content: from __future__ import division, print_function
  
  import numpy as np
  from itertools import product
  import warnings
  from scipy.sparse import csr_matrix
  
  from sklearn import datasets
  from sklearn import svm
  from sklearn import ensemble
  
  from sklearn.datasets import make_multilabel_classification
  from sklearn.random_projection import sparse_random_matrix
  from sklearn.utils.validation import check_array, check_consistent_length
  from sklearn.utils.validation import check_random_state
  
  from sklearn.utils.testing import assert_raises, clean_warning_registry
  from sklearn.utils.testing import assert_raise_message
  from sklearn.utils.testing import assert_equal
  from sklearn.utils.testing import assert_almost_equal
  from sklearn.utils.testing import assert_array_equal
  from sklearn.utils.testing import assert_array_almost_equal
  from sklearn.utils.testing import assert_warns
  
  from sklearn.metrics import auc
  from sklearn.metrics import average_precision_score
  from sklearn.metrics import coverage_error
  from sklearn.metrics import label_ranking_average_precision_score
  from sklearn.metrics import precision_recall_curve
  from sklearn.metrics import label_ranking_loss
  from sklearn.metrics import roc_auc_score
  from sklearn.metrics import roc_curve
  
  from sklearn.exceptions import UndefinedMetricWarning
  
  
  ###############################################################################
  # Utilities for testing
  
  def make_prediction(dataset=None, binary=False):
      """Make some classification predictions on a toy dataset using a SVC
  
      If binary is True restrict to a binary classification problem instead of a
      multiclass classification problem
      """
  
      if dataset is None:
          # import some data to play with
          dataset = datasets.load_iris()
  
      X = dataset.data
      y = dataset.target
  
      if binary:
          # restrict to a binary classification task
          X, y = X[y < 2], y[y < 2]
  
      n_samples, n_features = X.shape
      p = np.arange(n_samples)
  
      rng = check_random_state(37)
      rng.shuffle(p)
      X, y = X[p], y[p]
      half = int(n_samples / 2)
  
      # add noisy features to make the problem harder and avoid perfect results
      rng = np.random.RandomState(0)
      X = np.c_[X, rng.randn(n_samples, 200 * n_features)]
  
      # run classifier, get class probabilities and label predictions
      clf = svm.SVC(kernel='linear', probability=True, random_state=0)
      probas_pred = clf.fit(X[:half], y[:half]).predict_proba(X[half:])
  
      if binary:
          # only interested in probabilities of the positive case
          # XXX: do we really want a special API for the binary case?
          probas_pred = probas_pred[:, 1]
  
      y_pred = clf.predict(X[half:])
      y_true = y[half:]
      return y_true, y_pred, probas_pred
  
  
  ###############################################################################
  # Tests
  
  def _auc(y_true, y_score):
      """Alternative implementation to check for correctness of
      `roc_auc_score`."""
      pos_label = np.unique(y_true)[1]
  
      # Count the number of times positive samples are correctly ranked above
      # negative samples.
      pos = y_score[y_true == pos_label]
      neg = y_score[y_true != pos_label]
      diff_matrix = pos.reshape(1, -1) - neg.reshape(-1, 1)
      n_correct = np.sum(diff_matrix > 0)
  
      return n_correct / float(len(pos) * len(neg))
  
  
  def _average_precision(y_true, y_score):
      """Alternative implementation to check for correctness of
      `average_precision_score`."""
      pos_label = np.unique(y_true)[1]
      n_pos = np.sum(y_true == pos_label)
      order = np.argsort(y_score)[::-1]
      y_score = y_score[order]
      y_true = y_true[order]
  
      score = 0
      for i in range(len(y_score)):
          if y_true[i] == pos_label:
              # Compute precision up to document i
              # i.e, percentage of relevant documents up to document i.
              prec = 0
              for j in range(0, i + 1):
                  if y_true[j] == pos_label:
                      prec += 1.0
              prec /= (i + 1.0)
              score += prec
  
      return score / n_pos
  
  
  def test_roc_curve():
      # Test Area under Receiver Operating Characteristic (ROC) curve
      y_true, _, probas_pred = make_prediction(binary=True)
      expected_auc = _auc(y_true, probas_pred)
  
      for drop in [True, False]:
          fpr, tpr, thresholds = roc_curve(y_true, probas_pred,
                                           drop_intermediate=drop)
          roc_auc = auc(fpr, tpr)
          assert_array_almost_equal(roc_auc, expected_auc, decimal=2)
          assert_almost_equal(roc_auc, roc_auc_score(y_true, probas_pred))
          assert_equal(fpr.shape, tpr.shape)
          assert_equal(fpr.shape, thresholds.shape)
  
  
  def test_roc_curve_end_points():
      # Make sure that roc_curve returns a curve start at 0 and ending and
      # 1 even in corner cases
      rng = np.random.RandomState(0)
      y_true = np.array([0] * 50 + [1] * 50)
      y_pred = rng.randint(3, size=100)
      fpr, tpr, thr = roc_curve(y_true, y_pred, drop_intermediate=True)
      assert_equal(fpr[0], 0)
      assert_equal(fpr[-1], 1)
      assert_equal(fpr.shape, tpr.shape)
      assert_equal(fpr.shape, thr.shape)
  
  
  def test_roc_returns_consistency():
      # Test whether the returned threshold matches up with tpr
      # make small toy dataset
      y_true, _, probas_pred = make_prediction(binary=True)
      fpr, tpr, thresholds = roc_curve(y_true, probas_pred)
  
      # use the given thresholds to determine the tpr
      tpr_correct = []
      for t in thresholds:
          tp = np.sum((probas_pred >= t) & y_true)
          p = np.sum(y_true)
          tpr_correct.append(1.0 * tp / p)
  
      # compare tpr and tpr_correct to see if the thresholds' order was correct
      assert_array_almost_equal(tpr, tpr_correct, decimal=2)
      assert_equal(fpr.shape, tpr.shape)
      assert_equal(fpr.shape, thresholds.shape)
  
  
  def test_roc_nonrepeating_thresholds():
      # Test to ensure that we don't return spurious repeating thresholds.
      # Duplicated thresholds can arise due to machine precision issues.
      dataset = datasets.load_digits()
      X = dataset['data']
      y = dataset['target']
  
