1 #define PETSCMAT_DLL 2 3 4 #include "../src/mat/impls/aij/seq/aij.h" 5 #include "petscbt.h" 6 #include "../src/mat/utils/freespace.h" 7 8 EXTERN_C_BEGIN 9 #undef __FUNCT__ 10 #define __FUNCT__ "MatOrdering_Flow_SeqAIJ" 11 /* 12 Computes an ordering to get most of the large numerical values in the lower triangular part of the matrix 13 */ 14 PetscErrorCode MatOrdering_Flow_SeqAIJ(Mat mat,const MatOrderingType type,IS *irow,IS *icol) 15 { 16 Mat_SeqAIJ *a = (Mat_SeqAIJ*)mat->data; 17 PetscErrorCode ierr; 18 PetscInt i,j,jj,k, kk,n = mat->rmap->n, current = 0, newcurrent = 0,*order; 19 const PetscInt *ai = a->i, *aj = a->j; 20 const PetscScalar *aa = a->a; 21 PetscTruth *done; 22 PetscReal best,past = 0,future; 23 24 PetscFunctionBegin; 25 /* pick initial row */ 26 best = -1; 27 for (i=0; i<n; i++) { 28 future = 0; 29 for (j=ai[i]; j<ai[i+1]; j++) { 30 if (aj[j] != i) future += PetscAbsScalar(aa[j]); else past = PetscAbsScalar(aa[j]); 31 } 32 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 33 if (past/future > best) { 34 best = past/future; 35 current = i; 36 } 37 } 38 39 ierr = PetscMalloc(n*sizeof(PetscTruth),&done);CHKERRQ(ierr); 40 ierr = PetscMalloc(n*sizeof(PetscInt),&order);CHKERRQ(ierr); 41 ierr = PetscMemzero(done,n*sizeof(PetscTruth));CHKERRQ(ierr); 42 order[0] = current; 43 for (i=0; i<n-1; i++) { 44 done[current] = PETSC_TRUE; 45 best = -1; 46 /* loop over all neighbors of current pivot */ 47 for (j=ai[current]; j<ai[current+1]; j++) { 48 jj = aj[j]; 49 if (done[jj]) continue; 50 /* loop over columns of potential next row computing weights for below and above diagonal */ 51 past = future = 0.0; 52 for (k=ai[jj]; k<ai[jj+1]; k++) { 53 kk = aj[k]; 54 if (done[kk]) past += PetscAbsScalar(aa[k]); 55 else if (kk != jj) future += PetscAbsScalar(aa[k]); 56 } 57 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 58 if (past/future > best) { 59 best = past/future; 60 newcurrent = jj; 61 } 62 } 63 if (best == -1) { /* no neighbors to select from so select best of all that remain */ 64 best = -1; 65 for (k=0; k<n; k++) { 66 if (done[k]) continue; 67 future = 0; 68 past = 0; 69 for (j=ai[k]; j<ai[k+1]; j++) { 70 kk = aj[j]; 71 if (done[kk]) past += PetscAbsScalar(aa[j]); 72 else if (kk != k) future += PetscAbsScalar(aa[j]); 73 } 74 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 75 if (past/future > best) { 76 best = past/future; 77 newcurrent = k; 78 } 79 } 80 } 81 if (current == newcurrent) SETERRQ(PETSC_ERR_PLIB,"newcurrent cannot be current"); 82 current = newcurrent; 83 order[i+1] = current; 84 } 85 ierr = ISCreateGeneral(PETSC_COMM_SELF,n,order,irow);CHKERRQ(ierr); 86 *icol = *irow; 87 ierr = PetscObjectReference((PetscObject)*irow);CHKERRQ(ierr); 88 ierr = PetscFree(done);CHKERRQ(ierr); 89 ierr = PetscFree(order);CHKERRQ(ierr); 90 PetscFunctionReturn(0); 91 } 92 EXTERN_C_END 93 94 EXTERN_C_BEGIN 95 #undef __FUNCT__ 96 #define __FUNCT__ "MatGetFactorAvailable_seqaij_petsc" 97 PetscErrorCode MatGetFactorAvailable_seqaij_petsc(Mat A,MatFactorType ftype,PetscTruth *flg) 98 { 99 PetscFunctionBegin; 100 *flg = PETSC_TRUE; 101 PetscFunctionReturn(0); 102 } 103 EXTERN_C_END 104 105 EXTERN_C_BEGIN 106 #undef __FUNCT__ 107 #define __FUNCT__ "MatGetFactor_seqaij_petsc" 108 PetscErrorCode MatGetFactor_seqaij_petsc(Mat A,MatFactorType ftype,Mat *B) 109 { 110 PetscInt n = A->rmap->n; 111 PetscErrorCode ierr; 112 113 PetscFunctionBegin; 114 ierr = MatCreate(((PetscObject)A)->comm,B);CHKERRQ(ierr); 115 ierr = MatSetSizes(*B,n,n,n,n);CHKERRQ(ierr); 116 if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT){ 117 ierr = MatSetType(*B,MATSEQAIJ);CHKERRQ(ierr); 118 (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJ; 119 (*B)->ops->lufactorsymbolic = MatLUFactorSymbolic_SeqAIJ; 120 (*B)->ops->iludtfactor = MatILUDTFactor_SeqAIJ; 121 } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) { 122 ierr = MatSetType(*B,MATSEQSBAIJ);CHKERRQ(ierr); 123 ierr = MatSeqSBAIJSetPreallocation(*B,1,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 124 (*B)->ops->iccfactorsymbolic = MatICCFactorSymbolic_SeqAIJ; 125 (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJ; 126 } else SETERRQ(PETSC_ERR_SUP,"Factor type not supported"); 127 (*B)->factor = ftype; 128 PetscFunctionReturn(0); 129 } 130 EXTERN_C_END 131 132 #undef __FUNCT__ 133 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ" 134 PetscErrorCode MatLUFactorSymbolic_SeqAIJ(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 135 { 136 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 137 IS isicol; 138 PetscErrorCode ierr; 139 const PetscInt *r,*ic; 140 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j; 141 PetscInt *bi,*bj,*ajtmp; 142 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 143 PetscReal f; 144 PetscInt nlnk,*lnk,k,**bi_ptr; 145 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 146 PetscBT lnkbt; 147 148 PetscFunctionBegin; 149 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square"); 150 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 151 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 152 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 153 154 /* get new row pointers */ 155 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 156 bi[0] = 0; 157 158 /* bdiag is location of diagonal in factor */ 159 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 160 bdiag[0] = 0; 161 162 /* linked list for storing column indices of the active row */ 163 nlnk = n + 1; 164 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 165 166 ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr); 167 168 /* initial FreeSpace size is f*(ai[n]+1) */ 169 f = info->fill; 170 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 171 current_space = free_space; 172 173 for (i=0; i<n; i++) { 174 /* copy previous fill into linked list */ 175 nzi = 0; 176 nnz = ai[r[i]+1] - ai[r[i]]; 177 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 178 ajtmp = aj + ai[r[i]]; 179 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 180 nzi += nlnk; 181 182 /* add pivot rows into linked list */ 183 row = lnk[n]; 184 while (row < i) { 185 nzbd = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */ 186 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 187 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 188 nzi += nlnk; 189 row = lnk[row]; 190 } 191 bi[i+1] = bi[i] + nzi; 192 im[i] = nzi; 193 194 /* mark bdiag */ 195 nzbd = 0; 196 nnz = nzi; 197 k = lnk[n]; 198 while (nnz-- && k < i){ 199 nzbd++; 200 k = lnk[k]; 201 } 202 bdiag[i] = bi[i] + nzbd; 203 204 /* if free space is not available, make more free space */ 205 if (current_space->local_remaining<nzi) { 206 nnz = (n - i)*nzi; /* estimated and max additional space needed */ 207 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 208 reallocs++; 209 } 210 211 /* copy data into free space, then initialize lnk */ 212 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 213 bi_ptr[i] = current_space->array; 214 current_space->array += nzi; 215 current_space->local_used += nzi; 216 current_space->local_remaining -= nzi; 217 } 218 #if defined(PETSC_USE_INFO) 219 if (ai[n] != 0) { 220 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 221 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 222 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 223 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr); 224 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 225 } else { 226 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 227 } 228 #endif 229 230 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 231 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 232 233 /* destroy list of free space and other temporary array(s) */ 234 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 235 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); 236 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 237 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 238 239 /* put together the new matrix */ 240 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 241 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 242 b = (Mat_SeqAIJ*)(B)->data; 243 b->free_a = PETSC_TRUE; 244 b->free_ij = PETSC_TRUE; 245 b->singlemalloc = PETSC_FALSE; 246 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 247 b->j = bj; 248 b->i = bi; 249 b->diag = bdiag; 250 b->ilen = 0; 251 b->imax = 0; 252 b->row = isrow; 253 b->col = iscol; 254 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 255 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 256 b->icol = isicol; 257 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 258 259 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 260 ierr = PetscLogObjectMemory(B,(bi[n]-n)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 261 b->maxnz = b->nz = bi[n] ; 262 263 (B)->factor = MAT_FACTOR_LU; 264 (B)->info.factor_mallocs = reallocs; 265 (B)->info.fill_ratio_given = f; 266 267 if (ai[n]) { 268 (B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 269 } else { 270 (B)->info.fill_ratio_needed = 0.0; 271 } 272 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 273 (B)->ops->solve = MatSolve_SeqAIJ; 274 (B)->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 275 /* switch to inodes if appropriate */ 276 ierr = MatLUFactorSymbolic_Inode(B,A,isrow,iscol,info);CHKERRQ(ierr); 277 PetscFunctionReturn(0); 278 } 279 280 /* 281 Trouble in factorization, should we dump the original matrix? 