text: """
  Testing Recursive feature elimination
  """
  
  from operator import attrgetter
  import pytest
  import numpy as np
  from numpy.testing import assert_array_almost_equal, assert_array_equal
  from scipy import sparse
  
  from sklearn.base import BaseEstimator, ClassifierMixin
  from sklearn.feature_selection import RFE, RFECV
  from sklearn.datasets import load_iris, make_friedman1
  from sklearn.metrics import zero_one_loss
  from sklearn.svm import SVC, SVR, LinearSVR
  from sklearn.linear_model import LogisticRegression
  from sklearn.ensemble import RandomForestClassifier
  from sklearn.model_selection import cross_val_score
  from sklearn.model_selection import GroupKFold
  from sklearn.compose import TransformedTargetRegressor
  from sklearn.pipeline import make_pipeline
  from sklearn.preprocessing import StandardScaler
  
  from sklearn.utils import check_random_state
  from sklearn.utils._testing import ignore_warnings
  
  from sklearn.metrics import make_scorer
  from sklearn.metrics import get_scorer
  
  
  class MockClassifier:
      """
      Dummy classifier to test recursive feature elimination
      """
  
      def __init__(self, foo_param=0):
          self.foo_param = foo_param
  
      def fit(self, X, y):
          assert len(X) == len(y)
          self.coef_ = np.ones(X.shape[1], dtype=np.float64)
          return self
  
      def predict(self, T):
          return T.shape[0]
  
      predict_proba = predict
      decision_function = predict
      transform = predict
  
      def score(self, X=None, y=None):
          return 0.0
  
      def get_params(self, deep=True):
          return {"foo_param": self.foo_param}
  
      def set_params(self, **params):
          return self
  
      def _more_tags(self):
          return {"allow_nan": True}
  
  
  def test_rfe_features_importance():
      generator = check_random_state(0)
      iris = load_iris()
      X = np.c_[iris.data, generator.normal(size=(len(iris.data), 6))]
      y = iris.target
  
      clf = RandomForestClassifier(n_estimators=20, random_state=generator, max_depth=2)
      rfe = RFE(estimator=clf, n_features_to_select=4, step=0.1)
      rfe.fit(X, y)
      assert len(rfe.ranking_) == X.shape[1]
  
      clf_svc = SVC(kernel="linear")
      rfe_svc = RFE(estimator=clf_svc, n_features_to_select=4, step=0.1)
      rfe_svc.fit(X, y)
  
      # Check if the supports are equal
      assert_array_equal(rfe.get_support(), rfe_svc.get_support())
  
  
  def test_rfe():
      generator = check_random_state(0)
      iris = load_iris()
      X = np.c_[iris.data, generator.normal(size=(len(iris.data), 6))]
      X_sparse = sparse.csr_matrix(X)
      y = iris.target
  
      # dense model
      clf = SVC(kernel="linear")
      rfe = RFE(estimator=clf, n_features_to_select=4, step=0.1)
      rfe.fit(X, y)
      X_r = rfe.transform(X)
      clf.fit(X_r, y)
      assert len(rfe.ranking_) == X.shape[1]
  
      # sparse model
      clf_sparse = SVC(kernel="linear")
      rfe_sparse = RFE(estimator=clf_sparse, n_features_to_select=4, step=0.1)
      rfe_sparse.fit(X_sparse, y)
      X_r_sparse = rfe_sparse.transform(X_sparse)
  
      assert X_r.shape == iris.data.shape
      assert_array_almost_equal(X_r[:10], iris.data[:10])
  
      assert_array_almost_equal(rfe.predict(X), clf.predict(iris.data))
      assert rfe.score(X, y) == clf.score(iris.data, iris.target)
      assert_array_almost_equal(X_r, X_r_sparse.toarray())
  
  
  def test_RFE_fit_score_params():
      # Make sure RFE passes the metadata down to fit and score methods of the
      # underlying estimator
      class TestEstimator(BaseEstimator, ClassifierMixin):
          def fit(self, X, y, prop=None):
              if prop is None:
                  raise ValueError("fit: prop cannot be None")
              self.svc_ = SVC(kernel="linear").fit(X, y)
              self.coef_ = self.svc_.coef_
              return self
  
          def score(self, X, y, prop=None):
              if prop is None:
                  raise ValueError("score: prop cannot be None")
              return self.svc_.score(X, y)
  
