] = current_space->array; 1817 bjlvl_ptr[i] = current_space_lvl->array; 1818 1819 /* make sure the active row i has diagonal entry */ 1820 if (*(bj_ptr[i]+bdiag[i]) != i) { 1821 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 1822 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1823 } 1824 1825 current_space->array += nzi; 1826 current_space->local_used += nzi; 1827 current_space->local_remaining -= nzi; 1828 current_space_lvl->array += nzi; 1829 current_space_lvl->local_used += nzi; 1830 current_space_lvl->local_remaining -= nzi; 1831 } 1832 1833 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1834 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1835 1836 /* destroy list of free space and other temporary arrays */ 1837 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 1838 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */ 1839 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1840 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1841 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 1842 1843 #if defined(PETSC_USE_INFO) 1844 { 1845 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1846 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 1847 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1848 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 1849 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1850 if (diagonal_fill) { 1851 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 1852 } 1853 } 1854 #endif 1855 1856 /* put together the new matrix */ 1857 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 1858 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 1859 b = (Mat_SeqAIJ*)(fact)->data; 1860 b->free_a = PETSC_TRUE; 1861 b->free_ij = PETSC_TRUE; 1862 b->singlemalloc = PETSC_FALSE; 1863 ierr = PetscMalloc(bi[n]*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 1864 b->j = bj; 1865 b->i = bi; 1866 for (i=0; i<n; i++) bdiag[i] += bi[i]; 1867 b->diag = bdiag; 1868 b->ilen = 0; 1869 b->imax = 0; 1870 b->row = isrow; 1871 b->col = iscol; 1872 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1873 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1874 b->icol = isicol; 1875 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1876 /* In b structure: Free imax, ilen, old a, old j. 1877 Allocate bdiag, solve_work, new a, new j */ 1878 ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1879 b->maxnz = b->nz = bi[n] ; 1880 (fact)->info.factor_mallocs = reallocs; 1881 (fact)->info.fill_ratio_given = f; 1882 (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1883 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1884 ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1885 PetscFunctionReturn(0); 1886 } 1887 1888 #undef __FUNCT__ 1889 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ_newdatastruct" 1890 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info) 1891 { 1892 Mat C = B; 1893 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 1894 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 1895 IS ip=b->row,iip = b->icol; 1896 PetscErrorCode ierr; 1897 const PetscInt *rip,*riip; 1898 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp; 1899 PetscInt *ai=a->i,*aj=a->j; 1900 PetscInt k,jmin,jmax,*c2r,*il,col,nexti,ili,nz; 1901 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 1902 PetscTruth perm_identity; 1903 1904 LUShift_Ctx sctx; 1905 PetscInt newshift; 1906 PetscReal rs; 1907 MatScalar d,*v; 1908 1909 PetscFunctionBegin; 1910 /* MatPivotSetUp(): initialize shift context sctx */ 1911 ierr = PetscMemzero(&sctx,sizeof(LUShift_Ctx));CHKERRQ(ierr); 1912 1913 /* if both shift schemes are chosen by user, only use info->shiftpd */ 1914 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 1915 sctx.shift_top = info->zeropivot; 1916 for (i=0; i<mbs; i++) { 1917 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 1918 d = (aa)[a->diag[i]]; 1919 rs = -PetscAbsScalar(d) - PetscRealPart(d); 1920 v = aa+ai[i]; 1921 nz = ai[i+1] - ai[i]; 1922 for (j=0; j<nz; j++) 1923 rs += PetscAbsScalar(v[j]); 1924 if (rs>sctx.shift_top) sctx.shift_top = rs; 1925 } 1926 sctx.shift_top *= 1.1; 1927 sctx.nshift_max = 5; 1928 sctx.shift_lo = 0.; 1929 sctx.shift_hi = 1.; 1930 } 1931 1932 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 1933 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 1934 1935 /* allocate working arrays 1936 c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col 1937 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 1938 */ 1939 ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&c2r);CHKERRQ(ierr); 1940 1941 do { 1942 sctx.lushift = PETSC_FALSE; 1943 1944 for (i=0; i<mbs; i++) c2r[i] = mbs; 1945 il[0] = 0; 1946 1947 for (k = 0; k<mbs; k++){ 1948 /* zero rtmp */ 1949 nz = bi[k+1] - bi[k]; 1950 bjtmp = bj + bi[k]; 1951 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 1952 1953 /* load in initial unfactored row */ 1954 bval = ba + bi[k]; 1955 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 1956 for (j = jmin; j < jmax; j++){ 1957 col = riip[aj[j]]; 1958 if (col >= k){ /* only take upper triangular entry */ 1959 rtmp[col] = aa[j]; 1960 *bval++ = 0.0; /* for in-place factorization */ 1961 } 1962 } 1963 /* shift the diagonal of the matrix: ZeropivotApply() */ 1964 rtmp[k] += sctx.shift_amount; /* shift the diagonal of the matrix */ 1965 1966 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 1967 dk = rtmp[k]; 1968 i = c2r[k]; /* first row to be added to k_th row */ 1969 1970 while (i < k){ 1971 nexti = c2r[i]; /* next row to be added to k_th row */ 1972 1973 /* compute multiplier, update diag(k) and U(i,k) */ 1974 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 1975 uikdi = - ba[ili]*ba[bdiag[i]]; /* diagonal(k) */ 1976 dk += uikdi*ba[ili]; /* update diag[k] */ 1977 ba[ili] = uikdi; /* -U(i,k) */ 1978 1979 /* add multiple of row i to k-th row */ 1980 jmin = ili + 1; jmax = bi[i+1]; 1981 if (jmin < jmax){ 1982 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 1983 /* update il and c2r for row i */ 1984 il[i] = jmin; 1985 j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i; 1986 } 1987 i = nexti; 1988 } 1989 1990 /* copy data into U(k,:) */ 1991 rs = 0.0; 1992 jmin = bi[k]; jmax = bi[k+1]-1; 1993 if (jmin < jmax) { 1994 for (j=jmin; j<jmax; j++){ 1995 col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]); 1996 } 1997 /* add the k-th row into il and c2r */ 1998 il[k] = jmin; 1999 i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k; 2000 } 2001 2002 /* MatPivotCheck() */ 2003 sctx.rs = rs; 2004 sctx.pv = dk; 2005 if (info->shiftnz){ 2006 ierr = MatPivotCheck_nz(info,sctx,k,newshift);CHKERRQ(ierr); 2007 } else if (info->shiftpd){ 2008 ierr = MatPivotCheck_pd(info,sctx,k,newshift);CHKERRQ(ierr); 2009 } else if (info->shiftinblocks){ 2010 ierr = MatPivotCheck_inblocks(info,sctx,k,newshift);CHKERRQ(ierr); 2011 } else { 2012 ierr = MatPivotCheck_none(info,sctx,k,newshift);CHKERRQ(ierr); 2013 } 2014 dk = sctx.pv; 2015 if (newshift == 1) break; 2016 2017 ba[bdiag[k]] = 1.0/dk; /* U(k,k) */ 2018 } 2019 } while (sctx.lushift); 2020 2021 ierr = PetscFree3(rtmp,il,c2r);CHKERRQ(ierr); 2022 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2023 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2024 