code: def test_logistic_sigmoid():
      # Check correctness and robustness of logistic sigmoid implementation
      def naive_log_logistic(x):
          return np.log(expit(x))
  
      x = np.linspace(-2, 2, 50)
      warn_msg = "`log_logistic` is deprecated and will be removed"
      with pytest.warns(FutureWarning, match=warn_msg):
          assert_array_almost_equal(
              log_logistic(x), naive_log_logistic(x)
          )
  
      extreme_x = np.array([-100.0, 100.0])
      with pytest.warns(FutureWarning, match=warn_msg):
          assert_array_almost_equal(log_logistic(extreme_x), [-100, 0])
  
imports: import numpy
  import pytest
  from scipy import linalg, sparse
  from scipy.linalg import eigh
  from scipy.sparse.linalg import eigsh
  from scipy.special import expit
  from sklearn.datasets import make_low_rank_matrix, make_sparse_spd_matrix
  from sklearn.utils import gen_batches
  from sklearn.utils._arpack import _init_arpack_v0
  from sklearn.utils._testing import assert_allclose, assert_allclose_dense_sparse, assert_almost_equal, assert_array_almost_equal, assert_array_equal, skip_if_32bit
  from sklearn.utils.extmath import _deterministic_vector_sign_flip, _incremental_mean_and_var, _randomized_eigsh, _safe_accumulator_op, cartesian, density, log_logistic, randomized_svd, row_norms, safe_sparse_dot, softmax, stable_cumsum, svd_flip, weighted_mode
  from sklearn.utils.fixes import COO_CONTAINERS, CSC_CONTAINERS, CSR_CONTAINERS, DOK_CONTAINERS, LIL_CONTAINERS, _mode
label_desc: Use image node_id 21 for calling a global function with example usage: test_logistic_sigmoid() and returns: np