1 #define PETSCMAT_DLL 2 3 #include "../src/mat/impls/aij/seq/aij.h" 4 #include "petscbt.h" 5 #include "../src/mat/utils/freespace.h" 6 7 EXTERN_C_BEGIN 8 #undef __FUNCT__ 9 #define __FUNCT__ "MatOrdering_Flow_SeqAIJ" 10 /* 11 Computes an ordering to get most of the large numerical values in the lower triangular part of the matrix 12 */ 13 PetscErrorCode MatOrdering_Flow_SeqAIJ(Mat mat,const MatOrderingType type,IS *irow,IS *icol) 14 { 15 Mat_SeqAIJ *a = (Mat_SeqAIJ*)mat->data; 16 PetscErrorCode ierr; 17 PetscInt i,j,jj,k, kk,n = mat->rmap->n, current = 0, newcurrent = 0,*order; 18 const PetscInt *ai = a->i, *aj = a->j; 19 const PetscScalar *aa = a->a; 20 PetscTruth *done; 21 PetscReal best,past = 0,future; 22 23 PetscFunctionBegin; 24 /* pick initial row */ 25 best = -1; 26 for (i=0; i<n; i++) { 27 future = 0; 28 for (j=ai[i]; j<ai[i+1]; j++) { 29 if (aj[j] != i) future += PetscAbsScalar(aa[j]); else past = PetscAbsScalar(aa[j]); 30 } 31 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 32 if (past/future > best) { 33 best = past/future; 34 current = i; 35 } 36 } 37 38 ierr = PetscMalloc(n*sizeof(PetscTruth),&done);CHKERRQ(ierr); 39 ierr = PetscMalloc(n*sizeof(PetscInt),&order);CHKERRQ(ierr); 40 ierr = PetscMemzero(done,n*sizeof(PetscTruth));CHKERRQ(ierr); 41 order[0] = current; 42 for (i=0; i<n-1; i++) { 43 done[current] = PETSC_TRUE; 44 best = -1; 45 /* loop over all neighbors of current pivot */ 46 for (j=ai[current]; j<ai[current+1]; j++) { 47 jj = aj[j]; 48 if (done[jj]) continue; 49 /* loop over columns of potential next row computing weights for below and above diagonal */ 50 past = future = 0.0; 51 for (k=ai[jj]; k<ai[jj+1]; k++) { 52 kk = aj[k]; 53 if (done[kk]) past += PetscAbsScalar(aa[k]); 54 else if (kk != jj) future += PetscAbsScalar(aa[k]); 55 } 56 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 57 if (past/future > best) { 58 best = past/future; 59 newcurrent = jj; 60 } 61 } 62 if (best == -1) { /* no neighbors to select from so select best of all that remain */ 63 best = -1; 64 for (k=0; k<n; k++) { 65 if (done[k]) continue; 66 future = 0; 67 past = 0; 68 for (j=ai[k]; j<ai[k+1]; j++) { 69 kk = aj[j]; 70 if (done[kk]) past += PetscAbsScalar(aa[j]); 71 else if (kk != k) future += PetscAbsScalar(aa[j]); 72 } 73 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 74 if (past/future > best) { 75 best = past/future; 76 newcurrent = k; 77 } 78 } 79 } 80 if (current == newcurrent) SETERRQ(PETSC_ERR_PLIB,"newcurrent cannot be current"); 81 current = newcurrent; 82 order[i+1] = current; 83 } 84 ierr = ISCreateGeneral(PETSC_COMM_SELF,n,order,irow);CHKERRQ(ierr); 85 *icol = *irow; 86 ierr = PetscObjectReference((PetscObject)*irow);CHKERRQ(ierr); 87 ierr = PetscFree(done);CHKERRQ(ierr); 88 ierr = PetscFree(order);CHKERRQ(ierr); 89 PetscFunctionReturn(0); 90 } 91 EXTERN_C_END 92 93 EXTERN_C_BEGIN 94 #undef __FUNCT__ 95 #define __FUNCT__ "MatGetFactorAvailable_seqaij_petsc" 96 PetscErrorCode MatGetFactorAvailable_seqaij_petsc(Mat A,MatFactorType ftype,PetscTruth *flg) 97 { 98 PetscFunctionBegin; 99 *flg = PETSC_TRUE; 100 PetscFunctionReturn(0); 101 } 102 EXTERN_C_END 103 104 EXTERN_C_BEGIN 105 #undef __FUNCT__ 106 #define __FUNCT__ "MatGetFactor_seqaij_petsc" 107 PetscErrorCode MatGetFactor_seqaij_petsc(Mat A,MatFactorType ftype,Mat *B) 108 { 109 PetscInt n = A->rmap->n; 110 PetscErrorCode ierr; 111 112 PetscFunctionBegin; 113 ierr = MatCreate(((PetscObject)A)->comm,B);CHKERRQ(ierr); 114 ierr = MatSetSizes(*B,n,n,n,n);CHKERRQ(ierr); 115 if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT){ 116 ierr = MatSetType(*B,MATSEQAIJ);CHKERRQ(ierr); 117 (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJ; 118 (*B)->ops->lufactorsymbolic = MatLUFactorSymbolic_SeqAIJ; 119 (*B)->ops->iludtfactor = MatILUDTFactor_SeqAIJ; 120 } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) { 121 ierr = MatSetType(*B,MATSEQSBAIJ);CHKERRQ(ierr); 122 ierr = MatSeqSBAIJSetPreallocation(*B,1,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 123 (*B)->ops->iccfactorsymbolic = MatICCFactorSymbolic_SeqAIJ; 124 (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJ; 125 } else SETERRQ(PETSC_ERR_SUP,"Factor type not supported"); 126 (*B)->factor = ftype; 127 PetscFunctionReturn(0); 128 } 129 EXTERN_C_END 130 131 #undef __FUNCT__ 132 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ" 133 PetscErrorCode MatLUFactorSymbolic_SeqAIJ(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 134 { 135 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 136 IS isicol; 137 PetscErrorCode ierr; 138 const PetscInt *r,*ic; 139 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j; 140 PetscInt *bi,*bj,*ajtmp; 141 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 142 PetscReal f; 143 PetscInt nlnk,*lnk,k,**bi_ptr; 144 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 145 PetscBT lnkbt; 146 147 PetscFunctionBegin; 148 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square"); 149 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 150 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 151 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 152 153 /* get new row pointers */ 154 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 155 bi[0] = 0; 156 157 /* bdiag is location of diagonal in factor */ 158 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 159 bdiag[0] = 0; 160 161 /* linked list for storing column indices of the active row */ 162 nlnk = n + 1; 163 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 164 165 ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr); 166 167 /* initial FreeSpace size is f*(ai[n]+1) */ 168 f = info->fill; 169 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 170 current_space = free_space; 171 172 for (i=0; i<n; i++) { 173 /* copy previous fill into linked list */ 174 nzi = 0; 175 nnz = ai[r[i]+1] - ai[r[i]]; 176 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 177 ajtmp = aj + ai[r[i]]; 178 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 179 nzi += nlnk; 180 181 /* add pivot rows into linked list */ 182 row = lnk[n]; 183 while (row < i) { 184 nzbd = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */ 185 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 186 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 187 nzi += nlnk; 188 row = lnk[row]; 189 } 190 bi[i+1] = bi[i] + nzi; 191 im[i] = nzi; 192 193 /* mark bdiag */ 194 nzbd = 0; 195 nnz = nzi; 196 k = lnk[n]; 197 while (nnz-- && k < i){ 198 nzbd++; 199 k = lnk[k]; 200 } 201 bdiag[i] = bi[i] + nzbd; 202 203 /* if free space is not available, make more free space */ 204 if (current_space->local_remaining<nzi) { 205 nnz = (n - i)*nzi; /* estimated and max additional space needed */ 206 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 207 reallocs++; 208 } 209 210 /* copy data into free space, then initialize lnk */ 211 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 212 bi_ptr[i] = current_space->array; 213 current_space->array += nzi; 214 current_space->local_used += nzi; 215 current_space->local_remaining -= nzi; 216 } 217 #if defined(PETSC_USE_INFO) 218 if (ai[n] != 0) { 219 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 220 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 221 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 222 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr); 223 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 224 } else { 225 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 226 } 227 #endif 228 229 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 230 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 231 232 /* destroy list of free space and other temporary array(s) */ 233 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 234 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); 235 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 236 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 237 238 /* put together the new matrix */ 239 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 240 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 241 b = (Mat_SeqAIJ*)(B)->data; 242 b->free_a = PETSC_TRUE; 243 b->free_ij = PETSC_TRUE; 244 b->singlemalloc = PETSC_FALSE; 245 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 246 b->j = bj; 247 b->i = bi; 248 b->diag = bdiag; 249 b->ilen = 0; 250 b->imax = 0; 251 b->row = isrow; 252 b->col = iscol; 253 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 254 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 255 b->icol = isicol; 256 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 257 258 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 259 ierr = PetscLogObjectMemory(B,(bi[n]-n)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 260 b->maxnz = b->nz = bi[n] ; 261 262 (B)->factor = MAT_FACTOR_LU; 263 (B)->info.factor_mallocs = reallocs; 264 (B)->info.fill_ratio_given = f; 265 266 if (ai[n]) { 267 (B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 268 } else { 269 (B)->info.fill_ratio_needed = 0.0; 270 } 271 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 272 (B)->ops->solve = MatSolve_SeqAIJ; 273 (B)->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 274 /* switch to inodes if appropriate */ 275 ierr = MatLUFactorSymbolic_Inode(B,A,isrow,iscol,info);CHKERRQ(ierr); 276 PetscFunctionReturn(0); 277 } 278 279 /* 280 Trouble in factorization, should we dump the original matrix? 