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 nz,row,i,j,n=A->rmap->n,diag; 429 const PetscInt *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 430 const PetscInt *ajtmp,*bjtmp,*diag_offset = b->diag,*pj; 431 MatScalar *pv,*rtmp,*pc,multiplier,d; 432 const MatScalar *v,*aa=a->a; 433 PetscReal rs=0.0; 434 LUShift_Ctx sctx; 435 PetscInt newshift,*ddiag; 436 437 PetscFunctionBegin; 438 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 439 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 440 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 441 ics = ic; 442 443 sctx.shift_top = 0; 444 sctx.nshift_max = 0; 445 sctx.shift_lo = 0; 446 sctx.shift_hi = 0; 447 sctx.shift_fraction = 0; 448 449 /* if both shift schemes are chosen by user, only use info->shiftpd */ 450 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 451 ddiag = a->diag; 452 sctx.shift_top = info->zeropivot; 453 for (i=0; i<n; i++) { 454 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 455 d = (aa)[ddiag[i]]; 456 rs = -PetscAbsScalar(d) - PetscRealPart(d); 457 v = aa+ai[i]; 458 nz = ai[i+1] - ai[i]; 459 for (j=0; j<nz; j++) 460 rs += PetscAbsScalar(v[j]); 461 if (rs>sctx.shift_top) sctx.shift_top = rs; 462 } 463 sctx.shift_top *= 1.1; 464 sctx.nshift_max = 5; 465 sctx.shift_lo = 0.; 466 sctx.shift_hi = 1.; 467 } 468 469 sctx.shift_amount = 0.0; 470 sctx.nshift = 0; 471 do { 472 sctx.lushift = PETSC_FALSE; 473 for (i=0; i<n; i++){ 474 nz = bi[i+1] - bi[i]; 475 bjtmp = bj + bi[i]; 476 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 477 478 /* load in initial (unfactored row) */ 479 nz = ai[r[i]+1] - ai[r[i]]; 480 ajtmp = aj + ai[r[i]]; 481 v = aa + ai[r[i]]; 482 for (j=0; j<nz; j++) { 483 rtmp[ics[ajtmp[j]]] = v[j]; 484 } 485 rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 486 /* if (sctx.shift_amount > 0.0) printf("row %d, shift %g\n",i,sctx.shift_amount); */ 487 488 row = *bjtmp++; 489 while (row < i) { 490 pc = rtmp + row; 491 if (*pc != 0.0) { 492 pv = b->a + diag_offset[row]; 493 pj = b->j + diag_offset[row] + 1; 494 multiplier = *pc / *pv++; 495 *pc = multiplier; 496 nz = bi[row+1] - diag_offset[row] - 1; 497 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 498 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 499 } 500 row = *bjtmp++; 501 } 502 /* finished row so stick it into b->a */ 503 pv = b->a + bi[i] ; 504 pj = b->j + bi[i] ; 505 nz = bi[i+1] - bi[i]; 506 diag = diag_offset[i] - bi[i]; 507 rs = 0.0; 508 for (j=0; j<nz; j++) { 509 pv[j] = rtmp[pj[j]]; 510 rs += PetscAbsScalar(pv[j]); 511 } 512 rs -= PetscAbsScalar(pv[diag]); 513 514 /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */ 515 sctx.rs = rs; 516 sctx.pv = pv[diag]; 517 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 518 if (newshift == 1) break; 519 } 520 521 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 522 /* 523 * if no shift in this attempt & shifting & started shifting & can refine, 524 * then try lower shift 525 */ 526 sctx.shift_hi = sctx.shift_fraction; 527 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 528 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 529 sctx.lushift = PETSC_TRUE; 530 sctx.nshift++; 531 } 532 } while (sctx.lushift); 533 534 /* invert diagonal entries for simplier triangular solves */ 535 for (i=0; i<n; i++) { 536 b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]]; 537 } 538 ierr = PetscFree(rtmp);CHKERRQ(ierr); 539 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 540 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 541 if (b->inode.use) { 542 C->ops->solve = MatSolve_Inode; 543 } else { 544 PetscTruth row_identity, col_identity; 545 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 546 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 547 if (row_identity && col_identity) { 548 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 549 } else { 550 C->ops->solve = MatSolve_SeqAIJ; 551 } 552 } 553 C->ops->solveadd = MatSolveAdd_SeqAIJ; 554 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 555 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 556 C->ops->matsolve = MatMatSolve_SeqAIJ; 557 C->assembled = PETSC_TRUE; 558 C->preallocated = PETSC_TRUE; 559 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 560 if (sctx.nshift){ 561 if (info->shiftpd) { 562 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); 563 } else if (info->shiftnz) { 564 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 565 } 566 } 567 PetscFunctionReturn(0); 568 } 569 570 /* 571 This routine implements inplace ILU(0) with row or/and column permutations. 572 Input: 573 A - original matrix 574 Output; 575 A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i] 576 a->j (col index) is permuted by the inverse of colperm, then sorted 577 a->a reordered accordingly with a->j 578 a->diag (ptr to diagonal elements) is updated. 579 */ 580 #undef __FUNCT__ 581 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_InplaceWithPerm" 582 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info) 583 { 584 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 585 IS isrow = a->row,isicol = a->icol; 586 PetscErrorCode ierr; 587 const PetscInt *r,*ic,*ics; 588 PetscInt i,j,n=A->rmap->n,*ai=a->i,*aj=a->j; 589 PetscInt *ajtmp,nz,row; 590 PetscInt *diag = a->diag,nbdiag,*pj; 591 PetscScalar *rtmp,*pc,multiplier,d; 592 MatScalar *v,*pv; 593 PetscReal rs; 594 LUShift_Ctx sctx; 595 PetscInt newshift; 596 597 PetscFunctionBegin; 598 if (A != B) SETERRQ(PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address"); 599 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 600 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 601 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&rtmp);CHKERRQ(ierr); 602 ierr = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr); 603 ics = ic; 604 605 sctx.shift_top = 0; 606 sctx.nshift_max = 0; 607 sctx.shift_lo = 0; 608 sctx.shift_hi = 0; 609 sctx.shift_fraction = 0; 610 611 /* if both shift schemes are chosen by user, only use info->shiftpd */ 612 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 613 sctx.shift_top = 0; 614 for (i=0; i<n; i++) { 615 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 616 d = (a->a)[diag[i]]; 617 rs = -PetscAbsScalar(d) - PetscRealPart(d); 618 v = a->a+ai[i]; 619 nz = ai[i+1] - ai[i]; 620 for (j=0; j<nz; j++) 621 rs += PetscAbsScalar(v[j]); 622 if (rs>sctx.shift_top) sctx.shift_top = rs; 623 } 624 if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot; 625 sctx.shift_top *= 1.1; 626 sctx.nshift_max = 5; 627 sctx.shift_lo = 0.; 628 sctx.shift_hi = 1.; 629 } 630 631 sctx.shift_amount = 0; 632 sctx.nshift = 0; 633 do { 634 sctx.lushift = PETSC_FALSE; 635 for (i=0; i<n; i++){ 636 /* load in initial unfactored row */ 637 nz = ai[r[i]+1] - ai[r[i]]; 638 ajtmp = aj + ai[r[i]]; 639 v = a->a + ai[r[i]]; 640 /* sort permuted ajtmp and values v accordingly */ 641 for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]]; 642 ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr); 643 644 diag[r[i]] = ai[r[i]]; 645 for (j=0; j<nz; j++) { 646 rtmp[ajtmp[j]] = v[j]; 647 if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */ 648 } 649 rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 650 651 row = *ajtmp++; 652 while (row < i) { 653 pc = rtmp + row; 654 if (*pc != 0.0) { 655 pv = a->a + diag[r[row]]; 656 pj = aj + diag[r[row]] + 1; 657 658 multiplier = *pc / *pv++; 659 *pc = multiplier; 660 nz = ai[r[row]+1] - diag[r[row]] - 1; 661 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 662 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 663 } 664 row = *ajtmp++; 665 } 666 /* finished row so overwrite it onto a->a */ 667 pv = a->a + ai[r[i]] ; 668 pj = aj + ai[r[i]] ; 669 nz = ai[r[i]+1] - ai[r[i]]; 670 nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */ 671 672 rs = 0.0; 673 for (j=0; j<nz; j++) { 674 pv[j] = rtmp[pj[j]]; 675 if (j != nbdiag) rs += PetscAbsScalar(pv[j]); 676 } 677 678 /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */ 679 sctx.rs = rs; 680 sctx.pv = pv[nbdiag]; 681 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 682 if (newshift == 1) break; 683 } 684 685 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 686 /* 687 * if no shift in this attempt & shifting & started shifting & can refine, 688 * then try lower shift 689 */ 690 sctx.shift_hi = sctx.shift_fraction; 691 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 692 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 693 sctx.lushift = PETSC_TRUE; 694 sctx.nshift++; 695 } 696 } while (sctx.lushift); 697 698 /* invert diagonal entries for simplier triangular solves */ 699 for (i=0; i<n; i++) { 700 a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]]; 701 } 702 703 ierr = PetscFree(rtmp);CHKERRQ(ierr); 704 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 705 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 706 A->ops->solve = MatSolve_SeqAIJ_InplaceWithPerm; 707 A->ops->solveadd = MatSolveAdd_SeqAIJ; 708 A->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 709 A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 710 A->assembled = PETSC_TRUE; 711 A->preallocated = PETSC_TRUE; 712 ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr); 713 if (sctx.nshift){ 714 if (info->shiftpd) { 715 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); 716 } else if (info->shiftnz) { 717 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 718 } 719 } 720 PetscFunctionReturn(0); 721 } 722 723 /* ----------------------------------------------------------- */ 724 #undef __FUNCT__ 725 #define __FUNCT__ "MatLUFactor_SeqAIJ" 726 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info) 727 { 728 PetscErrorCode ierr; 729 Mat C; 730 731 PetscFunctionBegin; 732 ierr = MatGetFactor(A,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr); 733 ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr); 734 ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr); 735 A->ops->solve = C->ops->solve; 736 A->ops->solvetranspose = C->ops->solvetranspose; 737 ierr = MatHeaderCopy(A,C);CHKERRQ(ierr); 738 ierr = PetscLogObjectParent(A,((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr); 739 PetscFunctionReturn(0); 740 } 741 /* ----------------------------------------------------------- */ 742 743 744 #undef __FUNCT__ 745 #define __FUNCT__ "MatSolve_SeqAIJ" 746 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx) 747 { 748 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 749 IS iscol = a->col,isrow = a->row; 750 PetscErrorCode ierr; 751 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 752 PetscInt nz; 753 const PetscInt *rout,*cout,*r,*c; 754 PetscScalar *x,*tmp,*tmps,sum; 755 const PetscScalar *b; 756 const MatScalar *aa = a->a,*v; 757 758 PetscFunctionBegin; 759 if (!n) PetscFunctionReturn(0); 760 761 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 762 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 763 tmp = a->solve_work; 764 765 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 766 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 767 768 /* forward solve the lower triangular */ 769 tmp[0] = b[*r++]; 770 tmps = tmp; 771 for (i=1; i<n; i++) { 772 v = aa + ai[i] ; 773 vi = aj + ai[i] ; 774 nz = a->diag[i] - ai[i]; 775 sum = b[*r++]; 776 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 777 tmp[i] = sum; 778 } 779 780 /* backward solve the upper triangular */ 781 for (i=n-1; i>=0; i--){ 782 v = aa + a->diag[i] + 1; 783 vi = aj + a->diag[i] + 1; 784 nz = ai[i+1] - a->diag[i] - 1; 785 sum = tmp[i]; 786 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 787 x[*c--] = tmp[i] = sum*aa[a->diag[i]]; 788 } 789 790 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 791 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 792 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 793 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 794 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 795 PetscFunctionReturn(0); 796 } 797 798 #undef __FUNCT__ 799 #define __FUNCT__ "MatMatSolve_SeqAIJ" 800 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X) 801 { 802 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 803 IS iscol = a->col,isrow = a->row; 804 PetscErrorCode ierr; 805 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 806 PetscInt nz,neq; 807 const PetscInt *rout,*cout,*r,*c; 808 PetscScalar *x,*b,*tmp,*tmps,sum; 809 const MatScalar *aa = a->a,*v; 810 PetscTruth bisdense,xisdense; 811 812 PetscFunctionBegin; 813 if (!n) PetscFunctionReturn(0); 814 815 ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr); 816 if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 817 ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr); 818 if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 819 820 ierr = MatGetArray(B,&b);CHKERRQ(ierr); 821 ierr = MatGetArray(X,&x);CHKERRQ(ierr); 822 823 tmp = a->solve_work; 824 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 825 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 826 827 for (neq=0; neq<B->cmap->n; neq++){ 828 /* forward solve the lower triangular */ 829 tmp[0] = b[r[0]]; 830 tmps = tmp; 831 for (i=1; i<n; i++) { 832 v = aa + ai[i] ; 833 vi = aj + ai[i] ; 834 nz = a->diag[i] - ai[i]; 835 sum = b[r[i]]; 836 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 837 tmp[i] = sum; 838 } 839 /* backward solve the upper triangular */ 840 for (i=n-1; i>=0; i--){ 841 v = aa + a->diag[i] + 1; 842 vi = aj + a->diag[i] + 1; 843 nz = ai[i+1] - a->diag[i] - 1; 844 sum = tmp[i]; 845 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 846 x[c[i]] = tmp[i] = sum*aa[a->diag[i]]; 847 } 848 849 b += n; 850 x += n; 851 } 852 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 853 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 854 ierr = MatRestoreArray(B,&b);CHKERRQ(ierr); 855 ierr = MatRestoreArray(X,&x);CHKERRQ(ierr); 856 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 857 PetscFunctionReturn(0); 858 } 859 860 #undef __FUNCT__ 861 #define __FUNCT__ "MatSolve_SeqAIJ_InplaceWithPerm" 862 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx) 863 { 864 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 865 IS iscol = a->col,isrow = a->row; 866 PetscErrorCode ierr; 867 const PetscInt *r,*c,*rout,*cout; 868 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 869 PetscInt nz,row; 870 PetscScalar *x,*b,*tmp,*tmps,sum; 871 const MatScalar *aa = a->a,*v; 872 873 PetscFunctionBegin; 874 if (!n) PetscFunctionReturn(0); 875 876 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 877 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 878 tmp = a->solve_work; 879 880 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 881 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 882 883 /* forward solve the lower triangular */ 884 tmp[0] = b[*r++]; 885 tmps = tmp; 886 for (row=1; row<n; row++) { 887 i = rout[row]; /* permuted row */ 888 v = aa + ai[i] ; 889 vi = aj + ai[i] ; 890 nz = a->diag[i] - ai[i]; 891 sum = b[*r++]; 892 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 893 tmp[row] = sum; 894 } 895 896 /* backward solve the upper triangular */ 897 for (row=n-1; row>=0; row--){ 898 i = rout[row]; /* permuted row */ 899 v = aa + a->diag[i] + 1; 900 vi = aj + a->diag[i] + 1; 901 nz = ai[i+1] - a->diag[i] - 1; 902 sum = tmp[row]; 903 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 904 x[*c--] = tmp[row] = sum*aa[a->diag[i]]; 905 } 906 907 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 908 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 909 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 910 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 911 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 912 PetscFunctionReturn(0); 913 } 914 915 /* ----------------------------------------------------------- */ 916 #include "../src/mat/impls/aij/seq/ftn-kernels/fsolve.h" 917 #undef __FUNCT__ 918 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering" 919 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx) 920 { 921 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 922 PetscErrorCode ierr; 923 PetscInt n = A->rmap->n; 924 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag; 925 PetscScalar *x; 926 const PetscScalar *b; 927 const MatScalar *aa = a->a; 928 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 929 PetscInt adiag_i,i,nz,ai_i; 930 const PetscInt *vi; 931 const MatScalar *v; 932 PetscScalar sum; 933 #endif 934 935 PetscFunctionBegin; 936 if (!n) PetscFunctionReturn(0); 937 938 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 939 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 940 941 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 942 fortransolveaij_(&n,x,ai,aj,adiag,aa,b); 943 #else 944 /* forward solve the lower triangular */ 945 x[0] = b[0]; 946 for (i=1; i<n; i++) { 947 ai_i = ai[i]; 948 v = aa + ai_i; 949 vi = aj + ai_i; 950 nz = adiag[i] - ai_i; 951 sum = b[i]; 952 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 953 x[i] = sum; 954 } 955 956 /* backward solve the upper triangular */ 957 for (i=n-1; i>=0; i--){ 958 adiag_i = adiag[i]; 959 v = aa + adiag_i + 1; 960 vi = aj + adiag_i + 1; 961 nz = ai[i+1] - adiag_i - 1; 962 sum = x[i]; 963 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 964 x[i] = sum*aa[adiag_i]; 965 } 966 #endif 967 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 968 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 969 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 970 PetscFunctionReturn(0); 971 } 972 973 #undef __FUNCT__ 974 #define __FUNCT__ "MatSolveAdd_SeqAIJ" 975 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx) 976 { 977 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 978 IS iscol = a->col,isrow = a->row; 979 PetscErrorCode ierr; 980 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 981 PetscInt nz; 982 const PetscInt *rout,*cout,*r,*c; 983 PetscScalar *x,*b,*tmp,sum; 984 const MatScalar *aa = a->a,*v; 985 986 PetscFunctionBegin; 987 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 988 989 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 990 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 991 tmp = a->solve_work; 992 993 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 994 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 995 996 /* forward solve the lower triangular */ 997 tmp[0] = b[*r++]; 998 for (i=1; i<n; i++) { 999 v = aa + ai[i] ; 1000 vi = aj + ai[i] ; 1001 nz = a->diag[i] - ai[i]; 1002 sum = b[*r++]; 1003 while (nz--) sum -= *v++ * tmp[*vi++ ]; 1004 tmp[i] = sum; 1005 } 1006 1007 /* backward solve the upper triangular */ 1008 for (i=n-1; i>=0; i--){ 1009 v = aa + a->diag[i] + 1; 1010 vi = aj + a->diag[i] + 1; 1011 nz = ai[i+1] - a->diag[i] - 1; 1012 sum = tmp[i]; 1013 while (nz--) sum -= *v++ * tmp[*vi++ ]; 1014 tmp[i] = sum*aa[a->diag[i]]; 1015 x[*c--] += tmp[i]; 1016 } 1017 1018 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1019 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1020 