code: def test_convergence(self):
      # Test that the convergence tolerances behave as expected
      rng = np.random.default_rng(2585255913088665241)
      p = rng.random(size=3)
      bracket = (-5, 0, 5)
      args = (p,)
      kwargs0 = dict(args=args, xatol=0, xrtol=0, fatol=0, frtol=0)
  
      kwargs = kwargs0.copy()
      kwargs["xatol"] = 1e-3
      res1 = _chandrupatla_minimize(self.f, *bracket, **kwargs)
      j1 = abs(res1.xr - res1.xl)
      assert_array_less(j1, 4 * kwargs["xatol"])
      kwargs["xatol"] = 1e-6
      res2 = _chandrupatla_minimize(self.f, *bracket, **kwargs)
      j2 = abs(res2.xr - res2.xl)
      assert_array_less(j2, 4 * kwargs["xatol"])
      assert_array_less(j2, j1)
  
      kwargs = kwargs0.copy()
      kwargs["xrtol"] = 1e-3
      res1 = _chandrupatla_minimize(self.f, *bracket, **kwargs)
      j1 = abs(res1.xr - res1.xl)
      assert_array_less(j1, 4 * kwargs["xrtol"] * abs(res1.x))
      kwargs["xrtol"] = 1e-6
      res2 = _chandrupatla_minimize(self.f, *bracket, **kwargs)
      j2 = abs(res2.xr - res2.xl)
      assert_array_less(j2, 4 * kwargs["xrtol"] * abs(res2.x))
      assert_array_less(j2, j1)
  
      kwargs = kwargs0.copy()
      kwargs["fatol"] = 1e-3
      res1 = _chandrupatla_minimize(self.f, *bracket, **kwargs)
      h1 = abs(res1.fl - 2 * res1.fm + res1.fr)
      assert_array_less(h1, 2 * kwargs["fatol"])
      kwargs["fatol"] = 1e-6
      res2 = _chandrupatla_minimize(self.f, *bracket, **kwargs)
      h2 = abs(res2.fl - 2 * res2.fm + res2.fr)
      assert_array_less(h2, 2 * kwargs["fatol"])
      assert_array_less(h2, h1)
  
      kwargs = kwargs0.copy()
      kwargs["frtol"] = 1e-3
      res1 = _chandrupatla_minimize(self.f, *bracket, **kwargs)
      h1 = abs(res1.fl - 2 * res1.fm + res1.fr)
      assert_array_less(h1, 2 * kwargs["frtol"] * abs(res1.fun))
      kwargs["frtol"] = 1e-6
      res2 = _chandrupatla_minimize(self.f, *bracket, **kwargs)
      h2 = abs(res2.fl - 2 * res2.fm + res2.fr)
      assert_array_less(h2, 2 * kwargs["frtol"] * abs(res2.fun))
      assert_array_less(h2, h1)
  
imports: import pytest
  import numpy
  from numpy.testing import assert_allclose, assert_equal, assert_array_less
  from scipy import stats
  import scipy.optimize._chandrupatla
  from scipy.optimize._chandrupatla import _chandrupatla_minimize
  from itertools import permutations
label_desc: Use image node_id 5 for calling the TestChandrupatlaMinimize obj's underlying member method code with example usage: obj.test_convergence() without return types