DLAS2(1) LAPACK auxiliary routine (version 3.2) DLAS2(1)NAME
DLAS2 - computes the singular values of the 2-by-2 matrix [ F G ] [ 0
H ]
SYNOPSIS
SUBROUTINE DLAS2( F, G, H, SSMIN, SSMAX )
DOUBLE PRECISION F, G, H, SSMAX, SSMIN
PURPOSE
DLAS2 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) DOUBLE PRECISION
The (1,1) element of the 2-by-2 matrix.
G (input) DOUBLE PRECISION
The (1,2) element of the 2-by-2 matrix.
H (input) DOUBLE PRECISION
The (2,2) element of the 2-by-2 matrix.
SSMIN (output) DOUBLE PRECISION
The smaller singular value.
SSMAX (output) DOUBLE PRECISION
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 over‐
flows, 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.
LAPACK auxiliary routine (versioNovember 2008 DLAS2(1)
