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 conjugate 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 ele
ments 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 PRECISION RT2I (output) DOUBLE PRECISION
The real and imaginary parts of the eigenvalues.
If the eigenvalues are a complex conjugate 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 possi
ble, that abs(RT1R) >= abs(RT2R).
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