1SLAS2(1)            LAPACK auxiliary routine (version 3.2)            SLAS2(1)
2
3
4

NAME

6       SLAS2 - computes the singular values of the 2-by-2 matrix  [ F G ]  [ 0
7       H ]
8

SYNOPSIS

10       SUBROUTINE SLAS2( F, G, H, SSMIN, SSMAX )
11
12           REAL          F, G, H, SSMAX, SSMIN
13

PURPOSE

15       SLAS2  computes the singular values of the 2-by-2 matrix
16          [  F   G  ]
17          [  0   H  ].  On return, SSMIN is the  smaller  singular  value  and
18       SSMAX is the larger singular value.
19

ARGUMENTS

21       F       (input) REAL
22               The (1,1) element of the 2-by-2 matrix.
23
24       G       (input) REAL
25               The (1,2) element of the 2-by-2 matrix.
26
27       H       (input) REAL
28               The (2,2) element of the 2-by-2 matrix.
29
30       SSMIN   (output) REAL
31               The smaller singular value.
32
33       SSMAX   (output) REAL
34               The larger singular value.
35

FURTHER DETAILS

37       Barring  over/underflow,  all output quantities are correct to within a
38       few units in the last place (ulps), even in  the  absence  of  a  guard
39       digit in addition/subtraction.
40       In  IEEE  arithmetic, the code works correctly if one matrix element is
41       infinite.
42       Overflow will not occur unless the largest singular value itself  over‐
43       flows,  or  is within a few ulps of overflow. (On machines with partial
44       overflow, like the Cray, overflow may occur  if  the  largest  singular
45       value is within a factor of 2 of overflow.)
46       Underflow  is  harmless if underflow is gradual. Otherwise, results may
47       correspond to a matrix modified  by  perturbations  of  size  near  the
48       underflow threshold.
49
50
51
52 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                        SLAS2(1)