def Ad(phi, v):
    """
    This is Ad(phi,v), the big adjoint action of a deformation phi on a
    velocity w.

        Ad(phi,v) = (Dphi \\circ phi^{-1}) v\\circ phi^{-1}

    This is a tricky computation, is not commonly needed in practice and
    will not be implemented until needed.

    Given phi^{-1}, Ad(phi, v) can be computed by first multiplying v by
    Dphi^{-1} then splatting the components of the resulting vector field.
    """
    raise NotImplementedError
