// CXSparse/Source/cs_house: create a Householder transformation
// CXSparse, Copyright (c) 2006-2022, Timothy A. Davis. All Rights Reserved.
// SPDX-License-Identifier: LGPL-2.1+
#include "cs.h"
/* create a Householder reflection [v,beta,s]=house(x), overwrite x with v,
 * where (I-beta*v*v')*x = s*e1 and e1 = [1 0 ... 0]'.
 * Note that this CXSparse version is different than CSparse.  See Higham,
 * Accuracy & Stability of Num Algorithms, 2nd ed, 2002, page 357. */
CS_ENTRY cs_house (CS_ENTRY *x, double *beta, CS_INT n)
{
    CS_ENTRY s = 0 ;
    CS_INT i ;
    if (!x || !beta) return (-1) ;          /* check inputs */
    /* s = norm(x) */
    for (i = 0 ; i < n ; i++) s += x [i] * CS_CONJ (x [i]) ;
    s = sqrt (s) ;
    if (s == 0)
    {
        (*beta) = 0 ;
        x [0] = 1 ;
    }
    else
    {
        /* s = sign(x[0]) * norm (x) ; */
        if (x [0] != 0)
        {
            s *= x [0] / CS_ABS (x [0]) ;
        }
        x [0] += s ;
        (*beta) = 1. / CS_REAL (CS_CONJ (s) * x [0]) ;
    }
    return (-s) ;
}