code: def test_qda():
      # QDA classification.
      # This checks that QDA implements fit and predict and returns
      # correct values for a simple toy dataset.
      clf = QuadraticDiscriminantAnalysis()
      y_pred = clf.fit(X6, y6).predict(X6)
      assert_array_equal(y_pred, y6)
  
      # Assure that it works with 1D data
      y_pred1 = clf.fit(X7, y6).predict(X7)
      assert_array_equal(y_pred1, y6)
  
      # Test probas estimates
      y_proba_pred1 = clf.predict_proba(X7)
      assert_array_equal((y_proba_pred1[:, 1] > 0.5) + 1, y6)
      y_log_proba_pred1 = clf.predict_log_proba(X7)
      assert_array_almost_equal(
          np.exp(y_log_proba_pred1), y_proba_pred1, 8
      )
  
      y_pred3 = clf.fit(X6, y7).predict(X6)
      # QDA shouldn't be able to separate those
      assert np.any(y_pred3 != y7)
  
      # Classes should have at least 2 elements
      with pytest.raises(ValueError):
          clf.fit(X6, y4)
  
imports: import numpy
  import pytest
  from scipy import linalg
  from sklearn.cluster import KMeans
  from sklearn.covariance import LedoitWolf, ShrunkCovariance, ledoit_wolf
  from sklearn.datasets import make_blobs
  from sklearn.discriminant_analysis import LinearDiscriminantAnalysis, QuadraticDiscriminantAnalysis, _cov
  from sklearn.preprocessing import StandardScaler
  from sklearn.utils import _IS_WASM, check_random_state
  from sklearn.utils._testing import _convert_container, assert_allclose, assert_almost_equal, assert_array_almost_equal, assert_array_equal
label_desc: Use image node_id 15 for calling a global function with example usage: test_qda() without return types