"""
This module contains the TreeGrower class.

TreeGrowee builds a regression tree fitting a Newton-Raphson step, based on
the gradients and hessians of the training data.
"""
# Author: Nicolas Hug

from heapq import heappush, heappop
import numpy as np
from timeit import default_timer as time
import numbers

from .splitting import Splitter
from .histogram import HistogramBuilder
from .predictor import TreePredictor, PREDICTOR_RECORD_DTYPE
from .utils import sum_parallel


class TreeNode:
    """Tree Node class used in TreeGrower.

    This isn't used for prediction purposes, only for training (see
    TreePredictor).

    Parameters
    ----------
    depth : int
        The depth of the node, i.e. its distance from the root.
    sample_indices : ndarray of unsigned int, shape (n_samples_at_node,)
        The indices of the samples at the node.
    sum_gradients : float
        The sum of the gradients of the samples at the node.
    sum_hessians : float
        The sum of the hessians of the samples at the node.
    parent : TreeNode or None, optional (default=None)
        The parent of the node. None for root.

    Attributes
    ----------
    depth : int
        The depth of the node, i.e. its distance from the root.
    sample_indices : ndarray of unsigned int, shape (n_samples_at_node,)
        The indices of the samples at the node.
    sum_gradients : float
        The sum of the gradients of the samples at the node.
    sum_hessians : float
        The sum of the hessians of the samples at the node.
    parent : TreeNode or None
        The parent of the node. None for root.
    split_info : SplitInfo or None
        The result of the split evaluation.
    left_child : TreeNode or None
        The left child of the node. None for leaves.
    right_child : TreeNode or None
        The right child of the node. None for leaves.
    value : float or None
        The value of the leaf, as computed in finalize_leaf(). None for
        non-leaf nodes.
    partition_start : int
        start position of the node's sample_indices in splitter.partition.
    partition_stop : int
        stop position of the node's sample_indices in splitter.partition.
    """

    split_info = None
    left_child = None
    right_child = None
    value = None
    histograms = None
    sibling = None
    parent = None

    # start and stop indices of the node in the splitter.partition
    # array. Concretely,
    # self.sample_indices = view(self.splitter.partition[start:stop])
    # Please see the comments about splitter.partition and
    # splitter.split_indices for more info about this design.
    # These 2 attributes are only used in _update_raw_prediction, because we
    # need to iterate over the leaves and I don't know how to efficiently
    # store the sample_indices views because they're all of different sizes.
    partition_start = 0
    partition_stop = 0

    def __init__(self, depth, sample_indices, sum_gradients,
                 sum_hessians, parent=None):
        self.depth = depth
        self.sample_indices = sample_indices
        self.n_samples = sample_indices.shape[0]
        self.sum_gradients = sum_gradients
        self.sum_hessians = sum_hessians
        self.parent = parent

    def __lt__(self, other_node):
        """Comparison for priority queue.

        Nodes with high gain are higher priority than nodes with low gain.

        heapq.heappush only need the '<' operator.
        heapq.heappop take the smallest item first (smaller is higher
        priority).

        Parameters
        ----------
        other_node : TreeNode
            The node to compare with.
        """
        return self.split_info.gain > other_node.split_info.gain


class TreeGrower:
    """Tree grower class used to build a tree.

    The tree is fitted to predict the values of a Newton-Raphson step. The
    splits are considered in a best-first fashion, and the quality of a
    split is defined in splitting._split_gain.

    Parameters
    ----------
    X_binned : ndarray of int, shape (n_samples, n_features)
        The binned input samples. Must be Fortran-aligned.
    gradients : ndarray, shape (n_samples,)
        The gradients of each training sample. Those are the gradients of the
        loss w.r.t the predictions, evaluated at iteration ``i - 1``.
    hessians : ndarray, shape (n_samples,)
        The hessians of each training sample. Those are the hessians of the
        loss w.r.t the predictions, evaluated at iteration ``i - 1``.
    max_leaf_nodes : int or None, optional (default=None)
        The maximum number of leaves for each tree. If None, there is no
        maximum limit.
    max_depth : int or None, optional (default=None)
        The maximum depth of each tree. The depth of a tree is the number of
        nodes to go from the root to the deepest leaf.
    min_samples_leaf : int, optional (default=20)
        The minimum number of samples per leaf.
    min_gain_to_split : float, optional (default=0.)
        The minimum gain needed to split a node. Splits with lower gain will
        be ignored.
    max_bins : int, optional (default=256)
        The maximum number of bins. Used to define the shape of the
        histograms.
    actual_n_bins : ndarray of int or int, optional (default=None)
        The actual number of bins needed for each feature, which is lower or
        equal to ``max_bins``. If it's an int, all features are considered to
        have the same number of bins. If None, all features are considered to
        have ``max_bins`` bins.
    l2_regularization : float, optional (default=0)
        The L2 regularization parameter.
    min_hessian_to_split : float, optional (default=1e-3)
        The minimum sum of hessians needed in each node. Splits that result in
        at least one child having a sum of hessians less than
        ``min_hessian_to_split`` are discarded.
    shrinkage : float, optional (default=1)
        The shrinkage parameter to apply to the leaves values, also known as
        learning rate.
    """
    def __init__(self, X_binned, gradients, hessians, max_leaf_nodes=None,
                 max_depth=None, min_samples_leaf=20, min_gain_to_split=0.,
                 max_bins=256, actual_n_bins=None, l2_regularization=0.,
                 min_hessian_to_split=1e-3, shrinkage=1.):

        self._validate_parameters(X_binned, max_leaf_nodes, max_depth,
                                  min_samples_leaf, min_gain_to_split,
                                  l2_regularization, min_hessian_to_split)

        if actual_n_bins is None:
            actual_n_bins = max_bins

        if isinstance(actual_n_bins, numbers.Integral):
            actual_n_bins = np.array(
                [actual_n_bins] * X_binned.shape[1],
                dtype=np.uint32)
        else:
            actual_n_bins = np.asarray(actual_n_bins, dtype=np.uint32)

        hessians_are_constant = hessians.shape[0] == 1
        self.histogram_builder = HistogramBuilder(
            X_binned, max_bins, gradients, hessians, hessians_are_constant)
        self.splitter = Splitter(
            X_binned, max_bins, actual_n_bins, l2_regularization,
            min_hessian_to_split, min_samples_leaf, min_gain_to_split,
            hessians_are_constant)
        self.max_leaf_nodes = max_leaf_nodes
        self.max_bins = max_bins
        self.n_features = X_binned.shape[1]
        self.max_depth = max_depth
        self.min_samples_leaf = min_samples_leaf
        self.X_binned = X_binned
        self.min_gain_to_split = min_gain_to_split
        self.shrinkage = shrinkage
        self.splittable_nodes = []
        self.finalized_leaves = []
        self.total_find_split_time = 0.  # time spent finding the best splits
        self.total_compute_hist_time = 0.  # time spent computing histograms
        self.total_apply_split_time = 0.  # time spent splitting nodes
        self._intilialize_root(gradients, hessians, hessians_are_constant)
        self.n_nodes = 1

    def _validate_parameters(self, X_binned, max_leaf_nodes, max_depth,
                             min_samples_leaf, min_gain_to_split,
                             l2_regularization, min_hessian_to_split):
        """Validate parameters passed to __init__.

        Also validate parameters passed to splitter.
        """
        if X_binned.dtype != np.uint8:
            raise NotImplementedError(
                "X_binned must be of type uint8.")
        if not X_binned.flags.f_contiguous:
            raise ValueError(
                "X_binned should be passed as Fortran contiguous "
                "array for maximum efficiency.")
        if max_leaf_nodes is not None and max_leaf_nodes <= 1:
            raise ValueError('max_leaf_nodes={} should not be'
                             ' smaller than 2'.format(max_leaf_nodes))
        if max_depth is not None and max_depth <= 1:
            raise ValueError('max_depth={} should not be'
                             ' smaller than 2'.format(max_depth))
        if min_samples_leaf < 1:
            raise ValueError('min_samples_leaf={} should '
                             'not be smaller than 1'.format(min_samples_leaf))
        if min_gain_to_split < 0:
            raise ValueError('min_gain_to_split={} '
                             'must be positive.'.format(min_gain_to_split))
        if l2_regularization < 0:
            raise ValueError('l2_regularization={} must be '
                             'positive.'.format(l2_regularization))
        if min_hessian_to_split < 0:
            raise ValueError('min_hessian_to_split={} '
                             'must be positive.'.format(min_hessian_to_split))

    def grow(self):
        """Grow the tree, from root to leaves."""
        while self.splittable_nodes:
            self.split_next()

    def _intilialize_root(self, gradients, hessians, hessians_are_constant):
        """Initialize root node and finalize it if needed."""
        n_samples = self.X_binned.shape[0]
        depth = 0
        sum_gradients = sum_parallel(gradients)
        if self.histogram_builder.hessians_are_constant:
            sum_hessians = hessians[0] * n_samples
        else:
            sum_hessians = sum_parallel(hessians)
        self.root = TreeNode(
            depth=depth,
            sample_indices=self.splitter.partition,
            sum_gradients=sum_gradients,
            sum_hessians=sum_hessians
        )

        self.root.partition_start = 0
        self.root.partition_stop = n_samples

        if self.root.n_samples < 2 * self.min_samples_leaf:
            # Do not even bother computing any splitting statistics.
            self._finalize_leaf(self.root)
            return
        if sum_hessians < self.splitter.min_hessian_to_split:
            self._finalize_leaf(self.root)
            return

        self.root.histograms = self.histogram_builder.compute_histograms_brute(
            self.root.sample_indices)
        self._compute_best_split_and_push(self.root)

    def _compute_best_split_and_push(self, node):
        """Compute the best possible split (SplitInfo) of a given node.

