subroutine slas2 (F, G, H, SSMIN, SSMAX)
SLAS2 computes singular values of a 2-by-2 triangular matrix.
SLAS2 computes singular values of a 2-by-2 triangular matrix.
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.
Parameters:
F is REAL
The (1,1) element of the 2-by-2 matrix.
G
G is REAL
The (1,2) element of the 2-by-2 matrix.
H
H is REAL
The (2,2) element of the 2-by-2 matrix.
SSMIN
SSMIN is REAL
The smaller singular value.
SSMAX
SSMAX is REAL
The larger singular value.
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
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.
Definition at line 109 of file slas2.f.
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