2025 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2026 if (perm_identity){ 2027 (B)->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_newdatastruct; 2028 (B)->ops->solvetranspose = 0; 2029 (B)->ops->forwardsolve = 0; 2030 (B)->ops->backwardsolve = 0; 2031 } else { 2032 (B)->ops->solve = MatSolve_SeqSBAIJ_1_newdatastruct; 2033 (B)->ops->solvetranspose = 0; 2034 (B)->ops->forwardsolve = 0; 2035 (B)->ops->backwardsolve = 0; 2036 } 2037 2038 C->assembled = PETSC_TRUE; 2039 C->preallocated = PETSC_TRUE; 2040 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2041 2042 /* MatPivotView() */ 2043 if (sctx.nshift){ 2044 if (info->shiftpd) { 2045 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); 2046 } else if (info->shiftnz) { 2047 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2048 } else if (info->shiftinblocks){ 2049 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftinblocks);CHKERRQ(ierr); 2050 } 2051 } 2052 PetscFunctionReturn(0); 2053 } 2054 2055 #undef __FUNCT__ 2056 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ" 2057 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 2058 { 2059 Mat C = B; 2060 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2061 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2062 IS ip=b->row,iip = b->icol; 2063 PetscErrorCode ierr; 2064 const PetscInt *rip,*riip; 2065 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol,*bjtmp; 2066 PetscInt *ai=a->i,*aj=a->j; 2067 PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz; 2068 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2069 PetscReal zeropivot,rs,shiftnz; 2070 PetscReal shiftpd; 2071 ChShift_Ctx sctx; 2072 PetscInt newshift; 2073 PetscTruth perm_identity; 2074 2075 PetscFunctionBegin; 2076 shiftnz = info->shiftnz; 2077 shiftpd = info->shiftpd; 2078 zeropivot = info->zeropivot; 2079 2080 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2081 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2082 2083 /* initialization */ 2084 ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr); 2085 sctx.shift_amount = 0; 2086 sctx.nshift = 0; 2087 do { 2088 sctx.chshift = PETSC_FALSE; 2089 for (i=0; i<mbs; i++) jl[i] = mbs; 2090 il[0] = 0; 2091 2092 for (k = 0; k<mbs; k++){ 2093 /* zero rtmp */ 2094 nz = bi[k+1] - bi[k]; 2095 bjtmp = bj + bi[k]; 2096 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2097 2098 bval = ba + bi[k]; 2099 /* initialize k-th row by the perm[k]-th row of A */ 2100 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2101 for (j = jmin; j < jmax; j++){ 2102 col = riip[aj[j]]; 2103 if (col >= k){ /* only take upper triangular entry */ 2104 rtmp[col] = aa[j]; 2105 *bval++ = 0.0; /* for in-place factorization */ 2106 } 2107 } 2108 /* shift the diagonal of the matrix */ 2109 if (sctx.nshift) rtmp[k] += sctx.shift_amount; 2110 2111 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2112 dk = rtmp[k]; 2113 i = jl[k]; /* first row to be added to k_th row */ 2114 2115 while (i < k){ 2116 nexti = jl[i]; /* next row to be added to k_th row */ 2117 2118 /* compute multiplier, update diag(k) and U(i,k) */ 2119 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2120 uikdi = - ba[ili]*ba[bi[i]]; /* diagonal(k) */ 2121 dk += uikdi*ba[ili]; 2122 ba[ili] = uikdi; /* -U(i,k) */ 2123 2124 /* add multiple of row i to k-th row */ 2125 jmin = ili + 1; jmax = bi[i+1]; 2126 if (jmin < jmax){ 2127 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2128 /* update il and jl for row i */ 2129 il[i] = jmin; 2130 j = bj[jmin]; jl[i] = jl[j]; jl[j] = i; 2131 } 2132 i = nexti; 2133 } 2134 2135 /* shift the diagonals when zero pivot is detected */ 2136 /* compute rs=sum of abs(off-diagonal) */ 2137 rs = 0.0; 2138 jmin = bi[k]+1; 2139 nz = bi[k+1] - jmin; 2140 bcol = bj + jmin; 2141 for (j=0; j<nz; j++) { 2142 rs += PetscAbsScalar(rtmp[bcol[j]]); 2143 } 2144 2145 sctx.rs = rs; 2146 sctx.pv = dk; 2147 ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr); 2148 2149 if (newshift == 1) { 2150 if (!sctx.shift_amount) { 2151 sctx.shift_amount = 1e-5; 2152 } 2153 break; 2154 } 2155 2156 /* copy data into U(k,:) */ 2157 ba[bi[k]] = 1.0/dk; /* U(k,k) */ 2158 jmin = bi[k]+1; jmax = bi[k+1]; 2159 if (jmin < jmax) { 2160 for (j=jmin; j<jmax; j++){ 2161 col = bj[j]; ba[j] = rtmp[col]; 2162 } 2163 /* add the k-th row into il and jl */ 2164 il[k] = jmin; 2165 i = bj[jmin]; jl[k] = jl[i]; jl[i] = k; 2166 } 2167 } 2168 } while (sctx.chshift); 2169 ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr); 2170 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2171 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2172 2173 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2174 if (perm_identity){ 2175 (B)->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2176 (B)->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2177 (B)->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering; 2178 (B)->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering; 2179 } else { 2180 (B)->ops->solve = MatSolve_SeqSBAIJ_1; 2181 (B)->ops->solvetranspose = MatSolve_SeqSBAIJ_1; 2182 (B)->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1; 2183 (B)->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1; 2184 } 2185 2186 C->assembled = PETSC_TRUE; 2187 C->preallocated = PETSC_TRUE; 2188 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2189 if (sctx.nshift){ 2190 if (shiftnz) { 2191 ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2192 } else if (shiftpd) { 2193 ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2194 } 2195 } 2196 PetscFunctionReturn(0); 2197 } 2198 2199 /* 2200 icc() under revised new data structure. 2201 Factored arrays bj and ba are stored as 2202 U(0,:),...,U(i,:),U(n-1,:) 2203 2204 ui=fact->i is an array of size n+1, in which 2205 ui+ 2206 ui[i]: points to 1st entry of U(i,:),i=0,...,n-1 2207 ui[n]: points to U(n-1,n-1)+1 2208 2209 udiag=fact->diag is an array of size n,in which 2210 udiag[i]: points to diagonal of U(i,:), i=0,...,n-1 2211 2212 U(i,:) contains udiag[i] as its last entry, i.e., 2213 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 2214 */ 2215 2216 #undef __FUNCT__ 2217 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ_newdatastruct" 2218 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2219 { 2220 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2221 Mat_SeqSBAIJ *b; 2222 PetscErrorCode ierr; 2223 PetscTruth perm_identity,missing; 2224 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2225 const PetscInt *rip,*riip; 2226 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2227 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2228 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2229 PetscReal fill=info->fill,levels=info->levels; 2230 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2231 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2232 PetscBT lnkbt; 2233 IS iperm; 2234 2235 PetscFunctionBegin; 2236 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); 2237 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2238 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2239 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2240 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2241 2242 