#!/usr/bin/env python2
"""
Module for creating Sankey diagrams using matplotlib
"""
from __future__ import (absolute_import, division, print_function,
                        unicode_literals)

from matplotlib.externals import six
from matplotlib.externals.six.moves import zip

# Original version by Yannick Copin (ycopin@ipnl.in2p3.fr) 10/2/2010, available
# at:
#     http://matplotlib.org/examples/api/sankey_demo_old.html
# Modifications by Kevin Davies (kld@alumni.carnegiemellon.edu) 6/3/2011:
#   --Used arcs for the curves (so that the widths of the paths are uniform)
#   --Converted the function to a class and created methods to join multiple
#     simple Sankey diagrams
#   --Provided handling for cases where the total of the inputs isn't 100
#     Now, the default layout is based on the assumption that the inputs sum to
#     1.  A scaling parameter can be used in other cases.
#   --The call structure was changed to be more explicit about layout,
#     including the length of the trunk, length of the paths, gap between the
#     paths, and the margin around the diagram.
#   --Allowed the lengths of paths to be adjusted individually, with an option
#     to automatically justify them
#   --The call structure was changed to make the specification of path
#     orientation more flexible.  Flows are passed through one array, with
#     inputs being positive and outputs being negative.  An orientation
#     argument specifies the direction of the arrows.  The "main"
#     inputs/outputs are now specified via an orientation of 0, and there may
#     be several of each.
#   --Changed assertions to ValueError to catch common calling errors (by
#     Francesco Montesano, franz.bergesung@gmail.com)
#   --Added the physical unit as a string argument to be used in the labels, so
#     that the values of the flows can usually be applied automatically
#   --Added an argument for a minimum magnitude below which flows are not shown
#   --Added a tapered trunk in the case that the flows do not sum to 0
#   --Allowed the diagram to be rotated

import numpy as np

from matplotlib.cbook import iterable, Bunch
from matplotlib.path import Path
from matplotlib.patches import PathPatch
from matplotlib.transforms import Affine2D
from matplotlib import verbose
from matplotlib import docstring

__author__ = "Kevin L. Davies"
__credits__ = ["Yannick Copin"]
__license__ = "BSD"
__version__ = "2011/09/16"

# Angles [deg/90]
RIGHT = 0
UP = 1
# LEFT = 2
DOWN = 3


class Sankey(object):
    """
    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) <http://en.wikipedia.org/wiki/Sankey_diagram>`_

    """

    def __init__(self, ax=None, scale=1.0, unit='', format='%G', gap=0.25,
                 radius=0.1, shoulder=0.03, offset=0.15, head_angle=100,
                 margin=0.4, tolerance=1e-6, **kwargs):
        """
        Create a new Sankey instance.

        Optional keyword arguments:

          ===============   ===================================================
          Field             Description
          ===============   ===================================================
          *ax*              axes onto which the data should be plotted
                            If *ax* isn't provided, new axes will be created.
          *scale*           scaling factor for the flows
                            *scale* sizes the width of the paths in order to
                            maintain proper layout.  The same scale is applied
                            to all subdiagrams.  The value should be chosen
                            such that the product of the scale and the sum of
                            the inputs is approximately 1.0 (and the product of
                            the scale and the sum of the outputs is
                            approximately -1.0).
          *unit*            string representing the physical unit associated
                            with the flow quantities
                            If *unit* is None, then none of the quantities are
                            labeled.
          *format*          a Python number formatting string to be used in
                            labeling the flow as a quantity (i.e., a number
                            times a unit, where the unit is given)
          *gap*             space between paths that break in/break away
                            to/from the top or bottom
          *radius*          inner radius of the vertical paths
          *shoulder*        size of the shoulders of output arrowS
          *offset*          text offset (from the dip or tip of the arrow)
          *head_angle*      angle of the arrow heads (and negative of the angle
                            of the tails) [deg]
          *margin*          minimum space between Sankey outlines and the edge
                            of the plot area
          *tolerance*       acceptable maximum of the magnitude of the sum of
                            flows
                            The magnitude of the sum of connected flows cannot
                            be greater than *tolerance*.
          ===============   ===================================================

        The optional arguments listed above are applied to all subdiagrams so
        that there is consistent alignment and formatting.

