def sym_exp_map(cls, q, eta):
        """Quaternion symmetrized exponential map.

        Find the symmetrized exponential map on the quaternion Riemannian
        manifold.

        Params:
             q: the base point as a Quaternion object
           eta: the tangent vector argument of the exponential map
                as a Quaternion object

        Returns:
            A quaternion p.

        Note:
            The symmetrized exponential formulation is akin to the exponential
            formulation for symmetric positive definite tensors [Source](http://www.academia.edu/7656761/On_the_Averaging_of_Symmetric_Positive-Definite_Tensors)
        """
        sqrt_q = q ** 0.5
        return sqrt_q * Quaternion.exp(eta) * sqrt_q
Quaternion symmetrized exponential map.

        Find the symmetrized exponential map on the quaternion Riemannian
        manifold.

        Params:
             q: the base point as a Quaternion object
           eta: the tangent vector argument of the exponential map
                as a Quaternion object

        Returns:
            A quaternion p.

        Note:
            The symmetrized exponential formulation is akin to the exponential
            formulation for symmetric positive definite tensors [Source](http://www.academia.edu/7656761/On_the_Averaging_of_Symmetric_Positive-Definite_Tensors)