GLOBAL void UMF_fsize
(
Int nn,
Int Fsize [ ],
Int Fnrows [ ],
Int Fncols [ ],
Int Parent [ ],
Int Npiv [ ]
)
{
Int j, parent, frsize, r, c ;
for (j = 0 ; j < nn ; j++)
{
Fsize [j] = EMPTY ;
}
/* ---------------------------------------------------------------------- */
/* find max front size for tree rooted at node j, for each front j */
/* ---------------------------------------------------------------------- */
DEBUG1 (("\n\n========================================FRONTS:\n")) ;
for (j = 0 ; j < nn ; j++)
{
if (Npiv [j] > 0)
{
/* this is a frontal matrix */
parent = Parent [j] ;
r = Fnrows [j] ;
c = Fncols [j] ;
frsize = r * c ;
/* avoid integer overflow */
if (INT_OVERFLOW (((double) r) * ((double) c)))
{
/* :: frsize int overflow :: */
frsize = Int_MAX ;
}
DEBUG1 ((""ID" : npiv "ID" size "ID" parent "ID" ",
j, Npiv [j], frsize, parent)) ;
Fsize [j] = MAX (Fsize [j], frsize) ;
DEBUG1 (("Fsize [j = "ID"] = "ID"\n", j, Fsize [j])) ;
if (parent != EMPTY)
{
/* find the maximum frontsize of self and children */
ASSERT (Npiv [parent] > 0) ;
ASSERT (parent > j) ;
Fsize [parent] = MAX (Fsize [parent], Fsize [j]) ;
DEBUG1 (("Fsize [parent = "ID"] = "ID"\n",
parent, Fsize [parent]));
}
}
}
}
GLOBAL Int UMF_mem_alloc_element
(
NumericType *Numeric,
Int nrows,
Int ncols,
Int **Rows,
Int **Cols,
Entry **C,
Int *size,
Element **epout
)
{
Element *ep ;
Unit *p ;
Int i ;
ASSERT (Numeric != (NumericType *) NULL) ;
ASSERT (Numeric->Memory != (Unit *) NULL) ;
*size = GET_ELEMENT_SIZE (nrows, ncols) ;
if (INT_OVERFLOW (DGET_ELEMENT_SIZE (nrows, ncols) + 1))
{
/* :: allocate element, int overflow :: */
return (0) ; /* problem is too large */
}
i = UMF_mem_alloc_tail_block (Numeric, *size) ;
(*size)++ ;
if (!i)
{
DEBUG0 (("alloc element failed - out of memory\n")) ;
return (0) ; /* out of memory */
}
p = Numeric->Memory + i ;
ep = (Element *) p ;
DEBUG2 (("alloc_element done ("ID" x "ID"): p: "ID" i "ID"\n",
nrows, ncols, (Int) (p-Numeric->Memory), i)) ;
/* Element data structure, in order: */
p += UNITS (Element, 1) ; /* (1) Element header */
*Cols = (Int *) p ; /* (2) col [0..ncols-1] indices */
*Rows = *Cols + ncols ; /* (3) row [0..nrows-1] indices */
p += UNITS (Int, ncols + nrows) ;
*C = (Entry *) p ; /* (4) C [0..nrows-1, 0..ncols-1] */
ep->nrows = nrows ; /* initialize the header information */
ep->ncols = ncols ;
ep->nrowsleft = nrows ;
ep->ncolsleft = ncols ;
ep->cdeg = 0 ;
ep->rdeg = 0 ;
ep->next = EMPTY ;
DEBUG2 (("new block size: "ID" ", GET_BLOCK_SIZE (Numeric->Memory + i))) ;
DEBUG2 (("Element size needed "ID"\n", GET_ELEMENT_SIZE (nrows, ncols))) ;
*epout = ep ;
/* return the offset into Numeric->Memory */
return (i) ;
}
GLOBAL Int UMFPACK_numeric
(
const Int Ap [ ],
const Int Ai [ ],
const double Ax [ ],
#ifdef COMPLEX
const double Az [ ],
#endif
void *SymbolicHandle,
void **NumericHandle,
const double Control [UMFPACK_CONTROL],
double User_Info [UMFPACK_INFO]
)
{
/* ---------------------------------------------------------------------- */
/* local variables */
/* ---------------------------------------------------------------------- */
double Info2 [UMFPACK_INFO], alloc_init, relpt, relpt2, droptol,
front_alloc_init, stats [2] ;
double *Info ;
WorkType WorkSpace, *Work ;
NumericType *Numeric ;
SymbolicType *Symbolic ;
Int n_row, n_col, n_inner, newsize, i, status, *inew, npiv, ulen, scale ;
Unit *mnew ;
/* ---------------------------------------------------------------------- */
/* get the amount of time used by the process so far */
/* ---------------------------------------------------------------------- */
umfpack_tic (stats) ;
/* ---------------------------------------------------------------------- */
/* initialize and check inputs */
/* ---------------------------------------------------------------------- */
#ifndef NDEBUG
UMF_dump_start ( ) ;
init_count = UMF_malloc_count ;
DEBUGm4 (("\nUMFPACK numeric: U transpose version\n")) ;
#endif
/* If front_alloc_init negative then allocate that size of front in
* UMF_start_front. If alloc_init negative, then allocate that initial
* size of Numeric->Memory. */
relpt = GET_CONTROL (UMFPACK_PIVOT_TOLERANCE,
UMFPACK_DEFAULT_PIVOT_TOLERANCE) ;
relpt2 = GET_CONTROL (UMFPACK_SYM_PIVOT_TOLERANCE,
UMFPACK_DEFAULT_SYM_PIVOT_TOLERANCE) ;
alloc_init = GET_CONTROL (UMFPACK_ALLOC_INIT, UMFPACK_DEFAULT_ALLOC_INIT) ;
front_alloc_init = GET_CONTROL (UMFPACK_FRONT_ALLOC_INIT,
UMFPACK_DEFAULT_FRONT_ALLOC_INIT) ;
scale = GET_CONTROL (UMFPACK_SCALE, UMFPACK_DEFAULT_SCALE) ;
droptol = GET_CONTROL (UMFPACK_DROPTOL, UMFPACK_DEFAULT_DROPTOL) ;
relpt = MAX (0.0, MIN (relpt, 1.0)) ;
relpt2 = MAX (0.0, MIN (relpt2, 1.0)) ;
droptol = MAX (0.0, droptol) ;
front_alloc_init = MIN (1.0, front_alloc_init) ;
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 ;
/* clear the parts of Info that are set by UMFPACK_numeric */
for (i = UMFPACK_NUMERIC_SIZE ; i <= UMFPACK_MAX_FRONT_NCOLS ; i++)
{
Info [i] = EMPTY ;
}
for (i = UMFPACK_NUMERIC_DEFRAG ; i < UMFPACK_IR_TAKEN ; i++)
{
Info [i] = EMPTY ;
}
}
else
{
/* no Info array passed - use local one instead */
Info = Info2 ;
for (i = 0 ; i < UMFPACK_INFO ; i++)
{
Info [i] = EMPTY ;
}
}
Symbolic = (SymbolicType *) SymbolicHandle ;
Numeric = (NumericType *) NULL ;
if (!UMF_valid_symbolic (Symbolic))
{
Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_Symbolic_object ;
return (UMFPACK_ERROR_invalid_Symbolic_object) ;
}
/* compute alloc_init automatically for AMD or other symmetric ordering */
if (/* Symbolic->ordering == UMFPACK_ORDERING_AMD */ alloc_init >= 0
&& Symbolic->amd_lunz > 0)
{
alloc_init = (Symbolic->nz + Symbolic->amd_lunz) / Symbolic->lunz_bound;
alloc_init = MIN (1.0, alloc_init) ;
alloc_init *= UMF_REALLOC_INCREASE ;
}
n_row = Symbolic->n_row ;
n_col = Symbolic->n_col ;
