Update

Optimization/Code/UnitBall.py

@@ -0,0 +1,42 @@
+import numpy as np
+import math
+from mpl_toolkits.mplot3d import Axes3D
+import matplotlib.pyplot as plt
+import scipy as sp
+
+## radious and p norms
+L = 1
+plist = [0.5, 1, 1.5, 2, 3, 8]
+
+## preparing matrix A
+v1 = np.array([2,1]); v1 = v1.reshape(2,1)/np.linalg.norm(v1)
+v2 = np.array([-1,2]); v2 = v2.reshape(2,1)/np.linalg.norm(v2)
+l1= 2; l2= 1
+A = l1*np.outer(v1,v1.T) + l2*np.outer(v2,v2.T)
+
+## preparing figures and subplots
+fig, axs = plt.subplots(2,len(plist), figsize=(12, 4), facecolor='w', edgecolor='k')
+fig.subplots_adjust(hspace = 0, wspace=.1)
+x = np.linspace(-L,L, 100)
+
+for j in range(len(plist)):
+    p = plist[j]
+    y = (L**p-np.abs(x)**p)**(1/p)
+    tmp = np.block([ [x, x[::-1]],
+                      [y, -y[::-1]]])
+    T = tmp
+    axs[0,j].plot(T[0,:], T[1,:],'b')
+    axs[0,j].set_title('p = '+str(plist[j]))
+    axs[1,j].plot(T[0,:], T[1,:],'b')
+    T = np.matmul(A, tmp)
+    axs[1,j].plot(T[0,:], T[1,:],'r')
+    axs[1,j].plot([0,2.5*v1[0]], [0,2.5*v1[1]], '--k', [0,2.5*v2[0]], [0,2.5*v2[1]], '--k')
+    axs[1,j].plot(T[0,:], T[1,:],'r')
+    for i in range(2):
+        axs[i,j].set_aspect(1)
+        axs[i,j].set_xlim([-2.5*L,2.5*L])
+        axs[i,j].set_ylim([-2.5*L,2.5*L])
+
+plt.tight_layout()
+plt.savefig('UnitBall.png')
+plt.show()

Optimization/README.md

@@ -18,6 +18,7 @@
 2. [OP02](Assignments): optimization SW.
 3. [OP03](Assignments): convex and affine combinations.
 4. OP04: the following problems from Ch2: 2, 4, 5, , 6, 7, 12, 15, 16.
+5. [OP05](Assignments): norms, metrics, and loss.
 
 ## **Announcements**