from collections import OrderedDict

import abc
import uuid
import warnings
from contextlib import contextmanager

import numpy as np
import pandas as pd

from fast_histogram import histogram1d, histogram2d

from glue.core.message import (DataUpdateMessage, DataRemoveComponentMessage,
                               DataAddComponentMessage, NumericalDataChangedMessage,
                               SubsetCreateMessage, ComponentsChangedMessage,
                               ComponentReplacedMessage, DataReorderComponentMessage,
                               ExternallyDerivableComponentsChangedMessage,
                               PixelAlignedDataChangedMessage)
from glue.core.decorators import clear_cache
from glue.core.util import split_component_view
from glue.core.hub import Hub
from glue.core.subset import Subset, SubsetState, SliceSubsetState
from glue.core.component_id import ComponentIDList
from glue.core.component_link import ComponentLink, CoordinateComponentLink
from glue.core.exceptions import IncompatibleAttribute
from glue.core.visual import VisualAttributes
from glue.core.contracts import contract
from glue.core.joins import get_mask_with_key_joins
from glue.config import settings, data_translator, subset_state_translator
from glue.utils import (compute_statistic, unbroadcast, iterate_chunks,
                        datetime64_to_mpl, categorical_ndarray,
                        format_choices, random_views_for_dask_array,
                        random_indices_for_array)
from glue.core.coordinate_helpers import axis_label


# Note: leave all the following imports for component and component_id since
# they are here for backward-compatibility (the code used to live in this
# file)
from glue.core.component import Component, CoordinateComponent, DerivedComponent
from glue.core.component_id import ComponentID, ComponentIDDict, PixelComponentID

try:
    import dask.array as da
    DASK_INSTALLED = True
except ImportError:
    DASK_INSTALLED = False

__all__ = ['Data', 'BaseCartesianData', 'BaseData']


class BaseData(object, metaclass=abc.ABCMeta):
    """
    Base class for any glue data object which indicates which methods should be
    provided at a minimum.

    For now, subclasses of BaseData are not guaranteed to work in glue, and you
    should instead subclass BaseCartesianData.
    """

    def __init__(self):

        # Metadata
        self.meta = OrderedDict()

        # Subsets of the data
        self._subsets = []

        # Hub that the data is attached to
        self.hub = None

        self.style = VisualAttributes(parent=self)

        self.uuid = str(uuid.uuid4())

    @property
    def label(self):
        """
        The name of the dataset
        """
        raise NotImplementedError()

    @abc.abstractmethod
    def get_kind(self, cid):
        """
        Get the kind of data for a given component.

        Parameters
        ----------
        cid : :class:`~glue.core.component_id.ComponentID`
            The component ID to get the data kind for

        Returns
        -------
        kind : {'numerical', 'categorical', 'datetime'}
            The kind of data for the given component ID.
        """
        raise NotImplementedError()

    @abc.abstractproperty
    def main_components(self):
        raise NotImplementedError()

    @property
    def components(self):
        """
        A list of :class:`~glue.core.component_id.ComponentID` giving all
        available components in the data
        """
        return self.pixel_component_ids + self.world_component_ids + self.main_components

    @property
    def coordinate_components(self):
        """
        A list of :class:`~glue.core.component_id.ComponentID` giving all
        coordinate components in the data
        """
        return self.pixel_component_ids + self.world_component_ids

    @property
    def pixel_component_ids(self):
        """
        A list of :class:`~glue.core.component_id.ComponentID` giving all
        pixel coordinate components in the data
        """
        if not hasattr(self, '_pixel_component_ids'):
            self._pixel_component_ids = []
            for i in range(self.ndim):
                pid = PixelComponentID(i, 'Pixel Axis {0}'.format(i), parent=self)
                self._pixel_component_ids.append(pid)
        return self._pixel_component_ids

    @property
    def world_component_ids(self):
        """
        A list of :class:`~glue.core.component_id.ComponentID` giving all
        world coordinate components in the data
        """
        return []

    @property
    def derived_components(self):
        return []

    def find_component_id(self, label):
        """
        Find a component ID by name.

        This returns the associated ComponentID if label is found and unique,
        and `None` otherwise.
        """

        # This is a simple implementation that relies on .components and should
        # not need to be overriden

        if isinstance(label, ComponentID):
            return label

        matches = [cid for cid in self.components if cid.label == label]

        if len(matches) == 1:
            return matches[0]
        elif len(matches) > 1:
            return None

    @contract(hub=Hub)
    def register_to_hub(self, hub):
        """ Connect to a hub.

        This method usually doesn't have to be called directly, as
        DataCollections manage the registration of data objects
        """
        if not isinstance(hub, Hub):
            raise TypeError("input is not a Hub object: %s" % type(hub))
        self.hub = hub

    @property
    def data(self):
        return self

    @contract(subset='isinstance(Subset)|None',
              color='color|None',
              label='string|None',
              returns=Subset)
    def new_subset(self, subset=None, **kwargs):
        """
        Create a new subset, and attach to self.

        Parameters
        ----------
        subset : :class:`~glue.core.subset.Subset` or :class:`~glue.core.subset.SubsetState`, optional
            Reference subset or subset state. If provided, the new subset
            will copy the logic of this subset.

        Returns
        -------
        The new subset object

        Notes
        -----
        The preferred way for creating subsets is via
        :meth:`~glue.core.data_collection.DataCollection.new_subset_group`.
        Manually-instantiated subsets will **not** be represented properly by the UI.
        """
        nsub = len(self.subsets)
        kwargs.setdefault("color", settings.SUBSET_COLORS[nsub % len(settings.SUBSET_COLORS)])
        kwargs.setdefault("label", "%s.%i" % (self.label, nsub + 1))
        new_subset = Subset(self, **kwargs)
        if subset is not None:
            new_subset.subset_state = subset.subset_state.copy()

        self.add_subset(new_subset)
        return new_subset

    @contract(subset='inst($Subset, $SubsetState)')
    def add_subset(self, subset, label=None):
        """Assign a pre-existing subset to this data object.

        Parameters
        ----------
        subset : :class:`~glue.core.subset.Subset` or :class:`~glue.core.subset.SubsetState`
            The subset to be assigned. If this is a `~glue.core.subset.SubsetState`,
            it will be wrapped in a new Subset automatically

        Notes
        -----
        The preferred way for creating subsets is via
        :meth:`~glue.core.data_collection.DataCollection.new_subset_group`.
        Manually-instantiated subsets will **not** be represented properly by the UI.
        """

        if subset in self.subsets:
            return  # prevents infinite recursion
        if isinstance(subset, SubsetState):
            # auto-wrap state in subset
            state = subset
            subset = Subset(None)
            subset.subset_state = state
            if label:
                subset.label = label

        self._subsets.append(subset)

        if subset.data is not self:
            subset.do_broadcast(False)
            subset.data = self
            subset.label = subset.label  # hacky. disambiguates name if needed

        if self.hub is not None:
            msg = SubsetCreateMessage(subset)
            self.hub.broadcast(msg)

        subset.do_broadcast(True)

    @contract(attribute='string')
    def broadcast(self, attribute):
        """
        Send a :class:`~glue.core.message.DataUpdateMessage` to the hub

        Parameters
        ----------
        attribute : str
            Name of an attribute that has changed (or None).
        """
        if not self.hub:
            return
        msg = DataUpdateMessage(self, attribute=attribute)
        self.hub.broadcast(msg)

    @property
    def subsets(self):
        """
        Tuple of subsets attached to this dataset.
        """
        return tuple(self._subsets)

    def get_object(self, cls=None, **kwargs):
        """
        Get the dataset represented as a non-glue object, using the translation
        infrastructure.

        Parameters
        ----------
        cls : `type`, optional
            The class to use for representing the data object. If a non-glue
            data object was added to the glue data collection, it should
            automatically be returned using the same class as it was provided
            in, and this argument shouldn't be needed.
        """

        if cls is None:
            if hasattr(self, '_preferred_translation'):
                cls = self._preferred_translation
            else:
                raise ValueError('Specify the object class to use with cls= - supported '
                                 'classes are:' + format_choices(data_translator.supported_classes))

        handler, _ = data_translator.get_handler_for(cls)

        return handler.to_object(self, **kwargs)

    @property
    def _subset_labels(self):
        return [subset.label for subset in self.subsets]

    def get_subset_object(self, subset_id=None, cls=None, **kwargs):
        """
        Get a subset represented as a non-glue object, using the translation
        infrastructure.

