text: """
  Public API for all plots supported by HoloViews, regardless of
  plotting package or backend. Every plotting classes must be a subclass
  of this Plot baseclass.
  """
  from __future__ import absolute_import
  
  import threading
  import uuid
  import warnings
  
  from collections import Counter, defaultdict
  from functools import partial
  from itertools import groupby, product
  
  import numpy as np
  import param
  
  from panel.config import config
  from panel.io.notebook import push
  from panel.io.state import state
  from pyviz_comms import JupyterComm
  
  from ..selection import NoOpSelectionDisplay
  from ..core import OrderedDict
  from ..core import util, traversal
  from ..core.element import Element, Element3D
  from ..core.overlay import Overlay, CompositeOverlay
  from ..core.layout import Empty, NdLayout, Layout
  from ..core.options import Store, Compositor, SkipRendering, lookup_options
  from ..core.overlay import NdOverlay
  from ..core.spaces import HoloMap, DynamicMap
  from ..core.util import stream_parameters, isfinite
  from ..element import Table, Graph, Contours
  from ..streams import Stream, RangeXY, RangeX, RangeY
  from ..util.transform import dim
  from .util import (get_dynamic_mode, initialize_unbounded, dim_axis_label,
                     attach_streams, traverse_setter, get_nested_streams,
                     compute_overlayable_zorders, get_nested_plot_frame,
                     split_dmap_overlay, get_axis_padding, get_range,
                     get_minimum_span, get_plot_frame, scale_fontsize)
  
  
  class Plot(param.Parameterized):
      """
      Base class of all Plot classes in HoloViews, designed to be
      general enough to use any plotting package or backend.
      """
  
      backend = None
  
      # A list of style options that may be supplied to the plotting
      # call
      style_opts = []
      # Sometimes matplotlib doesn't support the common aliases.
      # Use this list to disable any invalid style options
      _disabled_opts = []
  
      def __init__(self, renderer=None, root=None, **params):
          params = {k: v for k, v in params.items()
                    if k in self.param}
          super(Plot, self).__init__(**params)
          self.renderer = renderer if renderer else Store.renderers[self.backend].instance()
          self._force = False
          self._comm = None
          self._document = None
          self._root = None
          self._pane = None
          self._triggering = []
          self._trigger = []
          self.set_root(root)
  
  
      @property
      def state(self):
          """
          The plotting state that gets updated via the update method and
          used by the renderer to generate output.
          """
          raise NotImplementedError
  
  
      def set_root(self, root):
          """
          Sets the root model on all subplots.
          """
          if root is None:
              return
          for plot in self.traverse(lambda x: x):
              plot._root = root
  
  
      @property
      def root(self):
          if self._root:
              return self._root
          elif 'plot' in self.handles and self.top_level:
              return self.state
          else:
              return None
  
  
      @property
      def document(self):
          return self._document
  
      @document.setter
      def document(self, doc):
          if (doc and hasattr(doc, 'on_session_destroyed') and
              self.root is self.handles.get('plot') and
              not isinstance(self, GenericAdjointLayoutPlot)):
              doc.on_session_destroyed(self._session_destroy)
              if self._document:
                  if isinstance(self._document._session_destroyed_callbacks, set):
                      self._document._session_destroyed_callbacks.discard(self._session_destroy)
                  else:
                      self._document._session_destroyed_callbacks.pop(self._session_destroy, None)
  
          self._document = doc
          if self.subplots:
              for plot in self.subplots.values():
                  if plot is not None:
                      plot.document = doc
  
      @property
      def pane(self):
          return self._pane
  
      @pane.setter
      def pane(self, pane):
          if (config.console_output != 'disable' and self.root and
              self.root.ref['id'] not in state._handles and
              isinstance(self.comm, JupyterComm)):
              from IPython.display import display
              handle = display(display_id=uuid.uuid4().hex)
              state._handles[self.root.ref['id']] = (handle, [])
  
          self._pane = pane
          if self.subplots:
              for plot in self.subplots.values():
                  if plot is not None:
                      plot.pane = pane
                  if not plot.root:
                      continue
                  for cb in getattr(plot, 'callbacks', []):
                      if hasattr(pane, '_on_error') and getattr(cb, 'comm', None):
                          cb.comm._on_error = partial(pane._on_error, plot.root.ref['id'])
          elif self.root:
              for cb in getattr(self, 'callbacks', []):
                  if hasattr(pane, '_on_error') and getattr(cb, 'comm', None):
                      cb.comm._on_error = partial(pane._on_error, self.root.ref['id'])
  
      @property
      def comm(self):
          return self._comm
  
  
      @comm.setter
      def comm(self, comm):
          self._comm = comm
          if self.subplots:
              for plot in self.subplots.values():
                  if plot is not None:
                      plot.comm = comm
  
  
      def initialize_plot(self, ranges=None):
          """
          Initialize the matplotlib figure.
          """
          raise NotImplementedError
  
  
      def update(self, key):
          """
          Update the internal state of the Plot to represent the given
          key tuple (where integers represent frames). Returns this
          state.
          """
          return self.state
  
  
      def cleanup(self):
          """
          Cleans up references to the plot on the attached Stream
          subscribers.
          """
          plots = self.traverse(lambda x: x, [Plot])
          for plot in plots:
              if not isinstance(plot, (GenericCompositePlot, GenericElementPlot, GenericOverlayPlot)):
                  continue
              for stream in set(plot.streams):
                  stream._subscribers = [
                      (p, subscriber) for p, subscriber in stream._subscribers
                      if not util.is_param_method(subscriber) or
                      util.get_method_owner(subscriber) not in plots
                  ]
  
  
      def _session_destroy(self, session_context):
          self.cleanup()
  
  
      def refresh(self, **kwargs):
          """
          Refreshes the plot by rerendering it and then pushing
          the updated data if the plot has an associated Comm.
          """
          if self.renderer.mode == 'server':
              from bokeh.io import curdoc
              thread = threading.current_thread()
              thread_id = thread.ident if thread else None
              if (curdoc() is not self.document or (state._thread_id is not None and
                  thread_id != state._thread_id)):
                  # If we do not have the Document lock, schedule refresh as callback
                  self._triggering += [s for p in self.traverse(lambda x: x, [Plot])
                                       for s in getattr(p, 'streams', []) if s._triggering]
                  if self.document.session_context:
                      self.document.add_next_tick_callback(self.refresh)
                      return
  
          # Ensure that server based tick callbacks maintain stream triggering state
          for s in self._triggering:
              s._triggering = True
          try:
              traverse_setter(self, '_force', True)
              key = self.current_key if self.current_key else self.keys[0]
              dim_streams = [stream for stream in self.streams
                             if any(c in self.dimensions for c in stream.contents)]
              stream_params = stream_parameters(dim_streams)
              key = tuple(None if d in stream_params else k
                          for d, k in zip(self.dimensions, key))
              stream_key = util.wrap_tuple_streams(key, self.dimensions, self.streams)
  
              self._trigger_refresh(stream_key)
              if self.top_level:
                  self.push()
          except Exception as e:
              raise e
          finally:
              # Reset triggering state
              for s in self._triggering:
                  s._triggering = False
              self._triggering = []
  
  
      def _trigger_refresh(self, key):
          "Triggers update to a plot on a refresh event"
          # Update if not top-level, batched or an ElementPlot
          if not self.top_level or isinstance(self, GenericElementPlot):
              self.update(key)
  
  
      def push(self):
          """
          Pushes plot updates to the frontend.
          """
          root = self._root
          if (root and self.pane is not None and
              root.ref['id'] in self.pane._plots):
              child_pane = self.pane._plots[root.ref['id']][1]
          else:
              child_pane = None
  
          if self.renderer.backend != 'bokeh' and child_pane is not None:
              child_pane.object = self.renderer.get_plot_state(self)
          elif (self.renderer.mode != 'server' and root and
                'embedded' not in root.tags and self.document and self.comm):
              push(self.document, self.comm)
  
  
      @property
      def id(self):
          return self.comm.id if self.comm else id(self.state)
  
  
      def __len__(self):
          """
          Returns the total number of available frames.
          """
          raise NotImplementedError
  
  
      @classmethod
      def lookup_options(cls, obj, group):
          return lookup_options(obj, group, cls.backend)
  
  
  
  class PlotSelector(object):
      """
      Proxy that allows dynamic selection of a plotting class based on a
      function of the plotted object. Behaves like a Plot class and
      presents the same parameterized interface.
      """
  
