content: """Base and mixin classes for nearest neighbors"""
  # Authors: Jake Vanderplas <vanderplas@astro.washington.edu>
  #          Fabian Pedregosa <fabian.pedregosa@inria.fr>
  #          Alexandre Gramfort <alexandre.gramfort@inria.fr>
  #          Sparseness support by Lars Buitinck <L.J.Buitinck@uva.nl>
  #          Multi-output support by Arnaud Joly <a.joly@ulg.ac.be>
  #
  # License: BSD 3 clause (C) INRIA, University of Amsterdam
  import warnings
  from abc import ABCMeta, abstractmethod
  
  import numpy as np
  from scipy.sparse import csr_matrix, issparse
  
  from .ball_tree import BallTree
  from .kd_tree import KDTree
  from ..base import BaseEstimator
  from ..metrics import pairwise_distances
  from ..metrics.pairwise import PAIRWISE_DISTANCE_FUNCTIONS
  from ..utils import check_X_y, check_array
  from ..utils.fixes import argpartition
  from ..utils.validation import DataConversionWarning
  from ..externals import six
  
  
  VALID_METRICS = dict(ball_tree=BallTree.valid_metrics,
                       kd_tree=KDTree.valid_metrics,
                       # The following list comes from the
                       # sklearn.metrics.pairwise doc string
                       brute=(list(PAIRWISE_DISTANCE_FUNCTIONS.keys()) +
                              ['braycurtis', 'canberra', 'chebyshev',
                               'correlation', 'cosine', 'dice', 'hamming',
                               'jaccard', 'kulsinski', 'mahalanobis',
                               'matching', 'minkowski', 'rogerstanimoto',
                               'russellrao', 'seuclidean', 'sokalmichener',
                               'sokalsneath', 'sqeuclidean',
                               'yule', 'wminkowski']))
  
  
  VALID_METRICS_SPARSE = dict(ball_tree=[],
                              kd_tree=[],
                              brute=PAIRWISE_DISTANCE_FUNCTIONS.keys())
  
  
  class NeighborsWarning(UserWarning):
      pass
  
  
  # Make sure that NeighborsWarning are displayed more than once
  warnings.simplefilter("always", NeighborsWarning)
  
  
  def _check_weights(weights):
      """Check to make sure weights are valid"""
      if weights in (None, 'uniform', 'distance'):
          return weights
      elif callable(weights):
          return weights
      else:
          raise ValueError("weights not recognized: should be 'uniform', "
                           "'distance', or a callable function")
  
  
  def _get_weights(dist, weights):
      """Get the weights from an array of distances and a parameter ``weights``
  
      Parameters
      ===========
      dist: ndarray
          The input distances
      weights: {'uniform', 'distance' or a callable}
          The kind of weighting used
  
      Returns
      ========
      weights_arr: array of the same shape as ``dist``
          if ``weights == 'uniform'``, then returns None
      """
      if weights in (None, 'uniform'):
          return None
      elif weights == 'distance':
          with np.errstate(divide='ignore'):
              dist = 1. / dist
          return dist
      elif callable(weights):
          return weights(dist)
      else:
          raise ValueError("weights not recognized: should be 'uniform', "
                           "'distance', or a callable function")
  
  
  class NeighborsBase(six.with_metaclass(ABCMeta, BaseEstimator)):
      """Base class for nearest neighbors estimators."""
  
      @abstractmethod
      def __init__(self):
          pass
  
      def _init_params(self, n_neighbors=None, radius=None,
                       algorithm='auto', leaf_size=30, metric='minkowski',
                       p=2, metric_params=None, **kwargs):
          if kwargs:
              warnings.warn("Passing additional arguments to the metric "
                            "function as **kwargs is deprecated "
                            "and will no longer be supported in 0.18. "
                            "Use metric_params instead.",
                            DeprecationWarning, stacklevel=3)
              if metric_params is None:
                  metric_params = {}
              metric_params.update(kwargs)
  
          self.n_neighbors = n_neighbors
          self.radius = radius
          self.algorithm = algorithm
          self.leaf_size = leaf_size
          self.metric = metric
          self.metric_params = metric_params
          self.p = p
  
          if algorithm not in ['auto', 'brute',
                               'kd_tree', 'ball_tree']:
              raise ValueError("unrecognized algorithm: '%s'" % algorithm)
  
          if algorithm == 'auto':
              alg_check = 'ball_tree'
          else:
              alg_check = algorithm
  
