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LAPACK version 3.0
slanv2(3)

PURPOSE
  SLANV2 - compute the Schur factorization of a real 2-by-2 nonsymmetric
  matrix in standard form

SYNTAX
  SUBROUTINE SLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN )

      REAL	     A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R, SN

DESCRIPTION
  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 a complex conjugate pair, RT1I > 0.

  CS	  (output) REAL
	  SN	  (output) 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).