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2243 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2244 ui[0] = 0; 2245 2246 /* ICC(0) without matrix ordering: simply rearrange column indices */ 2247 if (!levels && perm_identity) { 2248 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2249 cols = uj; 2250 for (i=0; i<am; i++) { 2251 ncols = ai[i+1] - a->diag[i]; 2252 ui[i+1] = ui[i] + ncols; 2253 udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */ 2254 2255 aj = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */ 2256 ncols--; /* exclude diagonal */ 2257 for (j=0; j<ncols; j++) *cols++ = aj[j]; 2258 *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */ 2259 } 2260 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2261 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2262 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2263 2264 /* initialization */ 2265 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2266 2267 /* jl: linked list for storing indices of the pivot rows 2268 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2269 ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr); 2270 for (i=0; i<am; i++){ 2271 jl[i] = am; il[i] = 0; 2272 } 2273 2274 /* create and initialize a linked list for storing column indices of the active row k */ 2275 nlnk = am + 1; 2276 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2277 2278 /* initial FreeSpace size is fill*(ai[am]+1) */ 2279 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2280 current_space = free_space; 2281 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2282 current_space_lvl = free_space_lvl; 2283 2284 for (k=0; k<am; k++){ /* for each active row k */ 2285 /* initialize lnk by the column indices of row rip[k] of A */ 2286 nzk = 0; 2287 ncols = ai[rip[k]+1] - ai[rip[k]]; 2288 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2289 ncols_upper = 0; 2290 for (j=0; j<ncols; j++){ 2291 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2292 if (riip[i] >= k){ /* only take upper triangular entry */ 2293 ajtmp[ncols_upper] = i; 2294 ncols_upper++; 2295 } 2296 } 2297 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2298 nzk += nlnk; 2299 2300 /* update lnk by computing fill-in for each pivot row to be merged in */ 2301 prow = jl[k]; /* 1st pivot row */ 2302 2303 while (prow < k){ 2304 nextprow = jl[prow]; 2305 2306 /* merge prow into k-th row */ 2307 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2308 jmax = ui[prow+1]; 2309 ncols = jmax-jmin; 2310 i = jmin - ui[prow]; 2311 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2312 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2313 j = *(uj - 1); 2314 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2315 nzk += nlnk; 2316 2317 /* update il and jl for prow */ 2318 if (jmin < jmax){ 2319 il[prow] = jmin; 2320 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2321 } 2322 prow = nextprow; 2323 } 2324 2325 /* if free space is not available, make more free space */ 2326 if (current_space->local_remaining<nzk) { 2327 i = am - k + 1; /* num of unfactored rows */ 2328 i *= PetscMin(nzk, i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2329 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2330 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2331 reallocs++; 2332 } 2333 2334 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2335 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2336 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2337 2338 /* add the k-th row into il and jl */ 2339 if (nzk > 1){ 2340 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2341 jl[k] = jl[i]; jl[i] = k; 2342 il[k] = ui[k] + 1; 2343 } 2344 uj_ptr[k] = current_space->array; 2345 uj_lvl_ptr[k] = current_space_lvl->array; 2346 2347 current_space->array += nzk; 2348 current_space->local_used += nzk; 2349 current_space->local_remaining -= nzk; 2350 2351 current_space_lvl->array += nzk; 2352 current_space_lvl->local_used += nzk; 2353 current_space_lvl->local_remaining -= nzk; 2354 2355 ui[k+1] = ui[k] + nzk; 2356 } 2357 2358 #if defined(PETSC_USE_INFO) 2359 if (ai[am] != 0) { 2360 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2361 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2362 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2363 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2364 } else { 2365 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2366 } 2367 #endif 2368 2369 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2370 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2371 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2372 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2373 2374 /* destroy list of free space and other temporary array(s) */ 2375 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2376 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor in newdatastruct */ 2377 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2378 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2379 2380 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2381 2382 /* put together the new matrix in MATSEQSBAIJ format */ 2383 2384 b = (Mat_SeqSBAIJ*)(fact)->data; 2385 b->singlemalloc = PETSC_FALSE; 2386 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2387 b->j = uj; 2388 b->i = ui; 2389 b->diag = udiag; 2390 b->free_diag = PETSC_TRUE; 2391 b->ilen = 0; 2392 b->imax = 0; 2393 b->row = perm; 2394 b->col = perm; 2395 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2396 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2397 b->icol = iperm; 2398 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2399 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2400 ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2401 b->maxnz = b->nz = ui[am]; 2402 b->free_a = PETSC_TRUE; 2403 b->free_ij = PETSC_TRUE; 2404 2405 (fact)->info.factor_mallocs = reallocs; 2406 (fact)->info.fill_ratio_given = fill; 2407 if (ai[am] != 0) { 2408 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2409 } else { 2410 (fact)->info.fill_ratio_needed = 0.0; 2411 } 2412 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct; 2413 PetscFunctionReturn(0); 2414 } 2415 2416 #undef __FUNCT__ 2417 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ" 2418 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2419 { 2420 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2421 Mat_SeqSBAIJ *b; 2422 PetscErrorCode ierr; 2423 PetscTruth perm_identity,missing; 2424 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2425 const PetscInt *rip,*riip; 2426 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2427 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2428 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2429 PetscReal fill=info->fill,levels=info->levels; 2430 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2431 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2432 PetscBT lnkbt; 2433 IS iperm; 2434 PetscTruth newdatastruct=PETSC_FALSE; 2435 2436 PetscFunctionBegin; 2437 ierr = PetscOptionsGetTruth(PETSC_NULL,"-icc_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 2438 if(newdatastruct){ 2439 ierr = MatICCFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr); 2440 PetscFunctionReturn(0); 2441 } 2442 2443 