Int KLU_free_symbolic
(
KLU_symbolic **SymbolicHandle,
KLU_common *Common
)
{
KLU_symbolic *Symbolic ;
Int n ;
if (Common == NULL)
{
return (FALSE) ;
}
if (SymbolicHandle == NULL || *SymbolicHandle == NULL)
{
return (TRUE) ;
}
Symbolic = *SymbolicHandle ;
n = Symbolic->n ;
KLU_free (Symbolic->P, n, sizeof (Int), Common) ;
KLU_free (Symbolic->Q, n, sizeof (Int), Common) ;
KLU_free (Symbolic->R, n+1, sizeof (Int), Common) ;
KLU_free (Symbolic->Lnz, n, sizeof (double), Common) ;
KLU_free (Symbolic, 1, sizeof (KLU_symbolic), Common) ;
*SymbolicHandle = NULL ;
return (TRUE) ;
}
static KLU_symbolic *order_and_analyze /* returns NULL if error, or a valid
KLU_symbolic object if successful */
(
/* inputs, not modified */
Int n, /* A is n-by-n */
Int Ap [ ], /* size n+1, column pointers */
Int Ai [ ], /* size nz, row indices */
/* --------------------- */
KLU_common *Common
)
{
double work ;
KLU_symbolic *Symbolic ;
double *Lnz ;
Int *Qbtf, *Cp, *Ci, *Pinv, *Pblk, *Pbtf, *P, *Q, *R ;
Int nblocks, nz, block, maxblock, k1, k2, nk, do_btf, ordering, k, Cilen,
*Work ;
/* ---------------------------------------------------------------------- */
/* allocate the Symbolic object, and check input matrix */
/* ---------------------------------------------------------------------- */
Symbolic = KLU_alloc_symbolic (n, Ap, Ai, Common) ;
if (Symbolic == NULL)
{
return (NULL) ;
}
P = Symbolic->P ;
Q = Symbolic->Q ;
R = Symbolic->R ;
Lnz = Symbolic->Lnz ;
nz = Symbolic->nz ;
ordering = Common->ordering ;
if (ordering == 1)
{
/* COLAMD */
Cilen = COLAMD_recommended (nz, n, n) ;
}
else if (ordering == 0 || (ordering == 3 && Common->user_order != NULL))
{
/* AMD or user ordering function */
Cilen = nz+1 ;
}
else
{
/* invalid ordering */
Common->status = KLU_INVALID ;
KLU_free_symbolic (&Symbolic, Common) ;
return (NULL) ;
}
/* AMD memory management routines */
amd_malloc = Common->malloc_memory ;
amd_free = Common->free_memory ;
amd_calloc = Common->calloc_memory ;
amd_realloc = Common->realloc_memory ;
/* ---------------------------------------------------------------------- */
/* allocate workspace for BTF permutation */
/* ---------------------------------------------------------------------- */
Pbtf = KLU_malloc (n, sizeof (Int), Common) ;
Qbtf = KLU_malloc (n, sizeof (Int), Common) ;
if (Common->status < KLU_OK)
{
KLU_free (Pbtf, n, sizeof (Int), Common) ;
KLU_free (Qbtf, n, sizeof (Int), Common) ;
KLU_free_symbolic (&Symbolic, Common) ;
return (NULL) ;
}
/* ---------------------------------------------------------------------- */
/* get the common parameters for BTF and ordering method */
/* ---------------------------------------------------------------------- */
do_btf = Common->btf ;
do_btf = (do_btf) ? TRUE : FALSE ;
Symbolic->ordering = ordering ;
Symbolic->do_btf = do_btf ;
Symbolic->structural_rank = EMPTY ;
/* ---------------------------------------------------------------------- */
/* find the block triangular form (if requested) */
/* ---------------------------------------------------------------------- */
Common->work = 0 ;
if (do_btf)
{
Work = KLU_malloc (5*n, sizeof (Int), Common) ;
if (Common->status < KLU_OK)
{
/* out of memory */
KLU_free (Pbtf, n, sizeof (Int), Common) ;
KLU_free (Qbtf, n, sizeof (Int), Common) ;
KLU_free_symbolic (&Symbolic, Common) ;
return (NULL) ;
}
nblocks = BTF_order (n, Ap, Ai, Common->maxwork, &work, Pbtf, Qbtf, R,
&(Symbolic->structural_rank), Work) ;
Common->structural_rank = Symbolic->structural_rank ;
Common->work += work ;
KLU_free (Work, 5*n, sizeof (Int), Common) ;
/* unflip Qbtf if the matrix does not have full structural rank */
if (Symbolic->structural_rank < n)
{
for (k = 0 ; k < n ; k++)
{
Qbtf [k] = BTF_UNFLIP (Qbtf [k]) ;
}
}
/* find the size of the largest block */
maxblock = 1 ;
for (block = 0 ; block < nblocks ; block++)
{
k1 = R [block] ;
k2 = R [block+1] ;
nk = k2 - k1 ;
PRINTF (("block %d size %d\n", block, nk)) ;
maxblock = MAX (maxblock, nk) ;
}
