/* ========================================================================== */ /* === UMFPACK_qsymbolic ==================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Performs a symbolic factorization. See umfpack_qsymbolic.h and umfpack_symbolic.h for details. Dynamic memory usage: about (3.4nz + 8n + n) integers and n double's as workspace (via UMF_malloc, for a square matrix). All of it is free'd via UMF_free if an error occurs. If successful, the Symbolic object contains 12 to 14 objects allocated by UMF_malloc, with a total size of no more than about 13*n integers. */ #include "umf_internal.h" #include "umf_symbolic_usage.h" #include "umf_colamd.h" #include "umf_set_stats.h" #include "umf_analyze.h" #include "umf_transpose.h" #include "umf_is_permutation.h" #include "umf_malloc.h" #include "umf_free.h" #include "umf_2by2.h" #include "umf_singletons.h" typedef struct /* SWType */ { Int *Front_npivcol ; /* size n_col + 1 */ Int *Front_nrows ; /* size n_col */ Int *Front_ncols ; /* size n_col */ Int *Front_parent ; /* size n_col */ Int *Front_cols ; /* size n_col */ Int *InFront ; /* size n_row */ Int *Ci ; /* size Clen */ Int *Cperm1 ; /* size n_col */ Int *Rperm1 ; /* size n_row */ Int *InvRperm1 ; /* size n_row */ Int *Si ; /* size nz */ Int *Sp ; /* size n_col + 1 */ double *Rs ; /* size n_row */ Int *Rperm_2by2 ; /* size n_row */ } SWType ; PRIVATE void free_work ( SWType *SW ) ; PRIVATE void error ( SymbolicType **Symbolic, SWType *SW ) ; /* worst-case usage for SW object */ #define SYM_WORK_USAGE(n_col,n_row,Clen) \ (DUNITS (Int, Clen) + \ DUNITS (Int, nz) + \ 4 * DUNITS (Int, n_row) + \ 4 * DUNITS (Int, n_col) + \ 2 * DUNITS (Int, n_col + 1) + \ DUNITS (double, n_row)) /* required size of Ci for code that calls UMF_transpose and UMF_analyze below*/ #define UMF_ANALYZE_CLEN(nz,n_row,n_col,nn) \ ((n_col) + MAX ((nz),(n_col)) + 3*(nn)+1 + (n_col)) /* size of an element (in Units), including tuples */ #define ELEMENT_SIZE(r,c) \ (DGET_ELEMENT_SIZE (r, c) + 1 + (r + c) * UNITS (Tuple, 1)) #ifndef NDEBUG PRIVATE Int init_count ; #endif /* ========================================================================== */ /* === do_amd =============================================================== */ /* ========================================================================== */ PRIVATE void do_amd ( Int n, const Int Ap [ ], /* size n+1 */ const Int Ai [ ], /* size nz = Ap [n] */ Int Q [ ], /* output permutation, j = Q [k] */ Int Qinv [ ], /* output inverse permutation, Qinv [j] = k */ Int Sdeg [ ], /* degree of A+A', from AMD_aat */ Int Clen, /* size of Ci */ Int Ci [ ], /* size Ci workspace */ double amd_Control [ ], /* AMD control parameters */ double amd_Info [ ], /* AMD info */ SymbolicType *Symbolic, /* Symbolic object */ double Info [ ] /* UMFPACK info */ ) { if (n == 0) { Symbolic->amd_dmax = 0 ; Symbolic->amd_lunz = 0 ; Info [UMFPACK_SYMMETRIC_LUNZ] = 0 ; Info [UMFPACK_SYMMETRIC_FLOPS] = 0 ; Info [UMFPACK_SYMMETRIC_DMAX] = 0 ; Info [UMFPACK_SYMMETRIC_NDENSE] = 0 ; } else { AMD_1 (n, Ap, Ai, Q, Qinv, Sdeg, Clen, Ci, amd_Control, amd_Info) ; /* return estimates computed from AMD on PA+PA' */ Symbolic->amd_dmax = amd_Info [AMD_DMAX] ; Symbolic->amd_lunz = 2 * amd_Info [AMD_LNZ] + n ; Info [UMFPACK_SYMMETRIC_LUNZ] = Symbolic->amd_lunz ; Info [UMFPACK_SYMMETRIC_FLOPS] = DIV_FLOPS * amd_Info [AMD_NDIV] + MULTSUB_FLOPS * amd_Info [AMD_NMULTSUBS_LU] ; Info [UMFPACK_SYMMETRIC_DMAX] = Symbolic->amd_dmax ; Info [UMFPACK_SYMMETRIC_NDENSE] = amd_Info [AMD_NDENSE] ; Info [UMFPACK_SYMBOLIC_DEFRAG] += amd_Info [AMD_NCMPA] ; } } /* ========================================================================== */ /* === prune_singletons ===================================================== */ /* ========================================================================== */ /* Create the submatrix after removing the n1 singletons. The matrix has * row and column indices in the range 0 to n_row-n1 and 0 to n_col-n1, * respectively. */ PRIVATE Int prune_singletons ( Int n1, Int n_col, const Int Ap [ ], const Int Ai [ ], const double Ax [ ], #ifdef COMPLEX const double Az [ ], #endif Int Cperm1 [ ], Int InvRperm1 [ ], Int Si [ ], Int Sp [ ] #ifndef NDEBUG , Int Rperm1 [ ] , Int n_row #endif ) { Int row, k, pp, p, oldcol, newcol, newrow, nzdiag, do_nzdiag ; #ifdef COMPLEX Int split = SPLIT (Az) ; #endif nzdiag = 0 ; do_nzdiag = (Ax != (double *) NULL) ; #ifndef NDEBUG DEBUGm4 (("Prune : S = A (Cperm1 (n1+1:end), Rperm1 (n1+1:end))\n")) ; for (k = 0 ; k < n_row ; k++) { ASSERT (Rperm1 [k] >= 0 && Rperm1 [k] < n_row) ; ASSERT (InvRperm1 [Rperm1 [k]] == k) ; } #endif /* create the submatrix after removing singletons */ pp = 0 ; for (k = n1 ; k < n_col ; k++) { oldcol = Cperm1 [k] ; newcol = k - n1 ; DEBUG5 (("Prune singletons k "ID" oldcol "ID" newcol "ID": "ID"\n", k, oldcol, newcol, pp)) ; Sp [newcol] = pp ; /* load column pointers */ for (p = Ap [oldcol] ; p < Ap [oldcol+1] ; p++) { row = Ai [p] ; DEBUG5 ((" "ID": row "ID, pp, row)) ; ASSERT (row >= 0 && row < n_row) ; newrow = InvRperm1 [row] - n1 ; ASSERT (newrow < n_row - n1) ; if (newrow >= 0) { DEBUG5 ((" newrow "ID, newrow)) ; Si [pp++] = newrow ; if (do_nzdiag) { /* count the number of truly nonzero entries on the * diagonal of S, excluding entries that are present, * but numerically zero */ if (newrow == newcol) { /* this is the diagonal entry */ #ifdef COMPLEX if (split) { if (SCALAR_IS_NONZERO (Ax [p]) || SCALAR_IS_NONZERO (Az [p])) { nzdiag++ ; } } else { if (SCALAR_IS_NONZERO (Ax [2*p ]) || SCALAR_IS_NONZERO (Ax [2*p+1])) { nzdiag++ ; } } #else if (SCALAR_IS_NONZERO (Ax [p])) { nzdiag++ ; } #endif } } } DEBUG5 (("\n")) ; } } Sp [n_col - n1] = pp ; return (nzdiag) ; } /* ========================================================================== */ /* === combine_ordering ===================================================== */ /* ========================================================================== */ PRIVATE void combine_ordering ( Int n1, Int nempty_col, Int n_col, Int Cperm_init [ ], /* output permutation */ Int Cperm1 [ ], /* singleton and empty column ordering */ Int Qinv [ ] /* Qinv from AMD or COLAMD */ ) { Int k, oldcol, newcol, knew ; /* combine the singleton ordering with Qinv */ #ifndef NDEBUG for (k = 0 ; k < n_col ; k++) { Cperm_init [k] = EMPTY ; } #endif for (k = 0 ; k < n1 ; k++) { DEBUG1 ((ID" Initial singleton: "ID"\n", k, Cperm1 [k])) ; Cperm_init [k] = Cperm1 [k] ; } for (k = n1 ; k < n_col - nempty_col ; k++) { /* this is a non-singleton column */ oldcol = Cperm1 [k] ; /* user's name for this column */ newcol = k - n1 ; /* Qinv's name for this column */ knew = Qinv [newcol] ; /* Qinv's ordering for this column */ knew += n1 ; /* shift order, after singletons */ DEBUG1 ((" k "ID" oldcol "ID" newcol "ID" knew "ID"\n", k, oldcol, newcol, knew)) ; ASSERT (knew >= 0 && knew < n_col - nempty_col) ; ASSERT (Cperm_init [knew] == EMPTY) ; Cperm_init [knew] = oldcol ; } for (k = n_col - nempty_col ; k < n_col ; k++) { Cperm_init [k] = Cperm1 [k] ; } #ifndef NDEBUG { Int *W = (Int *) malloc ((n_col + 1) * sizeof (Int)) ; ASSERT (UMF_is_permutation (Cperm_init, W, n_col, n_col)) ; free (W) ; } #endif } /* ========================================================================== */ /* === UMFPACK_qsymbolic ==================================================== */ /* ========================================================================== */ GLOBAL Int UMFPACK_qsymbolic ( Int n_row, Int n_col, const Int Ap [ ], const Int Ai [ ], const double Ax [ ], #ifdef COMPLEX const double Az [ ], #endif const Int Quser [ ], void **SymbolicHandle, const double Control [UMFPACK_CONTROL], double User_Info [UMFPACK_INFO] ) { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ double knobs [COLAMD_KNOBS], flops, f, r, c, force_fixQ, Info2 [UMFPACK_INFO], drow, dcol, dtail_usage, dlf, duf, dmax_usage, dhead_usage, dlnz, dunz, dmaxfrsize, dClen, dClen_analyze, sym, amd_Info [AMD_INFO], dClen_amd, dr, dc, cr, cc, cp, amd_Control [AMD_CONTROL], stats [2], tol ; double *Info ; Int i, nz, j, newj, status, f1, f2, maxnrows, maxncols, nfr, col, nchains, maxrows, maxcols, p, nb, nn, *Chain_start, *Chain_maxrows, *Chain_maxcols, *Front_npivcol, *Ci, Clen, colamd_stats [COLAMD_STATS], fpiv, n_inner, child, parent, *Link, row, *Front_parent, analyze_compactions, k, chain, is_sym, *Si, *Sp, n2, do_UMF_analyze, fpivcol, fallrows, fallcols, *InFront, *F1, snz, *Front_1strow, f1rows, kk, *Cperm_init, *Rperm_init, newrow, *InvRperm1, *Front_leftmostdesc, Clen_analyze, strategy, Clen_amd, fixQ, prefer_diagonal, nzdiag, nzaat, *Wq, *Sdeg, *Fr_npivcol, nempty, *Fr_nrows, *Fr_ncols, *Fr_parent, *Fr_cols, nempty_row, nempty_col, user_auto_strategy, fail, max_rdeg, head_usage, tail_usage, lnz, unz, esize, *Esize, rdeg, *Cdeg, *Rdeg, *Cperm1, *Rperm1, n1, oldcol, newcol, n1c, n1r, *Rperm_2by2, oldrow, dense_row_threshold, tlen, aggressive, scale, *Rp, *Ri ; SymbolicType *Symbolic ; SWType SWspace, *SW ; #ifndef NDEBUG UMF_dump_start ( ) ; init_count = UMF_malloc_count ; PRINTF (( "**** Debugging enabled (UMFPACK will be exceedingly slow!) *****************\n" )) ; #endif /* ---------------------------------------------------------------------- */ /* get the amount of time used by the process so far */ /* ---------------------------------------------------------------------- */ umfpack_tic (stats) ; /* ---------------------------------------------------------------------- */ /* get control settings and check input parameters */ /* ---------------------------------------------------------------------- */ drow = GET_CONTROL (UMFPACK_DENSE_ROW, UMFPACK_DEFAULT_DENSE_ROW) ; dcol = GET_CONTROL (UMFPACK_DENSE_COL, UMFPACK_DEFAULT_DENSE_COL) ; nb = GET_CONTROL (UMFPACK_BLOCK_SIZE, UMFPACK_DEFAULT_BLOCK_SIZE) ; strategy = GET_CONTROL (UMFPACK_STRATEGY, UMFPACK_DEFAULT_STRATEGY) ; tol = GET_CONTROL (UMFPACK_2BY2_TOLERANCE, UMFPACK_DEFAULT_2BY2_TOLERANCE) ; scale = GET_CONTROL (UMFPACK_SCALE, UMFPACK_DEFAULT_SCALE) ; force_fixQ = GET_CONTROL (UMFPACK_FIXQ, UMFPACK_DEFAULT_FIXQ) ; AMD_defaults (amd_Control) ; amd_Control [AMD_DENSE] = GET_CONTROL (UMFPACK_AMD_DENSE, UMFPACK_DEFAULT_AMD_DENSE) ; aggressive = (GET_CONTROL (UMFPACK_AGGRESSIVE, UMFPACK_DEFAULT_AGGRESSIVE) != 0) ; amd_Control [AMD_AGGRESSIVE] = aggressive ; nb = MAX (2, nb) ; nb = MIN (nb, MAXNB) ; ASSERT (nb >= 0) ; if (nb % 2 == 1) nb++ ; /* make sure nb is even */ DEBUG0 (("UMFPACK_qsymbolic: nb = "ID" aggressive = "ID"\n", nb, aggressive)) ; tol = MAX (0.0, MIN (tol, 1.0)) ; if (scale != UMFPACK_SCALE_NONE && scale != UMFPACK_SCALE_MAX) { scale = UMFPACK_DEFAULT_SCALE ; } if (User_Info != (double *) NULL) { /* return Info in user's array */ Info = User_Info ; } else { /* no Info array passed - use local one instead */ Info = Info2 ; } /* clear all of Info */ for (i = 0 ; i < UMFPACK_INFO ; i++) { Info [i] = EMPTY ; } nn = MAX (n_row, n_col) ; n_inner = MIN (n_row, n_col) ; Info [UMFPACK_STATUS] = UMFPACK_OK ; Info [UMFPACK_NROW] = n_row ; Info [UMFPACK_NCOL] = n_col ; Info [UMFPACK_SIZE_OF_UNIT] = (double) (sizeof (Unit)) ; Info [UMFPACK_SIZE_OF_INT] = (double) (sizeof (int)) ; Info [UMFPACK_SIZE_OF_LONG] = (double) (sizeof (UF_long)) ; Info [UMFPACK_SIZE_OF_POINTER] = (double) (sizeof (void *)) ; Info [UMFPACK_SIZE_OF_ENTRY] = (double) (sizeof (Entry)) ; Info [UMFPACK_SYMBOLIC_DEFRAG] = 0 ; if (!Ai || !Ap || !SymbolicHandle) { Info [UMFPACK_STATUS] = UMFPACK_ERROR_argument_missing ; return (UMFPACK_ERROR_argument_missing) ; } *SymbolicHandle = (void *) NULL ; if (n_row <= 0 || n_col <= 0) /* n_row, n_col must be > 0 */ { Info [UMFPACK_STATUS] = UMFPACK_ERROR_n_nonpositive ; return (UMFPACK_ERROR_n_nonpositive) ; } nz = Ap [n_col] ; DEBUG0 (("n_row "ID" n_col "ID" nz "ID"\n", n_row, n_col, nz)) ; Info [UMFPACK_NZ] = nz ; if (nz < 0) { Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_matrix ; return (UMFPACK_ERROR_invalid_matrix) ; } /* ---------------------------------------------------------------------- */ /* get the requested strategy */ /* ---------------------------------------------------------------------- */ if (n_row != n_col) { /* if the matrix is rectangular, the only available strategy is * unsymmetric */ strategy = UMFPACK_STRATEGY_UNSYMMETRIC ; DEBUGm3 (("Rectangular: forcing unsymmetric strategy\n")) ; } if (strategy < UMFPACK_STRATEGY_AUTO || strategy > UMFPACK_STRATEGY_SYMMETRIC) { /* unrecognized strategy */ strategy = UMFPACK_STRATEGY_AUTO ; } if (Quser != (Int *) NULL) { /* when the user provides Q, only symmetric and unsymmetric strategies * are available */ if (strategy == UMFPACK_STRATEGY_2BY2) { strategy = UMFPACK_STRATEGY_SYMMETRIC ; } if (strategy != UMFPACK_STRATEGY_SYMMETRIC) { strategy = UMFPACK_STRATEGY_UNSYMMETRIC ; } } user_auto_strategy = (strategy == UMFPACK_STRATEGY_AUTO) ; /* ---------------------------------------------------------------------- */ /* determine amount of memory required for UMFPACK_symbolic */ /* ---------------------------------------------------------------------- */ /* The size of Clen required for UMF_colamd is always larger than */ /* UMF_analyze, but the max is included here in case that changes in */ /* future versions. */ /* This is about 2.2*nz + 9*n_col + 6*n_row, or nz/5 + 13*n_col + 6*n_row, * whichever is bigger. For square matrices, it works out to * 2.2nz + 15n, or nz/5 + 19n, whichever is bigger (typically 2.2nz+15n). */ dClen = UMF_COLAMD_RECOMMENDED ((double) nz, (double) n_row, (double) n_col) ; /* This is defined above, as max (nz,n_col) + 3*nn+1 + 2*n_col, where * nn = max (n_row,n_col). It is always smaller than the space required * for colamd or amd. */ dClen_analyze = UMF_ANALYZE_CLEN ((double) nz, (double) n_row, (double) n_col, (double) nn) ; dClen = MAX (dClen, dClen_analyze) ; /* The space for AMD can be larger than what's required for colamd: */ dClen_amd = 2.4 * (double) nz + 8 * (double) n_inner ; /* additional space for the 2-by-2 strategy */ dClen_amd += (double) MAX (nn, nz) ; dClen = MAX (dClen, dClen_amd) ; /* worst case total memory usage for UMFPACK_symbolic (revised below) */ Info [UMFPACK_SYMBOLIC_PEAK_MEMORY] = SYM_WORK_USAGE (n_col, n_row, dClen) + UMF_symbolic_usage (n_row, n_col, n_col, n_col, n_col, TRUE) ; if (INT_OVERFLOW (dClen * sizeof (Int))) { /* :: int overflow, Clen too large :: */ /* Problem is too large for array indexing (Ci [i]) with an Int i. */ /* Cannot even analyze the problem to determine upper bounds on */ /* memory usage. Need to use the UF_long version, umfpack_*l_*. */ DEBUGm4 (("out of memory: symbolic int overflow\n")) ; Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; return (UMFPACK_ERROR_out_of_memory) ; } /* repeat the size calculations, in integers */ Clen = UMF_COLAMD_RECOMMENDED (nz, n_row, n_col) ; Clen_analyze = UMF_ANALYZE_CLEN (nz, n_row, n_col, nn) ; Clen = MAX (Clen, Clen_analyze) ; Clen_amd = 2.4 * nz + 8 * n_inner ; Clen_amd += MAX (nn, nz) ; /* for Ri, in UMF_2by2 */ Clen = MAX (Clen, Clen_amd) ; /* ---------------------------------------------------------------------- */ /* allocate the first part of the Symbolic object (header and Cperm_init) */ /* ---------------------------------------------------------------------- */ /* (1) Five calls to UMF_malloc are made, for a total space of * 2 * (n_row + n_col) + 4 integers + sizeof (SymbolicType). * sizeof (SymbolicType) is a small constant. This space is part of the * Symbolic object and is not freed unless an error occurs. If A is square * then this is about 4*n integers. */ Symbolic = (SymbolicType *) UMF_malloc (1, sizeof (SymbolicType)) ; if (!Symbolic) { /* If we fail here, Symbolic is NULL and thus it won't be */ /* dereferenced by UMFPACK_free_symbolic, as called by error ( ). */ DEBUGm4 (("out of memory: symbolic object\n")) ; Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; error (&Symbolic, (SWType *) NULL) ; return (UMFPACK_ERROR_out_of_memory) ; } /* We now know that Symbolic has been allocated */ Symbolic->valid = 0 ; Symbolic->Chain_start = (Int *) NULL ; Symbolic->Chain_maxrows = (Int *) NULL ; Symbolic->Chain_maxcols = (Int *) NULL ; Symbolic->Front_npivcol = (Int *) NULL ; Symbolic->Front_parent = (Int *) NULL ; Symbolic->Front_1strow = (Int *) NULL ; Symbolic->Front_leftmostdesc = (Int *) NULL ; Symbolic->Esize = (Int *) NULL ; Symbolic->esize = 0 ; Symbolic->Cperm_init = (Int *) UMF_malloc (n_col+1, sizeof (Int)) ; Symbolic->Rperm_init = (Int *) UMF_malloc (n_row+1, sizeof (Int)) ; Symbolic->Cdeg = (Int *) UMF_malloc (n_col+1, sizeof (Int)) ; Symbolic->Rdeg = (Int *) UMF_malloc (n_row+1, sizeof (Int)) ; Symbolic->Diagonal_map = (Int *) NULL ; Cperm_init = Symbolic->Cperm_init ; Rperm_init = Symbolic->Rperm_init ; Cdeg = Symbolic->Cdeg ; Rdeg = Symbolic->Rdeg ; if (!Cperm_init || !Rperm_init || !Cdeg || !Rdeg) { DEBUGm4 (("out of memory: symbolic perm\n")) ; Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; error (&Symbolic, (SWType *) NULL) ; return (UMFPACK_ERROR_out_of_memory) ; } Symbolic->n_row = n_row ; Symbolic->n_col = n_col ; Symbolic->nz = nz ; Symbolic->nb = nb ; /* ---------------------------------------------------------------------- */ /* check user's input permutation */ /* ---------------------------------------------------------------------- */ if (Quser != (Int *) NULL) { /* use Cperm_init as workspace to check input permutation */ if (!UMF_is_permutation (Quser, Cperm_init, n_col, n_col)) { Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_permutation ; error (&Symbolic, (SWType *) NULL) ; return (UMFPACK_ERROR_invalid_permutation) ; } } /* ---------------------------------------------------------------------- */ /* allocate workspace */ /* ---------------------------------------------------------------------- */ /* (2) Eleven calls to UMF_malloc are made, for workspace of size * Clen + nz + 7*n_col + 2*n_row + 2 integers. Clen is the larger of * MAX (2*nz, 4*n_col) + 