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); 2444 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2445 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2446 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2447 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2448 2449 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2450 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2451 ui[0] = 0; 2452 2453 /* ICC(0) without matrix ordering: simply copies fill pattern */ 2454 if (!levels && perm_identity) { 2455 2456 for (i=0; i<am; i++) { 2457 ui[i+1] = ui[i] + ai[i+1] - a->diag[i]; 2458 udiag[i] = ui[i]; 2459 } 2460 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2461 cols = uj; 2462 for (i=0; i<am; i++) { 2463 aj = a->j + a->diag[i]; 2464 ncols = ui[i+1] - ui[i]; 2465 for (j=0; j<ncols; j++) *cols++ = *aj++; 2466 } 2467 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2468 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2469 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2470 2471 /* initialization */ 2472 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2473 2474 /* jl: linked list for storing indices of the pivot rows 2475 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2476 ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr); 2477 for (i=0; i<am; i++){ 2478 jl[i] = am; il[i] = 0; 2479 } 2480 2481 /* create and initialize a linked list for storing column indices of the active row k */ 2482 nlnk = am + 1; 2483 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2484 2485 /* initial FreeSpace size is fill*(ai[am]+1) */ 2486 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2487 current_space = free_space; 2488 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2489 current_space_lvl = free_space_lvl; 2490 2491 for (k=0; k<am; k++){ /* for each active row k */ 2492 /* initialize lnk by the column indices of row rip[k] of A */ 2493 nzk = 0; 2494 ncols = ai[rip[k]+1] - ai[rip[k]]; 2495 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2496 ncols_upper = 0; 2497 for (j=0; j<ncols; j++){ 2498 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2499 if (riip[i] >= k){ /* only take upper triangular entry */ 2500 ajtmp[ncols_upper] = i; 2501 ncols_upper++; 2502 } 2503 } 2504 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2505 nzk += nlnk; 2506 2507 /* update lnk by computing fill-in for each pivot row to be merged in */ 2508 prow = jl[k]; /* 1st pivot row */ 2509 2510 while (prow < k){ 2511 nextprow = jl[prow]; 2512 2513 /* merge prow into k-th row */ 2514 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2515 jmax = ui[prow+1]; 2516 ncols = jmax-jmin; 2517 i = jmin - ui[prow]; 2518 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2519 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2520 j = *(uj - 1); 2521 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2522 nzk += nlnk; 2523 2524 /* update il and jl for prow */ 2525 if (jmin < jmax){ 2526 il[prow] = jmin; 2527 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2528 } 2529 prow = nextprow; 2530 } 2531 2532 /* if free space is not available, make more free space */ 2533 if (current_space->local_remaining<nzk) { 2534 i = am - k + 1; /* num of unfactored rows */ 2535 i *= PetscMin(nzk, (i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2536 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2537 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2538 reallocs++; 2539 } 2540 2541 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2542 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2543 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2544 2545 /* add the k-th row into il and jl */ 2546 if (nzk > 1){ 2547 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2548 jl[k] = jl[i]; jl[i] = k; 2549 il[k] = ui[k] + 1; 2550 } 2551 uj_ptr[k] = current_space->array; 2552 uj_lvl_ptr[k] = current_space_lvl->array; 2553 2554 current_space->array += nzk; 2555 current_space->local_used += nzk; 2556 current_space->local_remaining -= nzk; 2557 2558 current_space_lvl->array += nzk; 2559 current_space_lvl->local_used += nzk; 2560 current_space_lvl->local_remaining -= nzk; 2561 2562 ui[k+1] = ui[k] + nzk; 2563 } 2564 2565 #if defined(PETSC_USE_INFO) 2566 if (ai[am] != 0) { 2567 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2568 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2569 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2570 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2571 } else { 2572 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2573 } 2574 #endif 2575 2576 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2577 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2578 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2579 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2580 2581 /* destroy list of free space and other temporary array(s) */ 2582 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2583 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 2584 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2585 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2586 2587 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2588 2589 /* put together the new matrix in MATSEQSBAIJ format */ 2590 2591 b = (Mat_SeqSBAIJ*)(fact)->data; 2592 b->singlemalloc = PETSC_FALSE; 2593 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2594 b->j = uj; 2595 b->i = ui; 2596 b->diag = udiag; 2597 b->free_diag = PETSC_TRUE; 2598 b->ilen = 0; 2599 b->imax = 0; 2600 b->row = perm; 2601 b->col = perm; 2602 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2603 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2604 b->icol = iperm; 2605 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2606 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2607 ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2608 b->maxnz = b->nz = ui[am]; 2609 b->free_a = PETSC_TRUE; 2610 b->free_ij = PETSC_TRUE; 2611 2612 (fact)->info.factor_mallocs = reallocs; 2613 (fact)->info.fill_ratio_given = fill; 2614 if (ai[am] != 0) { 2615 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2616 } else { 2617 (fact)->info.fill_ratio_needed = 0.0; 2618 } 2619 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2620 PetscFunctionReturn(0); 2621 } 2622 2623 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2624 { 2625 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2626 Mat_SeqSBAIJ *b; 2627 PetscErrorCode ierr; 2628 PetscTruth perm_identity; 2629 PetscReal fill = info->fill; 2630 const PetscInt *rip,*riip; 2631 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2632 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2633 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr,*udiag; 2634 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2635 PetscBT lnkbt; 2636 IS iperm; 2637 2638 PetscFunctionBegin; 2639 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); 2640 /* check whether perm is the identity mapping */ 2641 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2642 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2643 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2644 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2645 2646 /* initialization */ 2647 