      # This random forest classifier can only return probabilities
      # significant to two decimal places
      clf = ensemble.RandomForestClassifier(n_estimators=100, random_state=0)
  
      # How well can the classifier predict whether a digit is less than 5?
      # This task contributes floating point roundoff errors to the probabilities
      train, test = slice(None, None, 2), slice(1, None, 2)
      probas_pred = clf.fit(X[train], y[train]).predict_proba(X[test])
      y_score = probas_pred[:, :5].sum(axis=1)  # roundoff errors begin here
      y_true = [yy < 5 for yy in y[test]]
  
      # Check for repeating values in the thresholds
      fpr, tpr, thresholds = roc_curve(y_true, y_score, drop_intermediate=False)
      assert_equal(thresholds.size, np.unique(np.round(thresholds, 2)).size)
  
  
  def test_roc_curve_multi():
      # roc_curve not applicable for multi-class problems
      y_true, _, probas_pred = make_prediction(binary=False)
  
      assert_raises(ValueError, roc_curve, y_true, probas_pred)
  
  
  def test_roc_curve_confidence():
      # roc_curve for confidence scores
      y_true, _, probas_pred = make_prediction(binary=True)
  
      fpr, tpr, thresholds = roc_curve(y_true, probas_pred - 0.5)
      roc_auc = auc(fpr, tpr)
      assert_array_almost_equal(roc_auc, 0.90, decimal=2)
      assert_equal(fpr.shape, tpr.shape)
      assert_equal(fpr.shape, thresholds.shape)
  
  
  def test_roc_curve_hard():
      # roc_curve for hard decisions
      y_true, pred, probas_pred = make_prediction(binary=True)
  
      # always predict one
      trivial_pred = np.ones(y_true.shape)
      fpr, tpr, thresholds = roc_curve(y_true, trivial_pred)
      roc_auc = auc(fpr, tpr)
      assert_array_almost_equal(roc_auc, 0.50, decimal=2)
      assert_equal(fpr.shape, tpr.shape)
      assert_equal(fpr.shape, thresholds.shape)
  
      # always predict zero
      trivial_pred = np.zeros(y_true.shape)
      fpr, tpr, thresholds = roc_curve(y_true, trivial_pred)
      roc_auc = auc(fpr, tpr)
      assert_array_almost_equal(roc_auc, 0.50, decimal=2)
      assert_equal(fpr.shape, tpr.shape)
      assert_equal(fpr.shape, thresholds.shape)
  
      # hard decisions
      fpr, tpr, thresholds = roc_curve(y_true, pred)
      roc_auc = auc(fpr, tpr)
      assert_array_almost_equal(roc_auc, 0.78, decimal=2)
      assert_equal(fpr.shape, tpr.shape)
      assert_equal(fpr.shape, thresholds.shape)
  
  
  def test_roc_curve_one_label():
      y_true = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
      y_pred = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1]
      # assert there are warnings
      w = UndefinedMetricWarning
      fpr, tpr, thresholds = assert_warns(w, roc_curve, y_true, y_pred)
      # all true labels, all fpr should be nan
      assert_array_equal(fpr,
                         np.nan * np.ones(len(thresholds)))
      assert_equal(fpr.shape, tpr.shape)
      assert_equal(fpr.shape, thresholds.shape)
  
      # assert there are warnings
      fpr, tpr, thresholds = assert_warns(w, roc_curve,
                                          [1 - x for x in y_true],
                                          y_pred)
      # all negative labels, all tpr should be nan
      assert_array_equal(tpr,
                         np.nan * np.ones(len(thresholds)))
      assert_equal(fpr.shape, tpr.shape)
      assert_equal(fpr.shape, thresholds.shape)
  
  
  def test_roc_curve_toydata():
      # Binary classification
      y_true = [0, 1]
      y_score = [0, 1]
      tpr, fpr, _ = roc_curve(y_true, y_score)
      roc_auc = roc_auc_score(y_true, y_score)
      assert_array_almost_equal(tpr, [0, 1])
      assert_array_almost_equal(fpr, [1, 1])
      assert_almost_equal(roc_auc, 1.)
  
      y_true = [0, 1]
      y_score = [1, 0]
      tpr, fpr, _ = roc_curve(y_true, y_score)
      roc_auc = roc_auc_score(y_true, y_score)
      assert_array_almost_equal(tpr, [0, 1, 1])
      assert_array_almost_equal(fpr, [0, 0, 1])
      assert_almost_equal(roc_auc, 0.)
  
      y_true = [1, 0]
      y_score = [1, 1]
      tpr, fpr, _ = roc_curve(y_true, y_score)
      roc_auc = roc_auc_score(y_true, y_score)
      assert_array_almost_equal(tpr, [0, 1])
      assert_array_almost_equal(fpr, [0, 1])
      assert_almost_equal(roc_auc, 0.5)
  
      y_true = [1, 0]
      y_score = [1, 0]
      tpr, fpr, _ = roc_curve(y_true, y_score)
      roc_auc = roc_auc_score(y_true, y_score)
      assert_array_almost_equal(tpr, [0, 1])
      assert_array_almost_equal(fpr, [1, 1])
      assert_almost_equal(roc_auc, 1.)
  
      y_true = [1, 0]
      y_score = [0.5, 0.5]
      tpr, fpr, _ = roc_curve(y_true, y_score)
      roc_auc = roc_auc_score(y_true, y_score)
      assert_array_almost_equal(tpr, [0, 1])
      assert_array_almost_equal(fpr, [0, 1])
      assert_almost_equal(roc_auc, .5)
  
      y_true = [0, 0]
      y_score = [0.25, 0.75]
      # assert UndefinedMetricWarning because of no positive sample in y_true
      tpr, fpr, _ = assert_warns(UndefinedMetricWarning, roc_curve, y_true, y_score)
      assert_raises(ValueError, roc_auc_score, y_true, y_score)
      assert_array_almost_equal(tpr, [0., 0.5, 1.])
      assert_array_almost_equal(fpr, [np.nan, np.nan, np.nan])
  
      y_true = [1, 1]
      y_score = [0.25, 0.75]
      # assert UndefinedMetricWarning because of no negative sample in y_true
      tpr, fpr, _ = assert_warns(UndefinedMetricWarning, roc_curve, y_true, y_score)
      assert_raises(ValueError, roc_auc_score, y_true, y_score)
      assert_array_almost_equal(tpr, [np.nan, np.nan])
      assert_array_almost_equal(fpr, [0.5, 1.])
  
