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/* ========================================================================== */
/* === UMF_utsolve ========================================================== */
/* ========================================================================== */

/* -------------------------------------------------------------------------- */
/* 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 U'x = b or U.'x=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
#ifdef CONJUGATE_SOLVE
UMF_uhsolve         /* solve U'x=b  (complex conjugate transpose) */
#else
UMF_utsolve         /* solve U.'x=b (array transpose) */
#endif
(
    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, kstart, kend, up,
    *Uip, n, uhead, ulen, pos, 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 ;
    kend = 0 ;
    n1 = Numeric->n1 ;

#ifndef NDEBUG
    DEBUG4 (("Utsolve start: npiv "ID" n "ID"\n", npiv, n)) ;
    for (j = 0 ; j < n ; j++)
    {
    DEBUG4 (("Utsolve start "ID": ", j)) ;
    EDEBUG4 (X [j]) ;
    DEBUG4 (("\n")) ;
    }
#endif

    /* ---------------------------------------------------------------------- */
    /* singletons */
    /* ---------------------------------------------------------------------- */

    for (k = 0 ; k < n1 ; k++)
    {
    DEBUG4 (("Singleton k "ID"\n", k)) ;

#ifndef NO_DIVIDE_BY_ZERO
    /* Go ahead and divide by zero if D [k] is zero. */
#ifdef CONJUGATE_SOLVE
    /* xk = X [k] / conjugate (D [k]) ; */
    DIV_CONJ (xk, X [k], D [k]) ;
#else
    /* xk = X [k] / D [k] ; */
    DIV (xk, X [k], D [k]) ;
#endif
#else
    /* Do not divide by zero */
    if (IS_NONZERO (D [k]))
    {
#ifdef CONJUGATE_SOLVE
        /* xk = X [k] / conjugate (D [k]) ; */
        DIV_CONJ (xk, X [k], D [k]) ;
#else
        /* xk = X [k] / D [k] ; */
        DIV (xk, X [k], D [k]) ;
#endif
    }
#endif

    X [k] = xk ;
    deg = Uilen [k] ;
    if (deg > 0 && IS_NONZERO (xk))
    {
        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")) ;
#ifdef CONJUGATE_SOLVE
        /* X [Ui [j]] -= xk * conjugate (Uval [j]) ; */
        MULT_SUB_CONJ (X [Ui [j]], xk, Uval [j]) ;
#else
        /* X [Ui [j]] -= xk * Uval [j] ; */
        MULT_SUB (X [Ui [j]], xk, Uval [j]) ;
#endif
        }
    }
    }

    /* ---------------------------------------------------------------------- */
    /* nonsingletons */
    /* ---------------------------------------------------------------------- */

    for (kstart = n1 ; kstart < npiv ; kstart = kend + 1)
    {

    /* ------------------------------------------------------------------ */
    /* find the end of this Uchain */
    /* ------------------------------------------------------------------ */

    DEBUG4 (("kstart "ID" kend "ID"\n", kstart, kend)) ;
    /* for (kend = kstart ; kend < npiv && Uip [kend+1] > 0 ; kend++) ; */
    kend = kstart ;
    while (kend < npiv && Uip [kend+1] > 0)
    {
        kend++ ;
    }

    /* ------------------------------------------------------------------ */
    /* scan the whole Uchain to find the pattern of the first row of U */
    /* ------------------------------------------------------------------ */

    k = kend+1 ;
    DEBUG4 (("\nKend "ID" K "ID"\n", kend, k)) ;

    /* ------------------------------------------------------------------ */
    /* start with last row in Uchain of U in Pattern [0..deg-1] */
    /* ------------------------------------------------------------------ */

    if (k == npiv)
    {
        deg = Numeric->ulen ;
        if (deg > 0)
        {
        /* :: make last pivot row of U (singular matrices only) :: */
        for (j = 0 ; j < deg ; j++)
        {
            Pattern [j] = Numeric->Upattern [j] ;
        }
        }
    }
    else
    {
        ASSERT (k >= 0 && k < npiv) ;
        up = -Uip [k] ;
        ASSERT (up > 0) ;
        deg = Uilen [k] ;
        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 ;
        }
    }

    /* empty the stack at the bottom of Pattern */
    uhead = n ;

    for (k = kend ; k > kstart ; k--)
    {
        /* Pattern [0..deg-1] is the pattern of row k of U */

        /* -------------------------------------------------------------- */
        /* make row k-1 of U in Pattern [0..deg-1] */
        /* -------------------------------------------------------------- */