}
else
{
/* BTF not requested */
nblocks = 1 ;
maxblock = n ;
R [0] = 0 ;
R [1] = n ;
for (k = 0 ; k < n ; k++)
{
Pbtf [k] = k ;
Qbtf [k] = k ;
}
}
Symbolic->nblocks = nblocks ;
PRINTF (("maxblock size %d\n", maxblock)) ;
Symbolic->maxblock = maxblock ;
/* ---------------------------------------------------------------------- */
/* allocate more workspace, for analyze_worker */
/* ---------------------------------------------------------------------- */
Pblk = KLU_malloc (maxblock, sizeof (Int), Common) ;
Cp = KLU_malloc (maxblock + 1, sizeof (Int), Common) ;
Ci = KLU_malloc (MAX (Cilen, nz+1), sizeof (Int), Common) ;
Pinv = KLU_malloc (n, sizeof (Int), Common) ;
/* ---------------------------------------------------------------------- */
/* order each block of the BTF ordering, and a fill-reducing ordering */
/* ---------------------------------------------------------------------- */
if (Common->status == KLU_OK)
{
PRINTF (("calling analyze_worker\n")) ;
Common->status = analyze_worker (n, Ap, Ai, nblocks, Pbtf, Qbtf, R,
ordering, P, Q, Lnz, Pblk, Cp, Ci, Cilen, Pinv, Symbolic, Common) ;
PRINTF (("analyze_worker done\n")) ;
}
/* ---------------------------------------------------------------------- */
/* free all workspace */
/* ---------------------------------------------------------------------- */
KLU_free (Pblk, maxblock, sizeof (Int), Common) ;
KLU_free (Cp, maxblock+1, sizeof (Int), Common) ;
KLU_free (Ci, MAX (Cilen, nz+1), sizeof (Int), Common) ;
KLU_free (Pinv, n, sizeof (Int), Common) ;
KLU_free (Pbtf, n, sizeof (Int), Common) ;
KLU_free (Qbtf, n, sizeof (Int), Common) ;
/* ---------------------------------------------------------------------- */
/* return the symbolic object */
/* ---------------------------------------------------------------------- */
if (Common->status < KLU_OK)
{
KLU_free_symbolic (&Symbolic, Common) ;
}
return (Symbolic) ;
}
size_t KLU_kernel_factor /* 0 if failure, size of LU if OK */
(
/* inputs, not modified */
Int n, /* A is n-by-n. n must be > 0. */
Int Ap [ ], /* size n+1, column pointers for A */
Int Ai [ ], /* size nz = Ap [n], row indices for A */
Entry Ax [ ], /* size nz, values of A */
Int Q [ ], /* size n, optional column permutation */
double Lsize, /* estimate of number of nonzeros in L */
/* outputs, not defined on input */
Unit **p_LU, /* row indices and values of L and U */
Entry Udiag [ ], /* size n, diagonal of U */
Int Llen [ ], /* size n, column length of L */
Int Ulen [ ], /* size n, column length of U */
Int Lip [ ], /* size n, column pointers for L */
Int Uip [ ], /* size n, column pointers for U */
Int P [ ], /* row permutation, size n */
Int *lnz, /* size of L */
Int *unz, /* size of U */
/* workspace, undefined on input */
Entry *X, /* size n double's, zero on output */
Int *Work, /* size 5n Int's */
/* inputs, not modified on output */
Int k1, /* the block of A is from k1 to k2-1 */
Int PSinv [ ], /* inverse of P from symbolic factorization */
double Rs [ ], /* scale factors for A */
/* inputs, modified on output */
Int Offp [ ], /* off-diagonal matrix (modified by this routine) */
Int Offi [ ],
Entry Offx [ ],
/* --------------- */
KLU_common *Common
)
{
double maxlnz, dunits ;
Unit *LU ;
Int *Pinv, *Lpend, *Stack, *Flag, *Ap_pos, *W ;
Int lsize, usize, anz, ok ;
size_t lusize ;
ASSERT (Common != NULL) ;
/* ---------------------------------------------------------------------- */
/* get control parameters, or use defaults */
/* ---------------------------------------------------------------------- */
n = MAX (1, n) ;
anz = Ap [n+k1] - Ap [k1] ;
if (Lsize <= 0)
{
Lsize = -Lsize ;
Lsize = MAX (Lsize, 1.0) ;
lsize = Lsize * anz + n ;
}
else
{
lsize = Lsize ;
}
usize = lsize ;
lsize = MAX (n+1, lsize) ;
usize = MAX (n+1, usize) ;
maxlnz = (((double) n) * ((double) n) + ((double) n)) / 2. ;
maxlnz = MIN (maxlnz, ((double) INT_MAX)) ;
lsize = MIN (maxlnz, lsize) ;
usize = MIN (maxlnz, usize) ;