      # Multi-label classification task
      y_true = np.array([[0, 1], [0, 1]])
      y_score = np.array([[0, 1], [0, 1]])
      assert_raises(ValueError, roc_auc_score, y_true, y_score, average="macro")
      assert_raises(ValueError, roc_auc_score, y_true, y_score,
                    average="weighted")
      assert_almost_equal(roc_auc_score(y_true, y_score, average="samples"), 1.)
      assert_almost_equal(roc_auc_score(y_true, y_score, average="micro"), 1.)
  
      y_true = np.array([[0, 1], [0, 1]])
      y_score = np.array([[0, 1], [1, 0]])
      assert_raises(ValueError, roc_auc_score, y_true, y_score, average="macro")
      assert_raises(ValueError, roc_auc_score, y_true, y_score,
                    average="weighted")
      assert_almost_equal(roc_auc_score(y_true, y_score, average="samples"), 0.5)
      assert_almost_equal(roc_auc_score(y_true, y_score, average="micro"), 0.5)
  
      y_true = np.array([[1, 0], [0, 1]])
      y_score = np.array([[0, 1], [1, 0]])
      assert_almost_equal(roc_auc_score(y_true, y_score, average="macro"), 0)
      assert_almost_equal(roc_auc_score(y_true, y_score, average="weighted"), 0)
      assert_almost_equal(roc_auc_score(y_true, y_score, average="samples"), 0)
      assert_almost_equal(roc_auc_score(y_true, y_score, average="micro"), 0)
  
      y_true = np.array([[1, 0], [0, 1]])
      y_score = np.array([[0.5, 0.5], [0.5, 0.5]])
      assert_almost_equal(roc_auc_score(y_true, y_score, average="macro"), .5)
      assert_almost_equal(roc_auc_score(y_true, y_score, average="weighted"), .5)
      assert_almost_equal(roc_auc_score(y_true, y_score, average="samples"), .5)
      assert_almost_equal(roc_auc_score(y_true, y_score, average="micro"), .5)
  
  
  def test_roc_curve_drop_intermediate():
      # Test that drop_intermediate drops the correct thresholds
      y_true = [0, 0, 0, 0, 1, 1]
      y_score = [0., 0.2, 0.5, 0.6, 0.7, 1.0]
      tpr, fpr, thresholds = roc_curve(y_true, y_score, drop_intermediate=True)
      assert_array_almost_equal(thresholds, [1., 0.7, 0.])
  
      # Test dropping thresholds with repeating scores
      y_true = [0, 0, 0, 0, 0, 0, 0,
                1, 1, 1, 1, 1, 1]
      y_score = [0., 0.1, 0.6, 0.6, 0.7, 0.8, 0.9,
                 0.6, 0.7, 0.8, 0.9, 0.9, 1.0]
      tpr, fpr, thresholds = roc_curve(y_true, y_score, drop_intermediate=True)
      assert_array_almost_equal(thresholds,
                                [1.0, 0.9, 0.7, 0.6, 0.])
  
  
  def test_auc():
      # Test Area Under Curve (AUC) computation
      x = [0, 1]
      y = [0, 1]
      assert_array_almost_equal(auc(x, y), 0.5)
      x = [1, 0]
      y = [0, 1]
      assert_array_almost_equal(auc(x, y), 0.5)
      x = [1, 0, 0]
      y = [0, 1, 1]
      assert_array_almost_equal(auc(x, y), 0.5)
      x = [0, 1]
      y = [1, 1]
      assert_array_almost_equal(auc(x, y), 1)
      x = [0, 0.5, 1]
      y = [0, 0.5, 1]
      assert_array_almost_equal(auc(x, y), 0.5)
  
  
  def test_auc_duplicate_values():
      # Test Area Under Curve (AUC) computation with duplicate values
  
      # auc() was previously sorting the x and y arrays according to the indices
      # from numpy.argsort(x), which was reordering the tied 0's in this example
      # and resulting in an incorrect area computation. This test detects the
      # error.
      x = [-2.0, 0.0, 0.0, 0.0, 1.0]
      y1 = [2.0, 0.0, 0.5, 1.0, 1.0]
      y2 = [2.0, 1.0, 0.0, 0.5, 1.0]
      y3 = [2.0, 1.0, 0.5, 0.0, 1.0]
  
      for y in (y1, y2, y3):
          assert_array_almost_equal(auc(x, y, reorder=True), 3.0)
  
  
  def test_auc_errors():
      # Incompatible shapes
      assert_raises(ValueError, auc, [0.0, 0.5, 1.0], [0.1, 0.2])
  
      # Too few x values
      assert_raises(ValueError, auc, [0.0], [0.1])
  
      # x is not in order
      assert_raises(ValueError, auc, [1.0, 0.0, 0.5], [0.0, 0.0, 0.0])
  
  
  def test_auc_score_non_binary_class():
      # Test that roc_auc_score function returns an error when trying
      # to compute AUC for non-binary class values.
      rng = check_random_state(404)
      y_pred = rng.rand(10)
      # y_true contains only one class value
      y_true = np.zeros(10, dtype="int")
      assert_raise_message(ValueError, "ROC AUC score is not defined",
                           roc_auc_score, y_true, y_pred)
      y_true = np.ones(10, dtype="int")
      assert_raise_message(ValueError, "ROC AUC score is not defined",
                           roc_auc_score, y_true, y_pred)
      y_true = -np.ones(10, dtype="int")
      assert_raise_message(ValueError, "ROC AUC score is not defined",
                           roc_auc_score, y_true, y_pred)
      # y_true contains three different class values
      y_true = rng.randint(0, 3, size=10)
      assert_raise_message(ValueError, "multiclass format is not supported",
                           roc_auc_score, y_true, y_pred)
  
      clean_warning_registry()
      with warnings.catch_warnings(record=True):
          rng = check_random_state(404)
          y_pred = rng.rand(10)
          # y_true contains only one class value
          y_true = np.zeros(10, dtype="int")
          assert_raise_message(ValueError, "ROC AUC score is not defined",
                               roc_auc_score, y_true, y_pred)
          y_true = np.ones(10, dtype="int")
          assert_raise_message(ValueError, "ROC AUC score is not defined",
                               roc_auc_score, y_true, y_pred)
          y_true = -np.ones(10, dtype="int")
          assert_raise_message(ValueError, "ROC AUC score is not defined",
                               roc_auc_score, y_true, y_pred)
  