          if callable(metric):
              if algorithm == 'kd_tree':
                  # callable metric is only valid for brute force and ball_tree
                  raise ValueError(
                      "kd_tree algorithm does not support callable metric '%s'"
                      % metric)
          elif metric not in VALID_METRICS[alg_check]:
              raise ValueError("Metric '%s' not valid for algorithm '%s'"
                               % (metric, algorithm))
  
          if self.metric_params is not None and 'p' in self.metric_params:
              warnings.warn("Parameter p is found in metric_params. "
                            "The corresponding parameter from __init__ "
                            "is ignored.", SyntaxWarning, stacklevel=3)
              effective_p = metric_params['p']
          else:
              effective_p = self.p
  
          if self.metric in ['wminkowski', 'minkowski'] and effective_p < 1:
              raise ValueError("p must be greater than one for minkowski metric")
  
          self._fit_X = None
          self._tree = None
          self._fit_method = None
  
      def _fit(self, X):
          if self.metric_params is None:
              self.effective_metric_params_ = {}
          else:
              self.effective_metric_params_ = self.metric_params.copy()
  
          effective_p = self.effective_metric_params_.get('p', self.p)
          if self.metric in ['wminkowski', 'minkowski']:
              self.effective_metric_params_['p'] = effective_p
  
          self.effective_metric_ = self.metric
          # For minkowski distance, use more efficient methods where available
          if self.metric == 'minkowski':
              p = self.effective_metric_params_.pop('p', 2)
              if p < 1:
                  raise ValueError("p must be greater than one "
                                   "for minkowski metric")
              elif p == 1:
                  self.effective_metric_ = 'manhattan'
              elif p == 2:
                  self.effective_metric_ = 'euclidean'
              elif p == np.inf:
                  self.effective_metric_ = 'chebyshev'
              else:
                  self.effective_metric_params_['p'] = p
  
          if isinstance(X, NeighborsBase):
              self._fit_X = X._fit_X
              self._tree = X._tree
              self._fit_method = X._fit_method
              return self
  
          elif isinstance(X, BallTree):
              self._fit_X = X.data
              self._tree = X
              self._fit_method = 'ball_tree'
              return self
  
          elif isinstance(X, KDTree):
              self._fit_X = X.data
              self._tree = X
              self._fit_method = 'kd_tree'
              return self
  
          X = check_array(X, accept_sparse='csr')
  
          n_samples = X.shape[0]
          if n_samples == 0:
              raise ValueError("n_samples must be greater than 0")
  
          if issparse(X):
              if self.algorithm not in ('auto', 'brute'):
                  warnings.warn("cannot use tree with sparse input: "
                                "using brute force")
              if self.effective_metric_ not in VALID_METRICS_SPARSE['brute']:
                  raise ValueError("metric '%s' not valid for sparse input"
                                   % self.effective_metric_)
              self._fit_X = X.copy()
              self._tree = None
              self._fit_method = 'brute'
              return self
  
          self._fit_method = self.algorithm
          self._fit_X = X
  
          if self._fit_method == 'auto':
              # A tree approach is better for small number of neighbors,
              # and KDTree is generally faster when available
              if (self.n_neighbors is None
                      or self.n_neighbors < self._fit_X.shape[0] // 2):
                  if self.effective_metric_ in VALID_METRICS['kd_tree']:
                      self._fit_method = 'kd_tree'
                  else:
                      self._fit_method = 'ball_tree'
              else:
                  self._fit_method = 'brute'
  
          if self._fit_method == 'ball_tree':
              self._tree = BallTree(X, self.leaf_size,
                                    metric=self.effective_metric_,
                                    **self.effective_metric_params_)
          elif self._fit_method == 'kd_tree':
              self._tree = KDTree(X, self.leaf_size,
                                  metric=self.effective_metric_,
                                  **self.effective_metric_params_)
          elif self._fit_method == 'brute':
              self._tree = None
          else:
              raise ValueError("algorithm = '%s' not recognized"
                               % self.algorithm)
          return self
  
  
  class KNeighborsMixin(object):
      """Mixin for k-neighbors searches"""
  
      def kneighbors(self, X, n_neighbors=None, return_distance=True):
          """Finds the K-neighbors of a point.
  
          Returns distance
  
          Parameters
          ----------
          X : array-like, last dimension same as that of fit data
              The new point.
  
          n_neighbors : int
              Number of neighbors to get (default is the value
              passed to the constructor).
  
          return_distance : boolean, optional. Defaults to True.
              If False, distances will not be returned
  
          Returns
          -------
          dist : array
              Array representing the lengths to point, only present if
              return_distance=True
  
          ind : array
              Indices of the nearest points in the population matrix.
  
