class_docstr: Sankey diagram in matplotlib
  
    Sankey diagrams are a specific type of flow diagram, in which
    the width of the arrows is shown proportionally to the flow
    quantity.  They are typically used to visualize energy or
    material or cost transfers between processes.
    `Wikipedia (6/1/2011) <https://en.wikipedia.org/wiki/Sankey_diagram>`_
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docstr: Add a simple Sankey diagram with flows at the same hierarchical level.
  
  Return value is the instance of :class:`Sankey`.
  
  Optional keyword arguments:
  
    ===============   ===================================================
    Keyword           Description
    ===============   ===================================================
    *patchlabel*      label to be placed at the center of the diagram
                      Note: *label* (not *patchlabel*) will be passed to
                      the patch through ``**kwargs`` and can be used to
                      create an entry in the legend.
    *flows*           array of flow values
                      By convention, inputs are positive and outputs are
                      negative.
    *orientations*    list of orientations of the paths
                      Valid values are 1 (from/to the top), 0 (from/to
                      the left or right), or -1 (from/to the bottom).  If
                      *orientations* == 0, inputs will break in from the
                      left and outputs will break away to the right.
    *labels*          list of specifications of the labels for the flows
                      Each value may be *None* (no labels), '' (just
                      label the quantities), or a labeling string.  If a
                      single value is provided, it will be applied to all
                      flows.  If an entry is a non-empty string, then the
                      quantity for the corresponding flow will be shown
                      below the string.  However, if the *unit* of the
                      main diagram is None, then quantities are never
                      shown, regardless of the value of this argument.
    *trunklength*     length between the bases of the input and output
                      groups
    *pathlengths*     list of lengths of the arrows before break-in or
                      after break-away
                      If a single value is given, then it will be applied
                      to the first (inside) paths on the top and bottom,
                      and the length of all other arrows will be
                      justified accordingly.  The *pathlengths* are not
                      applied to the horizontal inputs and outputs.
    *prior*           index of the prior diagram to which this diagram
                      should be connected
    *connect*         a (prior, this) tuple indexing the flow of the
                      prior diagram and the flow of this diagram which
                      should be connected
                      If this is the first diagram or *prior* is *None*,
                      *connect* will be ignored.
    *rotation*        angle of rotation of the diagram [deg]
                      *rotation* is ignored if this diagram is connected
                      to an existing one (using *prior* and *connect*).
                      The interpretation of the *orientations* argument
                      will be rotated accordingly (e.g., if *rotation*
                      == 90, an *orientations* entry of 1 means to/from
                      the left).
    ===============   ===================================================
  
  Valid kwargs are :meth:`matplotlib.patches.PathPatch` arguments:
  
  %(Patch)s
  
  As examples, ``fill=False`` and ``label='A legend entry'``.
  By default, ``facecolor='#bfd1d4'`` (light blue) and
  ``linewidth=0.5``.
  
  The indexing parameters (*prior* and *connect*) are zero-based.
  
  The flows are placed along the top of the diagram from the inside out
  in order of their index within the *flows* list or array.  They are
  placed along the sides of the diagram from the top down and along the
  bottom from the outside in.
  
  If the sum of the inputs and outputs is nonzero, the discrepancy
  will appear as a cubic Bezier curve along the top and bottom edges of
  the trunk.
  
  .. seealso::
  
      :meth:`finish`
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code: def add(
      self,
      patchlabel="",
      flows=None,
      orientations=None,
      labels="",
      trunklength=1.0,
      pathlengths=0.25,
      prior=None,
      connect=(0, 0),
      rotation=0,
      **kwargs,
  ):
      """
      Add a simple Sankey diagram with flows at the same hierarchical level.
  
      Return value is the instance of :class:`Sankey`.
  
