SLAS2(l) — LAPACK auxiliary routine (version 2.0)

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 absence 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 machines with partial overflow, like the Cray, overflow may occur if the largest singular value is within a factor of 2 of overflow.)

Underflow is harmless if underflow is gradual. Otherwise, results may correspond to a matrix modified by perturbations of size near the underflow threshold.