DLANV2(l) ) DLANV2(l)NAME
DLANV2 - compute the Schur factorization of a real 2-by-2 nonsymmetric
matrix in standard form
SYNOPSIS
SUBROUTINE DLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN )
DOUBLE PRECISION A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R, SN
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 conju‐
gate eigenvalues.
ARGUMENTS
A (input/output) DOUBLE PRECISION
B (input/output) DOUBLE PRECISION C (input/output)
DOUBLE PRECISION D (input/output) DOUBLE PRECISION On
entry, the elements of the input matrix. On exit, they are
overwritten by the elements of the standardised Schur form.
RT1R (output) DOUBLE PRECISION
RT1I (output) DOUBLE PRECISION RT2R (output) DOUBLE PRE‐
CISION RT2I (output) DOUBLE PRECISION The real and imaginary
parts of the eigenvalues. If the eigenvalues are a complex con‐
jugate pair, RT1I > 0.
CS (output) DOUBLE PRECISION
SN (output) DOUBLE PRECISION 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 version 3.0 15 June 2000 DLANV2(l)
