code: def test_initialize(X, probs):
      d = Categorical()
      assert d.d is None
      assert d.probs is None
      assert d._initialized == False
      assert_raises(AttributeError, getattr, d, "_w_sum")
      assert_raises(AttributeError, getattr, d, "_xw_sum")
      assert_raises(AttributeError, getattr, d, "_log_probs")
  
      d._initialize(3, 5)
      assert d._initialized == True
      assert d.probs.shape == (3, 5)
      assert d.d == 3
      assert d.n_keys == 5
      assert_array_almost_equal(
          d.probs,
          [
              [0.0, 0.0, 0.0, 0.0, 0.0],
              [0.0, 0.0, 0.0, 0.0, 0.0],
              [0.0, 0.0, 0.0, 0.0, 0.0],
          ],
      )
      assert_array_almost_equal(d._w_sum, [0.0, 0.0, 0.0])
      assert_array_almost_equal(
          d._xw_sum,
          [
              [0.0, 0.0, 0.0, 0.0, 0.0],
              [0.0, 0.0, 0.0, 0.0, 0.0],
              [0.0, 0.0, 0.0, 0.0, 0.0],
          ],
      )
  
      d._initialize(2, 2)
      assert d._initialized == True
      assert d.probs.shape == (2, 2)
      assert d.d == 2
      assert d.n_keys == 2
      assert_array_almost_equal(d.probs, [[0.0, 0.0], [0.0, 0.0]])
      assert_array_almost_equal(d._w_sum, [0.0, 0.0])
      assert_array_almost_equal(d._xw_sum, [[0.0, 0.0], [0.0, 0.0]])
  
      d = Categorical(probs)
      assert d._initialized == True
      assert d.d == 3
      assert d.n_keys == 4
  
      d._initialize(3, 4)
      assert d._initialized == True
      assert d.probs.shape == (3, 4)
      assert d.d == 3
      assert d.n_keys == 4
      assert_array_almost_equal(
          d.probs,
          [
              [0.0, 0.0, 0.0, 0.0],
              [0.0, 0.0, 0.0, 0.0],
              [0.0, 0.0, 0.0, 0.0],
          ],
      )
  
      d = Categorical()
      d.summarize(X)
      d._initialize(4, 2)
      assert d._initialized == True
      assert d.probs.shape == (4, 2)
      assert d.d == 4
      assert d.n_keys == 2
      assert_array_almost_equal(d._w_sum, [0.0, 0.0, 0.0, 0.0])
      assert_array_almost_equal(
          d._xw_sum, [[0.0, 0.0], [0.0, 0.0], [0.0, 0.0], [0.0, 0.0]]
      )
  
imports: import os
  import numpy
  import torch
  import pytest
  from pomegranate.distributions import Categorical
  from ._utils import _test_initialization_raises_one_parameter
  from ._utils import _test_predictions
  from ._utils import _test_raises
  from nose.tools import assert_raises
  from numpy.testing import assert_array_almost_equal
label_desc: Use image node_id 11 for calling a global function with example usage: test_initialize(X, probs) without return types