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// CSparse/Source/cs_house: create a Householder transformation
// CSparse, 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. See Algo 5.1.1, Golub & Van Loan, 3rd ed. */
double cs_house (double *x, double *beta, csi n)
{
double s, sigma = 0 ;
csi i ;
if (!x || !beta) return (-1) ; /* check inputs */
for (i = 1 ; i < n ; i++) sigma += x [i] * x [i] ;
if (sigma == 0)
{
s = fabs (x [0]) ; /* s = |x(0)| */
(*beta) = (x [0] <= 0) ? 2 : 0 ;
x [0] = 1 ;
}
else
{
s = sqrt (x [0] * x [0] + sigma) ; /* s = norm (x) */
x [0] = (x [0] <= 0) ? (x [0] - s) : (-sigma / (x [0] + s)) ;
(*beta) = -1. / (s * x [0]) ;
}
return (s) ;
}
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