      X, y = load_iris(return_X_y=True)
      with pytest.raises(ValueError, match="fit: prop cannot be None"):
          RFE(estimator=TestEstimator()).fit(X, y)
      with pytest.raises(ValueError, match="score: prop cannot be None"):
          RFE(estimator=TestEstimator()).fit(X, y, prop="foo").score(X, y)
  
      RFE(estimator=TestEstimator()).fit(X, y, prop="foo").score(X, y, prop="foo")
  
  
  @pytest.mark.parametrize("n_features_to_select", [-1, 2.1])
  def test_rfe_invalid_n_features_errors(n_features_to_select):
      clf = SVC(kernel="linear")
  
      iris = load_iris()
      rfe = RFE(estimator=clf, n_features_to_select=n_features_to_select, step=0.1)
      msg = f"n_features_to_select must be .+ Got {n_features_to_select}"
      with pytest.raises(ValueError, match=msg):
          rfe.fit(iris.data, iris.target)
  
  
  def test_rfe_percent_n_features():
      # test that the results are the same
      generator = check_random_state(0)
      iris = load_iris()
      X = np.c_[iris.data, generator.normal(size=(len(iris.data), 6))]
      y = iris.target
      # there are 10 features in the data. We select 40%.
      clf = SVC(kernel="linear")
      rfe_num = RFE(estimator=clf, n_features_to_select=4, step=0.1)
      rfe_num.fit(X, y)
  
      rfe_perc = RFE(estimator=clf, n_features_to_select=0.4, step=0.1)
      rfe_perc.fit(X, y)
  
      assert_array_equal(rfe_perc.ranking_, rfe_num.ranking_)
      assert_array_equal(rfe_perc.support_, rfe_num.support_)
  
  
  def test_rfe_mockclassifier():
      generator = check_random_state(0)
      iris = load_iris()
      X = np.c_[iris.data, generator.normal(size=(len(iris.data), 6))]
      y = iris.target
  
      # dense model
      clf = MockClassifier()
      rfe = RFE(estimator=clf, n_features_to_select=4, step=0.1)
      rfe.fit(X, y)
      X_r = rfe.transform(X)
      clf.fit(X_r, y)
      assert len(rfe.ranking_) == X.shape[1]
      assert X_r.shape == iris.data.shape
  
  
  def test_rfecv():
      generator = check_random_state(0)
      iris = load_iris()
      X = np.c_[iris.data, generator.normal(size=(len(iris.data), 6))]
      y = list(iris.target)  # regression test: list should be supported
  
      # Test using the score function
      rfecv = RFECV(estimator=SVC(kernel="linear"), step=1)
      rfecv.fit(X, y)
      # non-regression test for missing worst feature:
      assert len(rfecv.grid_scores_) == X.shape[1]
      assert len(rfecv.ranking_) == X.shape[1]
      X_r = rfecv.transform(X)
  
      # All the noisy variable were filtered out
      assert_array_equal(X_r, iris.data)
  
      # same in sparse
      rfecv_sparse = RFECV(estimator=SVC(kernel="linear"), step=1)
      X_sparse = sparse.csr_matrix(X)
      rfecv_sparse.fit(X_sparse, y)
      X_r_sparse = rfecv_sparse.transform(X_sparse)
      assert_array_equal(X_r_sparse.toarray(), iris.data)
  
      # Test using a customized loss function
      scoring = make_scorer(zero_one_loss, greater_is_better=False)
      rfecv = RFECV(estimator=SVC(kernel="linear"), step=1, scoring=scoring)
      ignore_warnings(rfecv.fit)(X, y)
      X_r = rfecv.transform(X)
      assert_array_equal(X_r, iris.data)
  
