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+Machine Learning 2011 exercices (Octave/Matlab)
+===============================================
+
+http://www.ml-class.org/course/class/index
+
+
+| DIR.  | EXERCICE                                        |
+|-------+-------------------------------------------------|
+| ex01/ | Linear Regression                               |
+| ex02/ | Logistic Regression                             |
+| ex03/ | Multi-class classification and neural networks  |
+| ex04/ | Neural network learning                         |
+| ex05/ | Regularized linear regression and bias-variance |
+| ex06/ | Support Vector Machines                         |
+| ex07/ | K-Means Clustering and PCA                      |
+| ex08/ | Anomaly Detection and Recommender Systems       |
+
+--
+Pferor <pferor [AT] gmail [DOT] com>
+

# ex01/computeCost.m

+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.
+
+predictions = X * theta;
+sqrErrors = (predictions - y) .^ 2;
+J = 1 / (2 * m) * sum(sqrErrors);
+
+% =========================================================================
+
+end

# ex01/computeCostMulti.m

+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.
+
+
+predictions = X * theta;
+sqrErrors = (predictions - y) .^ 2;
+J = 1 / (2 * m) * sum(sqrErrors);
+
+
+
+% =========================================================================
+
+end

# ex01/ex1.m

+%% 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); # ex01/ex1_multi.m +%% 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); + # ex01/ex1data1.txt +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 # ex01/ex1data2.txt +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 # ex01/featureNormalize.m +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. +%  + +mu = mean(X); +sigma = std(X); + +X_norm(:, 1) = (X(:, 1) - mu(1)) / sigma(1); +X_norm(:, 2) = (X(:, 2) - mu(2)) / sigma(2); + +% ============================================================ + +end # ex01/gradientDescent.m +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. + % + + hipoteses = X * theta; + theta0 = theta(1) - alpha / m * sum((hipoteses - y) .* X(:,1)); + theta1 = theta(2) - alpha / m * sum((hipoteses - y) .* X(:,2)); + theta = [theta0; theta1]; + + # theta_temp = theta; + # theta(1) = theta_temp(1) - alpha * (1/m) * sum( X'(1, :) * ((X * theta_temp) - y)); + # theta(2) = theta_temp(2) - alpha * (1/m) * sum( X'(2, :) * ((X * theta_temp) - y)); + + % ============================================================ + + % Save the cost J in every iteration + J_history(iter) = computeCost(X, y, theta); + +end + +end + # ex01/gradientDescentMulti.m +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. + % + + + + gradJ = 1/(2*m) * 2 * (X'*X*theta - X'*y); + theta = theta - alpha * gradJ; + + % ============================================================ + + % Save the cost J in every iteration  + J_history(iter) = computeCostMulti(X, y, theta); + +end + +end # ex01/normalEqn.m +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 # ex01/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 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 + + +plot(x, y, 'rx', 'MarkerSize', 10); % Plot the data +ylabel('Profit in$10,000s');            % Set the y-axis label
+xlabel('Population fo City in 10,000s'); % Set the x-axis label
+
+
+% ============================================================
+
+end

# ex01/submit.m

+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

# ex01/warmUpExercise.m

+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. 
+
+
+%% Identity 5x5 matrix
+A = eye(5);
+
+
+% ===========================================
+
+
+end

# ex02/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
+%
+
+h = sigmoid(X*theta);
+J = ( (-y)' *log(h)-(1-y)' * log(1-h))/m;
+
+
+for i=1:m
+  hx = sigmoid(theta'*X(i,:)');
+  temp = hx - y(i);
+  for j=1:n
+    grad(j) = grad(j) + temp * X(i,j);
+  end
+end
+
+grad = grad / m;
+
+
+% =============================================================
+
+end

# ex02/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
+
+
+% features
+n = size(X,2);
+
+h = sigmoid(X*theta);
+
+
+J = ((-y)' *log(h) - (1-y)' * log(1-h)) / m;
+theta1 = [0 ; theta(2:size(theta), :)];
+
+sumat = 0;
+for j=1:n
+  sumat = sumat + (theta1(j) * theta1(j));
+end
+
+p = (lambda * sumat) / (2 * m);
+J = J + p;
+
+grad = ( X' * (h - y) + lambda * theta1 ) / m;
+
+
+% =============================================================
+
+end

# ex02/ex2.m

+%% 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 all; close all; clc
+
+%% Load Data
+%  The first two columns contains the exam scores and the third column
+%  contains the label.
+
+data = csvread('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 20 on exam 1 and 
+%  score 80 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;
+

# ex02/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 all; close all; clc
+
+%% Load Data
+%  The first two columns contains the exam scores and the third column
+%  contains the label.
+
+data = csvread('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);
+
+