        Also push it in the heap of splittable nodes if gain isn't zero.
        The gain of a node is 0 if either all the leaves are pure
        (best gain = 0), or if no split would satisfy the constraints,
        (min_hessians_to_split, min_gain_to_split, min_samples_leaf)
        """

        node.split_info = self.splitter.find_node_split(
            node.sample_indices, node.histograms, node.sum_gradients,
            node.sum_hessians)

        if node.split_info.gain <= 0:  # no valid split
            self._finalize_leaf(node)
        else:
            heappush(self.splittable_nodes, node)

    def split_next(self):
        """Split the node with highest potential gain.

        Returns
        -------
        left : TreeNode
            The resulting left child.
        right : TreeNode
            The resulting right child.
        """
        # Consider the node with the highest loss reduction (a.k.a. gain)
        node = heappop(self.splittable_nodes)

        tic = time()
        (sample_indices_left,
         sample_indices_right,
         right_child_pos) = self.splitter.split_indices(node.split_info,
                                                        node.sample_indices)
        self.total_apply_split_time += time() - tic

        depth = node.depth + 1
        n_leaf_nodes = len(self.finalized_leaves) + len(self.splittable_nodes)
        n_leaf_nodes += 2

        left_child_node = TreeNode(depth,
                                   sample_indices_left,
                                   node.split_info.sum_gradient_left,
                                   node.split_info.sum_hessian_left,
                                   parent=node)
        right_child_node = TreeNode(depth,
                                    sample_indices_right,
                                    node.split_info.sum_gradient_right,
                                    node.split_info.sum_hessian_right,
                                    parent=node)
        left_child_node.sibling = right_child_node
        right_child_node.sibling = left_child_node
        node.right_child = right_child_node
        node.left_child = left_child_node

        # set start and stop indices
        left_child_node.partition_start = node.partition_start
        left_child_node.partition_stop = node.partition_start + right_child_pos
        right_child_node.partition_start = left_child_node.partition_stop
        right_child_node.partition_stop = node.partition_stop

        self.n_nodes += 2

        if self.max_depth is not None and depth == self.max_depth:
            self._finalize_leaf(left_child_node)
            self._finalize_leaf(right_child_node)
            return left_child_node, right_child_node

        if (self.max_leaf_nodes is not None
                and n_leaf_nodes == self.max_leaf_nodes):
            self._finalize_leaf(left_child_node)
            self._finalize_leaf(right_child_node)
            self._finalize_splittable_nodes()
            return left_child_node, right_child_node

        if left_child_node.n_samples < self.min_samples_leaf * 2:
            self._finalize_leaf(left_child_node)
        if right_child_node.n_samples < self.min_samples_leaf * 2:
            self._finalize_leaf(right_child_node)

        # Compute histograms of childs, and compute their best possible split
        # (if needed)
        should_split_left = left_child_node.value is None  # node isn't a leaf
        should_split_right = right_child_node.value is None
        if should_split_left or should_split_right:

            # We will compute the histograms of both nodes even if one of them
            # is a leaf, since computing the second histogram is very cheap
            # (using histogram subtraction).
            n_samples_left = left_child_node.sample_indices.shape[0]
            n_samples_right = right_child_node.sample_indices.shape[0]
            if n_samples_left < n_samples_right:
                smallest_child = left_child_node
                largest_child = right_child_node
            else:
                smallest_child = right_child_node
                largest_child = left_child_node

            # We use the brute O(n_samples) method on the child that has the
            # smallest number of samples, and the subtraction trick O(n_bins)
            # on the other one.
            tic = time()
            smallest_child.histograms = \
                self.histogram_builder.compute_histograms_brute(
                    smallest_child.sample_indices)
            largest_child.histograms = \
                self.histogram_builder.compute_histograms_subtraction(
                    node.histograms, smallest_child.histograms)
            self.total_compute_hist_time += time() - tic

            tic = time()
            if should_split_left:
                self._compute_best_split_and_push(left_child_node)
            if should_split_right:
                self._compute_best_split_and_push(right_child_node)
            self.total_find_split_time += time() - tic

        return left_child_node, right_child_node

    def _finalize_leaf(self, node):
        """Compute the prediction value that minimizes the objective function.

        This sets the node.value attribute (node is a leaf iff node.value is
        not None).

        See Equation 5 of:
        XGBoost: A Scalable Tree Boosting System, T. Chen, C. Guestrin, 2016
        https://arxiv.org/abs/1603.02754
        """
        node.value = -self.shrinkage * node.sum_gradients / (
            node.sum_hessians + self.splitter.l2_regularization)
        self.finalized_leaves.append(node)

    def _finalize_splittable_nodes(self):
        """Transform all splittable nodes into leaves.

        Used when some constraint is met e.g. maximum number of leaves or
        maximum depth."""
        while len(self.splittable_nodes) > 0:
            node = self.splittable_nodes.pop()
            self._finalize_leaf(node)

    def make_predictor(self, bin_thresholds=None):
        """Make a TreePredictor object out of the current tree.

        Parameters
        ----------
        bin_thresholds : array-like of floats, optional (default=None)
            The actual thresholds values of each bin.

        Returns
        -------
        A TreePredictor object.
        """
        predictor_nodes = np.zeros(self.n_nodes, dtype=PREDICTOR_RECORD_DTYPE)
        _fill_predictor_node_array(predictor_nodes, self.root,
                                   bin_thresholds=bin_thresholds)
        return TreePredictor(predictor_nodes)


def _fill_predictor_node_array(predictor_nodes, grower_node,
                               bin_thresholds, next_free_idx=0):
    """Helper used in make_predictor to set the TreePredictor fields."""
    node = predictor_nodes[next_free_idx]
    node['count'] = grower_node.n_samples
    node['depth'] = grower_node.depth
    if grower_node.split_info is not None:
        node['gain'] = grower_node.split_info.gain
    else:
        node['gain'] = -1

    if grower_node.value is not None:
        # Leaf node
        node['is_leaf'] = True
        node['value'] = grower_node.value
        return next_free_idx + 1
    else:
        # Decision node
        split_info = grower_node.split_info
        feature_idx, bin_idx = split_info.feature_idx, split_info.bin_idx
        node['feature_idx'] = feature_idx
        node['bin_threshold'] = bin_idx
        if bin_thresholds is not None:
            threshold = bin_thresholds[feature_idx][bin_idx]
            node['threshold'] = threshold
        next_free_idx += 1

        node['left'] = next_free_idx
        next_free_idx = _fill_predictor_node_array(
            predictor_nodes, grower_node.left_child,
            bin_thresholds=bin_thresholds, next_free_idx=next_free_idx)

        node['right'] = next_free_idx
        return _fill_predictor_node_array(
            predictor_nodes, grower_node.right_child,
            bin_thresholds=bin_thresholds, next_free_idx=next_free_idx)

2a44bb5a483c38c8a00955b7460fc9ad5bce7871
<mask token>


class TreeGrower:
    <mask token>

    def __init__(self, X_binned, gradients, hessians, max_leaf_nodes=None,
        max_depth=None, min_samples_leaf=20, min_gain_to_split=0.0,
        max_bins=256, actual_n_bins=None, l2_regularization=0.0,
        min_hessian_to_split=0.001, shrinkage=1.0):
        self._validate_parameters(X_binned, max_leaf_nodes, max_depth,
            min_samples_leaf, min_gain_to_split, l2_regularization,
            min_hessian_to_split)
        if actual_n_bins is None:
            actual_n_bins = max_bins
        if isinstance(actual_n_bins, numbers.Integral):
            actual_n_bins = np.array([actual_n_bins] * X_binned.shape[1],
                dtype=np.uint32)
        else:
            actual_n_bins = np.asarray(actual_n_bins, dtype=np.uint32)
        hessians_are_constant = hessians.shape[0] == 1
        self.histogram_builder = HistogramBuilder(X_binned, max_bins,
            gradients, hessians, hessians_are_constant)
        self.splitter = Splitter(X_binned, max_bins, actual_n_bins,
            l2_regularization, min_hessian_to_split, min_samples_leaf,
            min_gain_to_split, hessians_are_constant)
        self.max_leaf_nodes = max_leaf_nodes
        self.max_bins = max_bins
        self.n_features = X_binned.shape[1]
        self.max_depth = max_depth
        self.min_samples_leaf = min_samples_leaf
        self.X_binned = X_binned
        self.min_gain_to_split = min_gain_to_split
        self.shrinkage = shrinkage
        self.splittable_nodes = []
        self.finalized_leaves = []
        self.total_find_split_time = 0.0
        self.total_compute_hist_time = 0.0
        self.total_apply_split_time = 0.0
        self._intilialize_root(gradients, hessians, hessians_are_constant)
        self.n_nodes = 1

    def _validate_parameters(self, X_binned, max_leaf_nodes, max_depth,
        min_samples_leaf, min_gain_to_split, l2_regularization,
        min_hessian_to_split):
        """Validate parameters passed to __init__.