        Parameters
        ----------
        subset_id : `str` or `int`, optional
            The name or index of the subset to retrieve.
        cls : `type`, optional
            The class to use for representing the data object. If a non-glue
            data object was added to the data collection, the subset should
            automatically be returned using the same class as it was provided
            in, and this argument shouldn't be needed.
        """

        if cls is None:
            if hasattr(self, '_preferred_translation'):
                cls = self._preferred_translation
            else:
                raise ValueError('Specify the object class to use with cls= - supported '
                                 'classes are:' + format_choices(data_translator.supported_classes))

        if len(self.subsets) == 0:
            raise ValueError("Dataset does not contain any subsets")
        elif subset_id is None:
            if len(self.subsets) == 1:
                subset = self.subsets[0]
            else:
                raise ValueError("Several subsets are present, specify which one to retrieve with subset_id= - valid options are:" + format_choices(self._subset_labels, index=True))
        elif isinstance(subset_id, str):
            matches = [subset for subset in self.subsets if subset.label == subset_id]
            if len(matches) == 0:
                raise ValueError("No subset found with the label '{0}'".format(subset_id))
            elif len(matches) > 1:
                raise ValueError("Several subsets were found with the label '{0}', use a numerical index instead".format(subset_id))
            else:
                subset = matches[0]
        else:
            subset = self.subsets[subset_id]

        handler, _ = data_translator.get_handler_for(cls)

        return handler.to_object(subset, **kwargs)

    def get_selection_definition(self, subset_id=None, format=None, **kwargs):
        """
        Get subset state represented as a non-glue object, using the
        translation infrastructure.

        Parameters
        ----------
        subset_id : `str` or `int`, optional
            The name or index of the subset to retrieve.
        format : `str`, optional
            The format to translate the subset state to.
        """

        if len(self.subsets) == 0:
            raise ValueError("Dataset does not contain any subsets")
        elif subset_id is None:
            if len(self.subsets) == 1:
                subset = self.subsets[0]
            else:
                raise ValueError("Several subsets are present, specify which one to retrieve with subset_id= - valid options are:" + format_choices(self._subset_labels, index=True))
        elif isinstance(subset_id, str):
            matches = [subset for subset in self.subsets if subset.label == subset_id]
            if len(matches) == 0:
                raise ValueError("No subset found with the label '{0}'".format(subset_id))
            elif len(matches) > 1:
                raise ValueError("Several subsets were found with the label '{0}', use a numerical index instead".format(subset_id))
            else:
                subset = matches[0]
        else:
            subset = self.subsets[subset_id]

        handler = subset_state_translator.get_handler_for(format)

        return handler.to_object(subset, **kwargs)


class BaseCartesianData(BaseData, metaclass=abc.ABCMeta):
    """
    Base class for any glue data object which indicates which methods should be
    provided at a minimum.

    The underlying data can be any kind of data (structured or unstructured) but
    it needs to expose an interface that looks like a regular n-dimensional
    cartesian dataset. This means exposing e.g. ``shape`` and ``ndim``, and
    means that get_data can expect ndarray slices. Non-regular datasets should
    therefore have the concept of 'virtual' pixel coordinates and should
    typically match the highest resolution a user might want to access the data
    at.
    """

    def __init__(self, coords=None):
        super(BaseCartesianData, self).__init__()
        self._coords = coords
        self._externally_derivable_components = OrderedDict()
        self._pixel_aligned_data = OrderedDict()

    @property
    def coords(self):
        """
        The coordinates object for the data.
        """
        return self._coords

    @abc.abstractproperty
    def shape(self):
        """
        The n-dimensional shape of the dataset, as a tuple.
        """
        raise NotImplementedError()

    @property
    def ndim(self):
        """
        The number of dimensions of the data, as an integer.
        """
        return len(self.shape)

    @property
    def size(self):
        """
        The size of the data (the product of the shape dimensions), as an integer.
        """
        return np.prod(self.shape)

    def get_data(self, cid, view=None):
        """
        Get the data values for a given component

        Parameters
        ----------
        cid : :class:`~glue.core.component_id.ComponentID`
            The component ID to get the data for.
        view : `slice`
            The 'view' on the data - anything that is considered a valid
            Numpy slice/index.
        """
        if cid in self.pixel_component_ids:
            shape = tuple(-1 if i == cid.axis else 1 for i in range(self.ndim))
            pix = np.arange(self.shape[cid.axis], dtype=float).reshape(shape)
            if view is None:
                return np.broadcast_to(pix, self.shape)
            else:
                return np.broadcast_to(pix, self.shape)[view]
        elif cid in self.world_component_ids:
            comp = self._world_components[cid]
        elif cid in self._externally_derivable_components:
            comp = self._externally_derivable_components[cid]
        else:
            raise IncompatibleAttribute(cid)

        # Note that above we have extracted Component objects from internal
        # properties - we don't actually expose Component objects in this class,
        # only in the Data class, but we use these components internally for
        # convenience.

        if view is None:
            return comp.data
        else:
            return comp[view]

    @abc.abstractmethod
    def get_mask(self, subset_state, view=None):
        """
        Get a boolean mask for a given subset state.

        Parameters
        ----------
        subset_state : :class:`~glue.core.subset.SubsetState`
            The subset state to use to compute the mask
        view : `slice`
            The 'view' on the mask - anything that is considered a valid
            Numpy slice/index.
        """
        raise NotImplementedError()

    @abc.abstractmethod
    def compute_statistic(self, statistic, cid, subset_state=None, axis=None,
                          finite=True, positive=False, percentile=None, view=None,
                          random_subset=None):
        """
        Compute a statistic for the data.

        Parameters
        ----------
        statistic : {'minimum', 'maximum', 'mean', 'median', 'sum', 'percentile'}
            The statistic to compute
        cid : :class:`~glue.core.component_id.ComponentID` or `str`
            The component ID to compute the statistic on - if given as a string
            this will be assumed to be for the component belonging to the dataset
            (not external links).
        subset_state : :class:`~glue.core.subset.SubsetState`, optional
            If specified, the statistic will only include the values that are in
            the subset specified by this subset state.
        axis : `int` or `tuple` of `int`, optional
            If specified, the axis/axes to compute the statistic over.
        finite : `bool`, optional
            Whether to include only finite values in the statistic. This should
            be `True` to ignore NaN/Inf values
        positive : `bool`, optional
            Whether to include only (strictly) positive values in the statistic.
            This is used for example when computing statistics of data shown in
            log space.
        percentile : `float`, optional
            If ``statistic`` is ``'percentile'``, the ``percentile`` argument
            should be given and specify the percentile to calculate in the
            range [0:100]
        random_subset : `int`, optional
            If specified, this should be an integer giving the number of values
            to use for the statistic. This can only be used if ``axis`` is `None`
        """
        raise NotImplementedError()

    @abc.abstractmethod
    def compute_histogram(self, cids, weights=None, range=None, bins=None,
                          log=None, subset_state=None, random_subset=None):
        """
        Compute an n-dimensional histogram with regularly spaced bins.

        Parameters
        ----------
        cids : `list` of `str` or :class:`~glue.core.component_id.ComponentID`
            Component IDs to compute the histogram over.
        weights : `str` or :class:`~glue.core.component_id.ComponentID`
            Component IDs to use for the histogram weights.
        range : `list` of `tuple`
            The ``(min, max)`` of the histogram range.
        bins : `list` of `int`
            The number of bins.
        log : `list` of `bool`
            Whether to compute the histogram in log space.
        subset_state : :class:`~glue.core.subset.SubsetState`, optional
            If specified, the histogram will only take into account values in
            the subset state.
        random_subset : `int`, optional
            If specified, this should be an integer giving the number of values
            to use for the statistic.
        """
        raise NotImplementedError()

    def compute_fixed_resolution_buffer(self, bounds, target_data=None, target_cid=None,
                                        subset_state=None, broadcast=True):
        """
        Get a fixed-resolution buffer.