281 */ 282 #undef __FUNCT__ 283 #define __FUNCT__ "MatFactorDumpMatrix" 284 PetscErrorCode MatFactorDumpMatrix(Mat A) 285 { 286 PetscErrorCode ierr; 287 PetscTruth flg = PETSC_FALSE; 288 289 PetscFunctionBegin; 290 ierr = PetscOptionsGetTruth(PETSC_NULL,"-mat_factor_dump_on_error",&flg,PETSC_NULL);CHKERRQ(ierr); 291 if (flg) { 292 PetscViewer viewer; 293 char filename[PETSC_MAX_PATH_LEN]; 294 295 ierr = PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);CHKERRQ(ierr); 296 ierr = PetscViewerBinaryOpen(((PetscObject)A)->comm,filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr); 297 ierr = MatView(A,viewer);CHKERRQ(ierr); 298 ierr = PetscViewerDestroy(viewer);CHKERRQ(ierr); 299 } 300 PetscFunctionReturn(0); 301 } 302 303 extern PetscErrorCode MatSolve_Inode(Mat,Vec,Vec); 304 305 /* ----------------------------------------------------------- */ 306 extern PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_iludt(Mat,Vec,Vec); 307 extern PetscErrorCode MatSolve_SeqAIJ_iludt(Mat,Vec,Vec); 308 309 #undef __FUNCT__ 310 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_newdatastruct" 311 PetscErrorCode MatLUFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info) 312 { 313 Mat C=B; 314 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 315 IS isrow = b->row,isicol = b->icol; 316 PetscErrorCode ierr; 317 const PetscInt *r,*ic,*ics; 318 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 319 PetscInt *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj; 320 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 321 PetscReal shift=info->shiftinblocks; 322 PetscTruth row_identity, col_identity; 323 324 PetscFunctionBegin; 325 /* printf("MatLUFactorNumeric_SeqAIJ_newdatastruct is called ...\n"); */ 326 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 327 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 328 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 329 ics = ic; 330 331 for (i=0; i<n; i++){ 332 /* zero rtmp */ 333 /* L part */ 334 nz = bi[i+1] - bi[i]; 335 bjtmp = bj + bi[i]; 336 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 337 338 /* U part */ 339 nz = bi[2*n-i+1] - bi[2*n-i]; 340 bjtmp = bj + bi[2*n-i]; 341 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 342 343 /* load in initial (unfactored row) */ 344 nz = ai[r[i]+1] - ai[r[i]]; 345 ajtmp = aj + ai[r[i]]; 346 v = aa + ai[r[i]]; 347 for (j=0; j<nz; j++) { 348 rtmp[ics[ajtmp[j]]] = v[j]; 349 } 350 if (rtmp[ics[r[i]]] == 0.0){ 351 rtmp[ics[r[i]]] += shift; /* shift the diagonal of the matrix */ 352 /* printf("row %d, shift %g\n",i,shift); */ 353 } 354 355 /* elimination */ 356 bjtmp = bj + bi[i]; 357 row = *bjtmp++; 358 nzL = bi[i+1] - bi[i]; 359 k = 0; 360 while (k < nzL) { 361 pc = rtmp + row; 362 if (*pc != 0.0) { 363 pv = b->a + bdiag[row]; 364 multiplier = *pc * (*pv); 365 *pc = multiplier; 366 pj = b->j + bi[2*n-row]; /* begining of U(row,:) */ 367 pv = b->a + bi[2*n-row]; 368 nz = bi[2*n-row+1] - bi[2*n-row] - 1; /* num of entries in U(row,:), excluding diag */ 369 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 370 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 371 } 372 row = *bjtmp++; k++; 373 } 374 375 /* finished row so stick it into b->a */ 376 /* L part */ 377 pv = b->a + bi[i] ; 378 pj = b->j + bi[i] ; 379 nz = bi[i+1] - bi[i]; 380 for (j=0; j<nz; j++) { 381 pv[j] = rtmp[pj[j]]; 382 } 383 384 /* Mark diagonal and invert diagonal for simplier triangular solves */ 385 pv = b->a + bdiag[i]; 386 pj = b->j + bdiag[i]; 387 /* if (*pj != i)SETERRQ2(PETSC_ERR_SUP,"row %d != *pj %d",i,*pj) */ 388 *pv = 1.0/rtmp[*pj]; 389 390 /* U part */ 391 pv = b->a + bi[2*n-i]; 392 pj = b->j + bi[2*n-i]; 393 nz = bi[2*n-i+1] - bi[2*n-i] - 1; 394 for (j=0; j<nz; j++) pv[j] = rtmp[pj[j]]; 395 } 396 ierr = PetscFree(rtmp);CHKERRQ(ierr); 397 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 398 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 399 400 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 401 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 402 if (row_identity && col_identity) { 403 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_iludt; 404 } else { 405 C->ops->solve = MatSolve_SeqAIJ_iludt; 406 } 407 408 C->ops->solveadd = 0; 409 C->ops->solvetranspose = 0; 410 C->ops->solvetransposeadd = 0; 411 C->ops->matsolve = 0; 412 C->assembled = PETSC_TRUE; 413 C->preallocated = PETSC_TRUE; 414 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 415 PetscFunctionReturn(0); 416 } 417 418 #undef __FUNCT__ 419 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ" 420 PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 421 { 422 Mat C=B; 423 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 424 IS isrow = b->row,isicol = b->icol; 425 PetscErrorCode ierr; 426 const PetscInt *r,*ic,*ics; 427 PetscInt i,j,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 428 PetscInt *ajtmp,*bjtmp,nz,row,*diag_offset = b->diag,diag,*pj; 429 MatScalar *rtmp,*pc,multiplier,*v,*pv,d,*aa=a->a; 430 PetscReal rs=0.0; 431 LUShift_Ctx sctx; 432 PetscInt newshift,*ddiag; 433 434 PetscFunctionBegin; 435 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 436 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 437 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 438 ics = ic; 439 440 sctx.shift_top = 0; 441 sctx.nshift_max = 0; 442 sctx.shift_lo = 0; 443 sctx.shift_hi = 0; 444 sctx.shift_fraction = 0; 445 446 /* if both shift schemes are chosen by user, only use info->shiftpd */ 447 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 448 ddiag = a->diag; 449 sctx.shift_top = info->zeropivot; 450 for (i=0; i<n; i++) { 451 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 452 d = (aa)[ddiag[i]]; 453 rs = -PetscAbsScalar(d) - PetscRealPart(d); 454 v = aa+ai[i]; 455 nz = ai[i+1] - ai[i]; 456 for (j=0; j<nz; j++) 457 rs += PetscAbsScalar(v[j]); 458 if (rs>sctx.shift_top) sctx.shift_top = rs; 459 } 460 sctx.shift_top *= 1.1; 461 sctx.nshift_max = 5; 462 sctx.shift_lo = 0.; 463 sctx.shift_hi = 1.; 464 } 465 466 sctx.shift_amount = 0.0; 467 sctx.nshift = 0; 468 do { 469 sctx.lushift = PETSC_FALSE; 470 for (i=0; i<n; i++){ 471 nz = bi[i+1] - bi[i]; 472 bjtmp = bj + bi[i]; 473 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 474 475 /* load in initial (unfactored row) */ 476 nz = ai[r[i]+1] - ai[r[i]]; 477 ajtmp = aj + ai[r[i]]; 478 v = aa + ai[r[i]]; 479 for (j=0; j<nz; j++) { 480 rtmp[ics[ajtmp[j]]] = v[j]; 481 } 482 rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 483 /* if (sctx.shift_amount > 0.0) printf("row %d, shift %g\n",i,sctx.shift_amount); */ 484 485 row = *bjtmp++; 486 while (row < i) { 487 pc = rtmp + row; 488 if (*pc != 0.0) { 489 pv = b->a + diag_offset[row]; 490 pj = b->j + diag_offset[row] + 1; 491 multiplier = *pc / *pv++; 492 *pc = multiplier; 493 nz = bi[row+1] - diag_offset[row] - 1; 494 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 495 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 496 } 497 row = *bjtmp++; 498 } 499 /* finished row so stick it into b->a */ 500 pv = b->a + bi[i] ; 501 pj = b->j + bi[i] ; 502 nz = bi[i+1] - bi[i]; 503 diag = diag_offset[i] - bi[i]; 504 rs = -PetscAbsScalar(pv[diag]); 505 for (j=0; j<nz; j++) { 506 pv[j] = rtmp[pj[j]]; 507 rs += PetscAbsScalar(pv[j]); 508 } 509 510 /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */ 511 sctx.rs = rs; 512 sctx.pv = pv[diag]; 513 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 514 if (newshift == 1) break; 515 } 516 517 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 518 /* 519 * if no shift in this attempt & shifting & started shifting & can refine, 520 * then try lower shift 521 */ 522 sctx.shift_hi = sctx.shift_fraction; 523 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 524 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 525 sctx.lushift = PETSC_TRUE; 526 sctx.nshift++; 527 } 528 } while (sctx.lushift); 529 530 /* invert diagonal entries for simplier triangular solves */ 531 for (i=0; i<n; i++) { 532 b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]]; 533 } 534 ierr = PetscFree(rtmp);CHKERRQ(ierr); 535 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 536 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 537 if (b->inode.use) { 538 C->ops->solve = MatSolve_Inode; 539 } else { 540 PetscTruth row_identity, col_identity; 541 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 542 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 543 if (row_identity && col_identity) { 544 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 545 } else { 546 C->ops->solve = MatSolve_SeqAIJ; 547 } 548 } 549 C->ops->solveadd = MatSolveAdd_SeqAIJ; 550 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 551 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 552 C->ops->matsolve = MatMatSolve_SeqAIJ; 553 C->assembled = PETSC_TRUE; 554 C->preallocated = PETSC_TRUE; 555 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 556 if (sctx.nshift){ 557 if (info->shiftpd) { 558 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); 559 } else if (info->shiftnz) { 560 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 561 } 562 } 563 PetscFunctionReturn(0); 564 } 565 566 /* 567 This routine implements inplace ILU(0) with row or/and column permutations. 568 Input: 569 A - original matrix 570 Output; 571 A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i] 572 a->j (col index) is permuted by the inverse of colperm, then sorted 573 a->a reordered accordingly with a->j 574 a->diag (ptr to diagonal elements) is updated. 