CXML
        	    
LAPACK version 3.0
zlaesy(3)

PURPOSE
  ZLAESY - compute the eigendecomposition of a 2-by-2 symmetric matrix ( ( A,
  B );( B, C ) ) provided the norm of the matrix of eigenvectors is larger
  than some threshold value

SYNTAX
  SUBROUTINE ZLAESY( A, B, C, RT1, RT2, EVSCAL, CS1, SN1 )

      COMPLEX*16     A, B, C, CS1, EVSCAL, RT1, RT2, SN1

DESCRIPTION
  ZLAESY computes the eigendecomposition of a 2-by-2 symmetric matrix ( ( A,
  B );( B, C ) ) provided the norm of the matrix of eigenvectors is larger
  than some threshold value.  RT1 is the eigenvalue of larger absolute value,
  and RT2 of smaller absolute value.  If the eigenvectors are computed, then
  on return ( CS1, SN1 ) is the unit eigenvector for RT1, hence

  [  CS1     SN1   ] . [ A  B ] . [ CS1	   -SN1	  ] = [ RT1  0	] [ -SN1
  CS1	]   [ B	 C ]   [ SN1	 CS1   ]   [  0	 RT2 ]

ARGUMENTS
  A	  (input) COMPLEX*16
	  The ( 1, 1 ) element of input matrix.

  B	  (input) COMPLEX*16
	  The ( 1, 2 ) element of input matrix.	 The ( 2, 1 ) element is also
	  given by B, since the 2-by-2 matrix is symmetric.

  C	  (input) COMPLEX*16
	  The ( 2, 2 ) element of input matrix.

  RT1	  (output) COMPLEX*16
	  The eigenvalue of larger modulus.

  RT2	  (output) COMPLEX*16
	  The eigenvalue of smaller modulus.

  EVSCAL  (output) COMPLEX*16
	  The complex value by which the eigenvector matrix was scaled to
	  make it orthonormal.	If EVSCAL is zero, the eigenvectors were not
	  computed.  This means one of two things:  the 2-by-2 matrix could
	  not be diagonalized, or the norm of the matrix of eigenvectors
	  before scaling was larger than the threshold value THRESH (set
	  below).

  CS1	  (output) COMPLEX*16
	  SN1	  (output) COMPLEX*16 If EVSCAL .NE. 0,	 ( CS1, SN1 ) is the
	  unit right eigenvector for RT1.