dlanv2 man page on Scientific

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```DLANV2(1)	      LAPACK driver routine (version 3.2)	     DLANV2(1)

NAME
DLANV2 - computes 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 driver routine (version 3November 2008			     DLANV2(1)
```
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