code: def test_actual_results_paa(X, start, end, arr_desired):
      """Test that the actual results are the expected ones."""
      X = np.asarray(X)
      start = np.asarray(start)
      end = np.asarray(end)
      n_timestamps_new = start.size
      n_samples, n_timestamps = X.shape
      arr_actual = _paa(
          X, n_samples, n_timestamps, start, end, n_timestamps_new
      )
      np.testing.assert_allclose(
          arr_actual, arr_desired, atol=1e-5, rtol=0.0
      )
  
imports: import numpy
  import pytest
  import re
  from pyts.approximation.paa import _paa
  from pyts.approximation import PiecewiseAggregateApproximation
label_desc: Use image node_id 1 for calling a global function with example usage: test_actual_results_paa(X, start, end, arr_desired) without return types