n_inner = MIN (n_row, n_col) ;
/* check for integer overflow in Numeric->Memory minimum size */
if (INT_OVERFLOW (Symbolic->dnum_mem_init_usage * sizeof (Unit)))
{
/* :: int overflow, initial Numeric->Memory size :: */
/* There's no hope to allocate a Numeric object big enough simply to
* hold the initial matrix, so return an out-of-memory condition */
DEBUGm4 (("out of memory: numeric int overflow\n")) ;
Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
return (UMFPACK_ERROR_out_of_memory) ;
}
Info [UMFPACK_STATUS] = UMFPACK_OK ;
Info [UMFPACK_NROW] = n_row ;
Info [UMFPACK_NCOL] = n_col ;
Info [UMFPACK_SIZE_OF_UNIT] = (double) (sizeof (Unit)) ;
if (!Ap || !Ai || !Ax || !NumericHandle)
{
Info [UMFPACK_STATUS] = UMFPACK_ERROR_argument_missing ;
return (UMFPACK_ERROR_argument_missing) ;
}
Info [UMFPACK_NZ] = Ap [n_col] ;
*NumericHandle = (void *) NULL ;
/* ---------------------------------------------------------------------- */
/* allocate the Work object */
/* ---------------------------------------------------------------------- */
/* (1) calls UMF_malloc 15 or 17 times, to obtain temporary workspace of
* size c+1 Entry's and 2*(n_row+1) + 3*(n_col+1) + (n_col+n_inner+1) +
* (nn+1) + * 3*(c+1) + 2*(r+1) + max(r,c) + (nfr+1) integers plus 2*nn
* more integers if diagonal pivoting is to be done. r is the maximum
* number of rows in any frontal matrix, c is the maximum number of columns
* in any frontal matrix, n_inner is min (n_row,n_col), nn is
* max (n_row,n_col), and nfr is the number of frontal matrices. For a
* square matrix, this is c+1 Entry's and about 8n + 3c + 2r + max(r,c) +
* nfr integers, plus 2n more for diagonal pivoting.
*/
Work = &WorkSpace ;
Work->n_row = n_row ;
Work->n_col = n_col ;
Work->nfr = Symbolic->nfr ;
Work->nb = Symbolic->nb ;
Work->n1 = Symbolic->n1 ;
if (!work_alloc (Work, Symbolic))
{
DEBUGm4 (("out of memory: numeric work\n")) ;
Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
error (&Numeric, Work) ;
return (UMFPACK_ERROR_out_of_memory) ;
}
ASSERT (UMF_malloc_count == init_count + 16 + 2*Symbolic->prefer_diagonal) ;
/* ---------------------------------------------------------------------- */
/* allocate Numeric object */
/* ---------------------------------------------------------------------- */
/* (2) calls UMF_malloc 10 or 11 times, for a total space of
* sizeof (NumericType) bytes, 4*(n_row+1) + 4*(n_row+1) integers, and
* (n_inner+1) Entry's, plus n_row Entry's if row scaling is to be done.
* sizeof (NumericType) is a small constant. Next, it calls UMF_malloc
* once, for the variable-sized part of the Numeric object
* (Numeric->Memory). The size of this object is the larger of
* (Control [UMFPACK_ALLOC_INIT]) * (the approximate upper bound computed
* by UMFPACK_symbolic), and the minimum required to start the numerical
* factorization. * This request is reduced if it fails.
*/
if (!numeric_alloc (&Numeric, Symbolic, alloc_init, scale))
{
DEBUGm4 (("out of memory: initial numeric\n")) ;
Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
error (&Numeric, Work) ;
return (UMFPACK_ERROR_out_of_memory) ;
}
DEBUG0 (("malloc: init_count "ID" UMF_malloc_count "ID"\n",
init_count, UMF_malloc_count)) ;
ASSERT (UMF_malloc_count == init_count
+ (16 + 2*Symbolic->prefer_diagonal)
+ (11 + (scale != UMFPACK_SCALE_NONE))) ;
/* set control parameters */
Numeric->relpt = relpt ;
Numeric->relpt2 = relpt2 ;
Numeric->droptol = droptol ;
Numeric->alloc_init = alloc_init ;
Numeric->front_alloc_init = front_alloc_init ;
Numeric->scale = scale ;
DEBUG0 (("umf relpt %g %g init %g %g inc %g red %g\n",
relpt, relpt2, alloc_init, front_alloc_init,
UMF_REALLOC_INCREASE, UMF_REALLOC_REDUCTION)) ;
/* ---------------------------------------------------------------------- */
/* scale and factorize */
/* ---------------------------------------------------------------------- */
/* (3) During numerical factorization (inside UMF_kernel), the variable-size
* block of memory is increased in size via a call to UMF_realloc if it is
* found to be too small. During factorization, this block holds the
* pattern and values of L and U at the top end, and the elements
* (contibution blocks) and the current frontal matrix (Work->F*) at the
* bottom end. The peak size of the variable-sized object is estimated in
* UMFPACK_*symbolic (Info [UMFPACK_VARIABLE_PEAK_ESTIMATE]), although this
* upper bound can be very loose. The size of the Symbolic object
* (which is currently allocated) is in Info [UMFPACK_SYMBOLIC_SIZE], and
* is between 2*n and 13*n integers.
*/
DEBUG0 (("Calling umf_kernel\n")) ;
status = UMF_kernel (Ap, Ai, Ax,
#ifdef COMPLEX
Az,
#endif
Numeric, Work, Symbolic) ;
Info [UMFPACK_STATUS] = status ;
if (status < UMFPACK_OK)
{
/* out of memory, or pattern has changed */
error (&Numeric, Work) ;
return (status) ;
}
Info [UMFPACK_FORCED_UPDATES] = Work->nforced ;
Info [UMFPACK_VARIABLE_INIT] = Numeric->init_usage ;
if (Symbolic->prefer_diagonal)
{
Info [UMFPACK_NOFF_DIAG] = Work->noff_diagonal ;
}
DEBUG0 (("malloc: init_count "ID" UMF_malloc_count "ID"\n",
init_count, UMF_malloc_count)) ;
npiv = Numeric->npiv ; /* = n_inner for nonsingular matrices */
ulen = Numeric->ulen ; /* = 0 for square nonsingular matrices */
/* ---------------------------------------------------------------------- */
/* free Work object */
/* ---------------------------------------------------------------------- */
/* (4) After numerical factorization all of the objects allocated in step
* (1) are freed via UMF_free, except that one object of size n_col+1 is
* kept if there are off-diagonal nonzeros in the last pivot row (can only
* occur for singular or rectangular matrices). This is Work->Upattern,
* which is transfered to Numeric->Upattern if ulen > 0.
