slanv2(3F)

NAME
     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 both real, abs(RT1R) >= abs(RT2R); if the
             eigenvalues are a complex conjugate pair, RT1I > 0.

     CS      (output) REAL
             SN      (output) REAL Parameters of the rotation matrix.