      Optional keyword arguments:
  
        ===============   ===================================================
        Keyword           Description
        ===============   ===================================================
        *patchlabel*      label to be placed at the center of the diagram
                          Note: *label* (not *patchlabel*) will be passed to
                          the patch through ``**kwargs`` and can be used to
                          create an entry in the legend.
        *flows*           array of flow values
                          By convention, inputs are positive and outputs are
                          negative.
        *orientations*    list of orientations of the paths
                          Valid values are 1 (from/to the top), 0 (from/to
                          the left or right), or -1 (from/to the bottom).  If
                          *orientations* == 0, inputs will break in from the
                          left and outputs will break away to the right.
        *labels*          list of specifications of the labels for the flows
                          Each value may be *None* (no labels), '' (just
                          label the quantities), or a labeling string.  If a
                          single value is provided, it will be applied to all
                          flows.  If an entry is a non-empty string, then the
                          quantity for the corresponding flow will be shown
                          below the string.  However, if the *unit* of the
                          main diagram is None, then quantities are never
                          shown, regardless of the value of this argument.
        *trunklength*     length between the bases of the input and output
                          groups
        *pathlengths*     list of lengths of the arrows before break-in or
                          after break-away
                          If a single value is given, then it will be applied
                          to the first (inside) paths on the top and bottom,
                          and the length of all other arrows will be
                          justified accordingly.  The *pathlengths* are not
                          applied to the horizontal inputs and outputs.
        *prior*           index of the prior diagram to which this diagram
                          should be connected
        *connect*         a (prior, this) tuple indexing the flow of the
                          prior diagram and the flow of this diagram which
                          should be connected
                          If this is the first diagram or *prior* is *None*,
                          *connect* will be ignored.
        *rotation*        angle of rotation of the diagram [deg]
                          *rotation* is ignored if this diagram is connected
                          to an existing one (using *prior* and *connect*).
                          The interpretation of the *orientations* argument
                          will be rotated accordingly (e.g., if *rotation*
                          == 90, an *orientations* entry of 1 means to/from
                          the left).
        ===============   ===================================================
  
      Valid kwargs are :meth:`matplotlib.patches.PathPatch` arguments:
  
      %(Patch)s
  
      As examples, ``fill=False`` and ``label='A legend entry'``.
      By default, ``facecolor='#bfd1d4'`` (light blue) and
      ``linewidth=0.5``.
  
      The indexing parameters (*prior* and *connect*) are zero-based.
  
      The flows are placed along the top of the diagram from the inside out
      in order of their index within the *flows* list or array.  They are
      placed along the sides of the diagram from the top down and along the
      bottom from the outside in.
  
      If the sum of the inputs and outputs is nonzero, the discrepancy
      will appear as a cubic Bezier curve along the top and bottom edges of
      the trunk.
  
      .. seealso::
  
          :meth:`finish`
      """
      # Check and preprocess the arguments.
      if flows is None:
          flows = np.array([1.0, -1.0])
      else:
          flows = np.array(flows)
      n = flows.shape[0]  # Number of flows
      if rotation is None:
          rotation = 0
      else:
          # In the code below, angles are expressed in deg/90.
          rotation /= 90.0
      if orientations is None:
          orientations = [0, 0]
      if len(orientations) != n:
          raise ValueError(
              "orientations and flows must have the same length.\n"
              "orientations has length %d, but flows has length %d."
              % (len(orientations), n)
          )
      if labels != "" and getattr(labels, "__iter__", False):
          # iterable() isn't used because it would give True if labels is a
          # string
          if len(labels) != n:
              raise ValueError(
                  "If labels is a list, then labels and flows must have the "
                  "same length.\nlabels has length %d, but flows has length %d."
                  % (len(labels), n)
              )
      else:
          labels = [labels] * n
      if trunklength < 0:
          raise ValueError(
              "trunklength is negative.\nThis isn't allowed, because it would "
              "cause poor layout."
          )
      if np.abs(np.sum(flows)) > self.tolerance:
          _log.info(
              "The sum of the flows is nonzero (%f).\nIs the "
              "system not at steady state?",
              np.sum(flows),
          )
      scaled_flows = self.scale * flows
      gain = sum(max(flow, 0) for flow in scaled_flows)
      loss = sum(min(flow, 0) for flow in scaled_flows)
      if not (0.5 <= gain <= 2.0):
          _log.info(
              "The scaled sum of the inputs is %f.\nThis may "
              "cause poor layout.\nConsider changing the scale so"
              " that the scaled sum is approximately 1.0.",
              gain,
          )
      if not (-2.0 <= loss <= -0.5):
          _log.info(
              "The scaled sum of the outputs is %f.\nThis may "
              "cause poor layout.\nConsider changing the scale so"
              " that the scaled sum is approximately 1.0.",
              gain,
          )
      if prior is not None:
          if prior < 0:
              raise ValueError(
                  "The index of the prior diagram is negative."
              )
          if min(connect) < 0:
              raise ValueError(
                  "At least one of the connection indices is negative."
              )
          if prior >= len(self.diagrams):
              raise ValueError(
                  "The index of the prior diagram is %d, but there are "
                  "only %d other diagrams.\nThe index is zero-based."
                  % (prior, len(self.diagrams))
              )
          if connect[0] >= len(self.diagrams[prior].flows):
              raise ValueError(
                  "The connection index to the source diagram is %d, but "
                  "that diagram has only %d flows.\nThe index is zero-based."
                  % (connect[0], len(self.diagrams[prior].flows))
              )
          if connect[1] >= n:
              raise ValueError(
                  "The connection index to this diagram is %d, but this diagram"
                  "has only %d flows.\n The index is zero-based."
                  % (connect[1], n)
              )
          if self.diagrams[prior].angles[connect[0]] is None:
              raise ValueError(
                  "The connection cannot be made.  Check that the magnitude "
                  "of flow %d of diagram %d is greater than or equal to the "
                  "specified tolerance." % (connect[0], prior)
              )
          flow_error = (
              self.diagrams[prior].flows[connect[0]] + flows[connect[1]]
          )
          if abs(flow_error) >= self.tolerance:
              raise ValueError(
                  "The scaled sum of the connected flows is %f, which is not "
                  "within the tolerance (%f)."
                  % (flow_error, self.tolerance)
              )
  
      # Determine if the flows are inputs.
      are_inputs = [None] * n
      for i, flow in enumerate(flows):
          if flow >= self.tolerance:
              are_inputs[i] = True
          elif flow <= -self.tolerance:
              are_inputs[i] = False
          else:
              _log.info(
                  "The magnitude of flow %d (%f) is below the "
                  "tolerance (%f).\nIt will not be shown, and it "
                  "cannot be used in a connection."
                  % (i, flow, self.tolerance)
              )
  
      # Determine the angles of the arrows (before rotation).
      angles = [None] * n
      for i, (orient, is_input) in enumerate(
          zip(orientations, are_inputs)
      ):
          if orient == 1:
              if is_input:
                  angles[i] = DOWN
              elif not is_input:
                  # Be specific since is_input can be None.
                  angles[i] = UP
          elif orient == 0:
              if is_input is not None:
                  angles[i] = RIGHT
          else:
              if orient != -1:
                  raise ValueError(
                      "The value of orientations[%d] is %d, "
                      "but it must be [ -1 | 0 | 1 ]." % (i, orient)
                  )
              if is_input:
                  angles[i] = UP
              elif not is_input:
                  angles[i] = DOWN
  
