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Miki Tebeka committed e9464a9

Start of ex2

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File ex2.pdf

Binary file added.
+import matplotlib.pylab as plt
+import numpy as np
+
+
+def parse_line(line):
+    return map(float, line.split(','))
+
+
+def load():
+    with open('ex2/ex2data1.txt') as fo:
+        return np.array([parse_line(line) for line in fo])
+
+
+def plot(data):
+    passed = data[data[:,2]==1]
+    failed = data[data[:,2]==0]
+
+    fig = plt.figure()
+    ax = fig.add_subplot(111)
+    ax.scatter(passed[:,0], passed[:,1], color='black', marker='+',
+               label='Admitted')
+    ax.scatter(failed[:,0], failed[:,1], color='orange', marker='o',
+              label='Not admitted')
+    ax.set_xlim(min(data[:,0]), max(data[:,0]))
+    ax.set_ylim(min(data[:,1]), max(data[:,1]))
+    ax.set_xlabel('Exam 1 score')
+    ax.set_ylabel('Exam 2 score')
+    plt.legend()
+    plt.show()
+
+

File ex2/costFunction.m

+function [J, grad] = costFunction(theta, X, y)
+%COSTFUNCTION Compute cost and gradient for logistic regression
+%   J = COSTFUNCTION(theta, X, y) computes the cost of using theta as the
+%   parameter for logistic regression and the gradient of the cost
+%   w.r.t. to the parameters.
+
+% Initialize some useful values
+m = length(y); % number of training examples
+
+% You need to return the following variables correctly 
+J = 0;
+grad = zeros(size(theta));
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: Compute the cost of a particular choice of theta.
+%               You should set J to the cost.
+%               Compute the partial derivatives and set grad to the partial
+%               derivatives of the cost w.r.t. each parameter in theta
+%
+% Note: grad should have the same dimensions as theta
+%
+
+
+
+
+
+
+
+
+% =============================================================
+
+end