282 */ 283 #undef __FUNCT__ 284 #define __FUNCT__ "MatFactorDumpMatrix" 285 PetscErrorCode MatFactorDumpMatrix(Mat A) 286 { 287 PetscErrorCode ierr; 288 PetscTruth flg = PETSC_FALSE; 289 290 PetscFunctionBegin; 291 ierr = PetscOptionsGetTruth(PETSC_NULL,"-mat_factor_dump_on_error",&flg,PETSC_NULL);CHKERRQ(ierr); 292 if (flg) { 293 PetscViewer viewer; 294 char filename[PETSC_MAX_PATH_LEN]; 295 296 ierr = PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);CHKERRQ(ierr); 297 ierr = PetscViewerBinaryOpen(((PetscObject)A)->comm,filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr); 298 ierr = MatView(A,viewer);CHKERRQ(ierr); 299 ierr = PetscViewerDestroy(viewer);CHKERRQ(ierr); 300 } 301 PetscFunctionReturn(0); 302 } 303 304 extern PetscErrorCode MatSolve_Inode(Mat,Vec,Vec); 305 306 /* ----------------------------------------------------------- */ 307 extern PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_iludt(Mat,Vec,Vec); 308 extern PetscErrorCode MatSolve_SeqAIJ_iludt(Mat,Vec,Vec); 309 310 #undef __FUNCT__ 311 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_newdatastruct" 312 PetscErrorCode MatLUFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info) 313 { 314 Mat C=B; 315 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 316 IS isrow = b->row,isicol = b->icol; 317 PetscErrorCode ierr; 318 const PetscInt *r,*ic,*ics; 319 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 320 PetscInt *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj; 321 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 322 PetscReal shift=info->shiftinblocks; 323 PetscTruth row_identity, col_identity; 324 325 PetscFunctionBegin; 326 /* printf("MatLUFactorNumeric_SeqAIJ_newdatastruct is called ...\n"); */ 327 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 328 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 329 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 330 ics = ic; 331 332 for (i=0; i<n; i++){ 333 /* zero rtmp */ 334 /* L part */ 335 nz = bi[i+1] - bi[i]; 336 bjtmp = bj + bi[i]; 337 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 338 339 /* U part */ 340 nz = bi[2*n-i+1] - bi[2*n-i]; 341 bjtmp = bj + bi[2*n-i]; 342 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 343 344 /* load in initial (unfactored row) */ 345 nz = ai[r[i]+1] - ai[r[i]]; 346 ajtmp = aj + ai[r[i]]; 347 v = aa + ai[r[i]]; 348 for (j=0; j<nz; j++) { 349 rtmp[ics[ajtmp[j]]] = v[j]; 350 } 351 if (rtmp[ics[r[i]]] == 0.0){ 352 rtmp[ics[r[i]]] += shift; /* shift the diagonal of the matrix */ 353 /* printf("row %d, shift %g\n",i,shift); */ 354 } 355 356 /* elimination */ 357 bjtmp = bj + bi[i]; 358 row = *bjtmp++; 359 nzL = bi[i+1] - bi[i]; 360 k = 0; 361 while (k < nzL) { 362 pc = rtmp + row; 363 if (*pc != 0.0) { 364 pv = b->a + bdiag[row]; 365 multiplier = *pc * (*pv); 366 *pc = multiplier; 367 pj = b->j + bi[2*n-row]; /* begining of U(row,:) */ 368 pv = b->a + bi[2*n-row]; 369 nz = bi[2*n-row+1] - bi[2*n-row] - 1; /* num of entries in U(row,:), excluding diag */ 370 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 371 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 372 } 373 row = *bjtmp++; k++; 374 } 375 376 /* finished row so stick it into b->a */ 377 /* L part */ 378 pv = b->a + bi[i] ; 379 pj = b->j + bi[i] ; 380 nz = bi[i+1] - bi[i]; 381 for (j=0; j<nz; j++) { 382 pv[j] = rtmp[pj[j]]; 383 } 384 385 /* Mark diagonal and invert diagonal for simplier triangular solves */ 386 pv = b->a + bdiag[i]; 387 pj = b->j + bdiag[i]; 388 /* if (*pj != i)SETERRQ2(PETSC_ERR_SUP,"row %d != *pj %d",i,*pj) */ 389 *pv = 1.0/rtmp[*pj]; 390 391 /* U part */ 392 pv = b->a + bi[2*n-i]; 393 pj = b->j + bi[2*n-i]; 394 nz = bi[2*n-i+1] - bi[2*n-i] - 1; 395 for (j=0; j<nz; j++) pv[j] = rtmp[pj[j]]; 396 } 397 ierr = PetscFree(rtmp);CHKERRQ(ierr); 398 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 399 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 400 401 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 402 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 403 if (row_identity && col_identity) { 404 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_iludt; 405 } else { 406 C->ops->solve = MatSolve_SeqAIJ_iludt; 407 } 408 409 C->ops->solveadd = 0; 410 C->ops->solvetranspose = 0; 411 C->ops->solvetransposeadd = 0; 412 C->ops->matsolve = 0; 413 C->assembled = PETSC_TRUE; 414 C->preallocated = PETSC_TRUE; 415 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 416 PetscFunctionReturn(0); 417 } 418 419 #undef __FUNCT__ 420 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ" 421 PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 422 { 423 Mat C=B; 424 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 425 IS isrow = b->row,isicol = b->icol; 426 PetscErrorCode ierr; 427 const PetscInt *r,*ic,*ics; 428 PetscInt i,j,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 429 PetscInt *ajtmp,*bjtmp,nz,row,*diag_offset = b->diag,diag,*pj; 430 MatScalar *rtmp,*pc,multiplier,*v,*pv,d,*aa=a->a; 431 PetscReal rs=0.0; 432 LUShift_Ctx sctx; 433 PetscInt newshift,*ddiag; 434 435 PetscFunctionBegin; 436 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 437 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 438 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 439 ics = ic; 440 441 sctx.shift_top = 0; 442 sctx.nshift_max = 0; 443 sctx.shift_lo = 0; 444 sctx.shift_hi = 0; 445 sctx.shift_fraction = 0; 446 447 /* if both shift schemes are chosen by user, only use info->shiftpd */ 448 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 449 ddiag = a->diag; 450 sctx.shift_top = info->zeropivot; 451 for (i=0; i<n; i++) { 452 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 453 d = (aa)[ddiag[i]]; 454 rs = -PetscAbsScalar(d) - PetscRealPart(d); 455 v = aa+ai[i]; 456 nz = ai[i+1] - ai[i]; 457 for (j=0; j<nz; j++) 458 rs += PetscAbsScalar(v[j]); 459 if (rs>sctx.shift_top) sctx.shift_top = rs; 460 } 461 sctx.shift_top *= 1.1; 462 sctx.nshift_max = 5; 463 sctx.shift_lo = 0.; 464 sctx.shift_hi = 1.; 465 } 466 467 sctx.shift_amount = 0.0; 468 sctx.nshift = 0; 469 do { 470 sctx.lushift = PETSC_FALSE; 471 for (i=0; i<n; i++){ 472 nz = bi[i+1] - bi[i]; 473 bjtmp = bj + bi[i]; 474 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 475 476 /* load in initial (unfactored row) */ 477 nz = ai[r[i]+1] - ai[r[i]]; 478 ajtmp = aj + ai[r[i]]; 479 v = aa + ai[r[i]]; 480 for (j=0; j<nz; j++) { 481 rtmp[ics[ajtmp[j]]] = v[j]; 482 } 483 rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 484 /* if (sctx.shift_amount > 0.0) printf("row %d, shift %g\n",i,sctx.shift_amount); */ 485 486 row = *bjtmp++; 487 while (row < i) { 488 pc = rtmp + row; 489 if (*pc != 0.0) { 490 pv = b->a + diag_offset[row]; 491 pj = b->j + diag_offset[row] + 1; 492 multiplier = *pc / *pv++; 493 *pc = multiplier; 494 nz = bi[row+1] - diag_offset[row] - 1; 495 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 496 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 497 } 498 row = *bjtmp++; 499 } 500 /* finished row so stick it into b->a */ 501 pv = b->a + bi[i] ; 502 pj = b->j + bi[i] ; 503 nz = bi[i+1] - bi[i]; 504 diag = diag_offset[i] - bi[i]; 505 rs = -PetscAbsScalar(pv[diag]); 506 for (j=0; j<nz; j++) { 507 pv[j] = rtmp[pj[j]]; 508 rs += PetscAbsScalar(pv[j]); 509 } 510 511 /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */ 512 sctx.rs = rs; 513 sctx.pv = pv[diag]; 514 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 515 if (newshift == 1) break; 516 } 517 518 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 519 /* 520 * if no shift in this attempt & shifting & started shifting & can refine, 521 * then try lower shift 522 */ 523 sctx.shift_hi = sctx.shift_fraction; 524 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 525 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 526 sctx.lushift = PETSC_TRUE; 527 sctx.nshift++; 528 } 529 } while (sctx.lushift); 530 531 /* invert diagonal entries for simplier triangular solves */ 532 for (i=0; i<n; i++) { 533 b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]]; 534 } 535 ierr = PetscFree(rtmp);CHKERRQ(ierr); 536 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 537 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 538 if (b->inode.use) { 539 C->ops->solve = MatSolve_Inode; 540 } else { 541 PetscTruth row_identity, col_identity; 542 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 543 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 544 if (row_identity && col_identity) { 545 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 546 } else { 547 C->ops->solve = MatSolve_SeqAIJ; 548 } 549 } 550 C->ops->solveadd = MatSolveAdd_SeqAIJ; 551 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 552 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 553 C->ops->matsolve = MatMatSolve_SeqAIJ; 554 C->assembled = PETSC_TRUE; 555 C->preallocated = PETSC_TRUE; 556 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 557 if (sctx.nshift){ 558 if (info->shiftpd) { 559 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); 560 } else if (info->shiftnz) { 561 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 562 } 563 } 564 PetscFunctionReturn(0); 565 } 566 567 /* 568 This routine implements inplace ILU(0) with row or/and column permutations. 569 Input: 570 A - original matrix 571 Output; 572 A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i] 573 a->j (col index) is permuted by the inverse of colperm, then sorted 574 a->a reordered accordingly with a->j 575 a->diag (ptr to diagonal elements) is updated. 