code: def check_smw_solver(p, q, r, s):
      # Helper to check that _smw_solver results do in fact solve the desired
      # SMW equation
      d = q - r
  
      A = np.random.normal(size=(p, q))
      AtA = np.dot(A.T, A)
  
      B = np.zeros((q, q))
      B[0:r, 0:r] = np.random.normal(size=(r, r))
      di = np.random.uniform(size=d)
      B[r:q, r:q] = np.diag(1 / di)
      Qi = np.linalg.inv(B[0:r, 0:r])
      s = 0.5
  
      x = np.random.normal(size=p)
      y2 = np.linalg.solve(
          s * np.eye(p, p) + np.dot(A, np.dot(B, A.T)), x
      )
  
      f = _smw_solver(s, A, AtA, Qi, di)
      y1 = f(x)
      assert_allclose(y1, y2)
  
      f = _smw_solver(
          s, sparse.csr_matrix(A), sparse.csr_matrix(AtA), Qi, di
      )
      y1 = f(x)
      assert_allclose(y1, y2)
  
imports: from statsmodels.compat.platform import PLATFORM_OSX
  import os
  import csv
  import warnings
  import numpy
  import pandas
  from scipy import sparse
  import pytest
  from statsmodels.regression.mixed_linear_model import MixedLM, MixedLMParams, _smw_solver, _smw_logdet
  from numpy.testing import assert_almost_equal, assert_equal, assert_allclose, assert_
  from statsmodels.base import _penalties
  import statsmodels.tools.numdiff
  from .results import lme_r_results
label_desc: Use image node_id 9 for calling a global function with example usage: check_smw_solver(p, q, r, s) without return types