// CSparse/Source/cs_updown: sparse Cholesky update/downdate
// CSparse, Copyright (c) 2006-2022, Timothy A. Davis. All Rights Reserved.
// SPDX-License-Identifier: LGPL-2.1+
#include "cs.h"
/* sparse Cholesky update/downdate, L*L' + sigma*w*w' (sigma = +1 or -1) */
csi cs_updown (cs *L, csi sigma, const cs *C, const csi *parent)
{
    csi n, p, f, j, *Lp, *Li, *Cp, *Ci ;
    double *Lx, *Cx, alpha, beta = 1, delta, gamma, w1, w2, *w, beta2 = 1 ;
    if (!CS_CSC (L) || !CS_CSC (C) || !parent) return (0) ;  /* check inputs */
    Lp = L->p ; Li = L->i ; Lx = L->x ; n = L->n ;
    Cp = C->p ; Ci = C->i ; Cx = C->x ;
    if ((p = Cp [0]) >= Cp [1]) return (1) ;        /* return if C empty */
    w = cs_malloc (n, sizeof (double)) ;            /* get workspace */
    if (!w) return (0) ;                            /* out of memory */
    f = Ci [p] ;
    for ( ; p < Cp [1] ; p++) f = CS_MIN (f, Ci [p]) ;  /* f = min (find (C)) */
    for (j = f ; j != -1 ; j = parent [j]) w [j] = 0 ;  /* clear workspace w */
    for (p = Cp [0] ; p < Cp [1] ; p++) w [Ci [p]] = Cx [p] ; /* w = C */
    for (j = f ; j != -1 ; j = parent [j])          /* walk path f up to root */
    {
        p = Lp [j] ;
        alpha = w [j] / Lx [p] ;                    /* alpha = w(j) / L(j,j) */
        beta2 = beta*beta + sigma*alpha*alpha ;
        if (beta2 <= 0) break ;                     /* not positive definite */
        beta2 = sqrt (beta2) ;
        delta = (sigma > 0) ? (beta / beta2) : (beta2 / beta) ;
        gamma = sigma * alpha / (beta2 * beta) ;
        Lx [p] = delta * Lx [p] + ((sigma > 0) ? (gamma * w [j]) : 0) ;
        beta = beta2 ;
        for (p++ ; p < Lp [j+1] ; p++)
        {
            w1 = w [Li [p]] ;
            w [Li [p]] = w2 = w1 - alpha * Lx [p] ;
            Lx [p] = delta * Lx [p] + gamma * ((sigma > 0) ? w1 : w2) ;
        }
    }
    cs_free (w) ;
    return (beta2 > 0) ;
}