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2648 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2649 ui[0] = 0; 2650 2651 /* jl: linked list for storing indices of the pivot rows 2652 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2653 ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr); 2654 for (i=0; i<am; i++){ 2655 jl[i] = am; il[i] = 0; 2656 } 2657 2658 /* create and initialize a linked list for storing column indices of the active row k */ 2659 nlnk = am + 1; 2660 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2661 2662 /* initial FreeSpace size is fill*(ai[am]+1) */ 2663 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2664 current_space = free_space; 2665 2666 for (k=0; k<am; k++){ /* for each active row k */ 2667 /* initialize lnk by the column indices of row rip[k] of A */ 2668 nzk = 0; 2669 ncols = ai[rip[k]+1] - ai[rip[k]]; 2670 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2671 ncols_upper = 0; 2672 for (j=0; j<ncols; j++){ 2673 i = riip[*(aj + ai[rip[k]] + j)]; 2674 if (i >= k){ /* only take upper triangular entry */ 2675 cols[ncols_upper] = i; 2676 ncols_upper++; 2677 } 2678 } 2679 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2680 nzk += nlnk; 2681 2682 /* update lnk by computing fill-in for each pivot row to be merged in */ 2683 prow = jl[k]; /* 1st pivot row */ 2684 2685 while (prow < k){ 2686 nextprow = jl[prow]; 2687 /* merge prow into k-th row */ 2688 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2689 jmax = ui[prow+1]; 2690 ncols = jmax-jmin; 2691 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2692 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2693 nzk += nlnk; 2694 2695 /* update il and jl for prow */ 2696 if (jmin < jmax){ 2697 il[prow] = jmin; 2698 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 2699 } 2700 prow = nextprow; 2701 } 2702 2703 /* if free space is not available, make more free space */ 2704 if (current_space->local_remaining<nzk) { 2705 i = am - k + 1; /* num of unfactored rows */ 2706 i *= PetscMin(nzk,i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2707 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2708 reallocs++; 2709 } 2710 2711 /* copy data into free space, then initialize lnk */ 2712 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 2713 2714 /* add the k-th row into il and jl */ 2715 if (nzk-1 > 0){ 2716 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2717 jl[k] = jl[i]; jl[i] = k; 2718 il[k] = ui[k] + 1; 2719 } 2720 ui_ptr[k] = current_space->array; 2721 current_space->array += nzk; 2722 current_space->local_used += nzk; 2723 current_space->local_remaining -= nzk; 2724 2725 ui[k+1] = ui[k] + nzk; 2726 } 2727 2728 #if defined(PETSC_USE_INFO) 2729 if (ai[am] != 0) { 2730 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 2731 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2732 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2733 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2734 } else { 2735 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2736 } 2737 #endif 2738 2739 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2740 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2741 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 2742 2743 /* destroy list of free space and other temporary array(s) */ 2744 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2745 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor in newdatastruct */ 2746 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2747 2748 /* put together the new matrix in MATSEQSBAIJ format */ 2749 2750 b = (Mat_SeqSBAIJ*)(fact)->data; 2751 b->singlemalloc = PETSC_FALSE; 2752 b->free_a = PETSC_TRUE; 2753 b->free_ij = PETSC_TRUE; 2754 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2755 b->j = uj; 2756 b->i = ui; 2757 b->diag = udiag; 2758 b->free_diag = PETSC_TRUE; 2759 b->ilen = 0; 2760 b->imax = 0; 2761 b->row = perm; 2762 b->col = perm; 2763 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2764 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2765 b->icol = iperm; 2766 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2767 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2768 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2769 b->maxnz = b->nz = ui[am]; 2770 2771 (fact)->info.factor_mallocs = reallocs; 2772 (fact)->info.fill_ratio_given = fill; 2773 if (ai[am] != 0) { 2774 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2775 } else { 2776 (fact)->info.fill_ratio_needed = 0.0; 2777 } 2778 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct; 2779 PetscFunctionReturn(0); 2780 } 2781 2782 #undef __FUNCT__ 2783 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ" 2784 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2785 { 2786 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2787 Mat_SeqSBAIJ *b; 2788 PetscErrorCode ierr; 2789 PetscTruth perm_identity; 2790 PetscReal fill = info->fill; 2791 const PetscInt *rip,*riip; 2792 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2793 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2794 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr; 2795 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2796 PetscBT lnkbt; 2797 IS iperm; 2798 PetscTruth newdatastruct=PETSC_FALSE; 2799 2800 PetscFunctionBegin; 2801 ierr = PetscOptionsGetTruth(PETSC_NULL,"-cholesky_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 2802 if(newdatastruct){ 2803 ierr = MatCholeskyFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr); 2804 PetscFunctionReturn(0); 2805 } 2806 2807 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); 2808 /* check whether perm is the identity mapping */ 2809 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2810 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2811 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2812 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2813 2814 /* initialization */ 2815 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2816 ui[0] = 0; 2817 2818 /* jl: linked list for storing indices of the pivot rows 2819 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2820 ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr); 2821 for (i=0; i<am; i++){ 2822 jl[i] = am; il[i] = 0; 2823 } 2824 2825 /* create and initialize a linked list for storing column indices of the active row k */ 2826 nlnk = am + 1; 2827 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2828 2829 /* initial FreeSpace size is fill*(ai[am]+1) */ 2830 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2831 current_space = free_space; 2832 2833 for (k=0; k<am; k++){ /* for each active row k */ 2834 /* initialize lnk by the column indices of row rip[k] of A */ 2835 nzk = 0; 2836 ncols = ai[rip[k]+1] - ai[rip[k]]; 2837 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2838 ncols_upper = 0; 2839 for (j=0; j<ncols; j++){ 2840 i = riip[*(aj + ai[rip[k]] + j)]; 2841 if (i >= k){ /* only take upper triangular entry */ 2842 cols[ncols_upper] = i; 2843 ncols_upper++; 2844 } 2845 } 2846 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2847 nzk += nlnk; 2848 2849 /* update lnk by computing fill-in for each pivot row to be merged in */ 2850 prow = jl[k]; /* 1st pivot row */ 2851 