---
name: "slanv2"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/slanv2/3lapack"
---

# slanv2(3lapack)

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

## NAME

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

## SYNOPSIS

- SUBROUTINE SLANV2(

  A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN )

- REAL

  A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R, SN

## 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.\

## ARGUMENTS

- A (input/output) REAL

  B       (input/output) REAL             C       (input/output) REAL             D       (input/output) REAL             On entry, the elements of the input matrix. On exit, they are overwritten by the elements of the standardised Schur form.

- RT1R (output) REAL

  RT1I    (output) REAL             RT2R    (output) REAL             RT2I    (output) REAL             The real and imaginary parts of the eigenvalues. If the eigenvalues are a complex conjugate pair, RT1I \> 0.

- CS (output) REAL

  SN      (output) REAL             Parameters of the rotation matrix.

## 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).\