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NAME
     zlaev2 - compute the eigendecomposition of a  2-by-2  Hermi-
     tian matrix  [ A B ]  [ CONJG(B) C ]

SYNOPSIS
     SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 )

     DOUBLE PRECISION CS1, RT1, RT2

     COMPLEX*16 A, B, C, SN1



     #include <sunperf.h>

     void zlaev2(doublecomplex *za, doublecomplex *zb, doublecom-
               plex  *zc,  double *rt1, double *rt2, double *cs1,
               doublecomplex *sn1) ;

PURPOSE
     ZLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian
     matrix

        [  A         B  ]
        [  CONJG(B)  C  ].

     On return, RT1 is the eigenvalue of larger  absolute  value,
     RT2  is  the  eigenvalue  of  smaller  absolute  value,  and
     (CS1,SN1) is the unit right eigenvector for RT1, giving  the
     decomposition

     [ CS1  CONJG(SN1) ] [    A     B ] [ CS1 -CONJG(SN1) ] = [ RT1  0  ]
     [-SN1     CS1     ] [ CONJG(B) C ] [ SN1     CS1     ]   [  0  RT2 ]


ARGUMENTS
     A         (input) COMPLEX*16
               The (1,1) element of the 2-by-2 matrix.

     B         (input) COMPLEX*16
               The (1,2) element and the conjugate of  the  (2,1)
               element of the 2-by-2 matrix.

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

     RT1       (output) DOUBLE PRECISION
               The eigenvalue of larger absolute value.

     RT2       (output) DOUBLE PRECISION
               The eigenvalue of smaller absolute value.

     CS1       (output) DOUBLE PRECISION
               SN1    (output) COMPLEX*16 The vector  (CS1,  SN1)
               is a unit right eigenvector for RT1.

FURTHER DETAILS
     RT1 is accurate to a few ulps barring over/underflow.

     RT2 may be inaccurate if there is  massive  cancellation  in
     the  determinant  A*C-B*B;  higher  precision  or  correctly
     rounded or correctly truncated arithmetic would be needed to
     compute RT2 accurately in all cases.

     CS1  and  SN1  are  accurate   to   a   few   ulps   barring
     over/underflow.

     Overflow is possible only if RT1 is within a factor of 5  of
     overflow.   Underflow  is harmless if the input data is 0 or
     exceeds
        underflow_threshold / macheps.

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