File ex2/costFunctionReg.m

+function [J, grad] = costFunctionReg(theta, X, y, lambda)
+%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
+%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
+%   theta as the parameter for regularized logistic regression and the
+%   gradient of the cost w.r.t. to the parameters. 
+
+% Initialize some useful values
+m = length(y); % number of training examples
+
+% You need to return the following variables correctly 
+J = 0;
+grad = zeros(size(theta));
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: Compute the cost of a particular choice of theta.
+%               You should set J to the cost.
+%               Compute the partial derivatives and set grad to the partial
+%               derivatives of the cost w.r.t. each parameter in theta
+
+
+
+
+
+
+% =============================================================
+
+end
+%% Machine Learning Online Class - Exercise 2: Logistic Regression
+%
+%  Instructions
+%  ------------
+% 
+%  This file contains code that helps you get started on the logistic
+%  regression exercise. You will need to complete the following functions 
+%  in this exericse:
+%
+%     sigmoid.m
+%     costFunction.m
+%     predict.m
+%     costFunctionReg.m
+%
+%  For this exercise, you will not need to change any code in this file,
+%  or any other files other than those mentioned above.
+%
+
+%% Initialization
+clear ; close all; clc
+
+%% Load Data
+%  The first two columns contains the exam scores and the third column
+%  contains the label.
+
+data = load('ex2data1.txt');
+X = data(:, [1, 2]); y = data(:, 3);
+
+%% ==================== Part 1: Plotting ====================
+%  We start the exercise by first plotting the data to understand the 
+%  the problem we are working with.
+
+fprintf(['Plotting data with + indicating (y = 1) examples and o ' ...
+         'indicating (y = 0) examples.\n']);
+
+plotData(X, y);
+
+% Put some labels 
+hold on;
+% Labels and Legend
+xlabel('Exam 1 score')
+ylabel('Exam 2 score')
+
+% Specified in plot order
+legend('Admitted', 'Not admitted')
+hold off;
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+
+
+%% ============ Part 2: Compute Cost and Gradient ============
+%  In this part of the exercise, you will implement the cost and gradient
+%  for logistic regression. You neeed to complete the code in 
+%  costFunction.m
+
+%  Setup the data matrix appropriately, and add ones for the intercept term
+[m, n] = size(X);
+
+% Add intercept term to x and X_test
+X = [ones(m, 1) X];
+
+% Initialize fitting parameters
+initial_theta = zeros(n + 1, 1);
+
+% Compute and display initial cost and gradient
+[cost, grad] = costFunction(initial_theta, X, y);
+
+fprintf('Cost at initial theta (zeros): %f\n', cost);
+fprintf('Gradient at initial theta (zeros): \n');
+fprintf(' %f \n', grad);
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+
+
+%% ============= Part 3: Optimizing using fminunc  =============
+%  In this exercise, you will use a built-in function (fminunc) to find the
+%  optimal parameters theta.
+
+%  Set options for fminunc
+options = optimset('GradObj', 'on', 'MaxIter', 400);
+
+%  Run fminunc to obtain the optimal theta
+%  This function will return theta and the cost 
+[theta, cost] = ...
+	fminunc(@(t)(costFunction(t, X, y)), initial_theta, options);
+
+% Print theta to screen
+fprintf('Cost at theta found by fminunc: %f\n', cost);
+fprintf('theta: \n');
+fprintf(' %f \n', theta);
+
+% Plot Boundary
+plotDecisionBoundary(theta, X, y);
+
+% Put some labels 
+hold on;
+% Labels and Legend
+xlabel('Exam 1 score')
+ylabel('Exam 2 score')
+
+% Specified in plot order
+legend('Admitted', 'Not admitted')
+hold off;
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+
+%% ============== Part 4: Predict and Accuracies ==============
+%  After learning the parameters, you'll like to use it to predict the outcomes
+%  on unseen data. In this part, you will use the logistic regression model
+%  to predict the probability that a student with score 45 on exam 1 and 
+%  score 85 on exam 2 will be admitted.
+%
+%  Furthermore, you will compute the training and test set accuracies of 
+%  our model.
+%
+%  Your task is to complete the code in predict.m
+
+%  Predict probability for a student with score 45 on exam 1 
+%  and score 85 on exam 2 
+
+prob = sigmoid([1 45 85] * theta);
+fprintf(['For a student with scores 45 and 85, we predict an admission ' ...
+         'probability of %f\n\n'], prob);
+
+% Compute accuracy on our training set
+p = predict(theta, X);
+
+fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100);
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+

File ex2/ex2_reg.m

+%% Machine Learning Online Class - Exercise 2: Logistic Regression
+%
+%  Instructions
+%  ------------
+% 
+%  This file contains code that helps you get started on the second part
+%  of the exercise which covers regularization with logistic regression.
+%
+%  You will need to complete the following functions in this exericse:
+%
+%     sigmoid.m
+%     costFunction.m
+%     predict.m
+%     costFunctionReg.m
+%
+%  For this exercise, you will not need to change any code in this file,
+%  or any other files other than those mentioned above.
+%
+
+%% Initialization
+clear ; close all; clc
+
+%% Load Data
+%  The first two columns contains the X values and the third column
+%  contains the label (y).
+
+data = load('ex2data2.txt');
+X = data(:, [1, 2]); y = data(:, 3);
+
+plotData(X, y);
+
+% Put some labels 
+hold on;
+
+% Labels and Legend
+xlabel('Microchip Test 1')
+ylabel('Microchip Test 2')
+
+% Specified in plot order
+legend('y = 1', 'y = 0')
+hold off;
+
+
+%% =========== Part 1: Regularized Logistic Regression ============
+%  In this part, you are given a dataset with data points that are not
+%  linearly separable. However, you would still like to use logistic 
+%  regression to classify the data points. 
+%
+%  To do so, you introduce more features to use -- in particular, you add
+%  polynomial features to our data matrix (similar to polynomial
+%  regression).
+%
+
+% Add Polynomial Features
+
+% Note that mapFeature also adds a column of ones for us, so the intercept
+% term is handled
+X = mapFeature(X(:,1), X(:,2));
+
+% Initialize fitting parameters
+initial_theta = zeros(size(X, 2), 1);
+
+% Set regularization parameter lambda to 1
+lambda = 1;
+
+% Compute and display initial cost and gradient for regularized logistic
+% regression
+[cost, grad] = costFunctionReg(initial_theta, X, y, lambda);
+
+fprintf('Cost at initial theta (zeros): %f\n', cost);
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+
+%% ============= Part 2: Regularization and Accuracies =============
+%  Optional Exercise:
+%  In this part, you will get to try different values of lambda and 
+%  see how regularization affects the decision coundart
+%
+%  Try the following values of lambda (0, 1, 10, 100).
+%
+%  How does the decision boundary change when you vary lambda? How does
+%  the training set accuracy vary?
+%
+
+% Initialize fitting parameters
+initial_theta = zeros(size(X, 2), 1);
+
+% Set regularization parameter lambda to 1 (you should vary this)
+lambda = 1;
+
+% Set Options
+options = optimset('GradObj', 'on', 'MaxIter', 400);
+
+% Optimize
+[theta, J, exit_flag] = ...
+	fminunc(@(t)(costFunctionReg(t, X, y, lambda)), initial_theta, options);
+
+% Plot Boundary
+plotDecisionBoundary(theta, X, y);
+hold on;
+title(sprintf('lambda = %g', lambda))
+
+% Labels and Legend
+xlabel('Microchip Test 1')
+ylabel('Microchip Test 2')
+
+legend('y = 1', 'y = 0', 'Decision boundary')
+hold off;
+
+% Compute accuracy on our training set
+p = predict(theta, X);
+
+fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100);
+
+

File ex2/ex2data1.txt

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File ex2/ex2data2.txt

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File ex2/mapFeature.m

+function out = mapFeature(X1, X2)
+% MAPFEATURE Feature mapping function to polynomial features
+%
+%   MAPFEATURE(X1, X2) maps the two input features
+%   to quadratic features used in the regularization exercise.
+%
+%   Returns a new feature array with more features, comprising of 
+%   X1, X2, X1.^2, X2.^2, X1*X2, X1*X2.^2, etc..
+%
+%   Inputs X1, X2 must be the same size
+%
+
+degree = 6;
+out = ones(size(X1(:,1)));
+for i = 1:degree
+    for j = 0:i
+        out(:, end+1) = (X1.^(i-j)).*(X2.^j);
+    end
+end
+
+end

File ex2/plotData.m

+function plotData(X, y)
+%PLOTDATA Plots the data points X and y into a new figure 
+%   PLOTDATA(x,y) plots the data points with + for the positive examples
+%   and o for the negative examples. X is assumed to be a Mx2 matrix.
+
+% Create New Figure
+figure; hold on;
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: Plot the positive and negative examples on a
+%               2D plot, using the option 'k+' for the positive
+%               examples and 'ko' for the negative examples.
+%
+
+
+
+
+
+
+
+
+
+% =========================================================================
+
+
+
+hold off;
+
+end

File ex2/plotDecisionBoundary.m

+function plotDecisionBoundary(theta, X, y)
+%PLOTDECISIONBOUNDARY Plots the data points X and y into a new figure with
+%the decision boundary defined by theta
+%   PLOTDECISIONBOUNDARY(theta, X,y) plots the data points with + for the 
+%   positive examples and o for the negative examples. X is assumed to be 
+%   a either 
+%   1) Mx3 matrix, where the first column is an all-ones column for the 
+%      intercept.
+%   2) MxN, N>3 matrix, where the first column is all-ones
+
+% Plot Data
+plotData(X(:,2:3), y);
+hold on
+
+if size(X, 2) <= 3
+    % Only need 2 points to define a line, so choose two endpoints
+    plot_x = [min(X(:,2))-2,  max(X(:,2))+2];
+
+    % Calculate the decision boundary line
+    plot_y = (-1./theta(3)).*(theta(2).*plot_x + theta(1));
+
+    % Plot, and adjust axes for better viewing
+    plot(plot_x, plot_y)
+    
+    % Legend, specific for the exercise
+    legend('Admitted', 'Not admitted', 'Decision Boundary')
+    axis([30, 100, 30, 100])
+else
+    % Here is the grid range
+    u = linspace(-1, 1.5, 50);
+    v = linspace(-1, 1.5, 50);
+
+    z = zeros(length(u), length(v));
+    % Evaluate z = theta*x over the grid
+    for i = 1:length(u)
+        for j = 1:length(v)
+            z(i,j) = mapFeature(u(i), v(j))*theta;
+        end
+    end
+    z = z'; % important to transpose z before calling contour
+
+    % Plot z = 0
+    % Notice you need to specify the range [0, 0]
+    contour(u, v, z, [0, 0], 'LineWidth', 2)
+end
+hold off
+
+end

