Multivariable linear regression

mvar_lin_reg.py

# -*- coding: utf-8 -*-
"""
MIT License
Created on Wed Feb 11 13:05:36 2015

@author: xevaquor
"""

import numpy as np

TrainingData = np.array([
[1.,1.	,4.5],
[1.,1.	,3. ],
[1.,1.	,4. ],
[1.,2.	,3.5],
[1.,2.	,5. ],
[1.,2.	,3. ],
[1.,3.	,3. ],
[1.,3.	,4.5],
[1.,3.	,4. ],
[1.,4.	,3. ],
[1.,4.	,3.5],
[1.,4.	,5. ],
[1.,5.	,4. ],
[1.,5.	,3. ],
[1.,5.	,3.5],
[1.,6.	,4.5],
[1.,6.	,4.5],
[1.,6.	,4.5],
[1.,7.	,4. ],
[1.,7.	,3. ],
[1.,7.	,5. ],
[1.,8.	,3. ],
[1.,8.	,4. ],
[1.,8.	,3.5],
[1.,9.	,3. ],
[1.,9.	,4. ],
[1.,10.	,4.5],
[1.,10.	,5. ],
[1.,10.	,3. ]])

m,n = TrainingData.shape

alpha = 0.01
epsylon = 0.001
    
Y = [8,5,7,6,8,6,4,6,7,5,6,7,5,3,4,7,6,8,6,4,6,1,4,3,2,5,5,6,0]

def h(Theta, X):
    return Theta.transpose().dot(X)
    
def Jpartial(j,Theta):
    sum = 0
    for i in range(m):
        sum += (h(Theta, TrainingData[i,:]) - Y[i]) * TrainingData[i][j]
    return 2 * sum / m


def gradient_descent(startTheta):
    theta = startTheta
    converge = False
    i = 0
    while not converge:
        differentials = np.zeros(n)
        for j in range(n):
            differentials[j] = Jpartial(j, theta)
        for j in range(n):
           theta[j] -= alpha * differentials[j]    

        if i % 500 == 0:
            print (np.amax(differentials))
        converge = np.amax(differentials) < epsylon
    return theta
    
   
startT = np.array([1.,1.,1.])
t = gradient_descent(startT)
print(t)
print(h(t, [1.,0.,5.]))
print(h(t, [1.,10.,3.]))
print(h(t, [1.,2.,3.5]))
print(h(t, [1.,5.,3.5]))