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/* ========================================================================== */
/* === UMF_ltsolve ========================================================== */
/* ========================================================================== */
/* -------------------------------------------------------------------------- */
/* UMFPACK Version 4.6, Copyright (c) 2005 by Timothy A. Davis. CISE Dept, */
/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
/* -------------------------------------------------------------------------- */
/* Solves L'x = b or L.'x=b, where L is the lower triangular factor of a */
/* matrix. B is overwritten with the solution X. */
/* Returns the floating point operation count */
#include "umf_internal.h"
GLOBAL double
#ifdef CONJUGATE_SOLVE
UMF_lhsolve /* solve L'x=b (complex conjugate transpose) */
#else
UMF_ltsolve /* solve L.'x=b (array transpose) */
#endif
(
NumericType *Numeric,
Entry X [ ], /* b on input, solution x on output */
Int Pattern [ ] /* a work array of size n */
)
{
Entry xk ;
Entry *xp, *Lval ;
Int k, deg, *ip, j, row, *Lpos, *Lilen, kstart, kend, *Lip, llen,
lp, pos, npiv, n1, *Li ;
/* ---------------------------------------------------------------------- */
if (Numeric->n_row != Numeric->n_col) return (0.) ;
npiv = Numeric->npiv ;
Lpos = Numeric->Lpos ;
Lilen = Numeric->Lilen ;
Lip = Numeric->Lip ;
kstart = npiv ;
n1 = Numeric->n1 ;
#ifndef NDEBUG
DEBUG4 (("Ltsolve start:\n")) ;
for (j = 0 ; j < Numeric->n_row ; j++)
{
DEBUG4 (("Ltsolve start "ID": ", j)) ;
EDEBUG4 (X [j]) ;
DEBUG4 (("\n")) ;
}
#endif
/* ---------------------------------------------------------------------- */
/* non-singletons */
/* ---------------------------------------------------------------------- */
for (kend = npiv-1 ; kend >= n1 ; kend = kstart-1)
{
/* ------------------------------------------------------------------ */
/* find the start of this Lchain */
/* ------------------------------------------------------------------ */
/* for (kstart = kend ; kstart >= 0 && Lip [kstart] > 0 ; kstart--) ; */
kstart = kend ;
while (kstart >= 0 && Lip [kstart] > 0)
{
kstart-- ;
}
/* the Lchain goes from kstart to kend */
/* ------------------------------------------------------------------ */
/* scan the whole chain to find the pattern of the last column of L */
/* ------------------------------------------------------------------ */
deg = 0 ;
DEBUG4 (("start of chain for column of L\n")) ;
for (k = kstart ; k <= kend ; k++)
{
ASSERT (k >= 0 && k < npiv) ;
/* -------------------------------------------------------------- */
/* make column k of L in Pattern [0..deg-1] */
/* -------------------------------------------------------------- */
/* remove pivot row */
pos = Lpos [k] ;
if (pos != EMPTY)
{
DEBUG4 ((" k "ID" removing row "ID" at position "ID"\n",
k, Pattern [pos], pos)) ;
ASSERT (k != kstart) ;
ASSERT (deg > 0) ;
ASSERT (pos >= 0 && pos < deg) ;
ASSERT (Pattern [pos] == k) ;
Pattern [pos] = Pattern [--deg] ;
}
/* concatenate the pattern */
lp = Lip [k] ;
if (k == kstart)
{
lp = -lp ;
}
ASSERT (lp > 0) ;
ip = (Int *) (Numeric->Memory + lp) ;
llen = Lilen [k] ;
for (j = 0 ; j < llen ; j++)
{
row = *ip++ ;
DEBUG4 ((" row "ID" k "ID"\n", row, k)) ;
ASSERT (row > k) ;
Pattern [deg++] = row ;
}
}
/* Pattern [0..deg-1] is now the pattern of column kend */
/* ------------------------------------------------------------------ */
/* solve using this chain, in reverse order */
/* ------------------------------------------------------------------ */
DEBUG4 (("Unwinding Lchain\n")) ;
for (k = kend ; k >= kstart ; k--)
{
/* -------------------------------------------------------------- */
/* use column k of L */
/* -------------------------------------------------------------- */
ASSERT (k >= 0 && k < npiv) ;
lp = Lip [k] ;
if (k == kstart)
{
lp = -lp ;
}
ASSERT (lp > 0) ;
llen = Lilen [k] ;
xp = (Entry *) (Numeric->Memory + lp + UNITS (Int, llen)) ;
xk = X [k] ;
for (j = 0 ; j < deg ; j++)
{
DEBUG4 ((" row "ID" k "ID" value", Pattern [j], k)) ;
EDEBUG4 (*xp) ;
DEBUG4 (("\n")) ;
#ifdef CONJUGATE_SOLVE
/* xk -= X [Pattern [j]] * conjugate (*xp) ; */
MULT_SUB_CONJ (xk, X [Pattern [j]], *xp) ;
#else
/* xk -= X [Pattern [j]] * (*xp) ; */
MULT_SUB (xk, X [Pattern [j]], *xp) ;
#endif
xp++ ;
}
X [k] = xk ;
/* -------------------------------------------------------------- */
/* construct column k-1 of L */
/* -------------------------------------------------------------- */
/* un-concatenate the pattern */
deg -= llen ;
/* add pivot row */
pos = Lpos [k] ;
if (pos != EMPTY)
{
DEBUG4 ((" k "ID" adding row "ID" at position "ID"\n",
k, k, pos)) ;
ASSERT (k != kstart) ;
ASSERT (pos >= 0 && pos <= deg) ;
Pattern [deg++] = Pattern [pos] ;
Pattern [pos] = k ;
}
}
}
/* ---------------------------------------------------------------------- */
/* singletons */
/* ---------------------------------------------------------------------- */
for (k = n1 - 1 ; k >= 0 ; k--)
{
DEBUG4 (("Singleton k "ID"\n", k)) ;
deg = Lilen [k] ;
if (deg > 0)
{
xk = X [k] ;
lp = Lip [k] ;
Li = (Int *) (Numeric->Memory + lp) ;
lp += UNITS (Int, deg) ;
Lval = (Entry *) (Numeric->Memory + lp) ;
for (j = 0 ; j < deg ; j++)
{
DEBUG4 ((" row "ID" k "ID" value", Li [j], k)) ;
EDEBUG4 (Lval [j]) ;
DEBUG4 (("\n")) ;
#ifdef CONJUGATE_SOLVE
/* xk -= X [Li [j]] * conjugate (Lval [j]) ; */
MULT_SUB_CONJ (xk, X [Li [j]], Lval [j]) ;
#else
/* xk -= X [Li [j]] * Lval [j] ; */
MULT_SUB (xk, X [Li [j]], Lval [j]) ;
#endif
}
X [k] = xk ;
}
}
#ifndef NDEBUG
for (j = 0 ; j < Numeric->n_row ; j++)
{
DEBUG4 (("Ltsolve done "ID": ", j)) ;
EDEBUG4 (X [j]) ;
DEBUG4 (("\n")) ;
}
DEBUG4 (("Ltsolve done.\n")) ;
#endif
return (MULTSUB_FLOPS * ((double) Numeric->lnz)) ;
}
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