        Also validate parameters passed to splitter.
        """
        if X_binned.dtype != np.uint8:
            raise NotImplementedError('X_binned must be of type uint8.')
        if not X_binned.flags.f_contiguous:
            raise ValueError(
                'X_binned should be passed as Fortran contiguous array for maximum efficiency.'
                )
        if max_leaf_nodes is not None and max_leaf_nodes <= 1:
            raise ValueError('max_leaf_nodes={} should not be smaller than 2'
                .format(max_leaf_nodes))
        if max_depth is not None and max_depth <= 1:
            raise ValueError('max_depth={} should not be smaller than 2'.
                format(max_depth))
        if min_samples_leaf < 1:
            raise ValueError('min_samples_leaf={} should not be smaller than 1'
                .format(min_samples_leaf))
        if min_gain_to_split < 0:
            raise ValueError('min_gain_to_split={} must be positive.'.
                format(min_gain_to_split))
        if l2_regularization < 0:
            raise ValueError('l2_regularization={} must be positive.'.
                format(l2_regularization))
        if min_hessian_to_split < 0:
            raise ValueError('min_hessian_to_split={} must be positive.'.
                format(min_hessian_to_split))

    def grow(self):
        """Grow the tree, from root to leaves."""
        while self.splittable_nodes:
            self.split_next()

    def _intilialize_root(self, gradients, hessians, hessians_are_constant):
        """Initialize root node and finalize it if needed."""
        n_samples = self.X_binned.shape[0]
        depth = 0
        sum_gradients = sum_parallel(gradients)
        if self.histogram_builder.hessians_are_constant:
            sum_hessians = hessians[0] * n_samples
        else:
            sum_hessians = sum_parallel(hessians)
        self.root = TreeNode(depth=depth, sample_indices=self.splitter.
            partition, sum_gradients=sum_gradients, sum_hessians=sum_hessians)
        self.root.partition_start = 0
        self.root.partition_stop = n_samples
        if self.root.n_samples < 2 * self.min_samples_leaf:
            self._finalize_leaf(self.root)
            return
        if sum_hessians < self.splitter.min_hessian_to_split:
            self._finalize_leaf(self.root)
            return
        self.root.histograms = self.histogram_builder.compute_histograms_brute(
            self.root.sample_indices)
        self._compute_best_split_and_push(self.root)

    def _compute_best_split_and_push(self, node):
        """Compute the best possible split (SplitInfo) of a given node.

        Also push it in the heap of splittable nodes if gain isn't zero.
        The gain of a node is 0 if either all the leaves are pure
        (best gain = 0), or if no split would satisfy the constraints,
        (min_hessians_to_split, min_gain_to_split, min_samples_leaf)
        """
        node.split_info = self.splitter.find_node_split(node.sample_indices,
            node.histograms, node.sum_gradients, node.sum_hessians)
        if node.split_info.gain <= 0:
            self._finalize_leaf(node)
        else:
            heappush(self.splittable_nodes, node)

    def split_next(self):
        """Split the node with highest potential gain.

        Returns
        -------
        left : TreeNode
            The resulting left child.
        right : TreeNode
            The resulting right child.
        """
        node = heappop(self.splittable_nodes)
        tic = time()
        sample_indices_left, sample_indices_right, right_child_pos = (self.
            splitter.split_indices(node.split_info, node.sample_indices))
        self.total_apply_split_time += time() - tic
        depth = node.depth + 1
        n_leaf_nodes = len(self.finalized_leaves) + len(self.splittable_nodes)
        n_leaf_nodes += 2
        left_child_node = TreeNode(depth, sample_indices_left, node.
            split_info.sum_gradient_left, node.split_info.sum_hessian_left,
            parent=node)
        right_child_node = TreeNode(depth, sample_indices_right, node.
            split_info.sum_gradient_right, node.split_info.
            sum_hessian_right, parent=node)
        left_child_node.sibling = right_child_node
        right_child_node.sibling = left_child_node
        node.right_child = right_child_node
        node.left_child = left_child_node
        left_child_node.partition_start = node.partition_start
        left_child_node.partition_stop = node.partition_start + right_child_pos
        right_child_node.partition_start = left_child_node.partition_stop
        right_child_node.partition_stop = node.partition_stop
        self.n_nodes += 2
        if self.max_depth is not None and depth == self.max_depth:
            self._finalize_leaf(left_child_node)
            self._finalize_leaf(right_child_node)
            return left_child_node, right_child_node
        if (self.max_leaf_nodes is not None and n_leaf_nodes == self.
            max_leaf_nodes):
            self._finalize_leaf(left_child_node)
            self._finalize_leaf(right_child_node)
            self._finalize_splittable_nodes()
            return left_child_node, right_child_node
        if left_child_node.n_samples < self.min_samples_leaf * 2:
            self._finalize_leaf(left_child_node)
        if right_child_node.n_samples < self.min_samples_leaf * 2:
            self._finalize_leaf(right_child_node)
        should_split_left = left_child_node.value is None
        should_split_right = right_child_node.value is None
        if should_split_left or should_split_right:
            n_samples_left = left_child_node.sample_indices.shape[0]
            n_samples_right = right_child_node.sample_indices.shape[0]
            if n_samples_left < n_samples_right:
                smallest_child = left_child_node
                largest_child = right_child_node
            else:
                smallest_child = right_child_node
                largest_child = left_child_node
            tic = time()
            smallest_child.histograms = (self.histogram_builder.
                compute_histograms_brute(smallest_child.sample_indices))
            largest_child.histograms = (self.histogram_builder.
                compute_histograms_subtraction(node.histograms,
                smallest_child.histograms))
            self.total_compute_hist_time += time() - tic
            tic = time()
            if should_split_left:
                self._compute_best_split_and_push(left_child_node)
            if should_split_right:
                self._compute_best_split_and_push(right_child_node)
            self.total_find_split_time += time() - tic
        return left_child_node, right_child_node

    def _finalize_leaf(self, node):
        """Compute the prediction value that minimizes the objective function.

        This sets the node.value attribute (node is a leaf iff node.value is
        not None).

        See Equation 5 of:
        XGBoost: A Scalable Tree Boosting System, T. Chen, C. Guestrin, 2016
        https://arxiv.org/abs/1603.02754
        """
        node.value = -self.shrinkage * node.sum_gradients / (node.
            sum_hessians + self.splitter.l2_regularization)
        self.finalized_leaves.append(node)

    def _finalize_splittable_nodes(self):
        """Transform all splittable nodes into leaves.

        Used when some constraint is met e.g. maximum number of leaves or
        maximum depth."""
        while len(self.splittable_nodes) > 0:
            node = self.splittable_nodes.pop()
            self._finalize_leaf(node)

    def make_predictor(self, bin_thresholds=None):
        """Make a TreePredictor object out of the current tree.

        Parameters
        ----------
        bin_thresholds : array-like of floats, optional (default=None)
            The actual thresholds values of each bin.

        Returns
        -------
        A TreePredictor object.
        """
        predictor_nodes = np.zeros(self.n_nodes, dtype=PREDICTOR_RECORD_DTYPE)
        _fill_predictor_node_array(predictor_nodes, self.root,
            bin_thresholds=bin_thresholds)
        return TreePredictor(predictor_nodes)


<mask token>

<mask token>


class TreeNode:
    <mask token>
    <mask token>
    <mask token>
    <mask token>
    <mask token>
    <mask token>
    <mask token>
    <mask token>
    <mask token>
    <mask token>
    <mask token>

    def __lt__(self, other_node):
        """Comparison for priority queue.

        Nodes with high gain are higher priority than nodes with low gain.

        heapq.heappush only need the '<' operator.
        heapq.heappop take the smallest item first (smaller is higher
        priority).

        Parameters
        ----------
        other_node : TreeNode
            The node to compare with.
        """
        return self.split_info.gain > other_node.split_info.gain


class TreeGrower:
    """Tree grower class used to build a tree.

    The tree is fitted to predict the values of a Newton-Raphson step. The
    splits are considered in a best-first fashion, and the quality of a
    split is defined in splitting._split_gain.

    Parameters
    ----------
    X_binned : ndarray of int, shape (n_samples, n_features)
        The binned input samples. Must be Fortran-aligned.
    gradients : ndarray, shape (n_samples,)
        The gradients of each training sample. Those are the gradients of the
        loss w.r.t the predictions, evaluated at iteration ``i - 1``.
    hessians : ndarray, shape (n_samples,)
        The hessians of each training sample. Those are the hessians of the
        loss w.r.t the predictions, evaluated at iteration ``i - 1``.
    max_leaf_nodes : int or None, optional (default=None)
        The maximum number of leaves for each tree. If None, there is no
        maximum limit.
    max_depth : int or None, optional (default=None)
        The maximum depth of each tree. The depth of a tree is the number of
        nodes to go from the root to the deepest leaf.
    min_samples_leaf : int, optional (default=20)
        The minimum number of samples per leaf.
    min_gain_to_split : float, optional (default=0.)
        The minimum gain needed to split a node. Splits with lower gain will
        be ignored.
    max_bins : int, optional (default=256)
        The maximum number of bins. Used to define the shape of the
        histograms.
    actual_n_bins : ndarray of int or int, optional (default=None)
        The actual number of bins needed for each feature, which is lower or
        equal to ``max_bins``. If it's an int, all features are considered to
        have the same number of bins. If None, all features are considered to
        have ``max_bins`` bins.
    l2_regularization : float, optional (default=0)
        The L2 regularization parameter.
    min_hessian_to_split : float, optional (default=1e-3)
        The minimum sum of hessians needed in each node. Splits that result in
        at least one child having a sum of hessians less than
        ``min_hessian_to_split`` are discarded.
    shrinkage : float, optional (default=1)
        The shrinkage parameter to apply to the leaves values, also known as
        learning rate.
    """

    def __init__(self, X_binned, gradients, hessians, max_leaf_nodes=None,
        max_depth=None, min_samples_leaf=20, min_gain_to_split=0.0,
        max_bins=256, actual_n_bins=None, l2_regularization=0.0,
        min_hessian_to_split=0.001, shrinkage=1.0):
        self._validate_parameters(X_binned, max_leaf_nodes, max_depth,
            min_samples_leaf, min_gain_to_split, l2_regularization,
            min_hessian_to_split)
        if actual_n_bins is None:
            actual_n_bins = max_bins
        if isinstance(actual_n_bins, numbers.Integral):
            actual_n_bins = np.array([actual_n_bins] * X_binned.shape[1],
                dtype=np.uint32)
        else:
            actual_n_bins = np.asarray(actual_n_bins, dtype=np.uint32)
        hessians_are_constant = hessians.shape[0] == 1
        self.histogram_builder = HistogramBuilder(X_binned, max_bins,
            gradients, hessians, hessians_are_constant)
        self.splitter = Splitter(X_binned, max_bins, actual_n_bins,
            l2_regularization, min_hessian_to_split, min_samples_leaf,
            min_gain_to_split, hessians_are_constant)
        self.max_leaf_nodes = max_leaf_nodes
        self.max_bins = max_bins
        self.n_features = X_binned.shape[1]
        self.max_depth = max_depth
        self.min_samples_leaf = min_samples_leaf
        self.X_binned = X_binned
        self.min_gain_to_split = min_gain_to_split
        self.shrinkage = shrinkage
        self.splittable_nodes = []
        self.finalized_leaves = []
        self.total_find_split_time = 0.0
        self.total_compute_hist_time = 0.0
        self.total_apply_split_time = 0.0
        self._intilialize_root(gradients, hessians, hessians_are_constant)
        self.n_nodes = 1

    def _validate_parameters(self, X_binned, max_leaf_nodes, max_depth,
        min_samples_leaf, min_gain_to_split, l2_regularization,
        min_hessian_to_split):
        """Validate parameters passed to __init__.