        Parameters
        ----------
        bounds : `list`
            The list of bounds for the fixed resolution buffer. This list should
            have as many items as there are dimensions in ``target_data``. Each
            item should either be a scalar value, or a tuple of ``(min, max, nsteps)``.
        target_data : :class:`~glue.core.data.Data`, optional
            The data in whose frame of reference the bounds are defined. Defaults
            to ``data``.
        target_cid : :class:`~glue.core.component_id.ComponentID`, optional
            If specified, gives the component ID giving the component to use for the
            data values. Alternatively, use ``subset_state`` to get a subset mask.
        subset_state : :class:`~glue.core.subset.SubsetState`, optional
            If specified, gives the subset state for which to compute a mask.
            Alternatively, use ``target_cid`` if you want to get data values.
        broadcast : `bool`, optional
            If `True`, then if a dimension in ``target_data`` for which ``bounds``
            is not a scalar does not affect any of the dimensions in ``data``,
            then the final array will be effectively broadcast along this
            dimension, otherwise an error will be raised.
        """
        raise NotImplementedError()

    def __getitem__(self, key):
        """
        Shortcut syntax to access the numerical data in a component.
        Equivalent to::

            component = data.get_data(component_id)

        The key can be either just a component name, component ID, or a
        component name/ID and a view.
        """

        # Note: this method is generic and shouldn't need to be overriden by
        # subclasses.

        key, view = split_component_view(key)
        if isinstance(key, str):
            _k = key
            key = self.find_component_id(key)
            if key is None:
                raise IncompatibleAttribute(_k)

        return self.get_data(key, view=view)

    def _ipython_key_completions_(self):
        return [cid.label for cid in self.components]

    @property
    def world_component_ids(self):
        """
        A list of :class:`~glue.core.component_id.ComponentID` giving all
        world coordinate component IDs in the data.
        """
        if self.coords is None:
            return []
        elif not hasattr(self, '_world_component_ids'):
            self._world_component_ids = []
            self._world_components = {}
            for i in range(self.ndim):
                # Note: we use a Component object here for convenience but we
                # don't actually expose it via the BaseCartesianData API - in
                # get_data we extract the data from the component.
                comp = CoordinateComponent(self, i, world=True)
                label = axis_label(self.coords, i)
                cid = ComponentID(label, parent=self)
                self._world_component_ids.append(cid)
                self._world_components[cid] = comp
        return self._world_component_ids

    def _set_externally_derivable_components(self, derivable_components):
        """
        Externally deriable components are components identified by component
        IDs from other datasets.

        This method is meant for internal use only and is called by the link
        manager. The ``derivable_components`` argument should be set to a
        dictionary where the keys are the derivable component IDs, and the
        values are DerivedComponent instances which can be used to get the
        data.
        """

        # Note that even though Component objects are not normally exposed as
        # part of the BaseCartesianData API, we use these internally here as
        # a convenience, and extract the data from them in get_data. The actual
        # derived components are however used in the Data class.

        if len(self._externally_derivable_components) == 0 and len(derivable_components) == 0:

            return

        elif len(self._externally_derivable_components) == len(derivable_components):

            for key in derivable_components:
                if key in self._externally_derivable_components:
                    if self._externally_derivable_components[key].link is not derivable_components[key].link:
                        break
                else:
                    break
            else:
                return  # Unchanged!

        self._externally_derivable_components = derivable_components

        if self.hub:
            msg = ExternallyDerivableComponentsChangedMessage(self)
            self.hub.broadcast(msg)

    def _get_external_link(self, cid):
        if cid in self._externally_derivable_components:
            return self._externally_derivable_components[cid].link
        else:
            return None

    def _get_coordinate_transform(self, world_cid):
        if world_cid in self._world_components:
            def transform(values):
                return self._world_components._calculate(view=values)
            return transform
        else:
            return None

    def _set_pixel_aligned_data(self, pixel_aligned_data):
        """
        Pixel-aligned data are datasets that contain pixel component IDs
        that are equivalent (identically, not transformed) with all pixel
        component IDs in the present dataset.

        Note that the other datasets may have more but not fewer dimensions, so
        this information may not be symmetric between datasets with differing
        numbers of dimensions.
        """

        # First check if anything has changed, as if not then we should just
        # leave things as-is and avoid emitting a message.
        if len(self._pixel_aligned_data) == len(pixel_aligned_data):
            for data in self._pixel_aligned_data:
                if data not in pixel_aligned_data or pixel_aligned_data[data] != self._pixel_aligned_data[data]:
                    break
            else:
                return

        self._pixel_aligned_data = pixel_aligned_data
        if self.hub:
            msg = PixelAlignedDataChangedMessage(self)
            self.hub.broadcast(msg)

    @property
    def pixel_aligned_data(self):
        """
        Information about other datasets in the same data collection that have
        matching or a subset of pixel component IDs.

        This is returned as a dictionary where each key is a dataset with
        matching pixel component IDs, and the value is the order in which the
        pixel component IDs of the other dataset can be found in the current
        one.
        """
        return self._pixel_aligned_data


class Data(BaseCartesianData):
    """
    The basic data container in Glue.

    The data object stores data as a collection of
    :class:`~glue.core.component.Component` objects.  Each component stored in a
    dataset must have the same shape.

    Catalog data sets are stored such that each column is a distinct
    1-dimensional :class:`~glue.core.component.Component`.

    There are several ways to extract the actual numerical data stored in a
    :class:`~glue.core.data.Data` object::

       data = Data(x=[1, 2, 3], label='data')
       xid = data.id['x']

       data[xid]
       data.get_component(xid).data
       data['x']  # if 'x' is a unique component name

    Likewise, datasets support :ref:`fancy indexing <numpy:basics.indexing>`::

        data[xid, 0:2]
        data[xid, [True, False, True]]

    Parameters
    ----------
    label : `str`
        The name of the dataset.
    coords : :class:`~glue.core.coordinates.Coordinates`
        The coordinates object to use to define world coordinates.
    """

    def __init__(self, label="", coords=None, **kwargs):

        super(Data, self).__init__()

        self.label = label

        self._shape = ()

        # Components
        self._components = OrderedDict()
        self._pixel_component_ids = ComponentIDList()
        self._world_component_ids = ComponentIDList()

        # Coordinate conversion object
        self.coords = coords

        self.id = ComponentIDDict(self)

        self._coordinate_links = []

        self.edit_subset = None

        for lbl, data in sorted(kwargs.items()):
            self.add_component(data, lbl)

        self._key_joins = {}

    @property
    def coords(self):
        """
        The coordinates object for the data.
        """
        return self._coords

    @coords.setter
    def coords(self, value):
        if (hasattr(self, '_coords') and self._coords != value) or not hasattr(self, '_coords'):
            self._coords = value
            if len(self.components) > 0:
                self._update_world_components(self.ndim)

    @property
    def ndim(self):
        return len(self.shape)

    @property
    def shape(self):
        return self._shape

    @property
    def label(self):
        return self._label

    @label.setter
    def label(self, value):
        if getattr(self, '_label', None) != value:
            self._label = value
            self.broadcast(attribute='label')
        elif value is None:
            self._label = value

    @property
    def size(self):
        return np.prod(self.shape)

    @contract(component=Component)
    def _check_can_add(self, component):
        if isinstance(component, DerivedComponent):
            return component._data is self
        else:
            if len(self._components) == 0:
                return True
            else:
                if all(comp.shape == () for comp in self._components.values()):
                    return True
                else:
                    return component.shape == self.shape

    @contract(cid=ComponentID, returns=np.dtype)
    def dtype(self, cid):
        """Lookup the dtype for the data associated with a ComponentID"""

        # grab a small piece of data
        ind = tuple([slice(0, 1)] * self.ndim)
        arr = self.get_data(cid, view=ind)
        return arr.dtype

    @contract(component_id=ComponentID)
    def remove_component(self, component_id):
        """ Remove a component from a data set

        Parameters
        ----------
        component_id : :class:`~glue.core.component_id.ComponentID`
            The component to remove.
        """
        # TODO: avoid too many messages when removing a component triggers
        # the removal of derived components.
        if component_id in self._components:
            self._components.pop(component_id)
            self._removed_derived_that_depend_on(component_id)
            if self.hub:
                msg = DataRemoveComponentMessage(self, component_id)
                self.hub.broadcast(msg)
                msg = ComponentsChangedMessage(self)
                self.hub.broadcast(msg)

    def _removed_derived_that_depend_on(self, component_id):
        """
        Remove internal derived components that can no longer be derived.
        """
        remove = []
        for cid in self.derived_components:
            comp = self.get_component(cid)
            if component_id in comp.link.get_from_ids():
                remove.append(cid)
        for cid in remove:
            self.remove_component(cid)

    @contract(other='isinstance(Data)',
              cid='cid_like',
              cid_other='cid_like')
    def join_on_key(self, other, cid, cid_other):
        """
        Create an *element* mapping to another dataset, by joining on values of
        ComponentIDs in both datasets.

        This join allows any subsets defined on `other` to be propagated to
        self. The different ways to call this method are described in the
        **Examples** section below.

        Parameters
        ----------
        other : :class:`~glue.core.data.Data`
            Data object to join with.
        cid : `str` or :class:`~glue.core.component_id.ComponentID` or `iterable` thereof
            Component(s) in this dataset to use as a key.
        cid_other : `str` or :class:`~glue.core.component_id.ComponentID` or `iterable` thereof
            Component(s) in the other dataset to use as a key.

        Examples
        --------

        There are several ways to use this function, depending on how many
        components are passed to ``cid`` and ``cid_other``.

        **Joining on single components**

        First, one can specify a single component ID for both ``cid`` and
        ``cid_other``: this is the standard mode, and joins one component from
        one dataset to the other:

            >>> d1 = Data(x=[1, 2, 3, 4, 5], k1=[0, 0, 1, 1, 2], label='d1')
            >>> d2 = Data(y=[2, 4, 5, 8, 4], k2=[1, 3, 1, 2, 3], label='d2')
            >>> d2.join_on_key(d1, 'k2', 'k1')

        Selecting all values in ``d1`` where x is greater than 2 returns
        the last three items as expected:

            >>> s = d1.new_subset()
            >>> s.subset_state = d1.id['x'] > 2
            >>> s.to_mask()
            array([False, False,  True,  True,  True], dtype=bool)

        The linking was done between k1 and k2, and the values of
        k1 for the last three items are 1 and 2 - this means that the
        first, third, and fourth item in ``d2`` will then get selected,
        since k2 has a value of either 1 or 2 for these items.

            >>> s = d2.new_subset()
            >>> s.subset_state = d1.id['x'] > 2
            >>> s.to_mask()
            array([ True, False,  True,  True, False], dtype=bool)

        **Joining on multiple components**

        .. note:: This mode is currently slow, and will be optimized
                  significantly in future.

        Next, one can specify several components for each dataset: in this
        case, the number of components given should match for both datasets.
        This causes items in both datasets to be linked when (and only when)
        the set of keys match between the two datasets:

            >>> d1 = Data(x=[1, 2, 3, 5, 5],
            ...           y=[0, 0, 1, 1, 2], label='d1')
            >>> d2 = Data(a=[2, 5, 5, 8, 4],
            ...           b=[1, 3, 2, 2, 3], label='d2')
            >>> d2.join_on_key(d1, ('a', 'b'), ('x', 'y'))

        Selecting all items where x is 5 in ``d1`` in which x is a
        component works as expected and selects the two last items::

            >>> s = d1.new_subset()
            >>> s.subset_state = d1.id['x'] == 5
            >>> s.to_mask()
            array([False, False, False,  True,  True], dtype=bool)

        If we apply this selection to ``d2``, only items where a is 5
        and b is 2 will be selected:

            >>> s = d2.new_subset()
            >>> s.subset_state = d1.id['x'] == 5
            >>> s.to_mask()
            array([False, False,  True, False, False], dtype=bool)

        and in particular, the second item (where a is 5 and b is 3) is not
        selected.

        **One-to-many and many-to-one joining**

        Finally, you can specify one component in one dataset and multiple ones
        in the other. In the case where one component is specified for this
        dataset and multiple ones for the other dataset, then when an item
        is selected in the other dataset, it will cause any item in the present
        dataset which matches any of the keys in the other data to be selected:

            >>> d1 = Data(x=[1, 2, 3], label='d1')
            >>> d2 = Data(a=[1, 1, 2],
            ...           b=[2, 3, 3], label='d2')
            >>> d1.join_on_key(d2, 'x', ('a', 'b'))

        In this case, if we select all items in ``d2`` where a is 2, this
        will select the third item:

            >>> s = d2.new_subset()
            >>> s.subset_state = d2.id['a'] == 2
            >>> s.to_mask()
            array([False, False,  True], dtype=bool)

        Since we have joined the datasets using both a and b, we select
        all items in ``d1`` where x is either the value or a or b
        (2 or 3) which means we select the second and third item:

            >>> s = d1.new_subset()
            >>> s.subset_state = d2.id['a'] == 2
            >>> s.to_mask()
            array([False,  True,  True], dtype=bool)

        We can also join the datasets the other way around:

            >>> d1 = Data(x=[1, 2, 3], label='d1')
            >>> d2 = Data(a=[1, 1, 2],
            ...           b=[2, 3, 3], label='d2')
            >>> d2.join_on_key(d1, ('a', 'b'), 'x')

        In this case, selecting items in ``d1`` where x is 1 selects the
        first item, as expected:

            >>> s = d1.new_subset()
            >>> s.subset_state = d1.id['x'] == 1
            >>> s.to_mask()
            array([ True, False, False], dtype=bool)

        This then causes any item in ``d2`` where either a or b are 1
        to be selected, i.e. the first two items:

            >>> s = d2.new_subset()
            >>> s.subset_state = d1.id['x'] == 1
            >>> s.to_mask()
            array([ True,  True, False], dtype=bool)
        """

        # To make things easier, we transform all component inputs to a tuple
        if isinstance(cid, str) or isinstance(cid, ComponentID):
            cid = (cid,)
        if isinstance(cid_other, str) or isinstance(cid_other, ComponentID):
            cid_other = (cid_other,)

        if len(cid) > 1 and len(cid_other) > 1 and len(cid) != len(cid_other):
            raise Exception("Either the number of components in the key join "
                            "sets should match, or one of the component sets "
                            "should contain a single component.")

        def get_component_id(data, name):
            if isinstance(name, ComponentID):
                return name
            else:
                cid = data.find_component_id(name)
                if cid is None:
                    raise ValueError("ComponentID not found in %s: %s" %
                                     (data.label, name))
                return cid

        cid = tuple(get_component_id(self, name) for name in cid)
        cid_other = tuple(get_component_id(other, name) for name in cid_other)

        self._key_joins[other] = (cid, cid_other)
        other._key_joins[self] = (cid_other, cid)

    @contract(component='component_like', label='cid_like')
    def add_component(self, component, label):
        """ Add a new component to this data set.

        Parameters
        ----------
        component : :class:`~glue.core.component.Component` or array-like
            Object to add.
        label : `str` or :class:`~glue.core.component_id.ComponentID`
              The label. If this is a string, a new
              :class:`glue.core.component_id.ComponentID`
              with this label will be created and associated with the Component.

        Raises
        ------
           `TypeError`, if label is invalid.
           `ValueError`, if the component has an incompatible shape.

