umf_usolve.c
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/* ========================================================================== */
/* === UMF_usolve =========================================================== */
/* ========================================================================== */
/* -------------------------------------------------------------------------- */
/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
/* -------------------------------------------------------------------------- */
/* solves Ux = b, where U is the upper triangular factor of a matrix. */
/* B is overwritten with the solution X. */
/* Returns the floating point operation count */
#include "umf_internal.h"
GLOBAL double UMF_usolve
(
NumericType *Numeric,
Entry X [ ], /* b on input, solution x on output */
Int Pattern [ ] /* a work array of size n */
)
{
/* ---------------------------------------------------------------------- */
/* local variables */
/* ---------------------------------------------------------------------- */
Entry xk ;
Entry *xp, *D, *Uval ;
Int k, deg, j, *ip, col, *Upos, *Uilen, pos,
*Uip, n, ulen, up, newUchain, npiv, n1, *Ui ;
/* ---------------------------------------------------------------------- */
/* get parameters */
/* ---------------------------------------------------------------------- */
if (Numeric->n_row != Numeric->n_col) return (0.) ;
n = Numeric->n_row ;
npiv = Numeric->npiv ;
Upos = Numeric->Upos ;
Uilen = Numeric->Uilen ;
Uip = Numeric->Uip ;
D = Numeric->D ;
n1 = Numeric->n1 ;
#ifndef NDEBUG
DEBUG4 (("Usolve start: npiv = "ID" n = "ID"\n", npiv, n)) ;
for (j = 0 ; j < n ; j++)
{
DEBUG4 (("Usolve start "ID": ", j)) ;
EDEBUG4 (X [j]) ;
DEBUG4 (("\n")) ;
}
#endif
/* ---------------------------------------------------------------------- */
/* singular case */
/* ---------------------------------------------------------------------- */
#ifndef NO_DIVIDE_BY_ZERO
/* handle the singular part of D, up to just before the last pivot */
for (k = n-1 ; k >= npiv ; k--)
{
/* This is an *** intentional *** divide-by-zero, to get Inf or Nan,
* as appropriate. It is not a bug. */
ASSERT (IS_ZERO (D [k])) ;
xk = X [k] ;
/* X [k] = xk / D [k] ; */
DIV (X [k], xk, D [k]) ;
}
#else
/* Do not divide by zero */
#endif
deg = Numeric->ulen ;
if (deg > 0)
{
/* :: make last pivot row of U (singular matrices only) :: */
for (j = 0 ; j < deg ; j++)
{
DEBUG1 (("Last row of U: j="ID"\n", j)) ;
DEBUG1 (("Last row of U: Upattern[j]="ID"\n",
Numeric->Upattern [j]) );
Pattern [j] = Numeric->Upattern [j] ;
}
}
/* ---------------------------------------------------------------------- */
/* nonsingletons */
/* ---------------------------------------------------------------------- */
for (k = npiv-1 ; k >= n1 ; k--)
{
/* ------------------------------------------------------------------ */
/* use row k of U */
/* ------------------------------------------------------------------ */
up = Uip [k] ;
ulen = Uilen [k] ;
newUchain = (up < 0) ;
if (newUchain)
{
up = -up ;
xp = (Entry *) (Numeric->Memory + up + UNITS (Int, ulen)) ;
}
else
{
xp = (Entry *) (Numeric->Memory + up) ;
}
xk = X [k] ;
for (j = 0 ; j < deg ; j++)
{
DEBUG4 ((" k "ID" col "ID" value", k, Pattern [j])) ;
EDEBUG4 (*xp) ;
DEBUG4 (("\n")) ;
/* xk -= X [Pattern [j]] * (*xp) ; */
MULT_SUB (xk, X [Pattern [j]], *xp) ;
xp++ ;
}
#ifndef NO_DIVIDE_BY_ZERO
/* Go ahead and divide by zero if D [k] is zero */
/* X [k] = xk / D [k] ; */
DIV (X [k], xk, D [k]) ;
#else
/* Do not divide by zero */
if (IS_NONZERO (D [k]))
{
/* X [k] = xk / D [k] ; */
DIV (X [k], xk, D [k]) ;
}
#endif
/* ------------------------------------------------------------------ */
/* make row k-1 of U in Pattern [0..deg-1] */
/* ------------------------------------------------------------------ */
if (k == n1) break ;
if (newUchain)
{
/* next row is a new Uchain */
deg = ulen ;
ASSERT (IMPLIES (k == 0, deg == 0)) ;
DEBUG4 (("end of chain for row of U "ID" deg "ID"\n", k-1, deg)) ;
ip = (Int *) (Numeric->Memory + up) ;
for (j = 0 ; j < deg ; j++)
{
col = *ip++ ;
DEBUG4 ((" k "ID" col "ID"\n", k-1, col)) ;
ASSERT (k <= col) ;
Pattern [j] = col ;
}
}
else
{
deg -= ulen ;
DEBUG4 (("middle of chain for row of U "ID" deg "ID"\n", k, deg)) ;
ASSERT (deg >= 0) ;
pos = Upos [k] ;
if (pos != EMPTY)
{
/* add the pivot column */
DEBUG4 (("k "ID" add pivot entry at pos "ID"\n", k, pos)) ;
ASSERT (pos >= 0 && pos <= deg) ;
Pattern [deg++] = Pattern [pos] ;
Pattern [pos] = k ;
}
}
}
/* ---------------------------------------------------------------------- */
/* singletons */
/* ---------------------------------------------------------------------- */
for (k = n1 - 1 ; k >= 0 ; k--)
{
deg = Uilen [k] ;
xk = X [k] ;
DEBUG4 (("Singleton k "ID"\n", k)) ;
if (deg > 0)
{
up = Uip [k] ;
Ui = (Int *) (Numeric->Memory + up) ;
up += UNITS (Int, deg) ;
Uval = (Entry *) (Numeric->Memory + up) ;
for (j = 0 ; j < deg ; j++)
{
DEBUG4 ((" k "ID" col "ID" value", k, Ui [j])) ;
EDEBUG4 (Uval [j]) ;
DEBUG4 (("\n")) ;
/* xk -= X [Ui [j]] * Uval [j] ; */
ASSERT (Ui [j] >= 0 && Ui [j] < n) ;
MULT_SUB (xk, X [Ui [j]], Uval [j]) ;
}
}
#ifndef NO_DIVIDE_BY_ZERO
/* Go ahead and divide by zero if D [k] is zero */
/* X [k] = xk / D [k] ; */
DIV (X [k], xk, D [k]) ;
#else
/* Do not divide by zero */
if (IS_NONZERO (D [k]))
{
/* X [k] = xk / D [k] ; */
DIV (X [k], xk, D [k]) ;
}
#endif
}
#ifndef NDEBUG
for (j = 0 ; j < n ; j++)
{
DEBUG4 (("Usolve done "ID": ", j)) ;
EDEBUG4 (X [j]) ;
DEBUG4 (("\n")) ;
}
DEBUG4 (("Usolve done.\n")) ;
#endif
return (DIV_FLOPS * ((double) n) + MULTSUB_FLOPS * ((double) Numeric->unz));
}