        Also validate parameters passed to splitter.
        """
        if X_binned.dtype != np.uint8:
            raise NotImplementedError('X_binned must be of type uint8.')
        if not X_binned.flags.f_contiguous:
            raise ValueError(
                'X_binned should be passed as Fortran contiguous array for maximum efficiency.'
                )
        if max_leaf_nodes is not None and max_leaf_nodes <= 1:
            raise ValueError('max_leaf_nodes={} should not be smaller than 2'
                .format(max_leaf_nodes))
        if max_depth is not None and max_depth <= 1:
            raise ValueError('max_depth={} should not be smaller than 2'.
                format(max_depth))
        if min_samples_leaf < 1:
            raise ValueError('min_samples_leaf={} should not be smaller than 1'
                .format(min_samples_leaf))
        if min_gain_to_split < 0:
            raise ValueError('min_gain_to_split={} must be positive.'.
                format(min_gain_to_split))
        if l2_regularization < 0:
            raise ValueError('l2_regularization={} must be positive.'.
                format(l2_regularization))
        if min_hessian_to_split < 0:
            raise ValueError('min_hessian_to_split={} must be positive.'.
                format(min_hessian_to_split))

    def grow(self):
        """Grow the tree, from root to leaves."""
        while self.splittable_nodes:
            self.split_next()

    def _intilialize_root(self, gradients, hessians, hessians_are_constant):
        """Initialize root node and finalize it if needed."""
        n_samples = self.X_binned.shape[0]
        depth = 0
        sum_gradients = sum_parallel(gradients)
        if self.histogram_builder.hessians_are_constant:
            sum_hessians = hessians[0] * n_samples
        else:
            sum_hessians = sum_parallel(hessians)
        self.root = TreeNode(depth=depth, sample_indices=self.splitter.
            partition, sum_gradients=sum_gradients, sum_hessians=sum_hessians)
        self.root.partition_start = 0
        self.root.partition_stop = n_samples
        if self.root.n_samples < 2 * self.min_samples_leaf:
            self._finalize_leaf(self.root)
            return
        if sum_hessians < self.splitter.min_hessian_to_split:
            self._finalize_leaf(self.root)
            return
        self.root.histograms = self.histogram_builder.compute_histograms_brute(
            self.root.sample_indices)
        self._compute_best_split_and_push(self.root)

    def _compute_best_split_and_push(self, node):
        """Compute the best possible split (SplitInfo) of a given node.

        Also push it in the heap of splittable nodes if gain isn't zero.
        The gain of a node is 0 if either all the leaves are pure
        (best gain = 0), or if no split would satisfy the constraints,
        (min_hessians_to_split, min_gain_to_split, min_samples_leaf)
        """
        node.split_info = self.splitter.find_node_split(node.sample_indices,
            node.histograms, node.sum_gradients, node.sum_hessians)
        if node.split_info.gain <= 0:
            self._finalize_leaf(node)
        else:
            heappush(self.splittable_nodes, node)

    def split_next(self):
        """Split the node with highest potential gain.

        Returns
        -------
        left : TreeNode
            The resulting left child.
        right : TreeNode
            The resulting right child.
        """
        node = heappop(self.splittable_nodes)
        tic = time()
        sample_indices_left, sample_indices_right, right_child_pos = (self.
            splitter.split_indices(node.split_info, node.sample_indices))
        self.total_apply_split_time += time() - tic
        depth = node.depth + 1
        n_leaf_nodes = len(self.finalized_leaves) + len(self.splittable_nodes)
        n_leaf_nodes += 2
        left_child_node = TreeNode(depth, sample_indices_left, node.
            split_info.sum_gradient_left, node.split_info.sum_hessian_left,
            parent=node)
        right_child_node = TreeNode(depth, sample_indices_right, node.
            split_info.sum_gradient_right, node.split_info.
            sum_hessian_right, parent=node)
        left_child_node.sibling = right_child_node
        right_child_node.sibling = left_child_node
        node.right_child = right_child_node
        node.left_child = left_child_node
        left_child_node.partition_start = node.partition_start
        left_child_node.partition_stop = node.partition_start + right_child_pos
        right_child_node.partition_start = left_child_node.partition_stop
        right_child_node.partition_stop = node.partition_stop
        self.n_nodes += 2
        if self.max_depth is not None and depth == self.max_depth:
            self._finalize_leaf(left_child_node)
            self._finalize_leaf(right_child_node)
            return left_child_node, right_child_node
        if (self.max_leaf_nodes is not None and n_leaf_nodes == self.
            max_leaf_nodes):
            self._finalize_leaf(left_child_node)
            self._finalize_leaf(right_child_node)
            self._finalize_splittable_nodes()
            return left_child_node, right_child_node
        if left_child_node.n_samples < self.min_samples_leaf * 2:
            self._finalize_leaf(left_child_node)
        if right_child_node.n_samples < self.min_samples_leaf * 2:
            self._finalize_leaf(right_child_node)
        should_split_left = left_child_node.value is None
        should_split_right = right_child_node.value is None
        if should_split_left or should_split_right:
            n_samples_left = left_child_node.sample_indices.shape[0]
            n_samples_right = right_child_node.sample_indices.shape[0]
            if n_samples_left < n_samples_right:
                smallest_child = left_child_node
                largest_child = right_child_node
            else:
                smallest_child = right_child_node
                largest_child = left_child_node
            tic = time()
            smallest_child.histograms = (self.histogram_builder.
                compute_histograms_brute(smallest_child.sample_indices))
            largest_child.histograms = (self.histogram_builder.
                compute_histograms_subtraction(node.histograms,
                smallest_child.histograms))
            self.total_compute_hist_time += time() - tic
            tic = time()
            if should_split_left:
                self._compute_best_split_and_push(left_child_node)
            if should_split_right:
                self._compute_best_split_and_push(right_child_node)
            self.total_find_split_time += time() - tic
        return left_child_node, right_child_node

    def _finalize_leaf(self, node):
        """Compute the prediction value that minimizes the objective function.

        This sets the node.value attribute (node is a leaf iff node.value is
        not None).

        See Equation 5 of:
        XGBoost: A Scalable Tree Boosting System, T. Chen, C. Guestrin, 2016
        https://arxiv.org/abs/1603.02754
        """
        node.value = -self.shrinkage * node.sum_gradients / (node.
            sum_hessians + self.splitter.l2_regularization)
        self.finalized_leaves.append(node)

    def _finalize_splittable_nodes(self):
        """Transform all splittable nodes into leaves.

        Used when some constraint is met e.g. maximum number of leaves or
        maximum depth."""
        while len(self.splittable_nodes) > 0:
            node = self.splittable_nodes.pop()
            self._finalize_leaf(node)

    def make_predictor(self, bin_thresholds=None):
        """Make a TreePredictor object out of the current tree.

        Parameters
        ----------
        bin_thresholds : array-like of floats, optional (default=None)
            The actual thresholds values of each bin.

        Returns
        -------
        A TreePredictor object.
        """
        predictor_nodes = np.zeros(self.n_nodes, dtype=PREDICTOR_RECORD_DTYPE)
        _fill_predictor_node_array(predictor_nodes, self.root,
            bin_thresholds=bin_thresholds)
        return TreePredictor(predictor_nodes)


<mask token>

<mask token>


class TreeNode:
    <mask token>
    <mask token>
    <mask token>
    <mask token>
    <mask token>
    <mask token>
    <mask token>
    <mask token>
    <mask token>
    <mask token>

    def __init__(self, depth, sample_indices, sum_gradients, sum_hessians,
        parent=None):
        self.depth = depth
        self.sample_indices = sample_indices
        self.n_samples = sample_indices.shape[0]
        self.sum_gradients = sum_gradients
        self.sum_hessians = sum_hessians
        self.parent = parent

    def __lt__(self, other_node):
        """Comparison for priority queue.

        Nodes with high gain are higher priority than nodes with low gain.

        heapq.heappush only need the '<' operator.
        heapq.heappop take the smallest item first (smaller is higher
        priority).

        Parameters
        ----------
        other_node : TreeNode
            The node to compare with.
        """
        return self.split_info.gain > other_node.split_info.gain


class TreeGrower:
    """Tree grower class used to build a tree.

    The tree is fitted to predict the values of a Newton-Raphson step. The
    splits are considered in a best-first fashion, and the quality of a
    split is defined in splitting._split_gain.