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1021 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1022 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1023 1024 PetscFunctionReturn(0); 1025 } 1026 /* -------------------------------------------------------------------*/ 1027 #undef __FUNCT__ 1028 #define __FUNCT__ "MatSolveTranspose_SeqAIJ" 1029 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx) 1030 { 1031 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1032 IS iscol = a->col,isrow = a->row; 1033 PetscErrorCode ierr; 1034 const PetscInt *rout,*cout,*r,*c; 1035 PetscInt i,n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1036 PetscInt nz,*diag = a->diag; 1037 PetscScalar *x,*b,*tmp,s1; 1038 const MatScalar *aa = a->a,*v; 1039 1040 PetscFunctionBegin; 1041 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1042 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1043 tmp = a->solve_work; 1044 1045 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1046 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1047 1048 /* copy the b into temp work space according to permutation */ 1049 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1050 1051 /* forward solve the U^T */ 1052 for (i=0; i<n; i++) { 1053 v = aa + diag[i] ; 1054 vi = aj + diag[i] + 1; 1055 nz = ai[i+1] - diag[i] - 1; 1056 s1 = tmp[i]; 1057 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1058 while (nz--) { 1059 tmp[*vi++ ] -= (*v++)*s1; 1060 } 1061 tmp[i] = s1; 1062 } 1063 1064 /* backward solve the L^T */ 1065 for (i=n-1; i>=0; i--){ 1066 v = aa + diag[i] - 1 ; 1067 vi = aj + diag[i] - 1 ; 1068 nz = diag[i] - ai[i]; 1069 s1 = tmp[i]; 1070 while (nz--) { 1071 tmp[*vi-- ] -= (*v--)*s1; 1072 } 1073 } 1074 1075 /* copy tmp into x according to permutation */ 1076 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1077 1078 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1079 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1080 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1081 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1082 1083 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1084 PetscFunctionReturn(0); 1085 } 1086 1087 #undef __FUNCT__ 1088 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ" 1089 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx) 1090 { 1091 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1092 IS iscol = a->col,isrow = a->row; 1093 PetscErrorCode ierr; 1094 const PetscInt *r,*c,*rout,*cout; 1095 PetscInt i,n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1096 PetscInt nz,*diag = a->diag; 1097 PetscScalar *x,*b,*tmp; 1098 const MatScalar *aa = a->a,*v; 1099 1100 PetscFunctionBegin; 1101 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1102 1103 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1104 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1105 tmp = a->solve_work; 1106 1107 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1108 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1109 1110 /* copy the b into temp work space according to permutation */ 1111 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1112 1113 /* forward solve the U^T */ 1114 for (i=0; i<n; i++) { 1115 v = aa + diag[i] ; 1116 vi = aj + diag[i] + 1; 1117 nz = ai[i+1] - diag[i] - 1; 1118 tmp[i] *= *v++; 1119 while (nz--) { 1120 tmp[*vi++ ] -= (*v++)*tmp[i]; 1121 } 1122 } 1123 1124 /* backward solve the L^T */ 1125 for (i=n-1; i>=0; i--){ 1126 v = aa + diag[i] - 1 ; 1127 vi = aj + diag[i] - 1 ; 1128 nz = diag[i] - ai[i]; 1129 while (nz--) { 1130 tmp[*vi-- ] -= (*v--)*tmp[i]; 1131 } 1132 } 1133 1134 /* copy tmp into x according to permutation */ 1135 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1136 1137 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1138 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1139 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1140 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1141 1142 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1143 PetscFunctionReturn(0); 1144 } 1145 /* ----------------------------------------------------------------*/ 1146 EXTERN PetscErrorCode Mat_CheckInode(Mat,PetscTruth); 1147 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth); 1148 1149 /* 1150 ilu(0) with natural ordering under new data structure. 1151 Factored arrays bj and ba are stored as 1152 L(0,:), L(1,:), ...,L(n-1,:), U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:) 1153 1154 bi=fact->i is an array of size 2n+2, in which 1155 bi+ 1156 bi[i] -> 1st entry of L(i,:),i=0,...,i-1 1157 bi[n] -> points to L(n-1,:)+1 1158 bi[n+1] -> 1st entry of U(n-1,:) 1159 bi[2n-i] -> 1st entry of U(i,:) 1160 bi[2n-i+1] -> end of U(i,:)+1, the 1st entry of U(i-1,:) 1161 bi[2n] -> 1st entry of U(0,:) 1162 bi[2n+1] -> points to U(0,:)+1 1163 1164 U(i,:) contains diag[i] as its last entry, i.e., 1165 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 1166 */ 1167 #undef __FUNCT__ 1168 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct" 1169 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1170 { 1171 1172 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1173 PetscErrorCode ierr; 1174 PetscInt n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag; 1175 PetscInt i,j,nz,*bi,*bj,*bdiag; 1176 1177 PetscFunctionBegin; 1178 /* printf("MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct ...\n"); */ 1179 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr); 1180 b = (Mat_SeqAIJ*)(fact)->data; 1181 1182 /* allocate matrix arrays for new data structure */ 1183 ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,2*n+2,PetscInt,&b->i);CHKERRQ(ierr); 1184 ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(2*n+2)*sizeof(PetscInt));CHKERRQ(ierr); 1185 b->singlemalloc = PETSC_TRUE; 1186 if (!b->diag){ 1187 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr); 1188 } 1189 bdiag = b->diag; 1190 1191 if (n > 0) { 1192 ierr = PetscMemzero(b->a,(ai[n])*sizeof(PetscScalar));CHKERRQ(ierr); 1193 } 1194 1195 /* set bi and bj with new data structure */ 1196 bi = b->i; 1197 bj = b->j; 1198 1199 /* L part */ 1200 bi[0] = 0; 1201 for (i=0; i<n; i++){ 1202 nz = adiag[i] - ai[i]; 1203 bi[i+1] = bi[i] + nz; 1204 aj = a->j + ai[i]; 1205 for (j=0; j<nz; j++){ 1206 *bj = aj[j]; bj++; 1207 } 1208 } 1209 1210 /* U part */ 1211 bi[n+1] = bi[n]; 1212 for (i=n-1; i>=0; i--){ 1213 nz = ai[i+1] - adiag[i] - 1; 1214 bi[2*n-i+1] = bi[2*n-i] + nz + 1; 1215 aj = a->j + adiag[i] + 1; 1216 for (j=0; j<nz; j++){ 1217 *bj = aj[j]; bj++; 1218 } 1219 /* diag[i] */ 1220 *bj = i; bj++; 1221 bdiag[i] = bi[2*n-i+1]-1; 1222 } 1223 PetscFunctionReturn(0); 1224 } 1225 1226 #undef __FUNCT__ 1227 #define __FUNCT__ "PetscFreeSpaceContiguous_newdatastruct" 1228 PetscErrorCode PetscFreeSpaceContiguous_newdatastruct(PetscFreeSpaceList *head,PetscInt *space,PetscInt n,PetscInt *bi,PetscInt *bdiag) 1229 { 1230 PetscFreeSpaceList a; 1231 PetscErrorCode ierr; 1232 PetscInt row,nnz,*bj,*array,total; 1233 PetscInt nnzL,nnzU; 1234 1235 PetscFunctionBegin; 1236 bi[2*n+1] = bi[n]; 1237 row = 1; 1238 total = 0; 1239 nnzL = bdiag[0]; 1240 while ((*head)!=NULL) { 1241 total += (*head)->local_used; 1242 array = (*head)->array_head; 1243 1244 while (bi[row] <= total && row <=n){ 1245 /* copy array entries into bj for row-1 */ 1246 nnz = bi[row] - bi[row-1]; 1247 /* set bi[row-1] for new datastruct */ 1248 if (row -1 <= 1 ){ 1249 bi[row -1] = 0; 1250 } else { 1251 bi[row-1] = bi[row-2] + nnzL; /* nnzL of previous row */ 1252 } 1253 1254 /* L part */ 1255 nnzL = bdiag[row-1]; 1256 bj = space+bi[row-1]; 1257 ierr = PetscMemcpy(bj,array,nnzL*sizeof(PetscInt));CHKERRQ(ierr); 1258 1259 /* diagonal entry */ 1260 bdiag[row-1] = bi[2*n-(row-1)+1]-1; 1261 space[bdiag[row-1]] = row-1; 1262 1263 /* U part */ 1264 nnzU = nnz - nnzL; 1265 bi[2*n-(row-1)] = bi[2*n-(row-1)+1] - nnzU; 1266 nnzU --; /* exclude diagonal */ 1267 bj = space + bi[2*n-(row-1)]; 1268 ierr = PetscMemcpy(bj,array+nnzL+1,nnzU*sizeof(PetscInt));CHKERRQ(ierr); 1269 1270 array += nnz; 1271 row++; 1272 } 1273 1274 a = (*head)->more_space; 1275 ierr = PetscFree((*head)->array_head);CHKERRQ(ierr); 1276 ierr = PetscFree(*head);CHKERRQ(ierr); 1277 *head = a; 1278 } 1279 bi[n] = bi[n-1] + nnzL; 1280 if (bi[n] != bi[n+1]) SETERRQ2(1,"bi[n] %d != bi[n+1] %d",bi[n],bi[n+1]); 1281 PetscFunctionReturn(0); 1282 } 1283 1284 #undef __FUNCT__ 1285 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_newdatastruct" 1286 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1287 { 1288 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1289 IS isicol; 1290 PetscErrorCode ierr; 1291 const PetscInt *r,*ic; 1292 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,d; 1293 PetscInt *bi,*cols,nnz,*cols_lvl; 1294 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1295 PetscInt i,levels,diagonal_fill; 1296 PetscTruth col_identity,row_identity; 1297 PetscReal f; 1298 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1299 PetscBT lnkbt; 1300 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1301 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1302 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1303 PetscTruth missing; 1304 1305 PetscFunctionBegin; 1306 //printf("MatILUFactorSymbolic_SeqAIJ_newdatastruct ...