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# slasv2

```
NAME
SLASV2 - compute the singular value decomposition of a 2-
by-2 triangular matrix  [ F G ]  [ 0 H ]

SYNOPSIS
SUBROUTINE SLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL
)

REAL           CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN

PURPOSE
SLASV2 computes the singular value decomposition of a 2-by-2
triangular matrix
[  F   G  ]
[  0   H  ].  On return, abs(SSMAX) is the larger singu-
lar value, abs(SSMIN) is the smaller singular value, and
(CSL,SNL) and (CSR,SNR) are the left and right singular vec-
tors for abs(SSMAX), giving the decomposition

[ CSL  SNL ] [  F   G  ] [ CSR -SNR ]  =  [ SSMAX   0   ]
[-SNL  CSL ] [  0   H  ] [ SNR  CSR ]     [  0    SSMIN
].

ARGUMENTS
F       (input) REAL
The (1,1) entry of the 2-by-2 matrix.

G       (input) REAL
The (1,2) entry of the 2-by-2 matrix.

H       (input) REAL
The (2,2) entry of the 2-by-2 matrix.

SSMIN   (output) REAL
abs(SSMIN) is the smaller singular value.

SSMAX   (output) REAL
abs(SSMAX) is the larger singular value.

SNL     (output) REAL
CSL     (output) REAL The vector (CSL, SNL) is a
unit left singular vector for the singular value
abs(SSMAX).

SNR     (output) REAL
CSR     (output) REAL The vector (CSR, SNR) is a
unit right singular vector for the singular value
abs(SSMAX).

FURTHER DETAILS
Any input parameter may be aliased with any output

parameter.

Barring over/underflow and assuming a guard digit in sub-
traction, all output quantities are correct to within a few
units in the last place (ulps).

In IEEE arithmetic, the code works correctly if one matrix
entry 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.
```