/exercises/mlclass-ex1/gradientDescent.m

 1function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
 2%GRADIENTDESCENT Performs gradient descent to learn theta
 3%   theta = GRADIENTDESENT(X, y, theta, alpha, num_iters) updates theta by 
 4%   taking num_iters gradient steps with learning rate alpha
 5
 6% Initialize some useful values
 7m = length(y); % number of training examples
 8J_history = zeros(num_iters, 1);
 9num_vars=size(X,2);
10
11for iter = 1:num_iters
12
13    % ====================== YOUR CODE HERE ======================
14    % Instructions: Perform a single gradient step on the parameter vector
15    %               theta. 
16    %
17    % Hint: While debugging, it can be useful to print out the values
18    %       of the cost function (computeCost) and gradient here.
19    %
20  theta_tmp=zeros(num_vars,1);
21  for j=1:num_vars
22    theta_tmp(j)= theta(j) - (alpha/m) *  sum(((X*theta)-y).*X(:,j));
23  end
24  theta=theta_tmp;
25  % by @dnene
26  % theta = theta - (X' * (X * theta - y) * alpha / m);
27
28    % ============================================================
29
30    % Save the cost J in every iteration    
31    J_history(iter) = computeCost(X, y, theta);
32
33end
34
35end