import exercise 1: IV. Linear Regression with Multiple Variables (Week 2)
This commit is contained in:
commit
79825e97f4
15 changed files with 1245 additions and 0 deletions
22
ex1/computeCost.m
Normal file
22
ex1/computeCost.m
Normal file
|
|
@ -0,0 +1,22 @@
|
||||||
|
function J = computeCost(X, y, theta)
|
||||||
|
%COMPUTECOST Compute cost for linear regression
|
||||||
|
% J = COMPUTECOST(X, y, theta) computes the cost of using theta as the
|
||||||
|
% parameter for linear regression to fit the data points in X and y
|
||||||
|
|
||||||
|
% Initialize some useful values
|
||||||
|
m = length(y); % number of training examples
|
||||||
|
|
||||||
|
% You need to return the following variables correctly
|
||||||
|
J = 0;
|
||||||
|
|
||||||
|
% ====================== YOUR CODE HERE ======================
|
||||||
|
% Instructions: Compute the cost of a particular choice of theta
|
||||||
|
% You should set J to the cost.
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% =========================================================================
|
||||||
|
|
||||||
|
end
|
||||||
22
ex1/computeCostMulti.m
Normal file
22
ex1/computeCostMulti.m
Normal file
|
|
@ -0,0 +1,22 @@
|
||||||
|
function J = computeCostMulti(X, y, theta)
|
||||||
|
%COMPUTECOSTMULTI Compute cost for linear regression with multiple variables
|
||||||
|
% J = COMPUTECOSTMULTI(X, y, theta) computes the cost of using theta as the
|
||||||
|
% parameter for linear regression to fit the data points in X and y
|
||||||
|
|
||||||
|
% Initialize some useful values
|
||||||
|
m = length(y); % number of training examples
|
||||||
|
|
||||||
|
% You need to return the following variables correctly
|
||||||
|
J = 0;
|
||||||
|
|
||||||
|
% ====================== YOUR CODE HERE ======================
|
||||||
|
% Instructions: Compute the cost of a particular choice of theta
|
||||||
|
% You should set J to the cost.
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% =========================================================================
|
||||||
|
|
||||||
|
end
|
||||||
122
ex1/ex1.m
Normal file
122
ex1/ex1.m
Normal file
|
|
@ -0,0 +1,122 @@
|
||||||
|
%% Machine Learning Online Class - Exercise 1: Linear Regression
|
||||||
|
|
||||||
|
% Instructions
|
||||||
|
% ------------
|
||||||
|
%
|
||||||
|
% This file contains code that helps you get started on the
|
||||||
|
% linear exercise. You will need to complete the following functions
|
||||||
|
% in this exericse:
|
||||||
|
%
|
||||||
|
% warmUpExercise.m
|
||||||
|
% plotData.m
|
||||||
|
% gradientDescent.m
|
||||||
|
% computeCost.m
|
||||||
|
% gradientDescentMulti.m
|
||||||
|
% computeCostMulti.m
|
||||||
|
% featureNormalize.m
|
||||||
|
% normalEqn.m
|
||||||
|
%
|
||||||
|
% For this exercise, you will not need to change any code in this file,
|
||||||
|
% or any other files other than those mentioned above.
|
||||||
|
%
|
||||||
|
% x refers to the population size in 10,000s
|
||||||
|
% y refers to the profit in $10,000s
|
||||||
|
%
|
||||||
|
|
||||||
|
%% Initialization
|
||||||
|
clear ; 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);
|
||||||
BIN
ex1/ex1.pdf
Normal file
BIN
ex1/ex1.pdf
Normal file
Binary file not shown.
159
ex1/ex1_multi.m
Normal file
159
ex1/ex1_multi.m
Normal file
|
|
@ -0,0 +1,159 @@
|
||||||
|
%% Machine Learning Online Class
|
||||||
|
% Exercise 1: Linear regression with multiple variables
|
||||||
|
%
|
||||||
|
% Instructions
|
||||||
|
% ------------
|
||||||
|
%
|
||||||
|
% This file contains code that helps you get started on the
|
||||||
|
% linear regression exercise.
|
||||||
|
%
|
||||||
|
% You will need to complete the following functions in this
|
||||||
|
% exericse:
|
||||||
|
%
|
||||||
|
% warmUpExercise.m
|
||||||
|
% plotData.m
|
||||||
|
% gradientDescent.m
|
||||||
|
% computeCost.m
|
||||||
|
% gradientDescentMulti.m
|
||||||
|
% computeCostMulti.m
|
||||||
|
% featureNormalize.m
|
||||||
|
% normalEqn.m
|
||||||
|
%
|
||||||
|
% For this part of the exercise, you will need to change some
|
||||||
|
% parts of the code below for various experiments (e.g., changing
|
||||||
|
% learning rates).
|
||||||
|
%
|
||||||
|
|
||||||
|
%% Initialization
|
||||||
|
|
||||||
|
%% ================ Part 1: Feature Normalization ================
|
||||||
|
|
||||||
|
%% Clear and Close Figures
|
||||||
|
clear ; 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);
|
||||||
|
|
||||||
97
ex1/ex1data1.txt
Normal file
97
ex1/ex1data1.txt
Normal file
|
|
@ -0,0 +1,97 @@
|
||||||
|
6.1101,17.592
|
||||||
|
5.5277,9.1302
|
||||||
|
8.5186,13.662
|
||||||
|
7.0032,11.854
|
||||||
|
5.8598,6.8233
|
||||||
|
8.3829,11.886
|
||||||
|
7.4764,4.3483
|
||||||
|
8.5781,12
|
||||||
|
6.4862,6.5987
|
||||||
|
5.0546,3.8166
|
||||||
|
5.7107,3.2522
|
||||||
|
14.164,15.505
|
||||||
|
5.734,3.1551
|
||||||
|
8.4084,7.2258
|
||||||
|
5.6407,0.71618
|
||||||
|
5.3794,3.5129
|
||||||
|
6.3654,5.3048
|
||||||
|
5.1301,0.56077
|
||||||
|
6.4296,3.6518
|
||||||
|
7.0708,5.3893
|
||||||
|
6.1891,3.1386
|
||||||
|
20.27,21.767
|
||||||
|
5.4901,4.263
|
||||||
|
6.3261,5.1875
|
||||||
|
5.5649,3.0825
|
||||||
|
18.945,22.638
|
||||||
|
12.828,13.501
|
||||||
|
10.957,7.0467
|
||||||
|
13.176,14.692
|
||||||
|
22.203,24.147
|
||||||
|
5.2524,-1.22
|
||||||
|
6.5894,5.9966
|
||||||
|
9.2482,12.134
|
||||||
|
5.8918,1.8495
|
||||||
|
8.2111,6.5426
|
||||||
|
7.9334,4.5623
|
||||||
|
8.0959,4.1164
|
||||||
|
5.6063,3.3928
|
||||||
|
12.836,10.117
|
||||||
|
6.3534,5.4974
|
||||||
|
5.4069,0.55657
|
||||||
|
6.8825,3.9115
|
||||||
|
11.708,5.3854
|
||||||
|
5.7737,2.4406
|
||||||
|
7.8247,6.7318
|
||||||
|
7.0931,1.0463
|
||||||
|
5.0702,5.1337
|
||||||
|
5.8014,1.844
|
||||||
|
11.7,8.0043
|
||||||
|
5.5416,1.0179
|
||||||
|
7.5402,6.7504
|
||||||
|
5.3077,1.8396
|
||||||
|
7.4239,4.2885
|
||||||
|
7.6031,4.9981
|
||||||
|
6.3328,1.4233
|
||||||
|
6.3589,-1.4211
|
||||||
|
6.2742,2.4756
|
||||||
|
5.6397,4.6042
|
||||||
|
9.3102,3.9624
|
||||||
|
9.4536,5.4141
|
||||||
|
8.8254,5.1694
|
||||||
|
5.1793,-0.74279
|
||||||
|
21.279,17.929
|
||||||
|
14.908,12.054
|
||||||
|
18.959,17.054
|
||||||
|
7.2182,4.8852
|
||||||
|
8.2951,5.7442
|
||||||
|
10.236,7.7754
|
||||||
|
5.4994,1.0173
|
||||||
|
20.341,20.992
|
||||||
|
10.136,6.6799
|
||||||
|
7.3345,4.0259
|
||||||
|
6.0062,1.2784
|
||||||
|
7.2259,3.3411
|
||||||
|
5.0269,-2.6807
|
||||||
|
6.5479,0.29678
|
||||||
|
7.5386,3.8845
|
||||||
|
5.0365,5.7014
|
||||||
|
10.274,6.7526
|
||||||
|
5.1077,2.0576
|
||||||
|
5.7292,0.47953
|
||||||
|
5.1884,0.20421
|
||||||
|
6.3557,0.67861
|
||||||
|
9.7687,7.5435
|
||||||
|
6.5159,5.3436
|
||||||
|
8.5172,4.2415
|
||||||
|
9.1802,6.7981
|
||||||
|
6.002,0.92695
|
||||||
|
5.5204,0.152
|
||||||
|
5.0594,2.8214
|
||||||
|
5.7077,1.8451
|
||||||
|
7.6366,4.2959
|
||||||
|
5.8707,7.2029
|
||||||
|
5.3054,1.9869
|
||||||
|
8.2934,0.14454
|
||||||
|
13.394,9.0551
|
||||||
|
5.4369,0.61705
|
||||||
47
ex1/ex1data2.txt
Normal file
47
ex1/ex1data2.txt
Normal file
|
|
@ -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
|
||||||
39
ex1/featureNormalize.m
Normal file
39
ex1/featureNormalize.m
Normal file
|
|
@ -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
|
||||||
33
ex1/gradientDescent.m
Normal file
33
ex1/gradientDescent.m
Normal file
|
|
@ -0,0 +1,33 @@
|
||||||
|
function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
|
||||||
|
%GRADIENTDESCENT Performs gradient descent to learn theta
|
||||||
|
% theta = GRADIENTDESENT(X, y, theta, alpha, num_iters) updates theta by
|
||||||
|
% taking num_iters gradient steps with learning rate alpha
|
||||||
|
|
||||||
|
% Initialize some useful values
|
||||||
|
m = length(y); % number of training examples
|
||||||
|
J_history = zeros(num_iters, 1);
|
||||||
|
|
||||||
|
for iter = 1:num_iters
|
||||||
|
|
||||||
|
% ====================== YOUR CODE HERE ======================
|
||||||
|
% Instructions: Perform a single gradient step on the parameter vector
|
||||||
|
% theta.