575 */ 576 #undef __FUNCT__ 577 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_InplaceWithPerm" 578 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info) 579 { 580 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 581 IS isrow = a->row,isicol = a->icol; 582 PetscErrorCode ierr; 583 const PetscInt *r,*ic,*ics; 584 PetscInt i,j,n=A->rmap->n,*ai=a->i,*aj=a->j; 585 PetscInt *ajtmp,nz,row; 586 PetscInt *diag = a->diag,nbdiag,*pj; 587 PetscScalar *rtmp,*pc,multiplier,d; 588 MatScalar *v,*pv; 589 PetscReal rs; 590 LUShift_Ctx sctx; 591 PetscInt newshift; 592 593 PetscFunctionBegin; 594 if (A != B) SETERRQ(PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address"); 595 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 596 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 597 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&rtmp);CHKERRQ(ierr); 598 ierr = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr); 599 ics = ic; 600 601 sctx.shift_top = 0; 602 sctx.nshift_max = 0; 603 sctx.shift_lo = 0; 604 sctx.shift_hi = 0; 605 sctx.shift_fraction = 0; 606 607 /* if both shift schemes are chosen by user, only use info->shiftpd */ 608 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 609 sctx.shift_top = 0; 610 for (i=0; i<n; i++) { 611 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 612 d = (a->a)[diag[i]]; 613 rs = -PetscAbsScalar(d) - PetscRealPart(d); 614 v = a->a+ai[i]; 615 nz = ai[i+1] - ai[i]; 616 for (j=0; j<nz; j++) 617 rs += PetscAbsScalar(v[j]); 618 if (rs>sctx.shift_top) sctx.shift_top = rs; 619 } 620 if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot; 621 sctx.shift_top *= 1.1; 622 sctx.nshift_max = 5; 623 sctx.shift_lo = 0.; 624 sctx.shift_hi = 1.; 625 } 626 627 sctx.shift_amount = 0; 628 sctx.nshift = 0; 629 do { 630 sctx.lushift = PETSC_FALSE; 631 for (i=0; i<n; i++){ 632 /* load in initial unfactored row */ 633 nz = ai[r[i]+1] - ai[r[i]]; 634 ajtmp = aj + ai[r[i]]; 635 v = a->a + ai[r[i]]; 636 /* sort permuted ajtmp and values v accordingly */ 637 for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]]; 638 ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr); 639 640 diag[r[i]] = ai[r[i]]; 641 for (j=0; j<nz; j++) { 642 rtmp[ajtmp[j]] = v[j]; 643 if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */ 644 } 645 rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 646 647 row = *ajtmp++; 648 while (row < i) { 649 pc = rtmp + row; 650 if (*pc != 0.0) { 651 pv = a->a + diag[r[row]]; 652 pj = aj + diag[r[row]] + 1; 653 654 multiplier = *pc / *pv++; 655 *pc = multiplier; 656 nz = ai[r[row]+1] - diag[r[row]] - 1; 657 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 658 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 659 } 660 row = *ajtmp++; 661 } 662 /* finished row so overwrite it onto a->a */ 663 pv = a->a + ai[r[i]] ; 664 pj = aj + ai[r[i]] ; 665 nz = ai[r[i]+1] - ai[r[i]]; 666 nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */ 667 668 rs = 0.0; 669 for (j=0; j<nz; j++) { 670 pv[j] = rtmp[pj[j]]; 671 if (j != nbdiag) rs += PetscAbsScalar(pv[j]); 672 } 673 674 /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */ 675 sctx.rs = rs; 676 sctx.pv = pv[nbdiag]; 677 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 678 if (newshift == 1) break; 679 } 680 681 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 682 /* 683 * if no shift in this attempt & shifting & started shifting & can refine, 684 * then try lower shift 685 */ 686 sctx.shift_hi = sctx.shift_fraction; 687 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 688 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 689 sctx.lushift = PETSC_TRUE; 690 sctx.nshift++; 691 } 692 } while (sctx.lushift); 693 694 /* invert diagonal entries for simplier triangular solves */ 695 for (i=0; i<n; i++) { 696 a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]]; 697 } 698 699 ierr = PetscFree(rtmp);CHKERRQ(ierr); 700 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 701 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 702 A->ops->solve = MatSolve_SeqAIJ_InplaceWithPerm; 703 A->ops->solveadd = MatSolveAdd_SeqAIJ; 704 A->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 705 A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 706 A->assembled = PETSC_TRUE; 707 A->preallocated = PETSC_TRUE; 708 ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr); 709 if (sctx.nshift){ 710 if (info->shiftpd) { 711 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); 712 } else if (info->shiftnz) { 713 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 714 } 715 } 716 PetscFunctionReturn(0); 717 } 718 719 /* ----------------------------------------------------------- */ 720 #undef __FUNCT__ 721 #define __FUNCT__ "MatLUFactor_SeqAIJ" 722 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info) 723 { 724 PetscErrorCode ierr; 725 Mat C; 726 727 PetscFunctionBegin; 728 ierr = MatGetFactor(A,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr); 729 ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr); 730 ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr); 731 A->ops->solve = C->ops->solve; 732 A->ops->solvetranspose = C->ops->solvetranspose; 733 ierr = MatHeaderCopy(A,C);CHKERRQ(ierr); 734 ierr = PetscLogObjectParent(A,((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr); 735 PetscFunctionReturn(0); 736 } 737 /* ----------------------------------------------------------- */ 738 739 740 #undef __FUNCT__ 741 #define __FUNCT__ "MatSolve_SeqAIJ" 742 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx) 743 { 744 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 745 IS iscol = a->col,isrow = a->row; 746 PetscErrorCode ierr; 747 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 748 PetscInt nz; 749 const PetscInt *rout,*cout,*r,*c; 750 PetscScalar *x,*tmp,*tmps,sum; 751 const PetscScalar *b; 752 const MatScalar *aa = a->a,*v; 753 754 PetscFunctionBegin; 755 if (!n) PetscFunctionReturn(0); 756 757 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 758 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 759 tmp = a->solve_work; 760 761 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 762 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 763 764 /* forward solve the lower triangular */ 765 tmp[0] = b[*r++]; 766 tmps = tmp; 767 for (i=1; i<n; i++) { 768 v = aa + ai[i] ; 769 vi = aj + ai[i] ; 770 nz = a->diag[i] - ai[i]; 771 sum = b[*r++]; 772 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 773 tmp[i] = sum; 774 } 775 776 /* backward solve the upper triangular */ 777 for (i=n-1; i>=0; i--){ 778 v = aa + a->diag[i] + 1; 779 vi = aj + a->diag[i] + 1; 780 nz = ai[i+1] - a->diag[i] - 1; 781 sum = tmp[i]; 782 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 783 x[*c--] = tmp[i] = sum*aa[a->diag[i]]; 784 } 785 786 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 787 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 788 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 789 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 790 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 791 PetscFunctionReturn(0); 792 } 793 794 #undef __FUNCT__ 795 #define __FUNCT__ "MatMatSolve_SeqAIJ" 796 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X) 797 { 798 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 799 IS iscol = a->col,isrow = a->row; 800 PetscErrorCode ierr; 801 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 802 PetscInt nz,neq; 803 const PetscInt *rout,*cout,*r,*c; 804 PetscScalar *x,*b,*tmp,*tmps,sum; 805 const MatScalar *aa = a->a,*v; 806 PetscTruth bisdense,xisdense; 807 808 PetscFunctionBegin; 809 if (!n) PetscFunctionReturn(0); 810 811 ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr); 812 if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 813 ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr); 814 if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 815 816 ierr = MatGetArray(B,&b);CHKERRQ(ierr); 817 ierr = MatGetArray(X,&x);CHKERRQ(ierr); 818 819 tmp = a->solve_work; 820 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 821 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 822 823 for (neq=0; neq<B->cmap->n; neq++){ 824 /* forward solve the lower triangular */ 825 tmp[0] = b[r[0]]; 826 tmps = tmp; 827 for (i=1; i<n; i++) { 828 v = aa + ai[i] ; 829 vi = aj + ai[i] ; 830 nz = a->diag[i] - ai[i]; 831 sum = b[r[i]]; 832 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 833 tmp[i] = sum; 834 } 835 /* backward solve the upper triangular */ 836 for (i=n-1; i>=0; i--){ 837 v = aa + a->diag[i] + 1; 838 vi = aj + a->diag[i] + 1; 839 nz = ai[i+1] - a->diag[i] - 1; 840 sum = tmp[i]; 841 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 842 x[c[i]] = tmp[i] = sum*aa[a->diag[i]]; 843 } 844 845 b += n; 846 x += n; 847 } 848 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 849 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 850 ierr = MatRestoreArray(B,&b);CHKERRQ(ierr); 851 ierr = MatRestoreArray(X,&x);CHKERRQ(ierr); 852 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 853 PetscFunctionReturn(0); 854 } 855 856 #undef __FUNCT__ 857 #define __FUNCT__ "MatSolve_SeqAIJ_InplaceWithPerm" 858 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx) 859 { 860 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 861 IS iscol = a->col,isrow = a->row; 862 PetscErrorCode ierr; 863 const PetscInt *r,*c,*rout,*cout; 864 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 865 PetscInt nz,row; 866 PetscScalar *x,*b,*tmp,*tmps,sum; 867 const MatScalar *aa = a->a,*v; 868 869 PetscFunctionBegin; 870 if (!n) PetscFunctionReturn(0); 871 872 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 873 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 874 tmp = a->solve_work; 875 876 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 877 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 878 879 /* forward solve the lower triangular */ 880 tmp[0] = b[*r++]; 881 tmps = tmp; 882 for (row=1; row<n; row++) { 883 i = rout[row]; /* permuted row */ 884 v = aa + ai[i] ; 885 vi = aj + ai[i] ; 886 nz = a->diag[i] - ai[i]; 887 sum = b[*r++]; 888 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 889 tmp[row] = sum; 890 } 891 892 /* backward solve the upper triangular */ 893 for (row=n-1; row>=0; row--){ 894 i = rout[row]; /* permuted row */ 895 v = aa + a->diag[i] + 1; 896 vi = aj + a->diag[i] + 1; 897 nz = ai[i+1] - a->diag[i] - 1; 898 sum = tmp[row]; 899 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 900 x[*c--] = tmp[row] = sum*aa[a->diag[i]]; 901 } 902 903 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 904 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 905 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 906 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 907 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 908 PetscFunctionReturn(0); 909 } 910 911 /* ----------------------------------------------------------- */ 912 #undef __FUNCT__ 913 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering" 914 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx) 915 { 916 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 917 PetscErrorCode ierr; 918 PetscInt n = A->rmap->n; 919 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag,*vi; 920 PetscScalar *x; 921 const PetscScalar *b; 922 const MatScalar *aa = a->a; 923 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 