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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