SLANV2 (3lapack)

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.