8*n_col + 6*n_row + n_col + nz/5 and * 2.4*nz + 8 * MIN (n_row, n_col) + MAX (n_row, n_col, nz) * If A is square and non-singular, then Clen is * MAX (MAX (2*nz, 4*n) + 7*n + nz/5, 3.4*nz) + 8*n * If A has at least 4*n nonzeros then Clen is * MAX (2.2*nz + 7*n, 3.4*nz) + 8*n * If A has at least (7/1.2)*n nonzeros, (about 5.8*n), then Clen is * 3.4*nz + 8*n * This space will be free'd when this routine finishes. * * Total space thus far is about 3.4nz + 12n integers. * For the double precision, 32-bit integer version, the user's matrix * requires an equivalent space of 3*nz + n integers. So this space is just * slightly larger than the user's input matrix (including the numerical * values themselves). */ SW = &SWspace ; /* used for UMFPACK_symbolic only */ /* Note that SW->Front_* does not include the dummy placeholder front. */ /* This space is accounted for by the SYM_WORK_USAGE macro. */ /* this is free'd early */ SW->Si = (Int *) UMF_malloc (nz, sizeof (Int)) ; SW->Sp = (Int *) UMF_malloc (n_col + 1, sizeof (Int)) ; SW->InvRperm1 = (Int *) UMF_malloc (n_row, sizeof (Int)) ; SW->Cperm1 = (Int *) UMF_malloc (n_col, sizeof (Int)) ; /* this is free'd late */ SW->Ci = (Int *) UMF_malloc (Clen, sizeof (Int)) ; SW->Front_npivcol = (Int *) UMF_malloc (n_col + 1, sizeof (Int)) ; SW->Front_nrows = (Int *) UMF_malloc (n_col, sizeof (Int)) ; SW->Front_ncols = (Int *) UMF_malloc (n_col, sizeof (Int)) ; SW->Front_parent = (Int *) UMF_malloc (n_col, sizeof (Int)) ; SW->Front_cols = (Int *) UMF_malloc (n_col, sizeof (Int)) ; SW->Rperm1 = (Int *) UMF_malloc (n_row, sizeof (Int)) ; SW->InFront = (Int *) UMF_malloc (n_row, sizeof (Int)) ; /* this is allocated later, and free'd after Cperm1 but before Ci */ SW->Rperm_2by2 = (Int *) NULL ; /* will be nn Int's */ /* this is allocated last, and free'd first */ SW->Rs = (double *) NULL ; /* will be n_row double's */ Ci = SW->Ci ; Fr_npivcol = SW->Front_npivcol ; Fr_nrows = SW->Front_nrows ; Fr_ncols = SW->Front_ncols ; Fr_parent = SW->Front_parent ; Fr_cols = SW->Front_cols ; Cperm1 = SW->Cperm1 ; Rperm1 = SW->Rperm1 ; Si = SW->Si ; Sp = SW->Sp ; InvRperm1 = SW->InvRperm1 ; Rperm_2by2 = (Int *) NULL ; InFront = SW->InFront ; if (!Ci || !Fr_npivcol || !Fr_nrows || !Fr_ncols || !Fr_parent || !Fr_cols || !Cperm1 || !Rperm1 || !Si || !Sp || !InvRperm1 || !InFront) { DEBUGm4 (("out of memory: symbolic work\n")) ; Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; error (&Symbolic, SW) ; return (UMFPACK_ERROR_out_of_memory) ; } DEBUG0 (("Symbolic UMF_malloc_count - init_count = "ID"\n", UMF_malloc_count - init_count)) ; ASSERT (UMF_malloc_count == init_count + 17) ; /* ---------------------------------------------------------------------- */ /* find the row and column singletons */ /* ---------------------------------------------------------------------- */ /* [ use first nz + n_row + MAX (n_row, n_col) entries in Ci as workspace, * and use Rperm_init as workspace */ ASSERT (Clen >= nz + n_row + MAX (n_row, n_col)) ; status = UMF_singletons (n_row, n_col, Ap, Ai, Quser, strategy, Cdeg, Cperm1, Rdeg, Rperm1, InvRperm1, &n1, &n1c, &n1r, &nempty_col, &nempty_row, &is_sym, &max_rdeg, /* workspace: */ Rperm_init, Ci, Ci + nz, Ci + nz + n_row) ; /* ] done using Rperm_init and Ci as workspace */ /* InvRperm1 is now the inverse of Rperm1 */ if (status != UMFPACK_OK) { DEBUGm4 (("matrix invalid: UMF_singletons\n")) ; Info [UMFPACK_STATUS] = status ; error (&Symbolic, SW) ; return (status) ; } Info [UMFPACK_NEMPTY_COL] = nempty_col ; Info [UMFPACK_NEMPTY_ROW] = nempty_row ; Info [UMFPACK_NDENSE_COL] = 0 ; /* # dense rows/cols recomputed below */ Info [UMFPACK_NDENSE_ROW] = 0 ; Info [UMFPACK_COL_SINGLETONS] = n1c ; Info [UMFPACK_ROW_SINGLETONS] = n1r ; Info [UMFPACK_S_SYMMETRIC] = is_sym ; nempty = MIN (nempty_col, nempty_row) ; Symbolic->nempty_row = nempty_row ; Symbolic->nempty_col = nempty_col ; /* UMF_singletons has verified that the user's input matrix is valid */ ASSERT (AMD_valid (n_row, n_col, Ap, Ai) == AMD_OK) ; Symbolic->n1 = n1 ; Symbolic->nempty = nempty ; ASSERT (n1 <= n_inner) ; n2 = nn - n1 - nempty ; dense_row_threshold = UMFPACK_DENSE_DEGREE_THRESHOLD (drow, n_col - n1 - nempty_col) ; Symbolic->dense_row_threshold = dense_row_threshold ; if (!is_sym) { /* either the pruned submatrix rectangular, or it is square and * Rperm [n1 .. n-nempty-1] is not the same as Cperm [n1 .. n-nempty-1]. * Switch to the unsymmetric strategy, ignoring user-requested * strategy. */ strategy = UMFPACK_STRATEGY_UNSYMMETRIC ; DEBUGm4 (("Strategy: Unsymmetric singletons\n")) ; } /* ---------------------------------------------------------------------- */ /* determine symmetry, nzdiag, and degrees of S+S' */ /* ---------------------------------------------------------------------- */ /* S is the matrix obtained after removing singletons * = A (Cperm1 [n1..n_col-nempty_col-1], Rperm1 [n1..n_row-nempty_row-1]) */ Wq = Rperm_init ; /* use Rperm_init as workspace for Wq [ */ Sdeg = Cperm_init ; /* use Cperm_init as workspace for Sdeg [ */ sym = EMPTY ; nzaat = EMPTY ; nzdiag = EMPTY ; for (i = 0 ; i < AMD_INFO ; i++) { amd_Info [i] = EMPTY ; } if (strategy != UMFPACK_STRATEGY_UNSYMMETRIC) { /* This also determines the degree of each node in S+S' (Sdeg), which * is needed by the 2-by-2 strategy, the symmetry of S, and the number * of nonzeros on the diagonal of S. */ ASSERT (n_row == n_col) ; ASSERT (nempty_row == nempty_col) ; /* get the count of nonzeros on the diagonal of S, excluding explicitly * zero entries. nzdiag = amd_Info [AMD_NZDIAG] counts the zero entries * in S. */ nzdiag = prune_singletons (n1, nn, Ap, Ai, Ax, #ifdef COMPLEX Az, #endif Cperm1, InvRperm1, Si, Sp #ifndef NDEBUG , Rperm1, nn #endif ) ; /* use Ci as workspace to sort S into R, if needed [ */ if (Quser != (Int *) NULL) { /* need to sort the columns of S first */ Rp = Ci ; Ri = Ci + (n_row) + 1 ; (void) UMF_transpose (n2, n2, Sp, Si, (double *) NULL, (Int *) NULL, (Int *) NULL, 0, Rp, Ri, (double *) NULL, Wq, FALSE #ifdef COMPLEX , (double *) NULL, (double *) NULL, FALSE #endif ) ; } else { /* S already has sorted columns */ Rp = Sp ; Ri = Si ; } ASSERT (AMD_valid (n2, n2, Rp, Ri) == AMD_OK) ; nzaat = AMD_aat (n2, Rp, Ri, Sdeg, Wq, amd_Info) ; sym = amd_Info [AMD_SYMMETRY] ; Info [UMFPACK_N2] = n2 ; /* nzdiag = amd_Info [AMD_NZDIAG] counts the zero entries of S too */ /* done using Ci as workspace to sort S into R ] */ #ifndef NDEBUG for (k = 0 ; k < n2 ; k++) { ASSERT (Sdeg [k] >= 0 && Sdeg [k] < n2) ; } ASSERT (Sp [n2] - n2 <= nzaat && nzaat <= 2 * Sp [n2]) ; DEBUG0 (("Explicit zeros: "ID" %g\n", nzdiag, amd_Info [AMD_NZDIAG])) ; #endif } /* get statistics from amd_aat, if computed */ Symbolic->sym = sym ; Symbolic->nzaat = nzaat ; Symbolic->nzdiag = nzdiag ; Symbolic->amd_dmax = EMPTY ; Info [UMFPACK_PATTERN_SYMMETRY] = sym ; Info [UMFPACK_NZ_A_PLUS_AT] = nzaat ; Info [UMFPACK_NZDIAG] = nzdiag ; /* ---------------------------------------------------------------------- */ /* determine the initial strategy based on symmetry and nnz (diag (S)) */ /* ---------------------------------------------------------------------- */ if (strategy == UMFPACK_STRATEGY_AUTO) { if (sym < 0.10) { /* highly unsymmetric: use the unsymmetric strategy */ strategy = UMFPACK_STRATEGY_UNSYMMETRIC ; DEBUGm4 (("Strategy: select unsymmetric\n")) ; } else if (sym >= 0.7 && nzdiag == n2) { /* mostly symmetric, zero-free diagonal: use symmetric strategy */ strategy = UMFPACK_STRATEGY_SYMMETRIC ; DEBUGm4 (("Strategy: select symmetric\n")) ; } else { /* Evaluate the symmetric 2-by-2 strategy, and select it, or * the unsymmetric strategy if the 2-by-2 strategy doesn't look * promising. */ strategy = UMFPACK_STRATEGY_2BY2 ; DEBUGm4 (("Strategy: try 2-by-2\n")) ; } } /* ---------------------------------------------------------------------- */ /* try the 2-by-2 strategy */ /* ---------------------------------------------------------------------- */ /* (3) If the 2-by-2 strategy is attempted, additional workspace of size * nn integers and nn double's is allocated, where nn = n_row = n_col. * The real workspace is immediately free'd. The integer workspace of * size nn remains until the end of umfpack_qsymbolic. */ /* If the resulting matrix S (Rperm_2by2, :) is too unsymmetric, then the * unsymmetric strategy will be used instead. */ if (strategy == UMFPACK_STRATEGY_2BY2) { double sym2 ; Int *Blen, *W, nz_papat, nzd2, nweak, unmatched, Clen3 ; /* ------------------------------------------------------------------ */ /* get workspace for UMF_2by2 */ /* ------------------------------------------------------------------ */ ASSERT (n_row == n_col && nn == n_row) ; #ifndef NDEBUG for (k = 0 ; k < n2 ; k++) { ASSERT (Sdeg [k] >= 0 && Sdeg [k] < n2) ; } #endif /* allocate Rperm_2by2 */ SW->Rperm_2by2 = (Int *) UMF_malloc (nn, sizeof (Int)) ; Rperm_2by2 = SW->Rperm_2by2 ; if (Rperm_2by2 == (Int *) NULL) { DEBUGm4 (("out of memory: Rperm_2by2\n")) ; Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; error (&Symbolic, SW) ; return (UMFPACK_ERROR_out_of_memory) ; } /* allocate Ri from the tail end of Ci [ */ Clen3 = Clen - (MAX (nn, nz) + 1) ; Ri = Ci + Clen3 ; ASSERT (Clen3 >= nz) ; /* space required for UMF_2by2 */ /* use Fr_* as workspace for Rp, Blen, and W [ */ Rp = Fr_npivcol ; Blen = Fr_ncols ; W = Fr_cols ; if (scale != UMFPACK_SCALE_NONE) { SW->Rs = (double *) UMF_malloc (nn, sizeof (double)) ; if (SW->Rs == (double *) NULL) { DEBUGm4 (("out of memory: scale factors for 2-by-2\n")) ; Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; error (&Symbolic, SW) ; return (UMFPACK_ERROR_out_of_memory) ; } } /* ------------------------------------------------------------------ */ /* find the 2-by-2 row permutation */ /* ------------------------------------------------------------------ */ /* find a row permutation Rperm_2by2 such that S (Rperm_2by2, :) * has a healthy diagonal */ UMF_2by2 (nn, Ap, Ai, Ax, #ifdef COMPLEX Az, #endif tol, scale, Cperm1, #ifndef NDEBUG Rperm1, #endif InvRperm1, n1, nempty, Sdeg, Rperm_2by2, &nweak, &unmatched, Ri, Rp, SW->Rs, Blen, W, Ci, Wq) ; DEBUGm3 (("2by2: nweak "ID" unmatched "ID"\n", nweak, unmatched)) ; Info [UMFPACK_2BY2_NWEAK] = nweak ; Info [UMFPACK_2BY2_UNMATCHED] = unmatched ; SW->Rs = (double *) UMF_free ((void *) SW->Rs) ; /* R = S (Rperm_2by2,:)' */ (void) UMF_transpose (n2, n2, Sp, Si, (double *) NULL, Rperm_2by2, (Int *) NULL, 0, Rp, Ri, (double *) NULL, W, FALSE #ifdef COMPLEX , (double *) NULL, (double *) NULL, FALSE #endif ) ; ASSERT (AMD_valid (n2, n2, Rp, Ri) == AMD_OK) ; /* contents of Si and Sp no longer needed, but the space is * still needed */ /* ------------------------------------------------------------------ */ /* find symmetry of S (Rperm_2by2, :)', and prepare to order with AMD */ /* ------------------------------------------------------------------ */ for (i = 0 ; i < AMD_INFO ; i++) { amd_Info [i] = EMPTY ; } nz_papat = AMD_aat (n2, Rp, Ri, Sdeg, Wq, amd_Info) ; sym2 = amd_Info [AMD_SYMMETRY] ; nzd2 = amd_Info [AMD_NZDIAG] ; Info [UMFPACK_2BY2_PATTERN_SYMMETRY] = sym2 ; Info [UMFPACK_2BY2_NZ_PA_PLUS_PAT] = nz_papat ; Info [UMFPACK_2BY2_NZDIAG] = nzd2 ; DEBUG0 (("2by2: sym2 %g nzd2 "ID" n2 "ID"\n", sym2, nzd2, n2)) ; /* ------------------------------------------------------------------ */ /* evaluate the 2-by-2 results */ /* ------------------------------------------------------------------ */ if (user_auto_strategy) { if ((sym2 > 1.1 * sym) && (nzd2 > 0.9 * n2)) { /* 2-by-2 made it much more symmetric */ DEBUGm4 (("eval Strategy 2by2: much more symmetric: 2by2\n")) ; strategy = UMFPACK_STRATEGY_2BY2 ; } else if (sym2 < 0.7 * sym) { /* 2-by-2 made it much more unsymmetric */ DEBUGm4 (("eval Strategy 2by2: much more UNsymmetric:unsym\n")); strategy = UMFPACK_STRATEGY_UNSYMMETRIC ; } else if (sym2 < 0.25) { DEBUGm4 (("eval Strategy 2by2: is UNsymmetric: unsym\n")); strategy = UMFPACK_STRATEGY_UNSYMMETRIC ; } else if (sym2 >= 0.51) { DEBUGm4 (("eval Strategy 2by2: sym2 >= 0.51: 2by2\n")) ; strategy = UMFPACK_STRATEGY_2BY2 ; } else if (sym2 >= 0.999 * sym) { /* 2-by-2 improved symmetry, or made it only slightly worse */ DEBUGm4 (("eval Strategy 2by2: sym2 >= 0.999 sym: 2by2\n")) ; strategy = UMFPACK_STRATEGY_2BY2 ; } else { /* can't decide what to do, so pick the unsymmetric strategy */ DEBUGm4 (("eval Strategy 2by2: punt: unsym\n")); strategy = UMFPACK_STRATEGY_UNSYMMETRIC ; } } /* ------------------------------------------------------------------ */ /* if the 2-by-2 strategy is selected: */ /* ------------------------------------------------------------------ */ if (strategy == UMFPACK_STRATEGY_2BY2) { if (Quser == (Int *) NULL) { /* 2-by-2 strategy is successful */ /* compute amd (S) */ Int *Qinv = Fr_npivcol ; ASSERT (Clen3 >= (nz_papat + nz_papat/5 + nn) + 7*nn) ; do_amd (n2, Rp, Ri, Wq, Qinv, Sdeg, Clen3, Ci, amd_Control, amd_Info, Symbolic, Info) ; /* combine the singleton ordering and the AMD ordering */ combine_ordering (n1, nempty, nn, Cperm_init, Cperm1, Qinv) ; } /* fix Rperm_2by2 to reflect A, not S */ for (k = 0 ; k < n1 ; k++) { oldcol = Cperm1 [k] ; i = k ; oldrow = Rperm1 [k] ; W [oldcol] = oldrow ; } for (k = n1 ; k < nn - nempty ; k++) { oldcol = Cperm1 [k] ; i = Rperm_2by2 [k - n1] + n1 ; oldrow = Rperm1 [i] ; W [oldcol] = oldrow ; } for (k = nn - nempty ; k < nn ; k++) { oldcol = Cperm1 [k] ; i = k ; oldrow = Rperm1 [k] ; W [oldcol] = oldrow ; } for (k = 0 ; k < nn ; k++) { Rperm_2by2 [k] = W [k] ; } /* Now, the "diagonal" entry in oldcol (where oldcol is the user's * name for a column, is the entry in row oldrow (where oldrow is * the user's name for a row, and oldrow = Rperm_2by2 [oldcol] */ } /* Fr_* no longer needed for Rp, Blen, W ] */ } /* ---------------------------------------------------------------------- */ /* finalize the strategy, including fixQ and prefer_diagonal */ /* ---------------------------------------------------------------------- */ if (strategy == UMFPACK_STRATEGY_SYMMETRIC) { /* use given Quser or AMD (A+A'), fix Q during factorization, * prefer diagonal */ DEBUG0 (("\nStrategy: symmetric\n")) ; ASSERT (n_row == n_col) ; Symbolic->ordering = UMFPACK_ORDERING_AMD ; fixQ = TRUE ; prefer_diagonal = TRUE ; } else if (strategy == UMFPACK_STRATEGY_2BY2) { /* use Q = given Quser or Q = AMD (PA+PA'), fix Q during factorization, * prefer diagonal, and factorize PAQ, where P is found by UMF_2by2. */ DEBUG0 (("\nStrategy: symmetric 2-by-2\n")) ; ASSERT (n_row == n_col) ; Symbolic->ordering = UMFPACK_ORDERING_AMD ; fixQ = TRUE ; prefer_diagonal = TRUE ; } else { /* use given Quser or COLAMD (A), refine Q during factorization, * no diagonal preference */ ASSERT (strategy == UMFPACK_STRATEGY_UNSYMMETRIC) ; DEBUG0 (("\nStrategy: unsymmetric\n")) ; Symbolic->ordering = UMFPACK_ORDERING_COLAMD ; fixQ = FALSE ; prefer_diagonal = FALSE ; } if (Quser != (Int *) NULL) { Symbolic->ordering = UMFPACK_ORDERING_GIVEN ; } if (force_fixQ > 0) { fixQ = TRUE ; DEBUG0 (("Force fixQ true\n")) ; } else if (force_fixQ < 0) { fixQ = FALSE ; DEBUG0 (("Force fixQ false\n")) ; } DEBUG0 (("Strategy: ordering: "ID"\n", Symbolic->ordering)) ; DEBUG0 (("Strategy: fixQ: "ID"\n", fixQ)) ; DEBUG0 (("Strategy: prefer diag "ID"\n", prefer_diagonal)) ; /* get statistics from amd_aat, if computed */ Symbolic->strategy = strategy ; Symbolic->fixQ = fixQ ; Symbolic->prefer_diagonal = prefer_diagonal ; Info [UMFPACK_STRATEGY_USED] = strategy ; Info [UMFPACK_ORDERING_USED] = Symbolic->ordering ; Info [UMFPACK_QFIXED] = fixQ ; Info [UMFPACK_DIAG_PREFERRED] = prefer_diagonal ; /* ---------------------------------------------------------------------- */ /* get the AMD ordering for the symmetric strategy */ /* ---------------------------------------------------------------------- */ if (strategy == UMFPACK_STRATEGY_SYMMETRIC && Quser == (Int *) NULL) { /* symmetric strategy for a matrix with mostly symmetric pattern */ Int *Qinv = Fr_npivcol ; ASSERT (n_row == n_col && nn == n_row) ; ASSERT (Clen >= (nzaat + nzaat/5 + nn) + 7*nn) ; do_amd (n2, Sp, Si, Wq, Qinv, Sdeg, Clen, Ci, amd_Control, amd_Info, Symbolic, Info) ; /* combine the singleton ordering and the AMD ordering */ combine_ordering (n1, nempty, nn, Cperm_init, Cperm1, Qinv) ; } /* Sdeg no longer needed ] */ /* done using Rperm_init as workspace for Wq ] */ /* Contents of Si and Sp no longer needed, but the space is still needed */ /* ---------------------------------------------------------------------- */ /* use the user's input column ordering (already in Cperm1) */ /* ---------------------------------------------------------------------- */ if (Quser != (Int *) NULL) { for (k = 0 ; k < n_col ; k++) { Cperm_init [k] = Cperm1 [k] ; } } /* ---------------------------------------------------------------------- */ /* use COLAMD to order the matrix */ /* ---------------------------------------------------------------------- */ if (strategy == UMFPACK_STRATEGY_UNSYMMETRIC && Quser == (Int *) NULL) { /* ------------------------------------------------------------------ */ /* copy the matrix into colamd workspace (colamd destroys its input) */ /* ------------------------------------------------------------------ */ /* C = A (Cperm1 (n1+1:end), Rperm1 (n1+1:end)), where Ci is used as * the row indices and Cperm_init (on input) is used as the column * pointers. */ (void) prune_singletons (n1, n_col, Ap, Ai, (double *) NULL, #ifdef COMPLEX (double *) NULL, #endif Cperm1, InvRperm1, Ci, Cperm_init #ifndef NDEBUG , Rperm1, n_row #endif ) ; /* ------------------------------------------------------------------ */ /* set UMF_colamd defaults */ /* ------------------------------------------------------------------ */ UMF_colamd_set_defaults (knobs) ; knobs [COLAMD_DENSE_ROW] = drow ; knobs [COLAMD_DENSE_COL] = dcol ; knobs [COLAMD_AGGRESSIVE] = aggressive ; /* ------------------------------------------------------------------ */ /* check input matrix and find the initial column pre-ordering */ /* ------------------------------------------------------------------ */ /* NOTE: umf_colamd is not given any original empty rows or columns. * Those have already been removed via prune_singletons, above. The * umf_colamd routine has been modified to assume that all rows and * columns have at least one entry in them. It will break if it is * given empty rows or columns (an assertion is triggered when running * in debug mode. */ (void) UMF_colamd ( n_row - n1 - nempty_row, n_col - n1 - nempty_col, Clen, Ci, Cperm_init, knobs, colamd_stats, Fr_npivcol, Fr_nrows, Fr_ncols, Fr_parent, Fr_cols, &nfr, InFront) ; ASSERT (colamd_stats [COLAMD_EMPTY_ROW] == 0) ; ASSERT (colamd_stats [COLAMD_EMPTY_COL] == 0) ; /* # of dense rows will be recomputed below */ Info [UMFPACK_NDENSE_ROW] = colamd_stats [COLAMD_DENSE_ROW] ; Info [UMFPACK_NDENSE_COL] = colamd_stats [COLAMD_DENSE_COL] ; Info [UMFPACK_SYMBOLIC_DEFRAG] = colamd_stats [COLAMD_DEFRAG_COUNT] ; /* re-analyze if any "dense" rows or cols ignored by UMF_colamd */ do_UMF_analyze = colamd_stats [COLAMD_DENSE_ROW] > 0 || colamd_stats [COLAMD_DENSE_COL] > 0 ; /* Combine the singleton and colamd ordering into Cperm_init */ /* Note that colamd returns its inverse permutation in Ci */ combine_ordering (n1, nempty_col, n_col, Cperm_init, Cperm1, Ci) ; /* contents of Ci no longer needed */ #ifndef NDEBUG for (col = 0 ; col < n_col ; col++) { DEBUG1 (("Cperm_init ["ID"] = "ID"\n", col, Cperm_init[col])); } /* make sure colamd returned a valid permutation */ ASSERT (Cperm_init != (Int *) NULL) ; ASSERT (UMF_is_permutation (Cperm_init, Ci, n_col, n_col)) ; #endif } else { /* ------------------------------------------------------------------ */ /* do not call colamd - use input Quser or AMD instead */ /* ------------------------------------------------------------------ */ /* The ordering (Quser or Qamd) is already in Cperm_init */ do_UMF_analyze = TRUE ; } Cperm_init [n_col] = EMPTY ; /* unused in Cperm_init */ /* ---------------------------------------------------------------------- */ /* AMD ordering, if it exists, has been copied into Cperm_init */ /* ---------------------------------------------------------------------- */ #ifndef NDEBUG DEBUG3 (("Cperm_init column permutation:\n")) ; ASSERT (UMF_is_permutation (Cperm_init, Ci, n_col, n_col)) ; for (k = 0 ; k < n_col ; k++) { DEBUG3 ((ID"\n", Cperm_init [k])) ; } /* ensure that empty columns have been placed last in A (:,Cperm_init) */ for (newj = 0 ; newj < n_col ; newj++) { /* empty columns will be last in A (:, Cperm_init (1:n_col)) */ j = Cperm_init [newj] ; ASSERT (IMPLIES (newj >= n_col-nempty_col, Cdeg [j] == 0)) ; ASSERT (IMPLIES (newj < n_col-nempty_col, Cdeg [j] > 0)) ; } #endif /* ---------------------------------------------------------------------- */ /* symbolic factorization (unless colamd has already done it) */ /* ---------------------------------------------------------------------- */ if (do_UMF_analyze) { Int *W, *Bp, *Bi, *Cperm2, ok, *P, Clen2, bsize, Clen0 ; /* ------------------------------------------------------------------ */ /* construct column pre-ordered, pruned submatrix */ /* ------------------------------------------------------------------ */ /* S = column form submatrix after removing singletons and applying * initial column ordering (includes singleton ordering) */ (void) prune_singletons (n1, n_col, Ap, Ai, (double *) NULL, #ifdef COMPLEX (double *) NULL, #endif Cperm_init, InvRperm1, Si, Sp #ifndef NDEBUG , Rperm1, n_row #endif ) ; /* ------------------------------------------------------------------ */ /* Ci [0 .. Clen-1] holds the following work arrays: first Clen0 entries empty space, where Clen0 = Clen - (nn+1 + 2*nn + n_col) and Clen0 >= nz + n_col next nn+1 entries Bp [0..nn] next nn entries Link [0..nn-1] next nn entries W [0..nn-1] last n_col entries Cperm2 [0..n_col-1] We have Clen >= n_col + MAX (nz,n_col) + 3*nn+1 + n_col, So Clen0 >= 2*n_col as required for AMD_postorder and Clen0 >= n_col + nz as required */ Clen0 = Clen - (nn+1 + 2*nn + n_col) ; Bp = Ci + Clen0 ; Link = Bp + (nn+1) ; W = Link + nn ; Cperm2 = W + nn ; ASSERT (Cperm2 + n_col == Ci + Clen) ; ASSERT (Clen0 >= nz + n_col) ; ASSERT (Clen0 >= 2*n_col) ; /* ------------------------------------------------------------------ */ /* P = order that rows will be used in UMF_analyze */ /* ------------------------------------------------------------------ */ /* use W to mark rows, and use Link for row permutation P [ [ */ for (row = 0 ; row < n_row - n1 ; row++) { W [row] = FALSE ; } P = Link ; k = 0 ; for (col = 0 ; col < n_col - n1 ; col++) { /* empty columns are last in S */ for (p = Sp [col] ; p < Sp [col+1] ; p++) { row = Si [p] ; if (!W [row]) { /* this row has just been seen for the first time */ W [row] = TRUE ; P [k++] = row ; } } } /* If the matrix has truly empty rows, then P will not be */ /* complete, and visa versa. The matrix is structurally singular. */ nempty_row = n_row - n1 - k ; if (k < n_row - n1) { /* complete P by putting empty rows last in their natural order, */ /* rather than declaring an error (the matrix is singular) */ for (row = 0 ; row < n_row - n1 ; row++) { if (!W [row]) { /* W [row] = TRUE ; (not required) */ P [k++] = row ; } } } /* contents of W no longer needed ] */ #ifndef NDEBUG DEBUG3 (("Induced row permutation:\n")) ; ASSERT (k == n_row - n1) ; ASSERT (UMF_is_permutation (P, W, n_row - n1, n_row - n1)) ; for (k = 0 ; k < n_row - n1 ; k++) { DEBUG3 ((ID"\n", P [k])) ; } #endif /* ------------------------------------------------------------------ */ /* B = row-form of the pattern of S (excluding empty columns) */ /* ------------------------------------------------------------------ */ /* Ci [0 .. Clen-1] holds the following work arrays: first Clen2 entries empty space, must be at least >= n_col next max (nz,1) Bi [0..max (nz,1)-1] next nn+1 entries Bp [0..nn] next nn entries Link [0..nn-1] next nn entries W [0..nn-1] last n_col entries Cperm2 [0..n_col-1] This memory usage is accounted for by the UMF_ANALYZE_CLEN macro. */ Clen2 = Clen0 ; snz = Sp [n_col - n1] ; bsize = MAX (snz, 1) ; Clen2 -= bsize ; Bi = Ci + Clen2 ; ASSERT (Clen2 >= n_col) ; (void) UMF_transpose (n_row - n1, n_col - n1 - nempty_col, Sp, Si, (double *) NULL, P, (Int *) NULL, 0, Bp, Bi, (double *) NULL, W, FALSE #ifdef COMPLEX , (double *) NULL, (double *) NULL, FALSE #endif ) ; /* contents of Si and Sp no longer needed */ /* contents of P (same as Link) and W not needed */ /* still need Link and W as work arrays, though ] */ ASSERT (Bp [0] == 0) ; ASSERT (Bp [n_row - n1] == snz) ; /* increment Bp to point into Ci, not Bi */ for (i = 0 ; i <= n_row - n1 ; i++) { Bp [i] += Clen2 ; } ASSERT (Bp [0] == Clen0 - bsize) ; ASSERT (Bp [n_row - n1] <= Clen0) ; /* Ci [0 .. Clen-1] holds the following work arrays: first Clen0 entries Ci [0 .. Clen0-1], where the col indices of B are at the tail end of this part, and Bp [0] = Clen2 >= n_col. Note that Clen0 = Clen2 + max (snz,1). next nn+1 entries Bp [0..nn] next nn entries Link [0..nn-1] next nn entries W [0..nn-1] last n_col entries Cperm2 [0..n_col-1] */ /* ------------------------------------------------------------------ */ /* analyze */ /* ------------------------------------------------------------------ */ /* only analyze the non-empty, non-singleton part of the matrix */ ok = UMF_analyze ( n_row - n1 - nempty_row, n_col - n1 - nempty_col, Ci, Bp, Cperm2, fixQ, W, Link, Fr_ncols, Fr_nrows, Fr_npivcol, Fr_parent, &nfr, &analyze_compactions) ; if (!ok) { /* :: internal error in umf_analyze :: */ Info [UMFPACK_STATUS] = UMFPACK_ERROR_internal_error ; error (&Symbolic, SW) ; return (UMFPACK_ERROR_internal_error) ; } Info [UMFPACK_SYMBOLIC_DEFRAG] += analyze_compactions ; /* ------------------------------------------------------------------ */ /* combine the input permutation and UMF_analyze's permutation */ /* ------------------------------------------------------------------ */ if (!fixQ) { /* Cperm2 is the column etree post-ordering */ ASSERT (UMF_is_permutation (Cperm2, W, n_col-n1-nempty_col, n_col-n1-nempty_col)) ; /* Note that the empty columns remain at the end of Cperm_init */ for (k = 0 ; k < n_col - n1 - nempty_col ; k++) { W [k] = Cperm_init [n1 + Cperm2 [k]] ; } for (k = 0 ; k < n_col - n1 - nempty_col ; k++) { Cperm_init [n1 + k] = W [k] ; } } ASSERT (UMF_is_permutation (Cperm_init, W, n_col, n_col)) ; } /* ---------------------------------------------------------------------- */ /* free some of the workspace */ /* ---------------------------------------------------------------------- */ /* (4) The real workspace, Rs, of size n_row doubles has already been * free'd. An additional workspace of size nz + n_col+1 + n_col integers * is now free'd as well. */ SW->Si = (Int *) UMF_free ((void *) SW->Si) ; SW->Sp = (Int *) UMF_free ((void *) SW->Sp) ; SW->Cperm1 = (Int *) UMF_free ((void *) SW->Cperm1) ; ASSERT (SW->Rs == (double *) NULL) ; /* ---------------------------------------------------------------------- */ /* determine the size of the Symbolic object */ /* ---------------------------------------------------------------------- */ /* ---------------------------------------------------------------------- */ /* determine the size of the Symbolic object */ /* ---------------------------------------------------------------------- */ nchains = 0 ; for (i = 0 ; i < nfr ; i++) { if (Fr_parent [i] != i+1) { nchains++ ; } } Symbolic->nchains = nchains ; Symbolic->nfr = nfr ; Symbolic->esize = (max_rdeg > dense_row_threshold) ? (n_col - n1 - nempty_col) : 0 ; /* true size of Symbolic object */ Info [UMFPACK_SYMBOLIC_SIZE] = UMF_symbolic_usage (n_row, n_col, nchains, nfr, Symbolic->esize, prefer_diagonal) ; /* actual peak memory usage for UMFPACK_symbolic (actual nfr, nchains) */ Info [UMFPACK_SYMBOLIC_PEAK_MEMORY] = SYM_WORK_USAGE (n_col, n_row, Clen) + Info [UMFPACK_SYMBOLIC_SIZE] ; Symbolic->peak_sym_usage = Info [UMFPACK_SYMBOLIC_PEAK_MEMORY] ; DEBUG0 (("Number of fronts: "ID"\n", nfr)) ; /* ---------------------------------------------------------------------- */ /* allocate the second part of the Symbolic object (Front_*, Chain_*) */ /* ---------------------------------------------------------------------- */ /* (5) UMF_malloc is called 7 or 8 times, for a total space of * (4*(nfr+1) + 3*(nchains+1) + esize) integers, where nfr is the total * number of frontal matrices and nchains is the total number of frontal * matrix chains, and where nchains <= nfr <= n_col. esize is zero if there * are no dense rows, or n_col-n1-nempty_col otherwise (n1 is the number of * singletons and nempty_col is the number of empty columns). This space is * part of the Symbolic object and is not free'd unless an error occurs. * This is between 7 and about 8n integers when A is square. */ /* Note that Symbolic->Front_* does include the dummy placeholder front */ Symbolic->Front_npivcol = (Int *) UMF_malloc (nfr+1, sizeof (Int)) ; Symbolic->Front_parent = (Int *) UMF_malloc (nfr+1, sizeof (Int)) ; Symbolic->Front_1strow = (Int *) UMF_malloc (nfr+1, sizeof (Int)) ; Symbolic->Front_leftmostdesc = (Int *) UMF_malloc (nfr+1, sizeof (Int)) ; Symbolic->Chain_start = (Int *) UMF_malloc (nchains+1, sizeof (Int)) ; Symbolic->Chain_maxrows = (Int *) UMF_malloc (nchains+1, sizeof (Int)) ; Symbolic->Chain_maxcols = (Int *) UMF_malloc (nchains+1, sizeof (Int)) ; fail = (!Symbolic->Front_npivcol || !Symbolic->Front_parent || !Symbolic->Front_1strow || !Symbolic->Front_leftmostdesc || !Symbolic->Chain_start || !Symbolic->Chain_maxrows || !Symbolic->Chain_maxcols) ; if (Symbolic->esize > 0) { Symbolic->Esize = (Int *) UMF_malloc (Symbolic->esize, sizeof (Int)) ; fail = fail || !Symbolic->Esize ; } if (fail) { DEBUGm4 (("out of memory: rest of symbolic object\n")) ; Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; error (&Symbolic, SW) ; return (UMFPACK_ERROR_out_of_memory) ; } DEBUG0 (("Symbolic UMF_malloc_count - init_count = "ID"\n", UMF_malloc_count - init_count)) ; ASSERT (UMF_malloc_count == init_count + 21 + (SW->Rperm_2by2 != (Int *) NULL) + (Symbolic->Esize != (Int *) NULL)) ; Front_npivcol = Symbolic->Front_npivcol ; Front_parent = Symbolic->Front_parent ; Front_1strow = Symbolic->Front_1strow ; Front_leftmostdesc = Symbolic->Front_leftmostdesc ; Chain_start = Symbolic->Chain_start ; Chain_maxrows = Symbolic->Chain_maxrows ; Chain_maxcols = Symbolic->Chain_maxcols ; Esize = Symbolic->Esize ; /* ---------------------------------------------------------------------- */ /* assign rows to fronts */ /* ---------------------------------------------------------------------- */ /* find InFront, unless colamd has already computed it */ if (do_UMF_analyze) { DEBUGm4 ((">>>>>>>>>Computing Front_1strow from scratch\n")) ; /* empty rows go to dummy front nfr */ for (row = 0 ; row < n_row ; row++) { InFront [row] = nfr ; } /* assign the singleton pivot rows to the "empty" front */ for (k = 0 ; k < n1 ; k++) { row = Rperm1 [k] ; InFront [row] = EMPTY ; } DEBUG1 (("Front (EMPTY), singleton nrows "ID" ncols "ID"\n", k, k)) ; newj = n1 ; for (i = 0 ; i < nfr ; i++) { fpivcol = Fr_npivcol [i] ; f1rows = 0 ; /* for all pivot columns in front i */ for (kk = 0 ; kk < fpivcol ; kk++, newj++) { j = Cperm_init [newj] ; ASSERT (IMPLIES (newj >= n_col-nempty_col, Ap [j+1] - Ap [j] == 0)); for (p = Ap [j] ; p < Ap [j+1] ; p++) { row = Ai [p] ; if (InFront [row] == nfr) { /* this row belongs to front i */ DEBUG1 ((" Row "ID" in Front "ID"\n", row, i)) ; InFront [row] = i ; f1rows++ ; } } } Front_1strow [i] = f1rows ; DEBUG1 ((" Front "ID" has 1strows: "ID" pivcols "ID"\n", i, f1rows, fpivcol)) ; } } else { /* COLAMD has already computed InFront, but it is not yet * InFront [row] = front i, where row is an original row. It is * InFront [k-n1] = i for k in the range n1 to n_row-nempty_row, * and where row = Rperm1 [k]. Need to permute InFront. Also compute * # of original rows assembled into each front. * [ use Ci as workspace */ DEBUGm4 ((">>>>>>>>>Computing Front_1strow from colamd's InFront\n")) ; for (i = 0 ; i <= nfr ; i++) { Front_1strow [i] = 0 ; } /* assign the singleton pivot rows to "empty" front */ for (k = 0 ; k < n1 ; k++) { row = Rperm1 [k] ; Ci [row] = EMPTY ; } /* assign the non-empty rows to the front that assembled them */ for ( ; k < n_row - nempty_row ; k++) { row = Rperm1 [k] ; i = InFront [k - n1] ; ASSERT (i >= EMPTY && i < nfr) ; if (i != EMPTY) { Front_1strow [i]++ ; } /* use Ci as permuted version of InFront */ Ci [row] = i ; } /* empty rows go to the "dummy" front */ for ( ; k < n_row ; k++) { row = Rperm1 [k] ; Ci [row] = nfr ; } /* permute InFront so that InFront [row] = i if the original row is * in front i */ for (row = 0 ; row < n_row ; row++) { InFront [row] = Ci [row] ; } /* ] no longer need Ci as workspace */ } #ifndef NDEBUG for (row = 0 ; row < n_row ; row++) { if (InFront [row] == nfr) { DEBUG1 ((" Row "ID" in Dummy Front "ID"\n", row, nfr)) ; } else if (InFront [row] == EMPTY) { DEBUG1 ((" singleton Row "ID"\n", row)) ; } else { DEBUG1 ((" Row "ID" in Front "ID"\n", row, nfr)) ; } } #endif /* ---------------------------------------------------------------------- */ /* copy front information into Symbolic object */ /* ---------------------------------------------------------------------- */ k = n1 ; for (i = 0 ; i < nfr ; i++) { fpivcol = Fr_npivcol [i] ; DEBUG1 (("Front "ID" k "ID" npivcol "ID" nrows "ID" ncols "ID"\n", i, k, fpivcol, Fr_nrows [i], Fr_ncols [i])) ; k += fpivcol ; /* copy Front info into Symbolic object from SW */ Front_npivcol [i] = fpivcol ; Front_parent [i] = Fr_parent [i] ; } /* assign empty columns to dummy placehold front nfr */ DEBUG1 (("Dummy Cols in Front "ID" : "ID"\n", nfr, n_col-k)) ; Front_npivcol [nfr] = n_col - k ; Front_parent [nfr] = EMPTY ; /* ---------------------------------------------------------------------- */ /* find initial row permutation */ /* ---------------------------------------------------------------------- */ /* order the singleton pivot rows */ for (k = 0 ; k < n1 ; k++) { Rperm_init [k] = Rperm1 [k] ; } /* determine the first row in each front (in the new row ordering) */ for (i = 0 ; i < nfr ; i++) { f1rows = Front_1strow [i] ; DEBUG1 (("Front "ID" : npivcol "ID" parent "ID, i, Front_npivcol [i], Front_parent [i])) ; DEBUG1 ((" 1st rows in Front "ID" : "ID"\n", i, f1rows)) ; Front_1strow [i] = k ; k += f1rows ; } /* assign empty rows to dummy placehold front nfr */ DEBUG1 (("Rows in Front "ID" (dummy): "ID"\n", nfr, n_row-k)) ; Front_1strow [nfr] = k ; DEBUG1 (("nfr "ID" 1strow[nfr] "ID" nrow "ID"\n", nfr, k, n_row)) ; /* Use Ci as temporary workspace for F1 */ F1 = Ci ; /* [ of size nfr+1 */ ASSERT (Clen >= 2*n_row + nfr+1) ; for (i = 0 ; i <= nfr ; i++) { F1 [i] = Front_1strow [i] ; } for (row = 0 ; row < n_row ; row++) { i = InFront [row] ; if (i != EMPTY) { newrow = F1 [i]++ ; ASSERT (newrow >= n1) ; Rperm_init [newrow] = row ; } } Rperm_init [n_row] = EMPTY ; /* unused */ #ifndef NDEBUG for (k = 0 ; k < n_row ; k++) { DEBUG2 (("Rperm_init ["ID"] = "ID"\n", k, Rperm_init [k])) ; } #endif /* ] done using F1 */ /* ---------------------------------------------------------------------- */ /* find the diagonal map */ /* ---------------------------------------------------------------------- */ /* Rperm_init [newrow] = row gives the row permutation that is implied * by the column permutation, where "row" is a row index of the original * matrix A. It is not dependent on the Rperm_2by2 permutation, which * only redefines the "diagonal". Both are used to construct the * Diagonal_map. Diagonal_map only needs to be defined for * k = n1 to nn - nempty, but go ahead and define it for all of * k = 0 to nn */ if (prefer_diagonal) { Int *Diagonal_map ; ASSERT (n_row == n_col && nn == n_row) ; ASSERT (nempty_row == nempty_col && nempty == nempty_row) ; /* allocate the