*/
DEBUG0 (("malloc: init_count "ID" UMF_malloc_count "ID"\n",
init_count, UMF_malloc_count)) ;
free_work (Work) ;
DEBUG0 (("malloc: init_count "ID" UMF_malloc_count "ID"\n",
init_count, UMF_malloc_count)) ;
DEBUG0 (("Numeric->ulen: "ID" scale: "ID"\n", ulen, scale)) ;
ASSERT (UMF_malloc_count == init_count + (ulen > 0) +
(11 + (scale != UMFPACK_SCALE_NONE))) ;
/* ---------------------------------------------------------------------- */
/* reduce Lpos, Lilen, Lip, Upos, Uilen and Uip to size npiv+1 */
/* ---------------------------------------------------------------------- */
/* (5) Six components of the Numeric object are reduced in size if the
* matrix is singular or rectangular. The original size is 3*(n_row+1) +
* 3*(n_col+1) integers. The new size is 6*(npiv+1) integers. For
* square non-singular matrices, these two sizes are the same.
*/
if (npiv < n_row)
{
/* reduce Lpos, Uilen, and Uip from size n_row+1 to size npiv */
inew = (Int *) UMF_realloc (Numeric->Lpos, npiv+1, sizeof (Int)) ;
if (inew)
{
Numeric->Lpos = inew ;
}
inew = (Int *) UMF_realloc (Numeric->Uilen, npiv+1, sizeof (Int)) ;
if (inew)
{
Numeric->Uilen = inew ;
}
inew = (Int *) UMF_realloc (Numeric->Uip, npiv+1, sizeof (Int)) ;
if (inew)
{
Numeric->Uip = inew ;
}
}
if (npiv < n_col)
{
/* reduce Upos, Lilen, and Lip from size n_col+1 to size npiv */
inew = (Int *) UMF_realloc (Numeric->Upos, npiv+1, sizeof (Int)) ;
if (inew)
{
Numeric->Upos = inew ;
}
inew = (Int *) UMF_realloc (Numeric->Lilen, npiv+1, sizeof (Int)) ;
if (inew)
{
Numeric->Lilen = inew ;
}
inew = (Int *) UMF_realloc (Numeric->Lip, npiv+1, sizeof (Int)) ;
if (inew)
{
Numeric->Lip = inew ;
}
}
/* ---------------------------------------------------------------------- */
/* reduce Numeric->Upattern from size n_col+1 to size ulen+1 */
/* ---------------------------------------------------------------------- */
/* (6) The size of Numeric->Upattern (formerly Work->Upattern) is reduced
* from size n_col+1 to size ulen + 1. If ulen is zero, the object does
* not exist. */
DEBUG4 (("ulen: "ID" Upattern "ID"\n", ulen, (Int) Numeric->Upattern)) ;
ASSERT (IMPLIES (ulen == 0, Numeric->Upattern == (Int *) NULL)) ;
if (ulen > 0 && ulen < n_col)
{
inew = (Int *) UMF_realloc (Numeric->Upattern, ulen+1, sizeof (Int)) ;
if (inew)
{
Numeric->Upattern = inew ;
}
}
/* ---------------------------------------------------------------------- */
/* reduce Numeric->Memory to hold just the LU factors at the head */
/* ---------------------------------------------------------------------- */
/* (7) The variable-sized block (Numeric->Memory) is reduced to hold just L
* and U, via a call to UMF_realloc, since the frontal matrices are no
* longer needed.
*/
newsize = Numeric->ihead ;
if (newsize < Numeric->size)
{
mnew = (Unit *) UMF_realloc (Numeric->Memory, newsize, sizeof (Unit)) ;
if (mnew)
{
/* realloc succeeded (how can it fail since the size is reduced?) */
Numeric->Memory = mnew ;
Numeric->size = newsize ;
}
}
Numeric->ihead = Numeric->size ;
Numeric->itail = Numeric->ihead ;
Numeric->tail_usage = 0 ;
Numeric->ibig = EMPTY ;
/* UMF_mem_alloc_tail_block can no longer be called (no tail marker) */
/* ---------------------------------------------------------------------- */
/* report the results and return the Numeric object */
/* ---------------------------------------------------------------------- */
UMF_set_stats (
Info,
Symbolic,
(double) Numeric->max_usage, /* actual peak Numeric->Memory */
(double) Numeric->size, /* actual final Numeric->Memory */
Numeric->flops, /* actual "true flops" */
(double) Numeric->lnz + n_inner, /* actual nz in L */
(double) Numeric->unz + Numeric->nnzpiv, /* actual nz in U */
(double) Numeric->maxfrsize, /* actual largest front size */
(double) ulen, /* actual Numeric->Upattern size */
(double) npiv, /* actual # pivots found */
(double) Numeric->maxnrows, /* actual largest #rows in front */
(double) Numeric->maxncols, /* actual largest #cols in front */
scale != UMFPACK_SCALE_NONE,
Symbolic->prefer_diagonal,
ACTUAL) ;
Info [UMFPACK_ALLOC_INIT_USED] = Numeric->alloc_init ;
Info [UMFPACK_NUMERIC_DEFRAG] = Numeric->ngarbage ;
Info [UMFPACK_NUMERIC_REALLOC] = Numeric->nrealloc ;
Info [UMFPACK_NUMERIC_COSTLY_REALLOC] = Numeric->ncostly ;
Info [UMFPACK_COMPRESSED_PATTERN] = Numeric->isize ;
Info [UMFPACK_LU_ENTRIES] = Numeric->nLentries + Numeric->nUentries +
Numeric->npiv ;
Info [UMFPACK_UDIAG_NZ] = Numeric->nnzpiv ;
Info [UMFPACK_RSMIN] = Numeric->rsmin ;
Info [UMFPACK_RSMAX] = Numeric->rsmax ;
Info [UMFPACK_WAS_SCALED] = Numeric->scale ;
/* nz in L and U with no dropping of small entries */
Info [UMFPACK_ALL_LNZ] = Numeric->all_lnz + n_inner ;
Info [UMFPACK_ALL_UNZ] = Numeric->all_unz + Numeric->nnzpiv ;
Info [UMFPACK_NZDROPPED] =
(Numeric->all_lnz - Numeric->lnz)
+ (Numeric->all_unz - Numeric->unz) ;
/* estimate of the reciprocal of the condition number. */
if (SCALAR_IS_ZERO (Numeric->min_udiag)
|| SCALAR_IS_ZERO (Numeric->max_udiag)
|| SCALAR_IS_NAN (Numeric->min_udiag)
|| SCALAR_IS_NAN (Numeric->max_udiag))
{
/* rcond is zero if there is any zero or NaN on the diagonal */
Numeric->rcond = 0.0 ;
}
else
{
/* estimate of the recipricol of the condition number. */
/* This is NaN if diagonal is zero-free, but has one or more NaN's. */
Numeric->rcond = Numeric->min_udiag / Numeric->max_udiag ;
}
Info [UMFPACK_UMIN] = Numeric->min_udiag ;
Info [UMFPACK_UMAX] = Numeric->max_udiag ;
