code: def test_for_loop_fixpoint_correctly_identifies_loop_varying_residuals(
      self, for_impl
  ):
      def body(i, refs):
          a_ref, b_ref, c_ref = refs
          a = a_ref[i]
          b = b_ref[()]
          x = jnp.sin(a)
          b_ref[()] = jnp.sin(b * x)
          c_ref[i] = x * b
  
      def f(a, b):
          c = jnp.zeros_like(a)
          _, b, c = for_impl(5, body, (a, b, c))
          return b, c
  
      a = jnp.arange(5.0) + 1.0
      b = jnp.ones_like(a[0])
      _, f_lin = jax.linearize(f, a, b)
      expected_tangents = f_lin(a, b)
      _, actual_tangents = jax.jvp(f, (a, b), (a, b))
      np.testing.assert_allclose(
          actual_tangents[0], expected_tangents[0]
      )
      np.testing.assert_allclose(
          actual_tangents[1], expected_tangents[1]
      )
  
      def body2(_, refs):
          # Here we use `i_ref` as a loop counter
          a_ref, b_ref, c_ref, i_ref = refs
          i = i_ref[()]
          a = a_ref[i]
          b = b_ref[()]
          x = jnp.sin(a)
          b_ref[()] = jnp.sin(b * x)
          c_ref[i] = x * b
          i_ref[()] = i + 1
  
      def g(a, b):
          c = jnp.zeros_like(a)
          _, b, c, _ = for_impl(5, body2, (a, b, c, 0))
          return b, c
  
      a = jnp.arange(5.0) + 1.0
      b = jnp.ones_like(a[0])
      _, g_lin = jax.linearize(f, a, b)
      expected_tangents = g_lin(a, b)
      _, actual_tangents = jax.jvp(g, (a, b), (a, b))
      np.testing.assert_allclose(
          actual_tangents[0], expected_tangents[0]
      )
      np.testing.assert_allclose(
          actual_tangents[1], expected_tangents[1]
      )
  
imports: from functools import partial
  from absl.testing import absltest
  from absl.testing import parameterized
  import numpy
  import jax
  from jax import random
  from jax._src import test_util
  from jax._src.lax.control_flow import for_loop
  import jax.numpy
  from jax import config
label_desc: Use image node_id 4 for calling the ForLoopTransformationTest obj's underlying member method code with example usage: obj.test_for_loop_fixpoint_correctly_identifies_loop_varying_residuals(for_impl) and returns: b,  c, b,  c