      _disabled_opts = []
  
      def __init__(self, selector, plot_classes, allow_mismatch=False):
          """
          The selector function accepts a component instance and returns
          the appropriate key to index plot_classes dictionary.
          """
          self.selector = selector
          self.plot_classes = OrderedDict(plot_classes)
          interface = self._define_interface(self.plot_classes.values(), allow_mismatch)
          self.style_opts, self.plot_options = interface
  
      def selection_display(self, obj):
          plt_class = self.get_plot_class(obj)
          return getattr(plt_class, 'selection_display', None)
  
      def _define_interface(self, plots, allow_mismatch):
          parameters = [{k:v.precedence for k,v in plot.param.params().items()
                         if ((v.precedence is None) or (v.precedence >= 0))}
                        for plot in plots]
          param_sets = [set(params.keys()) for params in parameters]
          if not allow_mismatch and not all(pset == param_sets[0] for pset in param_sets):
              raise Exception("All selectable plot classes must have identical plot options.")
          styles= [plot.style_opts for plot in plots]
  
          if not allow_mismatch and not all(style == styles[0] for style in styles):
              raise Exception("All selectable plot classes must have identical style options.")
  
          plot_params = {p: v for params in parameters for p, v in params.items()}
          return [s for style in styles for s in style], plot_params
  
  
      def __call__(self, obj, **kwargs):
          plot_class = self.get_plot_class(obj)
          return plot_class(obj, **kwargs)
  
  
      def get_plot_class(self, obj):
          key = self.selector(obj)
          if key not in self.plot_classes:
              msg = "Key %s returned by selector not in set: %s"
              raise Exception(msg  % (key, ', '.join(self.plot_classes.keys())))
          return self.plot_classes[key]
  
  
      def __setattr__(self, label, value):
          try:
              return super(PlotSelector, self).__setattr__(label, value)
          except:
              raise Exception("Please set class parameters directly on classes %s"
                              % ', '.join(str(cls) for cls in self.__dict__['plot_classes'].values()))
  
      def params(self):
          return self.plot_options
  
      @property
      def param(self):
          return self.plot_options
  
  
  
  class DimensionedPlot(Plot):
      """
      DimensionedPlot implements a number of useful methods
      to compute dimension ranges and titles containing the
      dimension values.
      """
  
      fontsize = param.Parameter(default=None, allow_None=True,  doc="""
         Specifies various font sizes of the displayed text.
  
         Finer control is available by supplying a dictionary where any
         unmentioned keys revert to the default sizes, e.g:
  
            {'ticks':20, 'title':15,
             'ylabel':5, 'xlabel':5, 'zlabel':5,
             'legend':8, 'legend_title':13}
  
         You can set the font size of 'zlabel', 'ylabel' and 'xlabel'
         together using the 'labels' key.""")
  
      fontscale = param.Number(default=None, doc="""
         Scales the size of all fonts.""")
  
      #Allowed fontsize keys
      _fontsize_keys = ['xlabel','ylabel', 'zlabel', 'clabel', 'labels',
                        'xticks', 'yticks', 'zticks', 'cticks', 'ticks',
                        'minor_xticks', 'minor_yticks', 'minor_ticks',
                        'title', 'legend', 'legend_title',
                        ]
  
      show_title = param.Boolean(default=True, doc="""
          Whether to display the plot title.""")
  
      title = param.String(default="{label} {group}\n{dimensions}", doc="""
          The formatting string for the title of this plot, allows defining
          a label group separator and dimension labels.""")
  
      title_format = param.String(default=None, doc="Alias for title.")
  
      normalize = param.Boolean(default=True, doc="""
          Whether to compute ranges across all Elements at this level
          of plotting. Allows selecting normalization at different levels
          for nested data containers.""")
  
      projection = param.Parameter(default=None, doc="""
          Allows supplying a custom projection to transform the axis
          coordinates during display. Example projections include '3d'
          and 'polar' projections supported by some backends. Depending
          on the backend custom, projection objects may be supplied.""")
  
      def __init__(self, keys=None, dimensions=None, layout_dimensions=None,
                   uniform=True, subplot=False, adjoined=None, layout_num=0,
                   style=None, subplots=None, dynamic=False, **params):
          self.subplots = subplots
          self.adjoined = adjoined
          self.dimensions = dimensions
          self.layout_num = layout_num
          self.layout_dimensions = layout_dimensions
          self.subplot = subplot
          self.keys = keys if keys is None else list(keys)
          self.uniform = uniform
          self.dynamic = dynamic
          self.drawn = False
          self.handles = {}
          self.group = None
          self.label = None
          self.current_frame = None
          self.current_key = None
          self.ranges = {}
          self._updated = False # Whether the plot should be marked as updated
          super(DimensionedPlot, self).__init__(**params)
  
  
      def __getitem__(self, frame):
          """
          Get the state of the Plot for a given frame number.
          """
          if isinstance(frame, int) and frame > len(self):
              self.param.warning("Showing last frame available: %d" % len(self))
          if not self.drawn: self.handles['fig'] = self.initialize_plot()
          if not isinstance(frame, tuple):
              frame = self.keys[frame]
          self.update_frame(frame)
          return self.state
  
  
      def _get_frame(self, key):
          """
          Required on each MPLPlot type to get the data corresponding
          just to the current frame out from the object.
          """
          pass
  
  
      def matches(self, spec):
          """
          Matches a specification against the current Plot.
          """
          if callable(spec) and not isinstance(spec, type): return spec(self)
          elif isinstance(spec, type): return isinstance(self, spec)
          else:
              raise ValueError("Matching specs have to be either a type or a callable.")
  
  
      def traverse(self, fn=None, specs=None, full_breadth=True):
          """
          Traverses any nested DimensionedPlot returning a list
          of all plots that match the specs. The specs should
          be supplied as a list of either Plot types or callables,
          which should return a boolean given the plot class.
          """
          accumulator = []
          matches = specs is None
          if not matches:
              for spec in specs:
                  matches = self.matches(spec)
                  if matches: break
          if matches:
              accumulator.append(fn(self) if fn else self)
  
          # Assumes composite objects are iterables
          if hasattr(self, 'subplots') and self.subplots:
              for el in self.subplots.values():
                  if el is None:
                      continue
                  accumulator += el.traverse(fn, specs, full_breadth)
                  if not full_breadth: break
          return accumulator
  
  
      def _frame_title(self, key, group_size=2, separator='\n'):
          """
          Returns the formatted dimension group strings
          for a particular frame.
          """
          if self.layout_dimensions is not None:
              dimensions, key = zip(*self.layout_dimensions.items())
          elif not self.dynamic and (not self.uniform or len(self) == 1) or self.subplot:
              return ''
          else:
              key = key if isinstance(key, tuple) else (key,)
              dimensions = self.dimensions
          dimension_labels = [dim.pprint_value_string(k) for dim, k in
                              zip(dimensions, key)]
          groups = [', '.join(dimension_labels[i*group_size:(i+1)*group_size])
                    for i in range(len(dimension_labels))]
          return util.bytes_to_unicode(separator.join(g for g in groups if g))
  
  
      def _format_title(self, key, dimensions=True, separator='\n'):
          if self.title_format:
              self.param.warning('title_format is deprecated. Please use title instead')
  
          label, group, type_name, dim_title = self._format_title_components(
              key, dimensions=True, separator='\n'
          )
  
          custom_title = (self.title != self.param['title'].default)
          if custom_title and self.title_format:
              self.param.warning('Both title and title_format set. Using title')
          title_str = (
              self.title if custom_title or self.title_format is None
              else self.title_format
          )
  
          title = util.bytes_to_unicode(title_str).format(
              label=util.bytes_to_unicode(label),
              group=util.bytes_to_unicode(group),
              type=type_name,
              dimensions=dim_title
          )
          return title.strip(' \n')
  
  
      def _format_title_components(self, key, dimensions=True, separator='\n'):
          """
          Determine components of title as used by _format_title method.
  
          To be overridden in child classes.
  