          Examples
          --------
          In the following example, we construct a NeighborsClassifier
          class from an array representing our data set and ask who's
          the closest point to [1,1,1]
  
          >>> samples = [[0., 0., 0.], [0., .5, 0.], [1., 1., .5]]
          >>> from sklearn.neighbors import NearestNeighbors
          >>> neigh = NearestNeighbors(n_neighbors=1)
          >>> neigh.fit(samples) # doctest: +ELLIPSIS
          NearestNeighbors(algorithm='auto', leaf_size=30, ...)
          >>> print(neigh.kneighbors([1., 1., 1.])) # doctest: +ELLIPSIS
          (array([[ 0.5]]), array([[2]]...))
  
          As you can see, it returns [[0.5]], and [[2]], which means that the
          element is at distance 0.5 and is the third element of samples
          (indexes start at 0). You can also query for multiple points:
  
          >>> X = [[0., 1., 0.], [1., 0., 1.]]
          >>> neigh.kneighbors(X, return_distance=False) # doctest: +ELLIPSIS
          array([[1],
                 [2]]...)
  
          """
          if self._fit_method is None:
              raise ValueError("must fit neighbors before querying")
  
          X = check_array(X, accept_sparse='csr')
  
          if n_neighbors is None:
              n_neighbors = self.n_neighbors
  
          if self._fit_method == 'brute':
              # for efficiency, use squared euclidean distances
              if self.effective_metric_ == 'euclidean':
                  dist = pairwise_distances(X, self._fit_X, 'euclidean',
                                            squared=True)
              else:
                  dist = pairwise_distances(X, self._fit_X,
                                            self.effective_metric_,
                                            **self.effective_metric_params_)
  
              neigh_ind = argpartition(dist, n_neighbors - 1, axis=1)
              neigh_ind = neigh_ind[:, :n_neighbors]
              # argpartition doesn't guarantee sorted order, so we sort again
              j = np.arange(neigh_ind.shape[0])[:, None]
              neigh_ind = neigh_ind[j, np.argsort(dist[j, neigh_ind])]
              if return_distance:
                  if self.effective_metric_ == 'euclidean':
                      return np.sqrt(dist[j, neigh_ind]), neigh_ind
                  else:
                      return dist[j, neigh_ind], neigh_ind
              else:
                  return neigh_ind
          elif self._fit_method in ['ball_tree', 'kd_tree']:
              if issparse(X):
                  raise ValueError(
                      "%s does not work with sparse matrices. Densify the data, "
                      "or set algorithm='brute'" % self._fit_method)
              result = self._tree.query(X, n_neighbors,
                                        return_distance=return_distance)
              return result
          else:
              raise ValueError("internal: _fit_method not recognized")
  
      def kneighbors_graph(self, X, n_neighbors=None,
                           mode='connectivity'):
          """Computes the (weighted) graph of k-Neighbors for points in X
  
          Parameters
          ----------
          X : array-like, shape = [n_samples, n_features]
              Sample data
  
          n_neighbors : int
              Number of neighbors for each sample.
              (default is value passed to the constructor).
  
          mode : {'connectivity', 'distance'}, optional
              Type of returned matrix: 'connectivity' will return the
              connectivity matrix with ones and zeros, in 'distance' the
              edges are Euclidean distance between points.
  
          Returns
          -------
          A : sparse matrix in CSR format, shape = [n_samples, n_samples_fit]
              n_samples_fit is the number of samples in the fitted data
              A[i, j] is assigned the weight of edge that connects i to j.
  
          Examples
          --------
          >>> X = [[0], [3], [1]]
          >>> from sklearn.neighbors import NearestNeighbors
          >>> neigh = NearestNeighbors(n_neighbors=2)
          >>> neigh.fit(X) # doctest: +ELLIPSIS
          NearestNeighbors(algorithm='auto', leaf_size=30, ...)
          >>> A = neigh.kneighbors_graph(X)
          >>> A.toarray()
          array([[ 1.,  0.,  1.],
                 [ 0.,  1.,  1.],
                 [ 1.,  0.,  1.]])
  
          See also
          --------
          NearestNeighbors.radius_neighbors_graph
          """
          X = check_array(X, accept_sparse=['csr', 'csc', 'coo'])
  
          if n_neighbors is None:
              n_neighbors = self.n_neighbors
  
          n_samples1 = X.shape[0]
          n_samples2 = self._fit_X.shape[0]
          n_nonzero = n_samples1 * n_neighbors
          A_indptr = np.arange(0, n_nonzero + 1, n_neighbors)
  
