code: def single_integration_step(
      graph: jraph.GraphsTuple,
      time_step: float,
      integrator_fn: IntegratorType,
      hamiltonian_from_graph_fn: Callable[
          [jraph.GraphsTuple], jraph.GraphsTuple
      ],
  ) -> Tuple[float, jraph.GraphsTuple]:
      """Updates a graph state integrating by a single step.
  
      Args:
        graph: `GraphsTuple` representing a system state at time t.
        time_step: size of the timestep to integrate for.
        integrator_fn: Integrator to use. A function fn such that
           fn(position_t, momentum_t, time_step, state_derivatives_fn) ->
               (position_tp1, momentum_tp1)
        hamiltonian_from_graph_fn: Function that given a `GraphsTuple`, returns
            another one with a "hamiltonian" global field.
  
      Returns:
        `GraphsTuple` representing a system state at time `t + time_step`.
  
      """
  
      # Template graph with particle/interactions parameters and connectiviity
      # but without the state (position/momentum).
      static_graph = get_static_graph(graph)
  
      # Get the Hamiltonian function, and the function that returns the state
      # derivatives.
      hamiltonian_fn = get_hamiltonian_from_state_fn(
          static_graph=static_graph,
          hamiltonian_from_graph_fn=hamiltonian_from_graph_fn,
      )
      state_derivatives_fn = get_state_derivatives_from_hamiltonian_fn(
          hamiltonian_fn
      )
  
      # Get the current state.
      position, momentum = get_system_state(graph)
  
      # Calling the integrator to get the next state.
      next_position, next_momentum = integrator_fn(
          position, momentum, time_step, state_derivatives_fn
      )
      next_graph = set_system_state(
          static_graph, next_position, next_momentum
      )
  
      # Return the energy of the next state too for plotting.
      energy = hamiltonian_fn(next_position, next_momentum)
  
      return energy, next_graph
  
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 13 for calling a global function with example usage: single_integration_step(graph, time_step, integrator_fn, hamiltonian_from_graph_fn) and returns: energy,  next_graph