Mercurial > hg > machine-learning-hw1

changeset 0:7ddec0077b6f

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Initial commit
author Jordi Gutiérrez Hermoso <jordigh@octave.org>
date Tue, 18 Oct 2011 23:51:27 -0500
parents
children f6e454c0fd8e
files computeCost.m computeCostMulti.m ex1.m ex1_multi.m ex1data1.txt ex1data2.txt featureNormalize.m gradientDescent.m gradientDescentMulti.m normalEqn.m plotData.m submit.m warmUpExercise.m
diffstat 13 files changed, 984 insertions(+), 0 deletions(-) [+]
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new file mode 100644
--- /dev/null
+++ b/computeCost.m
@@ -0,0 +1,22 @@
+function J = computeCost(X, y, theta)
+%COMPUTECOST Compute cost for linear regression
+%   J = COMPUTECOST(X, y, theta) computes the cost of using theta as the
+%   parameter for linear regression to fit the data points in X and y
+
+% Initialize some useful values
+m = length(y); % number of training examples
+
+% You need to return the following variables correctly 
+J = 0;
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: Compute the cost of a particular choice of theta
+%               You should set J to the cost.
+
+
+
+
+
+% =========================================================================
+
+end
new file mode 100644
--- /dev/null
+++ b/computeCostMulti.m
@@ -0,0 +1,22 @@
+function J = computeCostMulti(X, y, theta)
+%COMPUTECOSTMULTI Compute cost for linear regression with multiple variables
+%   J = COMPUTECOSTMULTI(X, y, theta) computes the cost of using theta as the
+%   parameter for linear regression to fit the data points in X and y
+
+% Initialize some useful values
+m = length(y); % number of training examples
+
+% You need to return the following variables correctly 
+J = 0;
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: Compute the cost of a particular choice of theta
+%               You should set J to the cost.
+
+
+
+
+
+% =========================================================================
+
+end
new file mode 100644
--- /dev/null
+++ b/ex1.m
@@ -0,0 +1,122 @@
+%% Machine Learning Online Class - Exercise 1: Linear Regression
+
+%  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.m
+%     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
+clear all; close all; clc
+
+%% ==================== Part 1: Basic Function ====================
+% Complete warmUpExercise.m 
+fprintf('Running warmUpExercise ... \n');
+fprintf('5x5 Identity Matrix: \n');
+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);
new file mode 100644
--- /dev/null
+++ b/ex1_multi.m
@@ -0,0 +1,159 @@
+%% Machine Learning Online Class
+%  Exercise 1: Linear regression with multiple variables
+%
+%  Instructions
+%  ------------
+% 
+%  This file contains code that helps you get started on the
+%  linear regression exercise. 
+%
+%  You will need to complete the following functions in this 
+%  exericse:
+%
+%     warmUpExercise.m
+%     plotData.m
+%     gradientDescent.m
+%     computeCost.m
+%     gradientDescentMulti.m
+%     computeCostMulti.m
+%     featureNormalize.m
+%     normalEqn.m
+%
+%  For this part of the exercise, you will need to change some
+%  parts of the code below for various experiments (e.g., changing
+%  learning rates).
+%
+
+%% Initialization
+
+%% ================ Part 1: Feature Normalization ================
+
+%% Clear and Close Figures
+clear all; close all; clc
+
+fprintf('Loading data ...\n');
+
+%% Load Data
+data = load('ex1data2.txt');
+X = data(:, 1:2);
+y = data(:, 3);
+m = length(y);
+
+% Print out some data points
+fprintf('First 10 examples from the dataset: \n');
+fprintf(' x = [%.0f %.0f], y = %.0f \n', [X(1:10,:) y(1:10,:)]');
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+% Scale features and set them to zero mean
+fprintf('Normalizing Features ...\n');
+
+[X mu sigma] = featureNormalize(X);
+
+% Add intercept term to X
+X = [ones(m, 1) X];
+
+
+%% ================ Part 2: Gradient Descent ================
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: We have provided you with the following starter
+%               code that runs gradient descent with a particular
+%               learning rate (alpha). 
