In [1]:

    

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from mpl_toolkits.mplot3d import axes3d, Axes3D #<-- Note the capitalization! 
%matplotlib inline
sns.set_style("white")


    

In [30]:

    

#functions 

def feature_normalize(df_n) :
    return ( ( df_n - df_n.mean() ) / df_n.std() )

def cost_function(X,y,theta):
    h_theta = np.dot(theta.T,X.T).T
    J = sum( ( 1 / ( 2 * m ) ) * ((h_theta - y) ** 2))
    return J

def gradient_function():
    for n in range(iterations):
        global theta
        last_j[n] = cost_function(X,y,theta)
        h_theta = np.dot(theta.T,X.T).T
        theta = theta - (alpha / m) * np.dot((h_theta - y).T,X).T
    return theta


    

In [31]:

    

df = pd.read_csv('ex1data2.txt', sep=',', header=None)
df.describe()


    

    
Out[31]:






  

    

      

      
0
      
1
      
2
    
  
  

    

      
count
      
47.000000
      
47.000000
      
47.000000
    
    

      
mean
      
2000.680851
      
3.170213
      
340412.659574
    
    

      
std
      
794.702354
      
0.760982
      
125039.899586
    
    

      
min
      
852.000000
      
1.000000
      
169900.000000
    
    

      
25%
      
1432.000000
      
3.000000
      
249900.000000
    
    

      
50%
      
1888.000000
      
3.000000
      
299900.000000
    
    

      
75%
      
2269.000000
      
4.000000
      
384450.000000
    
    

      
max
      
4478.000000
      
5.000000
      
699900.000000
    
  

In [32]:

    

df.head()


    

    
Out[32]:






  

    

      

      
0
      
1
      
2
    
  
  

    

      
0
      
2104
      
3
      
399900
    
    

      
1
      
1600
      
3
      
329900
    
    

      
2
      
2400
      
3
      
369000
    
    

      
3
      
1416
      
2
      
232000
    
    

      
4
      
3000
      
4
      
539900
    
  

In [33]:

    

df_norm = feature_normalize(df)


    

In [34]:

    

m = df_norm.shape[0]


    

In [35]:

    

df_norm.insert(0,'3',np.ones(m))
df.insert(0,'3',np.ones(m))


    

In [36]:

    

df_norm.columns = np.arange(0,4)
df.columns = np.arange(0,4)


    

In [37]:

    

# initialization
theta = pd.Series(np.zeros(df_norm.columns.shape[0] - 1))
y = df_norm[3]
X = df_norm.T[0:3].T
alpha = 0.1
iterations = 50
last_j = np.zeros(50)


    

In [38]:

    

gradient_function()


    

    
Out[38]:





0   -1.185813e-16
1    8.327543e-01
2   -1.377203e-03
dtype: float64

In [18]:

    

# plotting Cost function versus Number of iterations
itr_list = np.arange(0,50)
fig = plt.figure(figsize=(12,8))
plt.plot(itr_list,last_j,'-b')


    

    
Out[18]:





[<matplotlib.lines.Line2D at 0xb089f82cf8>]






    

In [829]:

    

xx = ([1650, 3] - df.mean()[1:3]) / df.std()[1:3]
xx


    

    
Out[829]:





1   -0.441273
2   -0.223675
dtype: float64

In [830]:

    

xx = pd.DataFrame(xx).T
xx


    

    
Out[830]:






  

    

      

      
1
      
2
    
  
  

    

      
0
      
-0.441273
      
-0.223675
    
  

In [831]:

    

xx.insert(0,3,1)
xx


    

    
Out[831]:






  

    

      

      
3
      
1
      
2
    
  
  

    

      
0
      
1
      
-0.441273
      
-0.223675
    
  

In [832]:

    

xx.columns = np.arange(0,3)


    

In [835]:

    

np.dot(theta.T,xx.T)[0]


    

    
Out[835]:





-0.36716411456663245

In [848]:

    

y = df[3]
X = df.T[0:3].T


    

In [837]:

    

theta = np.dot(np.dot(np.dot(X.T,X),X.T),y)


    

In [849]:

    

theta


    

    
Out[849]:





array([  3.37743390e+15,   7.80063079e+18,   1.12666974e+16])

In [850]:

    

xx = [1650, 3]


    

In [851]:

    

xx = pd.DataFrame(xx).T


    

In [852]:

    

xx.insert(0,3,1)


    

In [853]:

    

xx.columns = np.arange(0,3)


    

In [854]:

    

np.dot(theta.T,xx.T)[0]


    

    
Out[854]:





1.2871077988282204e+22

In [ ]:

    




    

In [ ]: