newtonsMethodMinQuad.ipynb

Kernel: Unknown Kernel

import numpy as np
import matplotlib.pyplot as plt
import os

try:
    import probml_utils as pml
except ModuleNotFoundError:
    %pip install -qq git+https://github.com/probml/probml-utils.git
    import probml_utils as pml

xmin = -5
xmax = 0
ymin = -20
ymax = 150
domain = np.arange(xmin, xmax + 0.01, 0.01)


def f(x):
    return -np.power(x, 3)


Xk = -4


def f1(x):
    return -3 * np.power(x, 2)


def f2(x):
    return -6 * x


def t(x):
    return f(Xk) + f1(Xk) * (x - Xk) + (1 / 2) * f2(Xk) * np.power((x - Xk), 2)


minNDX = np.argmin(t(domain))
minimum = domain[minNDX]

h1 = plt.plot(domain, f(domain), "-r")
h2 = plt.plot(domain, t(domain), "--b")
plt.plot(Xk, f(Xk), ".k")
plt.plot([Xk, Xk], [ymin, f(Xk)], ":k")
plt.plot(minimum, t(minimum), ".k")
plt.plot([minimum, minimum], [ymin, t(minimum)], ":k")
plt.axis([xmin, xmax, ymin, ymax])
plt.xticks([], [])
plt.yticks([], [])
plt.text(-4.1, -30, "\u03B8" + "\u2096", fontsize=14)
plt.text(-2.1, -30, "\u03B8" + "\u2096" + "+" + "d" + "\u2096", fontsize=14)
pml.savefig(r"newtonsMethodMinQuadTheta.pdf")
plt.show()