content: """
  :mod:`~matplotlib.gridspec` is a module which specifies the location
  of the subplot in the figure.
  
      ``GridSpec``
          specifies the geometry of the grid that a subplot will be
          placed. The number of rows and number of columns of the grid
          need to be set. Optionally, the subplot layout parameters
          (e.g., left, right, etc.) can be tuned.
  
      ``SubplotSpec``
          specifies the location of the subplot in the given *GridSpec*.
  
  
  """
  
  from __future__ import (absolute_import, division, print_function,
                          unicode_literals)
  
  import six
  from six.moves import zip
  
  import matplotlib
  rcParams = matplotlib.rcParams
  
  import matplotlib.transforms as mtransforms
  
  import numpy as np
  import warnings
  
  class GridSpecBase(object):
      """
      A base class of GridSpec that specifies the geometry of the grid
      that a subplot will be placed.
      """
  
      def __init__(self, nrows, ncols,
                   height_ratios=None, width_ratios=None):
          """
          The number of rows and number of columns of the grid need to
          be set. Optionally, the ratio of heights and widths of rows and
          columns can be specified.
          """
          #self.figure = figure
          self._nrows , self._ncols = nrows, ncols
  
          self.set_height_ratios(height_ratios)
          self.set_width_ratios(width_ratios)
  
      def get_geometry(self):
          'get the geometry of the grid, e.g., 2,3'
          return self._nrows, self._ncols
  
      def get_subplot_params(self, fig=None):
          pass
  
      def new_subplotspec(self, loc, rowspan=1, colspan=1):
          """
          create and return a SuplotSpec instance.
          """
          loc1, loc2 = loc
          subplotspec = self[loc1:loc1+rowspan, loc2:loc2+colspan]
          return subplotspec
  
  
      def set_width_ratios(self, width_ratios):
          self._col_width_ratios = width_ratios
  
      def get_width_ratios(self):
          return self._col_width_ratios
  
      def set_height_ratios(self, height_ratios):
          self._row_height_ratios = height_ratios
  
      def get_height_ratios(self):
          return self._row_height_ratios
  
  
      def get_grid_positions(self, fig):
          """
          return lists of bottom and top position of rows, left and
          right positions of columns.
          """
          nrows, ncols = self.get_geometry()
  
          subplot_params = self.get_subplot_params(fig)
          left = subplot_params.left
          right = subplot_params.right
          bottom = subplot_params.bottom
          top = subplot_params.top
          wspace = subplot_params.wspace
          hspace = subplot_params.hspace
          totWidth = right-left
          totHeight = top-bottom
  
          # calculate accumulated heights of columns
          cellH = totHeight/(nrows + hspace*(nrows-1))
          sepH = hspace*cellH
  
          if self._row_height_ratios is not None:
              netHeight = cellH * nrows
              tr = float(sum(self._row_height_ratios))
              cellHeights = [netHeight*r/tr for r in self._row_height_ratios]
          else:
              cellHeights = [cellH] * nrows
  
          sepHeights = [0] + ([sepH] * (nrows-1))
          cellHs = np.add.accumulate(np.ravel(list(zip(sepHeights, cellHeights))))
  
  
          # calculate accumulated widths of rows
          cellW = totWidth/(ncols + wspace*(ncols-1))
          sepW = wspace*cellW
  
          if self._col_width_ratios is not None:
              netWidth = cellW * ncols
              tr = float(sum(self._col_width_ratios))
              cellWidths = [netWidth*r/tr for r in self._col_width_ratios]
          else:
              cellWidths = [cellW] * ncols
  
          sepWidths = [0] + ([sepW] * (ncols-1))
          cellWs = np.add.accumulate(np.ravel(list(zip(sepWidths, cellWidths))))
  
  
  
          figTops = [top - cellHs[2*rowNum] for rowNum in range(nrows)]
          figBottoms = [top - cellHs[2*rowNum+1] for rowNum in range(nrows)]
          figLefts = [left + cellWs[2*colNum] for colNum in range(ncols)]
          figRights = [left + cellWs[2*colNum+1] for colNum in range(ncols)]
  
  
          return figBottoms, figTops, figLefts, figRights
  
      def __getitem__(self, key):
          """
          create and return a SuplotSpec instance.
          """
          nrows, ncols = self.get_geometry()
          total = nrows*ncols
  
          if isinstance(key, tuple):
              try:
                  k1, k2 = key
              except ValueError:
                  raise ValueError("unrecognized subplot spec")
  
              if isinstance(k1, slice):
                  row1, row2, _ = k1.indices(nrows)
              else:
                  if k1 < 0:
                      k1 += nrows
                  if k1 >= nrows or k1 < 0 :
                      raise IndexError("index out of range")
                  row1, row2 = k1, k1+1
  
  
              if isinstance(k2, slice):
                  col1, col2, _ = k2.indices(ncols)
              else:
                  if k2 < 0:
                      k2 += ncols
                  if k2 >= ncols or k2 < 0 :
                      raise IndexError("index out of range")
                  col1, col2 = k2, k2+1
  
  
              num1 = row1*ncols + col1
              num2 = (row2-1)*ncols + (col2-1)
  
