820 lines
36 KiB
Python
820 lines
36 KiB
Python
|
"""
|
||
|
|
Module for creating Sankey diagrams using Matplotlib.
|
||
|
|
"""
|
||
|
|
|
||
|
|
import logging
|
||
|
|
from types import SimpleNamespace
|
||
|
|
|
||
|
|
import numpy as np
|
||
|
|
|
||
|
|
from matplotlib.path import Path
|
||
|
|
from matplotlib.patches import PathPatch
|
||
|
|
from matplotlib.transforms import Affine2D
|
||
|
|
from matplotlib import docstring
|
||
|
|
from matplotlib import rcParams
|
||
|
|
|
||
|
|
_log = logging.getLogger(__name__)
|
||
|
|
|
||
|
|
__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.
|
||
|
|
|
||
|
|
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>`_
|
||
|
|
|
||
|
|
"""
|
||
|
|
|
||
|
|
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()
|
||
|
|
|
||
|
|
See Also
|
||
|
|
--------
|
||
|
|
Sankey.add
|
||
|
|
Sankey.finish
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
|
||
|
|
.. plot:: gallery/specialty_plots/sankey_basics.py
|
||
|
|
"""
|
||
|
|
# Check the arguments.
|
||
|
|
if gap < 0:
|
||
|
|
raise ValueError(
|
||
|
|
"'gap' is negative, which is not allowed because it would "
|
||
|
|
"cause the paths to overlap")
|
||
|
|
if radius > gap:
|
||
|
|
raise ValueError(
|
||
|
|
"'radius' is greater than 'gap', which is not allowed because "
|
||
|
|
"it would cause the paths to overlap")
|
||
|
|
if head_angle < 0:
|
||
|
|
raise ValueError(
|
||
|
|
"'head_angle' is negative, which is not allowed because it "
|
||
|
|
"would cause inputs to look like outputs and vice versa")
|
||
|
|
if tolerance < 0:
|
||
|
|
raise ValueError(
|
||
|
|
"'tolerance' is negative, but it 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 reversible 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.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
patchlabel : str
|
||
|
|
Label to be placed at the center of the diagram.
|
||
|
|
Note that *label* (not *patchlabel*) can be passed as keyword
|
||
|
|
argument to create an entry in the legend.
|
||
|
|
|
||
|
|
flows : list of float
|
||
|
|
Array of flow values. By convention, inputs are positive and
|
||
|
|
outputs are negative.
|
||
|
|
|
||
|
|
Flows are placed along the top of the diagram from the inside out
|
||
|
|
in order of their index within *flows*. 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.
|
||
|
|
|
||
|
|
orientations : list of {-1, 0, 1}
|
||
|
|
List of orientations of the flows (or a single orientation to be
|
||
|
|
used for all flows). Valid values are 0 (inputs from
|
||
|
|
the left, outputs to the right), 1 (from and to the top) or -1
|
||
|
|
(from and to the bottom).
|
||
|
|
|
||
|
|
labels : list of (str or None)
|
||
|
|
List of labels for the flows (or a single label to be used for all
|
||
|
|
flows). Each label may be *None* (no label), or a labeling string.
|
||
|
|
If an entry is a (possibly 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 : float
|
||
|
|
Length between the bases of the input and output groups (in
|
||
|
|
data-space units).
|
||
|
|
|
||
|
|
pathlengths : list of float
|
||
|
|
List of lengths of the vertical 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 : int
|
||
|
|
Index of the prior diagram to which this diagram should be
|
||
|
|
connected.
|
||
|
|
|
||
|
|
connect : (int, int)
|
||
|
|
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 : float
|
||
|
|
Angle of rotation of the diagram in degrees. 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). *rotation* is ignored if this diagram is connected to an
|
||
|
|
existing one (using *prior* and *connect*).