# ex02/ex2data1.txt

+34.62365962451697,78.0246928153624,0
+30.28671076822607,43.89499752400101,0
+35.84740876993872,72.90219802708364,0
+60.18259938620976,86.30855209546826,1
+79.0327360507101,75.3443764369103,1
+45.08327747668339,56.3163717815305,0
+61.10666453684766,96.51142588489624,1
+75.02474556738889,46.55401354116538,1
+76.09878670226257,87.42056971926803,1
+84.43281996120035,43.53339331072109,1
+95.86155507093572,38.22527805795094,0
+75.01365838958247,30.60326323428011,0
+82.30705337399482,76.48196330235604,1
+69.36458875970939,97.71869196188608,1
+39.53833914367223,76.03681085115882,0
+53.9710521485623,89.20735013750205,1
+69.07014406283025,52.74046973016765,1
+67.94685547711617,46.67857410673128,0
+70.66150955499435,92.92713789364831,1
+76.97878372747498,47.57596364975532,1
+67.37202754570876,42.83843832029179,0
+89.67677575072079,65.79936592745237,1
+50.534788289883,48.85581152764205,0
+34.21206097786789,44.20952859866288,0
+77.9240914545704,68.9723599933059,1
+62.27101367004632,69.95445795447587,1
+80.1901807509566,44.82162893218353,1
+93.114388797442,38.80067033713209,0
+61.83020602312595,50.25610789244621,0
+38.78580379679423,64.99568095539578,0
+61.379289447425,72.80788731317097,1
+85.40451939411645,57.05198397627122,1
+52.10797973193984,63.12762376881715,0
+52.04540476831827,69.43286012045222,1
+40.23689373545111,71.16774802184875,0
+54.63510555424817,52.21388588061123,0
+33.91550010906887,98.86943574220611,0
+64.17698887494485,80.90806058670817,1
+74.78925295941542,41.57341522824434,0
+34.1836400264419,75.2377203360134,0
+83.90239366249155,56.30804621605327,1
+51.54772026906181,46.85629026349976,0
+94.44336776917852,65.56892160559052,1
+82.36875375713919,40.61825515970618,0
+51.04775177128865,45.82270145776001,0
+62.22267576120188,52.06099194836679,0
+77.19303492601364,70.45820000180959,1
+97.77159928000232,86.7278223300282,1
+62.07306379667647,96.76882412413983,1
+91.56497449807442,88.69629254546599,1
+79.94481794066932,74.16311935043758,1
+99.2725269292572,60.99903099844988,1
+90.54671411399852,43.39060180650027,1
+34.52451385320009,60.39634245837173,0
+50.2864961189907,49.80453881323059,0
+49.58667721632031,59.80895099453265,0
+97.64563396007767,68.86157272420604,1
+32.57720016809309,95.59854761387875,0
+74.24869136721598,69.82457122657193,1
+71.79646205863379,78.45356224515052,1
+75.3956114656803,85.75993667331619,1
+35.28611281526193,47.02051394723416,0
+56.25381749711624,39.26147251058019,0
+30.05882244669796,49.59297386723685,0
+44.66826172480893,66.45008614558913,0
+66.56089447242954,41.09209807936973,0
+40.45755098375164,97.53518548909936,1
+49.07256321908844,51.88321182073966,0
+80.27957401466998,92.11606081344084,1
+66.74671856944039,60.99139402740988,1
+32.72283304060323,43.30717306430063,0
+64.0393204150601,78.03168802018232,1
+72.34649422579923,96.22759296761404,1
+60.45788573918959,73.09499809758037,1
+58.84095621726802,75.85844831279042,1
+99.82785779692128,72.36925193383885,1
+47.26426910848174,88.47586499559782,1
+50.45815980285988,75.80985952982456,1
+60.45555629271532,42.50840943572217,0
+82.22666157785568,42.71987853716458,0
+88.9138964166533,69.80378889835472,1
+94.83450672430196,45.69430680250754,1
+67.31925746917527,66.58935317747915,1
+57.23870631569862,59.51428198012956,1
+80.36675600171273,90.96014789746954,1
+68.46852178591112,85.59430710452014,1
+42.0754545384731,78.84478600148043,0
+75.47770200533905,90.42453899753964,1
+78.63542434898018,96.64742716885644,1
+52.34800398794107,60.76950525602592,0
+94.09433112516793,77.15910509073893,1
+90.44855097096364,87.50879176484702,1
+55.48216114069585,35.57070347228866,0
+74.49269241843041,84.84513684930135,1
+89.84580670720979,45.35828361091658,1
+83.48916274498238,48.38028579728175,1
+42.2617008099817,87.10385094025457,1
+99.31500880510394,68.77540947206617,1
+55.34001756003703,64.9319380069486,1
+74.77589300092767,89.52981289513276,1

# ex02/ex2data2.txt

+0.051267,0.69956,1
+-0.092742,0.68494,1
+-0.21371,0.69225,1
+-0.375,0.50219,1
+-0.51325,0.46564,1
+-0.52477,0.2098,1
+-0.39804,0.034357,1
+-0.30588,-0.19225,1
+0.016705,-0.40424,1
+0.13191,-0.51389,1
+0.38537,-0.56506,1
+0.52938,-0.5212,1
+0.63882,-0.24342,1
+0.73675,-0.18494,1
+0.54666,0.48757,1
+0.322,0.5826,1
+0.16647,0.53874,1
+-0.046659,0.81652,1
+-0.17339,0.69956,1
+-0.47869,0.63377,1
+-0.60541,0.59722,1
+-0.62846,0.33406,1
+-0.59389,0.005117,1
+-0.42108,-0.27266,1
+-0.11578,-0.39693,1
+0.20104,-0.60161,1
+0.46601,-0.53582,1
+0.67339,-0.53582,1
+-0.13882,0.54605,1
+-0.29435,0.77997,1
+-0.26555,0.96272,1
+-0.16187,0.8019,1
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# ex02/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

# ex02/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

# ex02/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

# ex02/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
+%
+
+
+for i=1:m
+  if sigmoid(X(i,:) * theta) >= 0.5 , p(i) = 1;
+end
+
+
+% =========================================================================
+
+
+end

# ex02/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).
+
+i = size(z,1);
+j = size(z,2);
+
+for i=1:i
+  for j=1:j,
+    g(i,j) = 1 / ( 1 + e ^ (z(i,j)*-1));
+  end
+end
+
+% =============================================================
+
+end

# ex02/submit.m

+function submit(partId)
+%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
+  
+  % 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 = '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)
+  % 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
+
+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
+          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', ...
+          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;