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/* ========================================================================== */
/* === UMF_usolve =========================================================== */
/* ========================================================================== */

/* -------------------------------------------------------------------------- */
/* UMFPACK Version 4.5, 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 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));
}