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
Sankey
|
||
|
|
The current `.Sankey` instance.
|
||
|
|
|
||
|
|
Other Parameters
|
||
|
|
----------------
|
||
|
|
**kwargs
|
||
|
|
Additional keyword arguments set `matplotlib.patches.PathPatch`
|
||
|
|
properties, listed below. For example, one may want to use
|
||
|
|
``fill=False`` or ``label="A legend entry"``.
|
||
|
|
|
||
|
|
%(Patch)s
|
||
|
|
|
||
|
|
See Also
|
||
|
|
--------
|
||
|
|
Sankey.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
|
||
|
|
try:
|
||
|
|
orientations = np.broadcast_to(orientations, n)
|
||
|
|
except ValueError:
|
||
|
|
raise ValueError(
|
||
|
|
f"The shapes of 'flows' {np.shape(flows)} and 'orientations' "
|
||
|
|
f"{np.shape(orientations)} are incompatible"
|
||
|
|
) from None
|
||
|
|
try:
|
||
|
|
labels = np.broadcast_to(labels, n)
|
||
|
|
except ValueError:
|
||
|
|
raise ValueError(
|
||
|
|
f"The shapes of 'flows' {np.shape(flows)} and 'labels' "
|
||
|
|
f"{np.shape(labels)} are incompatible"
|
||
|
|
) from None
|
||
|
|
if trunklength < 0:
|
||
|
|
raise ValueError(
|
||
|
|
"'trunklength' is negative, which is not 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; patchlabel=%r); "
|
||
|
|
"is the system not at steady state?",
|
||
|
|
np.sum(flows), patchlabel)
|
||
|
|
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 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(
|
||
|
|
f"The index of the prior diagram is {prior}, but there "
|
||
|
|
f"are only {len(self.diagrams)} other diagrams")
|
||
|
|
if connect[0] >= len(self.diagrams[prior].flows):
|
||
|
|
raise ValueError(
|
||
|
|
"The connection index to the source diagram is {}, but "
|
||
|
|
"that diagram has only {} flows".format(
|
||
|
|
connect[0], len(self.diagrams[prior].flows)))
|
||
|
|
if connect[1] >= n:
|
||
|
|
raise ValueError(
|
||
|
|
f"The connection index to this diagram is {connect[1]}, "
|
||
|
|
f"but this diagram has only {n} flows")
|
||
|
|
if self.diagrams[prior].angles[connect[0]] is None:
|
||
|
|
raise ValueError(
|
||
|
|
f"The connection cannot be made, which may occur if the "
|
||
|
|
f"magnitude of flow {connect[0]} of diagram {prior} is "
|
||
|
|
f"less than the specified tolerance")
|
||
|
|
flow_error = (self.diagrams[prior].flows[connect[0]] +
|
||
|
|
flows[connect[1]])
|
||
|
|
if abs(flow_error) >= self.tolerance:
|
||
|
|
raise ValueError(
|
||
|
|
f"The scaled sum of the connected flows is {flow_error}, "
|
||
|
|
f"which is not within the tolerance ({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(
|
||
|
|
f"The value of orientations[{i}] is {orient}, "
|
||
|
|
f"but it must be -1, 0, or 1")
|
||
|
|
if is_input:
|
||
|
|
angles[i] = UP
|
||
|
|
elif not is_input:
|
||
|
|
angles[i] = DOWN
|
||
|
|
|
||
|
|
# Justify the lengths of the paths.
|
||
|
|
if np.iterable(pathlengths):
|
||
|
|
if len(pathlengths) != n:
|
||
|
|
raise ValueError(
|
||
|
|
f"The lengths of 'flows' ({n}) and 'pathlengths' "
|
||
|
|
f"({len(pathlengths)}) are incompatible")
|
||
|
|
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 = 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(
|
||
|
|
SimpleNamespace(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:`~matplotlib.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
|
||
|
|
=============== ===================================================
|
||
|
|
|
||
|
|
See Also
|
||
|
|
--------
|
||
|
|
Sankey.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
|