576 */ 577 #undef __FUNCT__ 578 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_InplaceWithPerm" 579 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info) 580 { 581 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 582 IS isrow = a->row,isicol = a->icol; 583 PetscErrorCode ierr; 584 const PetscInt *r,*ic,*ics; 585 PetscInt i,j,n=A->rmap->n,*ai=a->i,*aj=a->j; 586 PetscInt *ajtmp,nz,row; 587 PetscInt *diag = a->diag,nbdiag,*pj; 588 PetscScalar *rtmp,*pc,multiplier,d; 589 MatScalar *v,*pv; 590 PetscReal rs; 591 LUShift_Ctx sctx; 592 PetscInt newshift; 593 594 PetscFunctionBegin; 595 if (A != B) SETERRQ(PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address"); 596 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 597 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 598 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&rtmp);CHKERRQ(ierr); 599 ierr = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr); 600 ics = ic; 601 602 sctx.shift_top = 0; 603 sctx.nshift_max = 0; 604 sctx.shift_lo = 0; 605 sctx.shift_hi = 0; 606 sctx.shift_fraction = 0; 607 608 /* if both shift schemes are chosen by user, only use info->shiftpd */ 609 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 610 sctx.shift_top = 0; 611 for (i=0; i<n; i++) { 612 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 613 d = (a->a)[diag[i]]; 614 rs = -PetscAbsScalar(d) - PetscRealPart(d); 615 v = a->a+ai[i]; 616 nz = ai[i+1] - ai[i]; 617 for (j=0; j<nz; j++) 618 rs += PetscAbsScalar(v[j]); 619 if (rs>sctx.shift_top) sctx.shift_top = rs; 620 } 621 if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot; 622 sctx.shift_top *= 1.1; 623 sctx.nshift_max = 5; 624 sctx.shift_lo = 0.; 625 sctx.shift_hi = 1.; 626 } 627 628 sctx.shift_amount = 0; 629 sctx.nshift = 0; 630 do { 631 sctx.lushift = PETSC_FALSE; 632 for (i=0; i<n; i++){ 633 /* load in initial unfactored row */ 634 nz = ai[r[i]+1] - ai[r[i]]; 635 ajtmp = aj + ai[r[i]]; 636 v = a->a + ai[r[i]]; 637 /* sort permuted ajtmp and values v accordingly */ 638 for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]]; 639 ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr); 640 641 diag[r[i]] = ai[r[i]]; 642 for (j=0; j<nz; j++) { 643 rtmp[ajtmp[j]] = v[j]; 644 if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */ 645 } 646 rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 647 648 row = *ajtmp++; 649 while (row < i) { 650 pc = rtmp + row; 651 if (*pc != 0.0) { 652 pv = a->a + diag[r[row]]; 653 pj = aj + diag[r[row]] + 1; 654 655 multiplier = *pc / *pv++; 656 *pc = multiplier; 657 nz = ai[r[row]+1] - diag[r[row]] - 1; 658 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 659 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 660 } 661 row = *ajtmp++; 662 } 663 /* finished row so overwrite it onto a->a */ 664 pv = a->a + ai[r[i]] ; 665 pj = aj + ai[r[i]] ; 666 nz = ai[r[i]+1] - ai[r[i]]; 667 nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */ 668 669 rs = 0.0; 670 for (j=0; j<nz; j++) { 671 pv[j] = rtmp[pj[j]]; 672 if (j != nbdiag) rs += PetscAbsScalar(pv[j]); 673 } 674 675 /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */ 676 sctx.rs = rs; 677 sctx.pv = pv[nbdiag]; 678 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 679 if (newshift == 1) break; 680 } 681 682 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 683 /* 684 * if no shift in this attempt & shifting & started shifting & can refine, 685 * then try lower shift 686 */ 687 sctx.shift_hi = sctx.shift_fraction; 688 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 689 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 690 sctx.lushift = PETSC_TRUE; 691 sctx.nshift++; 692 } 693 } while (sctx.lushift); 694 695 /* invert diagonal entries for simplier triangular solves */ 696 for (i=0; i<n; i++) { 697 a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]]; 698 } 699 700 ierr = PetscFree(rtmp);CHKERRQ(ierr); 701 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 702 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 703 A->ops->solve = MatSolve_SeqAIJ_InplaceWithPerm; 704 A->ops->solveadd = MatSolveAdd_SeqAIJ; 705 A->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 706 A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 707 A->assembled = PETSC_TRUE; 708 A->preallocated = PETSC_TRUE; 709 ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr); 710 if (sctx.nshift){ 711 if (info->shiftpd) { 712 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); 713 } else if (info->shiftnz) { 714 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 715 } 716 } 717 PetscFunctionReturn(0); 718 } 719 720 /* ----------------------------------------------------------- */ 721 #undef __FUNCT__ 722 #define __FUNCT__ "MatLUFactor_SeqAIJ" 723 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info) 724 { 725 PetscErrorCode ierr; 726 Mat C; 727 728 PetscFunctionBegin; 729 ierr = MatGetFactor(A,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr); 730 ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr); 731 ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr); 732 A->ops->solve = C->ops->solve; 733 A->ops->solvetranspose = C->ops->solvetranspose; 734 ierr = MatHeaderCopy(A,C);CHKERRQ(ierr); 735 ierr = PetscLogObjectParent(A,((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr); 736 PetscFunctionReturn(0); 737 } 738 /* ----------------------------------------------------------- */ 739 740 741 #undef __FUNCT__ 742 #define __FUNCT__ "MatSolve_SeqAIJ" 743 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx) 744 { 745 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 746 IS iscol = a->col,isrow = a->row; 747 PetscErrorCode ierr; 748 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 749 PetscInt nz; 750 const PetscInt *rout,*cout,*r,*c; 751 PetscScalar *x,*tmp,*tmps,sum; 752 const PetscScalar *b; 753 const MatScalar *aa = a->a,*v; 754 755 PetscFunctionBegin; 756 if (!n) PetscFunctionReturn(0); 757 758 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 759 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 760 tmp = a->solve_work; 761 762 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 763 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 764 765 /* forward solve the lower triangular */ 766 tmp[0] = b[*r++]; 767 tmps = tmp; 768 for (i=1; i<n; i++) { 769 v = aa + ai[i] ; 770 vi = aj + ai[i] ; 771 nz = a->diag[i] - ai[i]; 772 sum = b[*r++]; 773 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 774 tmp[i] = sum; 775 } 776 777 /* backward solve the upper triangular */ 778 for (i=n-1; i>=0; i--){ 779 v = aa + a->diag[i] + 1; 780 vi = aj + a->diag[i] + 1; 781 nz = ai[i+1] - a->diag[i] - 1; 782 sum = tmp[i]; 783 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 784 x[*c--] = tmp[i] = sum*aa[a->diag[i]]; 785 } 786 787 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 788 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 789 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 790 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 791 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 792 PetscFunctionReturn(0); 793 } 794 795 #undef __FUNCT__ 796 #define __FUNCT__ "MatMatSolve_SeqAIJ" 797 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X) 798 { 799 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 800 IS iscol = a->col,isrow = a->row; 801 PetscErrorCode ierr; 802 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 803 PetscInt nz,neq; 804 const PetscInt *rout,*cout,*r,*c; 805 PetscScalar *x,*b,*tmp,*tmps,sum; 806 const MatScalar *aa = a->a,*v; 807 PetscTruth bisdense,xisdense; 808 809 PetscFunctionBegin; 810 if (!n) PetscFunctionReturn(0); 811 812 ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr); 813 if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 814 ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr); 815 if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 816 817 ierr = MatGetArray(B,&b);CHKERRQ(ierr); 818 ierr = MatGetArray(X,&x);CHKERRQ(ierr); 819 820 tmp = a->solve_work; 821 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 822 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 823 824 for (neq=0; neq<B->cmap->n; neq++){ 825 /* forward solve the lower triangular */ 826 tmp[0] = b[r[0]]; 827 tmps = tmp; 828 for (i=1; i<n; i++) { 829 v = aa + ai[i] ; 830 vi = aj + ai[i] ; 831 nz = a->diag[i] - ai[i]; 832 sum = b[r[i]]; 833 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 834 tmp[i] = sum; 835 } 836 /* backward solve the upper triangular */ 837 for (i=n-1; i>=0; i--){ 838 v = aa + a->diag[i] + 1; 839 vi = aj + a->diag[i] + 1; 840 nz = ai[i+1] - a->diag[i] - 1; 841 sum = tmp[i]; 842 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 843 x[c[i]] = tmp[i] = sum*aa[a->diag[i]]; 844 } 845 846 b += n; 847 x += n; 848 } 849 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 850 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 851 ierr = MatRestoreArray(B,&b);CHKERRQ(ierr); 852 ierr = MatRestoreArray(X,&x);CHKERRQ(ierr); 853 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 854 PetscFunctionReturn(0); 855 } 856 857 #undef __FUNCT__ 858 #define __FUNCT__ "MatSolve_SeqAIJ_InplaceWithPerm" 859 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx) 860 { 861 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 862 IS iscol = a->col,isrow = a->row; 863 PetscErrorCode ierr; 864 const PetscInt *r,*c,*rout,*cout; 865 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 866 PetscInt nz,row; 867 PetscScalar *x,*b,*tmp,*tmps,sum; 868 const MatScalar *aa = a->a,*v; 869 870 PetscFunctionBegin; 871 if (!n) PetscFunctionReturn(0); 872 873 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 874 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 875 tmp = a->solve_work; 876 877 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 878 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 879 880 /* forward solve the lower triangular */ 881 tmp[0] = b[*r++]; 882 tmps = tmp; 883 for (row=1; row<n; row++) { 884 i = rout[row]; /* permuted row */ 885 v = aa + ai[i] ; 886 vi = aj + ai[i] ; 887 nz = a->diag[i] - ai[i]; 888 sum = b[*r++]; 889 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 890 tmp[row] = sum; 891 } 892 893 /* backward solve the upper triangular */ 894 for (row=n-1; row>=0; row--){ 895 i = rout[row]; /* permuted row */ 896 v = aa + a->diag[i] + 1; 897 vi = aj + a->diag[i] + 1; 898 nz = ai[i+1] - a->diag[i] - 1; 899 sum = tmp[row]; 900 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 901 x[*c--] = tmp[row] = sum*aa[a->diag[i]]; 902 } 903 904 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 905 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 906 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 907 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 908 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 909 PetscFunctionReturn(0); 910 } 911 912 /* ----------------------------------------------------------- */ 913 #include "../src/mat/impls/aij/seq/ftn-kernels/fsolve.h" 914 #undef __FUNCT__ 915 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering" 916 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx) 917 { 918 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 919 PetscErrorCode ierr; 920 PetscInt n = A->rmap->n; 921 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag; 922 PetscScalar *x; 923 const PetscScalar *b; 924 const MatScalar *aa = a->a; 925 