          # y_true contains three different class values
          y_true = rng.randint(0, 3, size=10)
          assert_raise_message(ValueError, "multiclass format is not supported",
                               roc_auc_score, y_true, y_pred)
  
  
  def test_precision_recall_curve():
      y_true, _, probas_pred = make_prediction(binary=True)
      _test_precision_recall_curve(y_true, probas_pred)
  
      # Use {-1, 1} for labels; make sure original labels aren't modified
      y_true[np.where(y_true == 0)] = -1
      y_true_copy = y_true.copy()
      _test_precision_recall_curve(y_true, probas_pred)
      assert_array_equal(y_true_copy, y_true)
  
      labels = [1, 0, 0, 1]
      predict_probas = [1, 2, 3, 4]
      p, r, t = precision_recall_curve(labels, predict_probas)
      assert_array_almost_equal(p, np.array([0.5, 0.33333333, 0.5, 1., 1.]))
      assert_array_almost_equal(r, np.array([1., 0.5, 0.5, 0.5, 0.]))
      assert_array_almost_equal(t, np.array([1, 2, 3, 4]))
      assert_equal(p.size, r.size)
      assert_equal(p.size, t.size + 1)
  
  
  def test_precision_recall_curve_pos_label():
      y_true, _, probas_pred = make_prediction(binary=False)
      pos_label = 2
      p, r, thresholds = precision_recall_curve(y_true,
                                                probas_pred[:, pos_label],
                                                pos_label=pos_label)
      p2, r2, thresholds2 = precision_recall_curve(y_true == pos_label,
                                                   probas_pred[:, pos_label])
      assert_array_almost_equal(p, p2)
      assert_array_almost_equal(r, r2)
      assert_array_almost_equal(thresholds, thresholds2)
      assert_equal(p.size, r.size)
      assert_equal(p.size, thresholds.size + 1)
  
  
  def _test_precision_recall_curve(y_true, probas_pred):
      # Test Precision-Recall and aread under PR curve
      p, r, thresholds = precision_recall_curve(y_true, probas_pred)
      precision_recall_auc = auc(r, p)
      assert_array_almost_equal(precision_recall_auc, 0.85, 2)
      assert_array_almost_equal(precision_recall_auc,
                                average_precision_score(y_true, probas_pred))
      assert_almost_equal(_average_precision(y_true, probas_pred),
                          precision_recall_auc, 1)
      assert_equal(p.size, r.size)
      assert_equal(p.size, thresholds.size + 1)
      # Smoke test in the case of proba having only one value
      p, r, thresholds = precision_recall_curve(y_true,
                                                np.zeros_like(probas_pred))
      precision_recall_auc = auc(r, p)
      assert_array_almost_equal(precision_recall_auc, 0.75, 3)
      assert_equal(p.size, r.size)
      assert_equal(p.size, thresholds.size + 1)
  
  
  def test_precision_recall_curve_errors():
      # Contains non-binary labels
      assert_raises(ValueError, precision_recall_curve,
                    [0, 1, 2], [[0.0], [1.0], [1.0]])
  
  
  def test_precision_recall_curve_toydata():
      with np.errstate(all="raise"):
          # Binary classification
          y_true = [0, 1]
          y_score = [0, 1]
          p, r, _ = precision_recall_curve(y_true, y_score)
          auc_prc = average_precision_score(y_true, y_score)
          assert_array_almost_equal(p, [1, 1])
          assert_array_almost_equal(r, [1, 0])
          assert_almost_equal(auc_prc, 1.)
  
          y_true = [0, 1]
          y_score = [1, 0]
          p, r, _ = precision_recall_curve(y_true, y_score)
          auc_prc = average_precision_score(y_true, y_score)
          assert_array_almost_equal(p, [0.5, 0., 1.])
          assert_array_almost_equal(r, [1., 0.,  0.])
          assert_almost_equal(auc_prc, 0.25)
  
          y_true = [1, 0]
          y_score = [1, 1]
          p, r, _ = precision_recall_curve(y_true, y_score)
          auc_prc = average_precision_score(y_true, y_score)
          assert_array_almost_equal(p, [0.5, 1])
          assert_array_almost_equal(r, [1., 0])
          assert_almost_equal(auc_prc, .75)
  
          y_true = [1, 0]
          y_score = [1, 0]
          p, r, _ = precision_recall_curve(y_true, y_score)
          auc_prc = average_precision_score(y_true, y_score)
          assert_array_almost_equal(p, [1, 1])
          assert_array_almost_equal(r, [1, 0])
          assert_almost_equal(auc_prc, 1.)
  
          y_true = [1, 0]
          y_score = [0.5, 0.5]
          p, r, _ = precision_recall_curve(y_true, y_score)
          auc_prc = average_precision_score(y_true, y_score)
          assert_array_almost_equal(p, [0.5, 1])
          assert_array_almost_equal(r, [1, 0.])
          assert_almost_equal(auc_prc, .75)
  
          y_true = [0, 0]
          y_score = [0.25, 0.75]
          assert_raises(Exception, precision_recall_curve, y_true, y_score)
          assert_raises(Exception, average_precision_score, y_true, y_score)
  
          y_true = [1, 1]
          y_score = [0.25, 0.75]
          p, r, _ = precision_recall_curve(y_true, y_score)
          assert_almost_equal(average_precision_score(y_true, y_score), 1.)
          assert_array_almost_equal(p, [1., 1., 1.])
          assert_array_almost_equal(r, [1, 0.5, 0.])
  
