import colorsys
from typing import List
import numpy as np
from matplotlib import patches
from matplotlib import pyplot as plt
from matplotlib.path import Path
from tqdm import tqdm
from jmetal.core.solution import FloatSolution
[docs]
def polar_to_cartesian(r, theta):
return np.array([r * np.cos(theta), r * np.sin(theta)])
[docs]
def draw_sector(
start_angle=0, end_angle=60, radius=1.0, width=0.2, lw=2, ls="-", ax=None, fc=(1, 0, 0), ec=(0, 0, 0), z_order=1
):
if start_angle > end_angle:
start_angle, end_angle = end_angle, start_angle
start_angle *= np.pi / 180.0
end_angle *= np.pi / 180.0
# https://stackoverflow.com/questions/1734745/how-to-create-circle-with-b%C3%A9zier-curves
opt = 4.0 / 3.0 * np.tan((end_angle - start_angle) / 4.0) * radius
inner = radius * (1 - width)
vertsPath = [
polar_to_cartesian(radius, start_angle),
polar_to_cartesian(radius, start_angle) + polar_to_cartesian(opt, start_angle + 0.5 * np.pi),
polar_to_cartesian(radius, end_angle) + polar_to_cartesian(opt, end_angle - 0.5 * np.pi),
polar_to_cartesian(radius, end_angle),
polar_to_cartesian(inner, end_angle),
polar_to_cartesian(inner, end_angle) + polar_to_cartesian(opt * (1 - width), end_angle - 0.5 * np.pi),
polar_to_cartesian(inner, start_angle) + polar_to_cartesian(opt * (1 - width), start_angle + 0.5 * np.pi),
polar_to_cartesian(inner, start_angle),
polar_to_cartesian(radius, start_angle),
]
codesPaths = [
Path.MOVETO,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.LINETO,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.CLOSEPOLY,
]
if ax is None:
return vertsPath, codesPaths
else:
path = Path(vertsPath, codesPaths)
patch = patches.PathPatch(path, facecolor=fc, edgecolor=ec, lw=lw, linestyle=ls, zorder=z_order)
ax.add_patch(patch)
return patch
[docs]
def draw_chord(
start_angle1=0,
end_angle1=60,
start_angle2=180,
end_angle2=240,
radius=1.0,
chord_width=0.7,
ax=None,
color=(1, 0, 0),
z_order=1,
):
if start_angle1 > end_angle1:
start_angle1, end_angle1 = end_angle1, start_angle1
if start_angle2 > end_angle2:
start_angle2, end_angle2 = end_angle2, start_angle2
start_angle1 *= np.pi / 180.0
end_angle1 *= np.pi / 180.0
start_angle2 *= np.pi / 180.0
end_angle2 *= np.pi / 180.0
optAngle1 = 4.0 / 3.0 * np.tan((end_angle1 - start_angle1) / 4.0) * radius
optAngle2 = 4.0 / 3.0 * np.tan((end_angle2 - start_angle2) / 4.0) * radius
rchord = radius * (1 - chord_width)
vertsPath = [
polar_to_cartesian(radius, start_angle1),
polar_to_cartesian(radius, start_angle1) + polar_to_cartesian(optAngle1, start_angle1 + 0.5 * np.pi),
polar_to_cartesian(radius, end_angle1) + polar_to_cartesian(optAngle1, end_angle1 - 0.5 * np.pi),
polar_to_cartesian(radius, end_angle1),
polar_to_cartesian(rchord, end_angle1),
polar_to_cartesian(rchord, start_angle2),
polar_to_cartesian(radius, start_angle2),
polar_to_cartesian(radius, start_angle2) + polar_to_cartesian(optAngle2, start_angle2 + 0.5 * np.pi),
polar_to_cartesian(radius, end_angle2) + polar_to_cartesian(optAngle2, end_angle2 - 0.5 * np.pi),
polar_to_cartesian(radius, end_angle2),
polar_to_cartesian(rchord, end_angle2),
polar_to_cartesian(rchord, start_angle1),
polar_to_cartesian(radius, start_angle1),
]
codesPath = [
Path.MOVETO,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
]
if ax == None:
return vertsPath, codesPath
else:
path = Path(vertsPath, codesPath)
