# slasv2.f - Man Page

SRC/slasv2.f

## Synopsis

### Functions/Subroutines

subroutine slasv2 (f, g, h, ssmin, ssmax, snr, csr, snl, csl)
SLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix.

## Function/Subroutine Documentation

### subroutine slasv2 (real f, real g, real h, real ssmin, real ssmax, real snr, real csr, real snl, real csl)

SLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix.

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 singular value, abs(SSMIN) is the
smaller singular value, and (CSL,SNL) and (CSR,SNR) are the left and
right singular vectors for abs(SSMAX), giving the decomposition

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

F

```          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
abs(SSMIN) is the smaller singular value.```

SSMAX

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

SNL

`          SNL is REAL`

CSL

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

SNR

`          SNR is REAL`

CSR

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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

```  Any input parameter may be aliased with any output parameter.

Barring over/underflow and assuming a guard digit in subtraction, 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 element is
infinite.

Overflow will not occur unless the largest singular value itself
overflows or is within a few ulps 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 135 of file slasv2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page slasv2(3) is an alias of slasv2.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK