Setup

import matplotlib as mpl
import matplotlib.pyplot as plt
from matplotlib.ticker import StrMethodFormatter as SMF
import pandas as pd
import seaborn as sns

#Create Data
data = pd.DataFrame(columns = ['Verses',
                               'Forget',
                               'EV'])

for v in range(1, 10001):
    for f in [x/50000 for x in range(1, 251)]:
        ev = (1/f) * (1 / (1-f)**v - 1) / v
        data = data.append({'Verses' : v,
                            'Forget' : f,
                            'EV' : ev},
                           ignore_index = True)

sns.set()
fig = plt.figure(figsize = (16, 7))
ax = fig.add_subplot(xlim = (0, 10000),
                     ylim = (0, 0.002))

heatmap = plt.scatter(x = data[data['Forget'] < 0.0021]['Verses'],
                      y = data[data['Forget'] < 0.0021]['Forget'],
                      c = data[data['Forget'] < 0.0021]['EV'],
                      cmap = 'viridis_r',
                      marker = "s",
                      alpha = 0.8,
                      norm = mpl.colors.LogNorm())

#Title setup.
ax.set_title('N Bottles of Beer', fontsize = 24)

#X-axis setup.
ax.set_xlabel('Bottles of Beer on Wall', fontsize = 22)
ax.xaxis.set_major_formatter(SMF('{x:,.0f}'))
#Y-axis setup.
ax.set_ylabel('P(Forget Verse #)', fontsize = 22)
ax.tick_params(axis = 'both', which = 'major', labelsize = 18)

#Forget = 1/Verses.
end = data[(data['Forget'] < 0.0021) & (data['EV'] > 1.71) & (data['EV'] < 1.73)]
plt.plot(end['Verses'],
        end['Forget'],
        alpha = 1,
        c = 'k',
        lw = 1.1,
        zorder = 2)
ax.annotate("Avg. Ver. / Ver. ≈ e-1", (1500, 0.00075), fontsize = 18)

#Colorbar.
plt.colorbar(heatmap).set_label('Average Verses Sung / Verses', labelpad = -70, rotation = 90, fontsize = 22);

fig.savefig("2023.02.03 Classic.png",
            bbox_inches = 'tight')

Rohan Lewis

2023.02.06