PRINTF (("Welcome to klu: n %d anz %d k1 %d lsize %d usize %d maxlnz %g\n",
n, anz, k1, lsize, usize, maxlnz)) ;
/* ---------------------------------------------------------------------- */
/* allocate workspace and outputs */
/* ---------------------------------------------------------------------- */
/* return arguments are not yet assigned */
*p_LU = (Unit *) NULL ;
/* these computations are safe from size_t overflow */
W = Work ;
Pinv = (Int *) W ; W += n ;
Stack = (Int *) W ; W += n ;
Flag = (Int *) W ; W += n ;
Lpend = (Int *) W ; W += n ;
Ap_pos = (Int *) W ; W += n ;
dunits = DUNITS (Int, lsize) + DUNITS (Entry, lsize) +
DUNITS (Int, usize) + DUNITS (Entry, usize) ;
lusize = (size_t) dunits ;
ok = !INT_OVERFLOW (dunits) ;
LU = ok ? KLU_malloc (lusize, sizeof (Unit), Common) : NULL ;
if (LU == NULL)
{
/* out of memory, or problem too large */
Common->status = KLU_OUT_OF_MEMORY ;
lusize = 0 ;
return (lusize) ;
}
/* ---------------------------------------------------------------------- */
/* factorize */
/* ---------------------------------------------------------------------- */
/* with pruning, and non-recursive depth-first-search */
lusize = KLU_kernel (n, Ap, Ai, Ax, Q, lusize,
Pinv, P, &LU, Udiag, Llen, Ulen, Lip, Uip, lnz, unz,
X, Stack, Flag, Ap_pos, Lpend,
k1, PSinv, Rs, Offp, Offi, Offx, Common) ;
/* ---------------------------------------------------------------------- */
/* return LU factors, or return nothing if an error occurred */
/* ---------------------------------------------------------------------- */
if (Common->status < KLU_OK)
{
LU = KLU_free (LU, lusize, sizeof (Unit), Common) ;
lusize = 0 ;
}
*p_LU = LU ;
PRINTF ((" in klu noffdiag %d\n", Common->noffdiag)) ;
return (lusize) ;
}
KLU_symbolic<Entry, Int> *KLU_alloc_symbolic
(
Int n,
Int *Ap,
Int *Ai,
KLU_common<Entry, Int> *Common
)
{
KLU_symbolic<Entry, Int> *Symbolic ;
Int *P, *Q, *R ;
double *Lnz ;
Int nz, i, j, p, pend ;
if (Common == NULL)
{
return (NULL) ;
}
Common->status = KLU_OK ;
/* A is n-by-n, with n > 0. Ap [0] = 0 and nz = Ap [n] >= 0 required.
* Ap [j] <= Ap [j+1] must hold for all j = 0 to n-1. Row indices in Ai
* must be in the range 0 to n-1, and no duplicate entries can be present.
* The list of row indices in each column of A need not be sorted.
*/
if (n <= 0 || Ap == NULL || Ai == NULL)
{
/* Ap and Ai must be present, and n must be > 0 */
Common->status = KLU_INVALID ;
return (NULL) ;
}
nz = Ap [n] ;
if (Ap [0] != 0 || nz < 0)
{
/* nz must be >= 0 and Ap [0] must equal zero */
Common->status = KLU_INVALID ;
return (NULL) ;
}
for (j = 0 ; j < n ; j++)
{
if (Ap [j] > Ap [j+1])
{
/* column pointers must be non-decreasing */
Common->status = KLU_INVALID ;
return (NULL) ;
}
}
P = (Int *) KLU_malloc (n, sizeof (Int), Common) ;
if (Common->status < KLU_OK)
{
/* out of memory */
Common->status = KLU_OUT_OF_MEMORY ;
return (NULL) ;
}
for (i = 0 ; i < n ; i++)
{
P [i] = EMPTY ;
}
for (j = 0 ; j < n ; j++)
{
pend = Ap [j+1] ;
for (p = Ap [j] ; p < pend ; p++)
{
i = Ai [p] ;
if (i < 0 || i >= n || P [i] == j)
{
/* row index out of range, or duplicate entry */
KLU_free (P, n, sizeof (Int), Common) ;
Common->status = KLU_INVALID ;
return (NULL) ;
}
/* flag row i as appearing in column j */
P [i] = j ;
}
}
/* ---------------------------------------------------------------------- */
/* allocate the Symbolic object */
/* ---------------------------------------------------------------------- */
Symbolic = (KLU_symbolic<Entry, Int> *) KLU_malloc (sizeof (KLU_symbolic<Entry, Int>), 1, Common) ;
if (Common->status < KLU_OK)
{
/* out of memory */
KLU_free (P, n, sizeof (Int), Common) ;
Common->status = KLU_OUT_OF_MEMORY ;
return (NULL) ;
}
Q = (Int *) KLU_malloc (n, sizeof (Int), Common) ;
R = (Int *) KLU_malloc (n+1, sizeof (Int), Common) ;
Lnz = (double *) KLU_malloc (n, sizeof (double), Common) ;
Symbolic->n = n ;
Symbolic->nz = nz ;
Symbolic->P = P ;
Symbolic->Q = Q ;
Symbolic->R = R ;
Symbolic->Lnz = Lnz ;
if (Common->status < KLU_OK)
{