    Parameters
    ----------
    X_binned : ndarray of int, shape (n_samples, n_features)
        The binned input samples. Must be Fortran-aligned.
    gradients : ndarray, shape (n_samples,)
        The gradients of each training sample. Those are the gradients of the
        loss w.r.t the predictions, evaluated at iteration ``i - 1``.
    hessians : ndarray, shape (n_samples,)
        The hessians of each training sample. Those are the hessians of the
        loss w.r.t the predictions, evaluated at iteration ``i - 1``.
    max_leaf_nodes : int or None, optional (default=None)
        The maximum number of leaves for each tree. If None, there is no
        maximum limit.
    max_depth : int or None, optional (default=None)
        The maximum depth of each tree. The depth of a tree is the number of
        nodes to go from the root to the deepest leaf.
    min_samples_leaf : int, optional (default=20)
        The minimum number of samples per leaf.
    min_gain_to_split : float, optional (default=0.)
        The minimum gain needed to split a node. Splits with lower gain will
        be ignored.
    max_bins : int, optional (default=256)
        The maximum number of bins. Used to define the shape of the
        histograms.
    actual_n_bins : ndarray of int or int, optional (default=None)
        The actual number of bins needed for each feature, which is lower or
        equal to ``max_bins``. If it's an int, all features are considered to
        have the same number of bins. If None, all features are considered to
        have ``max_bins`` bins.
    l2_regularization : float, optional (default=0)
        The L2 regularization parameter.
    min_hessian_to_split : float, optional (default=1e-3)
        The minimum sum of hessians needed in each node. Splits that result in
        at least one child having a sum of hessians less than
        ``min_hessian_to_split`` are discarded.
    shrinkage : float, optional (default=1)
        The shrinkage parameter to apply to the leaves values, also known as
        learning rate.
    """

    def __init__(self, X_binned, gradients, hessians, max_leaf_nodes=None,
        max_depth=None, min_samples_leaf=20, min_gain_to_split=0.0,
        max_bins=256, actual_n_bins=None, l2_regularization=0.0,
        min_hessian_to_split=0.001, shrinkage=1.0):
        self._validate_parameters(X_binned, max_leaf_nodes, max_depth,
            min_samples_leaf, min_gain_to_split, l2_regularization,
            min_hessian_to_split)
        if actual_n_bins is None:
            actual_n_bins = max_bins
        if isinstance(actual_n_bins, numbers.Integral):
            actual_n_bins = np.array([actual_n_bins] * X_binned.shape[1],
                dtype=np.uint32)
        else:
            actual_n_bins = np.asarray(actual_n_bins, dtype=np.uint32)
        hessians_are_constant = hessians.shape[0] == 1
        self.histogram_builder = HistogramBuilder(X_binned, max_bins,
            gradients, hessians, hessians_are_constant)
        self.splitter = Splitter(X_binned, max_bins, actual_n_bins,
            l2_regularization, min_hessian_to_split, min_samples_leaf,
            min_gain_to_split, hessians_are_constant)
        self.max_leaf_nodes = max_leaf_nodes
        self.max_bins = max_bins
        self.n_features = X_binned.shape[1]
        self.max_depth = max_depth
        self.min_samples_leaf = min_samples_leaf
        self.X_binned = X_binned
        self.min_gain_to_split = min_gain_to_split
        self.shrinkage = shrinkage
        self.splittable_nodes = []
        self.finalized_leaves = []
        self.total_find_split_time = 0.0
        self.total_compute_hist_time = 0.0
        self.total_apply_split_time = 0.0
        self._intilialize_root(gradients, hessians, hessians_are_constant)
        self.n_nodes = 1

    def _validate_parameters(self, X_binned, max_leaf_nodes, max_depth,
        min_samples_leaf, min_gain_to_split, l2_regularization,
        min_hessian_to_split):
        """Validate parameters passed to __init__.

        Also validate parameters passed to splitter.
        """
        if X_binned.dtype != np.uint8:
            raise NotImplementedError('X_binned must be of type uint8.')
        if not X_binned.flags.f_contiguous:
            raise ValueError(
                'X_binned should be passed as Fortran contiguous array for maximum efficiency.'
                )
        if max_leaf_nodes is not None and max_leaf_nodes <= 1:
            raise ValueError('max_leaf_nodes={} should not be smaller than 2'
                .format(max_leaf_nodes))
        if max_depth is not None and max_depth <= 1:
            raise ValueError('max_depth={} should not be smaller than 2'.
                format(max_depth))
        if min_samples_leaf < 1:
            raise ValueError('min_samples_leaf={} should not be smaller than 1'
                .format(min_samples_leaf))
        if min_gain_to_split < 0:
            raise ValueError('min_gain_to_split={} must be positive.'.
                format(min_gain_to_split))
        if l2_regularization < 0:
            raise ValueError('l2_regularization={} must be positive.'.
                format(l2_regularization))
        if min_hessian_to_split < 0:
            raise ValueError('min_hessian_to_split={} must be positive.'.
                format(min_hessian_to_split))

    def grow(self):
        """Grow the tree, from root to leaves."""
        while self.splittable_nodes:
            self.split_next()

    def _intilialize_root(self, gradients, hessians, hessians_are_constant):
        """Initialize root node and finalize it if needed."""
        n_samples = self.X_binned.shape[0]
        depth = 0
        sum_gradients = sum_parallel(gradients)
        if self.histogram_builder.hessians_are_constant:
            sum_hessians = hessians[0] * n_samples
        else:
            sum_hessians = sum_parallel(hessians)
        self.root = TreeNode(depth=depth, sample_indices=self.splitter.
            partition, sum_gradients=sum_gradients, sum_hessians=sum_hessians)
        self.root.partition_start = 0
        self.root.partition_stop = n_samples
        if self.root.n_samples < 2 * self.min_samples_leaf:
            self._finalize_leaf(self.root)
            return
        if sum_hessians < self.splitter.min_hessian_to_split:
            self._finalize_leaf(self.root)
            return
        self.root.histograms = self.histogram_builder.compute_histograms_brute(
            self.root.sample_indices)
        self._compute_best_split_and_push(self.root)

    def _compute_best_split_and_push(self, node):
        """Compute the best possible split (SplitInfo) of a given node.

        Also push it in the heap of splittable nodes if gain isn't zero.
        The gain of a node is 0 if either all the leaves are pure
        (best gain = 0), or if no split would satisfy the constraints,
        (min_hessians_to_split, min_gain_to_split, min_samples_leaf)
        """
        node.split_info = self.splitter.find_node_split(node.sample_indices,
            node.histograms, node.sum_gradients, node.sum_hessians)
        if node.split_info.gain <= 0:
            self._finalize_leaf(node)
        else:
            heappush(self.splittable_nodes, node)

    def split_next(self):
        """Split the node with highest potential gain.

        Returns
        -------
        left : TreeNode
            The resulting left child.
        right : TreeNode
            The resulting right child.
        """
        node = heappop(self.splittable_nodes)
        tic = time()
        sample_indices_left, sample_indices_right, right_child_pos = (self.
            splitter.split_indices(node.split_info, node.sample_indices))
        self.total_apply_split_time += time() - tic
        depth = node.depth + 1
        n_leaf_nodes = len(self.finalized_leaves) + len(self.splittable_nodes)
        n_leaf_nodes += 2
        left_child_node = TreeNode(depth, sample_indices_left, node.
            split_info.sum_gradient_left, node.split_info.sum_hessian_left,
            parent=node)
        right_child_node = TreeNode(depth, sample_indices_right, node.
            split_info.sum_gradient_right, node.split_info.
            sum_hessian_right, parent=node)
        left_child_node.sibling = right_child_node
        right_child_node.sibling = left_child_node
        node.right_child = right_child_node
        node.left_child = left_child_node
        left_child_node.partition_start = node.partition_start
        left_child_node.partition_stop = node.partition_start + right_child_pos
        right_child_node.partition_start = left_child_node.partition_stop
        right_child_node.partition_stop = node.partition_stop
        self.n_nodes += 2
        if self.max_depth is not None and depth == self.max_depth:
            self._finalize_leaf(left_child_node)
            self._finalize_leaf(right_child_node)
            return left_child_node, right_child_node
        if (self.max_leaf_nodes is not None and n_leaf_nodes == self.
            max_leaf_nodes):
            self._finalize_leaf(left_child_node)
            self._finalize_leaf(right_child_node)
            self._finalize_splittable_nodes()
            return left_child_node, right_child_node
        if left_child_node.n_samples < self.min_samples_leaf * 2:
            self._finalize_leaf(left_child_node)
        if right_child_node.n_samples < self.min_samples_leaf * 2:
            self._finalize_leaf(right_child_node)
        should_split_left = left_child_node.value is None
        should_split_right = right_child_node.value is None
        if should_split_left or should_split_right:
            n_samples_left = left_child_node.sample_indices.shape[0]
            n_samples_right = right_child_node.sample_indices.shape[0]
            if n_samples_left < n_samples_right:
                smallest_child = left_child_node
                largest_child = right_child_node
            else:
                smallest_child = right_child_node
                largest_child = left_child_node
            tic = time()
            smallest_child.histograms = (self.histogram_builder.
                compute_histograms_brute(smallest_child.sample_indices))
            largest_child.histograms = (self.histogram_builder.
                compute_histograms_subtraction(node.histograms,
                smallest_child.histograms))
            self.total_compute_hist_time += time() - tic
            tic = time()
            if should_split_left:
                self._compute_best_split_and_push(left_child_node)
            if should_split_right:
                self._compute_best_split_and_push(right_child_node)
            self.total_find_split_time += time() - tic
        return left_child_node, right_child_node

    def _finalize_leaf(self, node):
        """Compute the prediction value that minimizes the objective function.

        This sets the node.value attribute (node is a leaf iff node.value is
        not None).

        See Equation 5 of:
        XGBoost: A Scalable Tree Boosting System, T. Chen, C. Guestrin, 2016
        https://arxiv.org/abs/1603.02754
        """
        node.value = -self.shrinkage * node.sum_gradients / (node.
            sum_hessians + self.splitter.l2_regularization)
        self.finalized_leaves.append(node)

    def _finalize_splittable_nodes(self):
        """Transform all splittable nodes into leaves.

