code: def test_add_cov(ddof):
      c1 = stats.Cov(ddof=ddof)
      c2 = stats.Cov(ddof=ddof)
  
      X = [random.random() for _ in range(30)]
      Y = [random.random() for _ in range(30)]
  
      W = [random.random() for _ in range(30)]
      Z = [random.random() for _ in range(30)]
  
      for i, (x, y, w, z) in enumerate(zip(X, Y, W, Z)):
          c1.update(x, y)
          c2.update(w, z)
          if i >= c1.ddof:
              assert math.isclose(
                  c1.get(),
                  np.cov(X[: i + 1], Y[: i + 1], ddof=ddof)[0, 1],
                  abs_tol=1e-10,
              )
              assert math.isclose(
                  c2.get(),
                  np.cov(W[: i + 1], Z[: i + 1], ddof=ddof)[0, 1],
                  abs_tol=1e-10,
              )
              assert math.isclose(
                  (c1 + c2).get(),
                  np.cov(
                      X[: i + 1] + W[: i + 1],
                      Y[: i + 1] + Z[: i + 1],
                      ddof=ddof,
                  )[0, 1],
                  abs_tol=1e-10,
              )
  
      c1 += c2
      assert math.isclose(
          c1.get(), np.cov(X + W, Y + Z, ddof=ddof)[0, 1], abs_tol=1e-10
      )
  
file_path: river/river/stats/test_parallel.py
imports: from __future__ import annotations
  import copy
  import math
  import random
  import numpy
  import pytest
  from river import stats
label_desc: Use image node_id 6 for calling a global function with example usage: test_add_cov(ddof) without return types