# slanv2.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine slanv2 (A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN)
SLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form.

## Function/Subroutine Documentation

### subroutine slanv2 (real A, real B, real C, real D, real RT1R, real RT1I, real RT2R, real RT2I, real CS, real SN)

SLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form.

Purpose:

``` SLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric
matrix in standard form:

[ A  B ] = [ CS -SN ] [ AA  BB ] [ CS  SN ]
[ C  D ]   [ SN  CS ] [ CC  DD ] [-SN  CS ]

where either
1) CC = 0 so that AA and DD are real eigenvalues of the matrix, or
2) AA = DD and BB*CC < 0, so that AA + or - sqrt(BB*CC) are complex
conjugate eigenvalues.```
Parameters:

A

`          A is REAL`

B

`          B is REAL`

C

`          C is REAL`

D

```          D is REAL
On entry, the elements of the input matrix.
On exit, they are overwritten by the elements of the
standardised Schur form.```

RT1R

`          RT1R is REAL`

RT1I

`          RT1I is REAL`

RT2R

`          RT2R is REAL`

RT2I

```          RT2I is REAL
The real and imaginary parts of the eigenvalues. If the
eigenvalues are a complex conjugate pair, RT1I > 0.```

CS

`          CS is REAL`

SN

```          SN is REAL
Parameters of the rotation matrix.```
Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

December 2016

Further Details:

```  Modified by V. Sima, Research Institute for Informatics, Bucharest,
Romania, to reduce the risk of cancellation errors,
when computing real eigenvalues, and to ensure, if possible, that
abs(RT1R) >= abs(RT2R).```

Definition at line 129 of file slanv2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page slanv2(3) is an alias of slanv2.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK