newtonsMethodNonConvex.ipynb

Kernel: Unknown Kernel

import numpy as np
import matplotlib.pyplot as plt

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 = -4
xmax = 13
ymin = -50
ymax = 600
domain = np.arange(xmin, xmax + 0.01, 0.01)


def f(x):
    return -np.power(x, 3) + 15 * np.power(x, 2)


Xk = 8


def f1(x):
    return -3 * np.power(x, 2) + 30 * x


def f2(x):
    return -6 * x + 30


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


val = np.max(t(domain))
maxNDX = np.argmax(t(domain))
maximum = domain[maxNDX]

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(maximum, t(maximum), ".k")
plt.plot([maximum, maximum], [ymin, t(maximum)], ":k")
plt.axis([xmin, xmax, ymin, ymax])
plt.xticks([], [])
plt.yticks([], [])
plt.text(7.8, -90, "\u03B8" + "\u2096", fontsize=14)
plt.text(10.3, -90, "\u03B8" + "\u2096" + "+" + "d" + "\u2096", fontsize=14)
pml.savefig(r"newtonsMethodNonConvexTheta.pdf")
plt.show()