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 perturba
tions of size near the underflow threshold.
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