        ASSERT (k >= 0 && k < npiv) ;
        ulen = Uilen [k] ;
        /* delete, and push on the stack */
        for (j = 0 ; j < ulen ; j++)
        {
        ASSERT (uhead >= deg) ;
        Pattern [--uhead] = Pattern [--deg] ;
        }
        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 position "ID"\n", k, pos)) ;
        ASSERT (pos >= 0 && pos <= deg) ;
        Pattern [deg++] = Pattern [pos] ;
        Pattern [pos] = k ;
        }
    }

    /* Pattern [0..deg-1] is now the pattern of the first row in Uchain */

    /* ------------------------------------------------------------------ */
    /* solve using this Uchain, in reverse order */
    /* ------------------------------------------------------------------ */

    DEBUG4 (("Unwinding Uchain\n")) ;
    for (k = kstart ; k <= kend ; k++)
    {

        /* -------------------------------------------------------------- */
        /* construct row k */
        /* -------------------------------------------------------------- */

        ASSERT (k >= 0 && k < npiv) ;
        pos = Upos [k] ;
        if (pos != EMPTY)
        {
        /* remove the pivot column */
        DEBUG4 (("k "ID" add pivot entry at position "ID"\n", k, pos)) ;
        ASSERT (k > kstart) ;
        ASSERT (pos >= 0 && pos < deg) ;
        ASSERT (Pattern [pos] == k) ;
        Pattern [pos] = Pattern [--deg] ;
        }

        up = Uip [k] ;
        ulen = Uilen [k] ;
        if (k > kstart)
        {
        /* concatenate the deleted pattern; pop from the stack */
        for (j = 0 ; j < ulen ; j++)
        {
            ASSERT (deg <= uhead && uhead < n) ;
            Pattern [deg++] = Pattern [uhead++] ;
        }
        DEBUG4 (("middle of chain, row of U "ID" deg "ID"\n", k, deg)) ;
        ASSERT (deg >= 0) ;
        }

        /* -------------------------------------------------------------- */
        /* use row k of U */
        /* -------------------------------------------------------------- */

#ifndef NO_DIVIDE_BY_ZERO
        /* Go ahead and divide by zero if D [k] is zero. */
#ifdef CONJUGATE_SOLVE
        /* xk = X [k] / conjugate (D [k]) ; */
        DIV_CONJ (xk, X [k], D [k]) ;
#else
        /* xk = X [k] / D [k] ; */
        DIV (xk, X [k], D [k]) ;
#endif
#else
        /* Do not divide by zero */
        if (IS_NONZERO (D [k]))
        {
#ifdef CONJUGATE_SOLVE
        /* xk = X [k] / conjugate (D [k]) ; */
        DIV_CONJ (xk, X [k], D [k]) ;
#else
        /* xk = X [k] / D [k] ; */
        DIV (xk, X [k], D [k]) ;
#endif
        }
#endif

        X [k] = xk ;
        if (IS_NONZERO (xk))
        {
        if (k == kstart)
        {
            up = -up ;
            xp = (Entry *) (Numeric->Memory + up + UNITS (Int, ulen)) ;
        }
        else
        {
            xp = (Entry *) (Numeric->Memory + up) ;
        }
        for (j = 0 ; j < deg ; j++)
        {
            DEBUG4 (("  k "ID" col "ID" value", k, Pattern [j])) ;
            EDEBUG4 (*xp) ;
            DEBUG4 (("\n")) ;
#ifdef CONJUGATE_SOLVE
            /* X [Pattern [j]] -= xk * conjugate (*xp) ; */
            MULT_SUB_CONJ (X [Pattern [j]], xk, *xp) ;
#else
            /* X [Pattern [j]] -= xk * (*xp) ; */
            MULT_SUB (X [Pattern [j]], xk, *xp) ;
#endif
            xp++ ;
        }
        }
    }
    ASSERT (uhead == n) ;
    }

#ifndef NO_DIVIDE_BY_ZERO
    for (k = npiv ; k < n ; 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])) ;
    /* For conjugate solve, D [k] == conjugate (D [k]), in this case */
    /* xk = X [k] / D [k] ; */
    DIV (xk, X [k], D [k]) ;
    X [k] = xk ;
    }
#endif

#ifndef NDEBUG
    for (j = 0 ; j < n ; j++)
    {
    DEBUG4 (("Utsolve done "ID": ", j)) ;
    EDEBUG4 (X [j]) ;
    DEBUG4 (("\n")) ;
    }
    DEBUG4 (("Utsolve done.\n")) ;
#endif

    return (DIV_FLOPS * ((double) n) + MULTSUB_FLOPS * ((double) Numeric->unz));
}