pca_1.py

import numpy as np
import matplotlib
import matplotlib.pyplot as plt

#Make a random array and then make it positive-definite
num_vars = 6
num_obs = 9
A = np.random.randn(num_obs, num_vars)
A = np.asmatrix(A.T) * np.asmatrix(A)
U, S, V = np.linalg.svd(A) 
eigvals = S**2 / np.cumsum(S)[-1]

fig = plt.figure(figsize=(8,5))
sing_vals = np.arange(num_vars) + 1
plt.plot(sing_vals, eigvals, 'ro-', linewidth=2)
plt.title('Scree Plot')
plt.xlabel('Principal Component')
plt.ylabel('Eigenvalue')
#I don't like the default legend so I typically make mine like below, e.g.
#with smaller fonts and a bit transparent so I do not cover up data, and make
#it moveable by the viewer in case upper-right is a bad place for it 
leg = plt.legend(['Eigenvalues from SVD'], loc='best', borderpad=0.3, 
                 shadow=False, prop=matplotlib.font_manager.FontProperties(size='small'),
                 markerscale=0.4)
leg.get_frame().set_alpha(0.4)
leg.draggable(state=True)
plt.show()