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Book4_Ch03_Python_Codes/Bk4_Ch3_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_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()