/* out of memory */
KLU_free_symbolic (&Symbolic, Common) ;
Common->status = KLU_OUT_OF_MEMORY ;
return (NULL) ;
}
return (Symbolic) ;
}
KLU_symbolic<Entry, Int> *KLU_analyze_given /* returns NULL if error, or a valid
KLU_symbolic object if successful */
(
/* inputs, not modified */
Int n, /* A is n-by-n */
Int Ap [ ], /* size n+1, column pointers */
Int Ai [ ], /* size nz, row indices */
Int Puser [ ], /* size n, user's row permutation (may be NULL) */
Int Quser [ ], /* size n, user's column permutation (may be NULL) */
/* -------------------- */
KLU_common<Entry, Int> *Common
)
{
KLU_symbolic<Entry, Int> *Symbolic ;
double *Lnz ;
Int nblocks, nz, block, maxblock, *P, *Q, *R, nzoff, p, pend, do_btf, k ;
/* ---------------------------------------------------------------------- */
/* determine if input matrix is valid, and get # of nonzeros */
/* ---------------------------------------------------------------------- */
Symbolic = KLU_alloc_symbolic (n, Ap, Ai, Common) ;
if (Symbolic == NULL)
{
return (NULL) ;
}
P = Symbolic->P ;
Q = Symbolic->Q ;
R = Symbolic->R ;
Lnz = Symbolic->Lnz ;
nz = Symbolic->nz ;
/* ---------------------------------------------------------------------- */
/* Q = Quser, or identity if Quser is NULL */
/* ---------------------------------------------------------------------- */
if (Quser == (Int *) NULL)
{
for (k = 0 ; k < n ; k++)
{
Q [k] = k ;
}
}
else
{
for (k = 0 ; k < n ; k++)
{
Q [k] = Quser [k] ;
}
}
/* ---------------------------------------------------------------------- */
/* get the control parameters for BTF and ordering method */
/* ---------------------------------------------------------------------- */
do_btf = Common->btf ;
do_btf = (do_btf) ? TRUE : FALSE ;
Symbolic->ordering = 2 ;
Symbolic->do_btf = do_btf ;
/* ---------------------------------------------------------------------- */
/* find the block triangular form, if requested */
/* ---------------------------------------------------------------------- */
if (do_btf)
{
/* ------------------------------------------------------------------ */
/* get workspace for BTF_strongcomp */
/* ------------------------------------------------------------------ */
Int *Pinv, *Work, *Bi, k1, k2, nk, oldcol ;
Work = (Int *) KLU_malloc (4*n, sizeof (Int), Common) ;
Pinv = (Int *) KLU_malloc (n, sizeof (Int), Common) ;
if (Puser != (Int *) NULL)
{
Bi = (Int *) KLU_malloc (nz+1, sizeof (Int), Common) ;
}
else
{
Bi = Ai ;
}
if (Common->status < KLU_OK)
{
/* out of memory */
KLU_free (Work, 4*n, sizeof (Int), Common) ;
KLU_free (Pinv, n, sizeof (Int), Common) ;
if (Puser != (Int *) NULL)
{
KLU_free (Bi, nz+1, sizeof (Int), Common) ;
}
KLU_free_symbolic (&Symbolic, Common) ;
Common->status = KLU_OUT_OF_MEMORY ;
return (NULL) ;
}
/* ------------------------------------------------------------------ */
/* B = Puser * A */
/* ------------------------------------------------------------------ */
if (Puser != (Int *) NULL)
{
for (k = 0 ; k < n ; k++)
{
Pinv [Puser [k]] = k ;
}
for (p = 0 ; p < nz ; p++)
{
Bi [p] = Pinv [Ai [p]] ;
}
}
/* ------------------------------------------------------------------ */
/* find the strongly-connected components */
/* ------------------------------------------------------------------ */
/* TODO : Correct version of BTF */
/* modifies Q, and determines P and R */
/*nblocks = BTF_strongcomp (n, Ap, Bi, Q, P, R, Work) ;*/
nblocks = KLU_OrdinalTraits<Int>::btf_strongcomp (n, Ap, Bi, Q, P, R,
Work) ;
/* ------------------------------------------------------------------ */
/* P = P * Puser */
/* ------------------------------------------------------------------ */
if (Puser != (Int *) NULL)
{
for (k = 0 ; k < n ; k++)
{
Work [k] = Puser [P [k]] ;
}
for (k = 0 ; k < n ; k++)
{
P [k] = Work [k] ;
}
}
/* ------------------------------------------------------------------ */
/* Pinv = inverse of P */
/* ------------------------------------------------------------------ */
for (k = 0 ; k < n ; k++)
