DLANV2 (3lapack)

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

  CS      (output) DOUBLE PRECISION
          SN      (output) DOUBLE PRECISION Parameters of the rotation
          matrix.