NAME

       lae2 - lae2: 2x2 eig, step in steqr, stemr

SYNOPSIS

   Functions
       subroutine dlae2 (a, b, c, rt1, rt2)
           DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.
       subroutine slae2 (a, b, c, rt1, rt2)
           SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.

Detailed Description

Function Documentation

   subroutine dlae2 (double precision a, double precision b, double precision c, double precision
       rt1, double precision rt2)
       DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.

       Purpose:

            DLAE2  computes the eigenvalues of a 2-by-2 symmetric matrix
               [  A   B  ]
               [  B   C  ].
            On return, RT1 is the eigenvalue of larger absolute value, and RT2
            is the eigenvalue of smaller absolute value.

       Parameters
           A

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

           B

                     B is DOUBLE PRECISION
                     The (1,2) and (2,1) elements of the 2-by-2 matrix.

           C

                     C is DOUBLE PRECISION
                     The (2,2) element of the 2-by-2 matrix.

           RT1

                     RT1 is DOUBLE PRECISION
                     The eigenvalue of larger absolute value.

           RT2

                     RT2 is DOUBLE PRECISION
                     The eigenvalue of smaller absolute value.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       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.

             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.

   subroutine slae2 (real a, real b, real c, real rt1, real rt2)
       SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.

       Purpose:

            SLAE2  computes the eigenvalues of a 2-by-2 symmetric matrix
               [  A   B  ]
               [  B   C  ].
            On return, RT1 is the eigenvalue of larger absolute value, and RT2
            is the eigenvalue of smaller absolute value.

       Parameters
           A

                     A is REAL
                     The (1,1) element of the 2-by-2 matrix.

           B

                     B is REAL
                     The (1,2) and (2,1) elements of the 2-by-2 matrix.

           C

                     C is REAL
                     The (2,2) element of the 2-by-2 matrix.

           RT1

                     RT1 is REAL
                     The eigenvalue of larger absolute value.

           RT2

                     RT2 is REAL
                     The eigenvalue of smaller absolute value.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       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.

             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.

Author

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