          # construct CSR matrix representation of the k-NN graph
          if mode == 'connectivity':
              A_data = np.ones((n_samples1, n_neighbors))
              A_ind = self.kneighbors(X, n_neighbors, return_distance=False)
  
          elif mode == 'distance':
              data, ind = self.kneighbors(X, n_neighbors + 1,
                                          return_distance=True)
              A_data, A_ind = data[:, 1:], ind[:, 1:]
  
          else:
              raise ValueError(
                  'Unsupported mode, must be one of "connectivity" '
                  'or "distance" but got "%s" instead' % mode)
  
          return csr_matrix((A_data.ravel(), A_ind.ravel(), A_indptr),
                            shape=(n_samples1, n_samples2))
  
  
  class RadiusNeighborsMixin(object):
      """Mixin for radius-based neighbors searches"""
  
      def radius_neighbors(self, X, radius=None, return_distance=True):
          """Finds the neighbors within a given radius of a point or points.
  
          Returns indices of and distances to the neighbors of each point.
  
          Parameters
          ----------
          X : array-like, last dimension same as that of fit data
              The new point or points
  
          radius : float
              Limiting distance of neighbors to return.
              (default is the value passed to the constructor).
  
          return_distance : boolean, optional. Defaults to True.
              If False, distances will not be returned
  
          Returns
          -------
          dist : array
              Array representing the euclidean distances to each point,
              only present if return_distance=True.
  
          ind : array
              Indices of the nearest points in the population matrix.
  
          Examples
          --------
          In the following example, we construct a NeighborsClassifier
          class from an array representing our data set and ask who's
          the closest point to [1,1,1]
  
          >>> samples = [[0., 0., 0.], [0., .5, 0.], [1., 1., .5]]
          >>> from sklearn.neighbors import NearestNeighbors
          >>> neigh = NearestNeighbors(radius=1.6)
          >>> neigh.fit(samples) # doctest: +ELLIPSIS
          NearestNeighbors(algorithm='auto', leaf_size=30, ...)
          >>> print(neigh.radius_neighbors([1., 1., 1.])) # doctest: +ELLIPSIS
          (array([[ 1.5,  0.5]]...), array([[1, 2]]...)
  
          The first array returned contains the distances to all points which
          are closer than 1.6, while the second array returned contains their
          indices.  In general, multiple points can be queried at the same time.
  
          Notes
          -----
          Because the number of neighbors of each point is not necessarily
          equal, the results for multiple query points cannot be fit in a
          standard data array.
          For efficiency, `radius_neighbors` returns arrays of objects, where
          each object is a 1D array of indices or distances.
          """
  
          if self._fit_method is None:
              raise ValueError("must fit neighbors before querying")
  
          X = check_array(X, accept_sparse='csr')
  
          if radius is None:
              radius = self.radius
  
          if self._fit_method == 'brute':
              # for efficiency, use squared euclidean distances
              if self.effective_metric_ == 'euclidean':
                  dist = pairwise_distances(X, self._fit_X, 'euclidean',
                                            squared=True)
                  radius *= radius
              else:
                  dist = pairwise_distances(X, self._fit_X,
                                            self.effective_metric_,
                                            **self.effective_metric_params_)
              neigh_ind = [np.where(d < radius)[0] for d in dist]
  
              # if there are the same number of neighbors for each point,
              # we can do a normal array.  Otherwise, we return an object
              # array with elements that are numpy arrays
              try:
                  neigh_ind = np.asarray(neigh_ind, dtype=int)
                  dtype_F = float
              except ValueError:
                  neigh_ind = np.asarray(neigh_ind, dtype='object')
                  dtype_F = object
  
              if return_distance:
                  if self.effective_metric_ == 'euclidean':
                      dist = np.array([np.sqrt(d[neigh_ind[i]])
                                       for i, d in enumerate(dist)],
                                      dtype=dtype_F)
                  else:
                      dist = np.array([d[neigh_ind[i]]
                                       for i, d in enumerate(dist)],
                                      dtype=dtype_F)
                  return dist, neigh_ind
              else:
                  return neigh_ind
          elif self._fit_method in ['ball_tree', 'kd_tree']:
              if issparse(X):
                  raise ValueError(
                      "%s does not work with sparse matrices. Densify the data, "
                      "or set algorithm='brute'" % self._fit_method)
              results = self._tree.query_radius(X, radius,
                                                return_distance=return_distance)
              if return_distance:
                  ind, dist = results
                  return dist, ind
              else:
                  return results
          else:
              raise ValueError("internal: _fit_method not recognized")
  
      def radius_neighbors_graph(self, X, radius=None, mode='connectivity'):
          """Computes the (weighted) graph of Neighbors for points in X
  
          Neighborhoods are restricted the points at a distance lower than
          radius.
  