patch = patches.PathPatch(path, facecolor=color + (0.5,), edgecolor=color + (0.4,), lw=2, alpha=0.5)
ax.add_patch(patch)
return patch
[docs]
def hover_over_bin(event, handle_tickers, handle_plots, colors, fig):
is_found = False
for iobj in range(len(handle_tickers)):
for ibin in range(len(handle_tickers[iobj])):
cont = False
if not is_found:
cont, ind = handle_tickers[iobj][ibin].contains(event)
if cont:
is_found = True
if cont:
plt.setp(handle_tickers[iobj][ibin], facecolor=colors[iobj])
[h.set_visible(True) for h in handle_plots[iobj][ibin]]
is_found = True
fig.canvas.draw_idle()
else:
plt.setp(handle_tickers[iobj][ibin], facecolor=(1, 1, 1))
for h in handle_plots[iobj][ibin]:
h.set_visible(False)
fig.canvas.draw_idle()
[docs]
def chord_diagram(
solutions: List[FloatSolution],
nbins="auto",
ax=None,
obj_labels=None,
prop_labels=dict(fontsize=13, ha="center", va="center"),
pad=6,
):
points_matrix = np.array([s.objectives for s in solutions])
(NPOINTS, NOBJ) = np.shape(points_matrix)
HSV_tuples = [(x * 1.0 / NOBJ, 0.5, 0.5) for x in range(NOBJ)]
colors = list(map(lambda x: colorsys.hsv_to_rgb(*x), HSV_tuples))
if ax is None:
fig = plt.figure(figsize=(6, 6))
ax = plt.axes([0, 0, 1, 1], aspect="equal")
ax.set_xlim(-2.3, 2.3)
ax.set_ylim(-2.3, 2.3)
ax.axis("off")
y = np.array([1.0 / NOBJ] * NOBJ) * (360 - pad * NOBJ)
sector_angles = []
labels_pos_and_ros = []
start_angle = 0
for i in range(NOBJ):
end_angle = start_angle + y[i]
sector_angles.append((start_angle, end_angle))
angle_diff = 0.5 * (start_angle + end_angle)
if -30 <= angle_diff <= 210:
angle_diff -= 90
else:
angle_diff -= 270
angleText = start_angle - 2.5
if -30 <= angleText <= 210:
angleText -= 90
else:
angleText -= 270
labels_pos_and_ros.append(
tuple(polar_to_cartesian(1.0, 0.5 * (start_angle + end_angle) * np.pi / 180.0))
+ (angle_diff,)
+ tuple(polar_to_cartesian(0.725, (start_angle - 2.5) * np.pi / 180.0))
+ (angleText,)
+ tuple(polar_to_cartesian(0.85, (start_angle - 2.5) * np.pi / 180.0))
+ (angleText,)
)
start_angle = end_angle + pad
arc_points = []
for point in points_matrix:
arc_points.append([])
idim = 0
for _ in point:
anglePoint = sector_angles[idim][0] + (sector_angles[idim][1] - sector_angles[idim][0]) * point[idim]
arc_points[-1].append((anglePoint, anglePoint))
idim = idim + 1
max_hist_values = []
handle_tickers = []
handle_plots = []
for iobj in tqdm(range(NOBJ), ascii=True, desc="Chord diagram"):
draw_sector(
start_angle=sector_angles[iobj][0],
end_angle=sector_angles[iobj][1],
radius=0.925,
width=0.225,
ax=ax,
fc=(1, 1, 1, 0.0),
ec=(0, 0, 0),
lw=2,
z_order=10,
)
draw_sector(
start_angle=sector_angles[iobj][0],
end_angle=sector_angles[iobj][1],
radius=0.925,
width=0.05,
ax=ax,
fc=colors[iobj],
ec=(0, 0, 0),
lw=2,
z_order=10,
)
draw_sector(
start_angle=sector_angles[iobj][0],
end_angle=sector_angles[iobj][1],
radius=0.7 + 0.15,
width=0.0,
ax=ax,
fc=colors[iobj],
ec=colors[iobj],
lw=2,
ls=":",
z_order=5,
)
histValues, binsDim = np.histogram(points_matrix[:, iobj], bins=nbins)
relativeHeightBinPre = 0.025
max_hist_values.append(max(histValues))
handle_tickers.append([])
handle_plots.append([])
for indexBin in range(len(histValues)):
startAngleBin = (
sector_angles[iobj][0] + (sector_angles[iobj][1] - sector_angles[iobj][0]) * binsDim[indexBin]
)
endAngleBin = (
