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NAME

       LAPACK-3  -  computes  the  eigendecomposition  of  a  2-by-2 Hermitian 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

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.

 LAPACK auxiliary routine (version 3.2)     April 2011                            ZLAEV2(3lapack)