+%
+%               Your task is to first make sure that your functions - 
+%               computeCost and gradientDescent already work with 
+%               this starter code and support multiple variables.
+%
+%               After that, try running gradient descent with 
+%               different values of alpha and see which one gives
+%               you the best result.
+%
+%               Finally, you should complete the code at the end
+%               to predict the price of a 1650 sq-ft, 3 br house.
+%
+% Hint: By using the 'hold on' command, you can plot multiple
+%       graphs on the same figure.
+%
+% Hint: At prediction, make sure you do the same feature normalization.
+%
+
+fprintf('Running gradient descent ...\n');
+
+% Choose some alpha value
+alpha = 0.01;
+num_iters = 100;
+
+% Init Theta and Run Gradient Descent 
+theta = zeros(3, 1);
+[theta, J_history] = gradientDescentMulti(X, y, theta, alpha, num_iters);
+
+% Plot the convergence graph
+figure;
+plot(1:numel(J_history), J_history, '-b', 'LineWidth', 2);
+xlabel('Number of iterations');
+ylabel('Cost J');
+
+% Display gradient descent's result
+fprintf('Theta computed from gradient descent: \n');
+fprintf(' %f \n', theta);
+fprintf('\n');
+
+% Estimate the price of a 1650 sq-ft, 3 br house
+% ====================== YOUR CODE HERE ======================
+% Recall that the first column of X is all-ones. Thus, it does
+% not need to be normalized.
+price = 0; % You should change this
+
+
+% ============================================================
+
+fprintf(['Predicted price of a 1650 sq-ft, 3 br house ' ...
+         '(using gradient descent):\n $%f\n'], price);
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+%% ================ Part 3: Normal Equations ================
+
+fprintf('Solving with normal equations...\n');
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: The following code computes the closed form 
+%               solution for linear regression using the normal
+%               equations. You should complete the code in 
+%               normalEqn.m
+%
+%               After doing so, you should complete this code 
+%               to predict the price of a 1650 sq-ft, 3 br house.
+%
+
+%% Load Data
+data = csvread('ex1data2.txt');
+X = data(:, 1:2);
+y = data(:, 3);
+m = length(y);
+
+% Add intercept term to X
+X = [ones(m, 1) X];
+
+% Calculate the parameters from the normal equation
+theta = normalEqn(X, y);
+
+% Display normal equation's result
+fprintf('Theta computed from the normal equations: \n');
+fprintf(' %f \n', theta);
+fprintf('\n');
+
+
+% Estimate the price of a 1650 sq-ft, 3 br house
+% ====================== YOUR CODE HERE ======================
+price = 0; % You should change this
+
+
+% ============================================================
+
+fprintf(['Predicted price of a 1650 sq-ft, 3 br house ' ...