File ex2/predict.m

+function p = predict(theta, X)
+%PREDICT Predict whether the label is 0 or 1 using learned logistic 
+%regression parameters theta
+%   p = PREDICT(theta, X) computes the predictions for X using a 
+%   threshold at 0.5 (i.e., if sigmoid(theta'*x) >= 0.5, predict 1)
+
+m = size(X, 1); % Number of training examples
+
+% You need to return the following variables correctly
+p = zeros(m, 1);
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: Complete the following code to make predictions using
+%               your learned logistic regression parameters. 
+%               You should set p to a vector of 0's and 1's
+%
+
+
+
+
+
+
+
+% =========================================================================
+
+
+end

File ex2/sigmoid.m

+function g = sigmoid(z)
+%SIGMOID Compute sigmoid functoon
+%   J = SIGMOID(z) computes the sigmoid of z.
+
+% You need to return the following variables correctly 
+g = zeros(size(z));
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: Compute the sigmoid of each value of z (z can be a matrix,
+%               vector or scalar).
+
+
+
+
+
+% =============================================================
+
+end

File ex2/submit.m

+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 = '2';
+end
+
+function [partNames] = validParts()
+  partNames = { 'Sigmoid Function ', ...
+                'Logistic Regression Cost', ...
+                'Logistic Regression Gradient', ...
+                'Predict', ...
+                'Regularized Logistic Regression Cost' ...
+                'Regularized Logistic Regression Gradient' ...
+                };
+end
+
+function srcs = sources()
+  % Separated by part
+  srcs = { { 'sigmoid.m' }, ...
+           { 'costFunction.m' }, ...
+           { 'costFunction.m' }, ...
+           { 'predict.m' }, ...
+           { 'costFunctionReg.m' }, ...
+           { 'costFunctionReg.m' } };
+end
+
+function out = output(partId, auxstring)
+  % Random Test Cases
+  X = [ones(20,1) (exp(1) * sin(1:1:20))' (exp(0.5) * cos(1:1:20))'];
+  y = sin(X(:,1) + X(:,2)) > 0;
+  if partId == 1
+    out = sprintf('%0.5f ', sigmoid(X));
+  elseif partId == 2
+    out = sprintf('%0.5f ', costFunction([0.25 0.5 -0.5]', X, y));
+  elseif partId == 3
+    [cost, grad] = costFunction([0.25 0.5 -0.5]', X, y);
+    out = sprintf('%0.5f ', grad);
+  elseif partId == 4
+    out = sprintf('%0.5f ', predict([0.25 0.5 -0.5]', X));
+  elseif partId == 5
+    out = sprintf('%0.5f ', costFunctionReg([0.25 0.5 -0.5]', X, y, 0.1));
+  elseif partId == 6
+    [cost, grad] = costFunctionReg([0.25 0.5 -0.5]', X, y, 0.1);
+    out = sprintf('%0.5f ', grad);
+  end 
+end
+
+
+% ====================== SERVER CONFIGURATION ===========================
+
+% ***************** REMOVE -staging WHEN YOU DEPLOY *********************
+function url = site_url()
+  url = 'http://www.coursera.org/ml';
+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

File ex2/submitWeb.m

+% 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
+