          # single key
          else:
              if isinstance(key, slice):
                  num1, num2, _ = key.indices(total)
                  num2 -= 1
              else:
                  if key < 0:
                      key += total
                  if key >= total or key < 0 :
                      raise IndexError("index out of range")
                  num1, num2 = key, None
  
  
          return SubplotSpec(self, num1, num2)
  
  
  class GridSpec(GridSpecBase):
      """
      A class that specifies the geometry of the grid that a subplot
      will be placed. The location of grid is determined by similar way
      as the SubplotParams.
      """
  
      def __init__(self, nrows, ncols,
                   left=None, bottom=None, right=None, top=None,
                   wspace=None, hspace=None,
                   width_ratios=None, height_ratios=None):
          """
          The number of rows and number of columns of the
          grid need to be set. Optionally, the subplot layout parameters
          (e.g., left, right, etc.) can be tuned.
          """
          #self.figure = figure
          self.left=left
          self.bottom=bottom
          self.right=right
          self.top=top
          self.wspace=wspace
          self.hspace=hspace
  
          GridSpecBase.__init__(self, nrows, ncols,
                                width_ratios=width_ratios,
                                height_ratios=height_ratios)
          #self.set_width_ratios(width_ratios)
          #self.set_height_ratios(height_ratios)
  
  
      _AllowedKeys = ["left", "bottom", "right", "top", "wspace", "hspace"]
  
      def update(self, **kwargs):
          """
          Update the current values.  If any kwarg is None, default to
          the current value, if set, otherwise to rc.
          """
  
          for k, v in six.iteritems(kwargs):
              if k in self._AllowedKeys:
                  setattr(self, k, v)
              else:
                  raise AttributeError("%s is unknown keyword" % (k,))
  
  
          from matplotlib import _pylab_helpers
          from matplotlib.axes import SubplotBase
          for figmanager in six.itervalues(_pylab_helpers.Gcf.figs):
              for ax in figmanager.canvas.figure.axes:
                  # copied from Figure.subplots_adjust
                  if not isinstance(ax, SubplotBase):
                      # Check if sharing a subplots axis
                      if ax._sharex is not None and isinstance(ax._sharex, SubplotBase):
                          if ax._sharex.get_subplotspec().get_gridspec() == self:
                              ax._sharex.update_params()
                              ax.set_position(ax._sharex.figbox)
                      elif ax._sharey is not None and isinstance(ax._sharey,SubplotBase):
                          if ax._sharey.get_subplotspec().get_gridspec() == self:
                              ax._sharey.update_params()
                              ax.set_position(ax._sharey.figbox)
                  else:
                      ss = ax.get_subplotspec().get_topmost_subplotspec()
                      if ss.get_gridspec() == self:
                          ax.update_params()
                          ax.set_position(ax.figbox)
  
  
  
      def get_subplot_params(self, fig=None):
          """
          return a dictionary of subplot layout parameters. The default
          parameters are from rcParams unless a figure attribute is set.
          """
          from matplotlib.figure import SubplotParams
          import copy
          if fig is None:
              kw = dict([(k, rcParams["figure.subplot."+k]) \
                         for k in self._AllowedKeys])
              subplotpars = SubplotParams(**kw)
          else:
              subplotpars = copy.copy(fig.subplotpars)
  
          update_kw = dict([(k, getattr(self, k)) for k in self._AllowedKeys])
          subplotpars.update(**update_kw)
  
          return subplotpars
  
      def locally_modified_subplot_params(self):
          return [k for k in self._AllowedKeys if getattr(self, k)]
  
  
      def tight_layout(self, fig, renderer=None, pad=1.08, h_pad=None, w_pad=None, rect=None):
          """
          Adjust subplot parameters to give specified padding.
  
          Parameters:
  
          pad : float
              padding between the figure edge and the edges of subplots, as a fraction of the font-size.
          h_pad, w_pad : float
              padding (height/width) between edges of adjacent subplots.
              Defaults to `pad_inches`.
          rect : if rect is given, it is interpreted as a rectangle
              (left, bottom, right, top) in the normalized figure
              coordinate that the whole subplots area (including
              labels) will fit into. Default is (0, 0, 1, 1).
          """
  
          from .tight_layout import (get_subplotspec_list,
                                     get_tight_layout_figure,
                                     get_renderer)
  
          subplotspec_list = get_subplotspec_list(fig.axes, grid_spec=self)
          if None in subplotspec_list:
              warnings.warn("This figure includes Axes that are not "
                            "compatible with tight_layout, so its "
                            "results might be incorrect.")
  
