Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3 - computes 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.

 LAPACK auxiliary routine (version 3.2)     April 2011                            DLAEV2(3lapack)