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 926 PetscInt adiag_i,i,nz,ai_i; 927 const PetscInt *vi; 928 const MatScalar *v; 929 PetscScalar sum; 930 #endif 931 932 PetscFunctionBegin; 933 if (!n) PetscFunctionReturn(0); 934 935 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 936 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 937 938 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 939 fortransolveaij_(&n,x,ai,aj,adiag,aa,b); 940 #else 941 /* forward solve the lower triangular */ 942 x[0] = b[0]; 943 for (i=1; i<n; i++) { 944 ai_i = ai[i]; 945 v = aa + ai_i; 946 vi = aj + ai_i; 947 nz = adiag[i] - ai_i; 948 sum = b[i]; 949 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 950 x[i] = sum; 951 } 952 953 /* backward solve the upper triangular */ 954 for (i=n-1; i>=0; i--){ 955 adiag_i = adiag[i]; 956 v = aa + adiag_i + 1; 957 vi = aj + adiag_i + 1; 958 nz = ai[i+1] - adiag_i - 1; 959 sum = x[i]; 960 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 961 x[i] = sum*aa[adiag_i]; 962 } 963 #endif 964 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 965 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 966 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 967 PetscFunctionReturn(0); 968 } 969 970 #undef __FUNCT__ 971 #define __FUNCT__ "MatSolveAdd_SeqAIJ" 972 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx) 973 { 974 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 975 IS iscol = a->col,isrow = a->row; 976 PetscErrorCode ierr; 977 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 978 PetscInt nz; 979 const PetscInt *rout,*cout,*r,*c; 980 PetscScalar *x,*b,*tmp,sum; 981 const MatScalar *aa = a->a,*v; 982 983 PetscFunctionBegin; 984 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 985 986 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 987 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 988 tmp = a->solve_work; 989 990 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 991 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 992 993 /* forward solve the lower triangular */ 994 tmp[0] = b[*r++]; 995 for (i=1; i<n; i++) { 996 v = aa + ai[i] ; 997 vi = aj + ai[i] ; 998 nz = a->diag[i] - ai[i]; 999 sum = b[*r++]; 1000 while (nz--) sum -= *v++ * tmp[*vi++ ]; 1001 tmp[i] = sum; 1002 } 1003 1004 /* backward solve the upper triangular */ 1005 for (i=n-1; i>=0; i--){ 1006 v = aa + a->diag[i] + 1; 1007 vi = aj + a->diag[i] + 1; 1008 nz = ai[i+1] - a->diag[i] - 1; 1009 sum = tmp[i]; 1010 while (nz--) sum -= *v++ * tmp[*vi++ ]; 1011 tmp[i] = sum*aa[a->diag[i]]; 1012 x[*c--] += tmp[i]; 1013 } 1014 1015 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1016 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1017 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1018 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1019 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1020 1021 PetscFunctionReturn(0); 1022 } 1023 /* -------------------------------------------------------------------*/ 1024 #undef __FUNCT__ 1025 #define __FUNCT__ "MatSolveTranspose_SeqAIJ" 1026 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx) 1027 { 1028 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1029 IS iscol = a->col,isrow = a->row; 1030 PetscErrorCode ierr; 1031 const PetscInt *rout,*cout,*r,*c; 1032 PetscInt i,n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1033 PetscInt nz,*diag = a->diag; 1034 PetscScalar *x,*b,*tmp,s1; 1035 const MatScalar *aa = a->a,*v; 1036 1037 PetscFunctionBegin; 1038 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1039 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1040 tmp = a->solve_work; 1041 1042 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1043 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1044 1045 /* copy the b into temp work space according to permutation */ 1046 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1047 1048 /* forward solve the U^T */ 1049 for (i=0; i<n; i++) { 1050 v = aa + diag[i] ; 1051 vi = aj + diag[i] + 1; 1052 nz = ai[i+1] - diag[i] - 1; 1053 s1 = tmp[i]; 1054 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1055 while (nz--) { 1056 tmp[*vi++ ] -= (*v++)*s1; 1057 } 1058 tmp[i] = s1; 1059 } 1060 1061 /* backward solve the L^T */ 1062 for (i=n-1; i>=0; i--){ 1063 v = aa + diag[i] - 1 ; 1064 vi = aj + diag[i] - 1 ; 1065 nz = diag[i] - ai[i]; 1066 s1 = tmp[i]; 1067 while (nz--) { 1068 tmp[*vi-- ] -= (*v--)*s1; 1069 } 1070 } 1071 1072 /* copy tmp into x according to permutation */ 1073 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1074 1075 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1076 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1077 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1078 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1079 1080 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1081 PetscFunctionReturn(0); 1082 } 1083 1084 #undef __FUNCT__ 1085 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ" 1086 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx) 1087 { 1088 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1089 IS iscol = a->col,isrow = a->row; 1090 PetscErrorCode ierr; 1091 const PetscInt *r,*c,*rout,*cout; 1092 PetscInt i,n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1093 PetscInt nz,*diag = a->diag; 1094 PetscScalar *x,*b,*tmp; 1095 const MatScalar *aa = a->a,*v; 1096 1097 PetscFunctionBegin; 1098 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1099 1100 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1101 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1102 tmp = a->solve_work; 1103 1104 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1105 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1106 1107 /* copy the b into temp work space according to permutation */ 1108 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1109 1110 /* forward solve the U^T */ 1111 for (i=0; i<n; i++) { 1112 v = aa + diag[i] ; 1113 vi = aj + diag[i] + 1; 1114 nz = ai[i+1] - diag[i] - 1; 1115 tmp[i] *= *v++; 1116 while (nz--) { 1117 tmp[*vi++ ] -= (*v++)*tmp[i]; 1118 } 1119 } 1120 1121 /* backward solve the L^T */ 1122 for (i=n-1; i>=0; i--){ 1123 v = aa + diag[i] - 1 ; 1124 vi = aj + diag[i] - 1 ; 1125 nz = diag[i] - ai[i]; 1126 while (nz--) { 1127 tmp[*vi-- ] -= (*v--)*tmp[i]; 1128 } 1129 } 1130 1131 /* copy tmp into x according to permutation */ 1132 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1133 1134 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1135 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1136 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1137 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1138 1139 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1140 PetscFunctionReturn(0); 1141 } 1142 /* ----------------------------------------------------------------*/ 1143 EXTERN PetscErrorCode Mat_CheckInode(Mat,PetscTruth); 1144 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption); 1145 1146 /* 1147 ilu(0) with natural ordering under new data structure. 1148 Factored arrays bj and ba are stored as 1149 L(0,:), L(1,:), ...,L(n-1,:), U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:) 1150 1151 bi=fact->i is an array of size 2n+2, in which 1152 bi+ 1153 bi[i] -> 1st entry of L(i,:),i=0,...,i-1 1154 bi[n] -> end of L(n-1,:)+1 1155 bi[n+1] -> 1st entry of U(n-1,:) 1156 bi[2n-i] -> 1st entry of U(i,:) 1157 bi[2n-i+1] -> end of U(i,:)+1, the 1st entry of U(i-1,:) 1158 bi[2n] -> end of U(0,:)+1 1159 1160 U(i,:) contains diag[i] as its last entry, i.e., 1161 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 1162 */ 1163 #undef __FUNCT__ 1164 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct" 1165 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1166 { 1167 1168 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1169 PetscErrorCode ierr; 1170 PetscInt n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag; 1171 PetscInt i,j,nz,*bi,*bj,*bdiag; 1172 1173 PetscFunctionBegin; 1174 /* printf("MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct ...\n"); */ 1175 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES);CHKERRQ(ierr); 1176 b = (Mat_SeqAIJ*)(fact)->data; 1177 1178 /* replace matrix arrays with single allocations, then reset values */ 1179 ierr = PetscFree3(b->a,b->j,b->i);CHKERRQ(ierr); 1180 ierr = PetscFree(b->diag);CHKERRQ(ierr); 1181 1182 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&b->i);CHKERRQ(ierr); 1183 ierr = PetscMalloc((ai[n]+1)*sizeof(PetscInt),&b->j);CHKERRQ(ierr); 1184 ierr = PetscMalloc((ai[n]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 1185 b->singlemalloc = PETSC_FALSE; 1186 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr); 1187 bdiag = b->diag; 1188 1189 if (n > 0) { 1190 ierr = PetscMemzero(b->a,(ai[n])*sizeof(PetscScalar));CHKERRQ(ierr); 1191 } 1192 1193 /* set bi and bj with new data structure */ 1194 bi = b->i; 1195 bj = b->j; 1196 1197 /* L part */ 1198 bi[0] = 0; 1199 for (i=0; i<n; i++){ 1200 nz = adiag[i] - ai[i]; 1201 bi[i+1] = bi[i] + nz; 1202 aj = a->j + ai[i]; 1203 for (j=0; j<nz; j++){ 1204 *bj = aj[j]; bj++; 1205 } 1206 } 1207 1208 /* U part */ 1209 bi[n+1] = bi[n]; 1210 for (i=n-1; i>=0; i--){ 1211 nz = ai[i+1] - adiag[i] - 1; 1212 bi[2*n-i+1] = bi[2*n-i] + nz + 1; 1213 aj = a->j + adiag[i] + 1; 1214 for (j=0; j<nz; j++){ 1215 *bj = aj[j]; bj++; 1216 } 1217 /* diag[i] */ 1218 *bj = i; bj++; 1219 bdiag[i] = bi[2*n-i+1]-1; 1220 } 1221 PetscFunctionReturn(0); 1222 } 1223 1224 #undef __FUNCT__ 1225 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ" 1226 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1227 { 1228 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1229 IS isicol; 1230 PetscErrorCode ierr; 1231 const PetscInt *r,*ic; 1232 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,d; 1233 PetscInt *bi,*cols,nnz,*cols_lvl; 1234 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1235 PetscInt i,levels,diagonal_fill; 1236 PetscTruth col_identity,row_identity; 1237 PetscReal f; 1238 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1239 PetscBT lnkbt; 1240 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1241 