EVOLUTION-MANAGER

Edit File: sankey.py

""" Module for creating Sankey diagrams using Matplotlib. """ import logging from types import SimpleNamespace import numpy as np import matplotlib as mpl from matplotlib.path import Path from matplotlib.patches import PathPatch from matplotlib.transforms import Affine2D from matplotlib import docstring _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: """ 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. The optional arguments listed below are applied to all subdiagrams so that there is consistent alignment and formatting. 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() Other Parameters ---------------- ax : `~.axes.Axes` Axes onto which the data should be plotted. If *ax* isn't provided, new Axes will be created. scale : float 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 : str The physical unit associated with the flow quantities. If *unit* is None, then none of the quantities are labeled. format : str 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 : float Space between paths that break in/break away to/from the top or bottom. radius : float Inner radius of the vertical paths. shoulder : float Size of the shoulders of output arrows. offset : float Text offset (from the dip or tip of the arrow). head_angle : float Angle, in degrees, of the arrow heads (and negative of the angle of the tails). margin : float Minimum space between Sankey outlines and the edge of the plot area. tolerance : float Acceptable maximum of the magnitude of the sum of flows. The magnitude of the sum of connected flows cannot be greater than *tolerance*. **kwargs Any additional keyword arguments will be passed to :meth:`add`, which will create the first subdiagram. 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. Other Parameters ---------------- quadrant : {0, 1, 2, 3}, default: 0 Uses 0-based indexing (0, 1, 2, or 3). cw : bool, default: True If True, the arc vertices are produced clockwise; counter-clockwise otherwise. radius : float, default: 1 The radius of the arc. center : (float, float), default: (0, 0) (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 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 mpl.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