code: def test_global_approximate_diffuse():
      # Test for global approximate diffuse initialization
  
      # - 1-dimensional -
      endog = np.zeros(10)
      mod = sarimax.SARIMAX(endog, order=(1, 0, 0))
  
      init = Initialization(mod.k_states, "approximate_diffuse")
      check_initialization(
          mod, init, [0], np.diag([0]), np.eye(1) * 1e6
      )
  
      init = Initialization(
          mod.k_states, "approximate_diffuse", constant=[1.2]
      )
      check_initialization(
          mod, init, [1.2], np.diag([0]), np.eye(1) * 1e6
      )
  
      init = Initialization(
          mod.k_states,
          "approximate_diffuse",
          approximate_diffuse_variance=1e10,
      )
      check_initialization(
          mod, init, [0], np.diag([0]), np.eye(1) * 1e10
      )
  
      # - n-dimensional -
      endog = np.zeros(10)
      mod = sarimax.SARIMAX(endog, order=(2, 0, 0))
  
      init = Initialization(mod.k_states, "approximate_diffuse")
      check_initialization(
          mod, init, [0, 0], np.diag([0, 0]), np.eye(2) * 1e6
      )
  
      init = Initialization(
          mod.k_states, "approximate_diffuse", constant=[1.2, -0.2]
      )
      check_initialization(
          mod, init, [1.2, -0.2], np.diag([0, 0]), np.eye(2) * 1e6
      )
  
      init = Initialization(
          mod.k_states,
          "approximate_diffuse",
          approximate_diffuse_variance=1e10,
      )
      check_initialization(
          mod, init, [0, 0], np.diag([0, 0]), np.eye(2) * 1e10
      )
  
file_path: statsmodels/statsmodels/tsa/statespace/tests/test_initialization.py
imports: import numpy
  from scipy.linalg import solve_discrete_lyapunov
  from statsmodels.tsa.statespace import sarimax, varmax
  from statsmodels.tsa.statespace.initialization import Initialization
  from numpy.testing import assert_allclose, assert_raises
label_desc: Use image node_id 4 for calling a global function with example usage: test_global_approximate_diffuse() without return types