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Bk4_Ch13_01.py
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Bk4_Ch13_01.py
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###############
# Authored by Weisheng Jiang
# Book 4 | From Basic Arithmetic to Machine Learning
# Published and copyrighted by Tsinghua University Press
# Beijing, China, 2022
###############
# Bk4_Ch13_01.py
import numpy as np
import matplotlib.pyplot as plt
A = np.array([[1.25, -0.75],
[-0.75, 1.25]])
xx1, xx2 = np.meshgrid(np.linspace(-8, 8, 9), np.linspace(-8, 8, 9))
num_vecs = np.prod(xx1.shape);
thetas = np.linspace(0, 2*np.pi, num_vecs)
thetas = np.reshape(thetas, (-1, 9))
thetas = np.flipud(thetas);
uu = np.cos(thetas);
vv = np.sin(thetas);
fig, ax = plt.subplots()
ax.quiver(xx1,xx2,uu,vv,
angles='xy', scale_units='xy',scale=1,
edgecolor='none', facecolor= 'b')
plt.ylabel('$x_2$')
plt.xlabel('$x_1$')
plt.axis('scaled')
ax.set_xlim([-10, 10])
ax.set_ylim([-10, 10])
ax.grid(linestyle='--', linewidth=0.25, color=[0.5,0.5,0.5])
ax.set_xticks(np.linspace(-10,10,11));
ax.set_yticks(np.linspace(-10,10,11));
plt.show()
# Matrix multiplication
V = np.array([uu.flatten(),vv.flatten()]).T;
W = V@A;
uu_new = np.reshape(W[:,0],(-1, 9));
vv_new = np.reshape(W[:,1],(-1, 9));
fig, ax = plt.subplots()
ax.quiver(xx1,xx2,uu,vv,
angles='xy', scale_units='xy',scale=1,
edgecolor='none', facecolor= 'b')
ax.quiver(xx1,xx2,uu_new,vv_new,
angles='xy', scale_units='xy',scale=1,
edgecolor='none', facecolor= 'r')
plt.ylabel('$x_2$')
plt.xlabel('$x_1$')
plt.axis('scaled')
ax.set_xlim([-10, 10])
ax.set_ylim([-10, 10])
ax.grid(linestyle='--', linewidth=0.25, color=[0.5,0.5,0.5])
ax.set_xticks(np.linspace(-10,10,11));
ax.set_yticks(np.linspace(-10,10,11));
plt.show()
fig, ax = plt.subplots()
ax.quiver(xx1*0,xx2*0,uu,vv,
angles='xy', scale_units='xy',scale=1,
edgecolor='none', facecolor= 'b')
ax.quiver(xx1*0,xx2*0,uu_new,vv_new,
angles='xy', scale_units='xy',scale=1,
edgecolor='none', facecolor= 'r')
plt.ylabel('$x_2$')
plt.xlabel('$x_1$')
plt.axis('scaled')
ax.set_xlim([-2, 2])
ax.set_ylim([-2, 2])
ax.grid(linestyle='--', linewidth=0.25, color=[0.5,0.5,0.5])
ax.set_xticks(np.linspace(-2,2,5));
ax.set_yticks(np.linspace(-2,2,5));
plt.show()