<filename>Week 2 - Linear Regression with Multiple Variables/Python_Scratch/Exercise1.py
# Necessary libraries
import os
import numpy as np
import pandas as pd
from matplotlib import cm
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

# Set Up Environment, import data
os.chdir('C:/Users/ntell/Documents/GitHub/Stanford-ML-Coursera')
data = pd.read_csv('Week 2 - Linear Regression with Multiple Variables/MATLAB/ex1data1.txt', header = None)

# Separate out X and y, store as NumPy arrays
X = data.iloc[:, 0].to_numpy()
y = data.iloc[:, 1].to_numpy()

# Visualize the data
plotData(X, y)


# Implementation of Gradient Descent
m = len(X) # number of examples
X = np.concatenate([np.expand_dims(np.ones(m), axis = 1),
                    np.expand_dims(X, axis = 1)], axis = 1) # add column for intercepts
theta = np.zeros([2, 1]) # Initializing Fitting Parameters
iterations = 1500
alpha = 0.01

computeCost(X, y, theta)
computeCost(X, y, np.array([-1, 2]).reshape(2, 1))


# Run gradient descent
theta, J_history = gradientDescent(X, y, theta, alpha, iterations)

# Plot the linear fit
plt.scatter(X[:, 1], y, c = 'red', marker = 'x', label = 'Training Data')
plt.plot([np.min(X[:, 1]), np.max(X[:, 1])],
         [np.min(X @ theta), np.max(X @ theta)],
         c = 'blue', label = 'Linear Regression')
plt.xlabel('Population of City in 10,000s')
plt.ylabel('Profit in $10,000s')

# Predictions
predict1 = ((np.array([1, 3.5]) @ theta) * 10000)[0]
print('For a population of 35k, we predict a profit of: %8.2f' % predict1)

predict2 = ((np.array([1, 7]) @ theta) * 10000)[0]
print('For a population of 35k, we predict a profit of: %8.2f' % predict2)


# Visualize J(theta), with 2 features instead of 1
theta0 = np.linspace(-10, 10, 100)
theta1 = np.linspace(-1, 4, 100)

# Empty matrix to hold the costs for every permutation of thetas
J_vals = np.zeros([len(theta0), len(theta1)])

# Fill out J
for i in range(len(theta0)):
    for j in range(len(theta1)):
        t = np.expand_dims(np.array([theta0[i], theta1[j]]), axis = 1)
        J_vals[i, j] = computeCost(X, y, t)
        
theta0, theta1 = np.meshgrid(theta0, theta1)

# Make into 3D Plot
fig = plt.figure()
ax = fig.gca(projection = '3d')
surf = ax.plot_surface(theta1, theta0, J_vals, cmap = cm.coolwarm,
                       linewidth = 0, antialiased = False)

# Contour plot
fig, ax = plt.subplots()
CS = ax.contour(theta0, theta1, J_vals)
plt.scatter(theta[0], theta[1], marker = 'x', c = 'red')
plt.xlabel(r'$\theta_0$')
plt.ylabel(r'$\theta_1$')