        Used when some constraint is met e.g. maximum number of leaves or
        maximum depth."""
        while len(self.splittable_nodes) > 0:
            node = self.splittable_nodes.pop()
            self._finalize_leaf(node)

    def make_predictor(self, bin_thresholds=None):
        """Make a TreePredictor object out of the current tree.

        Parameters
        ----------
        bin_thresholds : array-like of floats, optional (default=None)
            The actual thresholds values of each bin.

        Returns
        -------
        A TreePredictor object.
        """
        predictor_nodes = np.zeros(self.n_nodes, dtype=PREDICTOR_RECORD_DTYPE)
        _fill_predictor_node_array(predictor_nodes, self.root,
            bin_thresholds=bin_thresholds)
        return TreePredictor(predictor_nodes)


<mask token>

<mask token>


class TreeNode:
    <mask token>
    split_info = None
    left_child = None
    right_child = None
    value = None
    histograms = None
    sibling = None
    parent = None
    partition_start = 0
    partition_stop = 0

    def __init__(self, depth, sample_indices, sum_gradients, sum_hessians,
        parent=None):
        self.depth = depth
        self.sample_indices = sample_indices
        self.n_samples = sample_indices.shape[0]
        self.sum_gradients = sum_gradients
        self.sum_hessians = sum_hessians
        self.parent = parent

    def __lt__(self, other_node):
        """Comparison for priority queue.

        Nodes with high gain are higher priority than nodes with low gain.

        heapq.heappush only need the '<' operator.
        heapq.heappop take the smallest item first (smaller is higher
        priority).

        Parameters
        ----------
        other_node : TreeNode
            The node to compare with.
        """
        return self.split_info.gain > other_node.split_info.gain


class TreeGrower:
    """Tree grower class used to build a tree.

    The tree is fitted to predict the values of a Newton-Raphson step. The
    splits are considered in a best-first fashion, and the quality of a
    split is defined in splitting._split_gain.

    Parameters
    ----------
    X_binned : ndarray of int, shape (n_samples, n_features)
        The binned input samples. Must be Fortran-aligned.
    gradients : ndarray, shape (n_samples,)
        The gradients of each training sample. Those are the gradients of the
        loss w.r.t the predictions, evaluated at iteration ``i - 1``.
    hessians : ndarray, shape (n_samples,)
        The hessians of each training sample. Those are the hessians of the
        loss w.r.t the predictions, evaluated at iteration ``i - 1``.
    max_leaf_nodes : int or None, optional (default=None)
        The maximum number of leaves for each tree. If None, there is no
        maximum limit.
    max_depth : int or None, optional (default=None)
        The maximum depth of each tree. The depth of a tree is the number of
        nodes to go from the root to the deepest leaf.
    min_samples_leaf : int, optional (default=20)
        The minimum number of samples per leaf.
    min_gain_to_split : float, optional (default=0.)
        The minimum gain needed to split a node. Splits with lower gain will
        be ignored.
    max_bins : int, optional (default=256)
        The maximum number of bins. Used to define the shape of the
        histograms.
    actual_n_bins : ndarray of int or int, optional (default=None)
        The actual number of bins needed for each feature, which is lower or
        equal to ``max_bins``. If it's an int, all features are considered to
        have the same number of bins. If None, all features are considered to
        have ``max_bins`` bins.
    l2_regularization : float, optional (default=0)
        The L2 regularization parameter.
    min_hessian_to_split : float, optional (default=1e-3)
        The minimum sum of hessians needed in each node. Splits that result in
        at least one child having a sum of hessians less than
        ``min_hessian_to_split`` are discarded.
    shrinkage : float, optional (default=1)
        The shrinkage parameter to apply to the leaves values, also known as
        learning rate.
    """

    def __init__(self, X_binned, gradients, hessians, max_leaf_nodes=None,
        max_depth=None, min_samples_leaf=20, min_gain_to_split=0.0,
        max_bins=256, actual_n_bins=None, l2_regularization=0.0,
        min_hessian_to_split=0.001, shrinkage=1.0):
        self._validate_parameters(X_binned, max_leaf_nodes, max_depth,
            min_samples_leaf, min_gain_to_split, l2_regularization,
            min_hessian_to_split)
        if actual_n_bins is None:
            actual_n_bins = max_bins
        if isinstance(actual_n_bins, numbers.Integral):
            actual_n_bins = np.array([actual_n_bins] * X_binned.shape[1],
                dtype=np.uint32)
        else:
            actual_n_bins = np.asarray(actual_n_bins, dtype=np.uint32)
        hessians_are_constant = hessians.shape[0] == 1
        self.histogram_builder = HistogramBuilder(X_binned, max_bins,
            gradients, hessians, hessians_are_constant)
        self.splitter = Splitter(X_binned, max_bins, actual_n_bins,
            l2_regularization, min_hessian_to_split, min_samples_leaf,
            min_gain_to_split, hessians_are_constant)
        self.max_leaf_nodes = max_leaf_nodes
        self.max_bins = max_bins
        self.n_features = X_binned.shape[1]
        self.max_depth = max_depth
        self.min_samples_leaf = min_samples_leaf
        self.X_binned = X_binned
        self.min_gain_to_split = min_gain_to_split
        self.shrinkage = shrinkage
        self.splittable_nodes = []
        self.finalized_leaves = []
        self.total_find_split_time = 0.0
        self.total_compute_hist_time = 0.0
        self.total_apply_split_time = 0.0
        self._intilialize_root(gradients, hessians, hessians_are_constant)
        self.n_nodes = 1

    def _validate_parameters(self, X_binned, max_leaf_nodes, max_depth,
        min_samples_leaf, min_gain_to_split, l2_regularization,
        min_hessian_to_split):
        """Validate parameters passed to __init__.

        Also validate parameters passed to splitter.
        """
        if X_binned.dtype != np.uint8:
            raise NotImplementedError('X_binned must be of type uint8.')
        if not X_binned.flags.f_contiguous:
            raise ValueError(
                'X_binned should be passed as Fortran contiguous array for maximum efficiency.'
                )
        if max_leaf_nodes is not None and max_leaf_nodes <= 1:
            raise ValueError('max_leaf_nodes={} should not be smaller than 2'
                .format(max_leaf_nodes))
        if max_depth is not None and max_depth <= 1:
            raise ValueError('max_depth={} should not be smaller than 2'.
                format(max_depth))
        if min_samples_leaf < 1:
            raise ValueError('min_samples_leaf={} should not be smaller than 1'
                .format(min_samples_leaf))
        if min_gain_to_split < 0:
            raise ValueError('min_gain_to_split={} must be positive.'.
                format(min_gain_to_split))
        if l2_regularization < 0:
            raise ValueError('l2_regularization={} must be positive.'.
                format(l2_regularization))
        if min_hessian_to_split < 0:
            raise ValueError('min_hessian_to_split={} must be positive.'.
                format(min_hessian_to_split))

    def grow(self):
        """Grow the tree, from root to leaves."""
        while self.splittable_nodes:
            self.split_next()

    def _intilialize_root(self, gradients, hessians, hessians_are_constant):
        """Initialize root node and finalize it if needed."""
        n_samples = self.X_binned.shape[0]
        depth = 0
        sum_gradients = sum_parallel(gradients)
        if self.histogram_builder.hessians_are_constant:
            sum_hessians = hessians[0] * n_samples
        else:
            sum_hessians = sum_parallel(hessians)
        self.root = TreeNode(depth=depth, sample_indices=self.splitter.
            partition, sum_gradients=sum_gradients, sum_hessians=sum_hessians)
        self.root.partition_start = 0
        self.root.partition_stop = n_samples
        if self.root.n_samples < 2 * self.min_samples_leaf:
            self._finalize_leaf(self.root)
            return
        if sum_hessians < self.splitter.min_hessian_to_split:
            self._finalize_leaf(self.root)
            return
        self.root.histograms = self.histogram_builder.compute_histograms_brute(
            self.root.sample_indices)
        self._compute_best_split_and_push(self.root)

    def _compute_best_split_and_push(self, node):
        """Compute the best possible split (SplitInfo) of a given node.

        Also push it in the heap of splittable nodes if gain isn't zero.
        The gain of a node is 0 if either all the leaves are pure
        (best gain = 0), or if no split would satisfy the constraints,
        (min_hessians_to_split, min_gain_to_split, min_samples_leaf)
        """
        node.split_info = self.splitter.find_node_split(node.sample_indices,
            node.histograms, node.sum_gradients, node.sum_hessians)
        if node.split_info.gain <= 0:
            self._finalize_leaf(node)
        else:
            heappush(self.splittable_nodes, node)

    def split_next(self):
        """Split the node with highest potential gain.

