Add exercise 8
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function checkCostFunction(lambda)
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%CHECKCOSTFUNCTION Creates a collaborative filering problem
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%to check your cost function and gradients
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% CHECKCOSTFUNCTION(lambda) Creates a collaborative filering problem
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% to check your cost function and gradients, it will output the
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% analytical gradients produced by your code and the numerical gradients
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% (computed using computeNumericalGradient). These two gradient
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% computations should result in very similar values.
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% Set lambda
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if ~exist('lambda', 'var') || isempty(lambda)
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lambda = 0;
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end
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%% Create small problem
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X_t = rand(4, 3);
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Theta_t = rand(5, 3);
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% Zap out most entries
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Y = X_t * Theta_t';
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Y(rand(size(Y)) > 0.5) = 0;
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R = zeros(size(Y));
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R(Y ~= 0) = 1;
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%% Run Gradient Checking
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X = randn(size(X_t));
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Theta = randn(size(Theta_t));
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num_users = size(Y, 2);
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num_movies = size(Y, 1);
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num_features = size(Theta_t, 2);
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numgrad = computeNumericalGradient( ...
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@(t) cofiCostFunc(t, Y, R, num_users, num_movies, ...
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num_features, lambda), [X(:); Theta(:)]);
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[cost, grad] = cofiCostFunc([X(:); Theta(:)], Y, R, num_users, ...
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num_movies, num_features, lambda);
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disp([numgrad grad]);
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fprintf(['The above two columns you get should be very similar.\n' ...
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'(Left-Your Numerical Gradient, Right-Analytical Gradient)\n\n']);
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diff = norm(numgrad-grad)/norm(numgrad+grad);
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fprintf(['If your backpropagation implementation is correct, then \n' ...
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'the relative difference will be small (less than 1e-9). \n' ...
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'\nRelative Difference: %g\n'], diff);
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end
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function [J, grad] = cofiCostFunc(params, Y, R, num_users, num_movies, ...
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num_features, lambda)
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%COFICOSTFUNC Collaborative filtering cost function
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% [J, grad] = COFICOSTFUNC(params, Y, R, num_users, num_movies, ...
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% num_features, lambda) returns the cost and gradient for the
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% collaborative filtering problem.
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%
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% Unfold the U and W matrices from params
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X = reshape(params(1:num_movies*num_features), num_movies, num_features);
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Theta = reshape(params(num_movies*num_features+1:end), ...
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num_users, num_features);
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% You need to return the following values correctly
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J = 0;
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X_grad = zeros(size(X));
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Theta_grad = zeros(size(Theta));
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% ====================== YOUR CODE HERE ======================
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% Instructions: Compute the cost function and gradient for collaborative
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% filtering. Concretely, you should first implement the cost
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% function (without regularization) and make sure it is
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% matches our costs. After that, you should implement the
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% gradient and use the checkCostFunction routine to check
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% that the gradient is correct. Finally, you should implement
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% regularization.
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%
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% Notes: X - num_movies x num_features matrix of movie features
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% Theta - num_users x num_features matrix of user features
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% Y - num_movies x num_users matrix of user ratings of movies
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% R - num_movies x num_users matrix, where R(i, j) = 1 if the
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% i-th movie was rated by the j-th user
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%
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% You should set the following variables correctly:
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%
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% X_grad - num_movies x num_features matrix, containing the
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% partial derivatives w.r.t. to each element of X
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% Theta_grad - num_users x num_features matrix, containing the
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% partial derivatives w.r.t. to each element of Theta
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%
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% =============================================================
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grad = [X_grad(:); Theta_grad(:)];
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end
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function numgrad = computeNumericalGradient(J, theta)
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%COMPUTENUMERICALGRADIENT Computes the gradient using "finite differences"
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%and gives us a numerical estimate of the gradient.
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% numgrad = COMPUTENUMERICALGRADIENT(J, theta) computes the numerical
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% gradient of the function J around theta. Calling y = J(theta) should
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% return the function value at theta.
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% Notes: The following code implements numerical gradient checking, and
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% returns the numerical gradient.It sets numgrad(i) to (a numerical
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% approximation of) the partial derivative of J with respect to the
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% i-th input argument, evaluated at theta. (i.e., numgrad(i) should
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% be the (approximately) the partial derivative of J with respect
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% to theta(i).)
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%
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numgrad = zeros(size(theta));
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perturb = zeros(size(theta));
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e = 1e-4;
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for p = 1:numel(theta)
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% Set perturbation vector
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perturb(p) = e;
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loss1 = J(theta - perturb);
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loss2 = J(theta + perturb);
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% Compute Numerical Gradient
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numgrad(p) = (loss2 - loss1) / (2*e);
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perturb(p) = 0;
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end
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end
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function [mu sigma2] = estimateGaussian(X)
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%ESTIMATEGAUSSIAN This function estimates the parameters of a
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%Gaussian distribution using the data in X
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% [mu sigma2] = estimateGaussian(X),
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% The input X is the dataset with each n-dimensional data point in one row
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% The output is an n-dimensional vector mu, the mean of the data set
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% and the variances sigma^2, an n x 1 vector
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%
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% Useful variables
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[m, n] = size(X);
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% You should return these values correctly
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mu = zeros(n, 1);
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sigma2 = zeros(n, 1);
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% ====================== YOUR CODE HERE ======================
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% Instructions: Compute the mean of the data and the variances
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% In particular, mu(i) should contain the mean of
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% the data for the i-th feature and sigma2(i)
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% should contain variance of the i-th feature.
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%
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% =============================================================
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end
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@ -0,0 +1,123 @@
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%% Machine Learning Online Class
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% Exercise 8 | Anomaly Detection and Collaborative Filtering
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%
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% Instructions
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% ------------
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%
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% This file contains code that helps you get started on the
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% exercise. You will need to complete the following functions:
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%
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% estimateGaussian.m
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% selectThreshold.m
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% cofiCostFunc.m
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%
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% For this exercise, you will not need to change any code in this file,
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% or any other files other than those mentioned above.
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%
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%% Initialization
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clear ; close all; clc
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%% ================== Part 1: Load Example Dataset ===================
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% We start this exercise by using a small dataset that is easy to
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% visualize.
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%
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% Our example case consists of 2 network server statistics across
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% several machines: the latency and throughput of each machine.
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% This exercise will help us find possibly faulty (or very fast) machines.
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%
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fprintf('Visualizing example dataset for outlier detection.\n\n');
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% The following command loads the dataset. You should now have the
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% variables X, Xval, yval in your environment
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load('ex8data1.mat');
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% Visualize the example dataset
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plot(X(:, 1), X(:, 2), 'bx');
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axis([0 30 0 30]);
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xlabel('Latency (ms)');
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ylabel('Throughput (mb/s)');
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fprintf('Program paused. Press enter to continue.\n');
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pause
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%% ================== Part 2: Estimate the dataset statistics ===================
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% For this exercise, we assume a Gaussian distribution for the dataset.
