claev2(3F)

NAME
     CLAEV2 - compute the eigendecomposition of a 2-by-2 Hermitian matrix  [ A
     B ]  [ CONJG(B) C ]

SYNOPSIS
     SUBROUTINE CLAEV2( A, B, C, RT1, RT2, CS1, SN1 )

         REAL           CS1, RT1, RT2

         COMPLEX        A, B, C, SN1

PURPOSE
     CLAEV2 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
            The (1,1) element of the 2-by-2 matrix.

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

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

     RT1    (output) REAL
            The eigenvalue of larger absolute value.

     RT2    (output) REAL
            The eigenvalue of smaller absolute value.

     CS1    (output) REAL
            SN1    (output) COMPLEX 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.