        Returns
        -------
        left : TreeNode
            The resulting left child.
        right : TreeNode
            The resulting right child.
        """
        node = heappop(self.splittable_nodes)
        tic = time()
        sample_indices_left, sample_indices_right, right_child_pos = (self.
            splitter.split_indices(node.split_info, node.sample_indices))
        self.total_apply_split_time += time() - tic
        depth = node.depth + 1
        n_leaf_nodes = len(self.finalized_leaves) + len(self.splittable_nodes)
        n_leaf_nodes += 2
        left_child_node = TreeNode(depth, sample_indices_left, node.
            split_info.sum_gradient_left, node.split_info.sum_hessian_left,
            parent=node)
        right_child_node = TreeNode(depth, sample_indices_right, node.
            split_info.sum_gradient_right, node.split_info.
            sum_hessian_right, parent=node)
        left_child_node.sibling = right_child_node
        right_child_node.sibling = left_child_node
        node.right_child = right_child_node
        node.left_child = left_child_node
        left_child_node.partition_start = node.partition_start
        left_child_node.partition_stop = node.partition_start + right_child_pos
        right_child_node.partition_start = left_child_node.partition_stop
        right_child_node.partition_stop = node.partition_stop
        self.n_nodes += 2
        if self.max_depth is not None and depth == self.max_depth:
            self._finalize_leaf(left_child_node)
            self._finalize_leaf(right_child_node)
            return left_child_node, right_child_node
        if (self.max_leaf_nodes is not None and n_leaf_nodes == self.
            max_leaf_nodes):
            self._finalize_leaf(left_child_node)
            self._finalize_leaf(right_child_node)
            self._finalize_splittable_nodes()
            return left_child_node, right_child_node
        if left_child_node.n_samples < self.min_samples_leaf * 2:
            self._finalize_leaf(left_child_node)
        if right_child_node.n_samples < self.min_samples_leaf * 2:
            self._finalize_leaf(right_child_node)
        should_split_left = left_child_node.value is None
        should_split_right = right_child_node.value is None
        if should_split_left or should_split_right:
            n_samples_left = left_child_node.sample_indices.shape[0]
            n_samples_right = right_child_node.sample_indices.shape[0]
            if n_samples_left < n_samples_right:
                smallest_child = left_child_node
                largest_child = right_child_node
            else:
                smallest_child = right_child_node
                largest_child = left_child_node
            tic = time()
            smallest_child.histograms = (self.histogram_builder.
                compute_histograms_brute(smallest_child.sample_indices))
            largest_child.histograms = (self.histogram_builder.
                compute_histograms_subtraction(node.histograms,
                smallest_child.histograms))
            self.total_compute_hist_time += time() - tic
            tic = time()
            if should_split_left:
                self._compute_best_split_and_push(left_child_node)
            if should_split_right:
                self._compute_best_split_and_push(right_child_node)
            self.total_find_split_time += time() - tic
        return left_child_node, right_child_node

    def _finalize_leaf(self, node):
        """Compute the prediction value that minimizes the objective function.

        This sets the node.value attribute (node is a leaf iff node.value is
        not None).

        See Equation 5 of:
        XGBoost: A Scalable Tree Boosting System, T. Chen, C. Guestrin, 2016
        https://arxiv.org/abs/1603.02754
        """
        node.value = -self.shrinkage * node.sum_gradients / (node.
            sum_hessians + self.splitter.l2_regularization)
        self.finalized_leaves.append(node)

    def _finalize_splittable_nodes(self):
        """Transform all splittable nodes into leaves.

        Used when some constraint is met e.g. maximum number of leaves or
        maximum depth."""
        while len(self.splittable_nodes) > 0:
            node = self.splittable_nodes.pop()
            self._finalize_leaf(node)

    def make_predictor(self, bin_thresholds=None):
        """Make a TreePredictor object out of the current tree.

        Parameters
        ----------
        bin_thresholds : array-like of floats, optional (default=None)
            The actual thresholds values of each bin.

        Returns
        -------
        A TreePredictor object.
        """
        predictor_nodes = np.zeros(self.n_nodes, dtype=PREDICTOR_RECORD_DTYPE)
        _fill_predictor_node_array(predictor_nodes, self.root,
            bin_thresholds=bin_thresholds)
        return TreePredictor(predictor_nodes)


<mask token>

"""
This module contains the TreeGrower class.

TreeGrowee builds a regression tree fitting a Newton-Raphson step, based on
the gradients and hessians of the training data.
"""
# Author: Nicolas Hug

from heapq import heappush, heappop
import numpy as np
from timeit import default_timer as time
import numbers

from .splitting import Splitter
from .histogram import HistogramBuilder
from .predictor import TreePredictor, PREDICTOR_RECORD_DTYPE
from .utils import sum_parallel


class TreeNode:
    """Tree Node class used in TreeGrower.

    This isn't used for prediction purposes, only for training (see
    TreePredictor).

    Parameters
    ----------
    depth : int
        The depth of the node, i.e. its distance from the root.
    sample_indices : ndarray of unsigned int, shape (n_samples_at_node,)
        The indices of the samples at the node.
    sum_gradients : float
        The sum of the gradients of the samples at the node.
    sum_hessians : float
        The sum of the hessians of the samples at the node.
    parent : TreeNode or None, optional (default=None)
        The parent of the node. None for root.

    Attributes
    ----------
    depth : int
        The depth of the node, i.e. its distance from the root.
    sample_indices : ndarray of unsigned int, shape (n_samples_at_node,)
        The indices of the samples at the node.
    sum_gradients : float
        The sum of the gradients of the samples at the node.
    sum_hessians : float
        The sum of the hessians of the samples at the node.
    parent : TreeNode or None
        The parent of the node. None for root.
    split_info : SplitInfo or None
        The result of the split evaluation.
    left_child : TreeNode or None
        The left child of the node. None for leaves.
    right_child : TreeNode or None
        The right child of the node. None for leaves.
    value : float or None
        The value of the leaf, as computed in finalize_leaf(). None for
        non-leaf nodes.
    partition_start : int
        start position of the node's sample_indices in splitter.partition.
    partition_stop : int
        stop position of the node's sample_indices in splitter.partition.
    """

    split_info = None
    left_child = None
    right_child = None
    value = None
    histograms = None
    sibling = None
    parent = None

    # start and stop indices of the node in the splitter.partition
    # array. Concretely,
    # self.sample_indices = view(self.splitter.partition[start:stop])
    # Please see the comments about splitter.partition and
    # splitter.split_indices for more info about this design.
    # These 2 attributes are only used in _update_raw_prediction, because we
    # need to iterate over the leaves and I don't know how to efficiently
    # store the sample_indices views because they're all of different sizes.
    partition_start = 0
    partition_stop = 0

    def __init__(self, depth, sample_indices, sum_gradients,
                 sum_hessians, parent=None):
        self.depth = depth
        self.sample_indices = sample_indices
        self.n_samples = sample_indices.shape[0]
        self.sum_gradients = sum_gradients
        self.sum_hessians = sum_hessians
        self.parent = parent

    def __lt__(self, other_node):
        """Comparison for priority queue.

        Nodes with high gain are higher priority than nodes with low gain.

        heapq.heappush only need the '<' operator.
        heapq.heappop take the smallest item first (smaller is higher
        priority).

        Parameters
        ----------
        other_node : TreeNode
            The node to compare with.
        """
        return self.split_info.gain > other_node.split_info.gain


class TreeGrower:
    """Tree grower class used to build a tree.

    The tree is fitted to predict the values of a Newton-Raphson step. The
    splits are considered in a best-first fashion, and the quality of a
    split is defined in splitting._split_gain.

    Parameters
    ----------
    X_binned : ndarray of int, shape (n_samples, n_features)
        The binned input samples. Must be Fortran-aligned.
    gradients : ndarray, shape (n_samples,)
        The gradients of each training sample. Those are the gradients of the
        loss w.r.t the predictions, evaluated at iteration ``i - 1``.
    hessians : ndarray, shape (n_samples,)
        The hessians of each training sample. Those are the hessians of the
        loss w.r.t the predictions, evaluated at iteration ``i - 1``.
    max_leaf_nodes : int or None, optional (default=None)
        The maximum number of leaves for each tree. If None, there is no
        maximum limit.
    max_depth : int or None, optional (default=None)
        The maximum depth of each tree. The depth of a tree is the number of
        nodes to go from the root to the deepest leaf.
    min_samples_leaf : int, optional (default=20)
        The minimum number of samples per leaf.
    min_gain_to_split : float, optional (default=0.)
        The minimum gain needed to split a node. Splits with lower gain will
        be ignored.
    max_bins : int, optional (default=256)
        The maximum number of bins. Used to define the shape of the
        histograms.
    actual_n_bins : ndarray of int or int, optional (default=None)
        The actual number of bins needed for each feature, which is lower or
        equal to ``max_bins``. If it's an int, all features are considered to
        have the same number of bins. If None, all features are considered to
        have ``max_bins`` bins.
    l2_regularization : float, optional (default=0)
        The L2 regularization parameter.
    min_hessian_to_split : float, optional (default=1e-3)
        The minimum sum of hessians needed in each node. Splits that result in
        at least one child having a sum of hessians less than
        ``min_hessian_to_split`` are discarded.
    shrinkage : float, optional (default=1)
        The shrinkage parameter to apply to the leaves values, also known as
        learning rate.
    """
    def __init__(self, X_binned, gradients, hessians, max_leaf_nodes=None,
                 max_depth=None, min_samples_leaf=20, min_gain_to_split=0.,
                 max_bins=256, actual_n_bins=None, l2_regularization=0.,
                 min_hessian_to_split=1e-3, shrinkage=1.):

        self._validate_parameters(X_binned, max_leaf_nodes, max_depth,
                                  min_samples_leaf, min_gain_to_split,
                                  l2_regularization, min_hessian_to_split)

        if actual_n_bins is None:
            actual_n_bins = max_bins

        if isinstance(actual_n_bins, numbers.Integral):
            actual_n_bins = np.array(
                [actual_n_bins] * X_binned.shape[1],
                dtype=np.uint32)
        else:
            actual_n_bins = np.asarray(actual_n_bins, dtype=np.uint32)

        hessians_are_constant = hessians.shape[0] == 1
        self.histogram_builder = HistogramBuilder(
            X_binned, max_bins, gradients, hessians, hessians_are_constant)
        self.splitter = Splitter(
            X_binned, max_bins, actual_n_bins, l2_regularization,
            min_hessian_to_split, min_samples_leaf, min_gain_to_split,
            hessians_are_constant)
        self.max_leaf_nodes = max_leaf_nodes
        self.max_bins = max_bins
        self.n_features = X_binned.shape[1]
        self.max_depth = max_depth
        self.min_samples_leaf = min_samples_leaf
        self.X_binned = X_binned
        self.min_gain_to_split = min_gain_to_split
        self.shrinkage = shrinkage
        self.splittable_nodes = []
        self.finalized_leaves = []
        self.total_find_split_time = 0.  # time spent finding the best splits
        self.total_compute_hist_time = 0.  # time spent computing histograms
        self.total_apply_split_time = 0.  # time spent splitting nodes
        self._intilialize_root(gradients, hessians, hessians_are_constant)
        self.n_nodes = 1

    def _validate_parameters(self, X_binned, max_leaf_nodes, max_depth,
                             min_samples_leaf, min_gain_to_split,
                             l2_regularization, min_hessian_to_split):
        """Validate parameters passed to __init__.