924 PetscInt adiag_i,i,nz,ai_i; 925 const MatScalar *v; 926 PetscScalar sum; 927 #endif 928 929 PetscFunctionBegin; 930 if (!n) PetscFunctionReturn(0); 931 932 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 933 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 934 935 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 936 fortransolveaij_(&n,x,ai,aj,adiag,aa,b); 937 #else 938 /* forward solve the lower triangular */ 939 x[0] = b[0]; 940 for (i=1; i<n; i++) { 941 ai_i = ai[i]; 942 v = aa + ai_i; 943 vi = aj + ai_i; 944 nz = adiag[i] - ai_i; 945 sum = b[i]; 946 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 947 x[i] = sum; 948 } 949 950 /* backward solve the upper triangular */ 951 for (i=n-1; i>=0; i--){ 952 adiag_i = adiag[i]; 953 v = aa + adiag_i + 1; 954 vi = aj + adiag_i + 1; 955 nz = ai[i+1] - adiag_i - 1; 956 sum = x[i]; 957 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 958 x[i] = sum*aa[adiag_i]; 959 } 960 #endif 961 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 962 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 963 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 964 PetscFunctionReturn(0); 965 } 966 967 #undef __FUNCT__ 968 #define __FUNCT__ "MatSolveAdd_SeqAIJ" 969 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx) 970 { 971 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 972 IS iscol = a->col,isrow = a->row; 973 PetscErrorCode ierr; 974 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 975 PetscInt nz; 976 const PetscInt *rout,*cout,*r,*c; 977 PetscScalar *x,*b,*tmp,sum; 978 const MatScalar *aa = a->a,*v; 979 980 PetscFunctionBegin; 981 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 982 983 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 984 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 985 tmp = a->solve_work; 986 987 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 988 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 989 990 /* forward solve the lower triangular */ 991 tmp[0] = b[*r++]; 992 for (i=1; i<n; i++) { 993 v = aa + ai[i] ; 994 vi = aj + ai[i] ; 995 nz = a->diag[i] - ai[i]; 996 sum = b[*r++]; 997 while (nz--) sum -= *v++ * tmp[*vi++ ]; 998 tmp[i] = sum; 999 } 1000 1001 /* backward solve the upper triangular */ 1002 for (i=n-1; i>=0; i--){ 1003 v = aa + a->diag[i] + 1; 1004 vi = aj + a->diag[i] + 1; 1005 nz = ai[i+1] - a->diag[i] - 1; 1006 sum = tmp[i]; 1007 while (nz--) sum -= *v++ * tmp[*vi++ ]; 1008 tmp[i] = sum*aa[a->diag[i]]; 1009 x[*c--] += tmp[i]; 1010 } 1011 1012 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1013 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1014 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1015 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1016 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1017 1018 PetscFunctionReturn(0); 1019 } 1020 /* -------------------------------------------------------------------*/ 1021 #undef __FUNCT__ 1022 #define __FUNCT__ "MatSolveTranspose_SeqAIJ" 1023 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx) 1024 { 1025 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1026 IS iscol = a->col,isrow = a->row; 1027 PetscErrorCode ierr; 1028 const PetscInt *rout,*cout,*r,*c; 1029 PetscInt i,n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1030 PetscInt nz,*diag = a->diag; 1031 PetscScalar *x,*b,*tmp,s1; 1032 const MatScalar *aa = a->a,*v; 1033 1034 PetscFunctionBegin; 1035 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1036 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1037 tmp = a->solve_work; 1038 1039 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1040 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1041 1042 /* copy the b into temp work space according to permutation */ 1043 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1044 1045 /* forward solve the U^T */ 1046 for (i=0; i<n; i++) { 1047 v = aa + diag[i] ; 1048 vi = aj + diag[i] + 1; 1049 nz = ai[i+1] - diag[i] - 1; 1050 s1 = tmp[i]; 1051 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1052 while (nz--) { 1053 tmp[*vi++ ] -= (*v++)*s1; 1054 } 1055 tmp[i] = s1; 1056 } 1057 1058 /* backward solve the L^T */ 1059 for (i=n-1; i>=0; i--){ 1060 v = aa + diag[i] - 1 ; 1061 vi = aj + diag[i] - 1 ; 1062 nz = diag[i] - ai[i]; 1063 s1 = tmp[i]; 1064 while (nz--) { 1065 tmp[*vi-- ] -= (*v--)*s1; 1066 } 1067 } 1068 1069 /* copy tmp into x according to permutation */ 1070 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1071 1072 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1073 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1074 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1075 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1076 1077 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1078 PetscFunctionReturn(0); 1079 } 1080 1081 #undef __FUNCT__ 1082 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ" 1083 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx) 1084 { 1085 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1086 IS iscol = a->col,isrow = a->row; 1087 PetscErrorCode ierr; 1088 const PetscInt *r,*c,*rout,*cout; 1089 PetscInt i,n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1090 PetscInt nz,*diag = a->diag; 1091 PetscScalar *x,*b,*tmp; 1092 const MatScalar *aa = a->a,*v; 1093 1094 PetscFunctionBegin; 1095 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1096 1097 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1098 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1099 tmp = a->solve_work; 1100 1101 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1102 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1103 1104 /* copy the b into temp work space according to permutation */ 1105 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1106 1107 /* forward solve the U^T */ 1108 for (i=0; i<n; i++) { 1109 v = aa + diag[i] ; 1110 vi = aj + diag[i] + 1; 1111 nz = ai[i+1] - diag[i] - 1; 1112 tmp[i] *= *v++; 1113 while (nz--) { 1114 tmp[*vi++ ] -= (*v++)*tmp[i]; 1115 } 1116 } 1117 1118 /* backward solve the L^T */ 1119 for (i=n-1; i>=0; i--){ 1120 v = aa + diag[i] - 1 ; 1121 vi = aj + diag[i] - 1 ; 1122 nz = diag[i] - ai[i]; 1123 while (nz--) { 1124 tmp[*vi-- ] -= (*v--)*tmp[i]; 1125 } 1126 } 1127 1128 /* copy tmp into x according to permutation */ 1129 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1130 1131 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1132 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1133 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1134 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1135 1136 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1137 PetscFunctionReturn(0); 1138 } 1139 /* ----------------------------------------------------------------*/ 1140 EXTERN PetscErrorCode Mat_CheckInode(Mat,PetscTruth); 1141 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption); 1142 1143 /* 1144 ilu(0) with natural ordering under new data structure. 1145 Factored arrays bj and ba are stored as 1146 L(0,:), L(1,:), ...,L(n-1,:), U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:) 1147 1148 bi=fact->i is an array of size 2n+2, in which 1149 bi+ 1150 bi[i] -> 1st entry of L(i,:),i=0,...,i-1 1151 bi[n] -> end of L(n-1,:)+1 1152 bi[n+1] -> 1st entry of U(n-1,:) 1153 bi[2n-i] -> 1st entry of U(i,:) 1154 bi[2n-i+1] -> end of U(i,:)+1, the 1st entry of U(i-1,:) 1155 bi[2n] -> end of U(0,:)+1 1156 1157 U(i,:) contains diag[i] as its last entry, i.e., 1158 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 1159 */ 1160 #undef __FUNCT__ 1161 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct" 1162 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1163 { 1164 1165 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1166 PetscErrorCode ierr; 1167 PetscInt n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag; 1168 PetscInt i,j,nz,*bi,*bj,*bdiag; 1169 1170 PetscFunctionBegin; 1171 /* printf("MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct ...\n"); */ 1172 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES);CHKERRQ(ierr); 1173 b = (Mat_SeqAIJ*)(fact)->data; 1174 1175 /* replace matrix arrays with single allocations, then reset values */ 1176 ierr = PetscFree3(b->a,b->j,b->i);CHKERRQ(ierr); 1177 ierr = PetscFree(b->diag);CHKERRQ(ierr); 1178 1179 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&b->i);CHKERRQ(ierr); 1180 ierr = PetscMalloc((ai[n]+1)*sizeof(PetscInt),&b->j);CHKERRQ(ierr); 1181 ierr = PetscMalloc((ai[n]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 1182 b->singlemalloc = PETSC_FALSE; 1183 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr); 1184 bdiag = b->diag; 1185 1186 if (n > 0) { 1187 ierr = PetscMemzero(b->a,(ai[n])*sizeof(PetscScalar));CHKERRQ(ierr); 1188 } 1189 1190 /* set bi and bj with new data structure */ 1191 bi = b->i; 1192 bj = b->j; 1193 1194 /* L part */ 1195 bi[0] = 0; 1196 for (i=0; i<n; i++){ 1197 nz = adiag[i] - ai[i]; 1198 bi[i+1] = bi[i] + nz; 1199 aj = a->j + ai[i]; 1200 for (j=0; j<nz; j++){ 1201 *bj = aj[j]; bj++; 1202 } 1203 } 1204 1205 /* U part */ 1206 bi[n+1] = bi[n]; 1207 for (i=n-1; i>=0; i--){ 1208 nz = ai[i+1] - adiag[i] - 1; 1209 bi[2*n-i+1] = bi[2*n-i] + nz + 1; 1210 aj = a->j + adiag[i] + 1; 1211 for (j=0; j<nz; j++){ 1212 *bj = aj[j]; bj++; 1213 } 1214 /* diag[i] */ 1215 *bj = i; bj++; 1216 bdiag[i] = bi[2*n-i+1]-1; 1217 } 1218 PetscFunctionReturn(0); 1219 } 1220 1221 #undef __FUNCT__ 1222 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ" 1223 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1224 { 1225 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1226 IS isicol; 1227 PetscErrorCode ierr; 1228 const PetscInt *r,*ic; 1229 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,d; 1230 PetscInt *bi,*cols,nnz,*cols_lvl; 1231 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1232 PetscInt i,levels,diagonal_fill; 1233 PetscTruth col_identity,row_identity; 1234 PetscReal f; 1235 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1236 PetscBT lnkbt; 1237 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1238 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1239 