\n"); 1307 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); 1308 f = info->fill; 1309 levels = (PetscInt)info->levels; 1310 diagonal_fill = (PetscInt)info->diagonal_fill; 1311 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1312 1313 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1314 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1315 1316 if (!levels && row_identity && col_identity) { 1317 /* special case: ilu(0) with natural ordering */ 1318 ierr = MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1319 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 1320 1321 fact->factor = MAT_FACTOR_ILU; 1322 (fact)->info.factor_mallocs = 0; 1323 (fact)->info.fill_ratio_given = info->fill; 1324 (fact)->info.fill_ratio_needed = 1.0; 1325 b = (Mat_SeqAIJ*)(fact)->data; 1326 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 1327 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 1328 b->row = isrow; 1329 b->col = iscol; 1330 b->icol = isicol; 1331 ierr = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1332 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1333 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1334 /* ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */ 1335 PetscFunctionReturn(0); 1336 } 1337 1338 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1339 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1340 1341 /* get new row pointers */ 1342 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1343 bi[0] = 0; 1344 /* bdiag is location of diagonal in factor */ 1345 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1346 bdiag[0] = 0; 1347 1348 ierr = PetscMalloc((2*n+1)*sizeof(PetscInt**),&bj_ptr);CHKERRQ(ierr); 1349 bjlvl_ptr = (PetscInt**)(bj_ptr + n); 1350 1351 /* create a linked list for storing column indices of the active row */ 1352 nlnk = n + 1; 1353 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1354 1355 /* initial FreeSpace size is f*(ai[n]+1) */ 1356 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1357 current_space = free_space; 1358 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1359 current_space_lvl = free_space_lvl; 1360 1361 for (i=0; i<n; i++) { 1362 nzi = 0; 1363 /* copy current row into linked list */ 1364 nnz = ai[r[i]+1] - ai[r[i]]; 1365 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1366 cols = aj + ai[r[i]]; 1367 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1368 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1369 nzi += nlnk; 1370 1371 /* make sure diagonal entry is included */ 1372 if (diagonal_fill && lnk[i] == -1) { 1373 fm = n; 1374 while (lnk[fm] < i) fm = lnk[fm]; 1375 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1376 lnk[fm] = i; 1377 lnk_lvl[i] = 0; 1378 nzi++; dcount++; 1379 } 1380 1381 /* add pivot rows into the active row */ 1382 nzbd = 0; 1383 prow = lnk[n]; 1384 while (prow < i) { 1385 nnz = bdiag[prow]; 1386 cols = bj_ptr[prow] + nnz + 1; 1387 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1388 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1389 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1390 nzi += nlnk; 1391 prow = lnk[prow]; 1392 nzbd++; 1393 } 1394 bdiag[i] = nzbd; 1395 bi[i+1] = bi[i] + nzi; 1396 1397 /* if free space is not available, make more free space */ 1398 if (current_space->local_remaining<nzi) { 1399 nnz = 2*nzi*(n - i); /* estimated and max additional space needed */ 1400 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1401 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1402 reallocs++; 1403 } 1404 1405 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1406 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1407 bj_ptr[i] = current_space->array; 1408 bjlvl_ptr[i] = current_space_lvl->array; 1409 1410 /* make sure the active row i has diagonal entry */ 1411 if (*(bj_ptr[i]+bdiag[i]) != i) { 1412 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 1413 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1414 } 1415 1416 current_space->array += nzi; 1417 current_space->local_used += nzi; 1418 current_space->local_remaining -= nzi; 1419 current_space_lvl->array += nzi; 1420 current_space_lvl->local_used += nzi; 1421 current_space_lvl->local_remaining -= nzi; 1422 } 1423 1424 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1425 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1426 1427 /* destroy list of free space and other temporary arrays */ 1428 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 1429 1430 /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */ 1431 ierr = PetscFreeSpaceContiguous_newdatastruct(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 1432 1433 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1434 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1435 ierr = PetscFree(bj_ptr);CHKERRQ(ierr); 1436 1437 #if defined(PETSC_USE_INFO) 1438 { 1439 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1440 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 1441 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1442 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 1443 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1444 if (diagonal_fill) { 1445 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 1446 } 1447 } 1448 #endif 1449 1450 /* put together the new matrix */ 1451 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 1452 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 1453 b = (Mat_SeqAIJ*)(fact)->data; 1454 b->free_a = PETSC_TRUE; 1455 b->free_ij = PETSC_TRUE; 1456 b->singlemalloc = PETSC_FALSE; 1457 ierr = PetscMalloc( (bi[2*n+1] )*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 1458 b->j = bj; 1459 b->i = bi; 1460 b->diag = bdiag; 1461 b->ilen = 0; 1462 b->imax = 0; 1463 b->row = isrow; 1464 b->col = iscol; 1465 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1466 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1467 b->icol = isicol; 1468 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1469 /* In b structure: Free imax, ilen, old a, old j. 1470 Allocate bdiag, solve_work, new a, new j */ 1471 ierr = PetscLogObjectMemory(fact,bi[2*n+1] * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1472 b->maxnz = b->nz = bi[2*n+1] ; 1473 (fact)->info.factor_mallocs = reallocs; 1474 (fact)->info.fill_ratio_given = f; 1475 (fact)->info.fill_ratio_needed = ((PetscReal)bi[2*n+1])/((PetscReal)ai[n]); 1476 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 1477 /* ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */ 1478 PetscFunctionReturn(0); 1479 } 1480 1481 #undef __FUNCT__ 1482 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ" 1483 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1484 { 1485 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1486 IS isicol; 1487 PetscErrorCode ierr; 1488 const PetscInt *r,*ic; 1489 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,d; 1490 PetscInt *bi,*cols,nnz,*cols_lvl; 1491 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1492 PetscInt i,levels,diagonal_fill; 1493 PetscTruth col_identity,row_identity; 1494 PetscReal f; 1495 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1496 PetscBT lnkbt; 1497 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1498 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1499 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1500 PetscTruth missing; 1501 PetscTruth newdatastruct=PETSC_FALSE; 1502 1503 PetscFunctionBegin; 1504 ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 1505 if (newdatastruct){ 1506 ierr = MatILUFactorSymbolic_SeqAIJ_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1507 PetscFunctionReturn(0); 1508 } 1509 1510 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); 1511 f = info->fill; 1512 levels = (PetscInt)info->levels; 1513 diagonal_fill = (PetscInt)info->diagonal_fill; 1514 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1515 1516 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1517 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1518 if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */ 1519 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr); 1520 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1521 1522 fact->factor = MAT_FACTOR_ILU; 1523 (fact)->info.factor_mallocs = 0; 1524 (fact)->info.fill_ratio_given = info->fill; 1525 (fact)->info.fill_ratio_needed = 1.0; 1526 b = (Mat_SeqAIJ*)(fact)->data; 1527 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 1528 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 1529 b->row = isrow; 1530 b->col = iscol; 1531 b->icol = isicol; 1532 ierr = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1533 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1534 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1535 ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1536 PetscFunctionReturn(0); 1537 } 1538 1539 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1540 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1541 1542 /* get new row pointers */ 1543 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1544 bi[0] = 0; 1545 /* bdiag is location of diagonal in factor */ 1546 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1547 bdiag[0] = 0; 1548 1549 ierr = PetscMalloc((2*n+1)*sizeof(PetscInt**),&bj_ptr);CHKERRQ(ierr); 1550 bjlvl_ptr = (PetscInt**)(bj_ptr + n); 1551 1552 /* create a linked list for storing column indices of the active row */ 1553 nlnk = n + 1; 1554 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1555 1556 /* initial FreeSpace size is f*(ai[n]+1) */ 1557 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1558 current_space = free_space; 1559 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1560 