24 lines
684 B
C
24 lines
684 B
C
#include "cs.h"
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/* create a Householder reflection [v,beta,s]=house(x), overwrite x with v,
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* where (I-beta*v*v')*x = s*e1. See Algo 5.1.1, Golub & Van Loan, 3rd ed. */
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double cs_house (double *x, double *beta, int n)
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{
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double s, sigma = 0 ;
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int i ;
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if (!x || !beta) return (-1) ; /* check inputs */
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for (i = 1 ; i < n ; i++) sigma += x [i] * x [i] ;
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if (sigma == 0)
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{
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s = fabs (x [0]) ; /* s = |x(0)| */
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(*beta) = (x [0] <= 0) ? 2 : 0 ;
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x [0] = 1 ;
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}
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else
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{
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s = sqrt (x [0] * x [0] + sigma) ; /* s = norm (x) */
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x [0] = (x [0] <= 0) ? (x [0] - s) : (-sigma / (x [0] + s)) ;
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(*beta) = -1. / (s * x [0]) ;
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}
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return (s) ;
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}
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