{
Pinv [P [k]] = k ;
}
/* ------------------------------------------------------------------ */
/* analyze each block */
/* ------------------------------------------------------------------ */
nzoff = 0 ; /* nz in off-diagonal part */
maxblock = 1 ; /* size of the largest block */
for (block = 0 ; block < nblocks ; block++)
{
/* -------------------------------------------------------------- */
/* the block is from rows/columns k1 to k2-1 */
/* -------------------------------------------------------------- */
k1 = R [block] ;
k2 = R [block+1] ;
nk = k2 - k1 ;
PRINTF (("BLOCK %d, k1 %d k2-1 %d nk %d\n", block, k1, k2-1, nk)) ;
maxblock = MAX (maxblock, nk) ;
/* -------------------------------------------------------------- */
/* scan the kth block, C */
/* -------------------------------------------------------------- */
for (k = k1 ; k < k2 ; k++)
{
oldcol = Q [k] ;
pend = Ap [oldcol+1] ;
for (p = Ap [oldcol] ; p < pend ; p++)
{
if (Pinv [Ai [p]] < k1)
{
nzoff++ ;
}
}
}
/* fill-in not estimated */
Lnz [block] = EMPTY ;
}
/* ------------------------------------------------------------------ */
/* free all workspace */
/* ------------------------------------------------------------------ */
KLU_free (Work, 4*n, sizeof (Int), Common) ;
KLU_free (Pinv, n, sizeof (Int), Common) ;
if (Puser != (Int *) NULL)
{
KLU_free (Bi, nz+1, sizeof (Int), Common) ;
}
}
else
{
/* ------------------------------------------------------------------ */
/* BTF not requested */
/* ------------------------------------------------------------------ */
nzoff = 0 ;
nblocks = 1 ;
maxblock = n ;
R [0] = 0 ;
R [1] = n ;
Lnz [0] = EMPTY ;
/* ------------------------------------------------------------------ */
/* P = Puser, or identity if Puser is NULL */
/* ------------------------------------------------------------------ */
for (k = 0 ; k < n ; k++)
{
P [k] = (Puser == NULL) ? k : Puser [k] ;
}
}
/* ---------------------------------------------------------------------- */
/* return the symbolic object */
/* ---------------------------------------------------------------------- */
Symbolic->nblocks = nblocks ;
Symbolic->maxblock = maxblock ;
Symbolic->lnz = EMPTY ;
Symbolic->unz = EMPTY ;
Symbolic->nzoff = nzoff ;
return (Symbolic) ;
}
Int KLU_free_numeric
(
KLU_numeric **NumericHandle,
KLU_common *Common
)
{
KLU_numeric *Numeric ;
Unit **LUbx ;
size_t *LUsize ;
Int block, n, nzoff, nblocks ;
if (Common == NULL)
{
return (FALSE) ;
}
if (NumericHandle == NULL || *NumericHandle == NULL)
{
return (TRUE) ;
}
Numeric = *NumericHandle ;
n = Numeric->n ;
nzoff = Numeric->nzoff ;
nblocks = Numeric->nblocks ;
LUsize = Numeric->LUsize ;
LUbx = (Unit **) Numeric->LUbx ;
if (LUbx != NULL)
{
for (block = 0 ; block < nblocks ; block++)
{
KLU_free (LUbx [block], LUsize ? LUsize [block] : 0,
sizeof (Unit), Common) ;
}
}
KLU_free (Numeric->Pnum, n, sizeof (Int), Common) ;
KLU_free (Numeric->Offp, n+1, sizeof (Int), Common) ;
KLU_free (Numeric->Offi, nzoff+1, sizeof (Int), Common) ;
KLU_free (Numeric->Offx, nzoff+1, sizeof (Entry), Common) ;
KLU_free (Numeric->Lip, n, sizeof (Int), Common) ;
KLU_free (Numeric->Llen, n, sizeof (Int), Common) ;
KLU_free (Numeric->Uip, n, sizeof (Int), Common) ;
KLU_free (Numeric->Ulen, n, sizeof (Int), Common) ;
KLU_free (Numeric->LUsize, nblocks, sizeof (size_t), Common) ;
KLU_free (Numeric->LUbx, nblocks, sizeof (Unit *), Common) ;
KLU_free (Numeric->Udiag, n, sizeof (Entry), Common) ;
KLU_free (Numeric->Rs, n, sizeof (double), Common) ;
KLU_free (Numeric->Pinv, n, sizeof (Int), Common) ;
KLU_free (Numeric->Work, Numeric->worksize, 1, Common) ;
KLU_free (Numeric, 1, sizeof (KLU_numeric), Common) ;
*NumericHandle = NULL ;
return (TRUE) ;
}
Int KLU_refactor /* returns TRUE if successful, FALSE otherwise */
(
/* inputs, not modified */
Int Ap [ ], /* size n+1, column pointers */
Int Ai [ ], /* size nz, row indices */
double Ax [ ],
KLU_symbolic<Entry, Int> *Symbolic,
/* input/output */
KLU_numeric<Entry, Int> *Numeric,
KLU_common<Entry, Int> *Common
)
{
Entry ukk, ujk, s ;
Entry *Offx, *Lx, *Ux, *X, *Az, *Udiag ;
double *Rs ;
Int *P, *Q, *R, *Pnum, *Offp, *Offi, *Ui, *Li, *Pinv, *Lip, *Uip, *Llen,
*Ulen ;
Unit **LUbx ;
Unit *LU ;
Int k1, k2, nk, k, block, oldcol, pend, oldrow, n, p, newrow, scale,
nblocks, poff, i, j, up, ulen, llen, maxblock, nzoff ;
/* ---------------------------------------------------------------------- */
/* check inputs */
/* ---------------------------------------------------------------------- */
if (Common == NULL)
{
return (FALSE) ;
}
Common->status = KLU_OK ;
if (Numeric == NULL)
{
/* invalid Numeric object */
Common->status = KLU_INVALID ;
return (FALSE) ;
}
Common->numerical_rank = EMPTY ;
Common->singular_col = EMPTY ;
Az = (Entry *) Ax ;
/* ---------------------------------------------------------------------- */
/* get the contents of the Symbolic object */
/* ---------------------------------------------------------------------- */
n = Symbolic->n ;
P = Symbolic->P ;
Q = Symbolic->Q ;
R = Symbolic->R ;
nblocks = Symbolic->nblocks ;
maxblock = Symbolic->maxblock ;
/* ---------------------------------------------------------------------- */
/* get the contents of the Numeric object */
/* ---------------------------------------------------------------------- */
Pnum = Numeric->Pnum ;
Offp = Numeric->Offp ;
Offi = Numeric->Offi ;
Offx = (Entry *) Numeric->Offx ;
LUbx = (Unit **) Numeric->LUbx ;
scale = Common->scale ;
if (scale > 0)
{
/* factorization was not scaled, but refactorization is scaled */
if (Numeric->Rs == NULL)
{
Numeric->Rs = (double *)KLU_malloc (n, sizeof (double), Common) ;
if (Common->status < KLU_OK)
{
Common->status = KLU_OUT_OF_MEMORY ;
return (FALSE) ;
}
}
}
else
{
/* no scaling for refactorization; ensure Numeric->Rs is freed. This
* does nothing if Numeric->Rs is already NULL. */
Numeric->Rs = (double *) KLU_free (Numeric->Rs, n, sizeof (double), Common) ;
}
Rs = Numeric->Rs ;
Pinv = Numeric->Pinv ;
X = (Entry *) Numeric->Xwork ;
Common->nrealloc = 0 ;
Udiag = (Entry *) Numeric->Udiag ;
nzoff = Symbolic->nzoff ;
/* ---------------------------------------------------------------------- */
/* check the input matrix compute the row scale factors, Rs */
/* ---------------------------------------------------------------------- */
/* do no scale, or check the input matrix, if scale < 0 */
if (scale >= 0)
{
/* check for out-of-range indices, but do not check for duplicates */
if (!KLU_scale (scale, n, Ap, Ai, Ax, Rs, NULL, Common))
{
return (FALSE) ;
}
}
/* ---------------------------------------------------------------------- */
/* clear workspace X */
/* ---------------------------------------------------------------------- */
for (k = 0 ; k < maxblock ; k++)
{
/* X [k] = 0 */
CLEAR (X [k]) ;
}
poff = 0 ;
/* ---------------------------------------------------------------------- */
/* factor each block */
/* ---------------------------------------------------------------------- */
if (scale <= 0)
{
/* ------------------------------------------------------------------ */
/* no scaling */
/* ------------------------------------------------------------------ */
for (block = 0 ; block < nblocks ; block++)
{
/* -------------------------------------------------------------- */
/* the block is from rows/columns k1 to k2-1 */
/* -------------------------------------------------------------- */
k1 = R [block] ;
k2 = R [block+1] ;
nk = k2 - k1 ;
if (nk == 1)
{
/* ---------------------------------------------------------- */
/* singleton case */
/* ---------------------------------------------------------- */
oldcol = Q [k1] ;
pend = Ap [oldcol+1] ;
CLEAR (s) ;
for (p = Ap [oldcol] ; p < pend ; p++)
{
newrow = Pinv [Ai [p]] - k1 ;
if (newrow < 0 && poff < nzoff)
{
/* entry in off-diagonal block */
Offx [poff] = Az [p] ;
poff++ ;
}
else
{
/* singleton */
s = Az [p] ;
}
}
Udiag [k1] = s ;
}
else
{
/* ---------------------------------------------------------- */
/* construct and factor the kth block */
/* ---------------------------------------------------------- */
Lip = Numeric->Lip + k1 ;
Llen = Numeric->Llen + k1 ;
Uip = Numeric->Uip + k1 ;
Ulen = Numeric->Ulen + k1 ;
LU = LUbx [block] ;
for (k = 0 ; k < nk ; k++)
{
/* ------------------------------------------------------ */
/* scatter kth column of the block into workspace X */
/* ------------------------------------------------------ */
oldcol = Q [k+k1] ;
pend = Ap [oldcol+1] ;
for (p = Ap [oldcol] ; p < pend ; p++)
{
newrow = Pinv [Ai [p]] - k1 ;
if (newrow < 0 && poff < nzoff)
{
/* entry in off-diagonal block */
Offx [poff] = Az [p] ;
poff++ ;
}
else
{
/* (newrow,k) is an entry in the block */
X [newrow] = Az [p] ;
}
}
/* ------------------------------------------------------ */
/* compute kth column of U, and update kth column of A */
/* ------------------------------------------------------ */
GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, ulen) ;
for (up = 0 ; up < ulen ; up++)
{
j = Ui [up] ;
ujk = X [j] ;
/* X [j] = 0 */
CLEAR (X [j]) ;
Ux [up] = ujk ;
GET_POINTER (LU, Lip, Llen, Li, Lx, j, llen) ;
for (p = 0 ; p < llen ; p++)
{
/* X [Li [p]] -= Lx [p] * ujk */
MULT_SUB (X [Li [p]], Lx [p], ujk) ;
}
}
/* get the diagonal entry of U */
ukk = X [k] ;
/* X [k] = 0 */
CLEAR (X [k]) ;
/* singular case */
if (IS_ZERO (ukk))
{
/* matrix is numerically singular */
Common->status = KLU_SINGULAR ;
if (Common->numerical_rank == EMPTY)
{
Common->numerical_rank = k+k1 ;
Common->singular_col = Q [k+k1] ;
}
if (Common->halt_if_singular)
{
/* do not continue the factorization */
return (FALSE) ;
}
}
Udiag [k+k1] = ukk ;
/* gather and divide by pivot to get kth column of L */
GET_POINTER (LU, Lip, Llen, Li, Lx, k, llen) ;
for (p = 0 ; p < llen ; p++)
{
i = Li [p] ;
DIV (Lx [p], X [i], ukk) ;
CLEAR (X [i]) ;
}
}
}
}
}
else
{
/* ------------------------------------------------------------------ */
/* scaling */
/* ------------------------------------------------------------------ */
for (block = 0 ; block < nblocks ; block++)
{
/* -------------------------------------------------------------- */
/* the block is from rows/columns k1 to k2-1 */
/* -------------------------------------------------------------- */
k1 = R [block] ;
k2 = R [block+1] ;
nk = k2 - k1 ;
if (nk == 1)
{
/* ---------------------------------------------------------- */
/* singleton case */
/* ---------------------------------------------------------- */
oldcol = Q [k1] ;
pend = Ap [oldcol+1] ;
CLEAR (s) ;
for (p = Ap [oldcol] ; p < pend ; p++)
{
oldrow = Ai [p] ;
newrow = Pinv [oldrow] - k1 ;
if (newrow < 0 && poff < nzoff)
{
/* entry in off-diagonal block */
/* Offx [poff] = Az [p] / Rs [oldrow] */
SCALE_DIV_ASSIGN (Offx [poff], Az [p], Rs [oldrow]) ;
poff++ ;
}
else
{
/* singleton */
/* s = Az [p] / Rs [oldrow] */
SCALE_DIV_ASSIGN (s, Az [p], Rs [oldrow]) ;
}
}
Udiag [k1] = s ;
}
else
{
/* ---------------------------------------------------------- */
/* construct and factor the kth block */
/* ---------------------------------------------------------- */
Lip = Numeric->Lip + k1 ;
Llen = Numeric->Llen + k1 ;
Uip = Numeric->Uip + k1 ;
Ulen = Numeric->Ulen + k1 ;
LU = LUbx [block] ;
for (k = 0 ; k < nk ; k++)
{
/* ------------------------------------------------------ */
/* scatter kth column of the block into workspace X */
/* ------------------------------------------------------ */
oldcol = Q [k+k1] ;
pend = Ap [oldcol+1] ;
for (p = Ap [oldcol] ; p < pend ; p++)
{
oldrow = Ai [p] ;
newrow = Pinv [oldrow] - k1 ;
if (newrow < 0 && poff < nzoff)
{
/* entry in off-diagonal part */
/* Offx [poff] = Az [p] / Rs [oldrow] */
SCALE_DIV_ASSIGN (Offx [poff], Az [p], Rs [oldrow]);
poff++ ;
}
else
{
/* (newrow,k) is an entry in the block */
/* X [newrow] = Az [p] / Rs [oldrow] */
SCALE_DIV_ASSIGN (X [newrow], Az [p], Rs [oldrow]) ;
}
}
/* ------------------------------------------------------ */