sector_angles[iobj][0] + (sector_angles[iobj][1] - sector_angles[iobj][0]) * binsDim[indexBin + 1]
)
relativeHeightBin = 0.15 * histValues[indexBin] / max(histValues)
handle_tickers[-1].append(
draw_sector(
start_angle=startAngleBin,
end_angle=endAngleBin,
radius=0.69,
width=0.08,
ax=ax,
lw=1,
fc=(1, 1, 1),
ec=(0, 0, 0),
)
)
handle_plots[-1].append([])
if histValues[indexBin] > 0:
draw_sector(
start_angle=startAngleBin,
end_angle=endAngleBin,
radius=0.7 + relativeHeightBin,
width=0,
ax=ax,
lw=1,
fc=colors[iobj],
ec=colors[iobj],
)
plotPoint1 = polar_to_cartesian(0.7 + relativeHeightBinPre, startAngleBin * np.pi / 180.0)
plotPoint2 = polar_to_cartesian(0.7 + relativeHeightBin, startAngleBin * np.pi / 180.0)
plt.plot([plotPoint1[0], plotPoint2[0]], [plotPoint1[1], plotPoint2[1]], c=colors[iobj], lw=1)
relativeHeightBinPre = relativeHeightBin
else:
plotPoint1 = polar_to_cartesian(0.7 + relativeHeightBinPre, startAngleBin * np.pi / 180.0)
plotPoint2 = polar_to_cartesian(0.725 + relativeHeightBin, startAngleBin * np.pi / 180.0)
plt.plot([plotPoint1[0], plotPoint2[0]], [plotPoint1[1], plotPoint2[1]], c=colors[iobj], lw=1)
relativeHeightBinPre = 0.025
if indexBin == len(histValues) - 1:
plotPoint1 = polar_to_cartesian(0.7 + relativeHeightBin, endAngleBin * np.pi / 180.0)
plotPoint2 = polar_to_cartesian(0.725, endAngleBin * np.pi / 180.0)
plt.plot([plotPoint1[0], plotPoint2[0]], [plotPoint1[1], plotPoint2[1]], c=colors[iobj], lw=1)
for ipoint in range(len(points_matrix)):
plotPoint1 = polar_to_cartesian(0.6, arc_points[ipoint][iobj][0] * np.pi / 180.0)
plotPoint2 = polar_to_cartesian(0.6, arc_points[ipoint][iobj][0] * np.pi / 180.0)
plt.plot(
[plotPoint1[0], plotPoint2[0]],
[plotPoint1[1], plotPoint2[1]],
marker="o",
markersize=3,
c=colors[iobj],
lw=2,
)
if binsDim[indexBin] < points_matrix[ipoint, iobj] <= binsDim[indexBin + 1]:
for jdim in range(NOBJ):
if jdim >= 1:
handle_plots[iobj][indexBin].append(
draw_chord(
arc_points[ipoint][jdim - 1][0],
arc_points[ipoint][jdim - 1][1],
arc_points[ipoint][jdim][0],
arc_points[ipoint][jdim][1],
radius=0.55,
color=colors[iobj],
chord_width=1,
ax=ax,
)
)
handle_plots[iobj][indexBin][-1].set_visible(False)
handle_plots[iobj][indexBin].append(
draw_chord(
arc_points[ipoint][-1][0],
arc_points[ipoint][-1][1],
arc_points[ipoint][0][0],
arc_points[ipoint][0][1],
radius=0.55,
color=colors[iobj],
chord_width=1,
ax=ax,
)
)
handle_plots[iobj][indexBin][-1].set_visible(False)
if obj_labels is None:
obj_labels = ["$f_{" + str(i) + "}(\mathbf{x})$" for i in range(NOBJ)]
prop_legend_bins = dict(fontsize=9, ha="center", va="center")
for i in range(NOBJ):
p0, p1 = polar_to_cartesian(0.975, sector_angles[i][0] * np.pi / 180.0)
ax.text(p0, p1, "0", **prop_legend_bins)
p0, p1 = polar_to_cartesian(0.975, sector_angles[i][1] * np.pi / 180.0)
ax.text(p0, p1, "1", **prop_legend_bins)
ax.text(
labels_pos_and_ros[i][0],
labels_pos_and_ros[i][1],
obj_labels[i],
rotation=labels_pos_and_ros[i][2],
**prop_labels
)
ax.text(labels_pos_and_ros[i][3], labels_pos_and_ros[i][4], "0", **prop_legend_bins, color=colors[i])
ax.text(
labels_pos_and_ros[i][6],
labels_pos_and_ros[i][7],
str(max_hist_values[i]),
**prop_legend_bins,
color=colors[i]
)
plt.axis([-1.2, 1.2, -1.2, 1.2])
fig.canvas.mpl_connect(
"motion_notify_event", lambda event: hover_over_bin(event, handle_tickers, handle_plots, colors, fig)
)
plt.show()
