SLANV2  - compute the Schur factorization of a real 2-by-2
       nonsymmetric matrix in standard form


SYNOPSIS

       SUBROUTINE SLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS,
                          SN )

           REAL           A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R,
                          SN


PURPOSE

       SLANV2 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) REAL
               B       (input/output) REAL C       (input/output)
               REAL D       (input/output)  REAL  On  entry,  the
               elements  of  the input matrix.  On exit, they are
               overwritten by the elements  of  the  standardised
               Schur form.

       RT1R    (output) REAL
               RT1I     (output)  REAL RT2R    (output) REAL RT2I
               (output) REAL The real and imaginary parts of  the
               eigenvalues. If the eigenvalues are a complex con­
               jugate pair, RT1I > 0.

       CS      (output) REAL
               SN      (output) REAL 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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