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1242 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1243 PetscTruth missing; 1244 1245 PetscFunctionBegin; 1246 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); 1247 f = info->fill; 1248 levels = (PetscInt)info->levels; 1249 diagonal_fill = (PetscInt)info->diagonal_fill; 1250 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1251 1252 /* special case that simply copies fill pattern */ 1253 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1254 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1255 if (!levels && row_identity && col_identity) { 1256 1257 PetscTruth newdatastruct=PETSC_FALSE; 1258 ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 1259 if (newdatastruct){ 1260 ierr = MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1261 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 1262 } else { 1263 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES);CHKERRQ(ierr); 1264 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1265 } 1266 1267 fact->factor = MAT_FACTOR_ILU; 1268 (fact)->info.factor_mallocs = 0; 1269 (fact)->info.fill_ratio_given = info->fill; 1270 (fact)->info.fill_ratio_needed = 1.0; 1271 b = (Mat_SeqAIJ*)(fact)->data; 1272 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 1273 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 1274 b->row = isrow; 1275 b->col = iscol; 1276 b->icol = isicol; 1277 ierr = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1278 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1279 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1280 ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1281 PetscFunctionReturn(0); 1282 } 1283 1284 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1285 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1286 1287 /* get new row pointers */ 1288 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1289 bi[0] = 0; 1290 /* bdiag is location of diagonal in factor */ 1291 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1292 bdiag[0] = 0; 1293 1294 ierr = PetscMalloc((2*n+1)*sizeof(PetscInt**),&bj_ptr);CHKERRQ(ierr); 1295 bjlvl_ptr = (PetscInt**)(bj_ptr + n); 1296 1297 /* create a linked list for storing column indices of the active row */ 1298 nlnk = n + 1; 1299 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1300 1301 /* initial FreeSpace size is f*(ai[n]+1) */ 1302 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1303 current_space = free_space; 1304 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1305 current_space_lvl = free_space_lvl; 1306 1307 for (i=0; i<n; i++) { 1308 nzi = 0; 1309 /* copy current row into linked list */ 1310 nnz = ai[r[i]+1] - ai[r[i]]; 1311 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1312 cols = aj + ai[r[i]]; 1313 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1314 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1315 nzi += nlnk; 1316 1317 /* make sure diagonal entry is included */ 1318 if (diagonal_fill && lnk[i] == -1) { 1319 fm = n; 1320 while (lnk[fm] < i) fm = lnk[fm]; 1321 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1322 lnk[fm] = i; 1323 lnk_lvl[i] = 0; 1324 nzi++; dcount++; 1325 } 1326 1327 /* add pivot rows into the active row */ 1328 nzbd = 0; 1329 prow = lnk[n]; 1330 while (prow < i) { 1331 nnz = bdiag[prow]; 1332 cols = bj_ptr[prow] + nnz + 1; 1333 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1334 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1335 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1336 nzi += nlnk; 1337 prow = lnk[prow]; 1338 nzbd++; 1339 } 1340 bdiag[i] = nzbd; 1341 bi[i+1] = bi[i] + nzi; 1342 1343 /* if free space is not available, make more free space */ 1344 if (current_space->local_remaining<nzi) { 1345 nnz = nzi*(n - i); /* estimated and max additional space needed */ 1346 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1347 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1348 reallocs++; 1349 } 1350 1351 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1352 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1353 bj_ptr[i] = current_space->array; 1354 bjlvl_ptr[i] = current_space_lvl->array; 1355 1356 /* make sure the active row i has diagonal entry */ 1357 if (*(bj_ptr[i]+bdiag[i]) != i) { 1358 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 1359 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1360 } 1361 1362 current_space->array += nzi; 1363 current_space->local_used += nzi; 1364 current_space->local_remaining -= nzi; 1365 current_space_lvl->array += nzi; 1366 current_space_lvl->local_used += nzi; 1367 current_space_lvl->local_remaining -= nzi; 1368 } 1369 1370 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1371 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1372 1373 /* destroy list of free space and other temporary arrays */ 1374 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 1375 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); 1376 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1377 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1378 ierr = PetscFree(bj_ptr);CHKERRQ(ierr); 1379 1380 #if defined(PETSC_USE_INFO) 1381 { 1382 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1383 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 1384 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1385 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 1386 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1387 if (diagonal_fill) { 1388 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 1389 } 1390 } 1391 #endif 1392 1393 /* put together the new matrix */ 1394 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 1395 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 1396 b = (Mat_SeqAIJ*)(fact)->data; 1397 b->free_a = PETSC_TRUE; 1398 b->free_ij = PETSC_TRUE; 1399 b->singlemalloc = PETSC_FALSE; 1400 ierr = PetscMalloc( (bi[n] )*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 1401 b->j = bj; 1402 b->i = bi; 1403 for (i=0; i<n; i++) bdiag[i] += bi[i]; 1404 b->diag = bdiag; 1405 b->ilen = 0; 1406 b->imax = 0; 1407 b->row = isrow; 1408 b->col = iscol; 1409 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1410 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1411 b->icol = isicol; 1412 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1413 /* In b structure: Free imax, ilen, old a, old j. 1414 Allocate bdiag, solve_work, new a, new j */ 1415 ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1416 b->maxnz = b->nz = bi[n] ; 1417 (fact)->info.factor_mallocs = reallocs; 1418 (fact)->info.fill_ratio_given = f; 1419 (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1420 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1421 ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1422 PetscFunctionReturn(0); 1423 } 1424 1425 #include "../src/mat/impls/sbaij/seq/sbaij.h" 1426 #undef __FUNCT__ 1427 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ" 1428 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 1429 { 1430 Mat C = B; 1431 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 1432 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 1433 IS ip=b->row,iip = b->icol; 1434 PetscErrorCode ierr; 1435 const PetscInt *rip,*riip; 1436 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol; 1437 PetscInt *ai=a->i,*aj=a->j; 1438 PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz; 1439 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 1440 PetscReal zeropivot,rs,shiftnz; 1441 PetscReal shiftpd; 1442 ChShift_Ctx sctx; 1443 PetscInt newshift; 1444 PetscTruth perm_identity; 1445 1446 PetscFunctionBegin; 1447 1448 shiftnz = info->shiftnz; 1449 shiftpd = info->shiftpd; 1450 zeropivot = info->zeropivot; 1451 1452 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 1453 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 1454 1455 /* initialization */ 1456 nz = (2*mbs+1)*sizeof(PetscInt)+mbs*sizeof(MatScalar); 1457 ierr = PetscMalloc(nz,&il);CHKERRQ(ierr); 1458 jl = il + mbs; 1459 rtmp = (MatScalar*)(jl + mbs); 1460 1461 sctx.shift_amount = 0; 1462 sctx.nshift = 0; 1463 do { 1464 sctx.chshift = PETSC_FALSE; 1465 for (i=0; i<mbs; i++) { 1466 rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0; 1467 } 1468 1469 for (k = 0; k<mbs; k++){ 1470 bval = ba + bi[k]; 1471 /* initialize k-th row by the perm[k]-th row of A */ 1472 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 1473 for (j = jmin; j < jmax; j++){ 1474 col = riip[aj[j]]; 1475 if (col >= k){ /* only take upper triangular entry */ 1476 rtmp[col] = aa[j]; 1477 *bval++ = 0.0; /* for in-place factorization */ 1478 } 1479 } 1480 /* shift the diagonal of the matrix */ 1481 if (sctx.nshift) rtmp[k] += sctx.shift_amount; 1482 1483 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 1484 dk = rtmp[k]; 1485 i = jl[k]; /* first row to be added to k_th row */ 1486 1487 while (i < k){ 1488 nexti = jl[i]; /* next row to be added to k_th row */ 1489 1490 /* compute multiplier, update diag(k) and U(i,k) */ 1491 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 1492 uikdi = - ba[ili]*ba[bi[i]]; /* diagonal(k) */ 1493 dk += uikdi*ba[ili]; 1494 ba[ili] = uikdi; /* -U(i,k) */ 1495 1496 /* add multiple of row i to k-th row */ 1497 jmin = ili + 1; jmax = bi[i+1]; 1498 if (jmin < jmax){ 1499 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 1500 /* update il and jl for row i */ 1501 il[i] = jmin; 1502 j = bj[jmin]; jl[i] = jl[j]; jl[j] = i; 1503 } 1504 i = nexti; 1505 } 1506 1507 /* shift the diagonals when zero pivot is detected */ 1508 /* compute rs=sum of abs(off-diagonal) */ 1509 rs = 0.0; 1510 jmin = bi[k]+1; 1511 nz = bi[k+1] - jmin; 1512 bcol = bj + jmin; 1513 while (nz--){ 1514 rs += PetscAbsScalar(rtmp[*bcol]); 1515 bcol++; 1516 } 1517 1518 sctx.rs = rs; 1519 sctx.pv = dk; 1520 ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr); 1521 1522 if (newshift == 1) { 1523 if (!sctx.shift_amount) { 1524 sctx.shift_amount = 1e-5; 1525 } 1526 break; 1527 } 1528 1529 /* copy data into U(k,:) */ 1530 ba[bi[k]] = 1.0/dk; /* U(k,k) */ 1531 jmin = bi[k]+1; jmax = bi[k+1]; 1532 if (jmin < jmax) { 1533 for (j=jmin; j<jmax; j++){ 1534 col = bj[j]; ba[j] = rtmp[col]; rtmp[col] = 0.0; 1535 } 1536 /* add the k-th row into il and jl */ 1537 il[k] = jmin; 1538 i = bj[jmin]; jl[k] = jl[i]; jl[i] = k; 1539 } 1540 } 1541 } while (sctx.chshift); 1542 ierr = PetscFree(il);CHKERRQ(ierr); 1543 1544 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 1545 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 1546 1547 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 1548 if (perm_identity){ 1549 (B)->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering; 1550 (B)->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering; 1551 (B)->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering; 1552 (B)->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering; 1553 } else { 1554 (B)->ops->solve = MatSolve_SeqSBAIJ_1; 1555 (B)->ops->solvetranspose = MatSolve_SeqSBAIJ_1; 1556 (B)->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1; 1557 (B)->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1; 1558 } 1559 1560 C->assembled = PETSC_TRUE; 1561 C->preallocated = PETSC_TRUE; 1562 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 1563 if (sctx.nshift){ 1564 if (shiftnz) { 1565 ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 1566 } else if (shiftpd) { 1567 ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 1568 } 1569 } 1570 PetscFunctionReturn(0); 1571 } 1572 1573 #undef __FUNCT__ 1574 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ" 1575 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 1576 { 1577 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1578 Mat_SeqSBAIJ *b; 1579 PetscErrorCode ierr; 1580 PetscTruth perm_identity,missing; 1581 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui; 1582 const PetscInt *rip,*riip; 1583 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 1584 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 1585 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 1586 PetscReal fill=info->fill,levels=info->levels; 1587 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1588 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1589 PetscBT lnkbt; 1590 IS iperm; 1591 1592 PetscFunctionBegin; 1593 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); 1594 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 1595 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 1596 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 1597 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 1598 1599 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 1600 ui[0] = 0; 1601 1602 /* ICC(0) without matrix ordering: simply copies fill pattern */ 1603 if (!levels && perm_identity) { 1604 1605 for (i=0; i<am; i++) { 1606 ui[i+1] = ui[i] + ai[i+1] - a->diag[i]; 1607 } 1608 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 1609 cols = uj; 1610 for (i=0; i<am; i++) { 1611 aj = a->j + a->diag[i]; 1612 ncols = ui[i+1] - ui[i]; 1613 for (j=0; j<ncols; j++) *cols++ = *aj++; 1614 } 1615 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 1616 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 1617 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 1618 1619 /* initialization */ 1620 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 1621 1622 /* jl: linked list for storing indices of the pivot rows 1623 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 1624 ierr = PetscMalloc((2*am+1)*sizeof(PetscInt)+2*am*sizeof(PetscInt**),&jl);CHKERRQ(ierr); 1625 il = jl + am; 1626 uj_ptr = (PetscInt**)(il + am); 1627 uj_lvl_ptr = (PetscInt**)(uj_ptr + am); 1628 for (i=0; i<am; i++){ 1629 jl[i] = am; il[i] = 0; 1630 } 1631 1632 /* create and initialize a linked list for storing column indices of the active row k */ 1633 nlnk = am + 1; 1634 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1635 1636 /* initial FreeSpace size is fill*(ai[am]+1) */ 1637 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 1638 current_space = free_space; 1639 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 1640 current_space_lvl = free_space_lvl; 1641 1642 for (k=0; k<am; k++){ /* for each active row k */ 1643 /* initialize lnk by the column indices of row rip[k] of A */ 1644 nzk = 0; 1645 ncols = ai[rip[k]+1] - ai[rip[k]]; 1646 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 1647 ncols_upper = 0; 1648 for (j=0; j<ncols; j++){ 1649 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 1650 if (riip[i] >= k){ /* only take upper triangular entry */ 1651 ajtmp[ncols_upper] = i; 1652 ncols_upper++; 1653 } 1654 } 1655 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1656 nzk += nlnk; 1657 1658 /* update lnk by computing fill-in for each pivot row to be merged in */ 1659 prow = jl[k]; /* 1st pivot row */ 1660 1661 while (prow < k){ 1662 nextprow = jl[prow]; 1663 1664 /* merge prow into k-th row */ 1665 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 1666 jmax = ui[prow+1]; 1667 ncols = jmax-jmin; 1668 i = jmin - ui[prow]; 1669 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 1670 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 1671 j = *(uj - 1); 1672 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 1673 nzk += nlnk; 1674 1675 /* update il and jl for prow */ 1676 if (jmin < jmax){ 1677 il[prow] = jmin; 1678 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 1679 } 1680 prow = nextprow; 1681 } 1682 1683 /* if free space is not available, make more free space */ 1684 if (current_space->local_remaining<nzk) { 1685 i = am - k + 1; /* num of unfactored rows */ 1686 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 1687 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 1688 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 1689 reallocs++; 1690 } 1691 1692 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1693 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 1694 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1695 1696 /* add the k-th row into il and jl */ 1697 if (nzk > 1){ 1698 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 1699 jl[k] = jl[i]; jl[i] = k; 1700 il[k] = ui[k] + 1; 1701 } 1702 uj_ptr[k] = current_space->array; 1703 uj_lvl_ptr[k] = current_space_lvl->array; 1704 1705 current_space->array += nzk; 1706 current_space->local_used += nzk; 1707 current_space->local_remaining -= nzk; 1708 1709 current_space_lvl->array += nzk; 1710 current_space_lvl->local_used += nzk; 1711 current_space_lvl->local_remaining -= nzk; 1712 1713 ui[k+1] = ui[k] + nzk; 1714 } 1715 1716 #if defined(PETSC_USE_INFO) 1717 if (ai[am] != 0) { 1718 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 1719 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 1720 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1721 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 1722 } else { 1723 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 1724 } 1725 #endif 1726 1727 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 1728 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 1729 ierr = PetscFree(jl);CHKERRQ(ierr); 1730 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 1731 1732 /* destroy list of free space and other temporary array(s) */ 1733 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 1734 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 1735 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1736 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1737 1738 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 1739 1740 /* put together the new matrix in MATSEQSBAIJ format */ 1741 1742 b = (Mat_SeqSBAIJ*)(fact)->data; 1743 b->singlemalloc = PETSC_FALSE; 1744 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 1745 b->j = uj; 1746 b->i = ui; 1747 b->diag = 0; 1748 b->ilen = 0; 1749 b->imax = 0; 1750 b->row = perm; 1751 b->col = perm; 1752 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 1753 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 1754 b->icol = iperm; 1755 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 1756 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1757 ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 1758 b->maxnz = b->nz = ui[am]; 1759 b->free_a = PETSC_TRUE; 1760 b->free_ij = PETSC_TRUE; 1761 1762 (fact)->info.factor_mallocs = reallocs; 1763 (fact)->info.fill_ratio_given = fill; 1764 if (ai[am] != 0) { 1765 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 1766 } else { 1767 (fact)->info.fill_ratio_needed = 0.0; 1768 } 1769 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 1770 PetscFunctionReturn(0); 1771 } 1772 1773 #undef __FUNCT__ 1774 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ" 1775 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 1776 { 1777 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1778 Mat_SeqSBAIJ *b; 1779 PetscErrorCode ierr; 1780 PetscTruth perm_identity; 1781 PetscReal fill = info->fill; 1782 const PetscInt *rip,*riip; 1783 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 1784 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 1785 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr; 1786 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1787 PetscBT lnkbt; 1788 IS iperm; 1789 1790 PetscFunctionBegin; 1791 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); 1792 /* check whether perm is the identity mapping */ 1793 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 1794 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 1795 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 1796 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 1797 1798 /* initialization */ 1799 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 1800 ui[0] = 0; 1801 1802 /* jl: linked list for storing indices of the pivot rows 1803 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 1804 ierr = PetscMalloc((3*am+1)*sizeof(PetscInt)+am*sizeof(PetscInt**),&jl);CHKERRQ(ierr); 1805 il = jl + am; 1806 cols = il + am; 1807 ui_ptr = (PetscInt**)(cols + am); 1808 for (i=0; i<am; i++){ 1809 jl[i] = am; il[i] = 0; 1810 } 1811 1812 /* create and initialize a linked list for storing column indices of the active row k */ 1813 nlnk = am + 1; 1814 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 