/* ========================================================================== */
/* === UMFPACK_qsymbolic ==================================================== */
/* ========================================================================== */
/* -------------------------------------------------------------------------- */
/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by 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) ;
}
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