Info [UMFPACK_RCOND] = Numeric->rcond ;
if (Numeric->nnzpiv < n_inner
|| SCALAR_IS_ZERO (Numeric->rcond) || SCALAR_IS_NAN (Numeric->rcond))
{
/* there are zeros and/or NaN's on the diagonal of U */
DEBUG0 (("Warning, matrix is singular in umfpack_numeric\n")) ;
DEBUG0 (("nnzpiv "ID" n_inner "ID" rcond %g\n", Numeric->nnzpiv,
n_inner, Numeric->rcond)) ;
status = UMFPACK_WARNING_singular_matrix ;
Info [UMFPACK_STATUS] = status ;
}
Numeric->valid = NUMERIC_VALID ;
*NumericHandle = (void *) Numeric ;
/* Numeric has 11 to 13 objects */
ASSERT (UMF_malloc_count == init_count + 11 +
+ (ulen > 0) /* Numeric->Upattern */
+ (scale != UMFPACK_SCALE_NONE)) ; /* Numeric->Rs */
/* ---------------------------------------------------------------------- */
/* get the time used by UMFPACK_numeric */
/* ---------------------------------------------------------------------- */
umfpack_toc (stats) ;
Info [UMFPACK_NUMERIC_WALLTIME] = stats [0] ;
Info [UMFPACK_NUMERIC_TIME] = stats [1] ;
/* return UMFPACK_OK or UMFPACK_WARNING_singular_matrix */
return (status) ;
}
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) ;
}
GLOBAL Int UMF_grow_front
(
NumericType *Numeric,
Int fnr2, /* desired size is fnr2-by-fnc2 */
Int fnc2,
WorkType *Work,
Int do_what /* -1: UMF_start_front
* 0: UMF_init_front, do not recompute Fcpos
* 1: UMF_extend_front
* 2: UMF_init_front, recompute Fcpos */
)
{
/* ---------------------------------------------------------------------- */
/* local variables */
/* ---------------------------------------------------------------------- */
double s ;
Entry *Fcold, *Fcnew ;
Int j, i, col, *Fcpos, *Fcols, fnrows_max, fncols_max, fnr_curr, nb,
fnrows_new, fncols_new, fnr_min, fnc_min, minsize,
newsize, fnrows, fncols, *E, eloc ;
/* ---------------------------------------------------------------------- */
/* get parameters */
/* ---------------------------------------------------------------------- */
#ifndef NDEBUG
if (do_what != -1) UMF_debug++ ;
DEBUG0 (("\n\n====================GROW FRONT: do_what: "ID"\n", do_what)) ;
if (do_what != -1) UMF_debug-- ;
ASSERT (Work->do_grow) ;
ASSERT (Work->fnpiv == 0) ;
#endif
Fcols = Work->Fcols ;
Fcpos = Work->Fcpos ;
E = Work->E ;
/* ---------------------------------------------------------------------- */
/* The current front is too small, find the new size */
/* ---------------------------------------------------------------------- */
/* maximum size of frontal matrix for this chain */
nb = Work->nb ;
fnrows_max = Work->fnrows_max + nb ;
fncols_max = Work->fncols_max + nb ;
ASSERT (fnrows_max >= 0 && (fnrows_max % 2) == 1) ;
DEBUG0 (("Max size: "ID"-by-"ID" (incl. "ID" pivot block\n",
fnrows_max, fncols_max, nb)) ;
/* current dimensions of frontal matrix: fnr-by-fnc */
DEBUG0 (("Current : "ID"-by-"ID" (excl "ID" pivot blocks)\n",
Work->fnr_curr, Work->fnc_curr, nb)) ;
ASSERT (Work->fnr_curr >= 0) ;
ASSERT ((Work->fnr_curr % 2 == 1) || Work->fnr_curr == 0) ;
/* required dimensions of frontal matrix: fnr_min-by-fnc_min */
fnrows_new = Work->fnrows_new + 1 ;
fncols_new = Work->fncols_new + 1 ;
ASSERT (fnrows_new >= 0) ;
if (fnrows_new % 2 == 0) fnrows_new++ ;
fnrows_new += nb ;
fncols_new += nb ;
fnr_min = MIN (fnrows_new, fnrows_max) ;
fnc_min = MIN (fncols_new, fncols_max) ;
minsize = fnr_min * fnc_min ;
if (INT_OVERFLOW ((double) fnr_min * (double) fnc_min * sizeof (Entry)))
{
/* :: the minimum front size is bigger than the integer maximum :: */
return (FALSE) ;
}
ASSERT (fnr_min >= 0) ;
ASSERT (fnr_min % 2 == 1) ;
DEBUG0 (("Min : "ID"-by-"ID"\n", fnr_min, fnc_min)) ;
/* grow the front to fnr2-by-fnc2, but no bigger than the maximum,
* and no smaller than the minumum. */
DEBUG0 (("Desired : ("ID"+"ID")-by-("ID"+"ID")\n", fnr2, nb, fnc2, nb)) ;
fnr2 += nb ;
fnc2 += nb ;
ASSERT (fnr2 >= 0) ;
if (fnr2 % 2 == 0) fnr2++ ;
fnr2 = MAX (fnr2, fnr_min) ;
fnc2 = MAX (fnc2, fnc_min) ;
fnr2 = MIN (fnr2, fnrows_max) ;
fnc2 = MIN (fnc2, fncols_max) ;
DEBUG0 (("Try : "ID"-by-"ID"\n", fnr2, fnc2)) ;
ASSERT (fnr2 >= 0) ;
ASSERT (fnr2 % 2 == 1) ;
s = ((double) fnr2) * ((double) fnc2) ;
if (INT_OVERFLOW (s * sizeof (Entry)))
{
/* :: frontal matrix size int overflow :: */
/* the desired front size is bigger than the integer maximum */
/* compute a such that a*a*s < Int_MAX / sizeof (Entry) */
double a = 0.9 * sqrt ((Int_MAX / sizeof (Entry)) / s) ;
fnr2 = MAX (fnr_min, a * fnr2) ;
fnc2 = MAX (fnc_min, a * fnc2) ;
/* the new frontal size is a*r*a*c = a*a*s */
newsize = fnr2 * fnc2 ;
ASSERT (fnr2 >= 0) ;
if (fnr2 % 2 == 0) fnr2++ ;
fnc2 = newsize / fnr2 ;
}
fnr2 = MAX (fnr2, fnr_min) ;
fnc2 = MAX (fnc2, fnc_min) ;
newsize = fnr2 * fnc2 ;
ASSERT (fnr2 >= 0) ;
ASSERT (fnr2 % 2 == 1) ;
ASSERT (fnr2 >= fnr_min) ;
ASSERT (fnc2 >= fnc_min) ;
ASSERT (newsize >= minsize) ;
/* ---------------------------------------------------------------------- */
/* free the current front if it is empty of any numerical values */
/* ---------------------------------------------------------------------- */
if (E [0] && do_what != 1)
{
/* free the current front, if it exists and has nothing in it */
DEBUG0 (("Freeing empty front\n")) ;
UMF_mem_free_tail_block (Numeric, E [0]) ;
E [0] = 0 ;
Work->Flublock = (Entry *) NULL ;
Work->Flblock = (Entry *) NULL ;
Work->Fublock = (Entry *) NULL ;
Work->Fcblock = (Entry *) NULL ;
}
/* ---------------------------------------------------------------------- */
