---
name: "slanv2.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/slanv2.f"
---

# slanv2.f(3)

## NAME

SRC/slanv2.f

## 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

Univ. of Colorado Denver

NAG Ltd.

**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 **126** of file **slanv2.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.