        Returns
        -------
        :class:`glue.core.component_id.ComponentID`
           The ComponentID associated with the newly-added component.
        """

        if isinstance(component, ComponentLink):
            return self.add_component_link(component, label=label)

        if not isinstance(component, Component):
            component = Component.autotyped(component)

        if isinstance(component, DerivedComponent):
            if len(self._components) == 0:
                raise TypeError("Cannot add a derived component as a first component")
            component.set_parent(self)

        if not self._check_can_add(component):
            raise ValueError("The dimensions of component %s are "
                             "incompatible with the dimensions of this data: "
                             "%r vs %r" % (label, component.shape, self.shape))

        if isinstance(label, ComponentID):
            component_id = label
            if component_id.parent is None:
                component_id.parent = self
        else:
            component_id = ComponentID(label, parent=self)

        if len(self._components) == 0:
            # TODO: make sure the following doesn't raise a componentsraised message
            self._create_pixel_and_world_components(ndim=component.ndim)

        # In some cases, such as when loading a session, we actually disable the
        # auto-creation of pixel and world coordinates, so the first component
        # may be a coordinate component with no shape. Therefore we only set the
        # shape once a component has a valid shape rather than strictly on the
        # first component.
        if self._shape == () and component.shape != ():
            self._shape = component.shape

        is_present = component_id in self._components
        self._components[component_id] = component

        if self.hub and not is_present:
            msg = DataAddComponentMessage(self, component_id)
            self.hub.broadcast(msg)
            msg = ComponentsChangedMessage(self)
            self.hub.broadcast(msg)

        return component_id

    @contract(link=ComponentLink,
              label='cid_like|None',
              returns=DerivedComponent)
    def add_component_link(self, link, label=None):
        """
        Shortcut method for generating a new
        :class:`~glue.core.component.DerivedComponent` from a ComponentLink
        object, and adding it to a data set.

        Parameters
        ----------
        link : :class:`~glue.core.component_link.ComponentLink`
            The link to use to generate a new component
        label : :class:`~glue.core.component_id.ComponentID` or `str`
            The ComponentID or label to attach to.

        Returns
        -------
        component : :class:`~glue.core.component.DerivedComponent`
            The component that was added
        """
        if label is not None:
            if not isinstance(label, ComponentID):
                label = ComponentID(label, parent=self)
            link.set_to_id(label)

        if link.get_to_id() is None:
            raise TypeError("Cannot add component_link: "
                            "has no 'to' ComponentID")

        for cid in link.get_from_ids():
            if cid not in self.components:
                raise ValueError("Can only add internal links with add_component_link "
                                 "- use DataCollection.add_link to add inter-data links")

        dc = DerivedComponent(self, link)
        to_ = link.get_to_id()
        self.add_component(dc, label=to_)
        return dc

    def _create_pixel_and_world_components(self, ndim):
        self._update_pixel_components(ndim)
        self._update_world_components(ndim)

    def _update_pixel_components(self, ndim):
        for i in range(ndim):
            comp = CoordinateComponent(self, i)
            label = pixel_label(i, ndim)
            cid = PixelComponentID(i, "Pixel Axis %s" % label, parent=self)
            self.add_component(comp, cid)
            self._pixel_component_ids.append(cid)

    def _update_world_components(self, ndim):

        if self.hub:
            delay_callbacks = self.hub.delay_callbacks
        else:
            @contextmanager
            def delay_callbacks():
                yield

        with delay_callbacks():
            for cid in self._world_component_ids[:]:
                self.remove_component(cid)
                self._world_component_ids.remove(cid)
            if self.coords:
                for i in range(ndim):
                    comp = CoordinateComponent(self, i, world=True)
                    label = axis_label(self.coords, i)
                    cid = self.add_component(comp, label)
                    self._world_component_ids.append(cid)
                self._set_up_coordinate_component_links(ndim)

    def _set_up_coordinate_component_links(self, ndim):

        if self.coords is None:
            return

        result = []
        for i in range(ndim):
            link = CoordinateComponentLink(self._pixel_component_ids,
                                           self._world_component_ids[i],
                                           self.coords, i)
            result.append(link)
            link = CoordinateComponentLink(self._world_component_ids,
                                           self._pixel_component_ids[i],
                                           self.coords, i, pixel2world=False)
            result.append(link)

        self._coordinate_links = result
        return result

    @property
    def components(self):
        """All :class:`ComponentIDs <glue.core.component_id.ComponentID>` in the Data.

        Returns
        -------
        `list`
        """
        return list(self._components.keys())

    @property
    def externally_derivable_components(self):
        return list(self._externally_derivable_components.keys())

    @property
    def coordinate_components(self):
        """The ComponentIDs associated with a :class:`~glue.core.component.CoordinateComponent`.

        Returns
        -------
        `list`
        """
        return [c for c in self.component_ids() if
                isinstance(self._components[c], CoordinateComponent)]

    @property
    def main_components(self):
        return [c for c in self.component_ids() if
                not isinstance(self._components[c], (DerivedComponent, CoordinateComponent))]

    @property
    def derived_components(self):
        """The ComponentIDs for each :class:`~glue.core.component.DerivedComponent`.

        Returns
        -------
        `list`
        """
        return [c for c in self.component_ids() if
                isinstance(self._components[c], DerivedComponent)]

    @property
    def pixel_component_ids(self):
        """
        The :class:`ComponentIDs <glue.core.component_id.ComponentID>` for each pixel coordinate.
        """
        return self._pixel_component_ids

    @property
    def world_component_ids(self):
        """
        The :class:`ComponentIDs <glue.core.component_id.ComponentID>` for each world coordinate.
        """
        return self._world_component_ids

    @contract(label='cid_like', returns='inst($ComponentID)|None')
    def find_component_id(self, label):
        """ Retrieve component_ids associated by label name.

        Parameters
        ----------
        label ::class:`~glue.core.component_id.ComponentID` or `str`
            ComponentID to search for.

        Returns
        -------
        :class:`~glue.core.component_id.ComponentID` or `None`
            The associated ComponentID if label is found and unique, else None.
            First, this checks whether the component ID is present and unique in
            the primary (non-derived) components of the data, and if not then
            the derived components are checked. If there is one instance of the
            label in the primary and one in the derived components, the primary
            one takes precedence.
        """

        for cid_set in (self.main_components, self.derived_components, self.coordinate_components, list(self._externally_derivable_components)):

            result = []
            for cid in cid_set:
                if isinstance(label, ComponentID):
                    if cid is label:
                        result.append(cid)
                else:
                    if cid.label == label:
                        result.append(cid)

            if len(result) == 1:
                return result[0]
            elif len(result) > 1:
                return None
        return None

    @property
    def links(self):
        """
        A list of all the links internal to the dataset.
        """
        return self.coordinate_links + self.derived_links

    @property
    def coordinate_links(self):
        """
        A list of the ComponentLinks that connect pixel and world. If no
        coordinate transformation object is present, return an empty list.
        """
        return self._coordinate_links

    @property
    def derived_links(self):
        """
        A list of the links present inside all of the DerivedComponent objects
        in this dataset.
        """
        return [self.get_component(cid).link for cid in self.derived_components]

    @contract(returns='list(inst($ComponentID))')
    def component_ids(self):
        """
        Equivalent to :attr:`Data.components`
        """
        return ComponentIDList(self._components.keys())

    @contract(old=ComponentID, new=ComponentID)
    def update_id(self, old, new):
        """
        Reassign a component to a different :class:`glue.core.component_id.ComponentID`

        Parameters
        ----------
        old : :class:`~glue.core.component_id.ComponentID`
            The old component ID.
        new : :class:`~glue.core.component_id.ComponentID`
            The new component ID.
        """

        if new is old:
            return

        if new.parent is None:
            new.parent = self

        changed = False
        if old in self._components:

            # We want to keep the original order, so we can't just do:
            #   self._components[new] = self._components[old]
            # which will put the new component ID at the end, but instead
            # we need to do:
            self._components = OrderedDict((new, value) if key is old else (key, value)
                                           for key, value in self._components.items())
            changed = True

        try:
            index = self._pixel_component_ids.index(old)
            self._pixel_component_ids[index] = new
            changed = True
        except ValueError:
            pass
        try:
            index = self._world_component_ids.index(old)
            self._world_component_ids[index] = new
            changed = True
        except ValueError:
            pass

        if changed and self.hub is not None:

            # remove old component and broadcast the change
            # see #508 for discussion of this
            msg = ComponentReplacedMessage(self, old, new)
            self.hub.broadcast(msg)

    def __str__(self):
        s = "Data Set: %s\n" % self.label
        s += "Number of dimensions: %i\n" % self.ndim
        s += "Shape: %s\n" % ' x '.join([str(x) for x in self.shape])
        categories = [('Main', self.main_components),
                      ('Derived', self.derived_components),
                      ('Coordinate', self.coordinate_components)]
        for category, components in categories:
            if len(components) > 0:
                s += category + " components:\n"
                for cid in components:
                    comp = self.get_component(cid)
                    if comp.units is None or comp.units == '':
                        s += " - {0}\n".format(cid)
                    else:
                        s += " - {0} [{1}]\n".format(cid, comp.units)
        return s[:-1]

    def __repr__(self):
        return 'Data (label: %s)' % self.label

    def __setattr__(self, name, value):
        if name == "hub" and hasattr(self, 'hub') \
                and self.hub is not value and self.hub is not None:
            raise AttributeError("Data has already been assigned "
                                 "to a different hub")
        object.__setattr__(self, name, value)

    def get_data(self, cid, view=None):

        if isinstance(cid, ComponentLink):
            return cid.compute(self, view)

        if cid in self._components:
            comp = self._components[cid]
        elif cid in self._externally_derivable_components:
            comp = self._externally_derivable_components[cid]
        else:
            raise IncompatibleAttribute(cid)

        if view is not None:
            result = comp[view]
        else:
            result = comp.data

        return result

    def get_kind(self, cid):

        comp = self.get_component(cid)

        if comp.datetime:
            return 'datetime'
        elif comp.numeric:
            return 'numerical'
        elif comp.categorical:
            return 'categorical'
        elif comp.extended:
            return 'extended'
        else:
            raise TypeError("Unknown data kind")

    def get_mask(self, subset_state, view=None):
        try:
            return subset_state.to_mask(self, view=view)
        except IncompatibleAttribute:
            return get_mask_with_key_joins(self, self._key_joins, subset_state, view=view)

    def __setitem__(self, key, value):
        """
        Wrapper for data.add_component()
        """
        self.add_component(value, key)

    @contract(component_id='cid_like|None', returns=Component)
    def get_component(self, component_id):
        """Fetch the component corresponding to component_id.

        Parameters
        ----------
        component_id : :class:`~glue.core.component_id.ComponentID`
            The ID for the component to retrieve.
        """
        if component_id is None:
            raise IncompatibleAttribute()

        if isinstance(component_id, str):
            component_id = self.id[component_id]

        if component_id in self._components:
            return self._components[component_id]
        elif component_id in self._externally_derivable_components:
            return self._externally_derivable_components[component_id]
        else:
            raise IncompatibleAttribute(component_id)

    def to_dataframe(self, index=None):
        """Convert the Data object into a :class:`pandas.DataFrame` object.

        Parameters
        ----------
        index : index-like
            Any object that can be passed to the :class:`pandas.Series` constructor.

        Returns
        -------
        :class:`pandas.DataFrame`
        """

        h = lambda comp: self.get_component(comp).to_series(index=index)
        df = pd.DataFrame(dict((comp.label, h(comp)) for comp in self.components))
        order = [comp.label for comp in self.components]
        return df[order]

    def reorder_components(self, component_ids):
        """
        Reorder the components using a list of component IDs. The new set
        of component IDs has to match the existing set (though order may differ).
        """

        # We need to be careful because component IDs overload == so we can't
        # use the normal ways to test whether the component IDs are the same
        # as self.components - instead we need to explicitly use id

        if len(component_ids) != len(self.components):
            raise ValueError("Number of component in component_ids does not "
                             "match existing number of components")

        if set(id(c) for c in self.components) != set(id(c) for c in component_ids):
            raise ValueError("specified component_ids should match existing components")

        existing = self.components
        for idx in range(len(component_ids)):
            if component_ids[idx] is not existing[idx]:
                break
        else:
            # If we get here then the suggested order is the same as the existing one
            return

        # TODO: We could instead sort in-place using the move_to_end method on OrderedDict
        self._components = OrderedDict((key, self._components[key]) for key in component_ids)

        if self.hub:
            msg = DataReorderComponentMessage(self, list(self._components))
            self.hub.broadcast(msg)

    @contract(mapping="dict(inst($Component, $ComponentID):array_like)")
    def update_components(self, mapping):
        """
        Change the numerical data associated with some of the Components
        in this Data object.

        All changes to component numerical data should use this method,
        which broadcasts the state change to the appropriate places.

        Parameters
        ----------
        mapping : `dict`
            A dictionary mapping Components or ComponenIDs to arrays.

        This method has the following restrictions:
          - New components must have the same shape as old components
          - Component subclasses cannot be updated.
        """
        for comp, data in mapping.items():
            if isinstance(comp, ComponentID):
                comp = self.get_component(comp)
            data = np.asarray(data)
            if data.shape != self.shape:
                raise ValueError("Cannot change shape of data")

            comp._data = data

        # alert hub of the change
        if self.hub is not None:
            msg = NumericalDataChangedMessage(self, components_changed=list(mapping.keys()))
            self.hub.broadcast(msg)

        for subset in self.subsets:
            clear_cache(subset.subset_state.to_mask)

    def update_values_from_data(self, data):
        """
        Replace numerical values in data to match values from another dataset.

        Notes
        -----

        This method drops components that aren't present in the new data, and
        adds components that are in the new data that were not in the original
        data. The matching is done by component label, and components are
        resized if needed. This means that for components with matching labels
        in the original and new data, the
        :class:`~glue.core.component_id.ComponentID` are preserved, and
        existing plots and selections will be updated to reflect the new
        values. Note that the coordinates are also copied, but the style is
        **not** copied.
        """

        old_labels = [cid.label for cid in self.components]
        new_labels = [cid.label for cid in data.components]

        if len(old_labels) == len(set(old_labels)):
            old_labels = set(old_labels)
        else:
            raise ValueError("Non-unique component labels in original data")

        if len(new_labels) == len(set(new_labels)):
            new_labels = set(new_labels)
        else:
            raise ValueError("Non-unique component labels in new data")

        # Remove components that don't have a match in new data
        for cname in old_labels - new_labels:
            cid = self.find_component_id(cname)
            self.remove_component(cid)

        # Update shape
        self._shape = data._shape

        # Update components that exist in both. Note that we can't just loop
        # over old_labels & new_labels since we need to make sure we preserve
        # the order of the components, and sets don't preserve order.
        for cid in self.components:
            cname = cid.label
            if cname in old_labels & new_labels:
                comp_old = self.get_component(cname)
                comp_new = data.get_component(cname)
                comp_old._data = comp_new._data

        # Add components that didn't exist in original one. As above, we try
        # and preserve the order of components as much as possible.
        for cid in data.components:
            cname = cid.label
            if cname in new_labels - old_labels:
                cid = data.find_component_id(cname)
                comp_new = data.get_component(cname)
                self.add_component(comp_new, cid.label)

        # Update data label
        self.label = data.label

        # Update data coordinates
        self.coords = data.coords

        # alert hub of the change
        if self.hub is not None:
            msg = NumericalDataChangedMessage(self)
            self.hub.broadcast(msg)

        for subset in self.subsets:
            clear_cache(subset.subset_state.to_mask)

    # The following are methods for accessing the data in various ways that
    # can be overriden by subclasses that want to improve performance.

    def compute_statistic(self, statistic, cid, subset_state=None, axis=None,
                          finite=True, positive=False, percentile=None, view=None,
                          random_subset=None, n_chunk_max=40000000):
        """
        Compute a statistic for the data.

