# slanv2.f man page

slanv2.f —

## Synopsis

### Functions/Subroutines

subroutineslanv2(A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN)SLANV2computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form.

## Function/Subroutine Documentation

### subroutine slanv2 (realA, realB, realC, realD, realRT1R, realRT1I, realRT2R, realRT2I, realCS, realSN)

**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

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

**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 128 of file slanv2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

slanv2(3) is an alias of slanv2.f(3).