/* compute kth column of U, and update kth column of A */
/* ------------------------------------------------------ */
GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, ulen) ;
for (up = 0 ; up < ulen ; up++)
{
j = Ui [up] ;
ujk = X [j] ;
/* X [j] = 0 */
CLEAR (X [j]) ;
Ux [up] = ujk ;
GET_POINTER (LU, Lip, Llen, Li, Lx, j, llen) ;
for (p = 0 ; p < llen ; p++)
{
/* X [Li [p]] -= Lx [p] * ujk */
MULT_SUB (X [Li [p]], Lx [p], ujk) ;
}
}
/* get the diagonal entry of U */
ukk = X [k] ;
/* X [k] = 0 */
CLEAR (X [k]) ;
/* singular case */
if (IS_ZERO (ukk))
{
/* matrix is numerically singular */
Common->status = KLU_SINGULAR ;
if (Common->numerical_rank == EMPTY)
{
Common->numerical_rank = k+k1 ;
Common->singular_col = Q [k+k1] ;
}
if (Common->halt_if_singular)
{
/* do not continue the factorization */
return (FALSE) ;
}
}
Udiag [k+k1] = ukk ;
/* gather and divide by pivot to get kth column of L */
GET_POINTER (LU, Lip, Llen, Li, Lx, k, llen) ;
for (p = 0 ; p < llen ; p++)
{
i = Li [p] ;
DIV (Lx [p], X [i], ukk) ;
CLEAR (X [i]) ;
}
}
}
}
}
/* ---------------------------------------------------------------------- */
/* permute scale factors Rs according to pivotal row order */
/* ---------------------------------------------------------------------- */
if (scale > 0)
{
for (k = 0 ; k < n ; k++)
{
/* TODO : Check. REAL(X[k]) Can be just X[k] */
/* REAL (X [k]) = Rs [Pnum [k]] ; */
X [k] = Rs [Pnum [k]] ;
}
for (k = 0 ; k < n ; k++)
{
Rs [k] = REAL (X [k]) ;
}
}
#ifndef NDEBUGKLU2
ASSERT (Offp [n] == poff) ;
ASSERT (Symbolic->nzoff == poff) ;
PRINTF (("\n------------------- Off diagonal entries, new:\n")) ;
ASSERT (KLU_valid (n, Offp, Offi, Offx)) ;
if (Common->status == KLU_OK)
{
PRINTF (("\n ########### KLU_BTF_REFACTOR done, nblocks %d\n",nblocks));
for (block = 0 ; block < nblocks ; block++)
{
k1 = R [block] ;
k2 = R [block+1] ;
nk = k2 - k1 ;
PRINTF ((
"\n================KLU_refactor output: k1 %d k2 %d nk %d\n",
k1, k2, nk)) ;
if (nk == 1)
{
PRINTF (("singleton ")) ;
PRINT_ENTRY (Udiag [k1]) ;
}
else
{
Lip = Numeric->Lip + k1 ;
Llen = Numeric->Llen + k1 ;
LU = (Unit *) Numeric->LUbx [block] ;
PRINTF (("\n---- L block %d\n", block)) ;
ASSERT (KLU_valid_LU (nk, TRUE, Lip, Llen, LU)) ;
Uip = Numeric->Uip + k1 ;
Ulen = Numeric->Ulen + k1 ;
PRINTF (("\n---- U block %d\n", block)) ;
ASSERT (KLU_valid_LU (nk, FALSE, Uip, Ulen, LU)) ;
}
}
}
#endif
return (TRUE) ;
}
Int KLU_sort
(
KLU_symbolic<Entry, Int> *Symbolic,
KLU_numeric<Entry, Int> *Numeric,
KLU_common<Entry, Int> *Common
)
{
Int *R, *W, *Tp, *Ti, *Lip, *Uip, *Llen, *Ulen ;
Entry *Tx ;
Unit **LUbx ;
Int n, nk, nz, block, nblocks, maxblock, k1 ;
size_t m1 ;
if (Common == NULL)
{
return (FALSE) ;
}
Common->status = KLU_OK ;
n = Symbolic->n ;
R = Symbolic->R ;
nblocks = Symbolic->nblocks ;
maxblock = Symbolic->maxblock ;
Lip = Numeric->Lip ;
Llen = Numeric->Llen ;
Uip = Numeric->Uip ;
Ulen = Numeric->Ulen ;
LUbx = (Unit **) Numeric->LUbx ;
m1 = ((size_t) maxblock) + 1 ;
/* allocate workspace */
nz = MAX (Numeric->max_lnz_block, Numeric->max_unz_block) ;
W = (Int *) KLU_malloc (maxblock, sizeof (Int), Common) ;
Tp = (Int *) KLU_malloc (m1, sizeof (Int), Common) ;
Ti = (Int *) KLU_malloc (nz, sizeof (Int), Common) ;
Tx = (Entry *) KLU_malloc (nz, sizeof (Entry), Common) ;
PRINTF (("\n======================= Start sort:\n")) ;
if (Common->status == KLU_OK)
{
/* sort each block of L and U */
for (block = 0 ; block < nblocks ; block++)
{
k1 = R [block] ;
nk = R [block+1] - k1 ;
if (nk > 1)
{
PRINTF (("\n-------------------block: %d nk %d\n", block, nk)) ;
sort (nk, Lip + k1, Llen + k1, LUbx [block], Tp, Ti, Tx, W) ;
sort (nk, Uip + k1, Ulen + k1, LUbx [block], Tp, Ti, Tx, W) ;
}
}
}
PRINTF (("\n======================= sort done.\n")) ;
/* free workspace */
KLU_free (W, maxblock, sizeof (Int), Common) ;
KLU_free (Tp, m1, sizeof (Int), Common) ;
KLU_free (Ti, nz, sizeof (Int), Common) ;
KLU_free (Tx, nz, sizeof (Entry), Common) ;
return (Common->status == KLU_OK) ;
}