        Parameters
        ----------
        statistic : {'minimum', 'maximum', 'mean', 'median', 'sum', 'percentile'}
            The statistic to compute
        cid : :class:`~glue.core.component_id.ComponentID` or `str`
            The component ID to compute the statistic on - if given as a string
            this will be assumed to be for the component belonging to the dataset
            (not external links).
        subset_state : :class:`~glue.core.subset.SubsetState`, optional
            If specified, the statistic will only include the values that are in
            the subset specified by this subset state.
        axis : `int` or `tuple` of `int`, optional
            If specified, the axis/axes to compute the statistic over.
        finite : `bool`, optional
            Whether to include only finite values in the statistic. This should
            be `True` to ignore NaN/Inf values
        positive : `bool`, optional
            Whether to include only (strictly) positive values in the statistic.
            This is used for example when computing statistics of data shown in
            log space.
        percentile : `float`, optional
            If ``statistic`` is ``'percentile'``, the ``percentile`` argument
            should be given and specify the percentile to calculate in the
            range [0:100]
        random_subset : `int`, optional
            If specified, this should be an integer giving the number of values
            to use for the statistic. This can only be used if ``axis`` is `None`
        n_chunk_max : `int`, optional
            If there are more elements in the array than this value, operate in
            chunks with at most this size.
        """

        # TODO: generalize chunking to more types of axis

        # In recent version of Numpy, using lists is not the same as using
        # tuples, so we make sure we always use tuples to avoid confusion.
        if isinstance(view, list):
            view = tuple(view)

        if (view is None and
                isinstance(axis, tuple) and
                len(axis) > 0 and
                len(axis) == self.ndim - 1 and
                self.size > n_chunk_max and
                not isinstance(subset_state, SliceSubsetState)):

            # We operate in chunks here to avoid memory issues.

            axis_index = [a for a in range(self.ndim) if a not in axis][0]

            # In the specific case where the subset state depends only on pixel
            # component IDs but not the one for the chunk iteration axis used
            # here, we should not need to chunk. However this doesn't quite
            # work because compute_statistic still makes a copy of the data
            # so we need to make sure we never have too large arrays there.
            # efficient_subset_state = False
            # if subset_state is not None:
            #     from glue.core.link_manager import pixel_cid_to_pixel_cid_matrix
            #     for att in subset_state.attributes:
            #         # TODO: in principle we cold still deal with non-pixel
            #         # componnet IDs, so this should be fixed.
            #         if not isinstance(att, PixelComponentID):
            #             break
            #         matrix = pixel_cid_to_pixel_cid_matrix(att.parent, self)
            #         if matrix[att.axis, axis_index]:
            #             break
            #     else:
            #         efficient_subset_state = True

            # For now, just assume we always have to chunk
            efficient_subset_state = False

            if not efficient_subset_state:

                result = np.zeros(self.shape[axis_index])

                chunk_shape = list(self.shape)

                # Deliberately leave n_chunks as float to not round twice
                n_chunks = self.size / n_chunk_max

                chunk_shape[axis_index] = max(1, int(chunk_shape[axis_index] / n_chunks))

                for chunk_view in iterate_chunks(self.shape, chunk_shape=chunk_shape):
                    values = self.compute_statistic(statistic, cid, subset_state=subset_state,
                                                    axis=axis, finite=finite, positive=positive,
                                                    percentile=percentile, view=chunk_view)
                    result[chunk_view[axis_index]] = values

                return result

        # We initialize subarray_slices here because if it is set at any point
        # later we will need to pad out the result of compute_statistic.
        subarray_slices = None

        chunk_view = None
        if subset_state:
            if isinstance(subset_state, SliceSubsetState) and view is None:
                mask = None
                data = subset_state.to_array(self, cid)
            else:
                mask = subset_state.to_mask(self, view)

                unbroadcast_mask = unbroadcast(mask)

                if np.any(unbroadcast_mask):

                    # Find minimal subarray containing the masked area. At this
                    # point we've already accessed all the values in unbroadcast_mask
                    # so the calls to .any() below should not have a significant
                    # performance impact.
                    subarray_slices = []
                    for idim in range(mask.ndim):

                        # Check whether any values should be included for each
                        # element along the axis being considered. For efficiency
                        # we use the unbroadcast mask here.
                        collapse_axes = tuple(index for index in range(mask.ndim) if index != idim)
                        valid = unbroadcast_mask.any(axis=collapse_axes)

                        # Since we just used the unbroadcast mask, we need to
                        # broadcast it back to the original mask shape.
                        valid = np.broadcast_to(valid, mask.shape[idim:idim + 1])

                        # We now find the first and last value for which the mask
                        # is set, to determine the slice of the minimal subarray
                        indices = np.where(valid)[0]
                        subarray_slices.append(slice(np.min(indices), np.max(indices) + 1))

                    subarray_slices = tuple(subarray_slices)

                    # We now need to determine the view for which to extract the
                    # data, which essentially needs to combine the original view
                    # which was used to compute the mask, and the new view which
                    # extracts a subset of this mask.

                    # For some views we don't support this, so we keep track of
                    # whether we can actually use subarray_slices above
                    use_subarray_slices = True

                    if view is None or view is Ellipsis:
                        # In the case where view is None, things are pretty
                        # simple since we just use subarray_slices to view the data
                        view = subarray_slices
                    elif isinstance(view, (list, tuple)):
                        # At this point view is a list or a tuple, which could
                        # contain either scalar values or slice objects. In
                        # addition, it may contain fewer elements than are needed
                        # to slice the data, so we need to take this into account.
                        mask_idim = 0
                        new_view = []
                        for idim in range(self.ndim):
                            if idim >= len(view):
                                new_view.append(subarray_slices[mask_idim])
                                mask_idim += 1
                            elif isinstance(view[idim], slice):
                                if view[idim].step is not None and view[idim].step != 1:
                                    # This makes things more complicated, so bail out at this point
                                    use_subarray_slices = False
                                    new_view = view
                                    break
                                view_start, _, _ = view[idim].indices(self.shape[idim])
                                sub_start, sub_stop, _ = subarray_slices[mask_idim].indices(mask.shape[mask_idim])
                                new_view.append(slice(view_start + sub_start,
                                                      view_start + sub_stop))
                                mask_idim += 1
                            else:
                                new_view.append(view[idim])
                        # This is the chunk view, which we'll need later
                        chunk_view = view
                        view = tuple(new_view)
                    else:  # pragma: nocover
                        # This should probably never happen, but just in case!
                        use_subarray_slices = False

                    if use_subarray_slices:
                        # Extract the mask in the subarray region. The view will
                        # then also take into account the subarray slices in this
                        # case.
                        mask = mask[subarray_slices]

                    data = self.get_data(cid, view)

                else:
                    if axis is None:
                        return np.nan
                    else:
                        if isinstance(axis, int):
                            axis = [axis]
                        final_shape = [mask.shape[i] for i in range(mask.ndim) if i not in axis]
                        return np.broadcast_to(np.nan, final_shape)
        else:
            data = self.get_data(cid, view=view)
            mask = None

        if isinstance(data, categorical_ndarray):
            data = data.codes

        if axis is None and mask is None:
            # Since we are just finding overall statistics, not along axes, we
            # can remove any broadcasted dimension since these should not affect
            # the statistics.
            data = unbroadcast(data)

        if random_subset and data.size > random_subset:
            if DASK_INSTALLED and isinstance(data, da.Array):
                # We shouldn't cache _random_subset_indices_dask here because
                # it might be different for different dask arrays
                random_subset_indices_dask = (data.size, random_views_for_dask_array(data, random_subset, n_chunks=10))
                data = da.hstack([data[slices].ravel() for slices in random_subset_indices_dask[1]])
                if mask is not None:
                    mask = da.hstack([mask[slices].ravel() for slices in random_subset_indices_dask[1]])
            else:
                if not hasattr(self, '_random_subset_indices') or self._random_subset_indices[0] != data.shape:
                    self._random_subset_indices = (data.shape, random_indices_for_array(data, random_subset))
                data = data[self._random_subset_indices[1]]
                if mask is not None:
                    mask = mask[self._random_subset_indices[1]]

        result = compute_statistic(statistic, data, mask=mask, axis=axis, finite=finite,
                                   positive=positive, percentile=percentile)

        if subarray_slices is None or axis is None:
            return result
        else:
            # Since subarray_slices was set above, we need to determine the
            # shape of the full results had subarray_slices not been set,
            # then insert the result into it. If axis is None, then we don't
            # need to do anything, and this is covered by the first clause
            # of the if statement above. Likewise if a view was specified,
            # only the result within the view is returned.
            if not isinstance(axis, tuple):
                axis = (axis,)
            result_slices = tuple([subarray_slices[idim] for idim in range(self.ndim) if idim not in axis])

            if chunk_view is None:
                full_shape = [self.shape[idim] for idim in range(self.ndim) if idim not in axis]
            else:
                chunk_shape = subset_state.to_mask(self, chunk_view).shape
                full_shape = [chunk_shape[idim] for idim in range(self.ndim) if idim not in axis]

            full_result = np.zeros(full_shape) * np.nan
            full_result[result_slices] = result
            return full_result

    def compute_histogram(self, cids, weights=None, range=None, bins=None,
                          log=None, subset_state=None, random_subset=None):
        """
        Compute an n-dimensional histogram with regularly spaced bins.