+         '(using normal equations):\n $%f\n'], price);
+
new file mode 100644
--- /dev/null
+++ b/ex1data1.txt
@@ -0,0 +1,97 @@
+6.1101,17.592
+5.5277,9.1302
+8.5186,13.662
+7.0032,11.854
+5.8598,6.8233
+8.3829,11.886
+7.4764,4.3483
+8.5781,12
+6.4862,6.5987
+5.0546,3.8166
+5.7107,3.2522
+14.164,15.505
+5.734,3.1551
+8.4084,7.2258
+5.6407,0.71618
+5.3794,3.5129
+6.3654,5.3048
+5.1301,0.56077
+6.4296,3.6518
+7.0708,5.3893
+6.1891,3.1386
+20.27,21.767
+5.4901,4.263
+6.3261,5.1875
+5.5649,3.0825
+18.945,22.638
+12.828,13.501
+10.957,7.0467
+13.176,14.692
+22.203,24.147
+5.2524,-1.22
+6.5894,5.9966
+9.2482,12.134
+5.8918,1.8495
+8.2111,6.5426
+7.9334,4.5623
+8.0959,4.1164
+5.6063,3.3928
+12.836,10.117
+6.3534,5.4974
+5.4069,0.55657
+6.8825,3.9115
+11.708,5.3854
+5.7737,2.4406
+7.8247,6.7318
+7.0931,1.0463
+5.0702,5.1337
+5.8014,1.844
+11.7,8.0043
+5.5416,1.0179
+7.5402,6.7504
+5.3077,1.8396
+7.4239,4.2885
+7.6031,4.9981
+6.3328,1.4233
+6.3589,-1.4211
+6.2742,2.4756
+5.6397,4.6042
+9.3102,3.9624
+9.4536,5.4141
+8.8254,5.1694
+5.1793,-0.74279
+21.279,17.929
+14.908,12.054
+18.959,17.054
+7.2182,4.8852
+8.2951,5.7442
+10.236,7.7754
+5.4994,1.0173
+20.341,20.992
+10.136,6.6799
+7.3345,4.0259
+6.0062,1.2784
+7.2259,3.3411
+5.0269,-2.6807
+6.5479,0.29678
+7.5386,3.8845
+5.0365,5.7014
+10.274,6.7526
+5.1077,2.0576
+5.7292,0.47953
+5.1884,0.20421
+6.3557,0.67861
+9.7687,7.5435
+6.5159,5.3436
+8.5172,4.2415
+9.1802,6.7981
+6.002,0.92695
+5.5204,0.152
+5.0594,2.8214
+5.7077,1.8451
+7.6366,4.2959
+5.8707,7.2029
+5.3054,1.9869
+8.2934,0.14454
+13.394,9.0551
+5.4369,0.61705
new file mode 100644
--- /dev/null
+++ b/ex1data2.txt
@@ -0,0 +1,47 @@
+2104,3,399900
+1600,3,329900
+2400,3,369000
+1416,2,232000
+3000,4,539900
+1985,4,299900
+1534,3,314900
+1427,3,198999
+1380,3,212000
+1494,3,242500
+1940,4,239999
+2000,3,347000
+1890,3,329999
+4478,5,699900
+1268,3,259900
+2300,4,449900
+1320,2,299900
+1236,3,199900
+2609,4,499998
+3031,4,599000
+1767,3,252900
+1888,2,255000
+1604,3,242900
+1962,4,259900
+3890,3,573900
+1100,3,249900
+1458,3,464500
+2526,3,469000
+2200,3,475000
+2637,3,299900
+1839,2,349900
+1000,1,169900
+2040,4,314900
+3137,3,579900
+1811,4,285900
+1437,3,249900
+1239,3,229900
+2132,4,345000
+4215,4,549000
+2162,4,287000
+1664,2,368500
+2238,3,329900
+2567,4,314000
+1200,3,299000
+852,2,179900
+1852,4,299900
+1203,3,239500
new file mode 100644
--- /dev/null
+++ b/featureNormalize.m
@@ -0,0 +1,39 @@
+function [X_norm, mu, sigma] = featureNormalize(X)
+%FEATURENORMALIZE Normalizes the features in X 
+%   FEATURENORMALIZE(X) returns a normalized version of X where
+%   the mean value of each feature is 0 and the standard deviation
+%   is 1. This is often a good preprocessing step to do when
+%   working with learning algorithms.
+
+% You need to set these values correctly
+X_norm = X;
+mu = zeros(1, size(X, 2));
+sigma = zeros(1, size(X, 2));
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: First, for each feature dimension, compute the mean
+%               of the feature and subtract it from the dataset,
+%               storing the mean value in mu. Next, compute the 
+%               standard deviation of each feature and divide
+%               each feature by it's standard deviation, storing
+%               the standard deviation in sigma. 
+%
+%               Note that X is a matrix where each column is a 
+%               feature and each row is an example. You need 
+%               to perform the normalization separately for 
+%               each feature. 
+%
+% Hint: You might find the 'mean' and 'std' functions useful.