        If :class:`Sankey` is instantiated with any keyword arguments other
        than those explicitly listed above (``**kwargs``), they will be passed
        to :meth:`add`, which will create the first subdiagram.

        In order to draw a complex Sankey diagram, create an instance of
        :class:`Sankey` by calling it without any kwargs::

            sankey = Sankey()

        Then add simple Sankey sub-diagrams::

            sankey.add() # 1
            sankey.add() # 2
            #...
            sankey.add() # n

        Finally, create the full diagram::

            sankey.finish()

        Or, instead, simply daisy-chain those calls::

            Sankey().add().add...  .add().finish()

        .. seealso::

            :meth:`add`
            :meth:`finish`


        **Examples:**

            .. plot:: mpl_examples/api/sankey_demo_basics.py
        """
        # Check the arguments.
        if gap < 0:
            raise ValueError(
            "The gap is negative.\nThis isn't allowed because it "
            "would cause the paths to overlap.")
        if radius > gap:
            raise ValueError(
            "The inner radius is greater than the path spacing.\n"
            "This isn't allowed because it would cause the paths to overlap.")
        if head_angle < 0:
            raise ValueError(
            "The angle is negative.\nThis isn't allowed "
            "because it would cause inputs to look like "
            "outputs and vice versa.")
        if tolerance < 0:
            raise ValueError(
            "The tolerance is negative.\nIt must be a magnitude.")

        # Create axes if necessary.
        if ax is None:
            import matplotlib.pyplot as plt
            fig = plt.figure()
            ax = fig.add_subplot(1, 1, 1, xticks=[], yticks=[])

        self.diagrams = []

        # Store the inputs.
        self.ax = ax
        self.unit = unit
        self.format = format
        self.scale = scale
        self.gap = gap
        self.radius = radius
        self.shoulder = shoulder
        self.offset = offset
        self.margin = margin
        self.pitch = np.tan(np.pi * (1 - head_angle / 180.0) / 2.0)
        self.tolerance = tolerance

        # Initialize the vertices of tight box around the diagram(s).
        self.extent = np.array((np.inf, -np.inf, np.inf, -np.inf))

        # If there are any kwargs, create the first subdiagram.
        if len(kwargs):
            self.add(**kwargs)

    def _arc(self, quadrant=0, cw=True, radius=1, center=(0, 0)):
        """
        Return the codes and vertices for a rotated, scaled, and translated
        90 degree arc.

        Optional keyword arguments:

          ===============   ==========================================
          Keyword           Description
          ===============   ==========================================
          *quadrant*        uses 0-based indexing (0, 1, 2, or 3)
          *cw*              if True, clockwise
          *center*          (x, y) tuple of the arc's center
          ===============   ==========================================
        """
        # Note:  It would be possible to use matplotlib's transforms to rotate,
        # scale, and translate the arc, but since the angles are discrete,
        # it's just as easy and maybe more efficient to do it here.
        ARC_CODES = [Path.LINETO,
                     Path.CURVE4,
                     Path.CURVE4,
                     Path.CURVE4,
                     Path.CURVE4,
                     Path.CURVE4,
                     Path.CURVE4]
        # Vertices of a cubic Bezier curve approximating a 90 deg arc
        # These can be determined by Path.arc(0,90).
        ARC_VERTICES = np.array([[1.00000000e+00, 0.00000000e+00],
                                 [1.00000000e+00, 2.65114773e-01],
                                 [8.94571235e-01, 5.19642327e-01],
                                 [7.07106781e-01, 7.07106781e-01],
                                 [5.19642327e-01, 8.94571235e-01],
                                 [2.65114773e-01, 1.00000000e+00],
                                 # Insignificant
                                 # [6.12303177e-17, 1.00000000e+00]])
                                 [0.00000000e+00, 1.00000000e+00]])
        if quadrant == 0 or quadrant == 2:
            if cw:
                vertices = ARC_VERTICES
            else:
                vertices = ARC_VERTICES[:, ::-1]  # Swap x and y.
        elif quadrant == 1 or quadrant == 3:
            # Negate x.
            if cw:
                # Swap x and y.
                vertices = np.column_stack((-ARC_VERTICES[:, 1],
                                             ARC_VERTICES[:, 0]))
            else:
                vertices = np.column_stack((-ARC_VERTICES[:, 0],
                                             ARC_VERTICES[:, 1]))
        if quadrant > 1:
            radius = -radius  # Rotate 180 deg.
        return list(zip(ARC_CODES, radius * vertices +
                        np.tile(center, (ARC_VERTICES.shape[0], 1))))

