SLANV2(1) LAPACK driver routine (version 3.2) SLANV2(1)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 conju‐
gate 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 standard‐
ised 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).
LAPACK driver routine (version 3November 2008 SLANV2(1)