2852 while (prow < k){ 2853 nextprow = jl[prow]; 2854 /* merge prow into k-th row */ 2855 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2856 jmax = ui[prow+1]; 2857 ncols = jmax-jmin; 2858 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2859 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2860 nzk += nlnk; 2861 2862 /* update il and jl for prow */ 2863 if (jmin < jmax){ 2864 il[prow] = jmin; 2865 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 2866 } 2867 prow = nextprow; 2868 } 2869 2870 /* if free space is not available, make more free space */ 2871 if (current_space->local_remaining<nzk) { 2872 i = am - k + 1; /* num of unfactored rows */ 2873 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2874 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2875 reallocs++; 2876 } 2877 2878 /* copy data into free space, then initialize lnk */ 2879 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 2880 2881 /* add the k-th row into il and jl */ 2882 if (nzk-1 > 0){ 2883 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2884 jl[k] = jl[i]; jl[i] = k; 2885 il[k] = ui[k] + 1; 2886 } 2887 ui_ptr[k] = current_space->array; 2888 current_space->array += nzk; 2889 current_space->local_used += nzk; 2890 current_space->local_remaining -= nzk; 2891 2892 ui[k+1] = ui[k] + nzk; 2893 } 2894 2895 #if defined(PETSC_USE_INFO) 2896 if (ai[am] != 0) { 2897 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 2898 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2899 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2900 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2901 } else { 2902 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2903 } 2904 #endif 2905 2906 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2907 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2908 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 2909 2910 /* destroy list of free space and other temporary array(s) */ 2911 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2912 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 2913 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2914 2915 /* put together the new matrix in MATSEQSBAIJ format */ 2916 2917 b = (Mat_SeqSBAIJ*)(fact)->data; 2918 b->singlemalloc = PETSC_FALSE; 2919 b->free_a = PETSC_TRUE; 2920 b->free_ij = PETSC_TRUE; 2921 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2922 b->j = uj; 2923 b->i = ui; 2924 b->diag = 0; 2925 b->ilen = 0; 2926 b->imax = 0; 2927 b->row = perm; 2928 b->col = perm; 2929 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2930 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2931 b->icol = iperm; 2932 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2933 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2934 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2935 b->maxnz = b->nz = ui[am]; 2936 2937 (fact)->info.factor_mallocs = reallocs; 2938 (fact)->info.fill_ratio_given = fill; 2939 if (ai[am] != 0) { 2940 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2941 } else { 2942 (fact)->info.fill_ratio_needed = 0.0; 2943 } 2944 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2945 PetscFunctionReturn(0); 2946 } 2947 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 2998 #undef __FUNCT__ 2999 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct_v2" 3000 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct_v2(Mat A,Vec bb,Vec xx) 3001 { 3002 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3003 PetscErrorCode ierr; 3004 PetscInt n = A->rmap->n; 3005 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag,*vi; 3006 PetscScalar *x,sum; 3007 const PetscScalar *b; 3008 const MatScalar *aa = a->a,*v; 3009 PetscInt i,nz; 3010 3011 PetscFunctionBegin; 3012 if (!n) PetscFunctionReturn(0); 3013 3014 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3015 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3016 3017 /* forward solve the lower triangular */ 3018 x[0] = b[0]; 3019 v = aa; 3020 vi = aj; 3021 for (i=1; i<n; i++) { 3022 nz = ai[i+1] - ai[i]; 3023 sum = b[i]; 3024 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3025 v += nz; 3026 vi += nz; 3027 x[i] = sum; 3028 } 3029 3030 /* backward solve the upper triangular */ 3031 /* v = aa + ai[n+1]; 3032 vi = aj + ai[n+1]; */ 3033 v = aa + adiag[n-1]; 3034 vi = aj + adiag[n-1]; 3035 for (i=n-1; i>=0; i--){ 3036 nz = adiag[i] - adiag[i+1]-1; 3037 sum = x[i]; 3038 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3039 v += nz; 3040 vi += nz; vi++; 3041 x[i] = *v++ *sum; /* x[i]=aa[adiag[i]]*sum; v++; */ 3042 } 3043 3044 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 3045 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3046 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3047 PetscFunctionReturn(0); 3048 } 3049 3050 #undef __FUNCT__ 3051 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct" 3052 PetscErrorCode MatSolve_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx) 3053 { 3054 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3055 IS iscol = a->col,isrow = a->row; 3056 PetscErrorCode ierr; 3057 PetscInt i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,nz,k; 3058 const PetscInt *rout,*cout,*r,*c; 3059 PetscScalar *x,*tmp,*tmps,sum; 3060 const PetscScalar *b; 3061 const MatScalar *aa = a->a,*v; 3062 3063 PetscFunctionBegin; 3064 if (!n) PetscFunctionReturn(0); 3065 3066 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3067 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3068 tmp = a->solve_work; 3069 3070 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 3071 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 3072 3073 /* forward solve the lower triangular */ 3074 tmp[0] = b[*r++]; 3075 tmps = tmp; 3076 v = aa; 3077 vi = aj; 3078 for (i=1; i<n; i++) { 3079 nz = ai[i+1] - ai[i]; 3080 sum = b[*r++]; 3081 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 3082 tmp[i] = sum; 3083 v += nz; vi += nz; 3084 } 3085 3086 /* backward solve the upper triangular */ 3087 k = n+1; 3088 v = aa + ai[k]; /* 1st entry of U(n-1,:) */ 3089 vi = aj + ai[k]; 3090 for (i=n-1; i>=0; i--){ 3091 k = 2*n-i; 3092 nz = ai[k +1] - ai[k] - 1; 3093 sum = tmp[i]; 3094 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 3095 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 3096 v += nz+1; vi += nz+1; 3097 } 3098 3099 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 3100 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 3101 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3102 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3103 ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr); 3104 PetscFunctionReturn(0); 3105 } 3106 3107 #undef __FUNCT__ 3108 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct_v2" 3109 PetscErrorCode MatSolve_SeqAIJ_newdatastruct_v2(Mat A,Vec bb,Vec xx) 3110 { 3111 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3112 IS iscol = a->col,isrow = a->row; 3113 PetscErrorCode ierr; 3114 PetscInt i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz; 3115 const PetscInt *rout,*cout,*r,*c; 3116 PetscScalar *x,*tmp,sum; 3117 const PetscScalar *b; 3118 const MatScalar *aa = a->a,*v; 3119 3120 PetscFunctionBegin; 3121 if (!n) PetscFunctionReturn(0); 3122 3123 