    def _add_input(self, path, angle, flow, length):
        """
        Add an input to a path and return its tip and label locations.
        """
        if angle is None:
            return [0, 0], [0, 0]
        else:
            x, y = path[-1][1]  # Use the last point as a reference.
            dipdepth = (flow / 2) * self.pitch
            if angle == RIGHT:
                x -= length
                dip = [x + dipdepth, y + flow / 2.0]
                path.extend([(Path.LINETO, [x, y]),
                             (Path.LINETO, dip),
                             (Path.LINETO, [x, y + flow]),
                             (Path.LINETO, [x + self.gap, y + flow])])
                label_location = [dip[0] - self.offset, dip[1]]
            else:  # Vertical
                x -= self.gap
                if angle == UP:
                    sign = 1
                else:
                    sign = -1

                dip = [x - flow / 2, y - sign * (length - dipdepth)]
                if angle == DOWN:
                    quadrant = 2
                else:
                    quadrant = 1

                # Inner arc isn't needed if inner radius is zero
                if self.radius:
                    path.extend(self._arc(quadrant=quadrant,
                                          cw=angle == UP,
                                          radius=self.radius,
                                          center=(x + self.radius,
                                                  y - sign * self.radius)))
                else:
                    path.append((Path.LINETO, [x, y]))
                path.extend([(Path.LINETO, [x, y - sign * length]),
                             (Path.LINETO, dip),
                             (Path.LINETO, [x - flow, y - sign * length])])
                path.extend(self._arc(quadrant=quadrant,
                                      cw=angle == DOWN,
                                      radius=flow + self.radius,
                                      center=(x + self.radius,
                                              y - sign * self.radius)))
                path.append((Path.LINETO, [x - flow, y + sign * flow]))
                label_location = [dip[0], dip[1] - sign * self.offset]

            return dip, label_location

    def _add_output(self, path, angle, flow, length):
        """
        Append an output to a path and return its tip and label locations.

        .. note:: *flow* is negative for an output.
        """
        if angle is None:
            return [0, 0], [0, 0]
        else:
            x, y = path[-1][1]  # Use the last point as a reference.
            tipheight = (self.shoulder - flow / 2) * self.pitch
            if angle == RIGHT:
                x += length
                tip = [x + tipheight, y + flow / 2.0]
                path.extend([(Path.LINETO, [x, y]),
                             (Path.LINETO, [x, y + self.shoulder]),
                             (Path.LINETO, tip),
                             (Path.LINETO, [x, y - self.shoulder + flow]),
                             (Path.LINETO, [x, y + flow]),
                             (Path.LINETO, [x - self.gap, y + flow])])
                label_location = [tip[0] + self.offset, tip[1]]
            else:  # Vertical
                x += self.gap
                if angle == UP:
                    sign = 1
                else:
                    sign = -1

