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# dlanv2

```
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 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 standardized
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 both real, abs(RT1R) >=
abs(RT2R); if the eigenvalues are a complex conju-
gate pair, RT1I > 0.

CS      (output) DOUBLE PRECISION
SN      (output) DOUBLE PRECISION Parameters of the
rotation matrix.
```