ex1-multiple_var

import os
import numpy as np
import pandas as pd
from matplotlib import pyplot
import matplotlib.pyplot as plt


path = os.path.dirname(os.path.realpath(__file__)) + '\..\data\ex1data2.txt'
data = pd.read_csv(path, header=None, names=['Size', 'Bedrooms', 'Price'])
print('Data before normalizing:')
print(data.head(n=5))
#data.plot.bar()

# Feature normalization
data = (data - data.mean())/data.std()
print('Data after normalizing:')
print(data.head(n=5))
#data.plot.bar()

# Add a column of 1
data.insert(0, 'Ones', 1)
#print(data.head(n=5))

# Number of columns
cols = data.shape[1]

# some parameters
theta = np.mat(np.zeros(3))
iteration = 1500
alpha = 0.01

# inputs and outputs
X = data.iloc[:,:cols-1]
y = data.iloc[:,-1:]
print('Input:')
print(X.head(n=5))
print('Output:')
print(y.head(n=5))

X = np.mat(X)
y = np.mat(y)
m = len(X)

def computeCost(X, y, theta):
    inner = np.power((X * theta.T - y), 2)
    return np.sum(inner)/(2 * len(X))

# print cost before training
print('Initial cost')
print(computeCost(X, y, theta))

def gradientDescent(X, y, theta, alpha, iters):
    cost = np.zeros(iters)
    param = int(theta.ravel().shape[1])
    his_theta = np.zeros((iters, 3)) # to store all thetas

    for i in range(iters):
        error = X * theta.T - y

        for j in range(param):
            temp = np.multiply(error, X[:,j])
            theta[0,j] = theta[0,j] - (alpha / m) * np.sum(temp)
            his_theta[i,j] = theta[0,j]

        cost[i] = computeCost(X, y, theta)

    return theta, cost, his_theta

# perform gradient descent to "fit" the model parameters
g, cost, history = gradientDescent(X, y, theta, alpha, iteration)

print('The cost after training:')
print(computeCost(X, y, g))

################################################################
fig, ax = plt.subplots(figsize=(12, 8))

ax.plot(np.arange(iteration), cost, 'r')
ax.set_xlabel('Iterations')
ax.set_ylabel('Cost')
ax.set_title('Cost vs. Iterations')
ax.grid()

#plt.xticks(np.arange(1000))
#plt.yticks(np.arange(4, 7, 0.5))

pyplot.show()