        Also validate parameters passed to splitter.
        """
        if X_binned.dtype != np.uint8:
            raise NotImplementedError(
                "X_binned must be of type uint8.")
        if not X_binned.flags.f_contiguous:
            raise ValueError(
                "X_binned should be passed as Fortran contiguous "
                "array for maximum efficiency.")
        if max_leaf_nodes is not None and max_leaf_nodes <= 1:
            raise ValueError('max_leaf_nodes={} should not be'
                             ' smaller than 2'.format(max_leaf_nodes))
        if max_depth is not None and max_depth <= 1:
            raise ValueError('max_depth={} should not be'
                             ' smaller than 2'.format(max_depth))
        if min_samples_leaf < 1:
            raise ValueError('min_samples_leaf={} should '
                             'not be smaller than 1'.format(min_samples_leaf))
        if min_gain_to_split < 0:
            raise ValueError('min_gain_to_split={} '
                             'must be positive.'.format(min_gain_to_split))
        if l2_regularization < 0:
            raise ValueError('l2_regularization={} must be '
                             'positive.'.format(l2_regularization))
        if min_hessian_to_split < 0:
            raise ValueError('min_hessian_to_split={} '
                             'must be positive.'.format(min_hessian_to_split))

    def grow(self):
        """Grow the tree, from root to leaves."""
        while self.splittable_nodes:
            self.split_next()

    def _intilialize_root(self, gradients, hessians, hessians_are_constant):
        """Initialize root node and finalize it if needed."""
        n_samples = self.X_binned.shape[0]
        depth = 0
        sum_gradients = sum_parallel(gradients)
        if self.histogram_builder.hessians_are_constant:
            sum_hessians = hessians[0] * n_samples
        else:
            sum_hessians = sum_parallel(hessians)
        self.root = TreeNode(
            depth=depth,
            sample_indices=self.splitter.partition,
            sum_gradients=sum_gradients,
            sum_hessians=sum_hessians
        )

        self.root.partition_start = 0
        self.root.partition_stop = n_samples

        if self.root.n_samples < 2 * self.min_samples_leaf:
            # Do not even bother computing any splitting statistics.
            self._finalize_leaf(self.root)
            return
        if sum_hessians < self.splitter.min_hessian_to_split:
            self._finalize_leaf(self.root)
            return

        self.root.histograms = self.histogram_builder.compute_histograms_brute(
            self.root.sample_indices)
        self._compute_best_split_and_push(self.root)

    def _compute_best_split_and_push(self, node):
        """Compute the best possible split (SplitInfo) of a given node.

        Also push it in the heap of splittable nodes if gain isn't zero.
        The gain of a node is 0 if either all the leaves are pure
        (best gain = 0), or if no split would satisfy the constraints,
        (min_hessians_to_split, min_gain_to_split, min_samples_leaf)
        """

        node.split_info = self.splitter.find_node_split(
            node.sample_indices, node.histograms, node.sum_gradients,
            node.sum_hessians)

        if node.split_info.gain <= 0:  # no valid split
            self._finalize_leaf(node)
        else:
            heappush(self.splittable_nodes, node)

    def split_next(self):
        """Split the node with highest potential gain.

        Returns
        -------
        left : TreeNode
            The resulting left child.
        right : TreeNode
            The resulting right child.
        """
        # Consider the node with the highest loss reduction (a.k.a. gain)
        node = heappop(self.splittable_nodes)

        tic = time()
        (sample_indices_left,
         sample_indices_right,
         right_child_pos) = self.splitter.split_indices(node.split_info,
                                                        node.sample_indices)
        self.total_apply_split_time += time() - tic

        depth = node.depth + 1
        n_leaf_nodes = len(self.finalized_leaves) + len(self.splittable_nodes)
        n_leaf_nodes += 2

        left_child_node = TreeNode(depth,
                                   sample_indices_left,
                                   node.split_info.sum_gradient_left,
                                   node.split_info.sum_hessian_left,
                                   parent=node)
        right_child_node = TreeNode(depth,
                                    sample_indices_right,
                                    node.split_info.sum_gradient_right,
                                    node.split_info.sum_hessian_right,
                                    parent=node)
        left_child_node.sibling = right_child_node
        right_child_node.sibling = left_child_node
        node.right_child = right_child_node
        node.left_child = left_child_node

        # set start and stop indices
        left_child_node.partition_start = node.partition_start
        left_child_node.partition_stop = node.partition_start + right_child_pos
        right_child_node.partition_start = left_child_node.partition_stop
        right_child_node.partition_stop = node.partition_stop

        self.n_nodes += 2

        if self.max_depth is not None and depth == self.max_depth:
            self._finalize_leaf(left_child_node)
            self._finalize_leaf(right_child_node)
            return left_child_node, right_child_node

        if (self.max_leaf_nodes is not None
                and n_leaf_nodes == self.max_leaf_nodes):
            self._finalize_leaf(left_child_node)
            self._finalize_leaf(right_child_node)
            self._finalize_splittable_nodes()
            return left_child_node, right_child_node

        if left_child_node.n_samples < self.min_samples_leaf * 2:
            self._finalize_leaf(left_child_node)
        if right_child_node.n_samples < self.min_samples_leaf * 2:
            self._finalize_leaf(right_child_node)

        # Compute histograms of childs, and compute their best possible split
        # (if needed)
        should_split_left = left_child_node.value is None  # node isn't a leaf
        should_split_right = right_child_node.value is None
        if should_split_left or should_split_right:

            # We will compute the histograms of both nodes even if one of them
            # is a leaf, since computing the second histogram is very cheap
            # (using histogram subtraction).
            n_samples_left = left_child_node.sample_indices.shape[0]
            n_samples_right = right_child_node.sample_indices.shape[0]
            if n_samples_left < n_samples_right:
                smallest_child = left_child_node
                largest_child = right_child_node
            else:
                smallest_child = right_child_node
                largest_child = left_child_node

            # We use the brute O(n_samples) method on the child that has the
            # smallest number of samples, and the subtraction trick O(n_bins)
            # on the other one.
            tic = time()
            smallest_child.histograms = \
                self.histogram_builder.compute_histograms_brute(
                    smallest_child.sample_indices)
            largest_child.histograms = \
                self.histogram_builder.compute_histograms_subtraction(
                    node.histograms, smallest_child.histograms)
            self.total_compute_hist_time += time() - tic

            tic = time()
            if should_split_left:
                self._compute_best_split_and_push(left_child_node)
            if should_split_right:
                self._compute_best_split_and_push(right_child_node)
            self.total_find_split_time += time() - tic

        return left_child_node, right_child_node

    def _finalize_leaf(self, node):
        """Compute the prediction value that minimizes the objective function.

        This sets the node.value attribute (node is a leaf iff node.value is
        not None).

        See Equation 5 of:
        XGBoost: A Scalable Tree Boosting System, T. Chen, C. Guestrin, 2016
        https://arxiv.org/abs/1603.02754
        """
        node.value = -self.shrinkage * node.sum_gradients / (
            node.sum_hessians + self.splitter.l2_regularization)
        self.finalized_leaves.append(node)

    def _finalize_splittable_nodes(self):
        """Transform all splittable nodes into leaves.

        Used when some constraint is met e.g. maximum number of leaves or
        maximum depth."""
        while len(self.splittable_nodes) > 0:
            node = self.splittable_nodes.pop()
            self._finalize_leaf(node)

    def make_predictor(self, bin_thresholds=None):
        """Make a TreePredictor object out of the current tree.

        Parameters
        ----------
        bin_thresholds : array-like of floats, optional (default=None)
            The actual thresholds values of each bin.

        Returns
        -------
        A TreePredictor object.
        """
        predictor_nodes = np.zeros(self.n_nodes, dtype=PREDICTOR_RECORD_DTYPE)
        _fill_predictor_node_array(predictor_nodes, self.root,
                                   bin_thresholds=bin_thresholds)
        return TreePredictor(predictor_nodes)


def _fill_predictor_node_array(predictor_nodes, grower_node,
                               bin_thresholds, next_free_idx=0):
    """Helper used in make_predictor to set the TreePredictor fields."""
    node = predictor_nodes[next_free_idx]
    node['count'] = grower_node.n_samples
    node['depth'] = grower_node.depth
    if grower_node.split_info is not None:
        node['gain'] = grower_node.split_info.gain
    else:
        node['gain'] = -1

    if grower_node.value is not None:
        # Leaf node
        node['is_leaf'] = True
        node['value'] = grower_node.value
        return next_free_idx + 1
    else:
        # Decision node
        split_info = grower_node.split_info
        feature_idx, bin_idx = split_info.feature_idx, split_info.bin_idx
        node['feature_idx'] = feature_idx
        node['bin_threshold'] = bin_idx
        if bin_thresholds is not None:
            threshold = bin_thresholds[feature_idx][bin_idx]
            node['threshold'] = threshold
        next_free_idx += 1

        node['left'] = next_free_idx
        next_free_idx = _fill_predictor_node_array(
            predictor_nodes, grower_node.left_child,
            bin_thresholds=bin_thresholds, next_free_idx=next_free_idx)

        node['right'] = next_free_idx
        return _fill_predictor_node_array(
            predictor_nodes, grower_node.right_child,
            bin_thresholds=bin_thresholds, next_free_idx=next_free_idx)