      # Justify the lengths of the paths.
      if iterable(pathlengths):
          if len(pathlengths) != n:
              raise ValueError(
                  "If pathlengths is a list, then pathlengths and flows must "
                  "have the same length.\npathlengths has length %d, but flows "
                  "has length %d." % (len(pathlengths), n)
              )
      else:  # Make pathlengths into a list.
          urlength = pathlengths
          ullength = pathlengths
          lrlength = pathlengths
          lllength = pathlengths
          d = dict(RIGHT=pathlengths)
          pathlengths = [d.get(angle, 0) for angle in angles]
          # Determine the lengths of the top-side arrows
          # from the middle outwards.
          for i, (angle, is_input, flow) in enumerate(
              zip(angles, are_inputs, scaled_flows)
          ):
              if angle == DOWN and is_input:
                  pathlengths[i] = ullength
                  ullength += flow
              elif angle == UP and not is_input:
                  pathlengths[i] = urlength
                  urlength -= flow  # Flow is negative for outputs.
          # Determine the lengths of the bottom-side arrows
          # from the middle outwards.
          for i, (angle, is_input, flow) in enumerate(
              reversed(list(zip(angles, are_inputs, scaled_flows)))
          ):
              if angle == UP and is_input:
                  pathlengths[n - i - 1] = lllength
                  lllength += flow
              elif angle == DOWN and not is_input:
                  pathlengths[n - i - 1] = lrlength
                  lrlength -= flow
          # Determine the lengths of the left-side arrows
          # from the bottom upwards.
          has_left_input = False
          for i, (angle, is_input, spec) in enumerate(
              reversed(
                  list(
                      zip(
                          angles,
                          are_inputs,
                          zip(scaled_flows, pathlengths),
                      )
                  )
              )
          ):
              if angle == RIGHT:
                  if is_input:
                      if has_left_input:
                          pathlengths[n - i - 1] = 0
                      else:
                          has_left_input = True
          # Determine the lengths of the right-side arrows
          # from the top downwards.
          has_right_output = False
          for i, (angle, is_input, spec) in enumerate(
              zip(
                  angles,
                  are_inputs,
                  list(zip(scaled_flows, pathlengths)),
              )
          ):
              if angle == RIGHT:
                  if not is_input:
                      if has_right_output:
                          pathlengths[i] = 0
                      else:
                          has_right_output = True
  
      # Begin the subpaths, and smooth the transition if the sum of the flows
      # is nonzero.
      urpath = [
          (
              Path.MOVETO,
              [
                  (self.gap - trunklength / 2.0),  # Upper right
                  gain / 2.0,
              ],
          ),
          (
              Path.LINETO,
              [(self.gap - trunklength / 2.0) / 2.0, gain / 2.0],
          ),
          (
              Path.CURVE4,
              [(self.gap - trunklength / 2.0) / 8.0, gain / 2.0],
          ),
          (
              Path.CURVE4,
              [(trunklength / 2.0 - self.gap) / 8.0, -loss / 2.0],
          ),
          (
              Path.LINETO,
              [(trunklength / 2.0 - self.gap) / 2.0, -loss / 2.0],
          ),
          (Path.LINETO, [(trunklength / 2.0 - self.gap), -loss / 2.0]),
      ]
      llpath = [
          (
              Path.LINETO,
              [
                  (trunklength / 2.0 - self.gap),  # Lower left
                  loss / 2.0,
              ],
          ),
          (
              Path.LINETO,
              [(trunklength / 2.0 - self.gap) / 2.0, loss / 2.0],
          ),
          (
              Path.CURVE4,
              [(trunklength / 2.0 - self.gap) / 8.0, loss / 2.0],
          ),
          (
              Path.CURVE4,
              [(self.gap - trunklength / 2.0) / 8.0, -gain / 2.0],
          ),
          (
              Path.LINETO,
              [(self.gap - trunklength / 2.0) / 2.0, -gain / 2.0],
          ),
          (Path.LINETO, [(self.gap - trunklength / 2.0), -gain / 2.0]),
      ]
      lrpath = [
          (
              Path.LINETO,
              [
                  (trunklength / 2.0 - self.gap),  # Lower right
                  loss / 2.0,
              ],
          )
      ]
      ulpath = [
          (
              Path.LINETO,
              [self.gap - trunklength / 2.0, gain / 2.0],  # Upper left
          )
      ]
  