current_space_lvl = free_space_lvl; 1561 1562 for (i=0; i<n; i++) { 1563 nzi = 0; 1564 /* copy current row into linked list */ 1565 nnz = ai[r[i]+1] - ai[r[i]]; 1566 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1567 cols = aj + ai[r[i]]; 1568 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1569 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1570 nzi += nlnk; 1571 1572 /* make sure diagonal entry is included */ 1573 if (diagonal_fill && lnk[i] == -1) { 1574 fm = n; 1575 while (lnk[fm] < i) fm = lnk[fm]; 1576 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1577 lnk[fm] = i; 1578 lnk_lvl[i] = 0; 1579 nzi++; dcount++; 1580 } 1581 1582 /* add pivot rows into the active row */ 1583 nzbd = 0; 1584 prow = lnk[n]; 1585 while (prow < i) { 1586 nnz = bdiag[prow]; 1587 cols = bj_ptr[prow] + nnz + 1; 1588 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1589 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1590 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1591 nzi += nlnk; 1592 prow = lnk[prow]; 1593 nzbd++; 1594 } 1595 bdiag[i] = nzbd; 1596 bi[i+1] = bi[i] + nzi; 1597 1598 /* if free space is not available, make more free space */ 1599 if (current_space->local_remaining<nzi) { 1600 nnz = nzi*(n - i); /* estimated and max additional space needed */ 1601 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1602 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1603 reallocs++; 1604 } 1605 1606 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1607 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1608 bj_ptr[i] = current_space->array; 1609 bjlvl_ptr[i] = current_space_lvl->array; 1610 1611 /* make sure the active row i has diagonal entry */ 1612 if (*(bj_ptr[i]+bdiag[i]) != i) { 1613 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 1614 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1615 } 1616 1617 current_space->array += nzi; 1618 current_space->local_used += nzi; 1619 current_space->local_remaining -= nzi; 1620 current_space_lvl->array += nzi; 1621 current_space_lvl->local_used += nzi; 1622 current_space_lvl->local_remaining -= nzi; 1623 } 1624 1625 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1626 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1627 1628 /* destroy list of free space and other temporary arrays */ 1629 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 1630 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */ 1631 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1632 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1633 ierr = PetscFree(bj_ptr);CHKERRQ(ierr); 1634 1635 #if defined(PETSC_USE_INFO) 1636 { 1637 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1638 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 1639 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1640 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 1641 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1642 if (diagonal_fill) { 1643 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 1644 } 1645 } 1646 #endif 1647 1648 /* put together the new matrix */ 1649 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 1650 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 1651 b = (Mat_SeqAIJ*)(fact)->data; 1652 b->free_a = PETSC_TRUE; 1653 b->free_ij = PETSC_TRUE; 1654 b->singlemalloc = PETSC_FALSE; 1655 ierr = PetscMalloc( (bi[n] )*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 1656 b->j = bj; 1657 b->i = bi; 1658 for (i=0; i<n; i++) bdiag[i] += bi[i]; 1659 b->diag = bdiag; 1660 b->ilen = 0; 1661 b->imax = 0; 1662 b->row = isrow; 1663 b->col = iscol; 1664 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1665 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1666 b->icol = isicol; 1667 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1668 /* In b structure: Free imax, ilen, old a, old j. 1669 Allocate bdiag, solve_work, new a, new j */ 1670 ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1671 b->maxnz = b->nz = bi[n] ; 1672 (fact)->info.factor_mallocs = reallocs; 1673 (fact)->info.fill_ratio_given = f; 1674 (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1675 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1676 ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1677 PetscFunctionReturn(0); 1678 } 1679 1680 #include "../src/mat/impls/sbaij/seq/sbaij.h" 1681 #undef __FUNCT__ 1682 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ" 1683 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 1684 { 1685 Mat C = B; 1686 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 1687 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 1688 IS ip=b->row,iip = b->icol; 1689 PetscErrorCode ierr; 1690 const PetscInt *rip,*riip; 1691 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol; 1692 PetscInt *ai=a->i,*aj=a->j; 1693 PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz; 1694 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 1695 PetscReal zeropivot,rs,shiftnz; 1696 PetscReal shiftpd; 1697 ChShift_Ctx sctx; 1698 PetscInt newshift; 1699 PetscTruth perm_identity; 1700 1701 PetscFunctionBegin; 1702 1703 shiftnz = info->shiftnz; 1704 shiftpd = info->shiftpd; 1705 zeropivot = info->zeropivot; 1706 1707 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 1708 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 1709 1710 /* initialization */ 1711 nz = (2*mbs+1)*sizeof(PetscInt)+mbs*sizeof(MatScalar); 1712 ierr = PetscMalloc(nz,&il);CHKERRQ(ierr); 1713 jl = il + mbs; 1714 rtmp = (MatScalar*)(jl + mbs); 1715 1716 sctx.shift_amount = 0; 1717 sctx.nshift = 0; 1718 do { 1719 sctx.chshift = PETSC_FALSE; 1720 for (i=0; i<mbs; i++) { 1721 rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0; 1722 } 1723 1724 for (k = 0; k<mbs; k++){ 1725 bval = ba + bi[k]; 1726 /* initialize k-th row by the perm[k]-th row of A */ 1727 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 1728 for (j = jmin; j < jmax; j++){ 1729 col = riip[aj[j]]; 1730 if (col >= k){ /* only take upper triangular entry */ 1731 rtmp[col] = aa[j]; 1732 *bval++ = 0.0; /* for in-place factorization */ 1733 } 1734 } 1735 /* shift the diagonal of the matrix */ 1736 if (sctx.nshift) rtmp[k] += sctx.shift_amount; 1737 1738 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 1739 dk = rtmp[k]; 1740 i = jl[k]; /* first row to be added to k_th row */ 1741 1742 while (i < k){ 1743 nexti = jl[i]; /* next row to be added to k_th row */ 1744 1745 /* compute multiplier, update diag(k) and U(i,k) */ 1746 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 1747 uikdi = - ba[ili]*ba[bi[i]]; /* diagonal(k) */ 1748 dk += uikdi*ba[ili]; 1749 ba[ili] = uikdi; /* -U(i,k) */ 1750 1751 /* add multiple of row i to k-th row */ 1752 jmin = ili + 1; jmax = bi[i+1]; 1753 if (jmin < jmax){ 1754 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 1755 /* update il and jl for row i */ 1756 il[i] = jmin; 1757 j = bj[jmin]; jl[i] = jl[j]; jl[j] = i; 1758 } 1759 i = nexti; 1760 } 1761 1762 /* shift the diagonals when zero pivot is detected */ 1763 /* compute rs=sum of abs(off-diagonal) */ 1764 rs = 0.0; 1765 jmin = bi[k]+1; 1766 nz = bi[k+1] - jmin; 1767 bcol = bj + jmin; 1768 while (nz--){ 1769 rs += PetscAbsScalar(rtmp[*bcol]); 1770 bcol++; 1771 } 1772 1773 sctx.rs = rs; 1774 sctx.pv = dk; 1775 ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr); 1776 1777 if (newshift == 1) { 1778 if (!sctx.shift_amount) { 1779 sctx.shift_amount = 1e-5; 1780 } 1781 break; 1782 } 1783 1784 /* copy data into U(k,:) */ 1785 ba[bi[k]] = 1.0/dk; /* U(k,k) */ 1786 jmin = bi[k]+1; jmax = bi[k+1]; 1787 if (jmin < jmax) { 1788 for (j=jmin; j<jmax; j++){ 1789 col = bj[j]; ba[j] = rtmp[col]; rtmp[col] = 0.0; 1790 } 1791 /* add the k-th row into il and jl */ 1792 il[k] = jmin; 1793 i = bj[jmin]; jl[k] = jl[i]; jl[i] = k; 1794 } 1795 } 1796 } while (sctx.chshift); 1797 ierr = PetscFree(il);CHKERRQ(ierr); 1798 1799 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 1800 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 1801 1802 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 1803 if (perm_identity){ 1804 (B)->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering; 1805 (B)->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering; 1806 (B)->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering; 1807 (B)->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering; 1808 } else { 1809 (B)->ops->solve = MatSolve_SeqSBAIJ_1; 1810 (B)->ops->solvetranspose = MatSolve_SeqSBAIJ_1; 1811 (B)->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1; 1812 (B)->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1; 1813 } 1814 1815 C->assembled = PETSC_TRUE; 1816 C->preallocated = PETSC_TRUE; 1817 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 1818 if (sctx.nshift){ 1819 if (shiftnz) { 1820 ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 1821 } else if (shiftpd) { 1822 ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 1823 } 1824 } 1825 PetscFunctionReturn(0); 1826 } 1827 1828 #undef __FUNCT__ 1829 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ" 1830 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 1831 { 1832 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1833 Mat_SeqSBAIJ *b; 1834 PetscErrorCode ierr; 1835 PetscTruth perm_identity,missing; 1836 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui; 1837 const PetscInt *rip,*riip; 1838 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 1839 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 1840 