dlas23lapack
Computes the singular values of the 2-by-2 matrix [ f g ] [ 0 h ]
Usage
- 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 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.