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 = PetscMalloc(n*sizeof(PetscInt),&order);CHKERRQ(ierr); 42 ierr = PetscMemzero(done,n*sizeof(PetscTruth));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 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square"); 158 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 159 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 160 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 161 162 /* get new row pointers */ 163 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 164 bi[0] = 0; 165 166 /* bdiag is location of diagonal in factor */ 167 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 168 bdiag[0] = 0; 169 170 /* linked list for storing column indices of the active row */ 171 nlnk = n + 1; 172 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 173 174 ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr); 175 176 /* initial FreeSpace size is f*(ai[n]+1) */ 177 f = info->fill; 178 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 179 current_space = free_space; 180 181 for (i=0; i<n; i++) { 182 /* copy previous fill into linked list */ 183 nzi = 0; 184 nnz = ai[r[i]+1] - ai[r[i]]; 185 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 186 ajtmp = aj + ai[r[i]]; 187 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 188 nzi += nlnk; 189 190 /* add pivot rows into linked list */ 191 row = lnk[n]; 192 while (row < i) { 193 nzbd = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */ 194 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 195 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 196 nzi += nlnk; 197 row = lnk[row]; 198 } 199 bi[i+1] = bi[i] + nzi; 200 im[i] = nzi; 201 202 /* mark bdiag */ 203 nzbd = 0; 204 nnz = nzi; 205 k = lnk[n]; 206 while (nnz-- && k < i){ 207 nzbd++; 208 k = lnk[k]; 209 } 210 bdiag[i] = bi[i] + nzbd; 211 212 /* if free space is not available, make more free space */ 213 if (current_space->local_remaining<nzi) { 214 nnz = (n - i)*nzi; /* estimated and max additional space needed */ 215 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 216 reallocs++; 217 } 218 219 /* copy data into free space, then initialize lnk */ 220 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 221 bi_ptr[i] = current_space->array; 222 current_space->array += nzi; 223 current_space->local_used += nzi; 224 current_space->local_remaining -= nzi; 225 } 226 #if defined(PETSC_USE_INFO) 227 if (ai[n] != 0) { 228 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 229 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 230 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 231 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr); 232 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 233 } else { 234 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 235 } 236 #endif 237 238 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 239 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 240 241 /* destroy list of free space and other temporary array(s) */ 242 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 243 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); 244 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 245 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 246 247 /* put together the new matrix */ 248 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 249 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 250 b = (Mat_SeqAIJ*)(B)->data; 251 b->free_a = PETSC_TRUE; 252 b->free_ij = PETSC_TRUE; 253 b->singlemalloc = PETSC_FALSE; 254 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 255 b->j = bj; 256 b->i = bi; 257 b->diag = bdiag; 258 b->ilen = 0; 259 b->imax = 0; 260 b->row = isrow; 261 b->col = iscol; 262 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 263 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 264 b->icol = isicol; 265 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 266 267 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 268 ierr = PetscLogObjectMemory(B,(bi[n]-n)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 269 b->maxnz = b->nz = bi[n] ; 270 271 (B)->factor = MAT_FACTOR_LU; 272 (B)->info.factor_mallocs = reallocs; 273 (B)->info.fill_ratio_given = f; 274 275 if (ai[n]) { 276 (B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 277 } else { 278 (B)->info.fill_ratio_needed = 0.0; 279 } 280 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 281 (B)->ops->solve = MatSolve_SeqAIJ; 282 (B)->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 283 /* switch to inodes if appropriate */ 284 ierr = MatLUFactorSymbolic_Inode(B,A,isrow,iscol,info);CHKERRQ(ierr); 285 PetscFunctionReturn(0); 286 } 287 288 #undef __FUNCT__ 289 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ_newdatastruct" 290 PetscErrorCode MatLUFactorSymbolic_SeqAIJ_newdatastruct(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 291 { 292 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 293 IS isicol; 294 PetscErrorCode ierr; 295 const PetscInt *r,*ic; 296 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j; 297 PetscInt *bi,*bj,*ajtmp; 298 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 299 PetscReal f; 300 PetscInt nlnk,*lnk,k,**bi_ptr; 301 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 302 PetscBT lnkbt; 303 304 PetscFunctionBegin; 305 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square"); 306 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 307 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 308 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 309 310 /* get new row pointers */ 311 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 312 bi[0] = 0; 313 314 /* bdiag is location of diagonal in factor */ 315 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 316 bdiag[0] = 0; 317 318 /* linked list for storing column indices of the active row */ 319 nlnk = n + 1; 320 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 321 322 ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr); 323 324 /* initial FreeSpace size is f*(ai[n]+1) */ 325 f = info->fill; 326 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 327 current_space = free_space; 328 329 for (i=0; i<n; i++) { 330 /* copy previous fill into linked list */ 331 nzi = 0; 332 nnz = ai[r[i]+1] - ai[r[i]]; 333 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 334 ajtmp = aj + ai[r[i]]; 335 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 336 nzi += nlnk; 337 338 /* add pivot rows into linked list */ 339 row = lnk[n]; 340 while (row < i){ 341 nzbd = bdiag[row] + 1; /* num of entries in the row with column index <= row */ 342 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 343 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 344 nzi += nlnk; 345 row = lnk[row]; 346 } 347 bi[i+1] = bi[i] + nzi; 348 im[i] = nzi; 349 350 /* mark bdiag */ 351 nzbd = 0; 352 nnz = nzi; 353 k = lnk[n]; 354 while (nnz-- && k < i){ 355 nzbd++; 356 k = lnk[k]; 357 } 358 bdiag[i] = nzbd; /* note: bdiag[i] = nnzL as input for PetscFreeSpaceContiguous_LU() */ 359 360 /* if free space is not available, make more free space */ 361 if (current_space->local_remaining<nzi) { 362 nnz = 2*(n - i)*nzi; /* estimated and max additional space needed */ 363 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 364 reallocs++; 365 } 366 367 /* copy data into free space, then initialize lnk */ 368 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 369 bi_ptr[i] = current_space->array; 370 current_space->array += nzi; 371 current_space->local_used += nzi; 372 current_space->local_remaining -= nzi; 373 } 374 #if defined(PETSC_USE_INFO) 375 if (ai[n] != 0) { 376 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 377 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 378 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 379 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr); 380 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 381 } else { 382 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 383 } 384 #endif 385 386 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 387 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 388 389 /* destroy list of free space and other temporary array(s) */ 390 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 391 ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 392 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 393 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 394 395 /* put together the new matrix */ 396 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 397 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 398 b = (Mat_SeqAIJ*)(B)->data; 399 b->free_a = PETSC_TRUE; 400 b->free_ij = PETSC_TRUE; 401 b->singlemalloc = PETSC_FALSE; 402 ierr = PetscMalloc((bi[2*n+1])*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 403 b->j = bj; 404 b->i = bi; 405 b->diag = bdiag; 406 b->ilen = 0; 407 b->imax = 0; 408 b->row = isrow; 409 b->col = iscol; 410 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 411 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 412 b->icol = isicol; 413 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 414 415 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 416 ierr = PetscLogObjectMemory(B,bi[2*n+1]*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 417 b->maxnz = b->nz = bi[2*n+1] ; 418 419 (B)->factor = MAT_FACTOR_LU; 420 (B)->info.factor_mallocs = reallocs; 421 (B)->info.fill_ratio_given = f; 422 423 if (ai[n]) { 424 (B)->info.fill_ratio_needed = ((PetscReal)bi[2*n+1])/((PetscReal)ai[n]); 425 } else { 426 (B)->info.fill_ratio_needed = 0.0; 427 } 428 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 429 PetscFunctionReturn(0); 430 } 431 432 /* 433 Trouble in factorization, should we dump the original matrix? 434 */ 435 #undef __FUNCT__ 436 #define __FUNCT__ "MatFactorDumpMatrix" 437 PetscErrorCode MatFactorDumpMatrix(Mat A) 438 { 439 PetscErrorCode ierr; 440 PetscTruth flg = PETSC_FALSE; 441 442 PetscFunctionBegin; 443 ierr = PetscOptionsGetTruth(PETSC_NULL,"-mat_factor_dump_on_error",&flg,PETSC_NULL);CHKERRQ(ierr); 444 if (flg) { 445 PetscViewer viewer; 446 char filename[PETSC_MAX_PATH_LEN]; 447 448 ierr = PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);CHKERRQ(ierr); 449 ierr = PetscViewerBinaryOpen(((PetscObject)A)->comm,filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr); 450 ierr = MatView(A,viewer);CHKERRQ(ierr); 451 ierr = PetscViewerDestroy(viewer);CHKERRQ(ierr); 452 } 453 PetscFunctionReturn(0); 454 } 455 456 extern PetscErrorCode MatSolve_Inode(Mat,Vec,Vec); 457 458 /* ----------------------------------------------------------- */ 459 extern PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct(Mat,Vec,Vec); 460 extern PetscErrorCode MatSolve_SeqAIJ_newdatastruct(Mat,Vec,Vec); 461 462 #undef __FUNCT__ 463 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_newdatastruct" 464 PetscErrorCode MatLUFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info) 465 { 466 Mat C=B; 467 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 468 IS isrow = b->row,isicol = b->icol; 469 PetscErrorCode ierr; 470 const PetscInt *r,*ic,*ics; 471 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 472 PetscInt *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj; 473 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 474 PetscReal shift=info->shiftinblocks; 475 PetscTruth row_identity,col_identity; 476 477 PetscFunctionBegin; 478 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 479 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 480 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 481 ics = ic; 482 483 for (i=0; i<n; i++){ 484 /* zero rtmp */ 485 /* L part */ 486 nz = bi[i+1] - bi[i]; 487 bjtmp = bj + bi[i]; 488 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 489 490 /* U part */ 491 nz = bi[2*n-i+1] - bi[2*n-i]; 492 bjtmp = bj + bi[2*n-i]; 493 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 494 495 /* load in initial (unfactored row) */ 496 nz = ai[r[i]+1] - ai[r[i]]; 497 ajtmp = aj + ai[r[i]]; 498 v = aa + ai[r[i]]; 499 for (j=0; j<nz; j++) { 500 rtmp[ics[ajtmp[j]]] = v[j]; 501 } 502 if (rtmp[ics[r[i]]] == 0.0){ 503 rtmp[ics[r[i]]] += shift; /* shift the diagonal of the matrix */ 504 /* printf("row %d, shift %g\n",i,shift); */ 505 } 506 507 /* elimination */ 508 bjtmp = bj + bi[i]; 509 row = *bjtmp++; 510 nzL = bi[i+1] - bi[i]; 511 k = 0; 512 while (k < nzL) { 513 pc = rtmp + row; 514 if (*pc != 0.0) { 515 pv = b->a + bdiag[row]; 516 multiplier = *pc * (*pv); 517 *pc = multiplier; 518 pj = b->j + bi[2*n-row]; /* begining of U(row,:) */ 519 pv = b->a + bi[2*n-row]; 520 nz = bi[2*n-row+1] - bi[2*n-row] - 1; /* num of entries in U(row,:), excluding diag */ 521 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 522 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 523 } 524 row = *bjtmp++; k++; 525 } 526 527 /* finished row so stick it into b->a */ 528 /* L part */ 529 pv = b->a + bi[i] ; 530 pj = b->j + bi[i] ; 531 nz = bi[i+1] - bi[i]; 532 for (j=0; j<nz; j++) { 533 pv[j] = rtmp[pj[j]]; 534 } 535 536 /* Mark diagonal and invert diagonal for simplier triangular solves */ 537 pv = b->a + bdiag[i]; 538 pj = b->j + bdiag[i]; 539 /* if (*pj != i)SETERRQ2(PETSC_ERR_SUP,"row %d != *pj %d",i,*pj) */ 540 *pv = 1.0/rtmp[*pj]; 541 542 /* U part */ 543 pv = b->a + bi[2*n-i]; 544 pj = b->j + bi[2*n-i]; 545 nz = bi[2*n-i+1] - bi[2*n-i] - 1; 546 for (j=0; j<nz; j++) pv[j] = rtmp[pj[j]]; 547 } 548 ierr = PetscFree(rtmp);CHKERRQ(ierr); 549 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 550 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 551 552 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 553 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 554 if (row_identity && col_identity) { 555 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct; 556 } else { 557 C->ops->solve = MatSolve_SeqAIJ_newdatastruct; 558 } 559 560 C->ops->solveadd = 0; 561 C->ops->solvetranspose = 0; 562 C->ops->solvetransposeadd = 0; 563 C->ops->matsolve = 0; 564 C->assembled = PETSC_TRUE; 565 C->preallocated = PETSC_TRUE; 566 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 567 PetscFunctionReturn(0); 568 } 569 570 #undef __FUNCT__ 571 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ" 572 PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 573 { 574 Mat C=B; 575 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 576 IS isrow = b->row,isicol = b->icol; 577 PetscErrorCode ierr; 578 const PetscInt *r,*ic,*ics; 579 PetscInt nz,row,i,j,n=A->rmap->n,diag; 580 const PetscInt *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 581 const PetscInt *ajtmp,*bjtmp,*diag_offset = b->diag,*pj; 582 MatScalar *pv,*rtmp,*pc,multiplier,d; 583 const MatScalar *v,*aa=a->a; 584 PetscReal rs=0.0; 585 LUShift_Ctx sctx; 586 PetscInt newshift,*ddiag; 587 588 PetscFunctionBegin; 589 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 590 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 591 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 592 ics = ic; 593 594 sctx.shift_top = 0; 595 sctx.nshift_max = 0; 596 sctx.shift_lo = 0; 597 sctx.shift_hi = 0; 598 sctx.shift_fraction = 0; 599 600 /* if both shift schemes are chosen by user, only use info->shiftpd */ 601 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 602 ddiag = a->diag; 603 sctx.shift_top = info->zeropivot; 604 for (i=0; i<n; i++) { 605 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 606 d = (aa)[ddiag[i]]; 607 rs = -PetscAbsScalar(d) - PetscRealPart(d); 608 v = aa+ai[i]; 609 nz = ai[i+1] - ai[i]; 610 for (j=0; j<nz; j++) 611 rs += PetscAbsScalar(v[j]); 612 if (rs>sctx.shift_top) sctx.shift_top = rs; 613 } 614 sctx.shift_top *= 1.1; 615 sctx.nshift_max = 5; 616 sctx.shift_lo = 0.; 617 sctx.shift_hi = 1.; 618 } 619 620 sctx.shift_amount = 0.0; 621 sctx.nshift = 0; 622 do { 623 sctx.lushift = PETSC_FALSE; 624 for (i=0; i<n; i++){ 625 nz = bi[i+1] - bi[i]; 626 bjtmp = bj + bi[i]; 627 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 628 629 /* load in initial (unfactored row) */ 630 nz = ai[r[i]+1] - ai[r[i]]; 631 ajtmp = aj + ai[r[i]]; 632 v = aa + ai[r[i]]; 633 for (j=0; j<nz; j++) { 634 rtmp[ics[ajtmp[j]]] = v[j]; 635 } 636 rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 637 /* if (sctx.shift_amount > 0.0) printf("row %d, shift %g\n",i,sctx.shift_amount); */ 638 639 row = *bjtmp++; 640 while (row < i) { 641 pc = rtmp + row; 642 if (*pc != 0.0) { 643 pv = b->a + diag_offset[row]; 644 pj = b->j + diag_offset[row] + 1; 645 multiplier = *pc / *pv++; 646 *pc = multiplier; 647 nz = bi[row+1] - diag_offset[row] - 1; 648 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 649 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 650 } 651 row = *bjtmp++; 652 } 653 /* finished row so stick it into b->a */ 654 pv = b->a + bi[i] ; 655 pj = b->j + bi[i] ; 656 nz = bi[i+1] - bi[i]; 657 diag = diag_offset[i] - bi[i]; 658 rs = 0.0; 659 for (j=0; j<nz; j++) { 660 pv[j] = rtmp[pj[j]]; 661 rs += PetscAbsScalar(pv[j]); 662 } 663 rs -= PetscAbsScalar(pv[diag]); 664 665 /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */ 666 sctx.rs = rs; 667 sctx.pv = pv[diag]; 668 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 669 if (newshift == 1) break; 670 } 671 672 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 673 /* 674 * if no shift in this attempt & shifting & started shifting & can refine, 675 * then try lower shift 676 */ 677 sctx.shift_hi = sctx.shift_fraction; 678 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 679 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 680 sctx.lushift = PETSC_TRUE; 681 sctx.nshift++; 682 } 683 } while (sctx.lushift); 684 685 /* invert diagonal entries for simplier triangular solves */ 686 for (i=0; i<n; i++) { 687 b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]]; 688 } 689 ierr = PetscFree(rtmp);CHKERRQ(ierr); 690 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 691 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 692 if (b->inode.use) { 693 C->ops->solve = MatSolve_Inode; 694 } else { 695 PetscTruth row_identity, col_identity; 696 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 697 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 698 if (row_identity && col_identity) { 699 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 700 } else { 701 C->ops->solve = MatSolve_SeqAIJ; 702 } 703 } 704 C->ops->solveadd = MatSolveAdd_SeqAIJ; 705 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 706 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 707 C->ops->matsolve = MatMatSolve_SeqAIJ; 708 C->assembled = PETSC_TRUE; 709 C->preallocated = PETSC_TRUE; 710 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 711 if (sctx.nshift){ 712 if (info->shiftpd) { 713 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); 714 } else if (info->shiftnz) { 715 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 716 } 717 } 718 PetscFunctionReturn(0); 719 } 720 721 /* 722 This routine implements inplace ILU(0) with row or/and column permutations. 723 Input: 724 A - original matrix 725 Output; 726 A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i] 727 a->j (col index) is permuted by the inverse of colperm, then sorted 728 a->a reordered accordingly with a->j 729 a->diag (ptr to diagonal elements) is updated. 730 */ 731 #undef __FUNCT__ 732 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_InplaceWithPerm" 733 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info) 734 { 735 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 736 IS isrow = a->row,isicol = a->icol; 737 PetscErrorCode ierr; 738 const PetscInt *r,*ic,*ics; 739 PetscInt i,j,n=A->rmap->n,*ai=a->i,*aj=a->j; 740 PetscInt *ajtmp,nz,row; 741 PetscInt *diag = a->diag,nbdiag,*pj; 742 PetscScalar *rtmp,*pc,multiplier,d; 743 MatScalar *v,*pv; 744 PetscReal rs; 745 LUShift_Ctx sctx; 746 PetscInt newshift; 747 748 PetscFunctionBegin; 749 if (A != B) SETERRQ(PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address"); 750 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 751 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 752 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&rtmp);CHKERRQ(ierr); 753 ierr = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr); 754 ics = ic; 755 756 sctx.shift_top = 0; 757 sctx.nshift_max = 0; 758 sctx.shift_lo = 0; 759 sctx.shift_hi = 0; 760 sctx.shift_fraction = 0; 761 762 /* if both shift schemes are chosen by user, only use info->shiftpd */ 763 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 764 sctx.shift_top = 0; 765 for (i=0; i<n; i++) { 766 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 767 d = (a->a)[diag[i]]; 768 rs = -PetscAbsScalar(d) - PetscRealPart(d); 769 v = a->a+ai[i]; 770 nz = ai[i+1] - ai[i]; 771 for (j=0; j<nz; j++) 772 rs += PetscAbsScalar(v[j]); 773 if (rs>sctx.shift_top) sctx.shift_top = rs; 774 } 775 if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot; 776 sctx.shift_top *= 1.1; 777 sctx.nshift_max = 5; 778 sctx.shift_lo = 0.; 779 sctx.shift_hi = 1.; 780 } 781 782 sctx.shift_amount = 0; 783 sctx.nshift = 0; 784 do { 785 sctx.lushift = PETSC_FALSE; 786 for (i=0; i<n; i++){ 787 /* load in initial unfactored row */ 788 nz = ai[r[i]+1] - ai[r[i]]; 789 ajtmp = aj + ai[r[i]]; 790 v = a->a + ai[r[i]]; 791 /* sort permuted ajtmp and values v accordingly */ 792 for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]]; 793 ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr); 794 795 diag[r[i]] = ai[r[i]]; 796 for (j=0; j<nz; j++) { 797 rtmp[ajtmp[j]] = v[j]; 798 if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */ 799 } 800 rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 801 802 row = *ajtmp++; 803 while (row < i) { 804 pc = rtmp + row; 805 if (*pc != 0.0) { 806 pv = a->a + diag[r[row]]; 807 pj = aj + diag[r[row]] + 1; 808 809 multiplier = *pc / *pv++; 810 *pc = multiplier; 811 nz = ai[r[row]+1] - diag[r[row]] - 1; 812 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 813 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 814 } 815 row = *ajtmp++; 816 } 817 /* finished row so overwrite it onto a->a */ 818 pv = a->a + ai[r[i]] ; 819 pj = aj + ai[r[i]] ; 820 nz = ai[r[i]+1] - ai[r[i]]; 821 nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */ 822 823 rs = 0.0; 824 for (j=0; j<nz; j++) { 825 pv[j] = rtmp[pj[j]]; 826 if (j != nbdiag) rs += PetscAbsScalar(pv[j]); 827 } 828 829 /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */ 830 sctx.rs = rs; 831 sctx.pv = pv[nbdiag]; 832 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 833 if (newshift == 1) break; 834 } 835 836 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 837 /* 838 * if no shift in this attempt & shifting & started shifting & can refine, 839 * then try lower shift 840 */ 841 sctx.shift_hi = sctx.shift_fraction; 842 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 843 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 844 sctx.lushift = PETSC_TRUE; 845 sctx.nshift++; 846 } 847 } while (sctx.lushift); 848 849 /* invert diagonal entries for simplier triangular solves */ 850 for (i=0; i<n; i++) { 851 a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]]; 852 } 853 854 ierr = PetscFree(rtmp);CHKERRQ(ierr); 855 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 856 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 857 A->ops->solve = MatSolve_SeqAIJ_InplaceWithPerm; 858 A->ops->solveadd = MatSolveAdd_SeqAIJ; 859 A->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 860 A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 861 A->assembled = PETSC_TRUE; 862 A->preallocated = PETSC_TRUE; 863 ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr); 864 if (sctx.nshift){ 865 if (info->shiftpd) { 866 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); 867 } else if (info->shiftnz) { 868 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 869 } 870 } 871 PetscFunctionReturn(0); 872 } 873 874 /* ----------------------------------------------------------- */ 875 #undef __FUNCT__ 876 #define __FUNCT__ "MatLUFactor_SeqAIJ" 877 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info) 878 { 879 PetscErrorCode ierr; 880 Mat C; 881 882 PetscFunctionBegin; 883 ierr = MatGetFactor(A,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr); 884 ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr); 885 ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr); 886 A->ops->solve = C->ops->solve; 887 A->ops->solvetranspose = C->ops->solvetranspose; 888 ierr = MatHeaderCopy(A,C);CHKERRQ(ierr); 889 ierr = PetscLogObjectParent(A,((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr); 890 PetscFunctionReturn(0); 891 } 892 /* ----------------------------------------------------------- */ 893 894 895 #undef __FUNCT__ 896 #define __FUNCT__ "MatSolve_SeqAIJ" 897 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx) 898 { 899 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 900 IS iscol = a->col,isrow = a->row; 901 PetscErrorCode ierr; 902 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 903 PetscInt nz; 904 const PetscInt *rout,*cout,*r,*c; 