          Return signature: (label, group, type_name, dim_title)
          """
          return (self.label, self.group, type(self).__name__, '')
  
  
      def _get_fontsize_defaults(self):
          """
          Should returns default fontsize for the following keywords:
  
              * ticks
              * minor_ticks
              * label
              * title
              * legend
              * legend_title
  
          However may also provide more specific defaults for
          specific axis label or ticks, e.g. clabel or xticks.
          """
          return {}
  
  
      def _fontsize(self, key, label='fontsize', common=True):
          if not self.fontsize and not self.fontscale:
              return {}
          elif not isinstance(self.fontsize, dict) and self.fontsize is not None and common:
              return {label: scale_fontsize(self.fontsize, self.fontscale)}
  
          fontsize = self.fontsize if isinstance(self.fontsize, dict) else {}
          unknown_keys = set(fontsize.keys()) - set(self._fontsize_keys)
          if unknown_keys:
              msg = "Popping unknown keys %r from fontsize dictionary.\nValid keys: %r"
              self.param.warning(msg %  (list(unknown_keys), self._fontsize_keys))
              for key in unknown_keys: fontsize.pop(key, None)
  
          defaults = self._get_fontsize_defaults()
          size = None
          if key in fontsize:
              size = fontsize[key]
          elif key in ['zlabel', 'ylabel', 'xlabel', 'clabel']:
              size = fontsize.get('labels', defaults.get(key, defaults.get('label')))
          elif key in ['xticks', 'yticks', 'zticks', 'cticks']:
              size = fontsize.get('ticks', defaults.get(key, defaults.get('ticks')))
          elif key in ['minor_xticks', 'minor_yticks']:
              size = fontsize.get('minor_ticks', defaults.get(key, defaults.get('minor_ticks')))
          elif key in ('legend', 'legend_title', 'title'):
              size = defaults.get(key)
  
          if size is None:
              return {}
  
          return {label: scale_fontsize(size, self.fontscale)}
  
  
      def compute_ranges(self, obj, key, ranges):
          """
          Given an object, a specific key, and the normalization options,
          this method will find the specified normalization options on
          the appropriate OptionTree, group the elements according to
          the selected normalization option (i.e. either per frame or
          over the whole animation) and finally compute the dimension
          ranges in each group. The new set of ranges is returned.
          """
          all_table = all(isinstance(el, Table) for el in obj.traverse(lambda x: x, [Element]))
          if obj is None or not self.normalize or all_table:
              return OrderedDict()
          # Get inherited ranges
          ranges = self.ranges if ranges is None else {k: dict(v) for k, v in ranges.items()}
  
          # Get element identifiers from current object and resolve
          # with selected normalization options
          norm_opts = self._get_norm_opts(obj)
  
          # Traverse displayed object if normalization applies
          # at this level, and ranges for the group have not
          # been supplied from a composite plot
          return_fn = lambda x: x if isinstance(x, Element) else None
          for group, (axiswise, framewise) in norm_opts.items():
              axiswise = (not getattr(self, 'shared_axes', True)) or (axiswise)
              elements = []
              # Skip if ranges are cached or already computed by a
              # higher-level container object.
              framewise = framewise or self.dynamic or len(elements) == 1
              if not framewise: # Traverse to get all elements
                  elements = obj.traverse(return_fn, [group])
              elif key is not None: # Traverse to get elements for each frame
                  frame = self._get_frame(key)
                  elements = [] if frame is None else frame.traverse(return_fn, [group])
              # Only compute ranges if not axiswise on a composite plot
              # or not framewise on a Overlay or ElementPlot
              if (not (axiswise and not isinstance(obj, HoloMap)) or
                  (not framewise and isinstance(obj, HoloMap))):
                  self._compute_group_range(group, elements, ranges, framewise)
          self.ranges.update(ranges)
          return ranges
  
  
      def _get_norm_opts(self, obj):
          """
          Gets the normalization options for a LabelledData object by
          traversing the object to find elements and their ids.
          The id is then used to select the appropriate OptionsTree,
          accumulating the normalization options into a dictionary.
          Returns a dictionary of normalization options for each
          element in the tree.
          """
          norm_opts = {}
  
          # Get all elements' type.group.label specs and ids
          type_val_fn = lambda x: (x.id, (type(x).__name__, util.group_sanitizer(x.group, escape=False),
                                          util.label_sanitizer(x.label, escape=False))) \
              if isinstance(x, Element) else None
          element_specs = {(idspec[0], idspec[1]) for idspec in obj.traverse(type_val_fn)
                           if idspec is not None}
  
          # Group elements specs by ID and override normalization
          # options sequentially
          key_fn = lambda x: -1 if x[0] is None else x[0]
          id_groups = groupby(sorted(element_specs, key=key_fn), key_fn)
          for gid, element_spec_group in id_groups:
              gid = None if gid == -1 else gid
              group_specs = [el for _, el in element_spec_group]
  
              backend = self.renderer.backend
              optstree = Store.custom_options(
                  backend=backend).get(gid, Store.options(backend=backend))
              # Get the normalization options for the current id
              # and match against customizable elements
              for opts in optstree:
                  path = tuple(opts.path.split('.')[1:])
                  applies = any(path == spec[:i] for spec in group_specs
                                for i in range(1, 4))
                  if applies and 'norm' in opts.groups:
                      nopts = opts['norm'].options
                      if 'axiswise' in nopts or 'framewise' in nopts:
                          norm_opts.update({path: (nopts.get('axiswise', False),
                                                   nopts.get('framewise', False))})
          element_specs = [spec for _, spec in element_specs]
          norm_opts.update({spec: (False, False) for spec in element_specs
                            if not any(spec[:i] in norm_opts.keys() for i in range(1, 4))})
          return norm_opts
  
  
      @classmethod
      def _compute_group_range(cls, group, elements, ranges, framewise):
          # Iterate over all elements in a normalization group
          # and accumulate their ranges into the supplied dictionary.
          elements = [el for el in elements if el is not None]
          group_ranges = OrderedDict()
          for el in elements:
              if isinstance(el, (Empty, Table)): continue
              opts = cls.lookup_options(el, 'style')
              plot_opts = cls.lookup_options(el, 'plot')
  
              # Compute normalization for color dim transforms
              for k, v in dict(opts.kwargs, **plot_opts.kwargs).items():
                  if not isinstance(v, dim) or ('color' not in k and k != 'magnitude'):
                      continue
                  if isinstance(v, dim) and v.applies(el):
                      dim_name = repr(v)
                      if dim_name in ranges.get(group, {}) and not framewise:
                          continue
                      values = v.apply(el, expanded=False, all_values=True)
                      factors = None
                      if values.dtype.kind == 'M':
                          drange = values.min(), values.max()
                      elif util.isscalar(values):
                          drange = values, values
                      elif len(values) == 0:
                          drange = np.NaN, np.NaN
                      else:
                          try:
                              with warnings.catch_warnings():
                                  warnings.filterwarnings('ignore', r'All-NaN (slice|axis) encountered')
                                  drange = (np.nanmin(values), np.nanmax(values))
                          except:
                              factors = util.unique_array(values)
                      if dim_name not in group_ranges:
                          group_ranges[dim_name] = {'data': [], 'hard': [], 'soft': []}
                      if factors is not None:
                          if 'factors' not in group_ranges[dim_name]:
                              group_ranges[dim_name]['factors'] = []
                          group_ranges[dim_name]['factors'].append(factors)
                      else:
                          group_ranges[dim_name]['data'].append(drange)
  
              # Compute dimension normalization
              for el_dim in el.dimensions('ranges'):
                  dim_name = el_dim.name
                  if dim_name in ranges.get(group, {}) and not framewise:
                      continue
                  if hasattr(el, 'interface'):
                      if isinstance(el, Graph) and el_dim in el.nodes.dimensions():
                          dtype = el.nodes.interface.dtype(el.nodes, el_dim)
                      elif isinstance(el, Contours) and el.level is not None:
                          dtype = np.array([el.level]).dtype # Remove when deprecating level
                      else:
                          dtype = el.interface.dtype(el, el_dim)
                  else:
                      dtype = None
  
                  if all(util.isfinite(r) for r in el_dim.range):
                      data_range = (None, None)
                  elif dtype is not None and dtype.kind in 'SU':
                      data_range = ('', '')
                  elif isinstance(el, Graph) and el_dim in el.kdims[:2]:
                      data_range = el.nodes.range(2, dimension_range=False)
                  else:
                      data_range = el.range(el_dim, dimension_range=False)
  
