ars_envelope.ipynb

Kernel: Python 3 (ipykernel)

# -*- coding: utf-8 -*-
# based on https://github.com/probml/pmtk3/blob/master/demos/arsEnvelope.m
# author : Ang Ming Liang
import numpy as np
import matplotlib.pyplot as plt
import matplotlib

%matplotlib inline

try:
    from scipy.stats import norm
except ModuleNotFoundError:
    %pip install -qq scipy.stats
    from scipy.stats import norm

try:
    from probml_utils import savefig, latexify
except ModuleNotFoundError:
    %pip install -qq git+https://github.com/probml/probml-utils.git
    from probml_utils import savefig, latexify

latexify(width_scale_factor=3, fig_height=1.5)

xs = np.linspace(-1.5, 1.5, 50)
ps = norm.logpdf(xs)

dy_dx = lambda x: -x

fig, ax = plt.subplots()

# Hide the right and top spines
ax.spines["right"].set_visible(False)
ax.spines["top"].set_visible(False)

# Fix the plot size
ax.set_xlim(-1.6, 1.6)
ax.set_ylim(-2.2, -0.8)

# Plotting the log-concave distribution
ax.plot(xs, ps, "b-", linewidth=3)

# At x=-0.7
x1 = -0.7
ratio1 = dy_dx(x1)
ax.plot([x1 - 0.5, x1 + 0.5], [norm.logpdf(x1) - 0.5 * ratio1, norm.logpdf(x1) + 0.5 * ratio1], "-r", "LineWidth", 3)
ax.plot([x1, x1], [norm.logpdf(x1), -2.2], "--r", "LineWidth", 3)

# At x=0
x2 = 0
ratio2 = dy_dx(x2)
ax.plot([x2 - 0.5, x2 + 0.5], [norm.logpdf(x2) - 0.5 * ratio2, norm.logpdf(x2) + 0.5 * ratio2], "-r", "LineWidth", 3)
ax.plot([x2, x2], [norm.logpdf(x2), -2.2], "--r", "LineWidth", 3)

# At x=0.7
x3 = 0.7
ratio3 = dy_dx(x3)
ax.plot([x3 - 0.5, x3 + 0.5], [norm.logpdf(x3) - 0.5 * ratio3, norm.logpdf(x3) + 0.5 * ratio3], "-r", "LineWidth", 3)
ax.plot([x3, x3], [norm.logpdf(x3), -2.2], "--r", "LineWidth", 3)

# Remove the x-axis and y-axis ticks
plt.xticks([])
plt.yticks([])
savefig("ars_envelope")
plt.show()

saving image to ./ars_envelope_latexified.pdf
Figure size: [2.  1.5]