Diagonal_map */ Symbolic->Diagonal_map = (Int *) UMF_malloc (n_col+1, sizeof (Int)) ; Diagonal_map = Symbolic->Diagonal_map ; if (Diagonal_map == (Int *) NULL) { /* :: out of memory (diagonal map) :: */ DEBUGm4 (("out of memory: Diagonal map\n")) ; Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ; error (&Symbolic, SW) ; return (UMFPACK_ERROR_out_of_memory) ; } /* use Ci as workspace to compute the inverse of Rperm_init [ */ for (newrow = 0 ; newrow < nn ; newrow++) { oldrow = Rperm_init [newrow] ; ASSERT (oldrow >= 0 && oldrow < nn) ; Ci [oldrow] = newrow ; } if (strategy == UMFPACK_STRATEGY_2BY2) { ASSERT (Rperm_2by2 != (Int *) NULL) ; for (newcol = 0 ; newcol < nn ; newcol++) { oldcol = Cperm_init [newcol] ; /* 2-by-2 pivoting done in S */ oldrow = Rperm_2by2 [oldcol] ; newrow = Ci [oldrow] ; Diagonal_map [newcol] = newrow ; } } else { for (newcol = 0 ; newcol < nn ; newcol++) { oldcol = Cperm_init [newcol] ; /* no 2-by-2 pivoting in S */ oldrow = oldcol ; newrow = Ci [oldrow] ; Diagonal_map [newcol] = newrow ; } } #ifndef NDEBUG DEBUG1 (("\nDiagonal map:\n")) ; for (newcol = 0 ; newcol < nn ; newcol++) { oldcol = Cperm_init [newcol] ; DEBUG3 (("oldcol "ID" newcol "ID":\n", oldcol, newcol)) ; for (p = Ap [oldcol] ; p < Ap [oldcol+1] ; p++) { Entry aij ; CLEAR (aij) ; oldrow = Ai [p] ; newrow = Ci [oldrow] ; if (Ax != (double *) NULL) { ASSIGN (aij, Ax, Az, p, SPLIT (Az)) ; } if (oldrow == oldcol) { DEBUG2 ((" old diagonal : oldcol "ID" oldrow "ID" ", oldcol, oldrow)) ; EDEBUG2 (aij) ; DEBUG2 (("\n")) ; } if (newrow == Diagonal_map [newcol]) { DEBUG2 ((" MAP diagonal : newcol "ID" MAProw "ID" ", newcol, Diagonal_map [newrow])) ; EDEBUG2 (aij) ; DEBUG2 (("\n")) ; } } } #endif /* done using Ci as workspace ] */ } /* ---------------------------------------------------------------------- */ /* find the leftmost descendant of each front */ /* ---------------------------------------------------------------------- */ for (i = 0 ; i <= nfr ; i++) { Front_leftmostdesc [i] = EMPTY ; } for (i = 0 ; i < nfr ; i++) { /* start at i and walk up the tree */ DEBUG2 (("Walk up front tree from "ID"\n", i)) ; j = i ; while (j != EMPTY && Front_leftmostdesc [j] == EMPTY) { DEBUG3 ((" Leftmost desc of "ID" is "ID"\n", j, i)) ; Front_leftmostdesc [j] = i ; j = Front_parent [j] ; DEBUG3 ((" go to j = "ID"\n", j)) ; } } /* ---------------------------------------------------------------------- */ /* find the frontal matrix chains and max frontal matrix sizes */ /* ---------------------------------------------------------------------- */ maxnrows = 1 ; /* max # rows in any front */ maxncols = 1 ; /* max # cols in any front */ dmaxfrsize = 1 ; /* max frontal matrix size */ /* start the first chain */ nchains = 0 ; /* number of chains */ Chain_start [0] = 0 ; /* front 0 starts a new chain */ maxrows = 1 ; /* max # rows for any front in current chain */ maxcols = 1 ; /* max # cols for any front in current chain */ DEBUG1 (("Constructing chains:\n")) ; for (i = 0 ; i < nfr ; i++) { /* get frontal matrix info */ fpivcol = Front_npivcol [i] ; /* # candidate pivot columns */ fallrows = Fr_nrows [i] ; /* all rows (not just Schur comp) */ fallcols = Fr_ncols [i] ; /* all cols (not just Schur comp) */ parent = Front_parent [i] ; /* parent in column etree */ fpiv = MIN (fpivcol, fallrows) ; /* # pivot rows and cols */ maxrows = MAX (maxrows, fallrows) ; maxcols = MAX (maxcols, fallcols) ; DEBUG1 (("Front: "ID", pivcol "ID", "ID"-by-"ID" parent "ID ", npiv "ID" Chain: maxrows "ID" maxcols "ID"\n", i, fpivcol, fallrows, fallcols, parent, fpiv, maxrows, maxcols)) ; if (parent != i+1) { /* this is the end of a chain */ double s ; DEBUG1 (("\nEnd of chain "ID"\n", nchains)) ; /* make sure maxrows is an odd number */ ASSERT (maxrows >= 0) ; if (maxrows % 2 == 0) maxrows++ ; DEBUG1 (("Chain maxrows "ID" maxcols "ID"\n", maxrows, maxcols)) ; Chain_maxrows [nchains] = maxrows ; Chain_maxcols [nchains] = maxcols ; /* keep track of the maximum front size for all chains */ /* for Info only: */ s = (double) maxrows * (double) maxcols ; dmaxfrsize = MAX (dmaxfrsize, s) ; /* for the subsequent numerical factorization */ maxnrows = MAX (maxnrows, maxrows) ; maxncols = MAX (maxncols, maxcols) ; DEBUG1 (("Chain dmaxfrsize %g\n\n", dmaxfrsize)) ; /* start the next chain */ nchains++ ; Chain_start [nchains] = i+1 ; maxrows = 1 ; maxcols = 1 ; } } /* for Info only: */ dmaxfrsize = ceil (dmaxfrsize) ; DEBUGm1 (("dmaxfrsize %30.20g Int_MAX "ID"\n", dmaxfrsize, Int_MAX)) ; ASSERT (Symbolic->nchains == nchains) ; /* For allocating objects in umfpack_numeric (does not include all possible * pivots, particularly pivots from prior fronts in the chain. Need to add * nb to these to get the # of columns in the L block, for example. This * is the largest row dimension and largest column dimension of any frontal * matrix. maxnrows is always odd. */ Symbolic->maxnrows = maxnrows ; Symbolic->maxncols = maxncols ; DEBUGm3 (("maxnrows "ID" maxncols "ID"\n", maxnrows, maxncols)) ; /* ---------------------------------------------------------------------- */ /* find the initial element sizes */ /* ---------------------------------------------------------------------- */ if (max_rdeg > dense_row_threshold) { /* there are one or more dense rows in the input matrix */ /* count the number of dense rows in each column */ /* use Ci as workspace for inverse of Rperm_init [ */ ASSERT (Esize != (Int *) NULL) ; for (newrow = 0 ; newrow < n_row ; newrow++) { oldrow = Rperm_init [newrow] ; ASSERT (oldrow >= 0 && oldrow < nn) ; Ci [oldrow] = newrow ; } for (col = n1 ; col < n_col - nempty_col ; col++) { oldcol = Cperm_init [col] ; esize = Cdeg [oldcol] ; ASSERT (esize > 0) ; for (p = Ap [oldcol] ; p < Ap [oldcol+1] ; p++) { oldrow = Ai [p] ; newrow = Ci [oldrow] ; if (newrow >= n1 && Rdeg [oldrow] > dense_row_threshold) { esize-- ; } } ASSERT (esize >= 0) ; Esize [col - n1] = esize ; } /* done using Ci as workspace ] */ } /* If there are no dense rows, then Esize [col-n1] is identical to * Cdeg [col], once Cdeg is permuted below */ /* ---------------------------------------------------------------------- */ /* permute Cdeg and Rdeg according to initial column and row permutation */ /* ---------------------------------------------------------------------- */ /* use Ci as workspace [ */ for (k = 0 ; k < n_col ; k++) { Ci [k] = Cdeg [Cperm_init [k]] ; } for (k = 0 ; k < n_col ; k++) { Cdeg [k] = Ci [k] ; } for (k = 0 ; k < n_row ; k++) { Ci [k] = Rdeg [Rperm_init [k]] ; } for (k = 0 ; k < n_row ; k++) { Rdeg [k] = Ci [k] ; } /* done using Ci as workspace ] */ /* ---------------------------------------------------------------------- */ /* simulate UMF_kernel_init */ /* ---------------------------------------------------------------------- */ /* count elements and tuples at tail, LU factors of singletons, and * head and tail markers */ dlnz = n_inner ; /* upper limit of nz in L (incl diag) */ dunz = dlnz ; /* upper limit of nz in U (incl diag) */ /* head marker */ head_usage = 1 ; dhead_usage = 1 ; /* tail markers: */ tail_usage = 2 ; dtail_usage = 2 ; /* allocate the Rpi and Rpx workspace for UMF_kernel_init (incl. headers) */ tail_usage += UNITS (Int *, n_row+1) + UNITS (Entry *, n_row+1) + 2 ; dtail_usage += DUNITS (Int *, n_row+1) + DUNITS (Entry *, n_row+1) + 2 ; DEBUG1 (("Symbolic usage after Rpi/Rpx allocation: head "ID" tail "ID"\n", head_usage, tail_usage)) ; /* LU factors for singletons, at the head of memory */ for (k = 0 ; k < n1 ; k++) { lnz = Cdeg [k] - 1 ; unz = Rdeg [k] - 1 ; dlnz += lnz ; dunz += unz ; DEBUG1 (("singleton k "ID" pivrow "ID" pivcol "ID" lnz "ID" unz "ID"\n", k, Rperm_init [k], Cperm_init [k], lnz, unz)) ; head_usage += UNITS (Int, lnz) + UNITS (Entry, lnz) + UNITS (Int, unz) + UNITS (Entry, unz) ; dhead_usage += DUNITS (Int, lnz) + DUNITS (Entry, lnz) + DUNITS (Int, unz) + DUNITS (Entry, unz) ; } DEBUG1 (("Symbolic init head usage: "ID" for LU singletons\n",head_usage)) ; /* column elements: */ for (k = n1 ; k < n_col - nempty_col; k++) { esize = Esize ? Esize [k-n1] : Cdeg [k] ; DEBUG2 ((" esize: "ID"\n", esize)) ; ASSERT (esize >= 0) ; if (esize > 0) { tail_usage += GET_ELEMENT_SIZE (esize, 1) + 1 ; dtail_usage += DGET_ELEMENT_SIZE (esize, 1) + 1 ; } } /* dense row elements */ if (Esize) { Int nrow_elements = 0 ; for (k = n1 ; k < n_row - nempty_row ; k++) { rdeg = Rdeg [k] ; if (rdeg > dense_row_threshold) { tail_usage += GET_ELEMENT_SIZE (1, rdeg) + 1 ; dtail_usage += GET_ELEMENT_SIZE (1, rdeg) + 1 ; nrow_elements++ ; } } Info [UMFPACK_NDENSE_ROW] = nrow_elements ; } DEBUG1 (("Symbolic usage: "ID" = head "ID" + tail "ID" after els\n", head_usage + tail_usage, head_usage, tail_usage)) ; /* compute the tuple lengths */ if (Esize) { /* row tuples */ for (row = n1 ; row < n_row ; row++) { rdeg = Rdeg [row] ; tlen = (rdeg > dense_row_threshold) ? 