          # Multi-label classification task
          y_true = np.array([[0, 1], [0, 1]])
          y_score = np.array([[0, 1], [0, 1]])
          assert_raises(Exception, average_precision_score, y_true, y_score,
                        average="macro")
          assert_raises(Exception, average_precision_score, y_true, y_score,
                        average="weighted")
          assert_almost_equal(average_precision_score(y_true, y_score,
                              average="samples"), 1.)
          assert_almost_equal(average_precision_score(y_true, y_score,
                              average="micro"), 1.)
  
          y_true = np.array([[0, 1], [0, 1]])
          y_score = np.array([[0, 1], [1, 0]])
          assert_raises(Exception, average_precision_score, y_true, y_score,
                        average="macro")
          assert_raises(Exception, average_precision_score, y_true, y_score,
                        average="weighted")
          assert_almost_equal(average_precision_score(y_true, y_score,
                              average="samples"), 0.625)
          assert_almost_equal(average_precision_score(y_true, y_score,
                              average="micro"), 0.625)
  
          y_true = np.array([[1, 0], [0, 1]])
          y_score = np.array([[0, 1], [1, 0]])
          assert_almost_equal(average_precision_score(y_true, y_score,
                              average="macro"), 0.25)
          assert_almost_equal(average_precision_score(y_true, y_score,
                              average="weighted"), 0.25)
          assert_almost_equal(average_precision_score(y_true, y_score,
                              average="samples"), 0.25)
          assert_almost_equal(average_precision_score(y_true, y_score,
                              average="micro"), 0.25)
  
          y_true = np.array([[1, 0], [0, 1]])
          y_score = np.array([[0.5, 0.5], [0.5, 0.5]])
          assert_almost_equal(average_precision_score(y_true, y_score,
                              average="macro"), 0.75)
          assert_almost_equal(average_precision_score(y_true, y_score,
                              average="weighted"), 0.75)
          assert_almost_equal(average_precision_score(y_true, y_score,
                              average="samples"), 0.75)
          assert_almost_equal(average_precision_score(y_true, y_score,
                              average="micro"), 0.75)
  
  
  def test_score_scale_invariance():
      # Test that average_precision_score and roc_auc_score are invariant by
      # the scaling or shifting of probabilities
      y_true, _, probas_pred = make_prediction(binary=True)
  
      roc_auc = roc_auc_score(y_true, probas_pred)
      roc_auc_scaled = roc_auc_score(y_true, 100 * probas_pred)
      roc_auc_shifted = roc_auc_score(y_true, probas_pred - 10)
      assert_equal(roc_auc, roc_auc_scaled)
      assert_equal(roc_auc, roc_auc_shifted)
  
      pr_auc = average_precision_score(y_true, probas_pred)
      pr_auc_scaled = average_precision_score(y_true, 100 * probas_pred)
      pr_auc_shifted = average_precision_score(y_true, probas_pred - 10)
      assert_equal(pr_auc, pr_auc_scaled)
      assert_equal(pr_auc, pr_auc_shifted)
  
  
  def check_lrap_toy(lrap_score):
      # Check on several small example that it works
      assert_almost_equal(lrap_score([[0, 1]], [[0.25, 0.75]]), 1)
      assert_almost_equal(lrap_score([[0, 1]], [[0.75, 0.25]]), 1 / 2)
      assert_almost_equal(lrap_score([[1, 1]], [[0.75, 0.25]]), 1)
  
      assert_almost_equal(lrap_score([[0, 0, 1]], [[0.25, 0.5, 0.75]]), 1)
      assert_almost_equal(lrap_score([[0, 1, 0]], [[0.25, 0.5, 0.75]]), 1 / 2)
      assert_almost_equal(lrap_score([[0, 1, 1]], [[0.25, 0.5, 0.75]]), 1)
      assert_almost_equal(lrap_score([[1, 0, 0]], [[0.25, 0.5, 0.75]]), 1 / 3)
      assert_almost_equal(lrap_score([[1, 0, 1]], [[0.25, 0.5, 0.75]]),
                          (2 / 3 + 1 / 1) / 2)
      assert_almost_equal(lrap_score([[1, 1, 0]], [[0.25, 0.5, 0.75]]),
                          (2 / 3 + 1 / 2) / 2)
  
      assert_almost_equal(lrap_score([[0, 0, 1]], [[0.75, 0.5, 0.25]]), 1 / 3)
      assert_almost_equal(lrap_score([[0, 1, 0]], [[0.75, 0.5, 0.25]]), 1 / 2)
      assert_almost_equal(lrap_score([[0, 1, 1]], [[0.75, 0.5, 0.25]]),
                          (1 / 2 + 2 / 3) / 2)
      assert_almost_equal(lrap_score([[1, 0, 0]], [[0.75, 0.5, 0.25]]), 1)
      assert_almost_equal(lrap_score([[1, 0, 1]], [[0.75, 0.5, 0.25]]),
                          (1 + 2 / 3) / 2)
      assert_almost_equal(lrap_score([[1, 1, 0]], [[0.75, 0.5, 0.25]]), 1)
      assert_almost_equal(lrap_score([[1, 1, 1]], [[0.75, 0.5, 0.25]]), 1)
  
      assert_almost_equal(lrap_score([[0, 0, 1]], [[0.5, 0.75, 0.25]]), 1 / 3)
      assert_almost_equal(lrap_score([[0, 1, 0]], [[0.5, 0.75, 0.25]]), 1)
      assert_almost_equal(lrap_score([[0, 1, 1]], [[0.5, 0.75, 0.25]]),
                          (1 + 2 / 3) / 2)
      assert_almost_equal(lrap_score([[1, 0, 0]], [[0.5, 0.75, 0.25]]), 1 / 2)
      assert_almost_equal(lrap_score([[1, 0, 1]], [[0.5, 0.75, 0.25]]),
                          (1 / 2 + 2 / 3) / 2)
      assert_almost_equal(lrap_score([[1, 1, 0]], [[0.5, 0.75, 0.25]]), 1)
      assert_almost_equal(lrap_score([[1, 1, 1]], [[0.5, 0.75, 0.25]]), 1)
  