/* allocate the new front, doing garbage collection if necessary */
/* ---------------------------------------------------------------------- */
#ifndef NDEBUG
UMF_allocfail = FALSE ;
if (UMF_gprob > 0) /* a double relop, but ignore NaN case */
{
double rrr = ((double) (rand ( ))) / (((double) RAND_MAX) + 1) ;
DEBUG1 (("Check random %e %e\n", rrr, UMF_gprob)) ;
UMF_allocfail = rrr < UMF_gprob ;
if (UMF_allocfail) DEBUGm2 (("Random garbage collection (grow)\n")) ;
}
#endif
DEBUG0 (("Attempt size: "ID"-by-"ID"\n", fnr2, fnc2)) ;
eloc = UMF_mem_alloc_tail_block (Numeric, UNITS (Entry, newsize)) ;
if (!eloc)
{
/* Do garbage collection, realloc, and try again. Compact the current
* contribution block in the front to fnrows-by-fncols. Note that
* there are no pivot rows/columns in current front. Do not recompute
* Fcpos in UMF_garbage_collection. */
DEBUGm3 (("get_memory from umf_grow_front\n")) ;
if (!UMF_get_memory (Numeric, Work, 1 + UNITS (Entry, newsize),
Work->fnrows, Work->fncols, FALSE))
{
/* :: out of memory in umf_grow_front :: */
return (FALSE) ; /* out of memory */
}
DEBUG0 (("Attempt size: "ID"-by-"ID" again\n", fnr2, fnc2)) ;
eloc = UMF_mem_alloc_tail_block (Numeric, UNITS (Entry, newsize)) ;
}
/* try again with something smaller */
while ((fnr2 != fnr_min || fnc2 != fnc_min) && !eloc)
{
fnr2 = MIN (fnr2 - 2, fnr2 * UMF_REALLOC_REDUCTION) ;
fnc2 = MIN (fnc2 - 2, fnc2 * UMF_REALLOC_REDUCTION) ;
ASSERT (fnr_min >= 0) ;
ASSERT (fnr_min % 2 == 1) ;
fnr2 = MAX (fnr_min, fnr2) ;
fnc2 = MAX (fnc_min, fnc2) ;
ASSERT (fnr2 >= 0) ;
if (fnr2 % 2 == 0) fnr2++ ;
newsize = fnr2 * fnc2 ;
DEBUGm3 (("Attempt smaller size: "ID"-by-"ID" minsize "ID"-by-"ID"\n",
fnr2, fnc2, fnr_min, fnc_min)) ;
eloc = UMF_mem_alloc_tail_block (Numeric, UNITS (Entry, newsize)) ;
}
/* try again with the smallest possible size */
if (!eloc)
{
fnr2 = fnr_min ;
fnc2 = fnc_min ;
newsize = minsize ;
DEBUG0 (("Attempt minsize: "ID"-by-"ID"\n", fnr2, fnc2)) ;
eloc = UMF_mem_alloc_tail_block (Numeric, UNITS (Entry, newsize)) ;
}
if (!eloc)
{
/* out of memory */
return (FALSE) ;
}
ASSERT (fnr2 >= 0) ;
ASSERT (fnr2 % 2 == 1) ;
ASSERT (fnr2 >= fnr_min && fnc2 >= fnc_min) ;
/* ---------------------------------------------------------------------- */
/* copy the old frontal matrix into the new one */
/* ---------------------------------------------------------------------- */
/* old contribution block (if any) */
fnr_curr = Work->fnr_curr ; /* garbage collection can change fn*_curr */
ASSERT (fnr_curr >= 0) ;
ASSERT ((fnr_curr % 2 == 1) || fnr_curr == 0) ;
fnrows = Work->fnrows ;
fncols = Work->fncols ;
Fcold = Work->Fcblock ;
/* remove nb from the sizes */
fnr2 -= nb ;
fnc2 -= nb ;
/* new frontal matrix */
Work->Flublock = (Entry *) (Numeric->Memory + eloc) ;
Work->Flblock = Work->Flublock + nb * nb ;
Work->Fublock = Work->Flblock + nb * fnr2 ;
Work->Fcblock = Work->Fublock + nb * fnc2 ;
Fcnew = Work->Fcblock ;
if (E [0])
{
/* copy the old contribution block into the new one */
for (j = 0 ; j < fncols ; j++)
{
col = Fcols [j] ;
DEBUG1 (("copy col "ID" \n",col)) ;
ASSERT (col >= 0 && col < Work->n_col) ;
for (i = 0 ; i < fnrows ; i++)
{
Fcnew [i] = Fcold [i] ;
}
Fcnew += fnr2 ;
Fcold += fnr_curr ;
DEBUG1 (("new offset col "ID" "ID"\n",col, j * fnr2)) ;
Fcpos [col] = j * fnr2 ;
}
}
else if (do_what == 2)
{
/* just find the new column offsets */
for (j = 0 ; j < fncols ; j++)
{
col = Fcols [j] ;
DEBUG1 (("new offset col "ID" "ID"\n",col, j * fnr2)) ;
Fcpos [col] = j * fnr2 ;
}
}
/* free the old frontal matrix */
UMF_mem_free_tail_block (Numeric, E [0]) ;
/* ---------------------------------------------------------------------- */
/* new frontal matrix size */
/* ---------------------------------------------------------------------- */
E [0] = eloc ;
Work->fnr_curr = fnr2 ; /* C block is fnr2-by-fnc2 */
Work->fnc_curr = fnc2 ;
Work->fcurr_size = newsize ; /* including LU, L, U, and C blocks */
Work->do_grow = FALSE ; /* the front has just been grown */
ASSERT (Work->fnr_curr >= 0) ;
ASSERT (Work->fnr_curr % 2 == 1) ;
DEBUG0 (("Newly grown front: "ID"+"ID" by "ID"+"ID"\n", Work->fnr_curr,
nb, Work->fnc_curr, nb)) ;
return (TRUE) ;
}
GLOBAL Int UMF_start_front /* returns TRUE if successful, FALSE otherwise */
(
Int chain,
NumericType *Numeric,
WorkType *Work,
SymbolicType *Symbolic
)
{
Int fnrows_max, fncols_max, fnr2, fnc2, fsize, fcurr_size, maxfrsize,
overflow, nb, f, cdeg ;
double maxbytes ;
nb = Symbolic->nb ;
fnrows_max = Symbolic->Chain_maxrows [chain] ;
fncols_max = Symbolic->Chain_maxcols [chain] ;
DEBUGm2 (("Start Front for chain "ID". fnrows_max "ID" fncols_max "ID"\n",
chain, fnrows_max, fncols_max)) ;
Work->fnrows_max = fnrows_max ;
Work->fncols_max = fncols_max ;
Work->any_skip = FALSE ;
maxbytes = sizeof (Entry) *
(double) (fnrows_max + nb) * (double) (fncols_max + nb) ;
fcurr_size = Work->fcurr_size ;
if (Symbolic->prefer_diagonal)
{
/* Get a rough upper bound on the degree of the first pivot column in
* this front. Note that Col_degree is not maintained if diagonal
* pivoting is preferred. For most matrices, the first pivot column
* of the first frontal matrix of a new chain has only one tuple in
* it anyway, so this bound is exact in that case. */
Int col, tpi, e, *E, *Col_tuples, *Col_tlen, *Cols ;
Tuple *tp, *tpend ;
Unit *Memory, *p ;
Element *ep ;
E = Work->E ;
Memory = Numeric->Memory ;
Col_tuples = Numeric->Lip ;
Col_tlen = Numeric->Lilen ;
