ex1.R

## Machine Learning Online Class - Exercise 1: Linear Regression

#  R Instructions
#  ------------
# 
#  This file contains code that helps you get started on the
#  linear exercise. You will need to complete the following functions 
#  in this exericse:
#
#     warmUpExercise.R
#     plotData.m
#     gradientDescent.m
#     computeCost.m
#     gradientDescentMulti.m
#     computeCostMulti.m
#     featureNormalize.m
#     normalEqn.m
#
#  For this exercise, you will not need to change any code in this file,
#  or any other files other than those mentioned above.
#
# x refers to the population size in 10,000s
# y refers to the profit in $10,000s
#

## Initialization
rm(list=ls()) # clear all variable and functions in memory

## ==================== Part 1: Basic Function ====================
# Complete warmUpExercise.m 
cat('Running warmUpExercise ... \n5x5 Identity Matrix: \n')
source('warmUpExercise.R')
warmUpExercise()

#fprintf('Program paused. Press enter to continue.\n');
#pause;


## ======================= Part 2: Plotting =======================
#fprintf('Plotting Data ...\n')
#data = load('ex1data1.txt');
#X = data(:, 1); y = data(:, 2);
#m = length(y); # number of training examples

# Plot Data
# Note: You have to complete the code in plotData.m
#plotData(X, y);

#fprintf('Program paused. Press enter to continue.\n');
#pause;

## =================== Part 3: Gradient descent ===================
#fprintf('Running Gradient Descent ...\n')

#X = [ones(m, 1), data(:,1)]; # Add a column of ones to x
#theta = zeros(2, 1); # initialize fitting parameters

# Some gradient descent settings
#iterations = 1500;
#alpha = 0.01;

# compute and display initial cost
#computeCost(X, y, theta)

# run gradient descent
#theta = gradientDescent(X, y, theta, alpha, iterations);

# print theta to screen
#fprintf('Theta found by gradient descent: ');
#fprintf('#f #f \n', theta(1), theta(2));

# Plot the linear fit
#hold on; # keep previous plot visible
#plot(X(:,2), X*theta, '-')
#legend('Training data', 'Linear regression')
#hold off # don't overlay any more plots on this figure

# Predict values for population sizes of 35,000 and 70,000
#predict1 = [1, 3.5] *theta;
#fprintf('For population = 35,000, we predict a profit of #f\n',...
    #predict1*10000);
#predict2 = [1, 7] * theta;
#fprintf('For population = 70,000, we predict a profit of #f\n',...
    #predict2*10000);

#fprintf('Program paused. Press enter to continue.\n');
#pause;

## ============= Part 4: Visualizing J(theta_0, theta_1) =============
#fprintf('Visualizing J(theta_0, theta_1) ...\n')

# Grid over which we will calculate J
#theta0_vals = linspace(-10, 10, 100);
#theta1_vals = linspace(-1, 4, 100);

# initialize J_vals to a matrix of 0's
#J_vals = zeros(length(theta0_vals), length(theta1_vals));

# Fill out J_vals
#for i = 1:length(theta0_vals)
    #for j = 1:length(theta1_vals)
		#t = [theta0_vals(i); theta1_vals(j)];    
		#J_vals(i,j) = computeCost(X, y, t);
    #end
#end


# Because of the way meshgrids work in the surf command, we need to 
# transpose J_vals before calling surf, or else the axes will be flipped
#J_vals = J_vals';
## Surface plot
#figure;
#surf(theta0_vals, theta1_vals, J_vals)
#xlabel('\theta_0'); ylabel('\theta_1');

## Contour plot
#figure;
## Plot J_vals as 15 contours spaced logarithmically between 0.01 and 100
#contour(theta0_vals, theta1_vals, J_vals, logspace(-2, 3, 20))
#xlabel('\theta_0'); ylabel('\theta_1');
#hold on;
#plot(theta(1), theta(2), 'rx', 'MarkerSize', 10, 'LineWidth', 2);