905 PetscScalar *x,*tmp,*tmps,sum; 906 const PetscScalar *b; 907 const MatScalar *aa = a->a,*v; 908 909 PetscFunctionBegin; 910 if (!n) PetscFunctionReturn(0); 911 912 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 913 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 914 tmp = a->solve_work; 915 916 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 917 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 918 919 /* forward solve the lower triangular */ 920 tmp[0] = b[*r++]; 921 tmps = tmp; 922 for (i=1; i<n; i++) { 923 v = aa + ai[i] ; 924 vi = aj + ai[i] ; 925 nz = a->diag[i] - ai[i]; 926 sum = b[*r++]; 927 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 928 tmp[i] = sum; 929 } 930 931 /* backward solve the upper triangular */ 932 for (i=n-1; i>=0; i--){ 933 v = aa + a->diag[i] + 1; 934 vi = aj + a->diag[i] + 1; 935 nz = ai[i+1] - a->diag[i] - 1; 936 sum = tmp[i]; 937 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 938 x[*c--] = tmp[i] = sum*aa[a->diag[i]]; 939 } 940 941 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 942 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 943 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 944 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 945 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 946 PetscFunctionReturn(0); 947 } 948 949 #undef __FUNCT__ 950 #define __FUNCT__ "MatMatSolve_SeqAIJ" 951 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X) 952 { 953 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 954 IS iscol = a->col,isrow = a->row; 955 PetscErrorCode ierr; 956 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 957 PetscInt nz,neq; 958 const PetscInt *rout,*cout,*r,*c; 959 PetscScalar *x,*b,*tmp,*tmps,sum; 960 const MatScalar *aa = a->a,*v; 961 PetscTruth bisdense,xisdense; 962 963 PetscFunctionBegin; 964 if (!n) PetscFunctionReturn(0); 965 966 ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr); 967 if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 968 ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr); 969 if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 970 971 ierr = MatGetArray(B,&b);CHKERRQ(ierr); 972 ierr = MatGetArray(X,&x);CHKERRQ(ierr); 973 974 tmp = a->solve_work; 975 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 976 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 977 978 for (neq=0; neq<B->cmap->n; neq++){ 979 /* forward solve the lower triangular */ 980 tmp[0] = b[r[0]]; 981 tmps = tmp; 982 for (i=1; i<n; i++) { 983 v = aa + ai[i] ; 984 vi = aj + ai[i] ; 985 nz = a->diag[i] - ai[i]; 986 sum = b[r[i]]; 987 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 988 tmp[i] = sum; 989 } 990 /* backward solve the upper triangular */ 991 for (i=n-1; i>=0; i--){ 992 v = aa + a->diag[i] + 1; 993 vi = aj + a->diag[i] + 1; 994 nz = ai[i+1] - a->diag[i] - 1; 995 sum = tmp[i]; 996 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 997 x[c[i]] = tmp[i] = sum*aa[a->diag[i]]; 998 } 999 1000 b += n; 1001 x += n; 1002 } 1003 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1004 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1005 ierr = MatRestoreArray(B,&b);CHKERRQ(ierr); 1006 ierr = MatRestoreArray(X,&x);CHKERRQ(ierr); 1007 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 1008 PetscFunctionReturn(0); 1009 } 1010 1011 #undef __FUNCT__ 1012 #define __FUNCT__ "MatSolve_SeqAIJ_InplaceWithPerm" 1013 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx) 1014 { 1015 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1016 IS iscol = a->col,isrow = a->row; 1017 PetscErrorCode ierr; 1018 const PetscInt *r,*c,*rout,*cout; 1019 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1020 PetscInt nz,row; 1021 PetscScalar *x,*b,*tmp,*tmps,sum; 1022 const MatScalar *aa = a->a,*v; 1023 1024 PetscFunctionBegin; 1025 if (!n) PetscFunctionReturn(0); 1026 1027 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1028 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1029 tmp = a->solve_work; 1030 1031 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1032 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1033 1034 /* forward solve the lower triangular */ 1035 tmp[0] = b[*r++]; 1036 tmps = tmp; 1037 for (row=1; row<n; row++) { 1038 i = rout[row]; /* permuted row */ 1039 v = aa + ai[i] ; 1040 vi = aj + ai[i] ; 1041 nz = a->diag[i] - ai[i]; 1042 sum = b[*r++]; 1043 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1044 tmp[row] = sum; 1045 } 1046 1047 /* backward solve the upper triangular */ 1048 for (row=n-1; row>=0; row--){ 1049 i = rout[row]; /* permuted row */ 1050 v = aa + a->diag[i] + 1; 1051 vi = aj + a->diag[i] + 1; 1052 nz = ai[i+1] - a->diag[i] - 1; 1053 sum = tmp[row]; 1054 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1055 x[*c--] = tmp[row] = sum*aa[a->diag[i]]; 1056 } 1057 1058 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1059 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1060 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1061 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1062 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1063 PetscFunctionReturn(0); 1064 } 1065 1066 /* ----------------------------------------------------------- */ 1067 #include "../src/mat/impls/aij/seq/ftn-kernels/fsolve.h" 1068 #undef __FUNCT__ 1069 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering" 1070 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx) 1071 { 1072 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1073 PetscErrorCode ierr; 1074 PetscInt n = A->rmap->n; 1075 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag; 1076 PetscScalar *x; 1077 const PetscScalar *b; 1078 const MatScalar *aa = a->a; 1079 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1080 PetscInt adiag_i,i,nz,ai_i; 1081 const PetscInt *vi; 1082 const MatScalar *v; 1083 PetscScalar sum; 1084 #endif 1085 1086 PetscFunctionBegin; 1087 if (!n) PetscFunctionReturn(0); 1088 1089 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1090 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1091 1092 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1093 fortransolveaij_(&n,x,ai,aj,adiag,aa,b); 1094 #else 1095 /* forward solve the lower triangular */ 1096 x[0] = b[0]; 1097 for (i=1; i<n; i++) { 1098 ai_i = ai[i]; 1099 v = aa + ai_i; 1100 vi = aj + ai_i; 1101 nz = adiag[i] - ai_i; 1102 sum = b[i]; 1103 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1104 x[i] = sum; 1105 } 1106 1107 /* backward solve the upper triangular */ 1108 for (i=n-1; i>=0; i--){ 1109 adiag_i = adiag[i]; 1110 v = aa + adiag_i + 1; 1111 vi = aj + adiag_i + 1; 1112 nz = ai[i+1] - adiag_i - 1; 1113 sum = x[i]; 1114 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1115 x[i] = sum*aa[adiag_i]; 1116 } 1117 #endif 1118 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1119 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1120 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1121 PetscFunctionReturn(0); 1122 } 1123 1124 #undef __FUNCT__ 1125 #define __FUNCT__ "MatSolveAdd_SeqAIJ" 1126 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx) 1127 { 1128 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1129 IS iscol = a->col,isrow = a->row; 1130 PetscErrorCode ierr; 1131 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1132 PetscInt nz; 1133 const PetscInt *rout,*cout,*r,*c; 1134 PetscScalar *x,*b,*tmp,sum; 1135 const MatScalar *aa = a->a,*v; 1136 1137 PetscFunctionBegin; 1138 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 1139 1140 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1141 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1142 tmp = a->solve_work; 1143 1144 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1145 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1146 1147 /* forward solve the lower triangular */ 1148 tmp[0] = b[*r++]; 1149 for (i=1; i<n; i++) { 1150 v = aa + ai[i] ; 1151 vi = aj + ai[i] ; 1152 nz = a->diag[i] - ai[i]; 1153 sum = b[*r++]; 1154 while (nz--) sum -= *v++ * tmp[*vi++ ]; 1155 tmp[i] = sum; 1156 } 1157 1158 /* backward solve the upper triangular */ 1159 for (i=n-1; i>=0; i--){ 1160 v = aa + a->diag[i] + 1; 1161 vi = aj + a->diag[i] + 1; 1162 nz = ai[i+1] - a->diag[i] - 1; 1163 sum = tmp[i]; 1164 while (nz--) sum -= *v++ * tmp[*vi++ ]; 1165 tmp[i] = sum*aa[a->diag[i]]; 1166 x[*c--] += tmp[i]; 1167 } 1168 1169 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1170 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1171 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1172 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1173 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1174 1175 PetscFunctionReturn(0); 1176 } 1177 /* -------------------------------------------------------------------*/ 1178 #undef __FUNCT__ 1179 #define __FUNCT__ "MatSolveTranspose_SeqAIJ" 1180 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx) 1181 { 1182 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1183 IS iscol = a->col,isrow = a->row; 1184 PetscErrorCode ierr; 1185 const PetscInt *rout,*cout,*r,*c; 1186 PetscInt i,n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1187 PetscInt nz,*diag = a->diag; 1188 PetscScalar *x,*b,*tmp,s1; 1189 const MatScalar *aa = a->a,*v; 1190 1191 PetscFunctionBegin; 1192 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1193 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1194 tmp = a->solve_work; 1195 1196 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1197 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1198 1199 /* copy the b into temp work space according to permutation */ 1200 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1201 1202 /* forward solve the U^T */ 1203 for (i=0; i<n; i++) { 1204 v = aa + diag[i] ; 1205 vi = aj + diag[i] + 1; 1206 nz = ai[i+1] - diag[i] - 1; 1207 s1 = tmp[i]; 1208 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1209 while (nz--) { 1210 tmp[*vi++ ] -= (*v++)*s1; 1211 } 1212 tmp[i] = s1; 1213 } 1214 1215 /* backward solve the L^T */ 1216 for (i=n-1; i>=0; i--){ 1217 v = aa + diag[i] - 1 ; 1218 vi = aj + diag[i] - 1 ; 1219 nz = diag[i] - ai[i]; 1220 s1 = tmp[i]; 1221 while (nz--) { 1222 tmp[*vi-- ] -= (*v--)*s1; 1223 } 1224 } 1225 1226 /* copy tmp into x according to permutation */ 1227 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1228 1229 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1230 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1231 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1232 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1233 1234 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1235 PetscFunctionReturn(0); 1236 } 1237 1238 #undef __FUNCT__ 1239 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ" 1240 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx) 1241 { 1242 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1243 IS iscol = a->col,isrow = a->row; 1244 PetscErrorCode ierr; 1245 const PetscInt *r,*c,*rout,*cout; 1246 PetscInt i,n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1247 PetscInt nz,*diag = a->diag; 1248 PetscScalar *x,*b,*tmp; 1249 const MatScalar *aa = a->a,*v; 1250 1251 PetscFunctionBegin; 1252 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1253 1254 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1255 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1256 tmp = a->solve_work; 1257 1258 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1259 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1260 1261 /* copy the b into temp work space according to permutation */ 1262 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1263 1264 /* forward solve the U^T */ 1265 for (i=0; i<n; i++) { 1266 v = aa + diag[i] ; 1267 vi = aj + diag[i] + 1; 1268 nz = ai[i+1] - diag[i] - 1; 1269 tmp[i] *= *v++; 1270 while (nz--) { 1271 tmp[*vi++ ] -= (*v++)*tmp[i]; 1272 } 1273 } 1274 1275 /* backward solve the L^T */ 1276 for (i=n-1; i>=0; i--){ 1277 v = aa + diag[i] - 1 ; 1278 vi = aj + diag[i] - 1 ; 1279 nz = diag[i] - ai[i]; 1280 while (nz--) { 1281 tmp[*vi-- ] -= (*v--)*tmp[i]; 1282 } 1283 } 1284 1285 /* copy tmp into x according to permutation */ 1286 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1287 1288 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1289 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1290 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1291 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1292 1293 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1294 PetscFunctionReturn(0); 1295 } 1296 /* ----------------------------------------------------------------*/ 1297 EXTERN PetscErrorCode Mat_CheckInode(Mat,PetscTruth); 1298 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth); 1299 1300 /* 1301 ilu(0) with natural ordering under new data structure. 