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%
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% We first estimate the parameters of our assumed Gaussian distribution,
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% then compute the probabilities for each of the points and then visualize
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% both the overall distribution and where each of the points falls in
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% terms of that distribution.
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%
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fprintf('Visualizing Gaussian fit.\n\n');
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% Estimate my and sigma2
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[mu sigma2] = estimateGaussian(X);
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% Returns the density of the multivariate normal at each data point (row)
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% of X
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p = multivariateGaussian(X, mu, sigma2);
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% Visualize the fit
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visualizeFit(X, mu, sigma2);
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xlabel('Latency (ms)');
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ylabel('Throughput (mb/s)');
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fprintf('Program paused. Press enter to continue.\n');
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pause;
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%% ================== Part 3: Find Outliers ===================
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% Now you will find a good epsilon threshold using a cross-validation set
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% probabilities given the estimated Gaussian distribution
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%
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pval = multivariateGaussian(Xval, mu, sigma2);
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[epsilon F1] = selectThreshold(yval, pval);
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fprintf('Best epsilon found using cross-validation: %e\n', epsilon);
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fprintf('Best F1 on Cross Validation Set: %f\n', F1);
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fprintf(' (you should see a value epsilon of about 8.99e-05)\n\n');
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% Find the outliers in the training set and plot the
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outliers = find(p < epsilon);
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% Draw a red circle around those outliers
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hold on
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plot(X(outliers, 1), X(outliers, 2), 'ro', 'LineWidth', 2, 'MarkerSize', 10);
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hold off
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fprintf('Program paused. Press enter to continue.\n');
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pause;
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%% ================== Part 4: Multidimensional Outliers ===================
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% We will now use the code from the previous part and apply it to a
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% harder problem in which more features describe each datapoint and only
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% some features indicate whether a point is an outlier.
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%
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% Loads the second dataset. You should now have the
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% variables X, Xval, yval in your environment
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load('ex8data2.mat');
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% Apply the same steps to the larger dataset
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[mu sigma2] = estimateGaussian(X);
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% Training set
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p = multivariateGaussian(X, mu, sigma2);
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% Cross-validation set
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pval = multivariateGaussian(Xval, mu, sigma2);
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% Find the best threshold
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[epsilon F1] = selectThreshold(yval, pval);
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fprintf('Best epsilon found using cross-validation: %e\n', epsilon);
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fprintf('Best F1 on Cross Validation Set: %f\n', F1);
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fprintf('# Outliers found: %d\n', sum(p < epsilon));
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fprintf(' (you should see a value epsilon of about 1.38e-18)\n\n');
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pause
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%% Machine Learning Online Class
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% Exercise 8 | Anomaly Detection and Collaborative Filtering
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%
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% Instructions
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% ------------
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%
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% This file contains code that helps you get started on the
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% exercise. You will need to complete the following functions:
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%
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% estimateGaussian.m
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% selectThreshold.m
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% cofiCostFunc.m
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%
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% For this exercise, you will not need to change any code in this file,
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% or any other files other than those mentioned above.
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%
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%% =============== Part 1: Loading movie ratings dataset ================
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% You will start by loading the movie ratings dataset to understand the
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% structure of the data.
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%
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fprintf('Loading movie ratings dataset.\n\n');
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% Load data
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load ('ex8_movies.mat');
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% Y is a 1682x943 matrix, containing ratings (1-5) of 1682 movies on
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% 943 users
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%
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% R is a 1682x943 matrix, where R(i,j) = 1 if and only if user j gave a
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% rating to movie i
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% From the matrix, we can compute statistics like average rating.
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fprintf('Average rating for movie 1 (Toy Story): %f / 5\n\n', ...
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mean(Y(1, R(1, :))));
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% We can "visualize" the ratings matrix by plotting it with imagesc
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imagesc(Y);
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ylabel('Movies');
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xlabel('Users');
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fprintf('\nProgram paused. Press enter to continue.\n');
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pause;
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%% ============ Part 2: Collaborative Filtering Cost Function ===========
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% You will now implement the cost function for collaborative filtering.
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% To help you debug your cost function, we have included set of weights
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% that we trained on that. Specifically, you should complete the code in
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% cofiCostFunc.m to return J.
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% Load pre-trained weights (X, Theta, num_users, num_movies, num_features)
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load ('ex8_movieParams.mat');
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% Reduce the data set size so that this runs faster
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num_users = 4; num_movies = 5; num_features = 3;
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X = X(1:num_movies, 1:num_features);
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Theta = Theta(1:num_users, 1:num_features);
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Y = Y(1:num_movies, 1:num_users);
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R = R(1:num_movies, 1:num_users);
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% Evaluate cost function
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J = cofiCostFunc([X(:) ; Theta(:)], Y, R, num_users, num_movies, ...
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num_features, 0);
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fprintf(['Cost at loaded parameters: %f '...
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'\n(this value should be about 22.22)\n'], J);
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fprintf('\nProgram paused. Press enter to continue.\n');
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pause;
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%% ============== Part 3: Collaborative Filtering Gradient ==============
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% Once your cost function matches up with ours, you should now implement
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% the collaborative filtering gradient function. Specifically, you should
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% complete the code in cofiCostFunc.m to return the grad argument.
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%
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fprintf('\nChecking Gradients (without regularization) ... \n');
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% Check gradients by running checkNNGradients
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checkCostFunction;
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fprintf('\nProgram paused. Press enter to continue.\n');
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pause;
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%% ========= Part 4: Collaborative Filtering Cost Regularization ========
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% Now, you should implement regularization for the cost function for
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% collaborative filtering. You can implement it by adding the cost of
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% regularization to the original cost computation.
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%
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% Evaluate cost function
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J = cofiCostFunc([X(:) ; Theta(:)], Y, R, num_users, num_movies, ...
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num_features, 1.5);
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fprintf(['Cost at loaded parameters (lambda = 1.5): %f '...
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'\n(this value should be about 31.34)\n'], J);
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fprintf('\nProgram paused. Press enter to continue.\n');
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pause;
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%% ======= Part 5: Collaborative Filtering Gradient Regularization ======
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% Once your cost matches up with ours, you should proceed to implement
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% regularization for the gradient.
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%
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%
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fprintf('\nChecking Gradients (with regularization) ... \n');
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% Check gradients by running checkNNGradients
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checkCostFunction(1.5);
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fprintf('\nProgram paused. Press enter to continue.\n');
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pause;
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%% ============== Part 6: Entering ratings for a new user ===============
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% Before we will train the collaborative filtering model, we will first
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% add ratings that correspond to a new user that we just observed. This
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% part of the code will also allow you to put in your own ratings for the
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% movies in our dataset!
