CH04_SEC01_LinearRegression.ipynb

Kernel: Python 3

import numpy as np
import matplotlib.pyplot as plt
import scipy.optimize
from matplotlib import rcParams
rcParams['figure.figsize'] = [12, 8]
rcParams.update({'font.size': 18})


# Function definitions
def fit1(x0,t):
    x,y=t
    return np.max(np.abs(x0[0]*x + x0[1]-y))
def fit2(x0,t):
    x,y=t
    return np.sum(np.abs(x0[0]*x + x0[1]-y))
def fit3(x0,t):
    x,y=t
    return np.sum(np.power(np.abs(x0[0]*x + x0[1]-y),2))

# The data
x = np.arange(1,11)
y = np.array([0.2,0.5,0.3,3.5,1.0,1.5,1.8,2.0,2.3,2.2])
t = (x,y)

x0 = np.array([1,1])
p1 = scipy.optimize.fmin(fit1,x0,args=(t,));
p2 = scipy.optimize.fmin(fit2,x0,args=(t,));
p3 = scipy.optimize.fmin(fit3,x0,args=(t,));

xf = np.arange(0,11,0.1)
y1 = np.polyval(p1,xf)
y2 = np.polyval(p2,xf)
y3 = np.polyval(p3,xf)

plt.figure()
plt.plot(xf,y1,color='k',label='E_\infty')
plt.plot(xf,y2,'--',color='k',linewidth=2,label='E_1')
plt.plot(xf,y3,color='k',linewidth=2,label='E_2')
plt.plot(x,y,'o',color='r',linewidth=2)

plt.ylim(0,4)
plt.legend()
plt.show()

Optimization terminated successfully.
         Current function value: 1.464330
         Iterations: 52
         Function evaluations: 98
Optimization terminated successfully.
         Current function value: 3.640022
         Iterations: 64
         Function evaluations: 126
Optimization terminated successfully.
         Current function value: 6.234182
         Iterations: 49
         Function evaluations: 92

x = np.arange(1,11)
y = np.array([0.2,0.5,0.3,0.7,1.0,1.5,1.8,2.0,2.3,2.2])
t = (x,y)

x0 = np.array([1,1])
p1 = scipy.optimize.fmin(fit1,x0,args=(t,));
p2 = scipy.optimize.fmin(fit2,x0,args=(t,));
p3 = scipy.optimize.fmin(fit3,x0,args=(t,));

xf = np.arange(0,11,0.1)
y1 = np.polyval(p1,xf)
y2 = np.polyval(p2,xf)
y3 = np.polyval(p3,xf)

plt.figure()
plt.plot(xf,y1,color='k',label='E_\infty')
plt.plot(xf,y2,'--',color='k',linewidth=2,label='E_1')
plt.plot(xf,y3,color='k',linewidth=2,label='E_2')
plt.plot(x,y,'o',color='r',linewidth=2)

plt.ylim(0,4)
plt.legend()
plt.show()

Optimization terminated successfully.
         Current function value: 0.230040
         Iterations: 59
         Function evaluations: 115
Optimization terminated successfully.
         Current function value: 1.385764
         Iterations: 56
         Function evaluations: 105
Optimization terminated successfully.
         Current function value: 0.288000
         Iterations: 54
         Function evaluations: 102