dlaev2(3F)

NAME
     DLAEV2 - compute the eigendecomposition of a 2-by-2 symmetric matrix  [ A
     B ]  [ B C ]

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

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