CH04_SEC05_1_CrossValidate.ipynb

Kernel: Python 3

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import Rectangle
from matplotlib import rcParams
rcParams.update({'font.size': 18})
plt.rcParams['figure.figsize'] = [8,8]

n = 200
L = 8
x = np.linspace(0,L,n)
x1 = x[:100]    # Train
x2 = x[100:200] # Test
n1 = len(x1)
n2 = len(x2)
ftrain = np.power(x1,2) # Train parabola x = [0,4]
ftest = np.power(x2,2)  # Test parabola x = [4,8]

plt.plot(x1,ftrain,color='r',linewidth=2)
plt.plot(x2,ftest,color='b',linewidth=2)
plt.show()
M = 30 # number of model terms
Eni = np.zeros((100,M))
Ene = np.zeros((100,M))
for jj in range(M):
    phi_i = np.zeros((n1,jj+1))
    phi_e = np.zeros((n2,jj+1))
    for j in range(jj):
        phi_i[:,j] = np.power(x1,j) # interpolation key
        phi_e[:,j] = np.power(x2,j) # extrapolation key
    
    f = np.power(x,2)
    for j in range(100):
        fni = np.power(x1,2) + 0.1*np.random.randn(n1) # interpolation
        fne = np.power(x2,2) + 0.1*np.random.randn(n2) # extrapolation
        
        ani = np.linalg.pinv(phi_i) @ fni
        fnai = phi_i @ ani
        Eni[j,jj] = np.linalg.norm(ftrain-fnai,ord=2)/np.linalg.norm(ftrain,ord=2)
        
        fnae = phi_e @ ani # use loadings from x in [0,4]
        Ene[j,jj] = np.linalg.norm(ftest-fnae,ord=2)/np.linalg.norm(ftest,ord=2)
        
        

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

axs[0].boxplot(Eni)
axs[0].set_ylim(0,0.7)
axs[1].boxplot(Eni)
axs[1].set_ylim(0,0.02)
axs[2].boxplot(Ene)
axs[3].boxplot(np.log(Ene+1))
axs[3].set_ylim(0,30)

for ax in axs:
    ax.set_xticks((1,5,10,15,20,25,30))
    ax.set_xticklabels((1,5,10,15,20,25,30))

plt.show()