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.
A = eye(5)
% ===========================================
end
2.computeCost
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.
J = 1/(2*m) * sum((X*theta - y).^2);
% =========================================================================
end
3.gradientDescent
function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
%GRADIENTDESCENT Performs gradient descent to learn theta
% theta = GRADIENTDESCENT(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.
%
theta = theta - alpha * (1/m) * (X'*(X*theta - y));
% ============================================================
% Save the cost J in every iteration
J_history(iter) = computeCost(X, y, theta);
end
end