      # Add the subpaths and assign the locations of the tips and labels.
      tips = np.zeros((n, 2))
      label_locations = np.zeros((n, 2))
      # Add the top-side inputs and outputs from the middle outwards.
      for i, (angle, is_input, spec) in enumerate(
          zip(angles, are_inputs, list(zip(scaled_flows, pathlengths)))
      ):
          if angle == DOWN and is_input:
              tips[i, :], label_locations[i, :] = self._add_input(
                  ulpath, angle, *spec
              )
          elif angle == UP and not is_input:
              tips[i, :], label_locations[i, :] = self._add_output(
                  urpath, angle, *spec
              )
      # Add the bottom-side inputs and outputs from the middle outwards.
      for i, (angle, is_input, spec) in enumerate(
          reversed(
              list(
                  zip(
                      angles,
                      are_inputs,
                      list(zip(scaled_flows, pathlengths)),
                  )
              )
          )
      ):
          if angle == UP and is_input:
              tip, label_location = self._add_input(
                  llpath, angle, *spec
              )
              tips[n - i - 1, :] = tip
              label_locations[n - i - 1, :] = label_location
          elif angle == DOWN and not is_input:
              tip, label_location = self._add_output(
                  lrpath, angle, *spec
              )
              tips[n - i - 1, :] = tip
              label_locations[n - i - 1, :] = label_location
      # Add the left-side inputs from the bottom upwards.
      has_left_input = False
      for i, (angle, is_input, spec) in enumerate(
          reversed(
              list(
                  zip(
                      angles,
                      are_inputs,
                      list(zip(scaled_flows, pathlengths)),
                  )
              )
          )
      ):
          if angle == RIGHT and is_input:
              if not has_left_input:
                  # Make sure the lower path extends
                  # at least as far as the upper one.
                  if llpath[-1][1][0] > ulpath[-1][1][0]:
                      llpath.append(
                          (
                              Path.LINETO,
                              [ulpath[-1][1][0], llpath[-1][1][1]],
                          )
                      )
                  has_left_input = True
              tip, label_location = self._add_input(
                  llpath, angle, *spec
              )
              tips[n - i - 1, :] = tip
              label_locations[n - i - 1, :] = label_location
      # Add the right-side outputs from the top downwards.
      has_right_output = False
      for i, (angle, is_input, spec) in enumerate(
          zip(angles, are_inputs, list(zip(scaled_flows, pathlengths)))
      ):
          if angle == RIGHT and not is_input:
              if not has_right_output:
                  # Make sure the upper path extends
                  # at least as far as the lower one.
                  if urpath[-1][1][0] < lrpath[-1][1][0]:
                      urpath.append(
                          (
                              Path.LINETO,
                              [lrpath[-1][1][0], urpath[-1][1][1]],
                          )
                      )
                  has_right_output = True
              tips[i, :], label_locations[i, :] = self._add_output(
                  urpath, angle, *spec
              )
      # Trim any hanging vertices.
      if not has_left_input:
          ulpath.pop()
          llpath.pop()
      if not has_right_output:
          lrpath.pop()
          urpath.pop()
  
      # Concatenate the subpaths in the correct order (clockwise from top).
      path = (
          urpath
          + self._revert(lrpath)
          + llpath
          + self._revert(ulpath)
          + [(Path.CLOSEPOLY, urpath[0][1])]
      )
  