col = Work->nextcand ;
tpi = Col_tuples [col] ;
tp = (Tuple *) Memory + tpi ;
tpend = tp + Col_tlen [col] ;
cdeg = 0 ;
DEBUGm3 (("\n=============== start front: col "ID" tlen "ID"\n",
col, Col_tlen [col])) ;
for ( ; tp < tpend ; tp++)
{
DEBUG1 (("Tuple ("ID","ID")\n", tp->e, tp->f)) ;
e = tp->e ;
if (!E [e]) continue ;
f = tp->f ;
p = Memory + E [e] ;
ep = (Element *) p ;
p += UNITS (Element, 1) ;
Cols = (Int *) p ;
if (Cols [f] == EMPTY) continue ;
DEBUG1 ((" nrowsleft "ID"\n", ep->nrowsleft)) ;
cdeg += ep->nrowsleft ;
}
#ifndef NDEBUG
DEBUGm3 (("start front cdeg: "ID" col "ID"\n", cdeg, col)) ;
UMF_dump_rowcol (1, Numeric, Work, col, FALSE) ;
#endif
/* cdeg is now the rough upper bound on the degree of the next pivot
* column. */
/* If AMD was called, we know the maximum number of nonzeros in any
* column of L. Use this as an upper bound for cdeg, but add 2 to
* account for a small amount of off-diagonal pivoting. */
if (Symbolic->amd_dmax > 0)
{
cdeg = MIN (cdeg, Symbolic->amd_dmax) ;
}
/* Increase it to account for larger columns later on.
* Also ensure that it's larger than zero. */
cdeg += 2 ;
/* cdeg cannot be larger than fnrows_max */
cdeg = MIN (cdeg, fnrows_max) ;
}
else
{
/* don't do the above cdeg computation */
cdeg = 0 ;
}
DEBUGm2 (("fnrows max "ID" fncols_max "ID"\n", fnrows_max, fncols_max)) ;
/* the current frontal matrix is empty */
ASSERT (Work->fnrows == 0 && Work->fncols == 0 && Work->fnpiv == 0) ;
/* maximum row dimension is always odd, to avoid bad cache effects */
ASSERT (fnrows_max >= 0) ;
ASSERT (fnrows_max % 2 == 1) ;
/* ----------------------------------------------------------------------
* allocate working array for current frontal matrix:
* minimum size: 1-by-1
* maximum size: fnrows_max-by-fncols_max
* desired size:
*
* if Numeric->front_alloc_init >= 0:
*
* for unsymmetric matrices:
* Numeric->front_alloc_init * (fnrows_max-by-fncols_max)
*
* for symmetric matrices (diagonal pivoting preference, actually):
* Numeric->front_alloc_init * (fnrows_max-by-fncols_max), or
* cdeg*cdeg, whichever is smaller.
*
* if Numeric->front_alloc_init < 0:
* allocate a front of size -Numeric->front_alloc_init.
*
* Allocate the whole thing if it's small (less than 2*nb^2). Make sure the
* leading dimension of the frontal matrix is odd.
*
* Also allocate the nb-by-nb LU block, the dr-by-nb L block, and the
* nb-by-dc U block.
* ---------------------------------------------------------------------- */
/* get the maximum front size, avoiding integer overflow */
overflow = INT_OVERFLOW (maxbytes) ;
if (overflow)
{
/* :: int overflow, max front size :: */
maxfrsize = Int_MAX / sizeof (Entry) ;
}
else
{
maxfrsize = (fnrows_max + nb) * (fncols_max + nb) ;
}
ASSERT (!INT_OVERFLOW ((double) maxfrsize * sizeof (Entry))) ;
if (Numeric->front_alloc_init < 0)
{
/* allocate a front of -Numeric->front_alloc_init entries */
fsize = -Numeric->front_alloc_init ;
fsize = MAX (1, fsize) ;
}
else
{
if (INT_OVERFLOW (Numeric->front_alloc_init * maxbytes))
{
/* :: int overflow, requested front size :: */
fsize = Int_MAX / sizeof (Entry) ;
}
else
{
fsize = Numeric->front_alloc_init * maxfrsize ;
}
if (cdeg > 0)
{
/* diagonal pivoting is in use. cdeg was computed above */
Int fsize2 ;
/* add the L and U blocks */
cdeg += nb ;
if (INT_OVERFLOW (((double) cdeg * (double) cdeg) * sizeof (Entry)))
{
/* :: int overflow, symmetric front size :: */
fsize2 = Int_MAX / sizeof (Entry) ;
}
else
{
fsize2 = MAX (cdeg * cdeg, fcurr_size) ;
}
fsize = MIN (fsize, fsize2) ;
}
}
fsize = MAX (fsize, 2*nb*nb) ;
/* fsize and maxfrsize are now safe from integer overflow. They both
* include the size of the pivot blocks. */
ASSERT (!INT_OVERFLOW ((double) fsize * sizeof (Entry))) ;
Work->fnrows_new = 0 ;
Work->fncols_new = 0 ;
/* desired size is fnr2-by-fnc2 (includes L and U blocks): */
DEBUGm2 ((" fsize "ID" fcurr_size "ID"\n", fsize, fcurr_size)) ;
DEBUGm2 ((" maxfrsize "ID" fnr_curr "ID" fnc_curr "ID"\n", maxfrsize,
Work->fnr_curr, Work->fnc_curr)) ;
if (fsize >= maxfrsize && !overflow)
{
/* max working array is small, allocate all of it */
fnr2 = fnrows_max + nb ;
fnc2 = fncols_max + nb ;
fsize = maxfrsize ;
DEBUGm1 ((" sufficient for ("ID"+"ID")-by-("ID"+"ID")\n",
fnrows_max, nb, fncols_max, nb)) ;
}
else
{
/* allocate a smaller working array */
if (fnrows_max <= fncols_max)
{
fnr2 = (Int) sqrt ((double) fsize) ;
/* make sure fnr2 is odd */
fnr2 = MAX (fnr2, 1) ;
if (fnr2 % 2 == 0) fnr2++ ;
fnr2 = MIN (fnr2, fnrows_max + nb) ;
fnc2 = fsize / fnr2 ;
}
else
{
fnc2 = (Int) sqrt ((double) fsize) ;
fnc2 = MIN (fnc2, fncols_max + nb) ;
fnr2 = fsize / fnc2 ;
/* make sure fnr2 is odd */
fnr2 = MAX (fnr2, 1) ;
if (fnr2 % 2 == 0)
{
fnr2++ ;
fnc2 = fsize / fnr2 ;
}
}
DEBUGm1 ((" smaller "ID"-by-"ID"\n", fnr2, fnc2)) ;
}
fnr2 = MIN (fnr2, fnrows_max + nb) ;
fnc2 = MIN (fnc2, fncols_max + nb) ;
ASSERT (fnr2 % 2 == 1) ;
ASSERT (fnr2 * fnc2 <= fsize) ;
fnr2 -= nb ;
fnc2 -= nb ;
ASSERT (fnr2 >= 0) ;
ASSERT (fnc2 >= 0) ;
if (fsize > fcurr_size)
{
DEBUGm1 ((" Grow front \n")) ;
Work->do_grow = TRUE ;
if (!UMF_grow_front (Numeric, fnr2, fnc2, Work, -1))
{
/* since the minimum front size is 1-by-1, it would be nearly
* impossible to run out of memory here. */
DEBUGm4 (("out of memory: start front\n")) ;
return (FALSE) ;
}
}
else
{
/* use the existing front */
DEBUGm1 ((" existing front ok\n")) ;
Work->fnr_curr = fnr2 ;
Work->fnc_curr = fnc2 ;
