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NAME
     zlaesy - compute the eigendecomposition  of  a  2-by-2  sym-
     metric  matrix   (  ( A, B );( B, C ) ) provided the norm of
     the matrix of eigenvectors is  larger  than  some  threshold
     value

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

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



     #include <sunperf.h>

     void zlaesy(doublecomplex *za, doublecomplex *zb, doublecom-
               plex  *zc, doublecomplex *rt1, doublecomplex *rt2,
               doublecomplex *evscal, doublecomplex  *cs1,  doub-
               lecomplex *sn1) ;

PURPOSE
     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.

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