                  if dim_name not in group_ranges:
                      group_ranges[dim_name] = {'data': [], 'hard': [], 'soft': []}
                  group_ranges[dim_name]['data'].append(data_range)
                  group_ranges[dim_name]['hard'].append(el_dim.range)
                  group_ranges[dim_name]['soft'].append(el_dim.soft_range)
                  if (any(isinstance(r, util.basestring) for r in data_range) or
                      el_dim.type is not None and issubclass(el_dim.type, util.basestring)):
                      if 'factors' not in group_ranges[dim_name]:
                          group_ranges[dim_name]['factors'] = []
                      if el_dim.values not in ([], None):
                          values = el_dim.values
                      elif el_dim in el:
                          if isinstance(el, Graph) and el_dim in el.kdims[:2]:
                              # Graph start/end normalization should include all node indices
                              values = el.nodes.dimension_values(2, expanded=False)
                          else:
                              values = el.dimension_values(el_dim, expanded=False)
                      elif isinstance(el, Graph) and el_dim in el.nodes:
                          values = el.nodes.dimension_values(el_dim, expanded=False)
                      if (isinstance(values, np.ndarray) and values.dtype.kind == 'O' and
                          all(isinstance(v, (np.ndarray)) for v in values)):
                          values = np.concatenate(values)
                      factors = util.unique_array(values)
                      group_ranges[dim_name]['factors'].append(factors)
  
          group_dim_ranges = defaultdict(dict)
          for gdim, values in group_ranges.items():
              matching = True
              for t, rs in values.items():
                  if t == 'factors':
                      continue
                  matching &= (
                      len({'date' if isinstance(v, util.datetime_types) else 'number'
                           for rng in rs for v in rng if util.isfinite(v)}) < 2
                  )
              if matching:
                  group_dim_ranges[gdim] = values
  
          dim_ranges = []
          for gdim, values in group_dim_ranges.items():
              hard_range = util.max_range(values['hard'], combined=False)
              soft_range = util.max_range(values['soft'])
              data_range = util.max_range(values['data'])
              combined = util.dimension_range(data_range[0], data_range[1],
                                              hard_range, soft_range)
              dranges = {'data': data_range, 'hard': hard_range,
                         'soft': soft_range, 'combined': combined}
              if 'factors' in values:
                  dranges['factors'] = util.unique_array([
                      v for fctrs in values['factors'] for v in fctrs])
              dim_ranges.append((gdim, dranges))
          if group not in ranges:
              ranges[group] = OrderedDict(dim_ranges)
          else:
              ranges[group].update(OrderedDict(dim_ranges))
  
  
      @classmethod
      def _traverse_options(cls, obj, opt_type, opts, specs=None, keyfn=None, defaults=True):
          """
          Traverses the supplied object getting all options in opts for
          the specified opt_type and specs. Also takes into account the
          plotting class defaults for plot options. If a keyfn is
          supplied the returned options will be grouped by the returned
          keys.
          """
          def lookup(x):
              """
              Looks up options for object, including plot defaults.
              keyfn determines returned key otherwise None key is used.
              """
              options = cls.lookup_options(x, opt_type)
              selected = {o: options.options[o]
                          for o in opts if o in options.options}
              if opt_type == 'plot' and defaults:
                  plot = Store.registry[cls.backend].get(type(x))
                  selected['defaults'] = {o: getattr(plot, o) for o in opts
                                          if o not in selected and hasattr(plot, o)}
              key = keyfn(x) if keyfn else None
              return (key, selected)
  
          # Traverse object and accumulate options by key
          traversed = obj.traverse(lookup, specs)
          options = OrderedDict()
          default_opts = defaultdict(lambda: defaultdict(list))
          for key, opts in traversed:
              defaults = opts.pop('defaults', {})
              if key not in options:
                  options[key] = {}
              for opt, v in opts.items():
                  if opt not in options[key]:
                      options[key][opt] = []
                  options[key][opt].append(v)
              for opt, v in defaults.items():
                  default_opts[key][opt].append(v)
  
          # Merge defaults into dictionary if not explicitly specified
          for key, opts in default_opts.items():
              for opt, v in opts.items():
                  if opt not in options[key]:
                      options[key][opt] = v
          return options if keyfn else options[None]
  
  
      def _get_projection(cls, obj):
          """
          Uses traversal to find the appropriate projection
          for a nested object. Respects projections set on
          Overlays before considering Element based settings,
          before finally looking up the default projection on
          the plot type. If more than one non-None projection
          type is found an exception is raised.
          """
          isoverlay = lambda x: isinstance(x, CompositeOverlay)
          element3d = obj.traverse(lambda x: x, [Element3D])
          if element3d:
              return '3d'
          opts = cls._traverse_options(obj, 'plot', ['projection'],
                                       [CompositeOverlay, Element],
                                       keyfn=isoverlay)
          from_overlay = not all(p is None for p in opts.get(True, {}).get('projection', []))
          projections = opts.get(from_overlay, {}).get('projection', [])
          custom_projs = [p for p in projections if p is not None]
          if len(set(custom_projs)) > 1:
              raise Exception("An axis may only be assigned one projection type")
          return custom_projs[0] if custom_projs else None
  
  
      def update(self, key):
          if len(self) == 1 and ((key == 0) or (key == self.keys[0])) and not self.drawn:
              return self.initialize_plot()
          item = self.__getitem__(key)
          self.traverse(lambda x: setattr(x, '_updated', True))
          return item
  
  
      def __len__(self):
          """
          Returns the total number of available frames.
          """
          return len(self.keys)
  
  
  
  class CallbackPlot(object):
  
      backend = None
  
      def _construct_callbacks(self):
          """
          Initializes any callbacks for streams which have defined
          the plotted object as a source.
          """
          cb_classes = set()
          registry = list(Stream.registry.items())
          callbacks = Stream._callbacks[self.backend]
          for source in self.link_sources:
              streams = [
                  s for src, streams in registry for s in streams
                  if src is source or (src._plot_id is not None and
                                       src._plot_id == source._plot_id)]
              cb_classes |= {(callbacks[type(stream)], stream) for stream in streams
                             if type(stream) in callbacks and stream.linked
                             and stream.source is not None}
          cbs = []
          sorted_cbs = sorted(cb_classes, key=lambda x: id(x[0]))
          for cb, group in groupby(sorted_cbs, lambda x: x[0]):
              cb_streams = [s for _, s in group]
              cbs.append(cb(self, cb_streams, source))
          return cbs
  
      @property
      def link_sources(self):
          "Returns potential Link or Stream sources."
          if isinstance(self, GenericOverlayPlot):
              zorders = []
          elif self.batched:
              zorders = list(range(self.zorder, self.zorder+len(self.hmap.last)))
          else:
              zorders = [self.zorder]
  
          if isinstance(self, GenericOverlayPlot) and not self.batched:
              sources = []
          elif not self.static or isinstance(self.hmap, DynamicMap):
              sources = [o for i, inputs in self.stream_sources.items()
                         for o in inputs if i in zorders]
          else:
              sources = [self.hmap.last]
          return sources
  
  
  
  class GenericElementPlot(DimensionedPlot):
      """
      Plotting baseclass to render contents of an Element. Implements
      methods to get the correct frame given a HoloMap, axis labels and
      extents and titles.
      """
  
      apply_ranges = param.Boolean(default=True, doc="""
          Whether to compute the plot bounds from the data itself.""")
  
      apply_extents = param.Boolean(default=True, doc="""
          Whether to apply extent overrides on the Elements""")
  
      bgcolor = param.ClassSelector(class_=(str, tuple), default=None, doc="""
          If set bgcolor overrides the background color of the axis.""")
  
      default_span = param.ClassSelector(default=2.0, class_=(int, float, tuple), doc="""
          Defines the span of an axis if the axis range is zero, i.e. if
          the lower and upper end of an axis are equal or no range is
          defined at all. For example if there is a single datapoint at
          0 a default_span of 2.0 will result in axis ranges spanning
          from -1 to 1.""")
  
      hooks = param.HookList(default=[], doc="""
          Optional list of hooks called when finalizing a plot. The
          hook is passed the plot object and the displayed element, and
          other plotting handles can be accessed via plot.handles.""")
  
      invert_axes = param.Boolean(default=False, doc="""
          Whether to invert the x- and y-axis""")
  
      invert_xaxis = param.Boolean(default=False, doc="""
          Whether to invert the plot x-axis.""")
  
      invert_yaxis = param.Boolean(default=False, doc="""
          Whether to invert the plot y-axis.""")
  
      finalize_hooks = param.HookList(default=[], doc="""
          Deprecated; use hooks options instead.""")
  
      logx = param.Boolean(default=False, doc="""
          Whether the x-axis of the plot will be a log axis.""")
  
      logy = param.Boolean(default=False, doc="""
          Whether the y-axis of the plot will be a log axis.""")
  
      padding = param.ClassSelector(default=0.1, class_=(int, float, tuple), doc="""
          Fraction by which to increase auto-ranged extents to make
          datapoints more visible around borders.
  
