slas2(3)

NAME

SLAS2 - compute the singular values of the 2-by-2 matrix [

F G ] [ 0 H ]

SYNOPSIS

SUBROUTINE SLAS2( F, G, H, SSMIN, SSMAX )
    REAL          F, G, H, SSMAX, SSMIN

PURPOSE

SLAS2 computes the singular values of the 2-by-2 matrix [

F G ] [ 0 H ]. On return, SSMIN is the smaller singular value and

SSMAX is the larger singular value.

ARGUMENTS

F (input) REAL

The (1,1) element of the 2-by-2 matrix.

G (input) REAL

The (1,2) element of the 2-by-2 matrix.

H (input) REAL

The (2,2) element of the 2-by-2 matrix.

SSMIN (output) REAL

The smaller singular value.

SSMAX (output) REAL

The larger singular value.

FURTHER DETAILS

Barring over/underflow, all output quantities are correct

to within a few units in the last place (ulps), even in the ab

sence of a guard digit in addition/subtraction.

In IEEE arithmetic, the code works correctly if one matrix

element is infinite.

Overflow will not occur unless the largest singular value

itself overflows, or is within a few ulps of overflow. (On ma

chines with partial overflow, like the Cray, overflow may occur

if the largest singular value is within a factor of 2 of over

flow.)

Underflow is harmless if underflow is gradual. Otherwise,

results may correspond to a matrix modified by perturbations of

size near the underflow threshold.

LAPACK version 3.0 15 June 2000

SLAS2(3)