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 1841 PetscReal fill=info->fill,levels=info->levels; 1842 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1843 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1844 PetscBT lnkbt; 1845 IS iperm; 1846 1847 PetscFunctionBegin; 1848 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); 1849 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 1850 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 1851 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 1852 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 1853 1854 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 1855 ui[0] = 0; 1856 1857 /* ICC(0) without matrix ordering: simply copies fill pattern */ 1858 if (!levels && perm_identity) { 1859 1860 for (i=0; i<am; i++) { 1861 ui[i+1] = ui[i] + ai[i+1] - a->diag[i]; 1862 } 1863 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 1864 cols = uj; 1865 for (i=0; i<am; i++) { 1866 aj = a->j + a->diag[i]; 1867 ncols = ui[i+1] - ui[i]; 1868 for (j=0; j<ncols; j++) *cols++ = *aj++; 1869 } 1870 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 1871 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 1872 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 1873 1874 /* initialization */ 1875 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 1876 1877 /* jl: linked list for storing indices of the pivot rows 1878 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 1879 ierr = PetscMalloc((2*am+1)*sizeof(PetscInt)+2*am*sizeof(PetscInt**),&jl);CHKERRQ(ierr); 1880 il = jl + am; 1881 uj_ptr = (PetscInt**)(il + am); 1882 uj_lvl_ptr = (PetscInt**)(uj_ptr + am); 1883 for (i=0; i<am; i++){ 1884 jl[i] = am; il[i] = 0; 1885 } 1886 1887 /* create and initialize a linked list for storing column indices of the active row k */ 1888 nlnk = am + 1; 1889 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1890 1891 /* initial FreeSpace size is fill*(ai[am]+1) */ 1892 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 1893 current_space = free_space; 1894 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 1895 current_space_lvl = free_space_lvl; 1896 1897 for (k=0; k<am; k++){ /* for each active row k */ 1898 /* initialize lnk by the column indices of row rip[k] of A */ 1899 nzk = 0; 1900 ncols = ai[rip[k]+1] - ai[rip[k]]; 1901 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 1902 ncols_upper = 0; 1903 for (j=0; j<ncols; j++){ 1904 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 1905 if (riip[i] >= k){ /* only take upper triangular entry */ 1906 ajtmp[ncols_upper] = i; 1907 ncols_upper++; 1908 } 1909 } 1910 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1911 nzk += nlnk; 1912 1913 /* update lnk by computing fill-in for each pivot row to be merged in */ 1914 prow = jl[k]; /* 1st pivot row */ 1915 1916 while (prow < k){ 1917 nextprow = jl[prow]; 1918 1919 /* merge prow into k-th row */ 1920 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 1921 jmax = ui[prow+1]; 1922 ncols = jmax-jmin; 1923 i = jmin - ui[prow]; 1924 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 1925 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 1926 j = *(uj - 1); 1927 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 1928 nzk += nlnk; 1929 1930 /* update il and jl for prow */ 1931 if (jmin < jmax){ 1932 il[prow] = jmin; 1933 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 1934 } 1935 prow = nextprow; 1936 } 1937 1938 /* if free space is not available, make more free space */ 1939 if (current_space->local_remaining<nzk) { 1940 i = am - k + 1; /* num of unfactored rows */ 1941 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 1942 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 1943 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 1944 reallocs++; 1945 } 1946 1947 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1948 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 1949 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1950 1951 /* add the k-th row into il and jl */ 1952 if (nzk > 1){ 1953 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 1954 jl[k] = jl[i]; jl[i] = k; 1955 il[k] = ui[k] + 1; 1956 } 1957 uj_ptr[k] = current_space->array; 1958 uj_lvl_ptr[k] = current_space_lvl->array; 1959 1960 current_space->array += nzk; 1961 current_space->local_used += nzk; 1962 current_space->local_remaining -= nzk; 1963 1964 current_space_lvl->array += nzk; 1965 current_space_lvl->local_used += nzk; 1966 current_space_lvl->local_remaining -= nzk; 1967 1968 ui[k+1] = ui[k] + nzk; 1969 } 1970 1971 #if defined(PETSC_USE_INFO) 1972 if (ai[am] != 0) { 1973 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 1974 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 1975 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1976 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 1977 } else { 1978 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 1979 } 1980 #endif 1981 1982 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 1983 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 1984 ierr = PetscFree(jl);CHKERRQ(ierr); 1985 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 1986 1987 /* destroy list of free space and other temporary array(s) */ 1988 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 1989 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 1990 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1991 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1992 1993 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 1994 1995 /* put together the new matrix in MATSEQSBAIJ format */ 1996 1997 b = (Mat_SeqSBAIJ*)(fact)->data; 1998 b->singlemalloc = PETSC_FALSE; 1999 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2000 b->j = uj; 2001 b->i = ui; 2002 b->diag = 0; 2003 b->ilen = 0; 2004 b->imax = 0; 2005 b->row = perm; 2006 b->col = perm; 2007 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2008 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2009 b->icol = iperm; 2010 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2011 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2012 ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2013 b->maxnz = b->nz = ui[am]; 2014 b->free_a = PETSC_TRUE; 2015 b->free_ij = PETSC_TRUE; 2016 2017 (fact)->info.factor_mallocs = reallocs; 2018 (fact)->info.fill_ratio_given = fill; 2019 if (ai[am] != 0) { 2020 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2021 } else { 2022 (fact)->info.fill_ratio_needed = 0.0; 2023 } 2024 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2025 PetscFunctionReturn(0); 2026 } 2027 2028 #undef __FUNCT__ 2029 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ" 2030 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2031 { 2032 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2033 Mat_SeqSBAIJ *b; 2034 PetscErrorCode ierr; 2035 PetscTruth perm_identity; 2036 PetscReal fill = info->fill; 2037 const PetscInt *rip,*riip; 2038 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2039 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2040 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr; 2041 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2042 PetscBT lnkbt; 2043 IS iperm; 2044 2045 PetscFunctionBegin; 2046 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); 2047 /* check whether perm is the identity mapping */ 2048 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2049 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2050 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2051 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2052 2053 /* initialization */ 2054 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2055 ui[0] = 0; 2056 2057 /* jl: linked list for storing indices of the pivot rows 2058 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2059 ierr = PetscMalloc((3*am+1)*sizeof(PetscInt)+am*sizeof(PetscInt**),&jl);CHKERRQ(ierr); 2060 il = jl + am; 2061 cols = il + am; 2062 ui_ptr = (PetscInt**)(cols + am); 2063 for (i=0; i<am; i++){ 2064 jl[i] = am; il[i] = 0; 2065 } 2066 2067 /* create and initialize a linked list for storing column indices of the active row k */ 2068 nlnk = am + 1; 2069 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2070 2071 /* initial FreeSpace size is fill*(ai[am]+1) */ 2072 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2073 current_space = free_space; 2074 2075 for (k=0; k<am; k++){ /* for each active row k */ 2076 /* initialize lnk by the column indices of row rip[k] of A */ 2077 nzk = 0; 2078 ncols = ai[rip[k]+1] - ai[rip[k]]; 2079 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2080 ncols_upper = 0; 2081 for (j=0; j<ncols; j++){ 2082 i = riip[*(aj + ai[rip[k]] + j)]; 2083 if (i >= k){ /* only take upper triangular entry */ 2084 cols[ncols_upper] = i; 2085 ncols_upper++; 2086 } 2087 } 2088 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2089 nzk += nlnk; 2090 2091 /* update lnk by computing fill-in for each pivot row to be merged in */ 2092 prow = jl[k]; /* 1st pivot row */ 2093 2094 while (prow < k){ 2095 nextprow = jl[prow]; 2096 /* merge prow into k-th row */ 2097 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2098 jmax = ui[prow+1]; 2099 ncols = jmax-jmin; 2100 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2101 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2102 nzk += nlnk; 2103 2104 /* update il and jl for prow */ 2105 if (jmin < jmax){ 2106 il[prow] = jmin; 2107 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 