# lanv2 - Man Page

lanv2: 2x2 Schur factor

## Synopsis

### Functions

subroutine dlanv2 (a, b, c, d, rt1r, rt1i, rt2r, rt2i, cs, sn)
DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form.
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 Documentation

### subroutine dlanv2 (double precision a, double precision b, double precision c, double precision d, double precision rt1r, double precision rt1i, double precision rt2r, double precision rt2i, double precision cs, double precision sn)

DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form.

Purpose:

``` DLANV2 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 DOUBLE PRECISION`

B

`          B is DOUBLE PRECISION`

C

`          C is DOUBLE PRECISION`

D

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

RT1R

`          RT1R is DOUBLE PRECISION`

RT1I

`          RT1I is DOUBLE PRECISION`

RT2R

`          RT2R is DOUBLE PRECISION`

RT2I

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

CS

`          CS is DOUBLE PRECISION`

SN

```          SN is DOUBLE PRECISION
Parameters of the rotation matrix.```
Author

Univ. of Tennessee

Univ. of California Berkeley

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 dlanv2.f.

### 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.

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.

## Info

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK