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LAPACK version 3.0
dlanv2(3)

PURPOSE
  DLANV2 - compute the Schur factorization of a real 2-by-2 nonsymmetric
  matrix in standard form

SYNTAX
  SUBROUTINE DLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN )

      DOUBLE	     PRECISION A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R, SN

DESCRIPTION
  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 a complex conjugate pair,
	  RT1I > 0.

  CS	  (output) DOUBLE PRECISION
	  SN	  (output) DOUBLE PRECISION 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).