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70 lines
1.9 KiB
Python
70 lines
1.9 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_Ch9_02.py
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import numpy as np
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import matplotlib.pyplot as plt
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thetas = np.array([0, 15, 30, 45, 60, 75, 90, 120, 135])
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x = np.array([[4],
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[3]])
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i = 1
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fig = plt.figure()
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for theta in thetas:
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theta = theta/180*np.pi
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ax = fig.add_subplot(3, 3, i)
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v1 = np.array([[np.cos(theta)],
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[np.sin(theta)]])
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proj = v1.T@x
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print(proj)
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plt.plot([-v1[0]*6, v1[0]*6], [-v1[1]*6, v1[1]*6])
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plt.plot([x[0], v1[0]*proj], [x[1], v1[1]*proj],
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color = 'k', linestyle = '--')
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plt.plot(v1[0]*proj, v1[1]*proj, color = 'k', marker = 'x')
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plt.quiver (0, 0, v1[0], v1[1],
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angles='xy', scale_units='xy',
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scale=1, color = 'b')
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v2 = np.array([[-np.sin(theta)],
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[np.cos(theta)]])
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proj = v2.T@x
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print(proj)
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plt.plot([-v2[0]*6, v2[0]*6], [-v2[1]*6, v2[1]*6])
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plt.plot([x[0], v2[0]*proj], [x[1], v2[1]*proj],
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color = 'k', linestyle = '--')
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plt.plot(v2[0]*proj, v2[1]*proj, color = 'k', marker = 'x')
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plt.quiver (0, 0, v2[0], v2[1],
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angles='xy', scale_units='xy',
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scale=1,color = 'r')
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plt.axhline(y = 0, color = 'k')
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plt.axvline(x = 0, color = 'k')
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plt.plot(x[0],x[1], marker = 'x', color = 'r')
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plt.quiver(0, 0, x[0],x[1],
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angles='xy', scale_units='xy',
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scale=1, color = 'k')
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plt.axis('scaled')
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ax.grid(linestyle='--', linewidth=0.25, color=[0.75,0.75,0.75])
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plt.xlim([-6, 6])
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plt.ylim([-6, 6])
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plt.xticks(np.linspace(-6,6,13))
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plt.yticks(np.linspace(-6,6,13))
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i = i + 1
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