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%
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movieList = loadMovieList();
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% Initialize my ratings
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my_ratings = zeros(1682, 1);
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% Check the file movie_idx.txt for id of each movie in our dataset
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% For example, Toy Story (1995) has ID 1, so to rate it "4", you can set
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my_ratings(1) = 4;
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% Or suppose did not enjoy Silence of the Lambs (1991), you can set
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my_ratings(98) = 2;
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% We have selected a few movies we liked / did not like and the ratings we
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% gave are as follows:
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my_ratings(7) = 3;
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my_ratings(12)= 5;
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my_ratings(54) = 4;
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my_ratings(64)= 5;
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my_ratings(66)= 3;
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my_ratings(69) = 5;
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my_ratings(183) = 4;
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my_ratings(226) = 5;
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my_ratings(355)= 5;
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fprintf('\n\nNew user ratings:\n');
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for i = 1:length(my_ratings)
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if my_ratings(i) > 0
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fprintf('Rated %d for %s\n', my_ratings(i), ...
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movieList{i});
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end
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end
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fprintf('\nProgram paused. Press enter to continue.\n');
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pause;
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%% ================== Part 7: Learning Movie Ratings ====================
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% Now, you will train the collaborative filtering model on a movie rating
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% dataset of 1682 movies and 943 users
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%
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fprintf('\nTraining collaborative filtering...\n');
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% Load data
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load('ex8_movies.mat');
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% Y is a 1682x943 matrix, containing ratings (1-5) of 1682 movies by
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% 943 users
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%
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% R is a 1682x943 matrix, where R(i,j) = 1 if and only if user j gave a
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% rating to movie i
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% Add our own ratings to the data matrix
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Y = [my_ratings Y];
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R = [(my_ratings ~= 0) R];
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% Normalize Ratings
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[Ynorm, Ymean] = normalizeRatings(Y, R);
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% Useful Values
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num_users = size(Y, 2);
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num_movies = size(Y, 1);
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num_features = 10;
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% Set Initial Parameters (Theta, X)
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X = randn(num_movies, num_features);
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Theta = randn(num_users, num_features);
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initial_parameters = [X(:); Theta(:)];
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% Set options for fmincg
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options = optimset('GradObj', 'on', 'MaxIter', 100);
|
||||
|
||||
% Set Regularization
|
||||
lambda = 10;
|
||||
theta = fmincg (@(t)(cofiCostFunc(t, Y, R, num_users, num_movies, ...
|
||||
num_features, lambda)), ...
|
||||
initial_parameters, options);
|
||||
|
||||
% Unfold the returned theta back into U and W
|
||||
X = reshape(theta(1:num_movies*num_features), num_movies, num_features);
|
||||
Theta = reshape(theta(num_movies*num_features+1:end), ...
|
||||
num_users, num_features);
|
||||
|
||||
fprintf('Recommender system learning completed.\n');
|
||||
|
||||
fprintf('\nProgram paused. Press enter to continue.\n');
|
||||
pause;
|
||||
|
||||
%% ================== Part 8: Recommendation for you ====================
|
||||
% After training the model, you can now make recommendations by computing
|
||||
% the predictions matrix.
|
||||
%
|
||||
|
||||
p = X * Theta';
|
||||
my_predictions = p(:,1) + Ymean;
|
||||
|
||||
movieList = loadMovieList();
|
||||
|
||||
[r, ix] = sort(my_predictions, 'descend');
|
||||
fprintf('\nTop recommendations for you:\n');
|
||||
for i=1:10
|
||||
j = ix(i);
|
||||
fprintf('Predicting rating %.1f for movie %s\n', my_predictions(j), ...
|
||||
movieList{j});
|
||||
end
|
||||
|
||||
fprintf('\n\nOriginal ratings provided:\n');
|
||||
for i = 1:length(my_ratings)
|
||||
if my_ratings(i) > 0
|
||||
fprintf('Rated %d for %s\n', my_ratings(i), ...
|
||||
movieList{i});
|
||||
end
|
||||
end
|
||||
Binary file not shown.
Binary file not shown.
Binary file not shown.
Binary file not shown.
@ -0,0 +1,175 @@
|
||||
function [X, fX, i] = fmincg(f, X, options, P1, P2, P3, P4, P5)
|
||||
% Minimize a continuous differentialble multivariate function. Starting point
|
||||
% is given by "X" (D by 1), and the function named in the string "f", must
|
||||
% return a function value and a vector of partial derivatives. The Polack-
|
||||
% Ribiere flavour of conjugate gradients is used to compute search directions,
|
||||
% and a line search using quadratic and cubic polynomial approximations and the
|
||||
% Wolfe-Powell stopping criteria is used together with the slope ratio method
|
||||
% for guessing initial step sizes. Additionally a bunch of checks are made to
|
||||
% make sure that exploration is taking place and that extrapolation will not
|
||||
% be unboundedly large. The "length" gives the length of the run: if it is
|
||||
% positive, it gives the maximum number of line searches, if negative its
|
||||
% absolute gives the maximum allowed number of function evaluations. You can
|
||||
% (optionally) give "length" a second component, which will indicate the
|
||||
% reduction in function value to be expected in the first line-search (defaults
|
||||
% to 1.0). The function returns when either its length is up, or if no further
|
||||
% progress can be made (ie, we are at a minimum, or so close that due to
|
||||
% numerical problems, we cannot get any closer). If the function terminates
|
||||
% within a few iterations, it could be an indication that the function value
|
||||
% and derivatives are not consistent (ie, there may be a bug in the
|
||||
% implementation of your "f" function). The function returns the found
|
||||
% solution "X", a vector of function values "fX" indicating the progress made
|
||||
% and "i" the number of iterations (line searches or function evaluations,
|
||||
% depending on the sign of "length") used.
|
||||
%
|
||||
% Usage: [X, fX, i] = fmincg(f, X, options, P1, P2, P3, P4, P5)
|
||||
%
|
||||
% See also: checkgrad
|
||||
%
|
||||
% Copyright (C) 2001 and 2002 by Carl Edward Rasmussen. Date 2002-02-13
|
||||
%
|
||||
%
|
||||
% (C) Copyright 1999, 2000 & 2001, Carl Edward Rasmussen
|
||||
%
|
||||
% Permission is granted for anyone to copy, use, or modify these
|
||||
% programs and accompanying documents for purposes of research or
|
||||
% education, provided this copyright notice is retained, and note is
|
||||
% made of any changes that have been made.
|
||||
%
|
||||
% These programs and documents are distributed without any warranty,
|
||||
% express or implied. As the programs were written for research
|
||||
% purposes only, they have not been tested to the degree that would be
|
||||
% advisable in any important application. All use of these programs is
|
||||
% entirely at the user's own risk.
