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NAME
     dlaev2 - compute the eigendecomposition  of  a  2-by-2  sym-
     metric matrix  [ A B ]  [ B C ]

SYNOPSIS
     SUBROUTINE DLAEV2( A, B, C, RT1, RT2, CS1, SN1 )

     DOUBLE PRECISION A, B, C, CS1, RT1, RT2, SN1



     #include <sunperf.h>

     void dlaev2(double a, double b, double c, double *rt1,  dou-
               ble *rt2, double *cs1, double *sn1) ;

PURPOSE
     DLAEV2 computes the eigendecomposition of a 2-by-2 symmetric
     matrix

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


ARGUMENTS
     A         (input) DOUBLE PRECISION
               The (1,1) element of the 2-by-2 matrix.

     B         (input) DOUBLE PRECISION
               The (1,2) element and the conjugate of  the  (2,1)
               element of the 2-by-2 matrix.

     C         (input) DOUBLE PRECISION
               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) DOUBLE PRECISION 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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