          To compute padding, the axis whose screen size is largest is
          chosen, and the range of that axis is increased by the
          specified fraction along each axis.  Other axes are then
          padded ensuring that the amount of screen space devoted to
          padding is equal for all axes. If specified as a tuple, the
          int or float values in the tuple will be used for padding in
          each axis, in order (x,y or x,y,z).
  
          For example, for padding=0.2 on a 800x800-pixel plot, an x-axis
          with the range [0,10] will be padded by 20% to be [-1,11], while
          a y-axis with a range [0,1000] will be padded to be [-100,1100],
          which should make the padding be approximately the same number of
          pixels. But if the same plot is changed to have a height of only
          200, the y-range will then be [-400,1400] so that the y-axis
          padding will still match that of the x-axis.
  
          It is also possible to declare non-equal padding value for the
          lower and upper bound of an axis by supplying nested tuples,
          e.g. padding=(0.1, (0, 0.1)) will pad the x-axis lower and
          upper bound as well as the y-axis upper bound by a fraction of
          0.1 while the y-axis lower bound is not padded at all.""")
  
      show_legend = param.Boolean(default=True, doc="""
          Whether to show legend for the plot.""")
  
      show_grid = param.Boolean(default=False, doc="""
          Whether to show a Cartesian grid on the plot.""")
  
      xaxis = param.ObjectSelector(default='bottom',
                                   objects=['top', 'bottom', 'bare', 'top-bare',
                                            'bottom-bare', None, True, False], doc="""
          Whether and where to display the xaxis.
          The "bare" options allow suppressing all axis labels, including ticks and xlabel.
          Valid options are 'top', 'bottom', 'bare', 'top-bare' and 'bottom-bare'.""")
  
      yaxis = param.ObjectSelector(default='left',
                                        objects=['left', 'right', 'bare', 'left-bare',
                                                 'right-bare', None, True, False], doc="""
          Whether and where to display the yaxis.
          The "bare" options allow suppressing all axis labels, including ticks and ylabel.
          Valid options are 'left', 'right', 'bare', 'left-bare' and 'right-bare'.""")
  
      xlabel = param.String(default=None, doc="""
          An explicit override of the x-axis label, if set takes precedence
          over the dimension label.""")
  
      ylabel = param.String(default=None, doc="""
          An explicit override of the y-axis label, if set takes precedence
          over the dimension label.""")
  
      xlim = param.Tuple(default=(np.nan, np.nan), length=2, doc="""
         User-specified x-axis range limits for the plot, as a tuple (low,high).
         If specified, takes precedence over data and dimension ranges.""")
  
      ylim = param.Tuple(default=(np.nan, np.nan), length=2, doc="""
         User-specified x-axis range limits for the plot, as a tuple (low,high).
         If specified, takes precedence over data and dimension ranges.""")
  
      zlim = param.Tuple(default=(np.nan, np.nan), length=2, doc="""
         User-specified z-axis range limits for the plot, as a tuple (low,high).
         If specified, takes precedence over data and dimension ranges.""")
  
      xrotation = param.Integer(default=None, bounds=(0, 360), doc="""
          Rotation angle of the xticks.""")
  
      yrotation = param.Integer(default=None, bounds=(0, 360), doc="""
          Rotation angle of the yticks.""")
  
      xticks = param.Parameter(default=None, doc="""
          Ticks along x-axis specified as an integer, explicit list of
          tick locations, or bokeh Ticker object. If set to None default
          bokeh ticking behavior is applied.""")
  
      yticks = param.Parameter(default=None, doc="""
          Ticks along y-axis specified as an integer, explicit list of
          tick locations, or bokeh Ticker object. If set to None
          default bokeh ticking behavior is applied.""")
  
      # A dictionary mapping of the plot methods used to draw the
      # glyphs corresponding to the ElementPlot, can support two
      # keyword arguments a 'single' implementation to draw an individual
      # plot and a 'batched' method to draw multiple Elements at once
      _plot_methods = {}
  
      # Declares the options that are propagated from sub-elements of the
      # plot, mostly useful for inheriting options from individual
      # Elements on an OverlayPlot. Enabled by default in v1.7.
      _propagate_options = []
      v17_option_propagation = True
  
      _selection_display = NoOpSelectionDisplay()
  
      def __init__(self, element, keys=None, ranges=None, dimensions=None,
                   batched=False, overlaid=0, cyclic_index=0, zorder=0, style=None,
                   overlay_dims={}, stream_sources=[], streams=None, **params):
          self.zorder = zorder
          self.cyclic_index = cyclic_index
          self.overlaid = overlaid
          self.batched = batched
          self.overlay_dims = overlay_dims
  
          if not isinstance(element, (HoloMap, DynamicMap)):
              self.hmap = HoloMap(initial_items=(0, element),
                                 kdims=['Frame'], id=element.id)
          else:
              self.hmap = element
  
          if overlaid:
              self.stream_sources = stream_sources
          else:
              self.stream_sources = compute_overlayable_zorders(self.hmap)
  
          plot_element = self.hmap.last
          if self.batched and not isinstance(self, GenericOverlayPlot):
              plot_element = plot_element.last
  
          dynamic = isinstance(element, DynamicMap) and not element.unbounded
          self.top_level = keys is None
          if self.top_level:
              dimensions = self.hmap.kdims
              keys = list(self.hmap.data.keys())
  
          self.style = self.lookup_options(plot_element, 'style') if style is None else style
          plot_opts = self.lookup_options(plot_element, 'plot').options
          if self.v17_option_propagation:
              inherited = self._traverse_options(plot_element, 'plot',
                                                 self._propagate_options,
                                                 defaults=False)
              plot_opts.update(**{k: v[0] for k, v in inherited.items()
                                  if k not in plot_opts})
  
          super(GenericElementPlot, self).__init__(keys=keys, dimensions=dimensions,
                                                   dynamic=dynamic,
                                                   **dict(params, **plot_opts))
          self.streams = get_nested_streams(self.hmap) if streams is None else streams
  
          # Attach streams if not overlaid and not a batched ElementPlot
          if not (self.overlaid or (self.batched and not isinstance(self, GenericOverlayPlot))):
              attach_streams(self, self.hmap)
  
          # Update plot and style options for batched plots
          if self.batched:
              self.ordering = util.layer_sort(self.hmap)
              overlay_opts = self.lookup_options(self.hmap.last, 'plot').options.items()
              opts = {k: v for k, v in overlay_opts if k in self.param}
              self.param.set_param(**opts)
              self.style = self.lookup_options(plot_element, 'style').max_cycles(len(self.ordering))
          else:
              self.ordering = []
  
  
      def get_zorder(self, overlay, key, el):
          """
          Computes the z-order of element in the NdOverlay
          taking into account possible batching of elements.
          """
          spec = util.get_overlay_spec(overlay, key, el)
          return self.ordering.index(spec)
  
  
      def _updated_zorders(self, overlay):
          specs = [util.get_overlay_spec(overlay, key, el)
                   for key, el in overlay.data.items()]
          self.ordering = sorted(set(self.ordering+specs))
          return [self.ordering.index(spec) for spec in specs]
  
  
      def _get_frame(self, key):
          if isinstance(self.hmap, DynamicMap) and self.overlaid and self.current_frame:
              self.current_key = key
              return self.current_frame
          elif key == self.current_key and not self._force:
              return self.current_frame
  
          cached = self.current_key is None and not any(s._triggering for s in self.streams)
          key_map = dict(zip([d.name for d in self.dimensions], key))
          frame = get_plot_frame(self.hmap, key_map, cached)
          traverse_setter(self, '_force', False)
  
          if not key in self.keys and len(key) == self.hmap.ndims and self.dynamic:
              self.keys.append(key)
          self.current_frame = frame
          self.current_key = key
          return frame
  
  
      def _execute_hooks(self, element):
          """
          Executes finalize hooks
          """
          if self.hooks and self.finalize_hooks:
              self.param.warning(
                  "Supply either hooks or finalize_hooks not both, "
                  "using hooks and ignoring finalize_hooks.")
          elif self.finalize_hooks:
              self.param.warning(
                  "The finalize_hooks option is deprecated, use the "
                  "hooks option instead.")
          hooks = self.hooks or self.finalize_hooks
          for hook in hooks:
              try:
                  hook(self, element)
              except Exception as e:
                  self.param.warning("Plotting hook %r could not be "
                                     "applied:\n\n %s" % (hook, e))
  
