code: def get_state_derivatives_from_hamiltonian_fn(
      hamiltonian_from_state_fn: Callable[
          [np.ndarray, np.ndarray], float
      ],
  ) -> Callable[
      [np.ndarray, np.ndarray], Tuple[np.ndarray, np.ndarray]
  ]:
      """Returns fn(position, momentum, ...) -> (dposition_dt, dmomentum_dt).
  
      Args:
          hamiltonian_from_state_fn: Function that given a state
              (position, momentum)  returns the scalar Hamiltonian.
  
      Returns:
          Function that given a state (position, momentum) returns the time
          derivatives of the state (dposition_dt, dmomentum_dt) by applying
          Hamilton equations.
  
      """
  
      hamiltonian_gradients_fn = jax.grad(
          hamiltonian_from_state_fn, argnums=[0, 1]
      )
  
      def state_derivatives_from_hamiltonian_fn(
          position: np.ndarray, momentum: np.ndarray
      ) -> Tuple[np.ndarray, np.ndarray]:
          # Take the derivatives against position and momentum.
          dh_dposition, dh_dmomentum = hamiltonian_gradients_fn(
              position, momentum
          )
  
          # Hamilton equations.
          dposition_dt = dh_dmomentum
          dmomentum_dt = -dh_dposition
          return dposition_dt, dmomentum_dt
  
      return state_derivatives_from_hamiltonian_fn
  
imports: import functools
  from typing import Tuple, Callable
  from absl import app
  from frozendict import frozendict
  import jax
  import jax.numpy
  import jraph
  import matplotlib.pyplot
  import numpy
label_desc: Use image node_id 9 for calling a global function with example usage: get_state_derivatives_from_hamiltonian_fn(hamiltonian_from_state_fn) and returns: state_derivatives_from_hamiltonian_fn, dposition_dt,  dmomentum_dt