                tip = [x - flow / 2.0, y + sign * (length + tipheight)]
                if angle == UP:
                    quadrant = 3
                else:
                    quadrant = 0
                # Inner arc isn't needed if inner radius is zero
                if self.radius:
                    path.extend(self._arc(quadrant=quadrant,
                                          cw=angle == UP,
                                          radius=self.radius,
                                          center=(x - self.radius,
                                                  y + sign * self.radius)))
                else:
                    path.append((Path.LINETO, [x, y]))
                path.extend([(Path.LINETO, [x, y + sign * length]),
                             (Path.LINETO, [x - self.shoulder,
                                            y + sign * length]),
                             (Path.LINETO, tip),
                             (Path.LINETO, [x + self.shoulder - flow,
                                            y + sign * length]),
                             (Path.LINETO, [x - flow, y + sign * length])])
                path.extend(self._arc(quadrant=quadrant,
                                      cw=angle == DOWN,
                                      radius=self.radius - flow,
                                      center=(x - self.radius,
                                              y + sign * self.radius)))
                path.append((Path.LINETO, [x - flow, y + sign * flow]))
                label_location = [tip[0], tip[1] + sign * self.offset]
            return tip, label_location

    def _revert(self, path, first_action=Path.LINETO):
        """
        A path is not simply revertable by path[::-1] since the code
        specifies an action to take from the **previous** point.
        """
        reverse_path = []
        next_code = first_action
        for code, position in path[::-1]:
            reverse_path.append((next_code, position))
            next_code = code
        return reverse_path
        # This might be more efficient, but it fails because 'tuple' object
        # doesn't support item assignment:
        # path[1] = path[1][-1:0:-1]
        # path[1][0] = first_action
        # path[2] = path[2][::-1]
        # return path

    @docstring.dedent_interpd
    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.absolute(np.sum(flows)) > self.tolerance:
            verbose.report(
                "The sum of the flows is nonzero (%f).\nIs the "
                "system not at steady state?" % np.sum(flows), 'helpful')
        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):
            verbose.report(
                "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, 'helpful')
        if not (-2.0 <= loss <= -0.5):
            verbose.report(
                "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, 'helpful')
        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:
                verbose.report(
                    "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), 'helpful')

        # 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,  # Upper left
                                 gain / 2.0])]

        # 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 = list(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 False:  # Debug
            print("llpath\n", llpath)
            print("ulpath\n", self._revert(ulpath))
            print("urpath\n", urpath)
            print("lrpath\n", self._revert(lrpath))
            xs, ys = list(zip(*vertices))
            self.ax.plot(xs, ys, 'go-')
        patch = PathPatch(Path(vertices, codes),
                          fc=kwargs.pop('fc', kwargs.pop('facecolor',
                                        '#bfd1d4')),  # Custom defaults
                          lw=kwargs.pop('lw', kwargs.pop('linewidth', 0.5)),
                          **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

    def finish(self):
        """
        Adjust the axes and return a list of information about the Sankey
        subdiagram(s).

        Return value is a list of subdiagrams represented with the following
        fields:

          ===============   ===================================================
          Field             Description
          ===============   ===================================================
          *patch*           Sankey outline (an instance of
                            :class:`~maplotlib.patches.PathPatch`)
          *flows*           values of the flows (positive for input, negative
                            for output)
          *angles*          list of angles of the arrows [deg/90]
                            For example, if the diagram has not been rotated,
                            an input to the top side will have an angle of 3
                            (DOWN), and an output from the top side will have
                            an angle of 1 (UP).  If a flow has been skipped
                            (because its magnitude is less than *tolerance*),
                            then its angle will be *None*.
          *tips*            array in which each row is an [x, y] pair
                            indicating the positions of the tips (or "dips") of
                            the flow paths
                            If the magnitude of a flow is less the *tolerance*
                            for the instance of :class:`Sankey`, the flow is
                            skipped and its tip will be at the center of the
                            diagram.
          *text*            :class:`~matplotlib.text.Text` instance for the
                            label of the diagram
          *texts*           list of :class:`~matplotlib.text.Text` instances
                            for the labels of flows
          ===============   ===================================================

        .. seealso::

            :meth:`add`
        """
        self.ax.axis([self.extent[0] - self.margin,
                      self.extent[1] + self.margin,
                      self.extent[2] - self.margin,
                      self.extent[3] + self.margin])
        self.ax.set_aspect('equal', adjustable='datalim')
        return self.diagrams