          if renderer is None:
              renderer = get_renderer(fig)
  
          kwargs = get_tight_layout_figure(fig, fig.axes, subplotspec_list,
                                           renderer,
                                           pad=pad, h_pad=h_pad, w_pad=w_pad,
                                           rect=rect,
                                           )
  
          self.update(**kwargs)
  
  
  class GridSpecFromSubplotSpec(GridSpecBase):
      """
      GridSpec whose subplot layout parameters are inherited from the
      location specified by a given SubplotSpec.
      """
      def __init__(self, nrows, ncols,
                   subplot_spec,
                   wspace=None, hspace=None,
                   height_ratios=None, width_ratios=None):
          """
          The number of rows and number of columns of the grid need to
          be set. An instance of SubplotSpec is also needed to be set
          from which the layout parameters will be inherited. The wspace
          and hspace of the layout can be optionally specified or the
          default values (from the figure or rcParams) will be used.
          """
          self._wspace=wspace
          self._hspace=hspace
  
          self._subplot_spec = subplot_spec
  
          GridSpecBase.__init__(self, nrows, ncols,
                                width_ratios=width_ratios,
                                height_ratios=height_ratios)
  
  
      def get_subplot_params(self, fig=None):
          """
          return a dictionary of subplot layout parameters.
          """
  
          if fig is None:
              hspace = rcParams["figure.subplot.hspace"]
              wspace = rcParams["figure.subplot.wspace"]
          else:
              hspace = fig.subplotpars.hspace
              wspace = fig.subplotpars.wspace
  
          if self._hspace is not None:
              hspace = self._hspace
  
          if self._wspace is not None:
              wspace = self._wspace
  
          figbox = self._subplot_spec.get_position(fig, return_all=False)
  
          left, bottom, right, top = figbox.extents
  
          from matplotlib.figure import SubplotParams
          sp = SubplotParams(left=left,
                             right=right,
                             bottom=bottom,
                             top=top,
                             wspace=wspace,
                             hspace=hspace)
  
          return sp
  
  
      def get_topmost_subplotspec(self):
          'get the topmost SubplotSpec instance associated with the subplot'
          return self._subplot_spec.get_topmost_subplotspec()
  
  
  class SubplotSpec(object):
      """
      specifies the location of the subplot in the given *GridSpec*.
      """
  
      def __init__(self, gridspec, num1, num2=None):
          """
          The subplot will occupy the num1-th cell of the given
          gridspec.  If num2 is provided, the subplot will span between
          num1-th cell and num2-th cell.
  
          The index stars from 0.
          """
  
          rows, cols = gridspec.get_geometry()
          total = rows*cols
  
          self._gridspec = gridspec
          self.num1 = num1
          self.num2 = num2
  
      def get_gridspec(self):
          return self._gridspec
  
  
      def get_geometry(self):
          """
          get the subplot geometry, e.g., 2,2,3. Unlike SuplorParams,
          index is 0-based
          """
          rows, cols = self.get_gridspec().get_geometry()
          return rows, cols, self.num1, self.num2
  
  
      def get_position(self, fig, return_all=False):
          """
          update the subplot position from fig.subplotpars
          """
  
          gridspec = self.get_gridspec()
          nrows, ncols = gridspec.get_geometry()
  
          figBottoms, figTops, figLefts, figRights = \
                      gridspec.get_grid_positions(fig)
  
  
          rowNum, colNum =  divmod(self.num1, ncols)
          figBottom = figBottoms[rowNum]
          figTop = figTops[rowNum]
          figLeft = figLefts[colNum]
          figRight = figRights[colNum]
  
          if self.num2 is not None:
  
              rowNum2, colNum2 =  divmod(self.num2, ncols)
              figBottom2 = figBottoms[rowNum2]
              figTop2 = figTops[rowNum2]
              figLeft2 = figLefts[colNum2]
              figRight2 = figRights[colNum2]
  
              figBottom = min(figBottom, figBottom2)
              figLeft = min(figLeft, figLeft2)
              figTop = max(figTop, figTop2)
              figRight = max(figRight, figRight2)
  
          figbox = mtransforms.Bbox.from_extents(figLeft, figBottom,
                                                 figRight, figTop)
  
  
          if return_all:
              return figbox, rowNum, colNum, nrows, ncols
          else:
              return figbox
  
  
      def get_topmost_subplotspec(self):
          'get the topmost SubplotSpec instance associated with the subplot'
          gridspec = self.get_gridspec()
          if hasattr(gridspec, "get_topmost_subplotspec"):
              return gridspec.get_topmost_subplotspec()
          else:
              return self
  
      def __eq__(self, other):
          # check to make sure other has the attributes
          # we need to do the comparison
          if not (hasattr(other, '_gridspec') and
                  hasattr(other, 'num1') and
                  hasattr(other, 'num2')):
              return False
          return all((self._gridspec == other._gridspec,
                      self.num1 == other.num1,
                      self.num2 == other.num2))
  
      def __hash__(self):
          return (hash(self._gridspec) ^
                  hash(self.num1) ^
                  hash(self.num2))
  