1815 1816 /* initial FreeSpace size is fill*(ai[am]+1) */ 1817 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 1818 current_space = free_space; 1819 1820 for (k=0; k<am; k++){ /* for each active row k */ 1821 /* initialize lnk by the column indices of row rip[k] of A */ 1822 nzk = 0; 1823 ncols = ai[rip[k]+1] - ai[rip[k]]; 1824 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 1825 ncols_upper = 0; 1826 for (j=0; j<ncols; j++){ 1827 i = riip[*(aj + ai[rip[k]] + j)]; 1828 if (i >= k){ /* only take upper triangular entry */ 1829 cols[ncols_upper] = i; 1830 ncols_upper++; 1831 } 1832 } 1833 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 1834 nzk += nlnk; 1835 1836 /* update lnk by computing fill-in for each pivot row to be merged in */ 1837 prow = jl[k]; /* 1st pivot row */ 1838 1839 while (prow < k){ 1840 nextprow = jl[prow]; 1841 /* merge prow into k-th row */ 1842 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 1843 jmax = ui[prow+1]; 1844 ncols = jmax-jmin; 1845 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 1846 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 1847 nzk += nlnk; 1848 1849 /* update il and jl for prow */ 1850 if (jmin < jmax){ 1851 il[prow] = jmin; 1852 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 1853 } 1854 prow = nextprow; 1855 } 1856 1857 /* if free space is not available, make more free space */ 1858 if (current_space->local_remaining<nzk) { 1859 i = am - k + 1; /* num of unfactored rows */ 1860 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 1861 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 1862 reallocs++; 1863 } 1864 1865 /* copy data into free space, then initialize lnk */ 1866 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 1867 1868 /* add the k-th row into il and jl */ 1869 if (nzk-1 > 0){ 1870 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 1871 jl[k] = jl[i]; jl[i] = k; 1872 il[k] = ui[k] + 1; 1873 } 1874 ui_ptr[k] = current_space->array; 1875 current_space->array += nzk; 1876 current_space->local_used += nzk; 1877 current_space->local_remaining -= nzk; 1878 1879 ui[k+1] = ui[k] + nzk; 1880 } 1881 1882 #if defined(PETSC_USE_INFO) 1883 if (ai[am] != 0) { 1884 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 1885 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 1886 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1887 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 1888 } else { 1889 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 1890 } 1891 #endif 1892 1893 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 1894 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 1895 ierr = PetscFree(jl);CHKERRQ(ierr); 1896 1897 /* destroy list of free space and other temporary array(s) */ 1898 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 1899 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 1900 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1901 1902 /* put together the new matrix in MATSEQSBAIJ format */ 1903 1904 b = (Mat_SeqSBAIJ*)(fact)->data; 1905 b->singlemalloc = PETSC_FALSE; 1906 b->free_a = PETSC_TRUE; 1907 b->free_ij = PETSC_TRUE; 1908 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 1909 b->j = uj; 1910 b->i = ui; 1911 b->diag = 0; 1912 b->ilen = 0; 1913 b->imax = 0; 1914 b->row = perm; 1915 b->col = perm; 1916 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 1917 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 1918 b->icol = iperm; 1919 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 1920 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1921 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 1922 b->maxnz = b->nz = ui[am]; 1923 1924 (fact)->info.factor_mallocs = reallocs; 1925 (fact)->info.fill_ratio_given = fill; 1926 if (ai[am] != 0) { 1927 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 1928 } else { 1929 (fact)->info.fill_ratio_needed = 0.0; 1930 } 1931 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 1932 PetscFunctionReturn(0); 1933 } 1934 1935 #undef __FUNCT__ 1936 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_iludt" 1937 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_iludt(Mat A,Vec bb,Vec xx) 1938 { 1939 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1940 PetscErrorCode ierr; 1941 PetscInt n = A->rmap->n; 1942 const PetscInt *ai = a->i,*aj = a->j,*vi; 1943 PetscScalar *x,sum; 1944 const PetscScalar *b; 1945 const MatScalar *aa = a->a,*v; 1946 PetscInt i,nz; 1947 1948 PetscFunctionBegin; 1949 if (!n) PetscFunctionReturn(0); 1950 1951 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1952 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1953 1954 /* forward solve the lower triangular */ 1955 x[0] = b[0]; 1956 v = aa; 1957 vi = aj; 1958 for (i=1; i<n; i++) { 1959 nz = ai[i+1] - ai[i]; 1960 sum = b[i]; 1961 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1962 /* while (nz--) sum -= *v++ * x[*vi++];*/ 1963 v += nz; 1964 vi += nz; 1965 x[i] = sum; 1966 } 1967 1968 /* backward solve the upper triangular */ 1969 v = aa + ai[n+1]; 1970 vi = aj + ai[n+1]; 1971 for (i=n-1; i>=0; i--){ 1972 nz = ai[2*n-i +1] - ai[2*n-i]-1; 1973 sum = x[i]; 1974 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1975 /* while (nz--) sum -= *v++ * x[*vi++]; */ 1976 v += nz; 1977 vi += nz; vi++; 1978 x[i] = *v++ *sum; /* x[i]=aa[adiag[i]]*sum; v++; */ 1979 } 1980 1981 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1982 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1983 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1984 PetscFunctionReturn(0); 1985 } 1986 1987 #undef __FUNCT__ 1988 #define __FUNCT__ "MatSolve_SeqAIJ_iludt" 1989 PetscErrorCode MatSolve_SeqAIJ_iludt(Mat A,Vec bb,Vec xx) 1990 { 1991 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1992 IS iscol = a->col,isrow = a->row; 1993 PetscErrorCode ierr; 1994 PetscInt i,n=A->rmap->n,*vi,*ai = a->i,*aj = a->j,*adiag=a->diag; 1995 PetscInt nz; 1996 const PetscInt *rout,*cout,*r,*c; 1997 PetscScalar *x,*tmp,*tmps; 1998 const PetscScalar *b; 1999 const MatScalar *aa = a->a,*v; 2000 2001 PetscFunctionBegin; 2002 if (!n) PetscFunctionReturn(0); 2003 2004 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 2005 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 2006 tmp = a->solve_work; 2007 2008 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 2009 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 2010 2011 /* forward solve the lower triangular */ 2012 tmp[0] = b[*r++]; 2013 tmps = tmp; 2014 v = aa; 2015 vi = aj; 2016 for (i=1; i<n; i++) { 2017 nz = ai[i+1] - ai[i]; 2018 tmp[i] = b[*r++]; 2019 PetscSparseDenseMinusDot(tmp[i],tmps,v,vi,nz); 2020 v += nz; vi += nz; 2021 } 2022 2023 /* backward solve the upper triangular */ 2024 v = aa + adiag[n] + 1; 2025 vi = aj + adiag[n] + 1; 2026 for (i=n-1; i>=0; i--){ 2027 nz = adiag[i] - adiag[i+1] - 1; 2028 PetscSparseDenseMinusDot(tmp[i],tmps,v,vi,nz); 2029 x[*c--] = tmp[i] = tmp[i]*aa[adiag[i]]; 2030 v += nz+1; vi += nz+1; 2031 } 2032 2033 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 2034 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 2035 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 2036 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 2037 ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr); 2038 PetscFunctionReturn(0); 2039 } 2040 2041 #undef __FUNCT__ 2042 #define __FUNCT__ "MatILUDTFactor_SeqAIJ" 2043 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact) 2044 { 2045 Mat B = *fact; 2046 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b; 2047 IS isicol; 2048 PetscErrorCode ierr; 2049 const PetscInt *r,*ic; 2050 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag; 2051 PetscInt *bi,*bj,*bdiag,*bdiag_rev; 2052 PetscInt row,nzi,nzi_bl,nzi_bu,*im,dtcount,nzi_al,nzi_au; 2053 PetscInt nlnk,*lnk; 2054 PetscBT lnkbt; 2055 PetscTruth row_identity,icol_identity,both_identity; 2056 MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp; 2057 const PetscInt *ics; 2058 PetscInt j,nz,*pj,*bjtmp,k,ncut,*jtmp; 2059 PetscReal dt=info->dt,shift=info->shiftinblocks; 2060 PetscInt nnz_max; 2061 PetscTruth missing; 2062 2063 PetscFunctionBegin; 2064 /* ------- symbolic factorization, can be reused ---------*/ 2065 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 2066 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 2067 adiag=a->diag; 2068 2069 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 2070 2071 /* bdiag is location of diagonal in factor */ 2072 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 2073 bdiag_rev = bdiag + n+1; 2074 2075 /* allocate row pointers bi */ 2076 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 2077 2078 /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */ 2079 dtcount = (PetscInt)info->dtcount; 2080 if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */ 2081 nnz_max = ai[n]+2*n*dtcount+2; 2082 2083 ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 2084 ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr); 2085 2086 /* put together the new matrix */ 2087 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 2088 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 2089 b = (Mat_SeqAIJ*)(B)->data; 2090 b->free_a = PETSC_TRUE; 2091 b->free_ij = PETSC_TRUE; 2092 b->singlemalloc = PETSC_FALSE; 2093 b->a = ba; 2094 b->j = bj; 2095 b->i = bi; 2096 b->diag = bdiag; 2097 b->ilen = 0; 2098 b->imax = 0; 2099 b->row = isrow; 2100 b->col = iscol; 2101 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 2102 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 2103 b->icol = isicol; 2104 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2105 2106 ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2107 b->maxnz = nnz_max; 2108 2109 (B)->factor = MAT_FACTOR_ILUDT; 2110 (B)->info.factor_mallocs = 0; 2111 (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]); 2112 CHKMEMQ; 2113 /* ------- end of symbolic factorization ---------*/ 2114 2115 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 2116 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 2117 ics = ic; 2118 2119 /* linked list for storing column indices of the active row */ 