|
||||||
|
%
|
||||||
|
% Hint: While debugging, it can be useful to print out the values
|
||||||
|
% of the cost function (computeCost) and gradient here.
|
||||||
|
%
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% ============================================================
|
||||||
|
|
||||||
|
% Save the cost J in every iteration
|
||||||
|
J_history(iter) = computeCost(X, y, theta);
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
end
|
||||||
37
ex1/gradientDescentMulti.m
Normal file
37
ex1/gradientDescentMulti.m
Normal file
|
|
@ -0,0 +1,37 @@
|
||||||
|
function [theta, J_history] = gradientDescentMulti(X, y, theta, alpha, num_iters)
|
||||||
|
%GRADIENTDESCENTMULTI Performs gradient descent to learn theta
|
||||||
|
% theta = GRADIENTDESCENTMULTI(x, y, theta, alpha, num_iters) updates theta by
|
||||||
|
% taking num_iters gradient steps with learning rate alpha
|
||||||
|
|
||||||
|
% Initialize some useful values
|
||||||
|
m = length(y); % number of training examples
|
||||||
|
J_history = zeros(num_iters, 1);
|
||||||
|
|
||||||
|
for iter = 1:num_iters
|
||||||
|
|
||||||
|
% ====================== YOUR CODE HERE ======================
|
||||||
|
% Instructions: Perform a single gradient step on the parameter vector
|
||||||
|
% theta.
|
||||||
|
%
|
||||||
|
% Hint: While debugging, it can be useful to print out the values
|
||||||
|
% of the cost function (computeCostMulti) and gradient here.
|
||||||
|
%
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% ============================================================
|
||||||
|
|
||||||
|
% Save the cost J in every iteration
|
||||||
|
J_history(iter) = computeCostMulti(X, y, theta);
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
end
|
||||||
23
ex1/normalEqn.m
Normal file
23
ex1/normalEqn.m
Normal file
|
|
@ -0,0 +1,23 @@
|
||||||
|
function [theta] = normalEqn(X, y)
|
||||||
|
%NORMALEQN Computes the closed-form solution to linear regression
|
||||||
|
% NORMALEQN(X,y) computes the closed-form solution to linear
|
||||||
|
% regression using the normal equations.
|
||||||
|
|
||||||
|
theta = zeros(size(X, 2), 1);
|
||||||
|
|
||||||
|
% ====================== YOUR CODE HERE ======================
|
||||||
|
% Instructions: Complete the code to compute the closed form solution
|
||||||
|
% to linear regression and put the result in theta.
|
||||||
|
%
|
||||||
|
|
||||||
|
% ---------------------- Sample Solution ----------------------
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% -------------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
|
% ============================================================
|
||||||
|
|
||||||
|
end
|
||||||
26
ex1/plotData.m
Normal file
26
ex1/plotData.m
Normal file
|
|
@ -0,0 +1,26 @@
|
||||||
|
function plotData(x, y)
|
||||||
|
%PLOTDATA Plots the data points x and y into a new figure
|
||||||
|
% PLOTDATA(x,y) plots the data points and gives the figure axes labels of
|
||||||
|
% population and profit.
|
||||||
|
|
||||||
|
% ====================== YOUR CODE HERE ======================
|
||||||
|
% Instructions: Plot the training data into a figure using the
|
||||||
|
% "figure" and "plot" commands. Set the axes labels using
|
||||||
|
% the "xlabel" and "ylabel" commands. Assume the
|
||||||
|
% population and revenue data have been passed in
|
||||||
|
% as the x and y arguments of this function.
|
||||||
|
%
|
||||||
|
% Hint: You can use the 'rx' option with plot to have the markers
|
||||||
|
% appear as red crosses. Furthermore, you can make the
|
||||||
|
% markers larger by using plot(..., 'rx', 'MarkerSize', 10);
|
||||||
|
|
||||||
|
figure; % open a new figure window
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% ============================================================
|
||||||
|
|
||||||
|
end
|
||||||
577
ex1/submit.m
Normal file
577
ex1/submit.m
Normal file
|
|
@ -0,0 +1,577 @@
|
||||||
|
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
|
||||||
20
ex1/submitWeb.m
Normal file
20
ex1/submitWeb.m
Normal file
|
|
@ -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
|
||||||
|
|
||||||
21
ex1/warmUpExercise.m
Normal file
21
ex1/warmUpExercise.m
Normal file
|
|
@ -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
|
||||||
Reference in a new issue