2108 } 2109 prow = nextprow; 2110 } 2111 2112 /* if free space is not available, make more free space */ 2113 if (current_space->local_remaining<nzk) { 2114 i = am - k + 1; /* num of unfactored rows */ 2115 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2116 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2117 reallocs++; 2118 } 2119 2120 /* copy data into free space, then initialize lnk */ 2121 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 2122 2123 /* add the k-th row into il and jl */ 2124 if (nzk-1 > 0){ 2125 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2126 jl[k] = jl[i]; jl[i] = k; 2127 il[k] = ui[k] + 1; 2128 } 2129 ui_ptr[k] = current_space->array; 2130 current_space->array += nzk; 2131 current_space->local_used += nzk; 2132 current_space->local_remaining -= nzk; 2133 2134 ui[k+1] = ui[k] + nzk; 2135 } 2136 2137 #if defined(PETSC_USE_INFO) 2138 if (ai[am] != 0) { 2139 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 2140 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2141 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2142 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2143 } else { 2144 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2145 } 2146 #endif 2147 2148 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2149 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2150 ierr = PetscFree(jl);CHKERRQ(ierr); 2151 2152 /* destroy list of free space and other temporary array(s) */ 2153 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2154 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 2155 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2156 2157 /* put together the new matrix in MATSEQSBAIJ format */ 2158 2159 b = (Mat_SeqSBAIJ*)(fact)->data; 2160 b->singlemalloc = PETSC_FALSE; 2161 b->free_a = PETSC_TRUE; 2162 b->free_ij = PETSC_TRUE; 2163 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2164 b->j = uj; 2165 b->i = ui; 2166 b->diag = 0; 2167 b->ilen = 0; 2168 b->imax = 0; 2169 b->row = perm; 2170 b->col = perm; 2171 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2172 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2173 b->icol = iperm; 2174 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2175 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2176 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2177 b->maxnz = b->nz = ui[am]; 2178 2179 (fact)->info.factor_mallocs = reallocs; 2180 (fact)->info.fill_ratio_given = fill; 2181 if (ai[am] != 0) { 2182 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2183 } else { 2184 (fact)->info.fill_ratio_needed = 0.0; 2185 } 2186 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2187 PetscFunctionReturn(0); 2188 } 2189 2190 #undef __FUNCT__ 2191 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_iludt" 2192 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_iludt(Mat A,Vec bb,Vec xx) 2193 { 2194 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2195 PetscErrorCode ierr; 2196 PetscInt n = A->rmap->n; 2197 const PetscInt *ai = a->i,*aj = a->j,*vi; 2198 PetscScalar *x,sum; 2199 const PetscScalar *b; 2200 const MatScalar *aa = a->a,*v; 2201 PetscInt i,nz; 2202 2203 PetscFunctionBegin; 2204 if (!n) PetscFunctionReturn(0); 2205 2206 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 2207 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 2208 2209 /* forward solve the lower triangular */ 2210 x[0] = b[0]; 2211 v = aa; 2212 vi = aj; 2213 for (i=1; i<n; i++) { 2214 nz = ai[i+1] - ai[i]; 2215 sum = b[i]; 2216 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 2217 /* while (nz--) sum -= *v++ * x[*vi++];*/ 2218 v += nz; 2219 vi += nz; 2220 x[i] = sum; 2221 } 2222 2223 /* backward solve the upper triangular */ 2224 v = aa + ai[n+1]; 2225 vi = aj + ai[n+1]; 2226 for (i=n-1; i>=0; i--){ 2227 nz = ai[2*n-i +1] - ai[2*n-i]-1; 2228 sum = x[i]; 2229 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 2230 /* while (nz--) sum -= *v++ * x[*vi++]; */ 2231 v += nz; 2232 vi += nz; vi++; 2233 x[i] = *v++ *sum; /* x[i]=aa[adiag[i]]*sum; v++; */ 2234 } 2235 2236 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 2237 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 2238 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 2239 PetscFunctionReturn(0); 2240 } 2241 2242 #undef __FUNCT__ 2243 #define __FUNCT__ "MatSolve_SeqAIJ_iludt" 2244 PetscErrorCode MatSolve_SeqAIJ_iludt(Mat A,Vec bb,Vec xx) 2245 { 2246 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2247 IS iscol = a->col,isrow = a->row; 2248 PetscErrorCode ierr; 2249 PetscInt i,n=A->rmap->n,*vi,*ai = a->i,*aj = a->j,*adiag=a->diag; 2250 PetscInt nz; 2251 const PetscInt *rout,*cout,*r,*c; 2252 PetscScalar *x,*tmp,*tmps; 2253 const PetscScalar *b; 2254 const MatScalar *aa = a->a,*v; 2255 2256 PetscFunctionBegin; 2257 if (!n) PetscFunctionReturn(0); 2258 2259 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 2260 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 2261 tmp = a->solve_work; 2262 2263 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 2264 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 2265 2266 /* forward solve the lower triangular */ 2267 tmp[0] = b[*r++]; 2268 tmps = tmp; 2269 v = aa; 2270 vi = aj; 2271 for (i=1; i<n; i++) { 2272 nz = ai[i+1] - ai[i]; 2273 tmp[i] = b[*r++]; 2274 PetscSparseDenseMinusDot(tmp[i],tmps,v,vi,nz); 2275 v += nz; vi += nz; 2276 } 2277 2278 /* backward solve the upper triangular */ 2279 v = aa + adiag[n] + 1; 2280 vi = aj + adiag[n] + 1; 2281 for (i=n-1; i>=0; i--){ 2282 nz = adiag[i] - adiag[i+1] - 1; 2283 PetscSparseDenseMinusDot(tmp[i],tmps,v,vi,nz); 2284 x[*c--] = tmp[i] = tmp[i]*aa[adiag[i]]; 2285 v += nz+1; vi += nz+1; 2286 } 2287 2288 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 2289 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 2290 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 2291 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 2292 ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr); 2293 PetscFunctionReturn(0); 2294 } 2295 2296 #undef __FUNCT__ 2297 #define __FUNCT__ "MatILUDTFactor_SeqAIJ" 2298 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact) 2299 { 2300 Mat B = *fact; 2301 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b; 2302 IS isicol; 2303 PetscErrorCode ierr; 2304 const PetscInt *r,*ic; 2305 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag; 2306 PetscInt *bi,*bj,*bdiag,*bdiag_rev; 2307 PetscInt row,nzi,nzi_bl,nzi_bu,*im,dtcount,nzi_al,nzi_au; 2308 PetscInt nlnk,*lnk; 2309 PetscBT lnkbt; 2310 PetscTruth row_identity,icol_identity,both_identity; 2311 MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp; 2312 const PetscInt *ics; 2313 PetscInt j,nz,*pj,*bjtmp,k,ncut,*jtmp; 2314 PetscReal dt=info->dt,shift=info->shiftinblocks; 2315 PetscInt nnz_max; 2316 PetscTruth missing; 2317 2318 PetscFunctionBegin; 2319 /* ------- symbolic factorization, can be reused ---------*/ 2320 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 2321 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 2322 adiag=a->diag; 2323 2324 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 2325 2326 /* bdiag is location of diagonal in factor */ 2327 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 2328 bdiag_rev = bdiag + n+1; 2329 2330 /* allocate row pointers bi */ 2331 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 2332 2333 /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */ 2334 dtcount = (PetscInt)info->dtcount; 2335 if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */ 2336 nnz_max = ai[n]+2*n*dtcount+2; 2337 2338 ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 2339 ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr); 2340 2341 /* put together the new matrix */ 2342 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 2343 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 2344 b = (Mat_SeqAIJ*)(B)->data; 2345 b->free_a = PETSC_TRUE; 2346 b->free_ij = PETSC_TRUE; 2347 b->singlemalloc = PETSC_FALSE; 2348 b->a = ba; 2349 b->j = bj; 2350 b->i = bi; 2351 b->diag = bdiag; 2352 b->ilen = 0; 2353 b->imax = 0; 2354 b->row = isrow; 2355 b->col = iscol; 2356 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 2357 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 2358 b->icol = isicol; 2359 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2360 2361 ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2362 b->maxnz = nnz_max; 2363 2364 (B)->factor = MAT_FACTOR_ILUDT; 2365 (B)->info.factor_mallocs = 0; 2366 (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]); 2367 CHKMEMQ; 2368 /* ------- end of symbolic factorization ---------*/ 2369 2370 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 2371 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 2372 ics = ic; 2373 2374 /* linked list for storing column indices of the active row */ 2375 nlnk = n + 1; 2376 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2377 2378 /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */ 2379 ierr = PetscMalloc((2*n+1)*sizeof(PetscInt),&im);CHKERRQ(ierr); 2380 jtmp = im + n; 2381 /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */ 2382 ierr = PetscMalloc((2*n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 2383 ierr = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr); 2384 vtmp = rtmp + n; 2385 2386 bi[0] = 0; 2387 bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */ 2388 bdiag_rev[n] = bdiag[0]; 2389 bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */ 2390 