  
      def get_aspect(self, xspan, yspan):
          """
          Should define the aspect ratio of the plot.
          """
  
  
      def get_padding(self, obj, extents):
          """
          Computes padding along the axes taking into account the plot aspect.
          """
          (x0, y0, z0, x1, y1, z1) = extents
          padding_opt = self.lookup_options(obj, 'plot').kwargs.get('padding')
          if self.overlaid:
              padding = 0
          elif padding_opt is None:
              if self.param.objects('existing')['padding'].default is not self.padding:
                  padding = self.padding
              else:
                  opts = self._traverse_options(
                      obj, 'plot', ['padding'], specs=[Element], defaults=True
                  )
                  padding = opts.get('padding')
                  if padding:
                      padding = padding[0]
                  else:
                      padding = self.padding
          else:
              padding = padding_opt
          xpad, ypad, zpad = get_axis_padding(padding)
          if not self.overlaid and not self.batched:
              xspan = x1-x0 if util.is_number(x0) and util.is_number(x1) else None
              yspan = y1-y0 if util.is_number(y0) and util.is_number(y1) else None
              aspect = self.get_aspect(xspan, yspan)
              if aspect > 1:
                  xpad = tuple(xp/aspect for xp in xpad) if isinstance(xpad, tuple) else xpad/aspect
              else:
                  ypad = tuple(yp*aspect for yp in ypad) if isinstance(ypad, tuple) else ypad*aspect
          return xpad, ypad, zpad
  
  
      def _get_range_extents(self, element, ranges, range_type, xdim, ydim, zdim):
          dims = element.dimensions()
          ndims = len(dims)
          xdim = xdim or (dims[0] if ndims else None)
          ydim = ydim or (dims[1] if ndims > 1 else None)
          if self.projection == '3d':
              zdim = zdim or (dims[2] if ndims > 2 else None)
          else:
              zdim = None
  
          (x0, x1), xsrange, xhrange = get_range(element, ranges, xdim)
          (y0, y1), ysrange, yhrange = get_range(element, ranges, ydim)
          (z0, z1), zsrange, zhrange = get_range(element, ranges, zdim)
  
          if not self.overlaid and not self.batched:
              xspan, yspan, zspan = (v/2. for v in get_axis_padding(self.default_span))
              mx0, mx1 = get_minimum_span(x0, x1, xspan)
  
              # If auto-padding is enabled ensure RangeXY dependent plots
              # are recomputed before initial render
              if x0 != mx0 or x1 != mx1:
                  for stream in self.streams:
                      if isinstance(stream, (RangeX, RangeXY)):
                          stream.update(x_range=(mx0, mx1))
                          if stream not in self._trigger:
                              self._trigger.append(stream)
                  x0, x1 = mx0, mx1
              my0, my1 = get_minimum_span(y0, y1, yspan)
              if y0 != my0 or y1 != my1:
                  for stream in self.streams:
                      if isinstance(stream, (RangeY, RangeXY)):
                          stream.update(y_range=(my0, my1))
                          if stream not in self._trigger:
                              self._trigger.append(stream)
                  y0, y1 = my0, my1
  
              mz0, mz1 = get_minimum_span(z0, z1, zspan)
          xpad, ypad, zpad = self.get_padding(element, (x0, y0, z0, x1, y1, z1))
  
          if range_type == 'soft':
              x0, x1 = xsrange
          elif range_type == 'hard':
              x0, x1 = xhrange
          elif xdim == 'categorical':
              x0, x1 = '', ''
          elif range_type == 'combined':
              x0, x1 = util.dimension_range(x0, x1, xhrange, xsrange, xpad, self.logx)
  
          if range_type == 'soft':
              y0, y1 = ysrange
          elif range_type == 'hard':
              y0, y1 = yhrange
          elif range_type == 'combined':
              y0, y1 = util.dimension_range(y0, y1, yhrange, ysrange, ypad, self.logy)
          elif ydim == 'categorical':
              y0, y1 = '', ''
          elif ydim is None:
              y0, y1 = np.NaN, np.NaN
  
          if self.projection == '3d':
              if range_type == 'soft':
                  z0, z1 = zsrange
              elif range_type == 'data':
                  z0, z1 = zhrange
              elif range_type=='combined':
                  z0, z1 = util.dimension_range(z0, z1, zhrange, zsrange, zpad, self.logz)
              elif zdim == 'categorical':
                  z0, z1 = '', ''
              elif zdim is None:
                  z0, z1 = np.NaN, np.NaN
              return (x0, y0, z0, x1, y1, z1)
          return (x0, y0, x1, y1)
  
  
      def get_extents(self, element, ranges, range_type='combined', xdim=None, ydim=None, zdim=None):
          """
          Gets the extents for the axes from the current Element. The globally
          computed ranges can optionally override the extents.
  
          The extents are computed by combining the data ranges, extents
          and dimension ranges. Each of these can be obtained individually
          by setting the range_type to one of:
  
          * 'data': Just the data ranges
          * 'extents': Element.extents
          * 'soft': Dimension.soft_range values
          * 'hard': Dimension.range values
  
          To obtain the combined range, which includes range padding the
          default may be used:
  
          * 'combined': All the range types combined and padding applied
  
          This allows Overlay plots to obtain each range and combine them
          appropriately for all the objects in the overlay.
          """
          num = 6 if self.projection == '3d' else 4
          if self.apply_extents and range_type in ('combined', 'extents'):
              norm_opts = self.lookup_options(element, 'norm').options
              if norm_opts.get('framewise', False) or self.dynamic:
                  extents = element.extents
              else:
                  extent_list = self.hmap.traverse(lambda x: x.extents, [Element])
                  extents = util.max_extents(extent_list, self.projection == '3d')
          else:
              extents = (np.NaN,) * num
  
          if range_type == 'extents':
              return extents
  
          if self.apply_ranges:
              range_extents = self._get_range_extents(element, ranges, range_type, xdim, ydim, zdim)
          else:
              range_extents = (np.NaN,) * num
  
          if getattr(self, 'shared_axes', False) and self.subplot:
              combined = util.max_extents([range_extents, extents], self.projection == '3d')
          else:
              max_extent = []
              for l1, l2 in zip(range_extents, extents):
                  if isfinite(l2):
                      max_extent.append(l2)
                  else:
                      max_extent.append(l1)
              combined = tuple(max_extent)
  
          if self.projection == '3d':
              x0, y0, z0, x1, y1, z1 = combined
          else:
              x0, y0, x1, y1 = combined
  
          x0, x1 = util.dimension_range(x0, x1, self.xlim, (None, None))
          y0, y1 = util.dimension_range(y0, y1, self.ylim, (None, None))
          if self.projection == '3d':
              z0, z1 = util.dimension_range(z0, z1, self.zlim, (None, None))
              return (x0, y0, z0, x1, y1, z1)
          return (x0, y0, x1, y1)
  
  
      def _get_axis_labels(self, dimensions, xlabel=None, ylabel=None, zlabel=None):
          if self.xlabel is not None:
              xlabel = self.xlabel
          elif dimensions and xlabel is None:
              xdims = dimensions[0]
              xlabel = dim_axis_label(xdims) if xdims else ''
  
          if self.ylabel is not None:
              ylabel = self.ylabel
          elif len(dimensions) >= 2 and ylabel is None:
              ydims = dimensions[1]
              ylabel = dim_axis_label(ydims) if ydims else ''
  
          if getattr(self, 'zlabel', None) is not None:
              zlabel = self.zlabel
          elif self.projection == '3d' and len(dimensions) >= 3 and zlabel is None:
              zlabel = dim_axis_label(dimensions[2]) if dimensions[2] else ''
          return xlabel, ylabel, zlabel
  
  
      def _format_title_components(self, key, dimensions=True, separator='\n'):
          frame = self._get_frame(key)
          if frame is None:
              return ('', '', '', '')
          type_name = type(frame).__name__
          group = frame.group if frame.group != type_name else ''
          label = frame.label
  
          if self.layout_dimensions or dimensions:
              dim_title = self._frame_title(key, separator=separator)
          else:
              dim_title = ''
  
          return (label, group, type_name, dim_title)
  
  
      def update_frame(self, key, ranges=None):
          """
          Set the plot(s) to the given frame number.  Operates by
          manipulating the matplotlib objects held in the self._handles
          dictionary.
  