      # Tie handling
      assert_almost_equal(lrap_score([[1, 0]], [[0.5, 0.5]]), 0.5)
      assert_almost_equal(lrap_score([[0, 1]], [[0.5, 0.5]]), 0.5)
      assert_almost_equal(lrap_score([[1, 1]], [[0.5, 0.5]]), 1)
  
      assert_almost_equal(lrap_score([[0, 0, 1]], [[0.25, 0.5, 0.5]]), 0.5)
      assert_almost_equal(lrap_score([[0, 1, 0]], [[0.25, 0.5, 0.5]]), 0.5)
      assert_almost_equal(lrap_score([[0, 1, 1]], [[0.25, 0.5, 0.5]]), 1)
      assert_almost_equal(lrap_score([[1, 0, 0]], [[0.25, 0.5, 0.5]]), 1 / 3)
      assert_almost_equal(lrap_score([[1, 0, 1]], [[0.25, 0.5, 0.5]]),
                          (2 / 3 + 1 / 2) / 2)
      assert_almost_equal(lrap_score([[1, 1, 0]], [[0.25, 0.5, 0.5]]),
                          (2 / 3 + 1 / 2) / 2)
      assert_almost_equal(lrap_score([[1, 1, 1]], [[0.25, 0.5, 0.5]]), 1)
  
      assert_almost_equal(lrap_score([[1, 1, 0]], [[0.5, 0.5, 0.5]]), 2 / 3)
  
      assert_almost_equal(lrap_score([[1, 1, 1, 0]], [[0.5, 0.5, 0.5, 0.5]]),
                          3 / 4)
  
  
  def check_zero_or_all_relevant_labels(lrap_score):
      random_state = check_random_state(0)
  
      for n_labels in range(2, 5):
          y_score = random_state.uniform(size=(1, n_labels))
          y_score_ties = np.zeros_like(y_score)
  
          # No relevant labels
          y_true = np.zeros((1, n_labels))
          assert_equal(lrap_score(y_true, y_score), 1.)
          assert_equal(lrap_score(y_true, y_score_ties), 1.)
  
          # Only relevant labels
          y_true = np.ones((1, n_labels))
          assert_equal(lrap_score(y_true, y_score), 1.)
          assert_equal(lrap_score(y_true, y_score_ties), 1.)
  
      # Degenerate case: only one label
      assert_almost_equal(lrap_score([[1], [0], [1], [0]],
                                     [[0.5], [0.5], [0.5], [0.5]]), 1.)
  
  
  def check_lrap_error_raised(lrap_score):
      # Raise value error if not appropriate format
      assert_raises(ValueError, lrap_score,
                    [0, 1, 0], [0.25, 0.3, 0.2])
      assert_raises(ValueError, lrap_score, [0, 1, 2],
                    [[0.25, 0.75, 0.0], [0.7, 0.3, 0.0], [0.8, 0.2, 0.0]])
      assert_raises(ValueError, lrap_score, [(0), (1), (2)],
                    [[0.25, 0.75, 0.0], [0.7, 0.3, 0.0], [0.8, 0.2, 0.0]])
  
      # Check that y_true.shape != y_score.shape raise the proper exception
      assert_raises(ValueError, lrap_score, [[0, 1], [0, 1]], [0, 1])
      assert_raises(ValueError, lrap_score, [[0, 1], [0, 1]], [[0, 1]])
      assert_raises(ValueError, lrap_score, [[0, 1], [0, 1]], [[0], [1]])
      assert_raises(ValueError, lrap_score, [[0, 1]], [[0, 1], [0, 1]])
      assert_raises(ValueError, lrap_score, [[0], [1]], [[0, 1], [0, 1]])
      assert_raises(ValueError, lrap_score, [[0, 1], [0, 1]], [[0], [1]])
  
  
  def check_lrap_only_ties(lrap_score):
      # Check tie handling in score
      # Basic check with only ties and increasing label space
      for n_labels in range(2, 10):
          y_score = np.ones((1, n_labels))
  
          # Check for growing number of consecutive relevant
          for n_relevant in range(1, n_labels):
              # Check for a bunch of positions
              for pos in range(n_labels - n_relevant):
                  y_true = np.zeros((1, n_labels))
                  y_true[0, pos:pos + n_relevant] = 1
                  assert_almost_equal(lrap_score(y_true, y_score),
                                      n_relevant / n_labels)
  
  
  def check_lrap_without_tie_and_increasing_score(lrap_score):
      # Check that Label ranking average precision works for various
      # Basic check with increasing label space size and decreasing score
      for n_labels in range(2, 10):
          y_score = n_labels - (np.arange(n_labels).reshape((1, n_labels)) + 1)
  
          # First and last
          y_true = np.zeros((1, n_labels))
          y_true[0, 0] = 1
          y_true[0, -1] = 1
          assert_almost_equal(lrap_score(y_true, y_score),
                              (2 / n_labels + 1) / 2)
  
          # Check for growing number of consecutive relevant label
          for n_relevant in range(1, n_labels):
              # Check for a bunch of position
              for pos in range(n_labels - n_relevant):
                  y_true = np.zeros((1, n_labels))
                  y_true[0, pos:pos + n_relevant] = 1
                  assert_almost_equal(lrap_score(y_true, y_score),
                                      sum((r + 1) / ((pos + r + 1) * n_relevant)
                                          for r in range(n_relevant)))
  
  
  def _my_lrap(y_true, y_score):
      """Simple implementation of label ranking average precision"""
      check_consistent_length(y_true, y_score)
      y_true = check_array(y_true)
      y_score = check_array(y_score)
      n_samples, n_labels = y_true.shape
      score = np.empty((n_samples, ))
      for i in range(n_samples):
          # The best rank correspond to 1. Rank higher than 1 are worse.
          # The best inverse ranking correspond to n_labels.
          unique_rank, inv_rank = np.unique(y_score[i], return_inverse=True)
          n_ranks = unique_rank.size
          rank = n_ranks - inv_rank
  
          # Rank need to be corrected to take into account ties
          # ex: rank 1 ex aequo means that both label are rank 2.
          corr_rank = np.bincount(rank, minlength=n_ranks + 1).cumsum()
          rank = corr_rank[rank]
  
          relevant = y_true[i].nonzero()[0]
          if relevant.size == 0 or relevant.size == n_labels:
              score[i] = 1
              continue
  
          score[i] = 0.
          for label in relevant:
              # Let's count the number of relevant label with better rank
              # (smaller rank).
              n_ranked_above = sum(rank[r] <= rank[label] for r in relevant)
  