+%       
+
+
+
+
+
+
+
+
+
+% ============================================================
+
+end
new file mode 100644
--- /dev/null
+++ b/gradientDescent.m
@@ -0,0 +1,33 @@
+function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
+%GRADIENTDESCENT Performs gradient descent to learn theta
+%   theta = GRADIENTDESENT(X, y, theta, alpha, num_iters) updates theta by 
+%   taking num_iters gradient steps with learning rate alpha
+
+% Initialize some useful values
+m = length(y); % number of training examples
+J_history = zeros(num_iters, 1);
+
+for iter = 1:num_iters
+
+    % ====================== YOUR CODE HERE ======================
+    % Instructions: Perform a single gradient step on the parameter vector
+    %               theta. 
+    %
+    % Hint: While debugging, it can be useful to print out the values
+    %       of the cost function (computeCost) and gradient here.
+    %
+
+
+
+
+
+
+
+    % ============================================================
+
+    % Save the cost J in every iteration    
+    J_history(iter) = computeCost(X, y, theta);
+
+end
+
+end
new file mode 100644
--- /dev/null
+++ b/gradientDescentMulti.m
@@ -0,0 +1,37 @@
+function [theta, J_history] = gradientDescentMulti(X, y, theta, alpha, num_iters)
+%GRADIENTDESCENTMULTI Performs gradient descent to learn theta
+%   theta = GRADIENTDESCENTMULTI(x, y, theta, alpha, num_iters) updates theta by
+%   taking num_iters gradient steps with learning rate alpha
+
+% Initialize some useful values
+m = length(y); % number of training examples
+J_history = zeros(num_iters, 1);
+
+for iter = 1:num_iters
+
+    % ====================== YOUR CODE HERE ======================
+    % Instructions: Perform a single gradient step on the parameter vector
+    %               theta. 
+    %
+    % Hint: While debugging, it can be useful to print out the values
+    %       of the cost function (computeCostMulti) and gradient here.
+    %
+
+
+
+
+
+
+
+
+
+
+
+    % ============================================================
+
+    % Save the cost J in every iteration    
+    J_history(iter) = computeCostMulti(X, y, theta);
+
+end
+
+end
new file mode 100644
--- /dev/null
+++ b/normalEqn.m
@@ -0,0 +1,23 @@
+function [theta] = normalEqn(X, y)
+%NORMALEQN Computes the closed-form solution to linear regression 
+%   NORMALEQN(X,y) computes the closed-form solution to linear 
+%   regression using the normal equations.
+
+theta = zeros(size(X, 2), 1);
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: Complete the code to compute the closed form solution
+%               to linear regression and put the result in theta.
+%
+
+% ---------------------- Sample Solution ----------------------
+
+
+
+
+% -------------------------------------------------------------
+
+
+% ============================================================
+
+end
new file mode 100644
--- /dev/null
+++ b/plotData.m
@@ -0,0 +1,26 @@
+function plotData(x, y)
+%PLOTDATA Plots the data points x and y into a new figure 
+%   PLOTDATA(x,y) plots the data points and gives the figure axes labels of
+%   population and profit.
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: Plot the training data into a figure using the 
+%               "figure" and "plot" commands. Set the axes labels using
+%               the "xlabel" and "ylabel" commands. Assume the 
+%               population and revenue data have been passed in
+%               as the x and y arguments of this function.
+%
+% Hint: You can use the 'rx' option with plot to have the markers
+%       appear as red crosses. Furthermore, you can make the
+%       markers larger by using plot(..., 'rx', 'MarkerSize', 10);
+
+figure; % open a new figure window
+
+
+
+
+
+
+% ============================================================
+
+end
new file mode 100644
--- /dev/null
+++ b/submit.m
@@ -0,0 +1,336 @@
+function submit(part)
+%SUBMIT Submit your code and output to the ml-class servers
+%   SUBMIT() will connect to the ml-class server and submit your solution
+
+  fprintf('==\n== [ml-class] Submitting Solutions | Programming Exercise %s\n==\n', ...
