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Book4_Power-of-Matrix/Book4_Ch20_Python_Codes/Bk4_Ch20_02.py
2022-07-22 08:11:16 -04:00

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Python

###############
# Authored by Weisheng Jiang
# Book 4 | From Basic Arithmetic to Machine Learning
# Published and copyrighted by Tsinghua University Press
# Beijing, China, 2022
###############
# Bk4_Ch20_02.py
import numpy as np
import matplotlib.pyplot as plt
alphas = np.linspace(0, 2*np.pi, 100)
# unit circle
r = np.sqrt(1.0)
z1 = r*1/np.cos(alphas)
z2 = r*np.tan(alphas)
Z = np.array([z1, z2]).T # data of unit circle
# scale
S = np.array([[1, 0],
[0, 1]])
thetas = np.array([0, 30, 45, 60, 90, 120])
for theta in thetas:
# rotate
print('==== Rotate ====')
print(theta)
theta = theta/180*np.pi
R = np.array([[np.cos(theta), -np.sin(theta)],
[np.sin(theta), np.cos(theta)]])
X = Z@S@R.T;
x1 = X[:,0]
x2 = X[:,1]
fig, ax = plt.subplots(1)
ax.plot(z1, z2, 'b') # plot the unit circle
ax.plot(x1, x2, 'r') # plot the transformed shape
plt.axvline(x=0, color= 'k', zorder=0)
plt.axhline(y=0, color= 'k', zorder=0)
ax.set_aspect(1)
plt.xlim(-3,3)
plt.ylim(-3,3)
plt.grid(linestyle='--')
plt.show()
plt.xlabel('$x_1$')
plt.ylabel('$x_2$')