      # Create a patch with the Sankey outline.
      codes, vertices = zip(*path)
      vertices = np.array(vertices)
  
      def _get_angle(a, r):
          if a is None:
              return None
          else:
              return a + r
  
      if prior is None:
          if rotation != 0:  # By default, none of this is needed.
              angles = [_get_angle(angle, rotation) for angle in angles]
              rotate = (
                  Affine2D().rotate_deg(rotation * 90).transform_affine
              )
              tips = rotate(tips)
              label_locations = rotate(label_locations)
              vertices = rotate(vertices)
          text = self.ax.text(
              0, 0, s=patchlabel, ha="center", va="center"
          )
      else:
          rotation = (
              self.diagrams[prior].angles[connect[0]]
              - angles[connect[1]]
          )
          angles = [_get_angle(angle, rotation) for angle in angles]
          rotate = Affine2D().rotate_deg(rotation * 90).transform_affine
          tips = rotate(tips)
          offset = (
              self.diagrams[prior].tips[connect[0]] - tips[connect[1]]
          )
          translate = Affine2D().translate(*offset).transform_affine
          tips = translate(tips)
          label_locations = translate(rotate(label_locations))
          vertices = translate(rotate(vertices))
          kwds = dict(s=patchlabel, ha="center", va="center")
          text = self.ax.text(*offset, **kwds)
      if rcParams["_internal.classic_mode"]:
          fc = kwargs.pop("fc", kwargs.pop("facecolor", "#bfd1d4"))
          lw = kwargs.pop("lw", kwargs.pop("linewidth", 0.5))
      else:
          fc = kwargs.pop("fc", kwargs.pop("facecolor", None))
          lw = kwargs.pop("lw", kwargs.pop("linewidth", None))
      if fc is None:
          fc = next(self.ax._get_patches_for_fill.prop_cycler)["color"]
      patch = PathPatch(Path(vertices, codes), fc=fc, lw=lw, **kwargs)
      self.ax.add_patch(patch)
  
      # Add the path labels.
      texts = []
      for number, angle, label, location in zip(
          flows, angles, labels, label_locations
      ):
          if label is None or angle is None:
              label = ""
          elif self.unit is not None:
              quantity = self.format % abs(number) + self.unit
              if label != "":
                  label += "\n"
              label += quantity
          texts.append(
              self.ax.text(
                  x=location[0],
                  y=location[1],
                  s=label,
                  ha="center",
                  va="center",
              )
          )
      # Text objects are placed even they are empty (as long as the magnitude
      # of the corresponding flow is larger than the tolerance) in case the
      # user wants to provide labels later.
  
      # Expand the size of the diagram if necessary.
      self.extent = (
          min(
              np.min(vertices[:, 0]),
              np.min(label_locations[:, 0]),
              self.extent[0],
          ),
          max(
              np.max(vertices[:, 0]),
              np.max(label_locations[:, 0]),
              self.extent[1],
          ),
          min(
              np.min(vertices[:, 1]),
              np.min(label_locations[:, 1]),
              self.extent[2],
          ),
          max(
              np.max(vertices[:, 1]),
              np.max(label_locations[:, 1]),
              self.extent[3],
          ),
      )
      # Include both vertices _and_ label locations in the extents; there are
      # where either could determine the margins (e.g., arrow shoulders).
  
      # Add this diagram as a subdiagram.
      self.diagrams.append(
          Bunch(
              patch=patch,
              flows=flows,
              angles=angles,
              tips=tips,
              text=text,
              texts=texts,
          )
      )
  
      # Allow a daisy-chained call structure (see docstring for the class).
      return self
  
imports: from __future__ import absolute_import, division, print_function, unicode_literals
  import six
  import logging
  from six.moves import zip
  import numpy
  from matplotlib.cbook import iterable, Bunch
  from matplotlib.path import Path
  from matplotlib.patches import PathPatch
  from matplotlib.transforms import Affine2D
  from matplotlib import docstring
  from matplotlib import rcParams
label_desc: Use image node_id 6 for calling the Sankey obj's underlying member method code with example usage: obj.add(patchlabel, flows, orientations, labels, trunklength, pathlengths, prior, connect, rotation) and returns: self, None, unknown