Work->Flblock = Work->Flublock + nb * nb ;
Work->Fublock = Work->Flblock + nb * fnr2 ;
Work->Fcblock = Work->Fublock + nb * fnc2 ;
}
ASSERT (Work->Flblock == Work->Flublock + Work->nb*Work->nb) ;
ASSERT (Work->Fublock == Work->Flblock + Work->fnr_curr*Work->nb) ;
ASSERT (Work->Fcblock == Work->Fublock + Work->nb*Work->fnc_curr) ;
return (TRUE) ;
}
size_t TRILINOS_KLU_kernel /* final size of LU on output */
(
/* input, not modified */
Int n, /* A is n-by-n */
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 input permutation */
size_t lusize, /* initial size of LU on input */
/* output, not defined on input */
Int Pinv [ ], /* size n, inverse row permutation, where Pinv [i] = k if
* row i is the kth pivot row */
Int P [ ], /* size n, row permutation, where P [k] = i if row i is the
* kth pivot row. */
Unit **p_LU, /* LU array, size lusize on input */
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 *lnz, /* size of L*/
Int *unz, /* size of U*/
/* workspace, not defined on input */
Entry X [ ], /* size n, undefined on input, zero on output */
/* workspace, not defined on input or output */
Int Stack [ ], /* size n */
Int Flag [ ], /* size n */
Int Ap_pos [ ], /* size n */
/* other workspace: */
Int Lpend [ ], /* size n workspace, for pruning only */
/* 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 [ ],
/* --------------- */
TRILINOS_KLU_common *Common
)
{
Entry pivot ;
double abs_pivot, xsize, nunits, tol, memgrow ;
Entry *Ux ;
Int *Li, *Ui ;
Unit *LU ; /* LU factors (pattern and values) */
Int k, p, i, j, pivrow, kbar, diagrow, firstrow, lup, top, scale, len ;
size_t newlusize ;
#ifndef NDEBUG
Entry *Lx ;
#endif
ASSERT (Common != NULL) ;
scale = Common->scale ;
tol = Common->tol ;
memgrow = Common->memgrow ;
*lnz = 0 ;
*unz = 0 ;
/* ---------------------------------------------------------------------- */
/* get initial Li, Lx, Ui, and Ux */
/* ---------------------------------------------------------------------- */
PRINTF (("input: lusize %d \n", lusize)) ;
ASSERT (lusize > 0) ;
LU = *p_LU ;
/* ---------------------------------------------------------------------- */
/* initializations */
/* ---------------------------------------------------------------------- */
firstrow = 0 ;
lup = 0 ;
for (k = 0 ; k < n ; k++)
{
/* X [k] = 0 ; */
CLEAR (X [k]) ;
Flag [k] = EMPTY ;
Lpend [k] = EMPTY ; /* flag k as not pruned */
}
/* ---------------------------------------------------------------------- */
/* mark all rows as non-pivotal and determine initial diagonal mapping */
/* ---------------------------------------------------------------------- */
/* PSinv does the symmetric permutation, so don't do it here */
for (k = 0 ; k < n ; k++)
{
P [k] = k ;
Pinv [k] = FLIP (k) ; /* mark all rows as non-pivotal */
}
/* initialize the construction of the off-diagonal matrix */
Offp [0] = 0 ;
/* P [k] = row means that UNFLIP (Pinv [row]) = k, and visa versa.
* If row is pivotal, then Pinv [row] >= 0. A row is initially "flipped"
* (Pinv [k] < EMPTY), and then marked "unflipped" when it becomes
* pivotal. */
#ifndef NDEBUG
for (k = 0 ; k < n ; k++)
{
PRINTF (("Initial P [%d] = %d\n", k, P [k])) ;
}
#endif
/* ---------------------------------------------------------------------- */
/* factorize */
/* ---------------------------------------------------------------------- */
for (k = 0 ; k < n ; k++)
{
PRINTF (("\n\n==================================== k: %d\n", k)) ;
/* ------------------------------------------------------------------ */
/* determine if LU factors have grown too big */
/* ------------------------------------------------------------------ */
/* (n - k) entries for L and k entries for U */
nunits = DUNITS (Int, n - k) + DUNITS (Int, k) +
DUNITS (Entry, n - k) + DUNITS (Entry, k) ;
/* LU can grow by at most 'nunits' entries if the column is dense */
PRINTF (("lup %d lusize %g lup+nunits: %g\n", lup, (double) lusize,
lup+nunits));
xsize = ((double) lup) + nunits ;
if (xsize > (double) lusize)
{
/* check here how much to grow */
xsize = (memgrow * ((double) lusize) + 4*n + 1) ;
if (INT_OVERFLOW (xsize))
{
PRINTF (("Matrix is too large (Int overflow)\n")) ;
Common->status = TRILINOS_KLU_TOO_LARGE ;
return (lusize) ;
}
newlusize = memgrow * lusize + 2*n + 1 ;
/* Future work: retry mechanism in case of malloc failure */
LU = (Unit*) TRILINOS_KLU_realloc (newlusize, lusize, sizeof (Unit), LU, Common) ;
Common->nrealloc++ ;
*p_LU = LU ;
if (Common->status == TRILINOS_KLU_OUT_OF_MEMORY)
{
PRINTF (("Matrix is too large (LU)\n")) ;
return (lusize) ;
}
lusize = newlusize ;
PRINTF (("inc LU to %d done\n", lusize)) ;
}
/* ------------------------------------------------------------------ */
/* start the kth column of L and U */
/* ------------------------------------------------------------------ */
Lip [k] = lup ;
/* ------------------------------------------------------------------ */
/* compute the nonzero pattern of the kth column of L and U */
/* ------------------------------------------------------------------ */
#ifndef NDEBUG
for (i = 0 ; i < n ; i++)
{
ASSERT (Flag [i] < k) ;
/* ASSERT (X [i] == 0) ; */
ASSERT (IS_ZERO (X [i])) ;
}
#endif
top = lsolve_symbolic (n, k, Ap, Ai, Q, Pinv, Stack, Flag,
Lpend, Ap_pos, LU, lup, Llen, Lip, k1, PSinv) ;
#ifndef NDEBUG
PRINTF (("--- in U:\n")) ;
for (p = top ; p < n ; p++)
{
PRINTF (("pattern of X for U: %d : %d pivot row: %d\n",
p, Stack [p], Pinv [Stack [p]])) ;