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3124 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3125 tmp = a->solve_work; 3126 3127 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 3128 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 3129 3130 /* forward solve the lower triangular */ 3131 tmp[0] = b[r[0]]; 3132 v = aa; 3133 vi = aj; 3134 for (i=1; i<n; i++) { 3135 nz = ai[i+1] - ai[i]; 3136 sum = b[r[i]]; 3137 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3138 tmp[i] = sum; 3139 v += nz; vi += nz; 3140 } 3141 3142 /* backward solve the upper triangular */ 3143 v = aa + adiag[n-1]; /* 1st entry of U(n-1,:) */ 3144 vi = aj + adiag[n-1]; 3145 for (i=n-1; i>=0; i--){ 3146 nz = adiag[i]-adiag[i+1]-1; 3147 sum = tmp[i]; 3148 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3149 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 3150 v += nz+1; vi += nz+1; 3151 } 3152 3153 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 3154 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 3155 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3156 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3157 ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr); 3158 PetscFunctionReturn(0); 3159 } 3160 3161 #undef __FUNCT__ 3162 #define __FUNCT__ "MatILUDTFactor_SeqAIJ" 3163 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact) 3164 { 3165 Mat B = *fact; 3166 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b; 3167 IS isicol; 3168 PetscErrorCode ierr; 3169 const PetscInt *r,*ic; 3170 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag; 3171 PetscInt *bi,*bj,*bdiag,*bdiag_rev; 3172 PetscInt row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au; 3173 PetscInt nlnk,*lnk; 3174 PetscBT lnkbt; 3175 PetscTruth row_identity,icol_identity,both_identity; 3176 MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp; 3177 const PetscInt *ics; 3178 PetscInt j,nz,*pj,*bjtmp,k,ncut,*jtmp; 3179 PetscReal dt=info->dt,dtcol=info->dtcol,shift=info->shiftinblocks; 3180 PetscInt dtcount=(PetscInt)info->dtcount,nnz_max; 3181 PetscTruth missing; 3182 3183 PetscFunctionBegin; 3184 3185 if (dt == PETSC_DEFAULT) dt = 0.005; 3186 if (dtcol == PETSC_DEFAULT) dtcol = 0.01; /* XXX unused! */ 3187 if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax); 3188 3189 /* ------- symbolic factorization, can be reused ---------*/ 3190 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 3191 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 3192 adiag=a->diag; 3193 3194 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 3195 3196 /* bdiag is location of diagonal in factor */ 3197 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); /* becomes b->diag */ 3198 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag_rev);CHKERRQ(ierr); /* temporary */ 3199 3200 /* allocate row pointers bi */ 3201 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 3202 3203 /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */ 3204 if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */ 3205 nnz_max = ai[n]+2*n*dtcount+2; 3206 3207 ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 3208 ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr); 3209 3210 /* put together the new matrix */ 3211 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 3212 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 3213 b = (Mat_SeqAIJ*)(B)->data; 3214 b->free_a = PETSC_TRUE; 3215 b->free_ij = PETSC_TRUE; 3216 b->singlemalloc = PETSC_FALSE; 3217 b->a = ba; 3218 b->j = bj; 3219 b->i = bi; 3220 b->diag = bdiag; 3221 b->ilen = 0; 3222 b->imax = 0; 3223 b->row = isrow; 3224 b->col = iscol; 3225 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 3226 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 3227 b->icol = isicol; 3228 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 3229 3230 ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3231 b->maxnz = nnz_max; 3232 3233 (B)->factor = MAT_FACTOR_ILUDT; 3234 (B)->info.factor_mallocs = 0; 3235 (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]); 3236 CHKMEMQ; 3237 /* ------- end of symbolic factorization ---------*/ 3238 3239 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3240 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3241 ics = ic; 3242 3243 /* linked list for storing column indices of the active row */ 3244 nlnk = n + 1; 3245 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3246 3247 /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */ 3248 ierr = PetscMalloc2(n,PetscInt,&im,n,PetscInt,&jtmp);CHKERRQ(ierr); 3249 /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */ 3250 ierr = PetscMalloc2(n,MatScalar,&rtmp,n,MatScalar,&vtmp);CHKERRQ(ierr); 3251 ierr = PetscMemzero(rtmp,n*sizeof(MatScalar));CHKERRQ(ierr); 3252 3253 bi[0] = 0; 3254 bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */ 3255 bdiag_rev[n] = bdiag[0]; 3256 bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */ 3257 for (i=0; i<n; i++) { 3258 /* copy initial fill into linked list */ 3259 nzi = 0; /* nonzeros for active row i */ 3260 nzi = ai[r[i]+1] - ai[r[i]]; 3261 if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 3262 nzi_al = adiag[r[i]] - ai[r[i]]; 3263 nzi_au = ai[r[i]+1] - adiag[r[i]] -1; 3264 ajtmp = aj + ai[r[i]]; 3265 ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3266 3267 /* load in initial (unfactored row) */ 3268 aatmp = a->a + ai[r[i]]; 3269 for (j=0; j<nzi; j++) { 3270 rtmp[ics[*ajtmp++]] = *aatmp++; 3271 } 3272 3273 /* add pivot rows into linked list */ 3274 row = lnk[n]; 3275 while (row < i ) { 3276 nzi_bl = bi[row+1] - bi[row] + 1; 3277 bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */ 3278 ierr = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr); 3279 nzi += nlnk; 3280 row = lnk[row]; 3281 } 3282 3283 /* copy data from lnk into jtmp, then initialize lnk */ 3284 ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr); 3285 3286 /* numerical factorization */ 3287 bjtmp = jtmp; 3288 row = *bjtmp++; /* 1st pivot row */ 3289 while ( row < i ) { 3290 pc = rtmp + row; 3291 pv = ba + bdiag[row]; /* 1./(diag of the pivot row) */ 3292 multiplier = (*pc) * (*pv); 3293 *pc = multiplier; 3294 if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */ 3295 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3296 pv = ba + bdiag[row+1] + 1; 3297 /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */ 3298 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3299 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3300 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 3301 } 3302 row = *bjtmp++; 3303 } 3304 3305 /* copy sparse rtmp into contiguous vtmp; separate L and U part */ 3306 diag_tmp = rtmp[i]; /* save diagonal value - may not needed?? */ 3307 nzi_bl = 0; j = 0; 3308 while (jtmp[j] < i){ /* Note: jtmp is sorted */ 3309 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3310 nzi_bl++; j++; 3311 } 3312 nzi_bu = nzi - nzi_bl -1; 3313 while (j < nzi){ 3314 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3315 j++; 3316 } 3317 3318 bjtmp = bj + bi[i]; 3319 batmp = ba + bi[i]; 3320 /* apply level dropping rule to L part */ 3321 ncut = nzi_al + dtcount; 3322 if (ncut < nzi_bl){ 3323 ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr); 