          If n is greater than the number of available frames, update
          using the last available frame.
          """
  
  
  class GenericOverlayPlot(GenericElementPlot):
      """
      Plotting baseclass to render (Nd)Overlay objects. It implements
      methods to handle the creation of ElementPlots, coordinating style
      groupings and zorder for all layers across a HoloMap. It also
      allows collapsing of layers via the Compositor.
      """
  
      batched = param.Boolean(default=True, doc="""
          Whether to plot Elements NdOverlay in a batched plotting call
          if possible. Disables legends and zorder may not be preserved.""")
  
      legend_limit = param.Integer(default=25, doc="""
          Number of rendered glyphs before legends are disabled.""")
  
      show_legend = param.Boolean(default=True, doc="""
          Whether to show legend for the plot.""")
  
      style_grouping = param.Integer(default=2, doc="""
          The length of the type.group.label spec that will be used to
          group Elements into style groups.  A style_grouping value of
          1 will group just by type, a value of 2 will group by type and
          group, and a value of 3 will group by the full specification.""")
  
      _passed_handles = []
  
      def __init__(self, overlay, ranges=None, batched=True, keys=None, group_counter=None, **params):
          if 'projection' not in params:
              params['projection'] = self._get_projection(overlay)
  
          super(GenericOverlayPlot, self).__init__(overlay, ranges=ranges, keys=keys,
                                                   batched=batched, **params)
  
          # Apply data collapse
          self.hmap = self._apply_compositor(self.hmap, ranges, self.keys)
          self.map_lengths = Counter()
          self.group_counter = Counter() if group_counter is None else group_counter
          self.cyclic_index_lookup = {}
          self.zoffset = 0
          self.subplots = self._create_subplots(ranges)
          self.traverse(lambda x: setattr(x, 'comm', self.comm))
          self.top_level = keys is None
          self.dynamic_subplots = []
          if self.top_level:
              self.traverse(lambda x: attach_streams(self, x.hmap, 2),
                            [GenericElementPlot])
  
  
      def _apply_compositor(self, holomap, ranges=None, keys=None, dimensions=None):
          """
          Given a HoloMap compute the appropriate (mapwise or framewise)
          ranges in order to apply the Compositor collapse operations in
          display mode (data collapse should already have happened).
          """
          # Compute framewise normalization
          defaultdim = holomap.ndims == 1 and holomap.kdims[0].name != 'Frame'
  
          if keys and ranges and dimensions and not defaultdim:
              dim_inds = [dimensions.index(d) for d in holomap.kdims]
              sliced_keys = [tuple(k[i] for i in dim_inds) for k in keys]
              frame_ranges = OrderedDict([(slckey, self.compute_ranges(holomap, key, ranges[key]))
                                          for key, slckey in zip(keys, sliced_keys) if slckey in holomap.data.keys()])
          else:
              mapwise_ranges = self.compute_ranges(holomap, None, None)
              frame_ranges = OrderedDict([(key, self.compute_ranges(holomap, key, mapwise_ranges))
                                          for key in holomap.data.keys()])
          ranges = frame_ranges.values()
  
          return Compositor.collapse(holomap, (ranges, frame_ranges.keys()), mode='display')
  
  
      def _create_subplots(self, ranges):
          # Check if plot should be batched
          ordering = util.layer_sort(self.hmap)
          batched = self.batched and type(self.hmap.last) is NdOverlay
          if batched:
              backend = self.renderer.backend
              batchedplot = Store.registry[backend].get(self.hmap.last.type)
          if (batched and batchedplot and 'batched' in batchedplot._plot_methods and
              (not self.show_legend or len(ordering) > self.legend_limit)):
              self.batched = True
              keys, vmaps = [()], [self.hmap]
          else:
              self.batched = False
              keys, vmaps = self.hmap._split_overlays()
  
          if isinstance(self.hmap, DynamicMap):
              dmap_streams = [get_nested_streams(layer) for layer in
                              split_dmap_overlay(self.hmap)]
          else:
              dmap_streams = [None]*len(keys)
  
          # Compute global ordering
          length = self.style_grouping
          group_fn = lambda x: (x.type.__name__, x.last.group, x.last.label)
          for m in vmaps:
              self.map_lengths[group_fn(m)[:length]] += 1
  
          subplots = OrderedDict()
          for (key, vmap, streams) in zip(keys, vmaps, dmap_streams):
              subplot = self._create_subplot(key, vmap, streams, ranges)
              if subplot is None:
                  continue
              if not isinstance(key, tuple): key = (key,)
              subplots[key] = subplot
              if isinstance(subplot, GenericOverlayPlot):
                  self.zoffset += len(subplot.subplots.keys()) - 1
  
          if not subplots:
              raise SkipRendering("%s backend could not plot any Elements "
                                  "in the Overlay." % self.renderer.backend)
          return subplots
  
  
      def _create_subplot(self, key, obj, streams, ranges):
          registry = Store.registry[self.renderer.backend]
          ordering = util.layer_sort(self.hmap)
          overlay_type = 1 if self.hmap.type == Overlay else 2
          group_fn = lambda x: (x.type.__name__, x.last.group, x.last.label)
  
          opts = {'overlaid': overlay_type}
          if self.hmap.type == Overlay:
              style_key = (obj.type.__name__,) + key
              if self.overlay_dims:
                  opts['overlay_dims'] = self.overlay_dims
          else:
              if not isinstance(key, tuple): key = (key,)
              style_key = group_fn(obj) + key
              opts['overlay_dims'] = OrderedDict(zip(self.hmap.last.kdims, key))
  
          if self.batched:
              vtype = type(obj.last.last)
              oidx = 0
          else:
              vtype = type(obj.last)
              if style_key not in ordering:
                  ordering.append(style_key)
              oidx = ordering.index(style_key)
  
          plottype = registry.get(vtype, None)
          if plottype is None:
              self.param.warning(
                  "No plotting class for %s type and %s backend "
                  "found. " % (vtype.__name__, self.renderer.backend))
              return None
  
          # Get zorder and style counter
          length = self.style_grouping
          group_key = style_key[:length]
          zorder = self.zorder + oidx + self.zoffset
          cyclic_index = self.group_counter[group_key]
          self.cyclic_index_lookup[style_key] = cyclic_index
          self.group_counter[group_key] += 1
          group_length = self.map_lengths[group_key]
  
          if not isinstance(plottype, PlotSelector) and issubclass(plottype, GenericOverlayPlot):
              opts['group_counter'] = self.group_counter
              opts['show_legend'] = self.show_legend
              if not any(len(frame) for frame in obj):
                  self.param.warning('%s is empty and will be skipped '
                                     'during plotting' % obj.last)
                  return None
          elif self.batched and 'batched' in plottype._plot_methods:
              param_vals = dict(self.param.get_param_values())
              propagate = {opt: param_vals[opt] for opt in self._propagate_options
                           if opt in param_vals}
              opts['batched'] = self.batched
              opts['overlaid'] = self.overlaid
              opts.update(propagate)
          if len(ordering) > self.legend_limit:
              opts['show_legend'] = False
          style = self.lookup_options(obj.last, 'style').max_cycles(group_length)
          passed_handles = {k: v for k, v in self.handles.items()
                            if k in self._passed_handles}
          plotopts = dict(opts, cyclic_index=cyclic_index,
                          invert_axes=self.invert_axes,
                          dimensions=self.dimensions, keys=self.keys,
                          layout_dimensions=self.layout_dimensions,
                          ranges=ranges, show_title=self.show_title,
                          style=style, uniform=self.uniform,
                          fontsize=self.fontsize, streams=streams,
                          renderer=self.renderer, adjoined=self.adjoined,
                          stream_sources=self.stream_sources,
                          projection=self.projection, fontscale=self.fontscale,
                          zorder=zorder, root=self.root, **passed_handles)
          return plottype(obj, **plotopts)
  
  
      def _create_dynamic_subplots(self, key, items, ranges, **init_kwargs):
          """
          Handles the creation of new subplots when a DynamicMap returns
          a changing set of elements in an Overlay.
          """
          length = self.style_grouping
          group_fn = lambda x: (x.type.__name__, x.last.group, x.last.label)
          for i, (k, obj) in enumerate(items):
              vmap = self.hmap.clone([(key, obj)])
              self.map_lengths[group_fn(vmap)[:length]] += 1
              subplot = self._create_subplot(k, vmap, [], ranges)
              if subplot is None:
                  continue
              self.subplots[k] = subplot
              subplot.initialize_plot(ranges, **init_kwargs)
              subplot.update_frame(key, ranges, element=obj)
              self.dynamic_subplots.append(subplot)
  
  
      def _update_subplot(self, subplot, spec):
          """
          Updates existing subplots when the subplot has been assigned
          to plot an element that is not an exact match to the object
          it was initially assigned.
          """
  