1 : rdeg ; tail_usage += 1 + UNITS (Tuple, TUPLES (tlen)) ; dtail_usage += 1 + DUNITS (Tuple, TUPLES (tlen)) ; } /* column tuples */ for (col = n1 ; col < n_col - nempty_col ; col++) { /* tlen is 1 plus the number of dense rows in this column */ esize = Esize [col - n1] ; tlen = (esize > 0) + (Cdeg [col] - esize) ; tail_usage += 1 + UNITS (Tuple, TUPLES (tlen)) ; dtail_usage += 1 + DUNITS (Tuple, TUPLES (tlen)) ; } for ( ; col < n_col ; col++) { tail_usage += 1 + UNITS (Tuple, TUPLES (0)) ; dtail_usage += 1 + DUNITS (Tuple, TUPLES (0)) ; } } else { /* row tuples */ for (row = n1 ; row < n_row ; row++) { tlen = Rdeg [row] ; tail_usage += 1 + UNITS (Tuple, TUPLES (tlen)) ; dtail_usage += 1 + DUNITS (Tuple, TUPLES (tlen)) ; } /* column tuples */ for (col = n1 ; col < n_col ; col++) { tail_usage += 1 + UNITS (Tuple, TUPLES (1)) ; dtail_usage += 1 + DUNITS (Tuple, TUPLES (1)) ; } } Symbolic->num_mem_init_usage = head_usage + tail_usage ; DEBUG1 (("Symbolic usage: "ID" = head "ID" + tail "ID" final\n", Symbolic->num_mem_init_usage, head_usage, tail_usage)) ; ASSERT (UMF_is_permutation (Rperm_init, Ci, n_row, n_row)) ; /* initial head and tail usage in Numeric->Memory */ dmax_usage = dhead_usage + dtail_usage ; dmax_usage = MAX (Symbolic->num_mem_init_usage, ceil (dmax_usage)) ; Info [UMFPACK_VARIABLE_INIT_ESTIMATE] = dmax_usage ; /* In case Symbolic->num_mem_init_usage overflows, keep as a double, too */ Symbolic->dnum_mem_init_usage = dmax_usage ; /* free the Rpi and Rpx workspace */ tail_usage -= UNITS (Int *, n_row+1) + UNITS (Entry *, n_row+1) ; dtail_usage -= DUNITS (Int *, n_row+1) + DUNITS (Entry *, n_row+1) ; /* ---------------------------------------------------------------------- */ /* simulate UMF_kernel, assuming unsymmetric pivoting */ /* ---------------------------------------------------------------------- */ /* Use Ci as temporary workspace for link lists [ */ Link = Ci ; for (i = 0 ; i < nfr ; i++) { Link [i] = EMPTY ; } flops = 0 ; /* flop count upper bound */ for (chain = 0 ; chain < nchains ; chain++) { double fsize ; f1 = Chain_start [chain] ; f2 = Chain_start [chain+1] - 1 ; /* allocate frontal matrix working array (C, L, and U) */ dr = Chain_maxrows [chain] ; dc = Chain_maxcols [chain] ; fsize = nb*nb /* LU is nb-by-nb */ + dr*nb /* L is dr-by-nb */ + nb*dc /* U is nb-by-dc, stored by rows */ + dr*dc ; /* C is dr by dc */ dtail_usage += DUNITS (Entry, fsize) ; dmax_usage = MAX (dmax_usage, dhead_usage + dtail_usage) ; for (i = f1 ; i <= f2 ; i++) { /* get frontal matrix info */ fpivcol = Front_npivcol [i] ; /* # candidate pivot columns */ fallrows = Fr_nrows [i] ; /* all rows (not just Schur comp*/ fallcols = Fr_ncols [i] ; /* all cols (not just Schur comp*/ parent = Front_parent [i] ; /* parent in column etree */ fpiv = MIN (fpivcol, fallrows) ; /* # pivot rows and cols */ f = (double) fpiv ; r = fallrows - fpiv ; /* # rows in Schur comp. */ c = fallcols - fpiv ; /* # cols in Schur comp. */ /* assemble all children of front i in column etree */ for (child = Link [i] ; child != EMPTY ; child = Link [child]) { ASSERT (child >= 0 && child < i) ; ASSERT (Front_parent [child] == i) ; /* free the child element and remove it from tuple lists */ cp = MIN (Front_npivcol [child], Fr_nrows [child]) ; cr = Fr_nrows [child] - cp ; cc = Fr_ncols [child] - cp ; ASSERT (cp >= 0 && cr >= 0 && cc >= 0) ; dtail_usage -= ELEMENT_SIZE (cr, cc) ; } /* The flop count computed here is "canonical". */ /* factorize the frontal matrix */ flops += DIV_FLOPS * (f*r + (f-1)*f/2) /* scale pivot columns */ /* f outer products: */ + MULTSUB_FLOPS * (f*r*c + (r+c)*(f-1)*f/2 + (f-1)*f*(2*f-1)/6); /* count nonzeros and memory usage in double precision */ dlf = (f*f-f)/2 + f*r ; /* nz in L below diagonal */ duf = (f*f-f)/2 + f*c ; /* nz in U above diagonal */ dlnz += dlf ; dunz += duf ; /* store f columns of L and f rows of U */ dhead_usage += DUNITS (Entry, dlf + duf) /* numerical values (excl diag) */ + DUNITS (Int, r + c + f) ; /* indices (compressed) */ if (parent != EMPTY) { /* create new element and place in tuple lists */ dtail_usage += ELEMENT_SIZE (r, c) ; /* place in link list of parent */ Link [i] = Link [parent] ; Link [parent] = i ; } /* keep track of peak Numeric->Memory usage */ dmax_usage = MAX (dmax_usage, dhead_usage + dtail_usage) ; } /* free the current frontal matrix */ dtail_usage -= DUNITS (Entry, fsize) ; } dhead_usage = ceil (dhead_usage) ; dmax_usage = ceil (dmax_usage) ; Symbolic->num_mem_size_est = dhead_usage ; Symbolic->num_mem_usage_est = dmax_usage ; Symbolic->lunz_bound = dlnz + dunz - n_inner ; /* ] done using Ci as workspace for Link array */ /* ---------------------------------------------------------------------- */ /* estimate total memory usage in UMFPACK_numeric */ /* ---------------------------------------------------------------------- */ UMF_set_stats ( Info, Symbolic, dmax_usage, /* estimated peak size of Numeric->Memory */ dhead_usage, /* estimated final size of Numeric->Memory */ flops, /* estimated "true flops" */ dlnz, /* estimated nz in L */ dunz, /* estimated nz in U */ dmaxfrsize, /* estimated largest front size */ (double) n_col, /* worst case Numeric->Upattern size */ (double) n_inner, /* max possible pivots to be found */ (double) maxnrows, /* estimated largest #rows in front */ (double) maxncols, /* estimated largest #cols in front */ TRUE, /* assume scaling is to be performed */ prefer_diagonal, ESTIMATE) ; /* ---------------------------------------------------------------------- */ #ifndef NDEBUG for (i = 0 ; i < nchains ; i++) { DEBUG2 (("Chain "ID" start "ID" end "ID" maxrows "ID" maxcols "ID"\n", i, Chain_start [i], Chain_start [i+1] - 1, Chain_maxrows [i], Chain_maxcols [i])) ; UMF_dump_chain (Chain_start [i], Fr_parent, Fr_npivcol, Fr_nrows, Fr_ncols, nfr) ; } fpivcol = 0 ; for (i = 0 ; i < nfr ; i++) { fpivcol = MAX (fpivcol, Front_npivcol [i]) ; } DEBUG0 (("Max pivot cols in any front: "ID"\n", fpivcol)) ; DEBUG1 (("Largest front: maxnrows "ID" maxncols "ID" dmaxfrsize %g\n", maxnrows, maxncols, dmaxfrsize)) ; #endif /* ---------------------------------------------------------------------- */ /* UMFPACK_symbolic was successful, return the object handle */ /* ---------------------------------------------------------------------- */ Symbolic->valid = SYMBOLIC_VALID ; *SymbolicHandle = (void *) Symbolic ; /* ---------------------------------------------------------------------- */ /* free workspace */ /* ---------------------------------------------------------------------- */ /* (6) The last of the workspace is free'd. The final Symbolic object * consists of 12 to 14 allocated objects. Its final total size is lies * roughly between 4*n and 13*n for a square matrix, which is all that is * left of the memory allocated by this routine. If an error occurs, the * entire Symbolic object is free'd when this routine returns (the error * return routine, below). */ free_work (SW) ; DEBUG0 (("(3)Symbolic UMF_malloc_count - init_count = "ID"\n", UMF_malloc_count - init_count)) ; ASSERT (UMF_malloc_count == init_count + 12 + (Symbolic->Esize != (Int *) NULL) + (Symbolic->Diagonal_map != (Int *) NULL)) ; /* ---------------------------------------------------------------------- */ /* get the time used by UMFPACK_*symbolic */ /* ---------------------------------------------------------------------- */ umfpack_toc (stats) ; Info [UMFPACK_SYMBOLIC_WALLTIME] = stats [0] ; Info [UMFPACK_SYMBOLIC_TIME] = stats [1] ; return (UMFPACK_OK) ; } /* ========================================================================== */ /* === free_work ============================================================ */ /* ========================================================================== */ PRIVATE void free_work ( SWType *SW ) { if (SW) { SW->Rperm_2by2 = (Int *) UMF_free ((void *) SW->Rperm_2by2) ; SW->InvRperm1 = (Int *) UMF_free ((void *) SW->InvRperm1) ; SW->Rs = (double *) UMF_free ((void *) SW->Rs) ; SW->Si = (Int *) UMF_free ((void *) SW->Si) ; SW->Sp = (Int *) UMF_free ((void *) SW->Sp) ; SW->Ci = (Int *) UMF_free ((void *) SW->Ci) ; SW->Front_npivcol = (Int *) UMF_free ((void *) SW->Front_npivcol); SW->Front_nrows = (Int *) UMF_free ((void *) SW->Front_nrows) ; SW->Front_ncols = (Int *) UMF_free ((void *) SW->Front_ncols) ; SW->Front_parent = (Int *) UMF_free ((void *) SW->Front_parent) ; SW->Front_cols = (Int *) UMF_free ((void *) SW->Front_cols) ; SW->Cperm1 = (Int *) UMF_free ((void *) SW->Cperm1) ; SW->Rperm1 = (Int *) UMF_free ((void *) SW->Rperm1) ; SW->InFront = (Int *) UMF_free ((void *) SW->InFront) ; } } /* ========================================================================== */ /* === error ================================================================ */ /* ========================================================================== */ /* Error return from UMFPACK_symbolic. Free all allocated memory. */ PRIVATE void error ( SymbolicType **Symbolic, SWType *SW ) { free_work (SW) ; UMFPACK_free_symbolic ((void **) Symbolic) ; ASSERT (UMF_malloc_count == init_count) ; }