for (i=0; i<n; i++) { 2391 /* copy initial fill into linked list */ 2392 nzi = 0; /* nonzeros for active row i */ 2393 nzi = ai[r[i]+1] - ai[r[i]]; 2394 if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 2395 nzi_al = adiag[r[i]] - ai[r[i]]; 2396 nzi_au = ai[r[i]+1] - adiag[r[i]] -1; 2397 ajtmp = aj + ai[r[i]]; 2398 ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2399 2400 /* load in initial (unfactored row) */ 2401 aatmp = a->a + ai[r[i]]; 2402 for (j=0; j<nzi; j++) { 2403 rtmp[ics[*ajtmp++]] = *aatmp++; 2404 } 2405 2406 /* add pivot rows into linked list */ 2407 row = lnk[n]; 2408 while (row < i ) { 2409 nzi_bl = bi[row+1] - bi[row] + 1; 2410 bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */ 2411 ierr = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr); 2412 nzi += nlnk; 2413 row = lnk[row]; 2414 } 2415 2416 /* copy data from lnk into jtmp, then initialize lnk */ 2417 ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr); 2418 2419 /* numerical factorization */ 2420 bjtmp = jtmp; 2421 row = *bjtmp++; /* 1st pivot row */ 2422 while ( row < i ) { 2423 pc = rtmp + row; 2424 pv = ba + bdiag[row]; /* 1./(diag of the pivot row) */ 2425 multiplier = (*pc) * (*pv); 2426 *pc = multiplier; 2427 if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */ 2428 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 2429 pv = ba + bdiag[row+1] + 1; 2430 /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */ 2431 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 2432 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 2433 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 2434 } 2435 row = *bjtmp++; 2436 } 2437 2438 /* copy sparse rtmp into contiguous vtmp; separate L and U part */ 2439 diag_tmp = rtmp[i]; /* save diagonal value - may not needed?? */ 2440 nzi_bl = 0; j = 0; 2441 while (jtmp[j] < i){ /* Note: jtmp is sorted */ 2442 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 2443 nzi_bl++; j++; 2444 } 2445 nzi_bu = nzi - nzi_bl -1; 2446 while (j < nzi){ 2447 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 2448 j++; 2449 } 2450 2451 bjtmp = bj + bi[i]; 2452 batmp = ba + bi[i]; 2453 /* apply level dropping rule to L part */ 2454 ncut = nzi_al + dtcount; 2455 if (ncut < nzi_bl){ 2456 ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr); 2457 ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr); 2458 } else { 2459 ncut = nzi_bl; 2460 } 2461 for (j=0; j<ncut; j++){ 2462 bjtmp[j] = jtmp[j]; 2463 batmp[j] = vtmp[j]; 2464 /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */ 2465 } 2466 bi[i+1] = bi[i] + ncut; 2467 nzi = ncut + 1; 2468 2469 /* apply level dropping rule to U part */ 2470 ncut = nzi_au + dtcount; 2471 if (ncut < nzi_bu){ 2472 ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr); 2473 ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr); 2474 } else { 2475 ncut = nzi_bu; 2476 } 2477 nzi += ncut; 2478 2479 /* mark bdiagonal */ 2480 bdiag[i+1] = bdiag[i] - (ncut + 1); 2481 bdiag_rev[n-i-1] = bdiag[i+1]; 2482 bi[2*n - i] = bi[2*n - i +1] - (ncut + 1); 2483 bjtmp = bj + bdiag[i]; 2484 batmp = ba + bdiag[i]; 2485 *bjtmp = i; 2486 *batmp = diag_tmp; /* rtmp[i]; */ 2487 if (*batmp == 0.0) { 2488 *batmp = dt+shift; 2489 /* printf(" row %d add shift %g\n",i,shift); */ 2490 } 2491 *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */ 2492 /* printf(" (%d,%g),",*bjtmp,*batmp); */ 2493 2494 bjtmp = bj + bdiag[i+1]+1; 2495 batmp = ba + bdiag[i+1]+1; 2496 for (k=0; k<ncut; k++){ 2497 bjtmp[k] = jtmp[nzi_bl+1+k]; 2498 batmp[k] = vtmp[nzi_bl+1+k]; 2499 /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */ 2500 } 2501 /* printf("\n"); */ 2502 2503 im[i] = nzi; /* used by PetscLLAddSortedLU() */ 2504 /* 2505 printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]); 2506 printf(" ----------------------------\n"); 2507 */ 2508 } /* for (i=0; i<n; i++) */ 2509 /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */ 2510 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]); 2511 2512 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 2513 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 2514 2515 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2516 ierr = PetscFree(im);CHKERRQ(ierr); 2517 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2518 2519 ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr); 2520 b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n]; 2521 2522 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 2523 ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr); 2524 both_identity = (PetscTruth) (row_identity && icol_identity); 2525 if (row_identity && icol_identity) { 2526 B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_iludt; 2527 } else { 2528 B->ops->solve = MatSolve_SeqAIJ_iludt; 2529 } 2530 2531 B->ops->lufactorsymbolic = MatILUDTFactorSymbolic_SeqAIJ; 2532 B->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ; 2533 B->ops->solveadd = 0; 2534 B->ops->solvetranspose = 0; 2535 B->ops->solvetransposeadd = 0; 2536 B->ops->matsolve = 0; 2537 B->assembled = PETSC_TRUE; 2538 B->preallocated = PETSC_TRUE; 2539 PetscFunctionReturn(0); 2540 } 2541 2542 /* a wraper of MatILUDTFactor_SeqAIJ() */ 2543 #undef __FUNCT__ 2544 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ" 2545 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info) 2546 { 2547 PetscErrorCode ierr; 2548 2549 PetscFunctionBegin; 2550 ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr); 2551 2552 fact->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ; 2553 PetscFunctionReturn(0); 2554 } 2555 2556 /* 2557 same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors 2558 - intend to replace existing MatLUFactorNumeric_SeqAIJ() 2559 */ 2560 #undef __FUNCT__ 2561 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ" 2562 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info) 2563 { 2564 Mat C=fact; 2565 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 2566 IS isrow = b->row,isicol = b->icol; 2567 PetscErrorCode ierr; 2568 const PetscInt *r,*ic,*ics; 2569 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 2570 PetscInt *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj; 2571 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 2572 PetscReal dt=info->dt,shift=info->shiftinblocks; 2573 PetscTruth row_identity, col_identity; 2574 2575 PetscFunctionBegin; 2576 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 2577 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 2578 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 2579 ics = ic; 2580 2581 for (i=0; i<n; i++){ 2582 /* initialize rtmp array */ 2583 nzl = bi[i+1] - bi[i]; /* num of nozeros in L(i,:) */ 2584 bjtmp = bj + bi[i]; 2585 for (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0; 2586 rtmp[i] = 0.0; 2587 nzu = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */ 2588 bjtmp = bj + bdiag[i+1] + 1; 2589 for (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0; 2590 2591 /* load in initial unfactored row of A */ 2592 /* printf("row %d\n",i); */ 2593 nz = ai[r[i]+1] - ai[r[i]]; 2594 ajtmp = aj + ai[r[i]]; 2595 v = aa + ai[r[i]]; 2596 for (j=0; j<nz; j++) { 2597 rtmp[ics[*ajtmp++]] = v[j]; 2598 /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */ 2599 } 2600 /* printf("\n"); */ 2601 2602 /* numerical factorization */ 2603 bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */ 2604 nzl = bi[i+1] - bi[i]; /* num of entries in L(i,:) */ 2605 k = 0; 2606 while (k < nzl){ 2607 row = *bjtmp++; 2608 /* printf(" prow %d\n",row); */ 2609 pc = rtmp + row; 2610 pv = b->a + bdiag[row]; /* 1./(diag of the pivot row) */ 2611 multiplier = (*pc) * (*pv); 2612 *pc = multiplier; 2613 if (PetscAbsScalar(multiplier) > dt){ 2614 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 2615 pv = b->a + bdiag[row+1] + 1; 2616 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 2617 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 2618 /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */ 2619 } 2620 k++; 2621 } 2622 2623 /* finished row so stick it into b->a */ 2624 /* L-part */ 2625 pv = b->a + bi[i] ; 2626 pj = bj + bi[i] ; 2627 nzl = bi[i+1] - bi[i]; 2628 for (j=0; j<nzl; j++) { 2629 pv[j] = rtmp[pj[j]]; 2630 /* printf(" (%d,%g),",pj[j],pv[j]); */ 2631 } 2632 2633 /* diagonal: invert diagonal entries for simplier triangular solves */ 2634 if (rtmp[i] == 0.0) rtmp[i] = dt+shift; 2635 b->a[bdiag[i]] = 1.0/rtmp[i]; 2636 /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */ 2637 2638 /* U-part */ 2639 pv = b->a + bdiag[i+1] + 1; 2640 pj = bj + bdiag[i+1] + 1; 2641 nzu = bdiag[i] - bdiag[i+1] - 1; 2642 for (j=0; j<nzu; j++) { 2643 pv[j] = rtmp[pj[j]]; 2644 /* printf(" (%d,%g),",pj[j],pv[j]); */ 2645 } 2646 /* printf("\n"); */ 2647 } 2648 2649 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2650 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 2651 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 2652 2653 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 2654 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 2655 if (row_identity && col_identity) { 2656 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_iludt; 2657 } else { 2658 C->ops->solve = MatSolve_SeqAIJ_iludt; 2659 } 2660 C->ops->solveadd = 0; 2661 C->ops->solvetranspose = 0; 2662 C->ops->solvetransposeadd = 0; 2663 C->ops->matsolve = 0; 2664 C->assembled = PETSC_TRUE; 2665 C->preallocated = PETSC_TRUE; 2666 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 2667 PetscFunctionReturn(0); 2668 } 2669