2120 nlnk = n + 1; 2121 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2122 2123 /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */ 2124 ierr = PetscMalloc((2*n+1)*sizeof(PetscInt),&im);CHKERRQ(ierr); 2125 jtmp = im + n; 2126 /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */ 2127 ierr = PetscMalloc((2*n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 2128 ierr = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr); 2129 vtmp = rtmp + n; 2130 2131 bi[0] = 0; 2132 bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */ 2133 bdiag_rev[n] = bdiag[0]; 2134 bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */ 2135 for (i=0; i<n; i++) { 2136 /* copy initial fill into linked list */ 2137 nzi = 0; /* nonzeros for active row i */ 2138 nzi = ai[r[i]+1] - ai[r[i]]; 2139 if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 2140 nzi_al = adiag[r[i]] - ai[r[i]]; 2141 nzi_au = ai[r[i]+1] - adiag[r[i]] -1; 2142 ajtmp = aj + ai[r[i]]; 2143 ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2144 2145 /* load in initial (unfactored row) */ 2146 aatmp = a->a + ai[r[i]]; 2147 for (j=0; j<nzi; j++) { 2148 rtmp[ics[*ajtmp++]] = *aatmp++; 2149 } 2150 2151 /* add pivot rows into linked list */ 2152 row = lnk[n]; 2153 while (row < i ) { 2154 nzi_bl = bi[row+1] - bi[row] + 1; 2155 bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */ 2156 ierr = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr); 2157 nzi += nlnk; 2158 row = lnk[row]; 2159 } 2160 2161 /* copy data from lnk into jtmp, then initialize lnk */ 2162 ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr); 2163 2164 /* numerical factorization */ 2165 bjtmp = jtmp; 2166 row = *bjtmp++; /* 1st pivot row */ 2167 while ( row < i ) { 2168 pc = rtmp + row; 2169 pv = ba + bdiag[row]; /* 1./(diag of the pivot row) */ 2170 multiplier = (*pc) * (*pv); 2171 *pc = multiplier; 2172 if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */ 2173 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 2174 pv = ba + bdiag[row+1] + 1; 2175 /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */ 2176 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 2177 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 2178 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 2179 } 2180 row = *bjtmp++; 2181 } 2182 2183 /* copy sparse rtmp into contiguous vtmp; separate L and U part */ 2184 diag_tmp = rtmp[i]; /* save diagonal value - may not needed?? */ 2185 nzi_bl = 0; j = 0; 2186 while (jtmp[j] < i){ /* Note: jtmp is sorted */ 2187 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 2188 nzi_bl++; j++; 2189 } 2190 nzi_bu = nzi - nzi_bl -1; 2191 while (j < nzi){ 2192 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 2193 j++; 2194 } 2195 2196 bjtmp = bj + bi[i]; 2197 batmp = ba + bi[i]; 2198 /* apply level dropping rule to L part */ 2199 ncut = nzi_al + dtcount; 2200 if (ncut < nzi_bl){ 2201 ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr); 2202 ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr); 2203 } else { 2204 ncut = nzi_bl; 2205 } 2206 for (j=0; j<ncut; j++){ 2207 bjtmp[j] = jtmp[j]; 2208 batmp[j] = vtmp[j]; 2209 /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */ 2210 } 2211 bi[i+1] = bi[i] + ncut; 2212 nzi = ncut + 1; 2213 2214 /* apply level dropping rule to U part */ 2215 ncut = nzi_au + dtcount; 2216 if (ncut < nzi_bu){ 2217 ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr); 2218 ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr); 2219 } else { 2220 ncut = nzi_bu; 2221 } 2222 nzi += ncut; 2223 2224 /* mark bdiagonal */ 2225 bdiag[i+1] = bdiag[i] - (ncut + 1); 2226 bdiag_rev[n-i-1] = bdiag[i+1]; 2227 bi[2*n - i] = bi[2*n - i +1] - (ncut + 1); 2228 bjtmp = bj + bdiag[i]; 2229 batmp = ba + bdiag[i]; 2230 *bjtmp = i; 2231 *batmp = diag_tmp; /* rtmp[i]; */ 2232 if (*batmp == 0.0) { 2233 *batmp = dt+shift; 2234 /* printf(" row %d add shift %g\n",i,shift); */ 2235 } 2236 *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */ 2237 /* printf(" (%d,%g),",*bjtmp,*batmp); */ 2238 2239 bjtmp = bj + bdiag[i+1]+1; 2240 batmp = ba + bdiag[i+1]+1; 2241 for (k=0; k<ncut; k++){ 2242 bjtmp[k] = jtmp[nzi_bl+1+k]; 2243 batmp[k] = vtmp[nzi_bl+1+k]; 2244 /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */ 2245 } 2246 /* printf("\n"); */ 2247 2248 im[i] = nzi; /* used by PetscLLAddSortedLU() */ 2249 /* 2250 printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]); 2251 printf(" ----------------------------\n"); 2252 */ 2253 } /* for (i=0; i<n; i++) */ 2254 /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */ 2255 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]); 2256 2257 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 2258 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 2259 2260 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2261 ierr = PetscFree(im);CHKERRQ(ierr); 2262 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2263 2264 ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr); 2265 b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n]; 2266 2267 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 2268 ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr); 2269 both_identity = (PetscTruth) (row_identity && icol_identity); 2270 if (row_identity && icol_identity) { 2271 B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_iludt; 2272 } else { 2273 B->ops->solve = MatSolve_SeqAIJ_iludt; 2274 } 2275 2276 B->ops->lufactorsymbolic = MatILUDTFactorSymbolic_SeqAIJ; 2277 B->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ; 2278 B->ops->solveadd = 0; 2279 B->ops->solvetranspose = 0; 2280 B->ops->solvetransposeadd = 0; 2281 B->ops->matsolve = 0; 2282 B->assembled = PETSC_TRUE; 2283 B->preallocated = PETSC_TRUE; 2284 PetscFunctionReturn(0); 2285 } 2286 2287 /* a wraper of MatILUDTFactor_SeqAIJ() */ 2288 #undef __FUNCT__ 2289 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ" 2290 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info) 2291 { 2292 PetscErrorCode ierr; 2293 2294 PetscFunctionBegin; 2295 ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr); 2296 2297 fact->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ; 2298 PetscFunctionReturn(0); 2299 } 2300 2301 /* 2302 same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors 2303 - intend to replace existing MatLUFactorNumeric_SeqAIJ() 2304 */ 2305 #undef __FUNCT__ 2306 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ" 2307 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info) 2308 { 2309 Mat C=fact; 2310 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 2311 IS isrow = b->row,isicol = b->icol; 2312 PetscErrorCode ierr; 2313 const PetscInt *r,*ic,*ics; 2314 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 2315 PetscInt *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj; 2316 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 2317 PetscReal dt=info->dt,shift=info->shiftinblocks; 2318 PetscTruth row_identity, col_identity; 2319 2320 PetscFunctionBegin; 2321 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 2322 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 2323 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 2324 ics = ic; 2325 2326 for (i=0; i<n; i++){ 2327 /* initialize rtmp array */ 2328 nzl = bi[i+1] - bi[i]; /* num of nozeros in L(i,:) */ 2329 bjtmp = bj + bi[i]; 2330 for (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0; 2331 rtmp[i] = 0.0; 2332 nzu = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */ 2333 bjtmp = bj + bdiag[i+1] + 1; 2334 for (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0; 2335 2336 /* load in initial unfactored row of A */ 2337 /* printf("row %d\n",i); */ 2338 nz = ai[r[i]+1] - ai[r[i]]; 2339 ajtmp = aj + ai[r[i]]; 2340 v = aa + ai[r[i]]; 2341 for (j=0; j<nz; j++) { 2342 rtmp[ics[*ajtmp++]] = v[j]; 2343 /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */ 2344 } 2345 /* printf("\n"); */ 2346 2347 /* numerical factorization */ 2348 bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */ 2349 nzl = bi[i+1] - bi[i]; /* num of entries in L(i,:) */ 2350 k = 0; 2351 while (k < nzl){ 2352 row = *bjtmp++; 2353 /* printf(" prow %d\n",row); */ 2354 pc = rtmp + row; 2355 pv = b->a + bdiag[row]; /* 1./(diag of the pivot row) */ 2356 multiplier = (*pc) * (*pv); 2357 *pc = multiplier; 2358 if (PetscAbsScalar(multiplier) > dt){ 2359 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 2360 pv = b->a + bdiag[row+1] + 1; 2361 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 2362 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 2363 /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */ 2364 } 2365 k++; 2366 } 2367 2368 /* finished row so stick it into b->a */ 2369 /* L-part */ 2370 pv = b->a + bi[i] ; 2371 pj = bj + bi[i] ; 2372 nzl = bi[i+1] - bi[i]; 2373 for (j=0; j<nzl; j++) { 2374 pv[j] = rtmp[pj[j]]; 2375 /* printf(" (%d,%g),",pj[j],pv[j]); */ 2376 } 2377 2378 /* diagonal: invert diagonal entries for simplier triangular solves */ 2379 if (rtmp[i] == 0.0) rtmp[i] = dt+shift; 2380 b->a[bdiag[i]] = 1.0/rtmp[i]; 2381 /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */ 2382 2383 /* U-part */ 2384 pv = b->a + bdiag[i+1] + 1; 2385 pj = bj + bdiag[i+1] + 1; 2386 nzu = bdiag[i] - bdiag[i+1] - 1; 2387 for (j=0; j<nzu; j++) { 2388 pv[j] = rtmp[pj[j]]; 2389 /* printf(" (%d,%g),",pj[j],pv[j]); */ 2390 } 2391 /* printf("\n"); */ 2392 } 2393 2394 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2395 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 2396 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 2397 2398 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 2399 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 2400 if (row_identity && col_identity) { 2401 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_iludt; 2402 } else { 2403 C->ops->solve = MatSolve_SeqAIJ_iludt; 2404 } 2405 C->ops->solveadd = 0; 2406 C->ops->solvetranspose = 0; 2407 C->ops->solvetransposeadd = 0; 2408 C->ops->matsolve = 0; 2409 C->assembled = PETSC_TRUE; 2410 C->preallocated = PETSC_TRUE; 2411 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 2412 PetscFunctionReturn(0); 2413 } 2414