Add files via upload

Book4_Ch03_Python_Codes/Bk4_Ch3_01.py

@@ -0,0 +1,52 @@
+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+# Bk4_Ch3_01.py
+
+import matplotlib.pyplot as plt
+import numpy as np
+
+p_values = [0.05, 0.2, 0.5, 1, 1.5, 2, 4, 8, np.inf]
+
+x1 = np.linspace(-2.5, 2.5, num=101);
+x2 = x1;
+
+xx1, xx2 = np.meshgrid(x1,x2)
+
+fig, axes = plt.subplots(ncols=3,nrows=3,
+                         figsize=(12, 12))
+
+for p, ax in zip(p_values, axes.flat):
+    
+    if np.isinf(p):
+        zz = np.maximum(np.abs(xx1),np.abs(xx2))
+    else:
+        zz = ((np.abs((xx1))**p) + (np.abs((xx2))**p))**(1./p)
+    
+    # plot contour of Lp
+    ax.contourf(xx1, xx2, zz, 20, cmap='RdYlBu_r')
+    
+    # plot contour of Lp = 1
+    ax.contour (xx1, xx2, zz, [1], colors='k', linewidths = 2) 
+    
+    # decorations
+
+    ax.axhline(y=0, color='k', linewidth = 0.25)
+    ax.axvline(x=0, color='k', linewidth = 0.25)
+    ax.set_xlim(-2.5, 2.5)
+    ax.set_ylim(-2.5, 2.5)
+    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_title('p = ' + str(p))
+    ax.set_aspect('equal', adjustable='box')
+
+plt.show()

Book4_Ch03_Python_Codes/Bk4_Ch3_02.py

@@ -0,0 +1,53 @@
+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+# Bk4_Ch3_02.py
+
+import numpy as np
+from matplotlib import pyplot as plt
+import seaborn as sns
+
+u = [0,0,4, 3]
+v = [0,0,-2,4]
+u_bis = [4,3,v[2],v[3]]
+w = [0,0,2,7]
+
+fig, ax = plt.subplots()
+
+plt.quiver([u[0], u_bis[0], w[0]],
+           [u[1], u_bis[1], w[1]],
+           [u[2], u_bis[2], w[2]],
+           [u[3], u_bis[3], w[3]],
+           angles='xy', scale_units='xy', 
+           scale=1, color=sns.color_palette())
+
+plt.axvline(x=0, color='grey')
+plt.axhline(y=0, color='grey')
+
+plt.text(3, 1, r'$||\vec{u}||_2$', 
+         color=sns.color_palette()[0], size=12,
+         ha='center',va='center')
+
+plt.text(3, 6, r'$||\vec{v}||_2$', 
+         color=sns.color_palette()[1], size=12,
+         ha='center',va='center')
+
+plt.text(0, 4, r'$||\vec{u}+\vec{v}||_2$', 
+         color=sns.color_palette()[2], size=12,
+         ha='center',va='center')
+
+plt.ylabel('$x_2$')
+plt.xlabel('$x_1$')
+plt.axis('scaled')
+ax.set_xticks(np.arange(-2,8 + 1))
+ax.set_yticks(np.arange(-2,8 + 1))
+ax.set_xlim(-2, 8)
+ax.set_ylim(-2, 8)
+ax.grid(linestyle='--', linewidth=0.25, color=[0.5,0.5,0.5])
+
+# reference: Essential Math for Data Science