|
||||
%
|
||||
% [ml-class] Changes Made:
|
||||
% 1) Function name and argument specifications
|
||||
% 2) Output display
|
||||
%
|
||||
|
||||
% Read options
|
||||
if exist('options', 'var') && ~isempty(options) && isfield(options, 'MaxIter')
|
||||
length = options.MaxIter;
|
||||
else
|
||||
length = 100;
|
||||
end
|
||||
|
||||
|
||||
RHO = 0.01; % a bunch of constants for line searches
|
||||
SIG = 0.5; % RHO and SIG are the constants in the Wolfe-Powell conditions
|
||||
INT = 0.1; % don't reevaluate within 0.1 of the limit of the current bracket
|
||||
EXT = 3.0; % extrapolate maximum 3 times the current bracket
|
||||
MAX = 20; % max 20 function evaluations per line search
|
||||
RATIO = 100; % maximum allowed slope ratio
|
||||
|
||||
argstr = ['feval(f, X']; % compose string used to call function
|
||||
for i = 1:(nargin - 3)
|
||||
argstr = [argstr, ',P', int2str(i)];
|
||||
end
|
||||
argstr = [argstr, ')'];
|
||||
|
||||
if max(size(length)) == 2, red=length(2); length=length(1); else red=1; end
|
||||
S=['Iteration '];
|
||||
|
||||
i = 0; % zero the run length counter
|
||||
ls_failed = 0; % no previous line search has failed
|
||||
fX = [];
|
||||
[f1 df1] = eval(argstr); % get function value and gradient
|
||||
i = i + (length<0); % count epochs?!
|
||||
s = -df1; % search direction is steepest
|
||||
d1 = -s'*s; % this is the slope
|
||||
z1 = red/(1-d1); % initial step is red/(|s|+1)
|
||||
|
||||
while i < abs(length) % while not finished
|
||||
i = i + (length>0); % count iterations?!
|
||||
|
||||
X0 = X; f0 = f1; df0 = df1; % make a copy of current values
|
||||
X = X + z1*s; % begin line search
|
||||
[f2 df2] = eval(argstr);
|
||||
i = i + (length<0); % count epochs?!
|
||||
d2 = df2'*s;
|
||||
f3 = f1; d3 = d1; z3 = -z1; % initialize point 3 equal to point 1
|
||||
if length>0, M = MAX; else M = min(MAX, -length-i); end
|
||||
success = 0; limit = -1; % initialize quanteties
|
||||
while 1
|
||||
while ((f2 > f1+z1*RHO*d1) | (d2 > -SIG*d1)) & (M > 0)
|
||||
limit = z1; % tighten the bracket
|
||||
if f2 > f1
|
||||
z2 = z3 - (0.5*d3*z3*z3)/(d3*z3+f2-f3); % quadratic fit
|
||||
else
|
||||
A = 6*(f2-f3)/z3+3*(d2+d3); % cubic fit
|
||||
B = 3*(f3-f2)-z3*(d3+2*d2);
|
||||
z2 = (sqrt(B*B-A*d2*z3*z3)-B)/A; % numerical error possible - ok!
|
||||
end
|
||||
if isnan(z2) | isinf(z2)
|
||||
z2 = z3/2; % if we had a numerical problem then bisect
|
||||
end
|
||||
z2 = max(min(z2, INT*z3),(1-INT)*z3); % don't accept too close to limits
|
||||
z1 = z1 + z2; % update the step
|
||||
X = X + z2*s;
|
||||
[f2 df2] = eval(argstr);
|
||||
M = M - 1; i = i + (length<0); % count epochs?!
|
||||
d2 = df2'*s;
|
||||
z3 = z3-z2; % z3 is now relative to the location of z2
|
||||
end
|
||||
if f2 > f1+z1*RHO*d1 | d2 > -SIG*d1
|
||||
break; % this is a failure
|
||||
elseif d2 > SIG*d1
|
||||
success = 1; break; % success
|
||||
elseif M == 0
|
||||
break; % failure
|
||||
end
|
||||
A = 6*(f2-f3)/z3+3*(d2+d3); % make cubic extrapolation
|
||||
B = 3*(f3-f2)-z3*(d3+2*d2);
|
||||
z2 = -d2*z3*z3/(B+sqrt(B*B-A*d2*z3*z3)); % num. error possible - ok!
|
||||
if ~isreal(z2) | isnan(z2) | isinf(z2) | z2 < 0 % num prob or wrong sign?
|
||||
if limit < -0.5 % if we have no upper limit
|
||||
z2 = z1 * (EXT-1); % the extrapolate the maximum amount
|
||||
else
|
||||
z2 = (limit-z1)/2; % otherwise bisect
|
||||
end
|
||||
elseif (limit > -0.5) & (z2+z1 > limit) % extraplation beyond max?
|
||||
z2 = (limit-z1)/2; % bisect
|
||||
elseif (limit < -0.5) & (z2+z1 > z1*EXT) % extrapolation beyond limit
|
||||
z2 = z1*(EXT-1.0); % set to extrapolation limit
|
||||
elseif z2 < -z3*INT
|
||||
z2 = -z3*INT;
|
||||
elseif (limit > -0.5) & (z2 < (limit-z1)*(1.0-INT)) % too close to limit?
|
||||
z2 = (limit-z1)*(1.0-INT);
|
||||
end
|
||||
f3 = f2; d3 = d2; z3 = -z2; % set point 3 equal to point 2
|
||||
z1 = z1 + z2; X = X + z2*s; % update current estimates
|
||||
[f2 df2] = eval(argstr);
|
||||
M = M - 1; i = i + (length<0); % count epochs?!
|
||||
d2 = df2'*s;
|
||||
end % end of line search
|
||||
|
||||
if success % if line search succeeded
|
||||
f1 = f2; fX = [fX' f1]';
|
||||
fprintf('%s %4i | Cost: %4.6e\r', S, i, f1);
|
||||
s = (df2'*df2-df1'*df2)/(df1'*df1)*s - df2; % Polack-Ribiere direction
|
||||
tmp = df1; df1 = df2; df2 = tmp; % swap derivatives
|
||||
d2 = df1'*s;
|
||||
if d2 > 0 % new slope must be negative
|
||||
s = -df1; % otherwise use steepest direction
|
||||
d2 = -s'*s;
|
||||
end
|
||||
z1 = z1 * min(RATIO, d1/(d2-realmin)); % slope ratio but max RATIO
|
||||
d1 = d2;
|
||||
ls_failed = 0; % this line search did not fail
|
||||
else
|
||||
X = X0; f1 = f0; df1 = df0; % restore point from before failed line search
|
||||
if ls_failed | i > abs(length) % line search failed twice in a row
|
||||
break; % or we ran out of time, so we give up
|
||||
end
|
||||
tmp = df1; df1 = df2; df2 = tmp; % swap derivatives
|
||||
s = -df1; % try steepest
|
||||
d1 = -s'*s;
|
||||
z1 = 1/(1-d1);
|
||||
ls_failed = 1; % this line search failed
|
||||
end
|
||||
if exist('OCTAVE_VERSION')
|
||||
fflush(stdout);
|
||||
end
|
||||
end
|
||||
fprintf('\n');
|
||||
@ -0,0 +1,25 @@
|
||||
function movieList = loadMovieList()
|
||||
%GETMOVIELIST reads the fixed movie list in movie.txt and returns a
|
||||
%cell array of the words
|
||||
% movieList = GETMOVIELIST() reads the fixed movie list in movie.txt
|
||||
% and returns a cell array of the words in movieList.
