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// 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) ;
}
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