code: def test_tuple_variables(self, solver):
      alpha = np.float32(0.7)
      beta = np.float32(2.2)
      variable_1 = tf.Variable(alpha, name="alpha")
      variable_2 = tf.Variable(beta, name="beta")
  
      def ode_fn(time, state):
          del time
          x, y = state
          return variable_1 * x, (variable_1 + variable_2) * y
  
      initial_time = 0.0
      initial_x = np.float32(3.2)
      initial_y = np.float32(-4.2)
      initial_state = (initial_x, initial_y)
      final_time = 0.5
  
      solver_instance = solver(rtol=_RTOL, atol=_ATOL)
  
      with tf.GradientTape(persistent=True) as tape:
          tape.watch([variable_1, variable_2])
          results = solver_instance.solve(
              ode_fn,
              initial_time,
              initial_state,
              solution_times=[final_time],
          )
          final_state = results.states
      self.evaluate([variable_1.initializer, variable_2.initializer])
      actual_grad_1 = self.evaluate(
          tape.gradient(final_state[0], [variable_1])
      )
      actual_grad_2 = self.evaluate(
          tape.gradient(final_state[1], [variable_1])
      )
      actual_grad_3 = self.evaluate(
          tape.gradient(final_state[1], [variable_2])
      )
  
      expected_grad_1 = (
          initial_x
          * final_time
          * np.exp(alpha * final_time)[np.newaxis]
      )
      expected_grad_2 = (
          initial_y
          * final_time
          * np.exp((alpha + beta) * final_time)[np.newaxis]
      )
      expected_grad_3 = expected_grad_2
      self.assertAllClose(
          actual_grad_1, expected_grad_1, rtol=1e-4, atol=1e-4
      )
      self.assertAllClose(
          actual_grad_2, expected_grad_2, rtol=1e-4, atol=1e-4
      )
      self.assertAllClose(
          actual_grad_3, expected_grad_3, rtol=1e-4, atol=1e-4
      )
  
imports: from absl.testing import parameterized
  import numpy
  import tensorflow.compat.v1
  import tensorflow.compat.v2
  from tensorflow_probability.python.internal import test_util
  from tensorflow_probability.python.math import gradient
  from tensorflow_probability.python.math.ode import base
  from tensorflow_probability.python.math.ode import bdf
  from tensorflow_probability.python.math.ode import dormand_prince
label_desc: Use image node_id 3 for calling the GradientTestPforJacobian obj's underlying member method code with example usage: obj.test_tuple_variables(solver) and returns: unknown,  unknown