|
||||
|
||||
|
||||
%% Read the fixed movieulary list
|
||||
fid = fopen('movie_ids.txt');
|
||||
|
||||
% Store all movies in cell array movie{}
|
||||
n = 1682; % Total number of movies
|
||||
|
||||
movieList = cell(n, 1);
|
||||
for i = 1:n
|
||||
% Read line
|
||||
line = fgets(fid);
|
||||
% Word Index (can ignore since it will be = i)
|
||||
[idx, movieName] = strtok(line, ' ');
|
||||
% Actual Word
|
||||
movieList{i} = strtrim(movieName);
|
||||
end
|
||||
fclose(fid);
|
||||
|
||||
end
|
||||
File diff suppressed because it is too large
Load Diff
@ -0,0 +1,22 @@
|
||||
function p = multivariateGaussian(X, mu, Sigma2)
|
||||
%MULTIVARIATEGAUSSIAN Computes the probability density function of the
|
||||
%multivariate gaussian distribution.
|
||||
% p = MULTIVARIATEGAUSSIAN(X, mu, Sigma2) Computes the probability
|
||||
% density function of the examples X under the multivariate gaussian
|
||||
% distribution with parameters mu and Sigma2. If Sigma2 is a matrix, it is
|
||||
% treated as the covariance matrix. If Sigma2 is a vector, it is treated
|
||||
% as the \sigma^2 values of the variances in each dimension (a diagonal
|
||||
% covariance matrix)
|
||||
%
|
||||
|
||||
k = length(mu);
|
||||
|
||||
if (size(Sigma2, 2) == 1) || (size(Sigma2, 1) == 1)
|
||||
Sigma2 = diag(Sigma2);
|
||||
end
|
||||
|
||||
X = bsxfun(@minus, X, mu(:)');
|
||||
p = (2 * pi) ^ (- k / 2) * det(Sigma2) ^ (-0.5) * ...
|
||||
exp(-0.5 * sum(bsxfun(@times, X * pinv(Sigma2), X), 2));
|
||||
|
||||
end
|
||||
@ -0,0 +1,17 @@
|
||||
function [Ynorm, Ymean] = normalizeRatings(Y, R)
|
||||
%NORMALIZERATINGS Preprocess data by subtracting mean rating for every
|
||||
%movie (every row)
|
||||
% [Ynorm, Ymean] = NORMALIZERATINGS(Y, R) normalized Y so that each movie
|
||||
% has a rating of 0 on average, and returns the mean rating in Ymean.
|
||||
%
|
||||
|
||||
[m, n] = size(Y);
|
||||
Ymean = zeros(m, 1);
|
||||
Ynorm = zeros(size(Y));
|
||||
for i = 1:m
|
||||
idx = find(R(i, :) == 1);
|
||||
Ymean(i) = mean(Y(i, idx));
|
||||
Ynorm(i, idx) = Y(i, idx) - Ymean(i);
|
||||
end
|
||||
|
||||
end
|
||||
@ -0,0 +1,46 @@
|
||||
function [bestEpsilon bestF1] = selectThreshold(yval, pval)
|
||||
%SELECTTHRESHOLD Find the best threshold (epsilon) to use for selecting
|
||||
%outliers
|
||||
% [bestEpsilon bestF1] = SELECTTHRESHOLD(yval, pval) finds the best
|
||||
% threshold to use for selecting outliers based on the results from a
|
||||
% validation set (pval) and the ground truth (yval).
|
||||
%
|
||||
|
||||
bestEpsilon = 0;
|
||||
bestF1 = 0;
|
||||
F1 = 0;
|
||||
|
||||
stepsize = (max(pval) - min(pval)) / 1000;
|
||||
for epsilon = min(pval):stepsize:max(pval)
|
||||
|
||||
% ====================== YOUR CODE HERE ======================
|
||||
% Instructions: Compute the F1 score of choosing epsilon as the
|
||||
% threshold and place the value in F1. The code at the
|
||||
% end of the loop will compare the F1 score for this
|
||||
% choice of epsilon and set it to be the best epsilon if
|
||||
% it is better than the current choice of epsilon.
|
||||
%
|
||||
% Note: You can use predictions = (pval < epsilon) to get a binary vector
|
||||
% of 0's and 1's of the outlier predictions
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
% =============================================================
|
||||
|
||||
if F1 > bestF1
|
||||
bestF1 = F1;
|
||||
bestEpsilon = epsilon;
|
||||
end
|
||||
end
|
||||
|
||||
end
|
||||
@ -0,0 +1,588 @@
|
||||
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 = '8';
|
||||
end
|
||||
|
||||
function [partNames] = validParts()
|
||||
partNames = { 'Estimate Gaussian Parameters', ...
|
||||
'Select Threshold' ...
|
||||
'Collaborative Filtering Cost', ...
|
||||
'Collaborative Filtering Gradient', ...
|
||||
'Regularized Cost', ...
|
||||
'Regularized Gradient' ...
|
||||
};
|
||||
end
|
||||
|
||||
function srcs = sources()
|
||||
% Separated by part
|
||||
srcs = { { 'estimateGaussian.m' }, ...
|
||||
{ 'selectThreshold.m' }, ...
|
||||
{ 'cofiCostFunc.m' }, ...
|
||||
{ 'cofiCostFunc.m' }, ...
|
||||
{ 'cofiCostFunc.m' }, ...
|
||||
{ 'cofiCostFunc.m' }, ...
|
||||
};
|
||||
end
|
||||
|
||||
function out = output(partId, auxstring)
|
||||
% Random Test Cases
|
||||
n_u = 3; n_m = 4; n = 5;
|
||||
X = reshape(sin(1:n_m*n), n_m, n);
|
||||
Theta = reshape(cos(1:n_u*n), n_u, n);
|
||||
Y = reshape(sin(1:2:2*n_m*n_u), n_m, n_u);
|
||||
R = Y > 0.5;
|
||||
pval = [abs(Y(:)) ; 0.001; 1];
|
||||
yval = [R(:) ; 1; 0];
|
||||
params = [X(:); Theta(:)];
|
||||
if partId == 1
|
||||
[mu sigma2] = estimateGaussian(X);
|
||||
out = sprintf('%0.5f ', [mu(:); sigma2(:)]);
|
||||
elseif partId == 2
|
||||
[bestEpsilon bestF1] = selectThreshold(yval, pval);
|
||||
out = sprintf('%0.5f ', [bestEpsilon(:); bestF1(:)]);
|
||||
elseif partId == 3
|
||||
[J] = cofiCostFunc(params, Y, R, n_u, n_m, ...