+          homework_id());
+  if ~exist('part', 'var') || isempty(part)
+    partId = promptPart();
+  end
+  
+  % Check valid partId
+  partNames = validParts();
+  if ~isValidPartId(partId)
+    fprintf('!! Invalid homework part selected.\n');
+    fprintf('!! Expected an integer from 1 to %d.\n', numel(partNames) + 1);
+    fprintf('!! Submission Cancelled\n');
+    return
+  end
+
+  [login password] = loginPrompt();
+  if isempty(login)
+    fprintf('!! Submission Cancelled\n');
+    return
+  end
+
+  fprintf('\n== Connecting to ml-class ... '); 
+  if exist('OCTAVE_VERSION') 
+    fflush(stdout);
+  end
+  
+  % Setup submit list
+  if partId == numel(partNames) + 1
+    submitParts = 1:numel(partNames);
+  else
+    submitParts = [partId];
+  end
+
+  for s = 1:numel(submitParts)
+    % Submit this part
+    partId = submitParts(s);
+    
+    % Get Challenge
+    [login, ch, signature] = getChallenge(login);
+    if isempty(login) || isempty(ch) || isempty(signature)
+      % Some error occured, error string in first return element.
+      fprintf('\n!! Error: %s\n\n', login);
+      return
+    end
+  
+    % Attempt Submission with Challenge
+    ch_resp = challengeResponse(login, password, ch);
+    [result, str] = submitSolution(login, ch_resp, partId, output(partId), ...
+                                 source(partId), signature);
+                                 
+    fprintf('\n== [ml-class] Submitted Homework %s - Part %d - %s\n', ...
+            homework_id(), partId, partNames{partId});
+    fprintf('== %s\n', strtrim(str));
+    if exist('OCTAVE_VERSION') 
+      fflush(stdout);
+    end
+  end
+  
+end
+
+% ================== CONFIGURABLES FOR EACH HOMEWORK ==================
+
+function id = homework_id() 
+  id = '1';
+end
+
+function [partNames] = validParts()
+  partNames = { 'Warm up exercise ', ...
+                'Computing Cost (for one variable)', ...
+                'Gradient Descent (for one variable)', ...
+                'Feature Normalization', ...
+                'Computing Cost (for multiple variables)', ...
+                'Gradient Descent (for multiple variables)', ...
+                'Normal Equations'};
+end
+
+function srcs = sources()
+  % Separated by part
+  srcs = { { 'warmUpExercise.m' }, ...
+           { 'computeCost.m' }, ...
+           { 'gradientDescent.m' }, ...
+           { 'featureNormalize.m' }, ...
+           { 'computeCostMulti.m' }, ...
+           { 'gradientDescentMulti.m' }, ...
+           { 'normalEqn.m' }, ...