        Currently this only implements 1-D histograms.

        Parameters
        ----------
        cids : `list` of `str` or :class:`~glue.core.component_id.ComponentID`
            Component IDs to compute the histogram over.
        weights : `str` or :class:`~glue.core.component_id.ComponentID`
            Component ID to use for the histogram weights.
        range : `list` of `tuple`
            The ``(min, max)`` of the histogram range.
        bins : `list` of `int`
            The number of bins.
        log : `list` of `bool`
            Whether to compute the histogram in log space.
        subset_state : :class:`~glue.core.subset.SubsetState`, optional
            If specified, the histogram will only take into account values in
            the subset state.
        random_subset : `int`, optional
            If specified, this should be an integer giving the number of values
            to use for the statistic.
        """

        if len(cids) > 2:
            raise NotImplementedError()

        ndim = len(cids)

        x = self.get_data(cids[0])
        if isinstance(x, categorical_ndarray):
            x = x.codes

        if ndim > 1:
            y = self.get_data(cids[1])
            if isinstance(y, categorical_ndarray):
                y = y.codes

        if weights is not None:
            w = self.get_data(weights)
            if isinstance(w, categorical_ndarray):
                w = w.codes
        else:
            w = None

        # Some operations below don't work well when mixing dask and non-dask
        # arrays, so we make sure that if one is a dask array we convert the
        # other one too.
        if DASK_INSTALLED and ndim > 1:
            if isinstance(x, da.Array) and not isinstance(y, da.Array):
                y = da.asarray(y)
            if not isinstance(x, da.Array) and isinstance(y, da.Array):
                x = da.asarray(x)

        if subset_state is not None:
            mask = self.get_mask(subset_state)
            if DASK_INSTALLED and isinstance(x, da.Array) and not isinstance(mask, da.Array):
                x = x[da.asarray(mask)]
            else:
                x = x[mask]
            if ndim > 1:
                if DASK_INSTALLED and isinstance(y, da.Array) and not isinstance(mask, da.Array):
                    y = y[da.asarray(mask)]
                else:
                    y = y[mask]
            if w is not None:
                if DASK_INSTALLED and isinstance(w, da.Array) and not isinstance(mask, da.Array):
                    w = w[da.asarray(mask)]
                else:
                    w = w[mask]

        # TODO: avoid duplication of the following code block with compute_statistic

        if random_subset and x.size > random_subset:

            original_size = x.size

            if DASK_INSTALLED and isinstance(x, da.Array):
                # We shouldn't cache _random_subset_indices_dask here because
                # it might be different for different dask arrays
                random_subset_indices_dask = (x.size, random_views_for_dask_array(x, random_subset, n_chunks=10))
                x = da.hstack([x[slices].ravel() for slices in random_subset_indices_dask[1]])
                if ndim > 1:
                    y = da.hstack([y[slices].ravel() for slices in random_subset_indices_dask[1]])
                if w is not None:
                    w = da.hstack([w[slices].ravel() for slices in random_subset_indices_dask[1]])
            else:
                if not hasattr(self, '_random_subset_histogram_indices') or self._random_subset_histogram_indices[0] != x.shape:
                    self._random_subset_histogram_indices = (x.shape, random_indices_for_array(x, random_subset))
                x = x[self._random_subset_histogram_indices[1]]
                if ndim > 1:
                    y = y[self._random_subset_histogram_indices[1]]
                if w is not None:
                    w = w[self._random_subset_histogram_indices[1]]

            # Determine correction factor by which to scale the histogram so
            # that it still has the right order of magnitude
            correction = original_size / x.size

        else:

            correction = 1.

        if ndim == 1:
            xmin, xmax = range[0]
            xmin, xmax = sorted((xmin, xmax))
            keep = (x >= xmin) & (x <= xmax)
        else:
            (xmin, xmax), (ymin, ymax) = range
            xmin, xmax = sorted((xmin, xmax))
            ymin, ymax = sorted((ymin, ymax))
            keep = (x >= xmin) & (x <= xmax) & (y >= ymin) & (y <= ymax)

        if x.dtype.kind == 'M':
            x = datetime64_to_mpl(x)
            xmin = datetime64_to_mpl(xmin)
            xmax = datetime64_to_mpl(xmax)
        else:
            keep &= ~np.isnan(x)

        if ndim > 1:
            if y.dtype.kind == 'M':
                y = datetime64_to_mpl(y)
                ymin = datetime64_to_mpl(ymin)
                ymax = datetime64_to_mpl(ymax)
            else:
                keep &= ~np.isnan(y)

        x = x[keep]
        if ndim > 1:
            y = y[keep]
        if w is not None:
            w = w[keep]

        # For now, compute dask arrays at this point. In future we could delegate
        # the histogram calculation to dask. The extra call to
        # np.asarray is to coerce dask arrays read from
        # disk with lazy loaders to definitely be numpy arrays
        if DASK_INSTALLED:
            if isinstance(x, da.Array):
                x = np.asarray(x.compute())
            if ndim > 1 and isinstance(y, da.Array):
                y = np.asarray(y.compute())
            if isinstance(w, da.Array):
                w = np.asarray(w.compute())

        if len(x) == 0:
            return np.zeros(bins)

        if ndim > 1 and len(y) == 0:
            return np.zeros(bins)

        if log is not None and log[0]:
            if xmin < 0 or xmax < 0:
                return np.zeros(bins)
            xmin = np.log10(xmin)
            xmax = np.log10(xmax)
            x = np.log10(x)

        if ndim > 1 and log is not None and log[1]:
            if ymin < 0 or ymax < 0:
                return np.zeros(bins)
            ymin = np.log10(ymin)
            ymax = np.log10(ymax)
            y = np.log10(y)

        # By default fast-histogram drops values that are exactly xmax, so we
        # increase xmax very slightly to make sure that this doesn't happen, to
        # be consistent with np.histogram.
        if ndim >= 1:
            xmax += 10 * np.spacing(xmax)
        if ndim >= 2:
            ymax += 10 * np.spacing(ymax)

        if ndim == 1:
            range = (xmin, xmax)
            return histogram1d(x, range=range, bins=bins[0], weights=w) * correction
        elif ndim > 1:
            range = [(xmin, xmax), (ymin, ymax)]
            return histogram2d(x, y, range=range, bins=bins, weights=w) * correction

    def compute_fixed_resolution_buffer(self, *args, **kwargs):
        from .fixed_resolution_buffer import compute_fixed_resolution_buffer
        return compute_fixed_resolution_buffer(self, *args, **kwargs)

    # DEPRECATED

    @property
    def primary_components(self):
        """
        The ComponentIDs not associated with a :class:`~glue.core.component.DerivedComponent`

        This property is deprecated.
        """
        warnings.warn('Data.primary_components is deprecated', UserWarning)
        return [c for c in self.component_ids() if
                not isinstance(self._components[c], DerivedComponent)]

    @property
    def visible_components(self):
        """All :class:`ComponentIDs <glue.core.component_id.ComponentID>` in the Data that aren't coordinates.

        This property is deprecated.
        """
        warnings.warn('Data.visible_components is deprecated', UserWarning)
        return [cid for cid, comp in self._components.items()
                if not isinstance(comp, CoordinateComponent) and cid.parent is self]


@contract(i=int, ndim=int)
def pixel_label(i, ndim):
    label = "{0}".format(i)
    if 1 <= ndim <= 3:
        label += " [{0}]".format('xyz'[ndim - 1 - i])
    return label