|
||||
n, 0);
|
||||
out = sprintf('%0.5f ', J(:));
|
||||
elseif partId == 4
|
||||
[J, grad] = cofiCostFunc(params, Y, R, n_u, n_m, ...
|
||||
n, 0);
|
||||
out = sprintf('%0.5f ', grad(:));
|
||||
elseif partId == 5
|
||||
[J] = cofiCostFunc(params, Y, R, n_u, n_m, ...
|
||||
n, 1.5);
|
||||
out = sprintf('%0.5f ', J(:));
|
||||
elseif partId == 6
|
||||
[J, grad] = cofiCostFunc(params, Y, R, n_u, n_m, ...
|
||||
n, 1.5);
|
||||
out = sprintf('%0.5f ', grad(:));
|
||||
end
|
||||
end
|
||||
|
||||
% ====================== SERVER CONFIGURATION ===========================
|
||||
|
||||
% ***************** REMOVE -staging WHEN YOU DEPLOY *********************
|
||||
function url = site_url()
|
||||
url = 'http://class.coursera.org/ml-007';
|
||||
end
|
||||
|
||||
function url = challenge_url()
|
||||
url = [site_url() '/assignment/challenge'];
|
||||
end
|
||||
|
||||
function url = submit_url()
|
||||
url = [site_url() '/assignment/submit'];
|
||||
end
|
||||
|
||||
% ========================= CHALLENGE HELPERS =========================
|
||||
|
||||
function src = source(partId)
|
||||
src = '';
|
||||
src_files = sources();
|
||||
if partId <= numel(src_files)
|
||||
flist = src_files{partId};
|
||||
for i = 1:numel(flist)
|
||||
fid = fopen(flist{i});
|
||||
if (fid == -1)
|
||||
error('Error opening %s (is it missing?)', flist{i});
|
||||
end
|
||||
line = fgets(fid);
|
||||
while ischar(line)
|
||||
src = [src line];
|
||||
line = fgets(fid);
|
||||
end
|
||||
fclose(fid);
|
||||
src = [src '||||||||'];
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
function ret = isValidPartId(partId)
|
||||
partNames = validParts();
|
||||
ret = (~isempty(partId)) && (partId >= 1) && (partId <= numel(partNames) + 1);
|
||||
end
|
||||
|
||||
function partId = promptPart()
|
||||
fprintf('== Select which part(s) to submit:\n');
|
||||
partNames = validParts();
|
||||
srcFiles = sources();
|
||||
for i = 1:numel(partNames)
|
||||
fprintf('== %d) %s [', i, partNames{i});
|
||||
fprintf(' %s ', srcFiles{i}{:});
|
||||
fprintf(']\n');
|
||||
end
|
||||
fprintf('== %d) All of the above \n==\nEnter your choice [1-%d]: ', ...
|
||||
numel(partNames) + 1, numel(partNames) + 1);
|
||||
selPart = input('', 's');
|
||||
partId = str2num(selPart);
|
||||
if ~isValidPartId(partId)
|
||||
partId = -1;
|
||||
end
|
||||
end
|
||||
|
||||
function [email,ch,signature,auxstring] = getChallenge(email, part)
|
||||
str = urlread(challenge_url(), 'post', {'email_address', email, 'assignment_part_sid', [homework_id() '-' num2str(part)], 'response_encoding', 'delim'});
|
||||
|
||||
str = strtrim(str);
|
||||
r = struct;
|
||||
while(numel(str) > 0)
|
||||
[f, str] = strtok (str, '|');
|
||||
[v, str] = strtok (str, '|');
|
||||
r = setfield(r, f, v);
|
||||
end
|
||||
|
||||
email = getfield(r, 'email_address');
|
||||
ch = getfield(r, 'challenge_key');
|
||||
signature = getfield(r, 'state');
|
||||
auxstring = getfield(r, 'challenge_aux_data');
|
||||
end
|
||||
|
||||
function [result, str] = submitSolutionWeb(email, part, output, source)
|
||||
|
||||
result = ['{"assignment_part_sid":"' base64encode([homework_id() '-' num2str(part)], '') '",' ...
|
||||
'"email_address":"' base64encode(email, '') '",' ...
|
||||
'"submission":"' base64encode(output, '') '",' ...
|
||||
'"submission_aux":"' base64encode(source, '') '"' ...
|
||||
'}'];
|
||||
str = 'Web-submission';
|
||||
end
|
||||
|
||||
function [result, str] = submitSolution(email, ch_resp, part, output, ...
|
||||
source, signature)
|
||||
|
||||
params = {'assignment_part_sid', [homework_id() '-' num2str(part)], ...
|
||||
'email_address', email, ...
|
||||
'submission', base64encode(output, ''), ...
|
||||
'submission_aux', base64encode(source, ''), ...
|
||||
'challenge_response', ch_resp, ...
|
||||
'state', signature};
|
||||
|
||||
str = urlread(submit_url(), 'post', params);
|
||||
|
||||
% Parse str to read for success / failure
|
||||
result = 0;
|
||||
|
||||
end
|
||||
|
||||
% =========================== LOGIN HELPERS ===========================
|
||||
|
||||
function [login password] = loginPrompt()
|
||||
% Prompt for password
|
||||
[login password] = basicPrompt();
|
||||
|
||||
if isempty(login) || isempty(password)
|
||||
login = []; password = [];
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
function [login password] = basicPrompt()
|
||||
login = input('Login (Email address): ', 's');
|
||||
password = input('Password: ', 's');
|
||||
end
|
||||
|
||||
function [login password] = quickLogin(login,password)
|
||||
disp(['You are currently logged in as ' login '.']);
|
||||
cont_token = input('Is this you? (y/n - type n to reenter password)','s');
|
||||
if(isempty(cont_token) || cont_token(1)=='Y'||cont_token(1)=='y')
|
||||
return;
|
||||
else
|
||||
[login password] = loginPrompt();
|
||||
end
|
||||
end
|
||||
|
||||
function [str] = challengeResponse(email, passwd, challenge)
|
||||
str = sha1([challenge passwd]);
|
||||
end
|
||||
|
||||
% =============================== SHA-1 ================================
|
||||
|
||||
function hash = sha1(str)
|
||||
|
||||
% Initialize variables
|
||||
h0 = uint32(1732584193);
|
||||
h1 = uint32(4023233417);
|
||||
h2 = uint32(2562383102);
|
||||
h3 = uint32(271733878);
|
||||
h4 = uint32(3285377520);
|
||||
|
||||
% Convert to word array
|
||||
strlen = numel(str);
|
||||
|
||||
% Break string into chars and append the bit 1 to the message
|
||||
mC = [double(str) 128];
|
||||
mC = [mC zeros(1, 4-mod(numel(mC), 4), 'uint8')];
|
||||
|
||||
numB = strlen * 8;
|
||||
if exist('idivide')
|
||||
numC = idivide(uint32(numB + 65), 512, 'ceil');
|
||||
else
|
||||
numC = ceil(double(numB + 65)/512);
|
||||
end
|
||||
numW = numC * 16;
|
||||
mW = zeros(numW, 1, 'uint32');
|
||||
|
||||
idx = 1;
|
||||
for i = 1:4:strlen + 1
|
||||
mW(idx) = bitor(bitor(bitor( ...