              # Weight by the rank of the actual label
              score[i] += n_ranked_above / rank[label]
  
          score[i] /= relevant.size
  
      return score.mean()
  
  
  def check_alternative_lrap_implementation(lrap_score, n_classes=5,
                                            n_samples=20, random_state=0):
      _, y_true = make_multilabel_classification(n_features=1,
                                                 allow_unlabeled=False,
                                                 random_state=random_state,
                                                 n_classes=n_classes,
                                                 n_samples=n_samples)
  
      # Score with ties
      y_score = sparse_random_matrix(n_components=y_true.shape[0],
                                     n_features=y_true.shape[1],
                                     random_state=random_state)
  
      if hasattr(y_score, "toarray"):
          y_score = y_score.toarray()
      score_lrap = label_ranking_average_precision_score(y_true, y_score)
      score_my_lrap = _my_lrap(y_true, y_score)
      assert_almost_equal(score_lrap, score_my_lrap)
  
      # Uniform score
      random_state = check_random_state(random_state)
      y_score = random_state.uniform(size=(n_samples, n_classes))
      score_lrap = label_ranking_average_precision_score(y_true, y_score)
      score_my_lrap = _my_lrap(y_true, y_score)
      assert_almost_equal(score_lrap, score_my_lrap)
  
  
  def test_label_ranking_avp():
      for fn in [label_ranking_average_precision_score, _my_lrap]:
          yield check_lrap_toy, fn
          yield check_lrap_without_tie_and_increasing_score, fn
          yield check_lrap_only_ties, fn
          yield check_zero_or_all_relevant_labels, fn
          yield check_lrap_error_raised, label_ranking_average_precision_score
  
      for n_samples, n_classes, random_state in product((1, 2, 8, 20),
                                                        (2, 5, 10),
                                                        range(1)):
          yield (check_alternative_lrap_implementation,
                 label_ranking_average_precision_score,
                 n_classes, n_samples, random_state)
  
  
  def test_coverage_error():
      # Toy case
      assert_almost_equal(coverage_error([[0, 1]], [[0.25, 0.75]]), 1)
      assert_almost_equal(coverage_error([[0, 1]], [[0.75, 0.25]]), 2)
      assert_almost_equal(coverage_error([[1, 1]], [[0.75, 0.25]]), 2)
      assert_almost_equal(coverage_error([[0, 0]], [[0.75, 0.25]]), 0)
  
      assert_almost_equal(coverage_error([[0, 0, 0]], [[0.25, 0.5, 0.75]]), 0)
      assert_almost_equal(coverage_error([[0, 0, 1]], [[0.25, 0.5, 0.75]]), 1)
      assert_almost_equal(coverage_error([[0, 1, 0]], [[0.25, 0.5, 0.75]]), 2)
      assert_almost_equal(coverage_error([[0, 1, 1]], [[0.25, 0.5, 0.75]]), 2)
      assert_almost_equal(coverage_error([[1, 0, 0]], [[0.25, 0.5, 0.75]]), 3)
      assert_almost_equal(coverage_error([[1, 0, 1]], [[0.25, 0.5, 0.75]]), 3)
      assert_almost_equal(coverage_error([[1, 1, 0]], [[0.25, 0.5, 0.75]]), 3)
      assert_almost_equal(coverage_error([[1, 1, 1]], [[0.25, 0.5, 0.75]]), 3)
  
      assert_almost_equal(coverage_error([[0, 0, 0]], [[0.75, 0.5, 0.25]]), 0)
      assert_almost_equal(coverage_error([[0, 0, 1]], [[0.75, 0.5, 0.25]]), 3)
      assert_almost_equal(coverage_error([[0, 1, 0]], [[0.75, 0.5, 0.25]]), 2)
      assert_almost_equal(coverage_error([[0, 1, 1]], [[0.75, 0.5, 0.25]]), 3)
      assert_almost_equal(coverage_error([[1, 0, 0]], [[0.75, 0.5, 0.25]]), 1)
      assert_almost_equal(coverage_error([[1, 0, 1]], [[0.75, 0.5, 0.25]]), 3)
      assert_almost_equal(coverage_error([[1, 1, 0]], [[0.75, 0.5, 0.25]]), 2)
      assert_almost_equal(coverage_error([[1, 1, 1]], [[0.75, 0.5, 0.25]]), 3)
  
      assert_almost_equal(coverage_error([[0, 0, 0]], [[0.5, 0.75, 0.25]]), 0)
      assert_almost_equal(coverage_error([[0, 0, 1]], [[0.5, 0.75, 0.25]]), 3)
      assert_almost_equal(coverage_error([[0, 1, 0]], [[0.5, 0.75, 0.25]]), 1)
      assert_almost_equal(coverage_error([[0, 1, 1]], [[0.5, 0.75, 0.25]]), 3)
      assert_almost_equal(coverage_error([[1, 0, 0]], [[0.5, 0.75, 0.25]]), 2)
      assert_almost_equal(coverage_error([[1, 0, 1]], [[0.5, 0.75, 0.25]]), 3)
      assert_almost_equal(coverage_error([[1, 1, 0]], [[0.5, 0.75, 0.25]]), 2)
      assert_almost_equal(coverage_error([[1, 1, 1]], [[0.5, 0.75, 0.25]]), 3)
  
      # Non trival case
      assert_almost_equal(coverage_error([[0, 1, 0], [1, 1, 0]],
                                         [[0.1, 10., -3], [0, 1, 3]]),
                          (1 + 3) / 2.)
  
      assert_almost_equal(coverage_error([[0, 1, 0], [1, 1, 0], [0, 1, 1]],
                                         [[0.1, 10, -3], [0, 1, 3], [0, 2, 0]]),
                          (1 + 3 + 3) / 3.)
  
      assert_almost_equal(coverage_error([[0, 1, 0], [1, 1, 0], [0, 1, 1]],
                                         [[0.1, 10, -3], [3, 1, 3], [0, 2, 0]]),
                          (1 + 3 + 3) / 3.)
  
  
  def test_coverage_tie_handling():
      assert_almost_equal(coverage_error([[0, 0]], [[0.5, 0.5]]), 0)
      assert_almost_equal(coverage_error([[1, 0]], [[0.5, 0.5]]), 2)
      assert_almost_equal(coverage_error([[0, 1]], [[0.5, 0.5]]), 2)
      assert_almost_equal(coverage_error([[1, 1]], [[0.5, 0.5]]), 2)
  
      assert_almost_equal(coverage_error([[0, 0, 0]], [[0.25, 0.5, 0.5]]), 0)
      assert_almost_equal(coverage_error([[0, 0, 1]], [[0.25, 0.5, 0.5]]), 2)
      assert_almost_equal(coverage_error([[0, 1, 0]], [[0.25, 0.5, 0.5]]), 2)
      assert_almost_equal(coverage_error([[0, 1, 1]], [[0.25, 0.5, 0.5]]), 2)
      assert_almost_equal(coverage_error([[1, 0, 0]], [[0.25, 0.5, 0.5]]), 3)
      assert_almost_equal(coverage_error([[1, 0, 1]], [[0.25, 0.5, 0.5]]), 3)
      assert_almost_equal(coverage_error([[1, 1, 0]], [[0.25, 0.5, 0.5]]), 3)
      assert_almost_equal(coverage_error([[1, 1, 1]], [[0.25, 0.5, 0.5]]), 3)
  
  
  def test_label_ranking_loss():
      assert_almost_equal(label_ranking_loss([[0, 1]], [[0.25, 0.75]]), 0)
      assert_almost_equal(label_ranking_loss([[0, 1]], [[0.75, 0.25]]), 1)
  
      assert_almost_equal(label_ranking_loss([[0, 0, 1]], [[0.25, 0.5, 0.75]]),
                          0)
      assert_almost_equal(label_ranking_loss([[0, 1, 0]], [[0.25, 0.5, 0.75]]),
                          1 / 2)
      assert_almost_equal(label_ranking_loss([[0, 1, 1]], [[0.25, 0.5, 0.75]]),
                          0)
      assert_almost_equal(label_ranking_loss([[1, 0, 0]], [[0.25, 0.5, 0.75]]),
                          2 / 2)
      assert_almost_equal(label_ranking_loss([[1, 0, 1]], [[0.25, 0.5, 0.75]]),
                          1 / 2)
      assert_almost_equal(label_ranking_loss([[1, 1, 0]], [[0.25, 0.5, 0.75]]),
                          2 / 2)
  
      # Undefined metrics -  the ranking doesn't matter
      assert_almost_equal(label_ranking_loss([[0, 0]], [[0.75, 0.25]]), 0)
      assert_almost_equal(label_ranking_loss([[1, 1]], [[0.75, 0.25]]), 0)
      assert_almost_equal(label_ranking_loss([[0, 0]], [[0.5, 0.5]]), 0)
      assert_almost_equal(label_ranking_loss([[1, 1]], [[0.5, 0.5]]), 0)
  
      assert_almost_equal(label_ranking_loss([[0, 0, 0]], [[0.5, 0.75, 0.25]]),
                          0)
      assert_almost_equal(label_ranking_loss([[1, 1, 1]], [[0.5, 0.75, 0.25]]),
                          0)
      assert_almost_equal(label_ranking_loss([[0, 0, 0]], [[0.25, 0.5, 0.5]]),
                          0)
      assert_almost_equal(label_ranking_loss([[1, 1, 1]], [[0.25, 0.5, 0.5]]), 0)
  
      # Non trival case
      assert_almost_equal(label_ranking_loss([[0, 1, 0], [1, 1, 0]],
                                             [[0.1, 10., -3], [0, 1, 3]]),
                          (0 + 2 / 2) / 2.)
  
      assert_almost_equal(label_ranking_loss(
          [[0, 1, 0], [1, 1, 0], [0, 1, 1]],
          [[0.1, 10, -3], [0, 1, 3], [0, 2, 0]]),
          (0 + 2 / 2 + 1 / 2) / 3.)
  
      assert_almost_equal(label_ranking_loss(
          [[0, 1, 0], [1, 1, 0], [0, 1, 1]],
          [[0.1, 10, -3], [3, 1, 3], [0, 2, 0]]),
          (0 + 2 / 2 + 1 / 2) / 3.)
  
      # Sparse csr matrices
      assert_almost_equal(label_ranking_loss(
          csr_matrix(np.array([[0, 1, 0], [1, 1, 0]])),
          [[0.1, 10, -3], [3, 1, 3]]),
          (0 + 2 / 2) / 2.)
  
  
  def test_ranking_appropriate_input_shape():
      # Check that y_true.shape != y_score.shape raise the proper exception
      assert_raises(ValueError, label_ranking_loss, [[0, 1], [0, 1]], [0, 1])
      assert_raises(ValueError, label_ranking_loss, [[0, 1], [0, 1]], [[0, 1]])
      assert_raises(ValueError, label_ranking_loss,
                    [[0, 1], [0, 1]], [[0], [1]])
  
      assert_raises(ValueError, label_ranking_loss, [[0, 1]], [[0, 1], [0, 1]])
      assert_raises(ValueError, label_ranking_loss,
                    [[0], [1]], [[0, 1], [0, 1]])
      assert_raises(ValueError, label_ranking_loss, [[0, 1], [0, 1]], [[0], [1]])
  
  
  def test_ranking_loss_ties_handling():
      # Tie handling
      assert_almost_equal(label_ranking_loss([[1, 0]], [[0.5, 0.5]]), 1)
      assert_almost_equal(label_ranking_loss([[0, 1]], [[0.5, 0.5]]), 1)
      assert_almost_equal(label_ranking_loss([[0, 0, 1]], [[0.25, 0.5, 0.5]]),
                          1 / 2)
      assert_almost_equal(label_ranking_loss([[0, 1, 0]], [[0.25, 0.5, 0.5]]),
                          1 / 2)
      assert_almost_equal(label_ranking_loss([[0, 1, 1]], [[0.25, 0.5, 0.5]]), 0)
      assert_almost_equal(label_ranking_loss([[1, 0, 0]], [[0.25, 0.5, 0.5]]), 1)
      assert_almost_equal(label_ranking_loss([[1, 0, 1]], [[0.25, 0.5, 0.5]]), 1)
      assert_almost_equal(label_ranking_loss([[1, 1, 0]], [[0.25, 0.5, 0.5]]), 1)
  