          Parameters
          ----------
          X : array-like, shape = [n_samples, n_features]
              Sample data
  
          radius : float
              Radius of neighborhoods.
              (default is the value passed to the constructor).
  
          mode : {'connectivity', 'distance'}, optional
              Type of returned matrix: 'connectivity' will return the
              connectivity matrix with ones and zeros, in 'distance' the
              edges are Euclidean distance between points.
  
          Returns
          -------
          A : sparse matrix in CSR format, shape = [n_samples, n_samples]
              A[i, j] is assigned the weight of edge that connects i to j.
  
          Examples
          --------
          >>> X = [[0], [3], [1]]
          >>> from sklearn.neighbors import NearestNeighbors
          >>> neigh = NearestNeighbors(radius=1.5)
          >>> neigh.fit(X) # doctest: +ELLIPSIS
          NearestNeighbors(algorithm='auto', leaf_size=30, ...)
          >>> A = neigh.radius_neighbors_graph(X)
          >>> A.toarray()
          array([[ 1.,  0.,  1.],
                 [ 0.,  1.,  0.],
                 [ 1.,  0.,  1.]])
  
          See also
          --------
          kneighbors_graph
          """
          X = check_array(X, accept_sparse=['csr', 'csc', 'coo'])
  
          if radius is None:
              radius = self.radius
  
          n_samples1 = X.shape[0]
          n_samples2 = self._fit_X.shape[0]
  
          # construct CSR matrix representation of the NN graph
          if mode == 'connectivity':
              A_ind = self.radius_neighbors(X, radius,
                                            return_distance=False)
              A_data = None
          elif mode == 'distance':
              dist, A_ind = self.radius_neighbors(X, radius,
                                                  return_distance=True)
              A_data = np.concatenate(list(dist))
          else:
              raise ValueError(
                  'Unsupported mode, must be one of "connectivity", '
                  'or "distance" but got %s instead' % mode)
  
          n_neighbors = np.array([len(a) for a in A_ind])
          n_nonzero = np.sum(n_neighbors)
          if A_data is None:
              A_data = np.ones(n_nonzero)
          A_ind = np.concatenate(list(A_ind))
          A_indptr = np.concatenate((np.zeros(1, dtype=int),
                                     np.cumsum(n_neighbors)))
  
          return csr_matrix((A_data, A_ind, A_indptr),
                            shape=(n_samples1, n_samples2))
  
  
  class SupervisedFloatMixin(object):
      def fit(self, X, y):
          """Fit the model using X as training data and y as target values
  
          Parameters
          ----------
          X : {array-like, sparse matrix, BallTree, KDTree}
              Training data. If array or matrix, shape = [n_samples, n_features]
  
          y : {array-like, sparse matrix}
              Target values, array of float values, shape = [n_samples]
               or [n_samples, n_outputs]
          """
          if not isinstance(X, (KDTree, BallTree)):
              X, y = check_X_y(X, y, "csr", multi_output=True)
          self._y = y
          return self._fit(X)
  
  
  class SupervisedIntegerMixin(object):
      def fit(self, X, y):
          """Fit the model using X as training data and y as target values
  
          Parameters
          ----------
          X : {array-like, sparse matrix, BallTree, KDTree}
              Training data. If array or matrix, shape = [n_samples, n_features]
  
          y : {array-like, sparse matrix}
              Target values of shape = [n_samples] or [n_samples, n_outputs]
  
          """
          if not isinstance(X, (KDTree, BallTree)):
              X, y = check_X_y(X, y, "csr", multi_output=True)
  
          if y.ndim == 1 or y.ndim == 2 and y.shape[1] == 1:
              if y.ndim != 1:
                  warnings.warn("A column-vector y was passed when a 1d array "
                                "was expected. Please change the shape of y to "
                                "(n_samples, ), for example using ravel().",
                                DataConversionWarning, stacklevel=2)
  
              self.outputs_2d_ = False
              y = y.reshape((-1, 1))
          else:
              self.outputs_2d_ = True
  
          self.classes_ = []
          self._y = np.empty(y.shape, dtype=np.int)
          for k in range(self._y.shape[1]):
              classes, self._y[:, k] = np.unique(y[:, k], return_inverse=True)
              self.classes_.append(classes)
  
          if not self.outputs_2d_:
              self.classes_ = self.classes_[0]
              self._y = self._y.ravel()
  
          return self._fit(X)
  
  
  class UnsupervisedMixin(object):
      def fit(self, X, y=None):
          """Fit the model using X as training data
  
          Parameters
          ----------
          X : {array-like, sparse matrix, BallTree, KDTree}
              Training data. If array or matrix, shape = [n_samples, n_features]
          """
          return self._fit(X)
  