+         };
+end
+
+function out = output(partId)
+  % Random Test Cases
+  X1 = [ones(20,1) (exp(1) + exp(2) * (0.1:0.1:2))'];
+  Y1 = X1(:,2) + sin(X1(:,1)) + cos(X1(:,2));
+  X2 = [X1 X1(:,2).^0.5 X1(:,2).^0.25];
+  Y2 = Y1.^0.5 + Y1;
+  if partId == 1
+    out = sprintf('%0.5f ', warmUpExercise());
+  elseif partId == 2
+    out = sprintf('%0.5f ', computeCost(X1, Y1, [0.5 -0.5]'));
+  elseif partId == 3
+    out = sprintf('%0.5f ', gradientDescent(X1, Y1, [0.5 -0.5]', 0.01, 10));
+  elseif partId == 4
+    out = sprintf('%0.5f ', featureNormalize(X2(:,2:4)));
+  elseif partId == 5
+    out = sprintf('%0.5f ', computeCostMulti(X2, Y2, [0.1 0.2 0.3 0.4]'));
+  elseif partId == 6
+    out = sprintf('%0.5f ', gradientDescentMulti(X2, Y2, [-0.1 -0.2 -0.3 -0.4]', 0.01, 10));
+  elseif partId == 7
+    out = sprintf('%0.5f ', normalEqn(X2, Y2));
+  end 
+end
+
+function url = challenge_url()
+  url = 'http://www.ml-class.org/course/homework/challenge';
+end
+
+function url = submit_url()
+  url = 'http://www.ml-class.org/course/homework/submit';
+end
+
+% ========================= CHALLENGE HELPERS =========================
+
+function src = source(partId)
+  src = '';
+  src_files = sources();
+  if partId <= numel(src_files)
+      flist = src_files{partId};
+      for i = 1:numel(flist)
+          fid = fopen(flist{i});
+          while ~feof(fid)
+            line = fgets(fid);
+            src = [src line];
+          end
+          src = [src '||||||||'];
+      end
+  end
+end
+
+function ret = isValidPartId(partId)
+  partNames = validParts();
+  ret = (~isempty(partId)) && (partId >= 1) && (partId <= numel(partNames) + 1);
+end
+
+function partId = promptPart()
+  fprintf('== Select which part(s) to submit:\n', ...
+          homework_id());
+  partNames = validParts();
+  srcFiles = sources();
+  for i = 1:numel(partNames)
+    fprintf('==   %d) %s [', i, partNames{i});
+    fprintf(' %s ', srcFiles{i}{:});
+    fprintf(']\n');
+  end
+  fprintf('==   %d) All of the above \n==\nEnter your choice [1-%d]: ', ...
+          numel(partNames) + 1, numel(partNames) + 1);
+  selPart = input('', 's');
+  partId = str2num(selPart);
+  if ~isValidPartId(partId)
+    partId = -1;
+  end
+end
+
+function [email,ch,signature] = getChallenge(email)
+  str = urlread(challenge_url(), 'post', {'email_address', email});
+
+  str = strtrim(str);
+  [email, str] = strtok (str, '|');
+  [ch, str] = strtok (str, '|');
+  [signature, str] = strtok (str, '|');
+end
+
+
+function [result, str] = submitSolution(email, ch_resp, part, output, ...
+                                        source, signature)
+
+  params = {'homework', homework_id(), ...
+            'part', num2str(part), ...
+            'email', email, ...
+            'output', output, ...
+            'source', source, ...
+            'challenge_response', ch_resp, ...
+            'signature', signature};
+
+  str = urlread(submit_url(), 'post', params);
+  
+  % Parse str to read for success / failure
+  result = 0;
+
+end
+
+% =========================== LOGIN HELPERS ===========================
+
+function [login password] = loginPrompt()
+  % Prompt for password
+  [login password] = basicPrompt();
+  
+  if isempty(login) || isempty(password)
+    login = []; password = [];
+  end
+end
+
+
+function [login password] = basicPrompt()
+  login = input('Login (Email address): ', 's');
+  password = input('Password: ', 's');
+end
+
+
+function [str] = challengeResponse(email, passwd, challenge)
+  salt = ')~/|]QMB3[!W`?OVt7qC"@+}';
+  str = sha1([challenge sha1([salt email passwd])]);
+  sel = randperm(numel(str));
+  sel = sort(sel(1:16));
+  str = str(sel);
+end
+
+
+% =============================== SHA-1 ================================
+
+function hash = sha1(str)
+  
+  % Initialize variables
+  h0 = uint32(1732584193);
+  h1 = uint32(4023233417);
+  h2 = uint32(2562383102);
+  h3 = uint32(271733878);
+  h4 = uint32(3285377520);
+  
+  % Convert to word array
+  strlen = numel(str);
+
+  % Break string into chars and append the bit 1 to the message
+  mC = [double(str) 128];
+  mC = [mC zeros(1, 4-mod(numel(mC), 4), 'uint8')];
+  
+  numB = strlen * 8;
+  if exist('idivide')
+    numC = idivide(uint32(numB + 65), 512, 'ceil');
+  else
+    numC = ceil(double(numB + 65)/512);
+  end
+  numW = numC * 16;
+  mW = zeros(numW, 1, 'uint32');
+  
+  idx = 1;
+  for i = 1:4:strlen + 1
+    mW(idx) = bitor(bitor(bitor( ...