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1240 PetscTruth missing; 1241 1242 PetscFunctionBegin; 1243 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); 1244 f = info->fill; 1245 levels = (PetscInt)info->levels; 1246 diagonal_fill = (PetscInt)info->diagonal_fill; 1247 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1248 1249 /* special case that simply copies fill pattern */ 1250 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1251 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1252 if (!levels && row_identity && col_identity) { 1253 1254 PetscTruth newdatastruct=PETSC_FALSE; 1255 ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 1256 if (newdatastruct){ 1257 ierr = MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1258 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 1259 } else { 1260 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES);CHKERRQ(ierr); 1261 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1262 } 1263 1264 fact->factor = MAT_FACTOR_ILU; 1265 (fact)->info.factor_mallocs = 0; 1266 (fact)->info.fill_ratio_given = info->fill; 1267 (fact)->info.fill_ratio_needed = 1.0; 1268 b = (Mat_SeqAIJ*)(fact)->data; 1269 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 1270 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 1271 b->row = isrow; 1272 b->col = iscol; 1273 b->icol = isicol; 1274 ierr = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1275 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1276 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1277 ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1278 PetscFunctionReturn(0); 1279 } 1280 1281 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1282 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1283 1284 /* get new row pointers */ 1285 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1286 bi[0] = 0; 1287 /* bdiag is location of diagonal in factor */ 1288 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1289 bdiag[0] = 0; 1290 1291 ierr = PetscMalloc((2*n+1)*sizeof(PetscInt**),&bj_ptr);CHKERRQ(ierr); 1292 bjlvl_ptr = (PetscInt**)(bj_ptr + n); 1293 1294 /* create a linked list for storing column indices of the active row */ 1295 nlnk = n + 1; 1296 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1297 1298 /* initial FreeSpace size is f*(ai[n]+1) */ 1299 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1300 current_space = free_space; 1301 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1302 current_space_lvl = free_space_lvl; 1303 1304 for (i=0; i<n; i++) { 1305 nzi = 0; 1306 /* copy current row into linked list */ 1307 nnz = ai[r[i]+1] - ai[r[i]]; 1308 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1309 cols = aj + ai[r[i]]; 1310 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1311 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1312 nzi += nlnk; 1313 1314 /* make sure diagonal entry is included */ 1315 if (diagonal_fill && lnk[i] == -1) { 1316 fm = n; 1317 while (lnk[fm] < i) fm = lnk[fm]; 1318 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1319 lnk[fm] = i; 1320 lnk_lvl[i] = 0; 1321 nzi++; dcount++; 1322 } 1323 1324 /* add pivot rows into the active row */ 1325 nzbd = 0; 1326 prow = lnk[n]; 1327 while (prow < i) { 1328 nnz = bdiag[prow]; 1329 cols = bj_ptr[prow] + nnz + 1; 1330 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1331 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1332 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1333 nzi += nlnk; 1334 prow = lnk[prow]; 1335 nzbd++; 1336 } 1337 bdiag[i] = nzbd; 1338 bi[i+1] = bi[i] + nzi; 1339 1340 /* if free space is not available, make more free space */ 1341 if (current_space->local_remaining<nzi) { 1342 nnz = nzi*(n - i); /* estimated and max additional space needed */ 1343 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1344 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1345 reallocs++; 1346 } 1347 1348 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1349 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1350 bj_ptr[i] = current_space->array; 1351 bjlvl_ptr[i] = current_space_lvl->array; 1352 1353 /* make sure the active row i has diagonal entry */ 1354 if (*(bj_ptr[i]+bdiag[i]) != i) { 1355 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 1356 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1357 } 1358 1359 current_space->array += nzi; 1360 current_space->local_used += nzi; 1361 current_space->local_remaining -= nzi; 1362 current_space_lvl->array += nzi; 1363 current_space_lvl->local_used += nzi; 1364 current_space_lvl->local_remaining -= nzi; 1365 } 1366 1367 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1368 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1369 1370 /* destroy list of free space and other temporary arrays */ 1371 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 1372 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); 1373 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1374 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1375 ierr = PetscFree(bj_ptr);CHKERRQ(ierr); 1376 1377 #if defined(PETSC_USE_INFO) 1378 { 1379 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1380 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 1381 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1382 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 1383 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1384 if (diagonal_fill) { 1385 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 1386 } 1387 } 1388 #endif 1389 1390 /* put together the new matrix */ 1391 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 1392 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 1393 b = (Mat_SeqAIJ*)(fact)->data; 1394 b->free_a = PETSC_TRUE; 1395 b->free_ij = PETSC_TRUE; 1396 b->singlemalloc = PETSC_FALSE; 1397 ierr = PetscMalloc( (bi[n] )*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 1398 b->j = bj; 1399 b->i = bi; 1400 for (i=0; i<n; i++) bdiag[i] += bi[i]; 1401 b->diag = bdiag; 1402 b->ilen = 0; 1403 b->imax = 0; 1404 b->row = isrow; 1405 b->col = iscol; 1406 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1407 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1408 b->icol = isicol; 1409 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1410 /* In b structure: Free imax, ilen, old a, old j. 1411 Allocate bdiag, solve_work, new a, new j */ 1412 ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1413 b->maxnz = b->nz = bi[n] ; 1414 (fact)->info.factor_mallocs = reallocs; 1415 (fact)->info.fill_ratio_given = f; 1416 (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1417 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1418 ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1419 PetscFunctionReturn(0); 1420 } 1421 1422 #include "../src/mat/impls/sbaij/seq/sbaij.h" 1423 #undef __FUNCT__ 1424 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ" 1425 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 1426 { 1427 Mat C = B; 1428 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 1429 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 1430 IS ip=b->row,iip = b->icol; 1431 PetscErrorCode ierr; 1432 const PetscInt *rip,*riip; 1433 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol; 1434 PetscInt *ai=a->i,*aj=a->j; 1435 PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz; 1436 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 1437 PetscReal zeropivot,rs,shiftnz; 1438 PetscReal shiftpd; 1439 ChShift_Ctx sctx; 1440 PetscInt newshift; 1441 PetscTruth perm_identity; 1442 1443 PetscFunctionBegin; 1444 1445 shiftnz = info->shiftnz; 1446 shiftpd = info->shiftpd; 1447 zeropivot = info->zeropivot; 1448 1449 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 1450 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 1451 1452 /* initialization */ 1453 nz = (2*mbs+1)*sizeof(PetscInt)+mbs*sizeof(MatScalar); 1454 ierr = PetscMalloc(nz,&il);CHKERRQ(ierr); 1455 jl = il + mbs; 1456 rtmp = (MatScalar*)(jl + mbs); 1457 1458 sctx.shift_amount = 0; 1459 sctx.nshift = 0; 1460 do { 1461 sctx.chshift = PETSC_FALSE; 1462 for (i=0; i<mbs; i++) { 1463 rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0; 1464 } 1465 1466 for (k = 0; k<mbs; k++){ 1467 bval = ba + bi[k]; 1468 /* initialize k-th row by the perm[k]-th row of A */ 1469 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 1470 for (j = jmin; j < jmax; j++){ 1471 col = riip[aj[j]]; 1472 if (col >= k){ /* only take upper triangular entry */ 1473 rtmp[col] = aa[j]; 1474 *bval++ = 0.0; /* for in-place factorization */ 1475 } 1476 } 1477 /* shift the diagonal of the matrix */ 1478 if (sctx.nshift) rtmp[k] += sctx.shift_amount; 1479 1480 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 1481 dk = rtmp[k]; 1482 i = jl[k]; /* first row to be added to k_th row */ 1483 1484 while (i < k){ 1485 nexti = jl[i]; /* next row to be added to k_th row */ 1486 1487 /* compute multiplier, update diag(k) and U(i,k) */ 1488 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 1489 uikdi = - ba[ili]*ba[bi[i]]; /* diagonal(k) */ 1490 dk += uikdi*ba[ili]; 1491 ba[ili] = uikdi; /* -U(i,k) */ 1492 1493 /* add multiple of row i to k-th row */ 1494 jmin = ili + 1; jmax = bi[i+1]; 1495 if (jmin < jmax){ 1496 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 1497 /* update il and jl for row i */ 1498 il[i] = jmin; 1499 j = bj[jmin]; jl[i] = jl[j]; jl[j] = i; 1500 } 1501 i = nexti; 1502 } 1503 1504 /* shift the diagonals when zero pivot is detected */ 1505 /* compute rs=sum of abs(off-diagonal) */ 1506 rs = 0.0; 1507 jmin = bi[k]+1; 1508 nz = bi[k+1] - jmin; 1509 bcol = bj + jmin; 1510 while (nz--){ 1511 rs += PetscAbsScalar(rtmp[*bcol]); 1512 bcol++; 1513 } 1514 1515 sctx.rs = rs; 1516 sctx.pv = dk; 1517 ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr); 1518 1519 if (newshift == 1) { 1520 if (!sctx.shift_amount) { 1521 sctx.shift_amount = 1e-5; 1522 } 1523 break; 1524 } 1525 1526 /* copy data into U(k,:) */ 1527 ba[bi[k]] = 1.0/dk; /* U(k,k) */ 1528 jmin = bi[k]+1; jmax = bi[k+1]; 1529 if (jmin < jmax) { 1530 for (j=jmin; j<jmax; j++){ 1531 col = bj[j]; ba[j] = rtmp[col]; rtmp[col] = 0.0; 1532 } 1533 /* add the k-th row into il and jl */ 1534 il[k] = jmin; 1535 i = bj[jmin]; jl[k] = jl[i]; jl[i] = k; 1536 } 1537 } 1538 } while (sctx.chshift); 1539 ierr = PetscFree(il);CHKERRQ(ierr); 1540 1541 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 1542 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 1543 1544 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 1545 if (perm_identity){ 1546 (B)->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering; 1547 (B)->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering; 1548 (B)->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering; 1549 (B)->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering; 1550 } else { 1551 (B)->ops->solve = MatSolve_SeqSBAIJ_1; 1552 (B)->ops->solvetranspose = MatSolve_SeqSBAIJ_1; 1553 (B)->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1; 1554 (B)->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1; 1555 } 1556 1557 C->assembled = PETSC_TRUE; 1558 C->preallocated = PETSC_TRUE; 1559 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 1560 if (sctx.nshift){ 1561 if (shiftnz) { 1562 ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 1563 } else if (shiftpd) { 1564 ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 1565 } 1566 } 1567 PetscFunctionReturn(0); 1568 } 1569 1570 #undef __FUNCT__ 1571 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ" 1572 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 1573 { 1574 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1575 Mat_SeqSBAIJ *b; 1576 PetscErrorCode ierr; 1577 PetscTruth perm_identity,missing; 1578 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui; 1579 const PetscInt *rip,*riip; 1580 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 1581 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 1582 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 1583 PetscReal fill=info->fill,levels=info->levels; 1584 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1585 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1586 PetscBT lnkbt; 1587 IS iperm; 1588 1589 PetscFunctionBegin; 1590 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); 1591 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 1592 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 1593 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 1594 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 1595 1596 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 1597 ui[0] = 0; 1598 1599 /* ICC(0) without matrix ordering: simply copies fill pattern */ 1600 if (!levels && perm_identity) { 1601 1602 for (i=0; i<am; i++) { 1603 ui[i+1] = ui[i] + ai[i+1] - a->diag[i]; 1604 } 1605 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 1606 cols = uj; 1607 for (i=0; i<am; i++) { 1608 aj = a->j + a->diag[i]; 1609 ncols = ui[i+1] - ui[i]; 1610 for (j=0; j<ncols; j++) *cols++ = *aj++; 1611 } 1612 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 1613 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 1614 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 1615 1616 /* initialization */ 1617 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 1618 1619 /* jl: linked list for storing indices of the pivot rows 1620 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 1621 ierr = PetscMalloc((2*am+1)*sizeof(PetscInt)+2*am*sizeof(PetscInt**),&jl);CHKERRQ(ierr); 1622 il = jl + am; 1623 uj_ptr = (PetscInt**)(il + am); 1624 uj_lvl_ptr = (PetscInt**)(uj_ptr + am); 1625 for (i=0; i<am; i++){ 1626 jl[i] = am; il[i] = 0; 1627 } 1628 1629 /* create and initialize a linked list for storing column indices of the active row k */ 1630 nlnk = am + 1; 1631 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1632 1633 /* initial FreeSpace size is fill*(ai[am]+1) */ 1634 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 1635 current_space = free_space; 1636 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 1637 current_space_lvl = free_space_lvl; 1638 1639 for (k=0; k<am; k++){ /* for each active row k */ 1640 /* initialize lnk by the column indices of row rip[k] of A */ 1641 nzk = 0; 1642 ncols = ai[rip[k]+1] - ai[rip[k]]; 1643 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 1644 ncols_upper = 0; 1645 for (j=0; j<ncols; j++){ 1646 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 1647 if (riip[i] >= k){ /* only take upper triangular entry */ 1648 ajtmp[ncols_upper] = i; 1649 ncols_upper++; 1650 } 1651 } 1652 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1653 nzk += nlnk; 1654 1655 /* update lnk by computing fill-in for each pivot row to be merged in */ 1656 prow = jl[k]; /* 1st pivot row */ 1657 1658 while (prow < k){ 1659 nextprow = jl[prow]; 1660 1661 /* merge prow into k-th row */ 1662 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 1663 jmax = ui[prow+1]; 1664 ncols = jmax-jmin; 1665 i = jmin - ui[prow]; 1666 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 1667 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 1668 j = *(uj - 1); 1669 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 1670 nzk += nlnk; 1671 1672 /* update il and jl for prow */ 1673 if (jmin < jmax){ 1674 il[prow] = jmin; 1675 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 1676 } 1677 prow = nextprow; 1678 } 1679 1680 /* if free space is not available, make more free space */ 1681 if (current_space->local_remaining<nzk) { 1682 i = am - k + 1; /* num of unfactored rows */ 1683 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 1684 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 1685 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 1686 reallocs++; 1687 } 1688 1689 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1690 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 1691 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1692 1693 /* add the k-th row into il and jl */ 1694 if (nzk > 1){ 1695 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 1696 jl[k] = jl[i]; jl[i] = k; 1697 il[k] = ui[k] + 1; 1698 } 1699 uj_ptr[k] = current_space->array; 1700 uj_lvl_ptr[k] = current_space_lvl->array; 1701 1702 current_space->array += nzk; 1703 current_space->local_used += nzk; 1704 current_space->local_remaining -= nzk; 1705 1706 current_space_lvl->array += nzk; 1707 current_space_lvl->local_used += nzk; 1708 current_space_lvl->local_remaining -= nzk; 1709 1710 ui[k+1] = ui[k] + nzk; 1711 } 1712 1713 #if defined(PETSC_USE_INFO) 1714 if (ai[am] != 0) { 1715 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 1716 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 1717 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1718 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 1719 } else { 1720 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 1721 } 1722 #endif 1723 1724 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 1725 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 1726 ierr = PetscFree(jl);CHKERRQ(ierr); 1727 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 1728 1729 /* destroy list of free space and other temporary array(s) */ 1730 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 1731 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 1732 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1733 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1734 1735 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 1736 1737 /* put together the new matrix in MATSEQSBAIJ format */ 1738 1739 b = (Mat_SeqSBAIJ*)(fact)->data; 1740 b->singlemalloc = PETSC_FALSE; 1741 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 1742 b->j = uj; 1743 b->i = ui; 1744 b->diag = 0; 1745 b->ilen = 0; 1746 b->imax = 0; 1747 b->row = perm; 1748 b->col = perm; 1749 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 1750 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 1751 b->icol = iperm; 1752 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 1753 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1754 ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 1755 b->maxnz = b->nz = ui[am]; 1756 b->free_a = PETSC_TRUE; 1757 b->free_ij = PETSC_TRUE; 1758 1759 (fact)->info.factor_mallocs = reallocs; 1760 (fact)->info.fill_ratio_given = fill; 1761 if (ai[am] != 0) { 1762 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 1763 } else { 1764 (fact)->info.fill_ratio_needed = 0.0; 1765 } 1766 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 1767 PetscFunctionReturn(0); 1768 } 1769 1770 #undef __FUNCT__ 1771 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ" 1772 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 1773 { 1774 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1775 Mat_SeqSBAIJ *b; 1776 PetscErrorCode ierr; 1777 PetscTruth perm_identity; 1778 PetscReal fill = info->fill; 1779 const PetscInt *rip,*riip; 1780 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 1781 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 1782 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr; 1783 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1784 PetscBT lnkbt; 1785 IS iperm; 1786 1787 PetscFunctionBegin; 1788 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); 1789 /* check whether perm is the identity mapping */ 1790 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 1791 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 1792 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 1793 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 1794 1795 /* initialization */ 1796 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 1797 ui[0] = 0; 1798 1799 /* jl: linked list for storing indices of the pivot rows 1800 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 1801 ierr = PetscMalloc((3*am+1)*sizeof(PetscInt)+am*sizeof(PetscInt**),&jl);CHKERRQ(ierr); 1802 il = jl + am; 1803 cols = il + am; 1804 ui_ptr = (PetscInt**)(cols + am); 1805 for (i=0; i<am; i++){ 1806 jl[i] = am; il[i] = 0; 1807 } 1808 1809 /* create and initialize a linked list for storing column indices of the active row k */ 1810 nlnk = am + 1; 1811 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 1812 1813 /* initial FreeSpace size is fill*(ai[am]+1) */ 1814 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 1815 current_space = free_space; 1816 1817 for (k=0; k<am; k++){ /* for each active row k */ 1818 /* initialize lnk by the column indices of row rip[k] of A */ 1819 nzk = 0; 1820 ncols = ai[rip[k]+1] - ai[rip[k]]; 1821 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 1822 ncols_upper = 0; 1823 for (j=0; j<ncols; j++){ 1824 i = riip[*(aj + ai[rip[k]] + j)]; 1825 if (i >= k){ /* only take upper triangular entry */ 1826 cols[ncols_upper] = i; 1827 ncols_upper++; 1828 } 1829 } 1830 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 1831 nzk += nlnk; 1832 1833 /* update lnk by computing fill-in for each pivot row to be merged in */ 1834 prow = jl[k]; /* 1st pivot row */ 1835 1836 while (prow < k){ 1837 nextprow = jl[prow]; 1838 /* merge prow into k-th row */ 1839 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 1840 jmax = ui[prow+1]; 1841 ncols = jmax-jmin; 1842 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 1843 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 1844 nzk += nlnk; 1845 1846 /* update il and jl for prow */ 1847 if (jmin < jmax){ 1848 il[prow] = jmin; 1849 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 1850 } 1851 prow = nextprow; 1852 } 1853 1854 /* if free space is not available, make more free space */ 1855 if (current_space->local_remaining<nzk) { 1856 i = am - k + 1; /* num of unfactored rows */ 1857 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 1858 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 1859 reallocs++; 1860 } 1861 1862 /* copy data into free space, then initialize lnk */ 1863 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 1864 1865 /* add the k-th row into il and jl */ 1866 if (nzk-1 > 0){ 1867 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 1868 jl[k] = jl[i]; jl[i] = k; 1869 il[k] = ui[k] + 1; 1870 } 1871 ui_ptr[k] = current_space->array; 1872 current_space->array += nzk; 1873 current_space->local_used += nzk; 1874 current_space->local_remaining -= nzk; 1875 1876 ui[k+1] = ui[k] + nzk; 1877 } 1878 1879 #if defined(PETSC_USE_INFO) 1880 if (ai[am] != 0) { 1881 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 1882 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 1883 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1884 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 1885 } else { 1886 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 1887 } 1888 #endif 1889 1890 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 1891 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 1892 ierr = PetscFree(jl);CHKERRQ(ierr); 1893 1894 /* destroy list of free space and other temporary array(s) */ 1895 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 1896 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 1897 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1898 1899 /* put together the new matrix in MATSEQSBAIJ format */ 1900 1901 b = (Mat_SeqSBAIJ*)(fact)->data; 1902 b->singlemalloc = PETSC_FALSE; 1903 b->free_a = PETSC_TRUE; 1904 b->free_ij = PETSC_TRUE; 1905 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 1906 b->j = uj; 1907 b->i = ui; 1908 b->diag = 0; 1909 b->ilen = 0; 1910 b->imax = 0; 1911 b->row = perm; 1912 b->col = perm; 1913 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 1914 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 1915 b->icol = iperm; 1916 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 1917 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1918 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 1919 b->maxnz = b->nz = ui[am]; 1920 1921 (fact)->info.factor_mallocs = reallocs; 1922 (fact)->info.fill_ratio_given = fill; 1923 if (ai[am] != 0) { 1924 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 1925 } else { 1926 (fact)->info.fill_ratio_needed = 0.0; 1927 } 1928 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 1929 PetscFunctionReturn(0); 1930 } 1931 1932 #undef __FUNCT__ 1933 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_iludt" 1934 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_iludt(Mat A,Vec bb,Vec xx) 1935 { 1936 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1937 PetscErrorCode ierr; 1938 PetscInt n = A->rmap->n; 1939 const PetscInt *ai = a->i,*aj = a->j,*vi; 1940 PetscScalar *x,sum; 1941 const PetscScalar *b; 1942 const MatScalar *aa = a->a,*v; 1943 PetscInt i,nz; 1944 1945 PetscFunctionBegin; 1946 if (!n) PetscFunctionReturn(0); 1947 1948 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1949 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1950 1951 /* forward solve the lower triangular */ 1952 x[0] = b[0]; 1953 v = aa; 1954 vi = aj; 1955 for (i=1; i<n; i++) { 1956 nz = ai[i+1] - ai[i]; 1957 sum = b[i]; 1958 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1959 /* while (nz--) sum -= *v++ * x[*vi++];*/ 1960 v += nz; 1961 vi += nz; 1962 x[i] = sum; 1963 } 1964 1965 /* backward solve the upper triangular */ 1966 v = aa + ai[n+1]; 1967 vi = aj + ai[n+1]; 1968 for (i=n-1; i>=0; i--){ 1969 nz = ai[2*n-i +1] - ai[2*n-i]-1; 1970 sum = x[i]; 1971 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1972 /* while (nz--) sum -= *v++ * x[*vi++]; */ 1973 v += nz; 1974 vi += nz; vi++; 1975 x[i] = *v++ *sum; /* x[i]=aa[adiag[i]]*sum; v++; */ 1976 } 1977 1978 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1979 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1980 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1981 PetscFunctionReturn(0); 1982 } 1983 1984 #undef __FUNCT__ 1985 #define __FUNCT__ "MatSolve_SeqAIJ_iludt" 1986 PetscErrorCode MatSolve_SeqAIJ_iludt(Mat A,Vec bb,Vec xx) 1987 { 1988 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1989 IS iscol = a->col,isrow = a->row; 1990 PetscErrorCode ierr; 1991 PetscInt i,n=A->rmap->n,*vi,*ai = a->i,*aj = a->j,*adiag=a->diag; 1992 PetscInt nz; 1993 const PetscInt *rout,*cout,*r,*c; 1994 PetscScalar *x,*tmp,*tmps; 1995 const PetscScalar *b; 1996 const MatScalar *aa = a->a,*v; 1997 1998 PetscFunctionBegin; 1999 if (!n) PetscFunctionReturn(0); 2000 2001 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 2002 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 2003 tmp = a->solve_work; 2004 2005 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 2006 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 2007 2008 /* forward solve the lower triangular */ 2009 tmp[0] = b[*r++]; 2010 tmps = tmp; 2011 v = aa; 2012 vi = aj; 2013 for (i=1; i<n; i++) { 2014 nz = ai[i+1] - ai[i]; 2015 tmp[i] = b[*r++]; 2016 PetscSparseDenseMinusDot(tmp[i],tmps,v,vi,nz); 2017 v += nz; vi += nz; 2018 } 2019 2020 /* backward solve the upper triangular */ 2021 v = aa + adiag[n] + 1; 2022 vi = aj + adiag[n] + 1; 2023 for (i=n-1; i>=0; i--){ 2024 nz = adiag[i] - adiag[i+1] - 1; 2025 PetscSparseDenseMinusDot(tmp[i],tmps,v,vi,nz); 2026 x[*c--] = tmp[i] = tmp[i]*aa[adiag[i]]; 2027 v += nz+1; vi += nz+1; 2028 } 2029 2030 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 2031 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 2032 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 2033 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 2034 ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr); 2035 PetscFunctionReturn(0); 2036 } 2037 2038 #undef __FUNCT__ 2039 #define __FUNCT__ "MatILUDTFactor_SeqAIJ" 2040 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact) 2041 { 2042 Mat B = *fact; 2043 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b; 2044 IS isicol; 2045 PetscErrorCode ierr; 2046 const PetscInt *r,*ic; 2047 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag; 2048 PetscInt *bi,*bj,*bdiag,*bdiag_rev; 2049 PetscInt row,nzi,nzi_bl,nzi_bu,*im,dtcount,nzi_al,nzi_au; 2050 PetscInt nlnk,*lnk; 2051 PetscBT lnkbt; 2052 PetscTruth row_identity,icol_identity,both_identity; 2053 MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp; 2054 const PetscInt *ics; 2055 PetscInt j,nz,*pj,*bjtmp,k,ncut,*jtmp; 2056 PetscReal dt=info->dt,shift=info->shiftinblocks; 2057 PetscInt nnz_max; 2058 PetscTruth missing; 2059 2060 PetscFunctionBegin; 2061 /* ------- symbolic factorization, can be reused ---------*/ 2062 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 2063 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 2064 adiag=a->diag; 2065 2066 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 2067 2068 /* bdiag is location of diagonal in factor */ 2069 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 2070 bdiag_rev = bdiag + n+1; 2071 2072 /* allocate row pointers bi */ 2073 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 2074 2075 /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */ 2076 dtcount = (PetscInt)info->dtcount; 2077 if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */ 2078 nnz_max = ai[n]+2*n*dtcount+2; 2079 2080 ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 2081 ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr); 2082 2083 /* put together the new matrix */ 2084 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 2085 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 2086 b = (Mat_SeqAIJ*)(B)->data; 2087 b->free_a = PETSC_TRUE; 2088 b->free_ij = PETSC_TRUE; 2089 b->singlemalloc = PETSC_FALSE; 2090 b->a = ba; 2091 b->j = bj; 2092 b->i = bi; 2093 b->diag = bdiag; 2094 b->ilen = 0; 2095 b->imax = 0; 2096 b->row = isrow; 2097 b->col = iscol; 2098 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 2099 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 2100 b->icol = isicol; 2101 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2102 2103 ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2104 b->maxnz = nnz_max; 2105 2106 (B)->factor = MAT_FACTOR_ILUDT; 2107 (B)->info.factor_mallocs = 0; 2108 (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]); 2109 CHKMEMQ; 2110 /* ------- end of symbolic factorization ---------*/ 2111 2112 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 2113 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 2114 ics = ic; 2115 2116 /* linked list for storing column indices of the active row */ 2117 nlnk = n + 1; 2118 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2119 2120 /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */ 2121 ierr = PetscMalloc((2*n+1)*sizeof(PetscInt),&im);CHKERRQ(ierr); 2122 jtmp = im + n; 2123 /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */ 2124 ierr = PetscMalloc((2*n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 2125 ierr = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr); 2126 vtmp = rtmp + n; 2127 2128 bi[0] = 0; 2129 bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */ 2130 bdiag_rev[n] = bdiag[0]; 2131 bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */ 2132 for (i=0; i<n; i++) { 2133 /* copy initial fill into linked list */ 2134 nzi = 0; /* nonzeros for active row i */ 2135 nzi = ai[r[i]+1] - ai[r[i]]; 2136 if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 2137 nzi_al = adiag[r[i]] - ai[r[i]]; 2138 nzi_au = ai[r[i]+1] - adiag[r[i]] -1; 2139 ajtmp = aj + ai[r[i]]; 2140 ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2141 2142 /* load in initial (unfactored row) */ 2143 aatmp = a->a + ai[r[i]]; 2144 for (j=0; j<nzi; j++) { 2145 rtmp[ics[*ajtmp++]] = *aatmp++; 2146 } 2147 2148 /* add pivot rows into linked list */ 2149 row = lnk[n]; 2150 while (row < i ) { 2151 nzi_bl = bi[row+1] - bi[row] + 1; 2152 bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */ 2153 ierr = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr); 2154 nzi += nlnk; 2155 row = lnk[row]; 2156 } 2157 2158 /* copy data from lnk into jtmp, then initialize lnk */ 2159 ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr); 2160 2161 /* numerical factorization */ 2162 bjtmp = jtmp; 2163 row = *bjtmp++; /* 1st pivot row */ 2164 while ( row < i ) { 2165 pc = rtmp + row; 2166 pv = ba + bdiag[row]; /* 1./(diag of the pivot row) */ 2167 multiplier = (*pc) * (*pv); 2168 *pc = multiplier; 2169 if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */ 2170 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 2171 pv = ba + bdiag[row+1] + 1; 2172 /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */ 2173 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 2174 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 2175 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 2176 } 2177 row = *bjtmp++; 2178 } 2179 2180 /* copy sparse rtmp into contiguous vtmp; separate L and U part */ 2181 diag_tmp = rtmp[i]; /* save diagonal value - may not needed?? */ 2182 nzi_bl = 0; j = 0; 2183 while (jtmp[j] < i){ /* Note: jtmp is sorted */ 2184 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 2185 nzi_bl++; j++; 2186 } 2187 nzi_bu = nzi - nzi_bl -1; 2188 while (j < nzi){ 2189 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 2190 j++; 2191 } 2192 2193 bjtmp = bj + bi[i]; 2194 batmp = ba + bi[i]; 2195 /* apply level dropping rule to L part */ 2196 ncut = nzi_al + dtcount; 2197 if (ncut < nzi_bl){ 2198 ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr); 2199 ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr); 2200 } else { 2201 ncut = nzi_bl; 2202 } 2203 for (j=0; j<ncut; j++){ 2204 bjtmp[j] = jtmp[j]; 2205 batmp[j] = vtmp[j]; 2206 /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */ 2207 } 2208 bi[i+1] = bi[i] + ncut; 2209 nzi = ncut + 1; 2210 2211 /* apply level dropping rule to U part */ 2212 ncut = nzi_au + dtcount; 2213 if (ncut < nzi_bu){ 2214 ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr); 2215 ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr); 2216 } else { 2217 ncut = nzi_bu; 2218 } 2219 nzi += ncut; 2220 2221 /* mark bdiagonal */ 2222 bdiag[i+1] = bdiag[i] - (ncut + 1); 2223 bdiag_rev[n-i-1] = bdiag[i+1]; 2224 bi[2*n - i] = bi[2*n - i +1] - (ncut + 1); 2225 bjtmp = bj + bdiag[i]; 2226 batmp = ba + bdiag[i]; 2227 *bjtmp = i; 2228 *batmp = diag_tmp; /* rtmp[i]; */ 2229 if (*batmp == 0.0) { 2230 *batmp = dt+shift; 2231 /* printf(" row %d add shift %g\n",i,shift); */ 2232 } 2233 *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */ 2234 /* printf(" (%d,%g),",*bjtmp,*batmp); */ 2235 2236 bjtmp = bj + bdiag[i+1]+1; 2237 batmp = ba + bdiag[i+1]+1; 2238 for (k=0; k<ncut; k++){ 2239 bjtmp[k] = jtmp[nzi_bl+1+k]; 2240 batmp[k] = vtmp[nzi_bl+1+k]; 2241 /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */ 2242 } 2243 /* printf("\n"); */ 2244 2245 im[i] = nzi; /* used by PetscLLAddSortedLU() */ 2246 /* 2247 printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]); 2248 printf(" ----------------------------\n"); 2249 */ 2250 } /* for (i=0; i<n; i++) */ 2251 /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */ 2252 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]); 2253 2254 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 2255 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 2256 2257 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2258 ierr = PetscFree(im);CHKERRQ(ierr); 2259 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2260 2261 ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr); 2262 b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n]; 2263 2264 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 2265 ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr); 2266 both_identity = (PetscTruth) (row_identity && icol_identity); 2267 if (row_identity && icol_identity) { 2268 B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_iludt; 2269 } else { 2270 B->ops->solve = MatSolve_SeqAIJ_iludt; 2271 } 2272 2273 B->ops->lufactorsymbolic = MatILUDTFactorSymbolic_SeqAIJ; 2274 B->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ; 2275 B->ops->solveadd = 0; 2276 B->ops->solvetranspose = 0; 2277 B->ops->solvetransposeadd = 0; 2278 B->ops->matsolve = 0; 2279 B->assembled = PETSC_TRUE; 2280 B->preallocated = PETSC_TRUE; 2281 PetscFunctionReturn(0); 2282 } 2283 2284 /* a wraper of MatILUDTFactor_SeqAIJ() */ 2285 #undef __FUNCT__ 2286 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ" 2287 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info) 2288 { 2289 PetscErrorCode ierr; 2290 2291 PetscFunctionBegin; 2292 ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr); 2293 2294 fact->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ; 2295 PetscFunctionReturn(0); 2296 } 2297 2298 /* 2299 same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors 2300 - intend to replace existing MatLUFactorNumeric_SeqAIJ() 2301 */ 2302 #undef __FUNCT__ 2303 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ" 2304 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info) 2305 { 2306 Mat C=fact; 2307 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 2308 IS isrow = b->row,isicol = b->icol; 2309 PetscErrorCode ierr; 2310 const PetscInt *r,*ic,*ics; 2311 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 2312 PetscInt *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj; 2313 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 2314 PetscReal dt=info->dt,shift=info->shiftinblocks; 2315 PetscTruth row_identity, col_identity; 2316 2317 PetscFunctionBegin; 2318 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 2319 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 2320 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 2321 ics = ic; 2322 2323 for (i=0; i<n; i++){ 2324 /* initialize rtmp array */ 2325 nzl = bi[i+1] - bi[i]; /* num of nozeros in L(i,:) */ 2326 bjtmp = bj + bi[i]; 2327 for (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0; 2328 rtmp[i] = 0.0; 2329 nzu = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */ 2330 bjtmp = bj + bdiag[i+1] + 1; 2331 for (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0; 2332 2333 /* load in initial unfactored row of A */ 2334 /* printf("row %d\n",i); */ 2335 nz = ai[r[i]+1] - ai[r[i]]; 2336 ajtmp = aj + ai[r[i]]; 2337 v = aa + ai[r[i]]; 2338 for (j=0; j<nz; j++) { 2339 rtmp[ics[*ajtmp++]] = v[j]; 2340 /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */ 2341 } 2342 /* printf("\n"); */ 2343 2344 /* numerical factorization */ 2345 bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */ 2346 nzl = bi[i+1] - bi[i]; /* num of entries in L(i,:) */ 2347 k = 0; 2348 while (k < nzl){ 2349 row = *bjtmp++; 2350 /* printf(" prow %d\n",row); */ 2351 pc = rtmp + row; 2352 pv = b->a + bdiag[row]; /* 1./(diag of the pivot row) */ 2353 multiplier = (*pc) * (*pv); 2354 *pc = multiplier; 2355 if (PetscAbsScalar(multiplier) > dt){ 2356 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 2357 pv = b->a + bdiag[row+1] + 1; 2358 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 2359 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 2360 /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */ 2361 } 2362 k++; 2363 } 2364 2365 /* finished row so stick it into b->a */ 2366 /* L-part */ 2367 pv = b->a + bi[i] ; 2368 pj = bj + bi[i] ; 2369 nzl = bi[i+1] - bi[i]; 2370 for (j=0; j<nzl; j++) { 2371 pv[j] = rtmp[pj[j]]; 2372 /* printf(" (%d,%g),",pj[j],pv[j]); */ 2373 } 2374 2375 /* diagonal: invert diagonal entries for simplier triangular solves */ 2376 if (rtmp[i] == 0.0) rtmp[i] = dt+shift; 2377 b->a[bdiag[i]] = 1.0/rtmp[i]; 2378 /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */ 2379 2380 /* U-part */ 2381 pv = b->a + bdiag[i+1] + 1; 2382 pj = bj + bdiag[i+1] + 1; 2383 nzu = bdiag[i] - bdiag[i+1] - 1; 2384 for (j=0; j<nzu; j++) { 2385 pv[j] = rtmp[pj[j]]; 2386 /* printf(" (%d,%g),",pj[j],pv[j]); */ 2387 } 2388 /* printf("\n"); */ 2389 } 2390 2391 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2392 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 2393 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 2394 2395 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 2396 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 2397 if (row_identity && col_identity) { 2398 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_iludt; 2399 } else { 2400 C->ops->solve = MatSolve_SeqAIJ_iludt; 2401 } 2402 C->ops->solveadd = 0; 2403 C->ops->solvetranspose = 0; 2404 C->ops->solvetransposeadd = 0; 2405 C->ops->matsolve = 0; 2406 C->assembled = PETSC_TRUE; 2407 C->preallocated = PETSC_TRUE; 2408 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 2409 PetscFunctionReturn(0); 2410 } 2411