Gradient descent algorithm [Machine Learning]

gistfile1.matlab

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

    t = theta.';

    theta_p1 = theta(1,1);
    theta_p2 = theta(2,1);
    sump1 = 0;
    sump2 = 0;
    
    for n = 1:m
        sump1 = sump1 + ( ( (t(1) * X(n,1) + t(2) * X(n,2) ) - y(n,1) )*X(n,1) );
    end
    for n = 1:m
        sump2 = sump2 + ( ( (t(1) * X(n,1) + t(2) * X(n,2) ) - y(n,1) )*X(n,2) );
    end
    theta_p1 = theta_p1 - (alpha * (1/m) * sump1);
    theta_p2 = theta_p2 - (alpha * (1/m) * sump2);
    
    theta(1,1) = theta_p1;
    theta(2,1) = theta_p2;
    
    % ============================================================

    % Save the cost J in every iteration    
    J_history(iter) = computeCost(X, y, theta);

end

end