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Book4_Ch01_Python_Codes/Bk3_Ch1_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
+###############
+
+# Bk3_Ch1_01.py
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+def draw_vector(vector,RBG): 
+    array = np.array([[0, 0, vector[0], vector[1]]])
+    X, Y, U, V = zip(*array)
+    plt.quiver(X, Y, U, V,angles='xy', scale_units='xy',scale=1,color = RBG)
+
+fig, ax = plt.subplots()
+
+draw_vector([4,3],np.array([0,112,192])/255)
+draw_vector([-3,4],np.array([255,0,0])/255)
+
+plt.ylabel('$x_2$')
+plt.xlabel('$x_1$')
+plt.axis('scaled')
+ax.set_xlim([-5, 5])
+ax.set_ylim([-5, 5])
+ax.grid(linestyle='--', linewidth=0.25, color=[0.5,0.5,0.5])
+plt.show()

Book4_Ch01_Python_Codes/Bk3_Ch1_02.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
+###############
+
+# Bk3_Ch1_02.py
+
+import numpy as np
+
+# define two column vectors
+a = np.array([[4], [3]])
+b = np.array([[-3], [4]])
+
+# calculate L2 norm
+a_L2_norm = np.linalg.norm(a)
+b_L2_norm = np.linalg.norm(b)

Book4_Ch01_Python_Codes/Bk3_Ch1_03.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
+###############
+
+# Bk3_Ch1_03.py
+
+import matplotlib.pyplot as plt
+import numpy as np
+
+x1 = np.linspace(-10, 10, num=201);
+x2 = x1;
+
+xx1, xx2 = np.meshgrid(x1,x2)
+p = 2
+zz = ((np.abs((xx1))**p) + (np.abs((xx2))**p))**(1./p)
+
+fig, ax = plt.subplots(figsize=(12, 12))
+
+ax.contour(xx1, xx2, zz, levels = np.arange(11), cmap='RdYlBu_r')
+
+ax.axhline(y=0, color='k', linewidth = 0.25)
+ax.axvline(x=0, color='k', linewidth = 0.25)
+ax.set_xlim(-12, 12)
+ax.set_ylim(-12, 12)
+ax.spines['top'].set_visible(False)
+ax.spines['right'].set_visible(False)
+ax.spines['bottom'].set_visible(False)
+ax.spines['left'].set_visible(False)
+ax.set_xlabel('$x_1$')
+ax.set_ylabel('$x_2$')
+ax.set_aspect('equal', adjustable='box')
+plt.show()

Book4_Ch01_Python_Codes/Bk3_Ch1_04.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
+###############
+
+# Bk3_Ch1_04.py
+
+import numpy as np
+
+# define two column vectors
+a = np.array([[-2], [5]])
+b = np.array([[5], [-1]])
+
+# calculate vector addition
+a_plus_b = a + b
+a_plus_b_2 = np.add(a,b)
+
+# calculate vector subtraction
+a_minus_b = a - b
+a_minus_b_2 = np.subtract(a,b)
+
+b_minus_a = b - a
+b_minus_a_2 = np.subtract(b,a)

Book4_Ch01_Python_Codes/Bk3_Ch1_05.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
+###############
+
+# Bk3_Ch1_05.py
+
+import numpy as np
+
+# define a column vector
+a = np.array([[2], [2]])
+
+b = 2*a
+c = -1.5*a