EVSL  1.1.0 EigenValues Slicing Library
cs_house.c
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1 #include "cs.h"
2 /* create a Householder reflection [v,beta,s]=house(x), overwrite x with v,
3  * where (I-beta*v*v')*x = s*e1 and e1 = [1 0 ... 0]'.
4  * Note that this CXSparse version is different than CSparse. See Higham,
5  * Accuracy & Stability of Num Algorithms, 2nd ed, 2002, page 357. */
6 CS_ENTRY cs_house (CS_ENTRY *x, double *beta, CS_INT n)
7 {
8  CS_ENTRY s = 0 ;
9  CS_INT i ;
10  if (!x || !beta) return (-1) ; /* check inputs */
11  /* s = norm(x) */
12  for (i = 0 ; i < n ; i++) s += x [i] * CS_CONJ (x [i]) ;
13  s = sqrt (s) ;
14  if (s == 0)
15  {
16  (*beta) = 0 ;
17  x [0] = 1 ;
18  }
19  else
20  {
21  /* s = sign(x[0]) * norm (x) ; */
22  if (x [0] != 0)
23  {
24  s *= x [0] / CS_ABS (x [0]) ;
25  }
26  x [0] += s ;
27  (*beta) = 1. / CS_REAL (CS_CONJ (s) * x [0]) ;
28  }
29  return (-s) ;
30 }
CS_ENTRY cs_house(CS_ENTRY *x, double *beta, CS_INT n)
Definition: cs_house.c:6
#define CS_CONJ(x)
Definition: cs.h:649
#define CS_ENTRY
Definition: cs.h:635
#define CS_REAL(x)
Definition: cs.h:647
#define CS_ABS(x)
Definition: cs.h:650
#define CS_INT
Definition: cs.h:627