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import exercise 1: IV. Linear Regression with Multiple Variables (Week 2)

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neingeist 10 years ago
commit 79825e97f4

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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

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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

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%% 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 ; 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);

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%% 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 ; 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 = 400;
% 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);

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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

@ -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

@ -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

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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

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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

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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

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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

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function submit(partId, webSubmit)
%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('partId', 'var') || isempty(partId)
partId = promptPart();
end
if ~exist('webSubmit', 'var') || isempty(webSubmit)
webSubmit = 0; % submit directly by default
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
if ~exist('ml_login_data.mat','file')
[login password] = loginPrompt();
save('ml_login_data.mat','login','password');
else
load('ml_login_data.mat');
[login password] = quickLogin(login, password);
save('ml_login_data.mat','login','password');
end
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)
thisPartId = submitParts(s);
if (~webSubmit) % submit directly to server
[login, ch, signature, auxstring] = getChallenge(login, thisPartId);
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, thisPartId, ...
output(thisPartId, auxstring), source(thisPartId), signature);
partName = partNames{thisPartId};
fprintf('\n== [ml-class] Submitted Assignment %s - Part %d - %s\n', ...
homework_id(), thisPartId, partName);
fprintf('== %s\n', strtrim(str));
if exist('OCTAVE_VERSION')
fflush(stdout);
end
else
[result] = submitSolutionWeb(login, thisPartId, output(thisPartId), ...
source(thisPartId));
result = base64encode(result);
fprintf('\nSave as submission file [submit_ex%s_part%d.txt (enter to accept default)]:', ...
homework_id(), thisPartId);
saveAsFile = input('', 's');
if (isempty(saveAsFile))
saveAsFile = sprintf('submit_ex%s_part%d.txt', homework_id(), thisPartId);
end
fid = fopen(saveAsFile, 'w');
if (fid)
fwrite(fid, result);
fclose(fid);
fprintf('\nSaved your solutions to %s.\n\n', saveAsFile);
fprintf(['You can now submit your solutions through the web \n' ...
'form in the programming exercises. Select the corresponding \n' ...
'programming exercise to access the form.\n']);
else
fprintf('Unable to save to %s\n\n', saveAsFile);
fprintf(['You can create a submission file by saving the \n' ...
'following text in a file: (press enter to continue)\n\n']);
pause;
fprintf(result);
end
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, auxstring)
% 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
% ====================== SERVER CONFIGURATION ===========================
% ***************** REMOVE -staging WHEN YOU DEPLOY *********************
function url = site_url()
url = 'http://class.coursera.org/ml-007';
end
function url = challenge_url()
url = [site_url() '/assignment/challenge'];
end
function url = submit_url()
url = [site_url() '/assignment/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});
if (fid == -1)
error('Error opening %s (is it missing?)', flist{i});
end
line = fgets(fid);
while ischar(line)
src = [src line];
line = fgets(fid);
end
fclose(fid);
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');
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,auxstring] = getChallenge(email, part)
str = urlread(challenge_url(), 'post', {'email_address', email, 'assignment_part_sid', [homework_id() '-' num2str(part)], 'response_encoding', 'delim'});
str = strtrim(str);
r = struct;
while(numel(str) > 0)
[f, str] = strtok (str, '|');
[v, str] = strtok (str, '|');
r = setfield(r, f, v);
end
email = getfield(r, 'email_address');
ch = getfield(r, 'challenge_key');
signature = getfield(r, 'state');
auxstring = getfield(r, 'challenge_aux_data');
end
function [result, str] = submitSolutionWeb(email, part, output, source)
result = ['{"assignment_part_sid":"' base64encode([homework_id() '-' num2str(part)], '') '",' ...
'"email_address":"' base64encode(email, '') '",' ...
'"submission":"' base64encode(output, '') '",' ...
'"submission_aux":"' base64encode(source, '') '"' ...
'}'];
str = 'Web-submission';
end
function [result, str] = submitSolution(email, ch_resp, part, output, ...
source, signature)
params = {'assignment_part_sid', [homework_id() '-' num2str(part)], ...
'email_address', email, ...
'submission', base64encode(output, ''), ...
'submission_aux', base64encode(source, ''), ...
'challenge_response', ch_resp, ...
'state', 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 [login password] = quickLogin(login,password)
disp(['You are currently logged in as ' login '.']);
cont_token = input('Is this you? (y/n - type n to reenter password)','s');