|
||||
bitshift(uint32(mC(i)), 24), ...
|
||||
bitshift(uint32(mC(i+1)), 16)), ...
|
||||
bitshift(uint32(mC(i+2)), 8)), ...
|
||||
uint32(mC(i+3)));
|
||||
idx = idx + 1;
|
||||
end
|
||||
|
||||
% Append length of message
|
||||
mW(numW - 1) = uint32(bitshift(uint64(numB), -32));
|
||||
mW(numW) = uint32(bitshift(bitshift(uint64(numB), 32), -32));
|
||||
|
||||
% Process the message in successive 512-bit chs
|
||||
for cId = 1 : double(numC)
|
||||
cSt = (cId - 1) * 16 + 1;
|
||||
cEnd = cId * 16;
|
||||
ch = mW(cSt : cEnd);
|
||||
|
||||
% Extend the sixteen 32-bit words into eighty 32-bit words
|
||||
for j = 17 : 80
|
||||
ch(j) = ch(j - 3);
|
||||
ch(j) = bitxor(ch(j), ch(j - 8));
|
||||
ch(j) = bitxor(ch(j), ch(j - 14));
|
||||
ch(j) = bitxor(ch(j), ch(j - 16));
|
||||
ch(j) = bitrotate(ch(j), 1);
|
||||
end
|
||||
|
||||
% Initialize hash value for this ch
|
||||
a = h0;
|
||||
b = h1;
|
||||
c = h2;
|
||||
d = h3;
|
||||
e = h4;
|
||||
|
||||
% Main loop
|
||||
for i = 1 : 80
|
||||
if(i >= 1 && i <= 20)
|
||||
f = bitor(bitand(b, c), bitand(bitcmp(b), d));
|
||||
k = uint32(1518500249);
|
||||
elseif(i >= 21 && i <= 40)
|
||||
f = bitxor(bitxor(b, c), d);
|
||||
k = uint32(1859775393);
|
||||
elseif(i >= 41 && i <= 60)
|
||||
f = bitor(bitor(bitand(b, c), bitand(b, d)), bitand(c, d));
|
||||
k = uint32(2400959708);
|
||||
elseif(i >= 61 && i <= 80)
|
||||
f = bitxor(bitxor(b, c), d);
|
||||
k = uint32(3395469782);
|
||||
end
|
||||
|
||||
t = bitrotate(a, 5);
|
||||
t = bitadd(t, f);
|
||||
t = bitadd(t, e);
|
||||
t = bitadd(t, k);
|
||||
t = bitadd(t, ch(i));
|
||||
e = d;
|
||||
d = c;
|
||||
c = bitrotate(b, 30);
|
||||
b = a;
|
||||
a = t;
|
||||
|
||||
end
|
||||
h0 = bitadd(h0, a);
|
||||
h1 = bitadd(h1, b);
|
||||
h2 = bitadd(h2, c);
|
||||
h3 = bitadd(h3, d);
|
||||
h4 = bitadd(h4, e);
|
||||
|
||||
end
|
||||
|
||||
hash = reshape(dec2hex(double([h0 h1 h2 h3 h4]), 8)', [1 40]);
|
||||
|
||||
hash = lower(hash);
|
||||
|
||||
end
|
||||
|
||||
function ret = bitadd(iA, iB)
|
||||
ret = double(iA) + double(iB);
|
||||
ret = bitset(ret, 33, 0);
|
||||
ret = uint32(ret);
|
||||
end
|
||||
|
||||
function ret = bitrotate(iA, places)
|
||||
t = bitshift(iA, places - 32);
|
||||
ret = bitshift(iA, places);
|
||||
ret = bitor(ret, t);
|
||||
end
|
||||
|
||||
% =========================== Base64 Encoder ============================
|
||||
% Thanks to Peter John Acklam
|
||||
%
|
||||
|
||||
function y = base64encode(x, eol)
|
||||
%BASE64ENCODE Perform base64 encoding on a string.
|
||||
%
|
||||
% BASE64ENCODE(STR, EOL) encode the given string STR. EOL is the line ending
|
||||
% sequence to use; it is optional and defaults to '\n' (ASCII decimal 10).
|
||||
% The returned encoded string is broken into lines of no more than 76
|
||||
% characters each, and each line will end with EOL unless it is empty. Let
|
||||
% EOL be empty if you do not want the encoded string broken into lines.
|
||||
%
|
||||
% STR and EOL don't have to be strings (i.e., char arrays). The only
|
||||
% requirement is that they are vectors containing values in the range 0-255.
|
||||
%
|
||||
% This function may be used to encode strings into the Base64 encoding
|
||||
% specified in RFC 2045 - MIME (Multipurpose Internet Mail Extensions). The
|
||||
% Base64 encoding is designed to represent arbitrary sequences of octets in a
|
||||
% form that need not be humanly readable. A 65-character subset
|
||||
% ([A-Za-z0-9+/=]) of US-ASCII is used, enabling 6 bits to be represented per
|
||||
% printable character.
|
||||
%
|
||||
% Examples
|
||||
% --------
|
||||
%
|
||||
% If you want to encode a large file, you should encode it in chunks that are
|
||||
% a multiple of 57 bytes. This ensures that the base64 lines line up and
|
||||
% that you do not end up with padding in the middle. 57 bytes of data fills
|
||||
% one complete base64 line (76 == 57*4/3):
|
||||
%
|
||||
% If ifid and ofid are two file identifiers opened for reading and writing,
|
||||
% respectively, then you can base64 encode the data with
|
||||
%
|
||||
% while ~feof(ifid)
|
||||
% fwrite(ofid, base64encode(fread(ifid, 60*57)));
|
||||
% end
|
||||
%
|
||||
% or, if you have enough memory,
|
||||
%
|
||||
% fwrite(ofid, base64encode(fread(ifid)));
|
||||
%
|
||||
% See also BASE64DECODE.