+                  bitshift(uint32(mC(i)), 24), ...
+                  bitshift(uint32(mC(i+1)), 16)), ...
+                  bitshift(uint32(mC(i+2)), 8)), ...
+                  uint32(mC(i+3)));
+    idx = idx + 1;
+  end
+  
+  % Append length of message
+  mW(numW - 1) = uint32(bitshift(uint64(numB), -32));
+  mW(numW) = uint32(bitshift(bitshift(uint64(numB), 32), -32));
+
+  % Process the message in successive 512-bit chs
+  for cId = 1 : double(numC)
+    cSt = (cId - 1) * 16 + 1;
+    cEnd = cId * 16;
+    ch = mW(cSt : cEnd);
+    
+    % Extend the sixteen 32-bit words into eighty 32-bit words
+    for j = 17 : 80
+      ch(j) = ch(j - 3);
+      ch(j) = bitxor(ch(j), ch(j - 8));
+      ch(j) = bitxor(ch(j), ch(j - 14));
+      ch(j) = bitxor(ch(j), ch(j - 16));
+      ch(j) = bitrotate(ch(j), 1);
+    end
+  
+    % Initialize hash value for this ch
+    a = h0;
+    b = h1;
+    c = h2;
+    d = h3;
+    e = h4;
+    
+    % Main loop
+    for i = 1 : 80
+      if(i >= 1 && i <= 20)
+        f = bitor(bitand(b, c), bitand(bitcmp(b), d));
+        k = uint32(1518500249);
+      elseif(i >= 21 && i <= 40)
+        f = bitxor(bitxor(b, c), d);
+        k = uint32(1859775393);
+      elseif(i >= 41 && i <= 60)
+        f = bitor(bitor(bitand(b, c), bitand(b, d)), bitand(c, d));
+        k = uint32(2400959708);
+      elseif(i >= 61 && i <= 80)
+        f = bitxor(bitxor(b, c), d);
+        k = uint32(3395469782);
+      end
+      
+      t = bitrotate(a, 5);
+      t = bitadd(t, f);
+      t = bitadd(t, e);
+      t = bitadd(t, k);
+      t = bitadd(t, ch(i));
+      e = d;
+      d = c;
+      c = bitrotate(b, 30);
+      b = a;
+      a = t;
+      
+    end
+    h0 = bitadd(h0, a);
+    h1 = bitadd(h1, b);
+    h2 = bitadd(h2, c);
+    h3 = bitadd(h3, d);
+    h4 = bitadd(h4, e);
+
+  end
+
+  hash = reshape(dec2hex(double([h0 h1 h2 h3 h4]), 8)', [1 40]);
+  
+  hash = lower(hash);
+
+end
+
+function ret = bitadd(iA, iB)
+  ret = double(iA) + double(iB);
+  ret = bitset(ret, 33, 0);
+  ret = uint32(ret);
+end
+
+function ret = bitrotate(iA, places)
+  t = bitshift(iA, places - 32);
+  ret = bitshift(iA, places);
+  ret = bitor(ret, t);
+end
new file mode 100644
--- /dev/null
+++ b/warmUpExercise.m
@@ -0,0 +1,21 @@
+function A = warmUpExercise()
+%WARMUPEXERCISE Example function in octave
+%   A = WARMUPEXERCISE() is an example function that returns the 5x5 identity matrix
+
+A = [];
+% ============= YOUR CODE HERE ==============
+% Instructions: Return the 5x5 identity matrix 
+%               In octave, we return values by defining which variables
+%               represent the return values (at the top of the file)
+%               and then set them accordingly. 
+A = eye(5);
+
+
+
+
+
+
+% ===========================================
+
+
+end