SLANV2(3)      LAPACK routine of NEC Numeric Library Collection      SLANV2(3)



NAME
       SLANV2

SYNOPSIS
       SUBROUTINE SLANV2 (A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, 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)
                     A is REAL

           B         (input/output)
                     B is REAL

           C         (input/output)
                     C is REAL

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

           RT1R      (output)
                     RT1R is REAL

           RT1I      (output)
                     RT1I is REAL

           RT2R      (output)
                     RT2R is REAL

           RT2I      (output)
                     RT2I is REAL
                     The real and imaginary parts of the eigenvalues. If the
                     eigenvalues are a complex conjugate pair, RT1I > 0.

           CS        (output)
                     CS is REAL

           SN        (output)
                     SN is 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 possible, that
             abs(RT1R) >= abs(RT2R).



LAPACK routine                  31 October 2017                      SLANV2(3)