      # Test using a scorer
      scorer = get_scorer("accuracy")
      rfecv = RFECV(estimator=SVC(kernel="linear"), step=1, scoring=scorer)
      rfecv.fit(X, y)
      X_r = rfecv.transform(X)
      assert_array_equal(X_r, iris.data)
  
      # Test fix on grid_scores
      def test_scorer(estimator, X, y):
          return 1.0
  
      rfecv = RFECV(estimator=SVC(kernel="linear"), step=1, scoring=test_scorer)
      rfecv.fit(X, y)
      assert_array_equal(rfecv.grid_scores_, np.ones(len(rfecv.grid_scores_)))
      # In the event of cross validation score ties, the expected behavior of
      # RFECV is to return the FEWEST features that maximize the CV score.
      # Because test_scorer always returns 1.0 in this example, RFECV should
      # reduce the dimensionality to a single feature (i.e. n_features_ = 1)
      assert rfecv.n_features_ == 1
  
      # Same as the first two tests, but with step=2
      rfecv = RFECV(estimator=SVC(kernel="linear"), step=2)
      rfecv.fit(X, y)
      assert len(rfecv.grid_scores_) == 6
      assert len(rfecv.ranking_) == X.shape[1]
      X_r = rfecv.transform(X)
      assert_array_equal(X_r, iris.data)
  
      rfecv_sparse = RFECV(estimator=SVC(kernel="linear"), step=2)
      X_sparse = sparse.csr_matrix(X)
      rfecv_sparse.fit(X_sparse, y)
      X_r_sparse = rfecv_sparse.transform(X_sparse)
      assert_array_equal(X_r_sparse.toarray(), iris.data)
  
      # Verifying that steps < 1 don't blow up.
      rfecv_sparse = RFECV(estimator=SVC(kernel="linear"), step=0.2)
      X_sparse = sparse.csr_matrix(X)
      rfecv_sparse.fit(X_sparse, y)
      X_r_sparse = rfecv_sparse.transform(X_sparse)
      assert_array_equal(X_r_sparse.toarray(), iris.data)
  
  
  def test_rfecv_mockclassifier():
      generator = check_random_state(0)
      iris = load_iris()
      X = np.c_[iris.data, generator.normal(size=(len(iris.data), 6))]
      y = list(iris.target)  # regression test: list should be supported
  
      # Test using the score function
      rfecv = RFECV(estimator=MockClassifier(), step=1)
      rfecv.fit(X, y)
      # non-regression test for missing worst feature:
      assert len(rfecv.grid_scores_) == X.shape[1]
      assert len(rfecv.ranking_) == X.shape[1]
  
  
  def test_rfecv_verbose_output():
      # Check verbose=1 is producing an output.
      from io import StringIO
      import sys
  
      sys.stdout = StringIO()
  
      generator = check_random_state(0)
      iris = load_iris()
      X = np.c_[iris.data, generator.normal(size=(len(iris.data), 6))]
      y = list(iris.target)
  
      rfecv = RFECV(estimator=SVC(kernel="linear"), step=1, verbose=1)
      rfecv.fit(X, y)
  
      verbose_output = sys.stdout
      verbose_output.seek(0)
      assert len(verbose_output.readline()) > 0
  
  
  def test_rfecv_grid_scores_size():
      generator = check_random_state(0)
      iris = load_iris()
      X = np.c_[iris.data, generator.normal(size=(len(iris.data), 6))]
      y = list(iris.target)  # regression test: list should be supported
  