          # See if the precise spec has already been assigned a cyclic
          # index otherwise generate a new one
          if spec in self.cyclic_index_lookup:
              cyclic_index = self.cyclic_index_lookup[spec]
          else:
              group_key = spec[:self.style_grouping]
              self.group_counter[group_key] += 1
              cyclic_index = self.group_counter[group_key]
              self.cyclic_index_lookup[spec] = cyclic_index
  
          subplot.cyclic_index = cyclic_index
          if subplot.overlay_dims:
              odim_key = util.wrap_tuple(spec[-1])
              new_dims = zip(subplot.overlay_dims, odim_key)
              subplot.overlay_dims = util.OrderedDict(new_dims)
  
  
      def _get_subplot_extents(self, overlay, ranges, range_type):
          """
          Iterates over all subplots and collects the extents of each.
          """
          if range_type == 'combined':
              extents = {'extents': [], 'soft': [], 'hard': [], 'data': []}
          else:
              extents = {range_type: []}
          items = overlay.items()
          if self.batched and self.subplots:
              subplot = list(self.subplots.values())[0]
              subplots = [(k, subplot) for k in overlay.data.keys()]
          else:
              subplots = self.subplots.items()
  
          for key, subplot in subplots:
              found = False
              if subplot is None:
                  continue
              layer = overlay.data.get(key, None)
              if isinstance(self.hmap, DynamicMap) and layer is None:
                  for _, layer in items:
                      if isinstance(layer, subplot.hmap.type):
                          found = True
                          break
                  if not found:
                      layer = None
              if layer is None or not subplot.apply_ranges:
                  continue
  
              if isinstance(layer, CompositeOverlay):
                  sp_ranges = ranges
              else:
                  sp_ranges = util.match_spec(layer, ranges) if ranges else {}
              for rt in extents:
                  extent = subplot.get_extents(layer, sp_ranges, range_type=rt)
                  extents[rt].append(extent)
          return extents
  
  
      def get_extents(self, overlay, ranges, range_type='combined'):
          subplot_extents = self._get_subplot_extents(overlay, ranges, range_type)
          zrange = self.projection == '3d'
          extents = {k: util.max_extents(rs, zrange) for k, rs in subplot_extents.items()}
          if range_type != 'combined':
              return extents[range_type]
  
          # Unpack extents
          if len(extents['data']) == 6:
              x0, y0, z0, x1, y1, z1 = extents['data']
              sx0, sy0, sz0, sx1, sy1, sz1 = extents['soft']
              hx0, hy0, hz0, hx1, hy1, hz1 = extents['hard']
          else:
              x0, y0, x1, y1 = extents['data']
              sx0, sy0, sx1, sy1 = extents['soft']
              hx0, hy0, hx1, hy1 = extents['hard']
              z0, z1 = np.NaN, np.NaN
  
          # Apply minimum span
          xspan, yspan, zspan = (v/2. for v in get_axis_padding(self.default_span))
          x0, x1 = get_minimum_span(x0, x1, xspan)
          y0, y1 = get_minimum_span(y0, y1, yspan)
          z0, z1 = get_minimum_span(z0, z1, zspan)
  
          # Apply padding
          xpad, ypad, zpad = self.get_padding(overlay, (x0, y0, z0, x1, y1, z1))
          x0, x1 = util.dimension_range(x0, x1, (hx0, hx1), (sx0, sx1), xpad, self.logx)
          y0, y1 = util.dimension_range(y0, y1, (hy0, hy1), (sy0, sy1), ypad, self.logy)
          if len(extents['data']) == 6:
              z0, z1 = util.dimension_range(z0, z1, (hz0, hz1), (sz0, sz1), zpad, self.logz)
              padded = (x0, y0, z0, x1, y1, z1)
          else:
              padded = (x0, y0, x1, y1)
  
          # Combine with Element.extents
          combined = util.max_extents([padded, extents['extents']], zrange)
          if self.projection == '3d':
              x0, y0, z0, x1, y1, z1 = combined
          else:
              x0, y0, x1, y1 = combined
  
          # Apply xlim, ylim, zlim plot option
          x0, x1 = util.dimension_range(x0, x1, self.xlim, (None, None))
          y0, y1 = util.dimension_range(y0, y1, self.ylim, (None, None))
          if self.projection == '3d':
              z0, z1 = util.dimension_range(z0, z1, getattr(self, 'zlim', (None, None)), (None, None))
              return (x0, y0, z0, x1, y1, z1)
          return (x0, y0, x1, y1)
  
  
  class GenericCompositePlot(DimensionedPlot):
  
      def __init__(self, layout, keys=None, dimensions=None, **params):
          if 'uniform' not in params:
              params['uniform'] = traversal.uniform(layout)
  
          self.top_level = keys is None
          if self.top_level:
              dimensions, keys = traversal.unique_dimkeys(layout)
  
          dynamic, unbounded = get_dynamic_mode(layout)
          if unbounded:
              initialize_unbounded(layout, dimensions, keys[0])
          self.layout = layout
          super(GenericCompositePlot, self).__init__(keys=keys,
                                                     dynamic=dynamic,
                                                     dimensions=dimensions,
                                                     **params)
          nested_streams = layout.traverse(lambda x: get_nested_streams(x),
                                           [DynamicMap])
          self.streams = list(set([s for streams in nested_streams for s in streams]))
          self._link_dimensioned_streams()
  
      def _link_dimensioned_streams(self):
          """
          Should perform any linking required to update titles when dimensioned
          streams change.
          """
  
      def _get_frame(self, key):
          """
          Creates a clone of the Layout with the nth-frame for each
          Element.
          """
          cached = self.current_key is None
          layout_frame = self.layout.clone(shared_data=False)
          if key == self.current_key and not self._force:
              return self.current_frame
          else:
              self.current_key = key
  
          key_map = dict(zip([d.name for d in self.dimensions], key))
          for path, item in self.layout.items():
              frame = get_nested_plot_frame(item, key_map, cached)
              if frame is not None:
                  layout_frame[path] = frame
          traverse_setter(self, '_force', False)
  
          self.current_frame = layout_frame
          return layout_frame
  
  
      def _format_title_components(self, key, dimensions=True, separator='\n'):
          dim_title = self._frame_title(key, 3, separator) if dimensions else ''
          layout = self.layout
          type_name = type(self.layout).__name__
          group = util.bytes_to_unicode(layout.group if layout.group != type_name else '')
          label = util.bytes_to_unicode(layout.label)
          return (label, group, type_name, dim_title)
  
  
  class GenericLayoutPlot(GenericCompositePlot):
      """
      A GenericLayoutPlot accepts either a Layout or a NdLayout and
      displays the elements in a cartesian grid in scanline order.
      """
  
      transpose = param.Boolean(default=False, doc="""
          Whether to transpose the layout when plotting. Switches
          from row-based left-to-right and top-to-bottom scanline order
          to column-based top-to-bottom and left-to-right order.""")
  
      def __init__(self, layout, **params):
          if not isinstance(layout, (NdLayout, Layout)):
              raise ValueError("GenericLayoutPlot only accepts Layout objects.")
          if len(layout.values()) == 0:
              raise SkipRendering(warn=False)
  
          super(GenericLayoutPlot, self).__init__(layout, **params)
          self.subplots = {}
          self.rows, self.cols = layout.shape[::-1] if self.transpose else layout.shape
          self.coords = list(product(range(self.rows),
                                     range(self.cols)))
  
  
  class GenericAdjointLayoutPlot(Plot):
      """
      AdjointLayoutPlot allows placing up to three Views in a number of
      predefined and fixed layouts, which are defined by the layout_dict
      class attribute. This allows placing subviews next to a main plot
      in either a 'top' or 'right' position.
      """
  
      layout_dict = {'Single': {'positions': ['main']},
                     'Dual':   {'positions': ['main', 'right']},
                     'Triple': {'positions': ['main', 'right', 'top']}}
  