In [3]:
heatMap(2)
import math
from math import sqrt as mS
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from matplotlib.ticker import PercentFormatter as PF
import seaborn as sns
def createDistDF() :
"""
List of x, y, and z values
Parameters:
None.
Returns:
df - Dataframe of values.
"""
a = 2
Xs = []
Ys = []
Z1s = []
Zips = []
Zfs = []
Z2s = []
for x in [i/500 for i in range(501)] :
for y in [j/500 for j in range(501)] :
#All three targets, 9 outcomes.
no_strategy = (2*x*x + y*y) / 9
#Indistinguishiable pair only, 4 outcomes.
ind_pair = x*x / 2
#Far away only, 1 outcome.
far = y*y
Xs.append(x)
Ys.append(y)
Z1s.append(no_strategy)
Zips.append(ind_pair)
Zfs.append(far)
Z2s.append(max(ind_pair, far))
df = pd.DataFrame({'X' : Xs,
'Y' : Ys,
'Z1' : Z1s,
'Zips' : Zips,
'Zfs' : Zfs,
'Z2' : Z2s})
return(df)
def heatMap(Z) :
fig = plt.figure(figsize = (10, 8))
ax = fig.add_subplot(xlim = (0, 1),
ylim = (0, 1))
fig.subplots_adjust(left = 0.02, bottom = 0.02, right = 0.98, top = 0.98)
df = createDistDF()
cmap = plt.cm.viridis_r
heatmap = plt.scatter(x = df['X'],
y = df['Y'],
c = df['Z' + str(Z)],
cmap = cmap,
marker = "s",
s = 1,
vmin = 0,
vmax = 1,
plotnonfinite = True)
#Title setup.
ax.set_title('Can the Archers Coordinate?', fontsize = 24)
#X-axis setup.
ax.set_xlabel("Two, Closer, Indistinguishable Targets", fontsize = 22)
ax.xaxis.set_major_formatter(PF(xmax = 1))
#Y-axis setup.
ax.set_ylabel("Further Away Target", fontsize = 22)
ax.yaxis.set_major_formatter(PF(xmax = 1))
ax.tick_params(axis = 'both', which = 'major', labelsize = 16)
if Z == 2:
#50% & 25% cutoffs and line of equality.
a = 0
b = 0.5
c = 1/mS(2)
d = 1
for x, y in [([a, d], [c, c]),
([a, c], [b, b]),
([a, d], [a, c]),
([c, c], [0, b])] :
ax.plot(x,y,
lw = 1,
c = 'k',
ls = '--')
text = [("y ≈ 100%, P = 100%", (b, 0.97), 'k', 0),
("y ≈ 70.71%, P = 50%", (b, 0.68), 'k', 0),
("y = 50%, P = 25%", (c/2, 0.47), 'k', 0),
("y = x/√2", (b, c/2), 'k', 35.264),
("x = 100%, P = 50%", (0.98, 0.2), 'k', -90),
("x = 70.71%, P = 25%", (0.68, 0.1), 'k', -90)]
for t in text :
plt.annotate(text = t[0],
xy = t[1],
c = t[2],
size = 14,
ha = 'center',
rotation = t[3],
zorder = 4)
#Colorbar.
cb = plt.colorbar(heatmap, ax = ax, format = PF(xmax = 1))
cb.set_label('Prize Win %',
labelpad = -100,
fontsize = 20)
cb.ax.tick_params(labelsize = 16)
fig.savefig("2026.02.20 EC" + str(Z) + ".png", bbox_inches = "tight")
heatMap(2)