CH01_SEC07_3.ipynb

Kernel: Python 3

import matplotlib.pyplot as plt
import matplotlib.cm
import numpy as np
import skimage.transform

plt.rcParams['figure.figsize'] = [12,6]
plt.rcParams.update({'font.size': 18})

n = 1000
q = int(n/4)
X = np.zeros((n,n))
X[(q-1):(3*q),(q-1):(3*q)] = 1

nAngles = 12 # Sweep through 12 different angles, from 0:4:44 degrees
cm_np = np.array([[0,0,2/3],
                 [0,0,1],
                 [0,1/3,1],
                 [0,2/3,1],
                 [0,1,1],
                 [1/3,1,2/3],
                 [2/3,1,1/3],
                 [1,1,0],
                 [1,2/3,0],
                 [1,1/3,0],
                 [1,0,0],
                 [2/3,0,0]])


cmap = plt.cm.jet
cmap.set_bad(alpha = 0.0)

U, S, VT = np.linalg.svd(X,full_matrices=0)

fig1 = plt.figure()
ax1 = fig1.add_subplot(121)
plt.imshow(np.ma.masked_where(X == 0, X),vmin=0,vmax=nAngles)
plt.set_cmap(cmap)
plt.axis('off')


ax2 = fig1.add_subplot(122)
plt.semilogy(S,'-o',color=tuple(cm_np[0]))
plt.grid()

plt.show()

Xrot = X

fig, axs = plt.subplots(1,2)

for j in range(nAngles):
    Xrot = skimage.transform.rotate(X,j*4) #rotate by theta = j*4 degrees
    Xrot[np.nonzero(Xrot)] = j
    
    U, S, VT = np.linalg.svd(Xrot)

    axs[0].imshow(np.ma.masked_where(Xrot == 0, Xrot),vmin=0,vmax=nAngles)
    plt.set_cmap(cmap)
    axs[0].axis('off')

    axs[1].semilogy(S,'-o',color=tuple(cm_np[j]))
    axs[1].axis('on')
    axs[1].grid(1)

plt.show()