if(isempty(cont_token) || cont_token(1)=='Y'||cont_token(1)=='y')
return;
else
[login password] = loginPrompt();
end
end
function [str] = challengeResponse(email, passwd, challenge)
str = sha1([challenge passwd]);
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
% =========================== Base64 Encoder ============================
% Thanks to Peter John Acklam
%
function y = base64encode(x, eol)
%BASE64ENCODE Perform base64 encoding on a string.
%
% BASE64ENCODE(STR, EOL) encode the given string STR. EOL is the line ending
% sequence to use; it is optional and defaults to '\n' (ASCII decimal 10).
% The returned encoded string is broken into lines of no more than 76
% characters each, and each line will end with EOL unless it is empty. Let
% EOL be empty if you do not want the encoded string broken into lines.
%
% STR and EOL don't have to be strings (i.e., char arrays). The only
% requirement is that they are vectors containing values in the range 0-255.
%
% This function may be used to encode strings into the Base64 encoding
% specified in RFC 2045 - MIME (Multipurpose Internet Mail Extensions). The
% Base64 encoding is designed to represent arbitrary sequences of octets in a
% form that need not be humanly readable. A 65-character subset
% ([A-Za-z0-9+/=]) of US-ASCII is used, enabling 6 bits to be represented per
% printable character.
%
% Examples
% --------
%
% If you want to encode a large file, you should encode it in chunks that are
% a multiple of 57 bytes. This ensures that the base64 lines line up and
% that you do not end up with padding in the middle. 57 bytes of data fills
% one complete base64 line (76 == 57*4/3):
%
% If ifid and ofid are two file identifiers opened for reading and writing,
% respectively, then you can base64 encode the data with
%
% while ~feof(ifid)
% fwrite(ofid, base64encode(fread(ifid, 60*57)));
% end
%
% or, if you have enough memory,
%
% fwrite(ofid, base64encode(fread(ifid)));
%
% See also BASE64DECODE.
% Author: Peter John Acklam
% Time-stamp: 2004-02-03 21:36:56 +0100
% E-mail: pjacklam@online.no
% URL: http://home.online.no/~pjacklam
if isnumeric(x)
x = num2str(x);
end
% make sure we have the EOL value
if nargin < 2
eol = sprintf('\n');
else
if sum(size(eol) > 1) > 1
error('EOL must be a vector.');
end
if any(eol(:) > 255)
error('EOL can not contain values larger than 255.');
end
end
if sum(size(x) > 1) > 1
error('STR must be a vector.');
end
x = uint8(x);
eol = uint8(eol);
ndbytes = length(x); % number of decoded bytes
nchunks = ceil(ndbytes / 3); % number of chunks/groups
nebytes = 4 * nchunks; % number of encoded bytes
% add padding if necessary, to make the length of x a multiple of 3
if rem(ndbytes, 3)
x(end+1 : 3*nchunks) = 0;
end
x = reshape(x, [3, nchunks]); % reshape the data
y = repmat(uint8(0), 4, nchunks); % for the encoded data
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Split up every 3 bytes into 4 pieces
%
% aaaaaabb bbbbcccc ccdddddd
%
% to form
%
% 00aaaaaa 00bbbbbb 00cccccc 00dddddd
%
y(1,:) = bitshift(x(1,:), -2); % 6 highest bits of x(1,:)
y(2,:) = bitshift(bitand(x(1,:), 3), 4); % 2 lowest bits of x(1,:)
y(2,:) = bitor(y(2,:), bitshift(x(2,:), -4)); % 4 highest bits of x(2,:)
y(3,:) = bitshift(bitand(x(2,:), 15), 2); % 4 lowest bits of x(2,:)
y(3,:) = bitor(y(3,:), bitshift(x(3,:), -6)); % 2 highest bits of x(3,:)
y(4,:) = bitand(x(3,:), 63); % 6 lowest bits of x(3,:)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Now perform the following mapping
%
% 0 - 25 -> A-Z
% 26 - 51 -> a-z
% 52 - 61 -> 0-9
% 62 -> +
% 63 -> /
%
% We could use a mapping vector like
%
% ['A':'Z', 'a':'z', '0':'9', '+/']
%
% but that would require an index vector of class double.
%
z = repmat(uint8(0), size(y));
i = y <= 25; z(i) = 'A' + double(y(i));
i = 26 <= y & y <= 51; z(i) = 'a' - 26 + double(y(i));
i = 52 <= y & y <= 61; z(i) = '0' - 52 + double(y(i));
i = y == 62; z(i) = '+';
i = y == 63; z(i) = '/';
y = z;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Add padding if necessary.
%
npbytes = 3 * nchunks - ndbytes; % number of padding bytes
if npbytes
y(end-npbytes+1 : end) = '='; % '=' is used for padding
end
if isempty(eol)
% reshape to a row vector
y = reshape(y, [1, nebytes]);
else
nlines = ceil(nebytes / 76); % number of lines
neolbytes = length(eol); % number of bytes in eol string
% pad data so it becomes a multiple of 76 elements
y = [y(:) ; zeros(76 * nlines - numel(y), 1)];
y(nebytes + 1 : 76 * nlines) = 0;
y = reshape(y, 76, nlines);
% insert eol strings
eol = eol(:);
y(end + 1 : end + neolbytes, :) = eol(:, ones(1, nlines));
% remove padding, but keep the last eol string
m = nebytes + neolbytes * (nlines - 1);
n = (76+neolbytes)*nlines - neolbytes;
y(m+1 : n) = '';
% extract and reshape to row vector
y = reshape(y, 1, m+neolbytes);
end
% output is a character array
y = char(y);
end

@ -0,0 +1,20 @@
% submitWeb Creates files from your code and output for web submission.
%
% If the submit function does not work for you, use the web-submission mechanism.
% Call this function to produce a file for the part you wish to submit. Then,
% submit the file to the class servers using the "Web Submission" button on the
% Programming Exercises page on the course website.
%
% You should call this function without arguments (submitWeb), to receive
% an interactive prompt for submission; optionally you can call it with the partID
% if you so wish. Make sure your working directory is set to the directory
% containing the submitWeb.m file and your assignment files.
function submitWeb(partId)
if ~exist('partId', 'var') || isempty(partId)
partId = [];
end
submit(partId, 1);
end

@ -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.
% ===========================================
end