ASSERT (Flag [Stack [p]] == k) ;
}
PRINTF (("--- in L:\n")) ;
Li = (Int *) (LU + Lip [k]);
for (p = 0 ; p < Llen [k] ; p++)
{
PRINTF (("pattern of X in L: %d : %d pivot row: %d\n",
p, Li [p], Pinv [Li [p]])) ;
ASSERT (Flag [Li [p]] == k) ;
}
p = 0 ;
for (i = 0 ; i < n ; i++)
{
ASSERT (Flag [i] <= k) ;
if (Flag [i] == k) p++ ;
}
#endif
/* ------------------------------------------------------------------ */
/* get the column of the matrix to factorize and scatter into X */
/* ------------------------------------------------------------------ */
construct_column (k, Ap, Ai, Ax, Q, X,
k1, PSinv, Rs, scale, Offp, Offi, Offx) ;
/* ------------------------------------------------------------------ */
/* compute the numerical values of the kth column (s = L \ A (:,k)) */
/* ------------------------------------------------------------------ */
lsolve_numeric (Pinv, LU, Stack, Lip, top, n, Llen, X) ;
#ifndef NDEBUG
for (p = top ; p < n ; p++)
{
PRINTF (("X for U %d : ", Stack [p])) ;
PRINT_ENTRY (X [Stack [p]]) ;
}
Li = (Int *) (LU + Lip [k]) ;
for (p = 0 ; p < Llen [k] ; p++)
{
PRINTF (("X for L %d : ", Li [p])) ;
PRINT_ENTRY (X [Li [p]]) ;
}
#endif
/* ------------------------------------------------------------------ */
/* partial pivoting with diagonal preference */
/* ------------------------------------------------------------------ */
/* determine what the "diagonal" is */
diagrow = P [k] ; /* might already be pivotal */
PRINTF (("k %d, diagrow = %d, UNFLIP (diagrow) = %d\n",
k, diagrow, UNFLIP (diagrow))) ;
/* find a pivot and scale the pivot column */
if (!lpivot (diagrow, &pivrow, &pivot, &abs_pivot, tol, X, LU, Lip,
Llen, k, n, Pinv, &firstrow, Common))
{
/* matrix is structurally or numerically singular */
Common->status = TRILINOS_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 (lusize) ;
}
}
/* we now have a valid pivot row, even if the column has NaN's or
* has no entries on or below the diagonal at all. */
PRINTF (("\nk %d : Pivot row %d : ", k, pivrow)) ;
PRINT_ENTRY (pivot) ;
ASSERT (pivrow >= 0 && pivrow < n) ;
ASSERT (Pinv [pivrow] < 0) ;
/* set the Uip pointer */
Uip [k] = Lip [k] + UNITS (Int, Llen [k]) + UNITS (Entry, Llen [k]) ;
/* move the lup pointer to the position where indices of U
* should be stored */
lup += UNITS (Int, Llen [k]) + UNITS (Entry, Llen [k]) ;
Ulen [k] = n - top ;
/* extract Stack [top..n-1] to Ui and the values to Ux and clear X */
GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, len) ;
for (p = top, i = 0 ; p < n ; p++, i++)
{
j = Stack [p] ;
Ui [i] = Pinv [j] ;
Ux [i] = X [j] ;
CLEAR (X [j]) ;
}
/* position the lu index at the starting point for next column */
lup += UNITS (Int, Ulen [k]) + UNITS (Entry, Ulen [k]) ;
/* U(k,k) = pivot */
Udiag [k] = pivot ;
/* ------------------------------------------------------------------ */
/* log the pivot permutation */
/* ------------------------------------------------------------------ */
ASSERT (UNFLIP (Pinv [diagrow]) < n) ;
ASSERT (P [UNFLIP (Pinv [diagrow])] == diagrow) ;
if (pivrow != diagrow)
{
/* an off-diagonal pivot has been chosen */
Common->noffdiag++ ;
PRINTF ((">>>>>>>>>>>>>>>>> pivrow %d k %d off-diagonal\n",
pivrow, k)) ;
if (Pinv [diagrow] < 0)
{
/* the former diagonal row index, diagrow, has not yet been
* chosen as a pivot row. Log this diagrow as the "diagonal"
* entry in the column kbar for which the chosen pivot row,
* pivrow, was originally logged as the "diagonal" */
kbar = FLIP (Pinv [pivrow]) ;
P [kbar] = diagrow ;
Pinv [diagrow] = FLIP (kbar) ;
}
}
P [k] = pivrow ;
Pinv [pivrow] = k ;
#ifndef NDEBUG
for (i = 0 ; i < n ; i++) { ASSERT (IS_ZERO (X [i])) ;}
GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, len) ;
for (p = 0 ; p < len ; p++)
{
PRINTF (("Column %d of U: %d : ", k, Ui [p])) ;
PRINT_ENTRY (Ux [p]) ;
}
GET_POINTER (LU, Lip, Llen, Li, Lx, k, len) ;
for (p = 0 ; p < len ; p++)
{
PRINTF (("Column %d of L: %d : ", k, Li [p])) ;
PRINT_ENTRY (Lx [p]) ;
}
#endif
/* ------------------------------------------------------------------ */
/* symmetric pruning */
/* ------------------------------------------------------------------ */
prune (Lpend, Pinv, k, pivrow, LU, Uip, Lip, Ulen, Llen) ;
*lnz += Llen [k] + 1 ; /* 1 added to lnz for diagonal */
*unz += Ulen [k] + 1 ; /* 1 added to unz for diagonal */
}
/* ---------------------------------------------------------------------- */
/* finalize column pointers for L and U, and put L in the pivotal order */
/* ---------------------------------------------------------------------- */
for (p = 0 ; p < n ; p++)
{
Li = (Int *) (LU + Lip [p]) ;
for (i = 0 ; i < Llen [p] ; i++)
{
Li [i] = Pinv [Li [i]] ;
}
}
#ifndef NDEBUG
for (i = 0 ; i < n ; i++)
{
PRINTF (("P [%d] = %d Pinv [%d] = %d\n", i, P [i], i, Pinv [i])) ;
}
for (i = 0 ; i < n ; i++)
{
ASSERT (Pinv [i] >= 0 && Pinv [i] < n) ;
ASSERT (P [i] >= 0 && P [i] < n) ;
ASSERT (P [Pinv [i]] == i) ;
ASSERT (IS_ZERO (X [i])) ;
}
#endif
/* ---------------------------------------------------------------------- */
/* shrink the LU factors to just the required size */
/* ---------------------------------------------------------------------- */
newlusize = lup ;
ASSERT ((size_t) newlusize <= lusize) ;
/* this cannot fail, since the block is descreasing in size */
LU = (Unit*) TRILINOS_KLU_realloc (newlusize, lusize, sizeof (Unit), LU, Common) ;
*p_LU = LU ;
return (newlusize) ;
}