1302 Factored arrays bj and ba are stored as 1303 L(0,:), L(1,:), ...,L(n-1,:), U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:) 1304 1305 bi=fact->i is an array of size 2n+2, in which 1306 bi+ 1307 bi[i] -> 1st entry of L(i,:),i=0,...,i-1 1308 bi[n] -> points to L(n-1,:)+1 1309 bi[n+1] -> 1st entry of U(n-1,:) 1310 bi[2n-i] -> 1st entry of U(i,:) 1311 bi[2n-i+1] -> end of U(i,:)+1, the 1st entry of U(i-1,:) 1312 bi[2n] -> 1st entry of U(0,:) 1313 bi[2n+1] -> points to U(0,:)+1 1314 1315 U(i,:) contains diag[i] as its last entry, i.e., 1316 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 1317 */ 1318 #undef __FUNCT__ 1319 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct" 1320 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1321 { 1322 1323 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1324 PetscErrorCode ierr; 1325 PetscInt n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag; 1326 PetscInt i,j,nz,*bi,*bj,*bdiag; 1327 1328 PetscFunctionBegin; 1329 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr); 1330 b = (Mat_SeqAIJ*)(fact)->data; 1331 1332 /* allocate matrix arrays for new data structure */ 1333 ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,2*n+2,PetscInt,&b->i);CHKERRQ(ierr); 1334 ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(2*n+2)*sizeof(PetscInt));CHKERRQ(ierr); 1335 b->singlemalloc = PETSC_TRUE; 1336 if (!b->diag){ 1337 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr); 1338 } 1339 bdiag = b->diag; 1340 1341 if (n > 0) { 1342 ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr); 1343 } 1344 1345 /* set bi and bj with new data structure */ 1346 bi = b->i; 1347 bj = b->j; 1348 1349 /* L part */ 1350 bi[0] = 0; 1351 for (i=0; i<n; i++){ 1352 nz = adiag[i] - ai[i]; 1353 bi[i+1] = bi[i] + nz; 1354 aj = a->j + ai[i]; 1355 for (j=0; j<nz; j++){ 1356 *bj = aj[j]; bj++; 1357 } 1358 } 1359 1360 /* U part */ 1361 bi[n+1] = bi[n]; 1362 for (i=n-1; i>=0; i--){ 1363 nz = ai[i+1] - adiag[i] - 1; 1364 bi[2*n-i+1] = bi[2*n-i] + nz + 1; 1365 aj = a->j + adiag[i] + 1; 1366 for (j=0; j<nz; j++){ 1367 *bj = aj[j]; bj++; 1368 } 1369 /* diag[i] */ 1370 *bj = i; bj++; 1371 bdiag[i] = bi[2*n-i+1]-1; 1372 } 1373 PetscFunctionReturn(0); 1374 } 1375 1376 #undef __FUNCT__ 1377 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_newdatastruct" 1378 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1379 { 1380 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1381 IS isicol; 1382 PetscErrorCode ierr; 1383 const PetscInt *r,*ic; 1384 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,d; 1385 PetscInt *bi,*cols,nnz,*cols_lvl; 1386 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1387 PetscInt i,levels,diagonal_fill; 1388 PetscTruth col_identity,row_identity; 1389 PetscReal f; 1390 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1391 PetscBT lnkbt; 1392 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1393 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1394 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1395 PetscTruth missing; 1396 1397 PetscFunctionBegin; 1398 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); 1399 f = info->fill; 1400 levels = (PetscInt)info->levels; 1401 diagonal_fill = (PetscInt)info->diagonal_fill; 1402 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1403 1404 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1405 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1406 1407 if (!levels && row_identity && col_identity) { 1408 /* special case: ilu(0) with natural ordering */ 1409 ierr = MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1410 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 1411 1412 fact->factor = MAT_FACTOR_ILU; 1413 (fact)->info.factor_mallocs = 0; 1414 (fact)->info.fill_ratio_given = info->fill; 1415 (fact)->info.fill_ratio_needed = 1.0; 1416 b = (Mat_SeqAIJ*)(fact)->data; 1417 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 1418 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 1419 b->row = isrow; 1420 b->col = iscol; 1421 b->icol = isicol; 1422 ierr = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1423 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1424 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1425 /* ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */ 1426 PetscFunctionReturn(0); 1427 } 1428 1429 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1430 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1431 1432 /* get new row pointers */ 1433 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1434 bi[0] = 0; 1435 /* bdiag is location of diagonal in factor */ 1436 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1437 bdiag[0] = 0; 1438 1439 ierr = PetscMalloc((2*n+1)*sizeof(PetscInt**),&bj_ptr);CHKERRQ(ierr); 1440 bjlvl_ptr = (PetscInt**)(bj_ptr + n); 1441 1442 /* create a linked list for storing column indices of the active row */ 1443 nlnk = n + 1; 1444 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1445 1446 /* initial FreeSpace size is f*(ai[n]+1) */ 1447 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1448 current_space = free_space; 1449 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1450 current_space_lvl = free_space_lvl; 1451 1452 for (i=0; i<n; i++) { 1453 nzi = 0; 1454 /* copy current row into linked list */ 1455 nnz = ai[r[i]+1] - ai[r[i]]; 1456 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1457 cols = aj + ai[r[i]]; 1458 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1459 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1460 nzi += nlnk; 1461 1462 /* make sure diagonal entry is included */ 1463 if (diagonal_fill && lnk[i] == -1) { 1464 fm = n; 1465 while (lnk[fm] < i) fm = lnk[fm]; 1466 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1467 lnk[fm] = i; 1468 lnk_lvl[i] = 0; 1469 nzi++; dcount++; 1470 } 1471 1472 /* add pivot rows into the active row */ 1473 nzbd = 0; 1474 prow = lnk[n]; 1475 while (prow < i) { 1476 nnz = bdiag[prow]; 1477 cols = bj_ptr[prow] + nnz + 1; 1478 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1479 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1480 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1481 nzi += nlnk; 1482 prow = lnk[prow]; 1483 nzbd++; 1484 } 1485 bdiag[i] = nzbd; 1486 bi[i+1] = bi[i] + nzi; 1487 1488 /* if free space is not available, make more free space */ 1489 if (current_space->local_remaining<nzi) { 1490 nnz = 2*nzi*(n - i); /* estimated and max additional space needed */ 1491 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1492 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1493 reallocs++; 1494 } 1495 1496 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1497 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1498 bj_ptr[i] = current_space->array; 1499 bjlvl_ptr[i] = current_space_lvl->array; 1500 1501 /* make sure the active row i has diagonal entry */ 1502 if (*(bj_ptr[i]+bdiag[i]) != i) { 1503 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 1504 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1505 } 1506 1507 current_space->array += nzi; 1508 current_space->local_used += nzi; 1509 current_space->local_remaining -= nzi; 1510 current_space_lvl->array += nzi; 1511 current_space_lvl->local_used += nzi; 1512 current_space_lvl->local_remaining -= nzi; 1513 } 1514 1515 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1516 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1517 1518 /* destroy list of free space and other temporary arrays */ 1519 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 1520 1521 /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */ 1522 ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 1523 1524 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1525 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1526 ierr = PetscFree(bj_ptr);CHKERRQ(ierr); 1527 1528 #if defined(PETSC_USE_INFO) 1529 { 1530 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1531 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 1532 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1533 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 1534 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1535 if (diagonal_fill) { 1536 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 1537 } 1538 } 1539 #endif 1540 1541 /* put together the new matrix */ 1542 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 1543 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 1544 b = (Mat_SeqAIJ*)(fact)->data; 1545 b->free_a = PETSC_TRUE; 1546 b->free_ij = PETSC_TRUE; 1547 b->singlemalloc = PETSC_FALSE; 1548 ierr = PetscMalloc( (bi[2*n+1] )*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 1549 b->j = bj; 1550 b->i = bi; 1551 b->diag = bdiag; 1552 b->ilen = 0; 1553 b->imax = 0; 1554 b->row = isrow; 1555 b->col = iscol; 1556 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1557 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1558 b->icol = isicol; 1559 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1560 /* In b structure: Free imax, ilen, old a, old j. 1561 Allocate bdiag, solve_work, new a, new j */ 1562 ierr = PetscLogObjectMemory(fact,bi[2*n+1] * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1563 b->maxnz = b->nz = bi[2*n+1] ; 1564 (fact)->info.factor_mallocs = reallocs; 1565 (fact)->info.fill_ratio_given = f; 1566 (fact)->info.fill_ratio_needed = ((PetscReal)bi[2*n+1])/((PetscReal)ai[n]); 1567 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 1568 /* ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */ 1569 PetscFunctionReturn(0); 1570 } 1571 1572 #undef __FUNCT__ 1573 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ" 1574 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1575 { 1576 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1577 IS isicol; 1578 PetscErrorCode ierr; 1579 const PetscInt *r,*ic; 1580 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,d; 1581 PetscInt *bi,*cols,nnz,*cols_lvl; 1582 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1583 PetscInt i,levels,diagonal_fill; 1584 PetscTruth col_identity,row_identity; 1585 PetscReal f; 1586 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1587 PetscBT lnkbt; 1588 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1589 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1590 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1591 PetscTruth missing; 1592 PetscTruth newdatastruct=PETSC_FALSE; 1593 1594 PetscFunctionBegin; 1595 ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 1596 if (newdatastruct){ 1597 ierr = MatILUFactorSymbolic_SeqAIJ_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1598 PetscFunctionReturn(0); 1599 } 1600 1601 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); 1602 f = info->fill; 1603 levels = (PetscInt)info->levels; 1604 diagonal_fill = (PetscInt)info->diagonal_fill; 1605 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1606 1607 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1608 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1609 if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */ 1610 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr); 1611 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1612 1613 fact->factor = MAT_FACTOR_ILU; 1614 (fact)->info.factor_mallocs = 0; 1615 (fact)->info.fill_ratio_given = info->fill; 1616 (fact)->info.fill_ratio_needed = 1.0; 1617 b = (Mat_SeqAIJ*)(fact)->data; 1618 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 1619 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 1620 b->row = isrow; 1621 b->col = iscol; 1622 b->icol = isicol; 1623 ierr = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1624 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1625 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1626 ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1627 PetscFunctionReturn(0); 1628 } 1629 1630 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1631 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1632 1633 /* get new row pointers */ 1634 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1635 bi[0] = 0; 1636 /* bdiag is location of diagonal in factor */ 1637 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1638 bdiag[0] = 0; 1639 1640 ierr = PetscMalloc((2*n+1)*sizeof(PetscInt**),&bj_ptr);CHKERRQ(ierr); 1641 bjlvl_ptr = (PetscInt**)(bj_ptr + n); 1642 1643 /* create a linked list for storing column indices of the active row */ 1644 nlnk = n + 1; 1645 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1646 1647 /* initial FreeSpace size is f*(ai[n]+1) */ 1648 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1649 current_space = free_space; 1650 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1651 current_space_lvl = free_space_lvl; 1652 1653 for (i=0; i<n; i++) { 1654 nzi = 0; 1655 /* copy current row into linked list */ 1656 nnz = ai[r[i]+1] - ai[r[i]]; 1657 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1658 cols = aj + ai[r[i]]; 1659 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1660 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1661 nzi += nlnk; 1662 1663 /* make sure diagonal entry is included */ 1664 if (diagonal_fill && lnk[i] == -1) { 1665 fm = n; 1666 while (lnk[fm] < i) fm = lnk[fm]; 1667 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1668 lnk[fm] = i; 1669 lnk_lvl[i] = 0; 1670 nzi++; dcount++; 1671 } 1672 1673 /* add pivot rows into the active row */ 1674 nzbd = 0; 1675 prow = lnk[n]; 1676 while (prow < i) { 1677 nnz = bdiag[prow]; 1678 cols = bj_ptr[prow] + nnz + 1; 1679 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1680 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1681 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1682 nzi += nlnk; 1683 prow = lnk[prow]; 1684 nzbd++; 1685 } 1686 bdiag[i] = nzbd; 1687 bi[i+1] = bi[i] + nzi; 1688 1689 /* if free space is not available, make more free space */ 1690 if (current_space->local_remaining<nzi) { 1691 nnz = nzi*(n - i); /* estimated and max additional space needed */ 1692 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1693 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1694 reallocs++; 1695 } 1696 1697 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1698 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1699 bj_ptr[i] = current_space->array; 1700 bjlvl_ptr[i] = current_space_lvl->array; 1701 1702 /* make sure the active row i has diagonal entry */ 1703 if (*(bj_ptr[i]+bdiag[i]) != i) { 1704 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 1705 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1706 } 1707 1708 current_space->array += nzi; 1709 current_space->local_used += nzi; 1710 current_space->local_remaining -= nzi; 1711 current_space_lvl->array += nzi; 1712 current_space_lvl->local_used += nzi; 1713 current_space_lvl->local_remaining -= nzi; 1714 } 1715 1716 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1717 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1718 1719 /* destroy list of free space and other temporary arrays */ 1720 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 1721 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */ 1722 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1723 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1724 ierr = PetscFree(bj_ptr);CHKERRQ(ierr); 1725 1726 #if defined(PETSC_USE_INFO) 1727 { 1728 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1729 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 1730 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1731 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 1732 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1733 if (diagonal_fill) { 1734 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 1735 } 1736 } 1737 #endif 1738 1739 /* put together the new matrix */ 1740 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 1741 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 1742 b = (Mat_SeqAIJ*)(fact)->data; 1743 b->free_a = PETSC_TRUE; 1744 b->free_ij = PETSC_TRUE; 1745 b->singlemalloc = PETSC_FALSE; 1746 ierr = PetscMalloc( (bi[n] )*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 1747 b->j = bj; 1748 b->i = bi; 1749 for (i=0; i<n; i++) bdiag[i] += bi[i]; 1750 b->diag = bdiag; 1751 b->ilen = 0; 1752 b->imax = 0; 1753 b->row = isrow; 1754 b->col = iscol; 1755 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1756 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1757 b->icol = isicol; 1758 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1759 /* In b structure: Free imax, ilen, old a, old j. 1760 Allocate bdiag, solve_work, new a, new j */ 1761 ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1762 b->maxnz = b->nz = bi[n] ; 1763 (fact)->info.factor_mallocs = reallocs; 1764 (fact)->info.fill_ratio_given = f; 1765 (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1766 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1767 ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1768 PetscFunctionReturn(0); 1769 } 1770 1771 #undef __FUNCT__ 1772 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ_newdatastruct" 1773 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info) 1774 { 1775 Mat C = B; 1776 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 1777 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 1778 IS ip=b->row,iip = b->icol; 1779 PetscErrorCode ierr; 1780 const PetscInt *rip,*riip; 1781 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp; 1782 PetscInt *ai=a->i,*aj=a->j; 1783 PetscInt k,jmin,jmax,*c2r,*il,col,nexti,ili,nz; 1784 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 1785 PetscReal zeropivot,shiftnz; 1786 PetscReal shiftpd; 1787 PetscTruth perm_identity; 1788 1789 PetscFunctionBegin; 1790 1791 shiftnz = info->shiftnz; 1792 shiftpd = info->shiftpd; 1793 zeropivot = info->zeropivot; 1794 1795 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 1796 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 1797 1798 /* allocate working arrays 1799 c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col 1800 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 1801 */ 1802 nz = (2*mbs+1)*sizeof(PetscInt)+mbs*sizeof(MatScalar); 1803 ierr = PetscMalloc(nz,&il);CHKERRQ(ierr); 1804 c2r = il + mbs; 1805 rtmp = (MatScalar*)(c2r + mbs); 1806 1807 for (i=0; i<mbs; i++) { 1808 c2r[i] = mbs; 1809 } 1810 il[0] = 0; 1811 1812 for (k = 0; k<mbs; k++){ 1813 /* zero rtmp */ 1814 nz = bi[k+1] - bi[k]; 1815 bjtmp = bj + bi[k]; 1816 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 1817 1818 /* load in initial unfactored row */ 1819 bval = ba + bi[k]; 1820 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 1821 for (j = jmin; j < jmax; j++){ 1822 col = riip[aj[j]]; 1823 if (col >= k){ /* only take upper triangular entry */ 1824 rtmp[col] = aa[j]; 1825 *bval++ = 0.0; /* for in-place factorization */ 1826 } 1827 } 1828 /* shift the diagonal of the matrix */ 1829 1830 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 1831 dk = rtmp[k]; 1832 i = c2r[k]; /* first row to be added to k_th row */ 1833 1834 while (i < k){ 1835 nexti = c2r[i]; /* next row to be added to k_th row */ 1836 1837 /* compute multiplier, update diag(k) and U(i,k) */ 1838 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 1839 uikdi = - ba[ili]*ba[bdiag[i]]; /* diagonal(k) */ 1840 dk += uikdi*ba[ili]; /* update diag[k] */ 1841 ba[ili] = uikdi; /* -U(i,k) */ 1842 1843 /* add multiple of row i to k-th row */ 1844 jmin = ili + 1; jmax = bi[i+1]; 1845 if (jmin < jmax){ 1846 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 1847 /* update il and c2r for row i */ 1848 il[i] = jmin; 1849 j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i; 1850 } 1851 i = nexti; 1852 } 1853 1854 /* copy data into U(k,:) */ 1855 ba[bdiag[k]] = 1.0/dk; /* U(k,k) */ 1856 jmin = bi[k]; jmax = bi[k+1]-1; 1857 if (jmin < jmax) { 1858 for (j=jmin; j<jmax; j++){ 1859 col = bj[j]; ba[j] = rtmp[col]; 1860 } 1861 /* add the k-th row into il and c2r */ 1862 il[k] = jmin; 1863 i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k; 1864 } 1865 } 1866 1867 ierr = PetscFree(il);CHKERRQ(ierr); 1868 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 1869 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 1870 1871 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 1872 if (perm_identity){ 1873 (B)->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_newdatastruct; 1874 (B)->ops->solvetranspose = 0; 1875 (B)->ops->forwardsolve = 0; 1876 (B)->ops->backwardsolve = 0; 1877 } else { 1878 (B)->ops->solve = MatSolve_SeqSBAIJ_1_newdatastruct; 1879 (B)->ops->solvetranspose = 0; 1880 (B)->ops->forwardsolve = 0; 1881 (B)->ops->backwardsolve = 0; 1882 } 1883 1884 C->assembled = PETSC_TRUE; 1885 C->preallocated = PETSC_TRUE; 1886 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 1887 PetscFunctionReturn(0); 1888 } 1889 1890 #undef __FUNCT__ 1891 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ" 1892 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 1893 { 1894 Mat C = B; 1895 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 1896 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 1897 IS ip=b->row,iip = b->icol; 1898 PetscErrorCode ierr; 1899 const PetscInt *rip,*riip; 1900 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol; 1901 PetscInt *ai=a->i,*aj=a->j; 1902 PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz; 1903 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 1904 PetscReal zeropivot,rs,shiftnz; 1905 PetscReal shiftpd; 1906 ChShift_Ctx sctx; 1907 PetscInt newshift; 1908 PetscTruth perm_identity; 1909 1910 PetscFunctionBegin; 1911 shiftnz = info->shiftnz; 1912 shiftpd = info->shiftpd; 1913 zeropivot = info->zeropivot; 1914 1915 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 1916 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 1917 1918 /* initialization */ 1919 nz = (2*mbs+1)*sizeof(PetscInt)+mbs*sizeof(MatScalar); 1920 ierr = PetscMalloc(nz,&il);CHKERRQ(ierr); 1921 jl = il + mbs; 1922 rtmp = (MatScalar*)(jl + mbs); 1923 1924 sctx.shift_amount = 0; 1925 sctx.nshift = 0; 1926 do { 1927 sctx.chshift = PETSC_FALSE; 1928 for (i=0; i<mbs; i++) { 1929 rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0; 1930 } 1931 1932 for (k = 0; k<mbs; k++){ 1933 bval = ba + bi[k]; 1934 /* initialize k-th row by the perm[k]-th row of A */ 1935 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 1936 for (j = jmin; j < jmax; j++){ 1937 col = riip[aj[j]]; 1938 if (col >= k){ /* only take upper triangular entry */ 1939 rtmp[col] = aa[j]; 1940 *bval++ = 0.0; /* for in-place factorization */ 1941 } 1942 } 1943 /* shift the diagonal of the matrix */ 1944 if (sctx.nshift) rtmp[k] += sctx.shift_amount; 1945 1946 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 1947 dk = rtmp[k]; 1948 i = jl[k]; /* first row to be added to k_th row */ 1949 1950 while (i < k){ 1951 nexti = jl[i]; /* next row to be added to k_th row */ 1952 1953 /* compute multiplier, update diag(k) and U(i,k) */ 1954 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 1955 uikdi = - ba[ili]*ba[bi[i]]; /* diagonal(k) */ 1956 dk += uikdi*ba[ili]; 1957 ba[ili] = uikdi; /* -U(i,k) */ 1958 1959 /* add multiple of row i to k-th row */ 1960 jmin = ili + 1; jmax = bi[i+1]; 1961 if (jmin < jmax){ 1962 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 1963 /* update il and jl for row i */ 1964 il[i] = jmin; 1965 j = bj[jmin]; jl[i] = jl[j]; jl[j] = i; 1966 } 1967 i = nexti; 1968 } 1969 1970 /* shift the diagonals when zero pivot is detected */ 1971 /* compute rs=sum of abs(off-diagonal) */ 1972 rs = 0.0; 1973 jmin = bi[k]+1; 1974 nz = bi[k+1] - jmin; 1975 bcol = bj + jmin; 1976 while (nz--){ 1977 rs += PetscAbsScalar(rtmp[*bcol]); 1978 bcol++; 1979 } 1980 1981 sctx.rs = rs; 1982 sctx.pv = dk; 1983 ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr); 1984 1985 if (newshift == 1) { 1986 if (!sctx.shift_amount) { 1987 sctx.shift_amount = 1e-5; 1988 } 1989 break; 1990 } 1991 1992 /* copy data into U(k,:) */ 1993 ba[bi[k]] = 1.0/dk; /* U(k,k) */ 1994 jmin = bi[k]+1; jmax = bi[k+1]; 1995 if (jmin < jmax) { 1996 for (j=jmin; j<jmax; j++){ 1997 col = bj[j]; ba[j] = rtmp[col]; rtmp[col] = 0.0; 1998 } 1999 /* add the k-th row into il and jl */ 2000 il[k] = jmin; 2001 i = bj[jmin]; jl[k] = jl[i]; jl[i] = k; 2002 } 2003 } 2004 } while (sctx.chshift); 2005 ierr = PetscFree(il);CHKERRQ(ierr); 2006 2007 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2008 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2009 2010 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2011 if (perm_identity){ 2012 (B)->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2013 (B)->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2014 (B)->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering; 2015 (B)->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering; 