      # Non-regression test for varying combinations of step and
      # min_features_to_select.
      for step, min_features_to_select in [[2, 1], [2, 2], [3, 3]]:
          rfecv = RFECV(
              estimator=MockClassifier(),
              step=step,
              min_features_to_select=min_features_to_select,
          )
          rfecv.fit(X, y)
  
          score_len = np.ceil((X.shape[1] - min_features_to_select) / step) + 1
          assert len(rfecv.grid_scores_) == score_len
          assert len(rfecv.ranking_) == X.shape[1]
          assert rfecv.n_features_ >= min_features_to_select
  
  
  def test_rfe_estimator_tags():
      rfe = RFE(SVC(kernel="linear"))
      assert rfe._estimator_type == "classifier"
      # make sure that cross-validation is stratified
      iris = load_iris()
      score = cross_val_score(rfe, iris.data, iris.target)
      assert score.min() > 0.7
  
  
  def test_rfe_min_step():
      n_features = 10
      X, y = make_friedman1(n_samples=50, n_features=n_features, random_state=0)
      n_samples, n_features = X.shape
      estimator = SVR(kernel="linear")
  
      # Test when floor(step * n_features) <= 0
      selector = RFE(estimator, step=0.01)
      sel = selector.fit(X, y)
      assert sel.support_.sum() == n_features // 2
  
      # Test when step is between (0,1) and floor(step * n_features) > 0
      selector = RFE(estimator, step=0.20)
      sel = selector.fit(X, y)
      assert sel.support_.sum() == n_features // 2
  
      # Test when step is an integer
      selector = RFE(estimator, step=5)
      sel = selector.fit(X, y)
      assert sel.support_.sum() == n_features // 2
  
  
  def test_number_of_subsets_of_features():
      # In RFE, 'number_of_subsets_of_features'
      # = the number of iterations in '_fit'
      # = max(ranking_)
      # = 1 + (n_features + step - n_features_to_select - 1) // step
      # After optimization #4534, this number
      # = 1 + np.ceil((n_features - n_features_to_select) / float(step))
      # This test case is to test their equivalence, refer to #4534 and #3824
  
      def formula1(n_features, n_features_to_select, step):
          return 1 + ((n_features + step - n_features_to_select - 1) // step)
  
      def formula2(n_features, n_features_to_select, step):
          return 1 + np.ceil((n_features - n_features_to_select) / float(step))
  
      # RFE
      # Case 1, n_features - n_features_to_select is divisible by step
      # Case 2, n_features - n_features_to_select is not divisible by step
      n_features_list = [11, 11]
      n_features_to_select_list = [3, 3]
      step_list = [2, 3]
      for n_features, n_features_to_select, step in zip(
          n_features_list, n_features_to_select_list, step_list
      ):
          generator = check_random_state(43)
          X = generator.normal(size=(100, n_features))
          y = generator.rand(100).round()
          rfe = RFE(
              estimator=SVC(kernel="linear"),
              n_features_to_select=n_features_to_select,
              step=step,
          )
          rfe.fit(X, y)
          # this number also equals to the maximum of ranking_
          assert np.max(rfe.ranking_) == formula1(n_features, n_features_to_select, step)
          assert np.max(rfe.ranking_) == formula2(n_features, n_features_to_select, step)
  
      # In RFECV, 'fit' calls 'RFE._fit'
      # 'number_of_subsets_of_features' of RFE
      # = the size of 'grid_scores' of RFECV
      # = the number of iterations of the for loop before optimization #4534
  
      # RFECV, n_features_to_select = 1
      # Case 1, n_features - 1 is divisible by step
      # Case 2, n_features - 1 is not divisible by step
  
      n_features_to_select = 1
      n_features_list = [11, 10]
      step_list = [2, 2]
      for n_features, step in zip(n_features_list, step_list):
          generator = check_random_state(43)
          X = generator.normal(size=(100, n_features))
          y = generator.rand(100).round()
          rfecv = RFECV(estimator=SVC(kernel="linear"), step=step)
          rfecv.fit(X, y)
  
          assert rfecv.grid_scores_.shape[0] == formula1(
              n_features, n_features_to_select, step
          )
          assert rfecv.grid_scores_.shape[0] == formula2(
              n_features, n_features_to_select, step
          )
  
  
  def test_rfe_cv_n_jobs():
      generator = check_random_state(0)
      iris = load_iris()
      X = np.c_[iris.data, generator.normal(size=(len(iris.data), 6))]
      y = iris.target
  
