# 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

Univ. of Colorado Denver

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