2016 } else { 2017 (B)->ops->solve = MatSolve_SeqSBAIJ_1; 2018 (B)->ops->solvetranspose = MatSolve_SeqSBAIJ_1; 2019 (B)->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1; 2020 (B)->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1; 2021 } 2022 2023 C->assembled = PETSC_TRUE; 2024 C->preallocated = PETSC_TRUE; 2025 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2026 if (sctx.nshift){ 2027 if (shiftnz) { 2028 ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2029 } else if (shiftpd) { 2030 ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2031 } 2032 } 2033 PetscFunctionReturn(0); 2034 } 2035 2036 #undef __FUNCT__ 2037 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ_newdatastruct" 2038 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2039 { 2040 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2041 Mat_SeqSBAIJ *b; 2042 PetscErrorCode ierr; 2043 PetscTruth perm_identity,missing; 2044 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2045 const PetscInt *rip,*riip; 2046 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2047 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2048 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2049 PetscReal fill=info->fill,levels=info->levels; 2050 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2051 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2052 PetscBT lnkbt; 2053 IS iperm; 2054 2055 PetscFunctionBegin; 2056 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); 2057 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2058 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2059 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2060 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2061 2062 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2063 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2064 ui[0] = 0; 2065 2066 /* ICC(0) without matrix ordering: simply copies fill pattern */ 2067 if (!levels && perm_identity) { 2068 2069 for (i=0; i<am; i++) { 2070 ui[i+1] = ui[i] + ai[i+1] - a->diag[i]; 2071 udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */ 2072 } 2073 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2074 cols = uj; 2075 for (i=0; i<am; i++) { 2076 aj = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */ 2077 ncols = ui[i+1] - ui[i] - 1; 2078 for (j=0; j<ncols; j++) *cols++ = aj[j]; 2079 *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */ 2080 } 2081 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2082 2083 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2084 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2085 2086 /* initialization */ 2087 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2088 2089 /* jl: linked list for storing indices of the pivot rows 2090 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2091 ierr = PetscMalloc((2*am+1)*sizeof(PetscInt)+2*am*sizeof(PetscInt**),&jl);CHKERRQ(ierr); 2092 il = jl + am; 2093 uj_ptr = (PetscInt**)(il + am); 2094 uj_lvl_ptr = (PetscInt**)(uj_ptr + am); 2095 for (i=0; i<am; i++){ 2096 jl[i] = am; il[i] = 0; 2097 } 2098 2099 /* create and initialize a linked list for storing column indices of the active row k */ 2100 nlnk = am + 1; 2101 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2102 2103 /* initial FreeSpace size is fill*(ai[am]+1) */ 2104 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2105 current_space = free_space; 2106 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2107 current_space_lvl = free_space_lvl; 2108 2109 for (k=0; k<am; k++){ /* for each active row k */ 2110 /* initialize lnk by the column indices of row rip[k] of A */ 2111 nzk = 0; 2112 ncols = ai[rip[k]+1] - ai[rip[k]]; 2113 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2114 ncols_upper = 0; 2115 for (j=0; j<ncols; j++){ 2116 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2117 if (riip[i] >= k){ /* only take upper triangular entry */ 2118 ajtmp[ncols_upper] = i; 2119 ncols_upper++; 2120 } 2121 } 2122 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2123 nzk += nlnk; 2124 2125 /* update lnk by computing fill-in for each pivot row to be merged in */ 2126 prow = jl[k]; /* 1st pivot row */ 2127 2128 while (prow < k){ 2129 nextprow = jl[prow]; 2130 2131 /* merge prow into k-th row */ 2132 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2133 jmax = ui[prow+1]; 2134 ncols = jmax-jmin; 2135 i = jmin - ui[prow]; 2136 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2137 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2138 j = *(uj - 1); 2139 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2140 nzk += nlnk; 2141 2142 /* update il and jl for prow */ 2143 if (jmin < jmax){ 2144 il[prow] = jmin; 2145 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2146 } 2147 prow = nextprow; 2148 } 2149 2150 /* if free space is not available, make more free space */ 2151 if (current_space->local_remaining<nzk) { 2152 i = am - k + 1; /* num of unfactored rows */ 2153 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2154 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2155 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2156 reallocs++; 2157 } 2158 2159 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2160 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2161 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2162 2163 /* add the k-th row into il and jl */ 2164 if (nzk > 1){ 2165 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2166 jl[k] = jl[i]; jl[i] = k; 2167 il[k] = ui[k] + 1; 2168 } 2169 uj_ptr[k] = current_space->array; 2170 uj_lvl_ptr[k] = current_space_lvl->array; 2171 2172 current_space->array += nzk; 2173 current_space->local_used += nzk; 2174 current_space->local_remaining -= nzk; 2175 2176 current_space_lvl->array += nzk; 2177 current_space_lvl->local_used += nzk; 2178 current_space_lvl->local_remaining -= nzk; 2179 2180 ui[k+1] = ui[k] + nzk; 2181 } 2182 2183 #if defined(PETSC_USE_INFO) 2184 if (ai[am] != 0) { 2185 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2186 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2187 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2188 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2189 } else { 2190 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2191 } 2192 #endif 2193 2194 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2195 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2196 ierr = PetscFree(jl);CHKERRQ(ierr); 2197 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2198 2199 /* destroy list of free space and other temporary array(s) */ 2200 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2201 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); 2202 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2203 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2204 2205 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2206 2207 /* put together the new matrix in MATSEQSBAIJ format */ 2208 2209 b = (Mat_SeqSBAIJ*)(fact)->data; 2210 b->singlemalloc = PETSC_FALSE; 2211 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2212 b->j = uj; 2213 b->i = ui; 2214 b->diag = udiag; 2215 b->ilen = 0; 2216 b->imax = 0; 2217 b->row = perm; 2218 b->col = perm; 2219 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2220 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2221 b->icol = iperm; 2222 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2223 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2224 ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2225 b->maxnz = b->nz = ui[am]; 2226 b->free_a = PETSC_TRUE; 2227 b->free_ij = PETSC_TRUE; 2228 2229 (fact)->info.factor_mallocs = reallocs; 2230 (fact)->info.fill_ratio_given = fill; 2231 if (ai[am] != 0) { 2232 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2233 } else { 2234 (fact)->info.fill_ratio_needed = 0.0; 2235 } 2236 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct; 2237 PetscFunctionReturn(0); 2238 } 2239 2240 #undef __FUNCT__ 2241 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ" 2242 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2243 { 2244 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2245 Mat_SeqSBAIJ *b; 2246 PetscErrorCode ierr; 2247 PetscTruth perm_identity,missing; 2248 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2249 const PetscInt *rip,*riip; 2250 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2251 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2252 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2253 PetscReal fill=info->fill,levels=info->levels; 2254 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2255 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2256 PetscBT lnkbt; 2257 IS iperm; 2258 PetscTruth newdatastruct=PETSC_FALSE; 2259 2260 PetscFunctionBegin; 2261 ierr = PetscOptionsGetTruth(PETSC_NULL,"-icc_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 2262 if(newdatastruct){ 2263 ierr = MatICCFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr); 2264 PetscFunctionReturn(0); 2265 } 2266 2267 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); 2268 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2269 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2270 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2271 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2272 2273 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2274 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2275 ui[0] = 0; 2276 2277 /* ICC(0) without matrix ordering: simply copies fill pattern */ 2278 if (!levels && perm_identity) { 2279 2280 for (i=0; i<am; i++) { 2281 ui[i+1] = ui[i] + ai[i+1] - a->diag[i]; 2282 udiag[i] = ui[i]; 2283 } 2284 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2285 cols = uj; 2286 for (i=0; i<am; i++) { 2287 aj = a->j + a->diag[i]; 2288 ncols = ui[i+1] - ui[i]; 2289 for (j=0; j<ncols; j++) *cols++ = *aj++; 2290 } 2291 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2292 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2293 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2294 2295 /* initialization */ 2296 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2297 2298 /* jl: linked list for storing indices of the pivot rows 2299 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2300 ierr = PetscMalloc((2*am+1)*sizeof(PetscInt)+2*am*sizeof(PetscInt**),&jl);CHKERRQ(ierr); 2301 il = jl + am; 2302 uj_ptr = (PetscInt**)(il + am); 2303 uj_lvl_ptr = (PetscInt**)(uj_ptr + am); 2304 for (i=0; i<am; i++){ 2305 jl[i] = am; il[i] = 0; 2306 } 2307 2308 /* create and initialize a linked list for storing column indices of the active row k */ 2309 nlnk = am + 1; 2310 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2311 2312 /* initial FreeSpace size is fill*(ai[am]+1) */ 2313 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2314 current_space = free_space; 2315 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2316 current_space_lvl = free_space_lvl; 2317 2318 for (k=0; k<am; k++){ /* for each active row k */ 2319 /* initialize lnk by the column indices of row rip[k] of A */ 2320 nzk = 0; 2321 ncols = ai[rip[k]+1] - ai[rip[k]]; 2322 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2323 ncols_upper = 0; 2324 for (j=0; j<ncols; j++){ 2325 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2326 if (riip[i] >= k){ /* only take upper triangular entry */ 2327 ajtmp[ncols_upper] = i; 2328 ncols_upper++; 2329 } 2330 } 2331 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2332 nzk += nlnk; 2333 2334 /* update lnk by computing fill-in for each pivot row to be merged in */ 2335 prow = jl[k]; /* 1st pivot row */ 2336 2337 while (prow < k){ 2338 nextprow = jl[prow]; 2339 2340 /* merge prow into k-th row */ 2341 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2342 jmax = ui[prow+1]; 2343 ncols = jmax-jmin; 2344 i = jmin - ui[prow]; 2345 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2346 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2347 j = *(uj - 1); 2348 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2349 nzk += nlnk; 2350 2351 /* update il and jl for prow */ 2352 if (jmin < jmax){ 2353 il[prow] = jmin; 2354 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2355 } 2356 prow = nextprow; 2357 } 2358 2359 /* if free space is not available, make more free space */ 2360 if (current_space->local_remaining<nzk) { 2361 i = am - k + 1; /* num of unfactored rows */ 2362 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2363 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2364 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2365 reallocs++; 2366 } 2367 2368 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2369 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2370 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2371 2372 /* add the k-th row into il and jl */ 2373 if (nzk > 1){ 2374 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2375 jl[k] = jl[i]; jl[i] = k; 2376 il[k] = ui[k] + 1; 2377 } 2378 uj_ptr[k] = current_space->array; 2379 uj_lvl_ptr[k] = current_space_lvl->array; 2380 2381 current_space->array += nzk; 2382 current_space->local_used += nzk; 2383 current_space->local_remaining -= nzk; 2384 2385 current_space_lvl->array += nzk; 2386 current_space_lvl->local_used += nzk; 2387 current_space_lvl->local_remaining -= nzk; 2388 2389 ui[k+1] = ui[k] + nzk; 2390 } 2391 2392 #if defined(PETSC_USE_INFO) 2393 if (ai[am] != 0) { 2394 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2395 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2396 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2397 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2398 } else { 2399 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2400 } 2401 #endif 2402 2403 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2404 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2405 ierr = PetscFree(jl);CHKERRQ(ierr); 2406 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2407 2408 /* destroy list of free space and other temporary array(s) */ 2409 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2410 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 2411 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2412 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2413 2414 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2415 2416 /* put together the new matrix in MATSEQSBAIJ format */ 2417 2418 b = (Mat_SeqSBAIJ*)(fact)->data; 2419 b->singlemalloc = PETSC_FALSE; 2420 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2421 b->j = uj; 2422 b->i = ui; 2423 b->diag = udiag; 2424 b->ilen = 0; 2425 b->imax = 0; 2426 b->row = perm; 2427 b->col = perm; 2428 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2429 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2430 b->icol = iperm; 2431 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2432 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2433 ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2434 b->maxnz = b->nz = ui[am]; 2435 b->free_a = PETSC_TRUE; 2436 b->free_ij = PETSC_TRUE; 2437 2438 (fact)->info.factor_mallocs = reallocs; 2439 (fact)->info.fill_ratio_given = fill; 2440 if (ai[am] != 0) { 2441 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2442 } else { 2443 (fact)->info.fill_ratio_needed = 0.0; 2444 } 2445 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2446 PetscFunctionReturn(0); 2447 } 2448 2449 #undef __FUNCT__ 2450 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ" 2451 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2452 { 2453 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2454 Mat_SeqSBAIJ *b; 2455 PetscErrorCode ierr; 2456 PetscTruth perm_identity; 2457 PetscReal fill = info->fill; 2458 const PetscInt *rip,*riip; 2459 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2460 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2461 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr; 2462 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2463 PetscBT lnkbt; 2464 IS iperm; 2465 2466 PetscFunctionBegin; 2467 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); 2468 /* check whether perm is the identity mapping */ 2469 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2470 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2471 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2472 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2473 2474 /* initialization */ 2475 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2476 ui[0] = 0; 2477 2478 /* jl: linked list for storing indices of the pivot rows 2479 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2480 ierr = PetscMalloc((3*am+1)*sizeof(PetscInt)+am*sizeof(PetscInt**),&jl);CHKERRQ(ierr); 2481 il = jl + am; 2482 cols = il + am; 2483 ui_ptr = (PetscInt**)(cols + am); 2484 for (i=0; i<am; i++){ 2485 jl[i] = am; il[i] = 0; 2486 } 2487 2488 /* create and initialize a linked list for storing column indices of the active row k */ 2489 nlnk = am + 1; 2490 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2491 2492 /* initial FreeSpace size is fill*(ai[am]+1) */ 2493 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2494 current_space = free_space; 2495 2496 for (k=0; k<am; k++){ /* for each active row k */ 2497 /* initialize lnk by the column indices of row rip[k] of A */ 2498 nzk = 0; 2499 ncols = ai[rip[k]+1] - ai[rip[k]]; 2500 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2501 ncols_upper = 0; 2502 for (j=0; j<ncols; j++){ 2503 i = riip[*(aj + ai[rip[k]] + j)]; 2504 if (i >= k){ /* only take upper triangular entry */ 2505 cols[ncols_upper] = i; 2506 ncols_upper++; 2507 } 2508 } 2509 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2510 nzk += nlnk; 2511 2512 /* update lnk by computing fill-in for each pivot row to be merged in */ 2513 prow = jl[k]; /* 1st pivot row */ 2514 2515 while (prow < k){ 2516 nextprow = jl[prow]; 2517 /* merge prow into k-th row */ 2518 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2519 jmax = ui[prow+1]; 2520 ncols = jmax-jmin; 2521 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2522 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2523 nzk += nlnk; 2524 2525 /* update il and jl for prow */ 2526 if (jmin < jmax){ 2527 il[prow] = jmin; 2528 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 2529 } 2530 prow = nextprow; 2531 } 2532 2533 /* if free space is not available, make more free space */ 2534 if (current_space->local_remaining<nzk) { 2535 i = am - k + 1; /* num of unfactored rows */ 2536 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2537 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2538 reallocs++; 2539 } 2540 2541 /* copy data into free space, then initialize lnk */ 2542 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 2543 2544 /* add the k-th row into il and jl */ 2545 if (nzk-1 > 0){ 2546 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2547 jl[k] = jl[i]; jl[i] = k; 2548 il[k] = ui[k] + 1; 2549 } 2550 ui_ptr[k] = current_space->array; 2551 current_space->array += nzk; 2552 current_space->local_used += nzk; 2553 current_space->local_remaining -= nzk; 2554 2555 ui[k+1] = ui[k] + nzk; 2556 } 2557 2558 #if defined(PETSC_USE_INFO) 2559 if (ai[am] != 0) { 2560 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 2561 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2562 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2563 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2564 } else { 2565 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2566 } 2567 #endif 2568 2569 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2570 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2571 ierr = PetscFree(jl);CHKERRQ(ierr); 2572 2573 /* destroy list of free space and other temporary array(s) */ 2574 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2575 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 2576 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2577 2578 /* put together the new matrix in MATSEQSBAIJ format */ 2579 2580 b = (Mat_SeqSBAIJ*)(fact)->data; 2581 b->singlemalloc = PETSC_FALSE; 2582 b->free_a = PETSC_TRUE; 2583 b->free_ij = PETSC_TRUE; 2584 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2585 b->j = uj; 2586 b->i = ui; 2587 b->diag = 0; 2588 b->ilen = 0; 2589 b->imax = 0; 2590 b->row = perm; 2591 b->col = perm; 2592 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2593 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2594 b->icol = iperm; 2595 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2596 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2597 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2598 b->maxnz = b->nz = ui[am]; 2599 2600 (fact)->info.factor_mallocs = reallocs; 2601 (fact)->info.fill_ratio_given = fill; 2602 if (ai[am] != 0) { 2603 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2604 } else { 2605 (fact)->info.fill_ratio_needed = 0.0; 2606 } 2607 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2608 PetscFunctionReturn(0); 2609 } 2610 2611 #undef __FUNCT__ 2612 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct" 2613 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx) 2614 { 2615 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2616 PetscErrorCode ierr; 2617 PetscInt n = A->rmap->n; 2618 const PetscInt *ai = a->i,*aj = a->j,*vi; 2619 PetscScalar *x,sum; 2620 const PetscScalar *b; 2621 const MatScalar *aa = a->a,*v; 2622 PetscInt i,nz; 2623 2624 PetscFunctionBegin; 2625 if (!n) PetscFunctionReturn(0); 2626 2627 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 2628 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 2629 2630 /* forward solve the lower triangular */ 2631 x[0] = b[0]; 2632 v = aa; 2633 vi = aj; 2634 for (i=1; i<n; i++) { 2635 nz = ai[i+1] - ai[i]; 2636 sum = b[i]; 2637 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 2638 /* while (nz--) sum -= *v++ * x[*vi++];*/ 2639 v += nz; 2640 vi += nz; 2641 x[i] = sum; 2642 } 2643 2644 /* backward solve the upper triangular */ 2645 v = aa + ai[n+1]; 2646 vi = aj + ai[n+1]; 2647 for (i=n-1; i>=0; i--){ 2648 nz = ai[2*n-i +1] - ai[2*n-i]-1; 2649 sum = x[i]; 2650 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 2651 /* while (nz--) sum -= *v++ * x[*vi++]; */ 2652 v += nz; 2653 vi += nz; vi++; 2654 x[i] = *v++ *sum; /* x[i]=aa[adiag[i]]*sum; v++; */ 2655 } 2656 2657 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 2658 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 2659 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 2660 PetscFunctionReturn(0); 2661 } 2662 2663 #undef __FUNCT__ 2664 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct" 2665 PetscErrorCode MatSolve_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx) 2666 { 2667 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2668 IS iscol = a->col,isrow = a->row; 2669 PetscErrorCode ierr; 2670 PetscInt i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,nz,k; 2671 const PetscInt *rout,*cout,*r,*c; 2672 PetscScalar *x,*tmp,*tmps,sum; 2673 const PetscScalar *b; 2674 const MatScalar *aa = a->a,*v; 2675 2676 PetscFunctionBegin; 2677 if (!n) PetscFunctionReturn(0); 2678 2679 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 2680 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 2681 tmp = a->solve_work; 2682 2683 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 2684 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 2685 2686 /* forward solve the lower triangular */ 2687 tmp[0] = b[*r++]; 2688 tmps = tmp; 2689 v = aa; 2690 vi = aj; 2691 for (i=1; i<n; i++) { 2692 nz = ai[i+1] - ai[i]; 2693 sum = b[*r++]; 2694 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 2695 tmp[i] = sum; 2696 v += nz; vi += nz; 2697 } 2698 2699 /* backward solve the upper triangular */ 2700 k = n+1; 2701 v = aa + ai[k]; /* 1st entry of U(n-1,:) */ 2702 vi = aj + ai[k]; 2703 for (i=n-1; i>=0; i--){ 2704 k = 2*n-i; 2705 nz = ai[k +1] - ai[k] - 1; 2706 sum = tmp[i]; 2707 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 2708 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 2709 v += nz+1; vi += nz+1; 2710 } 2711 2712 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 2713 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 2714 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 2715 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 2716 ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr); 2717 PetscFunctionReturn(0); 2718 } 2719 2720 #undef __FUNCT__ 2721 #define __FUNCT__ "MatILUDTFactor_SeqAIJ" 2722 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact) 2723 { 2724 Mat B = *fact; 2725 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b; 2726 IS isicol; 2727 PetscErrorCode ierr; 2728 const PetscInt *r,*ic; 2729 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag; 2730 PetscInt *bi,*bj,*bdiag,*bdiag_rev; 2731 PetscInt row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au; 2732 PetscInt nlnk,*lnk; 2733 PetscBT lnkbt; 2734 PetscTruth row_identity,icol_identity,both_identity; 2735 MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp; 2736 const PetscInt *ics; 2737 PetscInt j,nz,*pj,*bjtmp,k,ncut,*jtmp; 2738 PetscReal dt=info->dt,dtcol=info->dtcol,shift=info->shiftinblocks; 2739 PetscInt dtcount=(PetscInt)info->dtcount,nnz_max; 2740 PetscTruth missing; 2741 2742 PetscFunctionBegin; 2743 2744 if (dt == PETSC_DEFAULT) dt = 0.005; 2745 if (dtcol == PETSC_DEFAULT) dtcol = 0.01; /* XXX unused! */ 2746 if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax); 2747 2748 /* ------- symbolic factorization, can be reused ---------*/ 2749 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 2750 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 2751 adiag=a->diag; 2752 2753 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 2754 2755 /* bdiag is location of diagonal in factor */ 2756 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 2757 bdiag_rev = bdiag + n+1; 2758 2759 /* allocate row pointers bi */ 2760 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 2761 2762 /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */ 2763 if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */ 2764 nnz_max = ai[n]+2*n*dtcount+2; 2765 2766 ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 2767 ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr); 2768 2769 /* put together the new matrix */ 2770 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 2771 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 2772 b = (Mat_SeqAIJ*)(B)->data; 2773 b->free_a = PETSC_TRUE; 2774 b->free_ij = PETSC_TRUE; 2775 b->singlemalloc = PETSC_FALSE; 2776 b->a = ba; 2777 b->j = bj; 2778 b->i = bi; 2779 b->diag = bdiag; 2780 b->ilen = 0; 2781 b->imax = 0; 2782 b->row = isrow; 2783 b->col = iscol; 2784 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 2785 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 2786 b->icol = isicol; 2787 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2788 2789 ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2790 b->maxnz = nnz_max; 2791 2792 (B)->factor = MAT_FACTOR_ILUDT; 2793 (B)->info.factor_mallocs = 0; 2794 (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]); 2795 CHKMEMQ; 2796 /* ------- end of symbolic factorization ---------*/ 2797 2798 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 2799 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 2800 ics = ic; 2801 2802 /* linked list for storing column indices of the active row */ 2803 nlnk = n + 1; 2804 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2805 2806 /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */ 2807 ierr = PetscMalloc((2*n+1)*sizeof(PetscInt),&im);CHKERRQ(ierr); 2808 jtmp = im + n; 2809 /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */ 2810 ierr = PetscMalloc((2*n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 2811 ierr = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr); 2812 vtmp = rtmp + n; 2813 2814 bi[0] = 0; 2815 bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */ 2816 bdiag_rev[n] = bdiag[0]; 2817 bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */ 2818 for (i=0; i<n; i++) { 2819 /* copy initial fill into linked list */ 2820 nzi = 0; /* nonzeros for active row i */ 2821 nzi = ai[r[i]+1] - ai[r[i]]; 2822 if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 2823 nzi_al = adiag[r[i]] - ai[r[i]]; 2824 nzi_au = ai[r[i]+1] - adiag[r[i]] -1; 2825 ajtmp = aj + ai[r[i]]; 2826 ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2827 2828 /* load in initial (unfactored row) */ 2829 aatmp = a->a + ai[r[i]]; 2830 for (j=0; j<nzi; j++) { 2831 rtmp[ics[*ajtmp++]] = *aatmp++; 2832 } 2833 2834 /* add pivot rows into linked list */ 2835 row = lnk[n]; 2836 while (row < i ) { 2837 nzi_bl = bi[row+1] - bi[row] + 1; 2838 bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */ 2839 ierr = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr); 2840 nzi += nlnk; 2841 row = lnk[row]; 2842 } 2843 2844 /* copy data from lnk into jtmp, then initialize lnk */ 2845 ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr); 2846 2847 /* numerical factorization */ 2848 bjtmp = jtmp; 2849 row = *bjtmp++; /* 1st pivot row */ 2850 while ( row < i ) { 2851 pc = rtmp + row; 2852 pv = ba + bdiag[row]; /* 1./(diag of the pivot row) */ 2853 multiplier = (*pc) * (*pv); 2854 *pc = multiplier; 2855 if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */ 2856 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 2857 pv = ba + bdiag[row+1] + 1; 2858 /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */ 2859 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 2860 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 2861 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 2862 } 2863 row = *bjtmp++; 2864 } 2865 2866 /* copy sparse rtmp into contiguous vtmp; separate L and U part */ 2867 diag_tmp = rtmp[i]; /* save diagonal value - may not needed?? */ 2868 nzi_bl = 0; j = 0; 2869 while (jtmp[j] < i){ /* Note: jtmp is sorted */ 2870 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 2871 nzi_bl++; j++; 2872 } 2873 nzi_bu = nzi - nzi_bl -1; 2874 while (j < nzi){ 2875 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 2876 j++; 2877 } 2878 2879 bjtmp = bj + bi[i]; 2880 batmp = ba + bi[i]; 2881 /* apply level dropping rule to L part */ 2882 ncut = nzi_al + dtcount; 2883 if (ncut < nzi_bl){ 2884 ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr); 2885 ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr); 2886 } else { 2887 ncut = nzi_bl; 2888 } 2889 for (j=0; j<ncut; j++){ 2890 bjtmp[j] = jtmp[j]; 2891 batmp[j] = vtmp[j]; 2892 /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */ 2893 } 2894 bi[i+1] = bi[i] + ncut; 2895 nzi = ncut + 1; 2896 2897 /* apply level dropping rule to U part */ 2898 ncut = nzi_au + dtcount; 2899 if (ncut < nzi_bu){ 2900 ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr); 2901 ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr); 2902 } else { 2903 ncut = nzi_bu; 2904 } 2905 nzi += ncut; 2906 2907 /* mark bdiagonal */ 2908 bdiag[i+1] = bdiag[i] - (ncut + 1); 2909 bdiag_rev[n-i-1] = bdiag[i+1]; 2910 bi[2*n - i] = bi[2*n - i +1] - (ncut + 1); 2911 bjtmp = bj + bdiag[i]; 2912 batmp = ba + bdiag[i]; 2913 *bjtmp = i; 2914 *batmp = diag_tmp; /* rtmp[i]; */ 2915 if (*batmp == 0.0) { 2916 *batmp = dt+shift; 2917 /* printf(" row %d add shift %g\n",i,shift); */ 2918 } 2919 *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */ 2920 /* printf(" (%d,%g),",*bjtmp,*batmp); */ 2921 2922 bjtmp = bj + bdiag[i+1]+1; 2923 batmp = ba + bdiag[i+1]+1; 2924 for (k=0; k<ncut; k++){ 2925 bjtmp[k] = jtmp[nzi_bl+1+k]; 2926 batmp[k] = vtmp[nzi_bl+1+k]; 2927 /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */ 2928 } 2929 /* printf("\n"); */ 2930 2931 im[i] = nzi; /* used by PetscLLAddSortedLU() */ 2932 /* 2933 printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]); 2934 printf(" ----------------------------\n"); 2935 */ 2936 } /* for (i=0; i<n; i++) */ 2937 /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */ 2938 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]); 2939 2940 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 2941 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 2942 2943 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2944 ierr = PetscFree(im);CHKERRQ(ierr); 2945 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2946 2947 ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr); 2948 b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n]; 2949 2950 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 2951 ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr); 2952 both_identity = (PetscTruth) (row_identity && icol_identity); 2953 if (row_identity && icol_identity) { 2954 B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct; 2955 } else { 2956 B->ops->solve = MatSolve_SeqAIJ_newdatastruct; 2957 } 2958 2959 B->ops->lufactorsymbolic = MatILUDTFactorSymbolic_SeqAIJ; 2960 B->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ; 2961 B->ops->solveadd = 0; 2962 B->ops->solvetranspose = 0; 2963 B->ops->solvetransposeadd = 0; 2964 B->ops->matsolve = 0; 2965 B->assembled = PETSC_TRUE; 2966 B->preallocated = PETSC_TRUE; 2967 PetscFunctionReturn(0); 2968 } 2969 2970 /* a wraper of MatILUDTFactor_SeqAIJ() */ 2971 #undef __FUNCT__ 2972 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ" 2973 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info) 2974 { 2975 PetscErrorCode ierr; 2976 2977 PetscFunctionBegin; 2978 ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr); 2979 2980 fact->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ; 2981 PetscFunctionReturn(0); 2982 } 2983 2984 /* 2985 same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors 2986 - intend to replace existing MatLUFactorNumeric_SeqAIJ() 2987 */ 2988 #undef __FUNCT__ 2989 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ" 2990 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info) 2991 { 2992 Mat C=fact; 2993 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 2994 IS isrow = b->row,isicol = b->icol; 2995 PetscErrorCode ierr; 2996 const PetscInt *r,*ic,*ics; 2997 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 2998 PetscInt *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj; 2999 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 3000 PetscReal dt=info->dt,shift=info->shiftinblocks; 3001 PetscTruth row_identity, col_identity; 3002 3003 PetscFunctionBegin; 3004 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3005 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3006 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 3007 ics = ic; 3008 3009 for (i=0; i<n; i++){ 3010 /* initialize rtmp array */ 3011 nzl = bi[i+1] - bi[i]; /* num of nozeros in L(i,:) */ 3012 bjtmp = bj + bi[i]; 3013 for (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0; 3014 rtmp[i] = 0.0; 3015 nzu = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */ 3016 bjtmp = bj + bdiag[i+1] + 1; 3017 for (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0; 3018 3019 /* load in initial unfactored row of A */ 3020 /* printf("row %d\n",i); */ 3021 nz = ai[r[i]+1] - ai[r[i]]; 3022 ajtmp = aj + ai[r[i]]; 3023 v = aa + ai[r[i]]; 3024 for (j=0; j<nz; j++) { 3025 rtmp[ics[*ajtmp++]] = v[j]; 3026 /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */ 3027 } 3028 /* printf("\n"); */ 3029 3030 /* numerical factorization */ 3031 bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */ 3032 nzl = bi[i+1] - bi[i]; /* num of entries in L(i,:) */ 3033 k = 0; 3034 while (k < nzl){ 3035 row = *bjtmp++; 3036 /* printf(" prow %d\n",row); */ 3037 pc = rtmp + row; 3038 pv = b->a + bdiag[row]; /* 1./(diag of the pivot row) */ 3039 multiplier = (*pc) * (*pv); 3040 *pc = multiplier; 3041 if (PetscAbsScalar(multiplier) > dt){ 3042 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3043 pv = b->a + bdiag[row+1] + 1; 3044 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3045 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3046 /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */ 3047 } 3048 k++; 3049 } 3050 3051 /* finished row so stick it into b->a */ 3052 /* L-part */ 3053 pv = b->a + bi[i] ; 3054 pj = bj + bi[i] ; 3055 nzl = bi[i+1] - bi[i]; 3056 for (j=0; j<nzl; j++) { 3057 pv[j] = rtmp[pj[j]]; 3058 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3059 } 3060 3061 /* diagonal: invert diagonal entries for simplier triangular solves */ 3062 if (rtmp[i] == 0.0) rtmp[i] = dt+shift; 3063 b->a[bdiag[i]] = 1.0/rtmp[i]; 3064 /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */ 3065 3066 /* U-part */ 3067 pv = b->a + bdiag[i+1] + 1; 3068 pj = bj + bdiag[i+1] + 1; 3069 nzu = bdiag[i] - bdiag[i+1] - 1; 3070 for (j=0; j<nzu; j++) { 3071 pv[j] = rtmp[pj[j]]; 3072 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3073 } 3074 /* printf("\n"); */ 3075 } 3076 3077 ierr = PetscFree(rtmp);CHKERRQ(ierr); 3078 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3079 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3080 3081 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3082 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 3083 if (row_identity && col_identity) { 3084 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct; 3085 } else { 3086 C->ops->solve = MatSolve_SeqAIJ_newdatastruct; 3087 } 3088 C->ops->solveadd = 0; 3089 C->ops->solvetranspose = 0; 3090 C->ops->solvetransposeadd = 0; 3091 C->ops->matsolve = 0; 3092 C->assembled = PETSC_TRUE; 3093 C->preallocated = PETSC_TRUE; 3094 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 3095 PetscFunctionReturn(0); 3096 } 3097