      rfecv = RFECV(estimator=SVC(kernel="linear"))
      rfecv.fit(X, y)
      rfecv_ranking = rfecv.ranking_
      rfecv_grid_scores = rfecv.grid_scores_
  
      rfecv.set_params(n_jobs=2)
      rfecv.fit(X, y)
      assert_array_almost_equal(rfecv.ranking_, rfecv_ranking)
      assert_array_almost_equal(rfecv.grid_scores_, rfecv_grid_scores)
  
  
  def test_rfe_cv_groups():
      generator = check_random_state(0)
      iris = load_iris()
      number_groups = 4
      groups = np.floor(np.linspace(0, number_groups, len(iris.target)))
      X = iris.data
      y = (iris.target > 0).astype(int)
  
      est_groups = RFECV(
          estimator=RandomForestClassifier(random_state=generator),
          step=1,
          scoring="accuracy",
          cv=GroupKFold(n_splits=2),
      )
      est_groups.fit(X, y, groups=groups)
      assert est_groups.n_features_ > 0
  
  
  @pytest.mark.parametrize(
      "importance_getter", [attrgetter("regressor_.coef_"), "regressor_.coef_"]
  )
  @pytest.mark.parametrize("selector, expected_n_features", [(RFE, 5), (RFECV, 4)])
  def test_rfe_wrapped_estimator(importance_getter, selector, expected_n_features):
      # Non-regression test for
      # https://github.com/scikit-learn/scikit-learn/issues/15312
      X, y = make_friedman1(n_samples=50, n_features=10, random_state=0)
      estimator = LinearSVR(random_state=0)
  
      log_estimator = TransformedTargetRegressor(
          regressor=estimator, func=np.log, inverse_func=np.exp
      )
  
      selector = selector(log_estimator, importance_getter=importance_getter)
      sel = selector.fit(X, y)
      assert sel.support_.sum() == expected_n_features
  
  
  @pytest.mark.parametrize(
      "importance_getter, err_type",
      [
          ("auto", ValueError),
          ("random", AttributeError),
          (lambda x: x.importance, AttributeError),
          ([0], ValueError),
      ],
  )
  @pytest.mark.parametrize("Selector", [RFE, RFECV])
  def test_rfe_importance_getter_validation(importance_getter, err_type, Selector):
      X, y = make_friedman1(n_samples=50, n_features=10, random_state=42)
      estimator = LinearSVR()
      log_estimator = TransformedTargetRegressor(
          regressor=estimator, func=np.log, inverse_func=np.exp
      )
  
      with pytest.raises(err_type):
          model = Selector(log_estimator, importance_getter=importance_getter)
          model.fit(X, y)
  
  
  @pytest.mark.parametrize("cv", [None, 5])
  def test_rfe_allow_nan_inf_in_x(cv):
      iris = load_iris()
      X = iris.data
      y = iris.target
  
      # add nan and inf value to X
      X[0][0] = np.NaN
      X[0][1] = np.Inf
  
      clf = MockClassifier()
      if cv is not None:
          rfe = RFECV(estimator=clf, cv=cv)
      else:
          rfe = RFE(estimator=clf)
      rfe.fit(X, y)
      rfe.transform(X)
  
  
  def test_w_pipeline_2d_coef_():
      pipeline = make_pipeline(StandardScaler(), LogisticRegression())
  
      data, y = load_iris(return_X_y=True)
      sfm = RFE(
          pipeline,
          n_features_to_select=2,
          importance_getter="named_steps.logisticregression.coef_",
      )
  
      sfm.fit(data, y)
      assert sfm.transform(data).shape[1] == 2
  
  
  @pytest.mark.parametrize("ClsRFE", [RFE, RFECV])
  def test_multioutput(ClsRFE):
      X = np.random.normal(size=(10, 3))
      y = np.random.randint(2, size=(10, 2))
      clf = RandomForestClassifier(n_estimators=5)
      rfe_test = ClsRFE(clf)
      rfe_test.fit(X, y)
  