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https://github.com/Visualize-ML/Book4_Power-of-Matrix.git
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90 lines
2.2 KiB
Python
90 lines
2.2 KiB
Python
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch13_01.py
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import numpy as np
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import matplotlib.pyplot as plt
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A = np.array([[1.25, -0.75],
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[-0.75, 1.25]])
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xx1, xx2 = np.meshgrid(np.linspace(-8, 8, 9), np.linspace(-8, 8, 9))
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num_vecs = np.prod(xx1.shape);
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thetas = np.linspace(0, 2*np.pi, num_vecs)
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thetas = np.reshape(thetas, (-1, 9))
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thetas = np.flipud(thetas);
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uu = np.cos(thetas);
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vv = np.sin(thetas);
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fig, ax = plt.subplots()
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ax.quiver(xx1,xx2,uu,vv,
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angles='xy', scale_units='xy',scale=1,
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edgecolor='none', facecolor= 'b')
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plt.ylabel('$x_2$')
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plt.xlabel('$x_1$')
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plt.axis('scaled')
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ax.set_xlim([-10, 10])
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ax.set_ylim([-10, 10])
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ax.grid(linestyle='--', linewidth=0.25, color=[0.5,0.5,0.5])
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ax.set_xticks(np.linspace(-10,10,11));
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ax.set_yticks(np.linspace(-10,10,11));
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plt.show()
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# Matrix multiplication
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V = np.array([uu.flatten(),vv.flatten()]).T;
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W = V@A;
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uu_new = np.reshape(W[:,0],(-1, 9));
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vv_new = np.reshape(W[:,1],(-1, 9));
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fig, ax = plt.subplots()
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ax.quiver(xx1,xx2,uu,vv,
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angles='xy', scale_units='xy',scale=1,
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edgecolor='none', facecolor= 'b')
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ax.quiver(xx1,xx2,uu_new,vv_new,
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angles='xy', scale_units='xy',scale=1,
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edgecolor='none', facecolor= 'r')
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plt.ylabel('$x_2$')
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plt.xlabel('$x_1$')
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plt.axis('scaled')
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ax.set_xlim([-10, 10])
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ax.set_ylim([-10, 10])
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ax.grid(linestyle='--', linewidth=0.25, color=[0.5,0.5,0.5])
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ax.set_xticks(np.linspace(-10,10,11));
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ax.set_yticks(np.linspace(-10,10,11));
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plt.show()
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fig, ax = plt.subplots()
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ax.quiver(xx1*0,xx2*0,uu,vv,
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angles='xy', scale_units='xy',scale=1,
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edgecolor='none', facecolor= 'b')
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ax.quiver(xx1*0,xx2*0,uu_new,vv_new,
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angles='xy', scale_units='xy',scale=1,
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edgecolor='none', facecolor= 'r')
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plt.ylabel('$x_2$')
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plt.xlabel('$x_1$')
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plt.axis('scaled')
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ax.set_xlim([-2, 2])
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ax.set_ylim([-2, 2])
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ax.grid(linestyle='--', linewidth=0.25, color=[0.5,0.5,0.5])
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ax.set_xticks(np.linspace(-2,2,5));
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ax.set_yticks(np.linspace(-2,2,5));
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plt.show()
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