|
||||
|
||||
% Author: Peter John Acklam
|
||||
% Time-stamp: 2004-02-03 21:36:56 +0100
|
||||
% E-mail: pjacklam@online.no
|
||||
% URL: http://home.online.no/~pjacklam
|
||||
|
||||
if isnumeric(x)
|
||||
x = num2str(x);
|
||||
end
|
||||
|
||||
% make sure we have the EOL value
|
||||
if nargin < 2
|
||||
eol = sprintf('\n');
|
||||
else
|
||||
if sum(size(eol) > 1) > 1
|
||||
error('EOL must be a vector.');
|
||||
end
|
||||
if any(eol(:) > 255)
|
||||
error('EOL can not contain values larger than 255.');
|
||||
end
|
||||
end
|
||||
|
||||
if sum(size(x) > 1) > 1
|
||||
error('STR must be a vector.');
|
||||
end
|
||||
|
||||
x = uint8(x);
|
||||
eol = uint8(eol);
|
||||
|
||||
ndbytes = length(x); % number of decoded bytes
|
||||
nchunks = ceil(ndbytes / 3); % number of chunks/groups
|
||||
nebytes = 4 * nchunks; % number of encoded bytes
|
||||
|
||||
% add padding if necessary, to make the length of x a multiple of 3
|
||||
if rem(ndbytes, 3)
|
||||
x(end+1 : 3*nchunks) = 0;
|
||||
end
|
||||
|
||||
x = reshape(x, [3, nchunks]); % reshape the data
|
||||
y = repmat(uint8(0), 4, nchunks); % for the encoded data
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Split up every 3 bytes into 4 pieces
|
||||
%
|
||||
% aaaaaabb bbbbcccc ccdddddd
|
||||
%
|
||||
% to form
|
||||
%
|
||||
% 00aaaaaa 00bbbbbb 00cccccc 00dddddd
|
||||
%
|
||||
y(1,:) = bitshift(x(1,:), -2); % 6 highest bits of x(1,:)
|
||||
|
||||
y(2,:) = bitshift(bitand(x(1,:), 3), 4); % 2 lowest bits of x(1,:)
|
||||
y(2,:) = bitor(y(2,:), bitshift(x(2,:), -4)); % 4 highest bits of x(2,:)
|
||||
|
||||
y(3,:) = bitshift(bitand(x(2,:), 15), 2); % 4 lowest bits of x(2,:)
|
||||
y(3,:) = bitor(y(3,:), bitshift(x(3,:), -6)); % 2 highest bits of x(3,:)
|
||||
|
||||
y(4,:) = bitand(x(3,:), 63); % 6 lowest bits of x(3,:)
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Now perform the following mapping
|
||||
%
|
||||
% 0 - 25 -> A-Z
|
||||
% 26 - 51 -> a-z
|
||||
% 52 - 61 -> 0-9
|
||||
% 62 -> +
|
||||
% 63 -> /
|
||||
%
|
||||
% We could use a mapping vector like
|
||||
%
|
||||
% ['A':'Z', 'a':'z', '0':'9', '+/']
|
||||
%
|
||||
% but that would require an index vector of class double.
|
||||
%
|
||||
z = repmat(uint8(0), size(y));
|
||||
i = y <= 25; z(i) = 'A' + double(y(i));
|
||||
i = 26 <= y & y <= 51; z(i) = 'a' - 26 + double(y(i));
|
||||
i = 52 <= y & y <= 61; z(i) = '0' - 52 + double(y(i));
|
||||
i = y == 62; z(i) = '+';
|
||||
i = y == 63; z(i) = '/';
|
||||
y = z;
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Add padding if necessary.
|
||||
%
|
||||
npbytes = 3 * nchunks - ndbytes; % number of padding bytes
|
||||
if npbytes
|
||||
y(end-npbytes+1 : end) = '='; % '=' is used for padding
|
||||
end
|
||||
|
||||
if isempty(eol)
|
||||
|
||||
% reshape to a row vector
|
||||
y = reshape(y, [1, nebytes]);
|
||||
|
||||
else
|
||||
|
||||
nlines = ceil(nebytes / 76); % number of lines
|
||||
neolbytes = length(eol); % number of bytes in eol string
|
||||
|
||||
% pad data so it becomes a multiple of 76 elements
|
||||
y = [y(:) ; zeros(76 * nlines - numel(y), 1)];
|
||||
y(nebytes + 1 : 76 * nlines) = 0;
|
||||
y = reshape(y, 76, nlines);
|
||||
|
||||
% insert eol strings
|
||||
eol = eol(:);
|
||||
y(end + 1 : end + neolbytes, :) = eol(:, ones(1, nlines));
|
||||
|
||||
% remove padding, but keep the last eol string
|
||||
m = nebytes + neolbytes * (nlines - 1);
|
||||
n = (76+neolbytes)*nlines - neolbytes;
|
||||
y(m+1 : n) = '';
|
||||
|
||||
% extract and reshape to row vector
|
||||
y = reshape(y, 1, m+neolbytes);
|
||||
|
||||
end
|
||||
|
||||
% output is a character array
|
||||
y = char(y);
|
||||
|
||||
end
|
||||
@ -0,0 +1,20 @@
|
||||
% submitWeb Creates files from your code and output for web submission.
|
||||
%
|
||||
% If the submit function does not work for you, use the web-submission mechanism.
|
||||
% Call this function to produce a file for the part you wish to submit. Then,
|
||||
% submit the file to the class servers using the "Web Submission" button on the
|
||||
% Programming Exercises page on the course website.
|
||||
%
|
||||
% You should call this function without arguments (submitWeb), to receive
|
||||
% an interactive prompt for submission; optionally you can call it with the partID
|
||||
% if you so wish. Make sure your working directory is set to the directory
|
||||
% containing the submitWeb.m file and your assignment files.
|
||||
|
||||
function submitWeb(partId)
|
||||
if ~exist('partId', 'var') || isempty(partId)
|
||||
partId = [];
|
||||
end
|
||||
|
||||
submit(partId, 1);
|
||||
end
|
||||
|
||||
@ -0,0 +1,20 @@
|
||||
function visualizeFit(X, mu, sigma2)
|
||||
%VISUALIZEFIT Visualize the dataset and its estimated distribution.
|
||||
% VISUALIZEFIT(X, p, mu, sigma2) This visualization shows you the
|
||||
% probability density function of the Gaussian distribution. Each example
|
||||
% has a location (x1, x2) that depends on its feature values.
|
||||
%
|
||||
|
||||
[X1,X2] = meshgrid(0:.5:35);
|
||||
Z = multivariateGaussian([X1(:) X2(:)],mu,sigma2);
|
||||
Z = reshape(Z,size(X1));
|
||||
|
||||
plot(X(:, 1), X(:, 2),'bx');
|
||||
hold on;
|
||||
% Do not plot if there are infinities
|
||||
if (sum(isinf(Z)) == 0)
|
||||
contour(X1, X2, Z, 10.^(-20:3:0)');
|
||||
end
|
||||
hold off;
|
||||
|
||||
end
|
||||
Reference in New Issue