code: def test_direct_callback(self, locally_biased):
      # test that callback does not change the result
      res = direct(
          self.sphere, self.bounds_sphere, locally_biased=locally_biased
      )
  
      def callback(x):
          x = 2 * x
          dummy = np.square(x)
          print("DIRECT minimization algorithm callback test")
          return dummy
  
      res_callback = direct(
          self.sphere,
          self.bounds_sphere,
          locally_biased=locally_biased,
          callback=callback,
      )
  
      assert_allclose(res.x, res_callback.x)
  
      assert res.nit == res_callback.nit
      assert res.nfev == res_callback.nfev
      assert res.status == res_callback.status
      assert res.success == res_callback.success
      assert res.fun == res_callback.fun
      assert_allclose(res.x, res_callback.x)
      assert res.message == res_callback.message
  
      # test accuracy
      assert_allclose(
          res_callback.x, self.optimum_sphere_pos, rtol=1e-3, atol=1e-3
      )
      assert_allclose(
          res_callback.fun, self.optimum_sphere, atol=1e-5, rtol=1e-5
      )
  
imports: from numpy.testing import assert_allclose, assert_array_less
  import pytest
  import numpy
  from scipy.optimize import direct, Bounds
label_desc: Use image node_id 8 for calling the TestDIRECT obj's underlying member method code with example usage: obj.test_direct_callback(locally_biased) and returns: dummy