3324 ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr); 3325 } else { 3326 ncut = nzi_bl; 3327 } 3328 for (j=0; j<ncut; j++){ 3329 bjtmp[j] = jtmp[j]; 3330 batmp[j] = vtmp[j]; 3331 /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */ 3332 } 3333 bi[i+1] = bi[i] + ncut; 3334 nzi = ncut + 1; 3335 3336 /* apply level dropping rule to U part */ 3337 ncut = nzi_au + dtcount; 3338 if (ncut < nzi_bu){ 3339 ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr); 3340 ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr); 3341 } else { 3342 ncut = nzi_bu; 3343 } 3344 nzi += ncut; 3345 3346 /* mark bdiagonal */ 3347 bdiag[i+1] = bdiag[i] - (ncut + 1); 3348 bdiag_rev[n-i-1] = bdiag[i+1]; 3349 bi[2*n - i] = bi[2*n - i +1] - (ncut + 1); 3350 bjtmp = bj + bdiag[i]; 3351 batmp = ba + bdiag[i]; 3352 *bjtmp = i; 3353 *batmp = diag_tmp; /* rtmp[i]; */ 3354 if (*batmp == 0.0) { 3355 *batmp = dt+shift; 3356 /* printf(" row %d add shift %g\n",i,shift); */ 3357 } 3358 *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */ 3359 /* printf(" (%d,%g),",*bjtmp,*batmp); */ 3360 3361 bjtmp = bj + bdiag[i+1]+1; 3362 batmp = ba + bdiag[i+1]+1; 3363 for (k=0; k<ncut; k++){ 3364 bjtmp[k] = jtmp[nzi_bl+1+k]; 3365 batmp[k] = vtmp[nzi_bl+1+k]; 3366 /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */ 3367 } 3368 /* printf("\n"); */ 3369 3370 im[i] = nzi; /* used by PetscLLAddSortedLU() */ 3371 /* 3372 printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]); 3373 printf(" ----------------------------\n"); 3374 */ 3375 } /* for (i=0; i<n; i++) */ 3376 /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */ 3377 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]); 3378 3379 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3380 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3381 3382 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3383 ierr = PetscFree2(im,jtmp);CHKERRQ(ierr); 3384 ierr = PetscFree2(rtmp,vtmp);CHKERRQ(ierr); 3385 ierr = PetscFree(bdiag_rev);CHKERRQ(ierr); 3386 3387 ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr); 3388 b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n]; 3389 3390 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3391 ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr); 3392 both_identity = (PetscTruth) (row_identity && icol_identity); 3393 if (row_identity && icol_identity) { 3394 B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct; 3395 } else { 3396 B->ops->solve = MatSolve_SeqAIJ_newdatastruct; 3397 } 3398 3399 B->ops->lufactorsymbolic = MatILUDTFactorSymbolic_SeqAIJ; 3400 B->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ; 3401 B->ops->solveadd = 0; 3402 B->ops->solvetranspose = 0; 3403 B->ops->solvetransposeadd = 0; 3404 B->ops->matsolve = 0; 3405 B->assembled = PETSC_TRUE; 3406 B->preallocated = PETSC_TRUE; 3407 PetscFunctionReturn(0); 3408 } 3409 3410 /* a wraper of MatILUDTFactor_SeqAIJ() */ 3411 #undef __FUNCT__ 3412 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ" 3413 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info) 3414 { 3415 PetscErrorCode ierr; 3416 3417 PetscFunctionBegin; 3418 ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr); 3419 3420 fact->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ; 3421 PetscFunctionReturn(0); 3422 } 3423 3424 /* 3425 same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors 3426 - intend to replace existing MatLUFactorNumeric_SeqAIJ() 3427 */ 3428 #undef __FUNCT__ 3429 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ" 3430 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info) 3431 { 3432 Mat C=fact; 3433 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 3434 IS isrow = b->row,isicol = b->icol; 3435 PetscErrorCode ierr; 3436 const PetscInt *r,*ic,*ics; 3437 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 3438 PetscInt *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj; 3439 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 3440 PetscReal dt=info->dt,shift=info->shiftinblocks; 3441 PetscTruth row_identity, col_identity; 3442 3443 PetscFunctionBegin; 3444 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3445 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3446 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 3447 ics = ic; 3448 3449 for (i=0; i<n; i++){ 3450 /* initialize rtmp array */ 3451 nzl = bi[i+1] - bi[i]; /* num of nozeros in L(i,:) */ 3452 bjtmp = bj + bi[i]; 3453 for (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0; 3454 rtmp[i] = 0.0; 3455 nzu = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */ 3456 bjtmp = bj + bdiag[i+1] + 1; 3457 for (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0; 3458 3459 /* load in initial unfactored row of A */ 3460 /* printf("row %d\n",i); */ 3461 nz = ai[r[i]+1] - ai[r[i]]; 3462 ajtmp = aj + ai[r[i]]; 3463 v = aa + ai[r[i]]; 3464 for (j=0; j<nz; j++) { 3465 rtmp[ics[*ajtmp++]] = v[j]; 3466 /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */ 3467 } 3468 /* printf("\n"); */ 3469 3470 /* numerical factorization */ 3471 bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */ 3472 nzl = bi[i+1] - bi[i]; /* num of entries in L(i,:) */ 3473 k = 0; 3474 while (k < nzl){ 3475 row = *bjtmp++; 3476 /* printf(" prow %d\n",row); */ 3477 pc = rtmp + row; 3478 pv = b->a + bdiag[row]; /* 1./(diag of the pivot row) */ 3479 multiplier = (*pc) * (*pv); 3480 *pc = multiplier; 3481 if (PetscAbsScalar(multiplier) > dt){ 3482 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3483 pv = b->a + bdiag[row+1] + 1; 3484 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3485 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3486 /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */ 3487 } 3488 k++; 3489 } 3490 3491 /* finished row so stick it into b->a */ 3492 /* L-part */ 3493 pv = b->a + bi[i] ; 3494 pj = bj + bi[i] ; 3495 nzl = bi[i+1] - bi[i]; 3496 for (j=0; j<nzl; j++) { 3497 pv[j] = rtmp[pj[j]]; 3498 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3499 } 3500 3501 /* diagonal: invert diagonal entries for simplier triangular solves */ 3502 if (rtmp[i] == 0.0) rtmp[i] = dt+shift; 3503 b->a[bdiag[i]] = 1.0/rtmp[i]; 3504 /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */ 3505 3506 /* U-part */ 3507 pv = b->a + bdiag[i+1] + 1; 3508 pj = bj + bdiag[i+1] + 1; 3509 nzu = bdiag[i] - bdiag[i+1] - 1; 3510 for (j=0; j<nzu; j++) { 3511 pv[j] = rtmp[pj[j]]; 3512 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3513 } 3514 /* printf("\n"); */ 3515 } 3516 3517 ierr = PetscFree(rtmp);CHKERRQ(ierr); 3518 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3519 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3520 3521 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3522 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 3523 if (row_identity && col_identity) { 3524 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct; 3525 } else { 3526 C->ops->solve = MatSolve_SeqAIJ_newdatastruct; 3527 } 3528 C->ops->solveadd = 0; 3529 C->ops->solvetranspose = 0; 3530 C->ops->solvetransposeadd = 0; 3531 C->ops->matsolve = 0; 3532 C->assembled = PETSC_TRUE; 3533 C->preallocated = PETSC_TRUE; 3534 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 3535 PetscFunctionReturn(0); 3536 } 3537