下面是多变量梯度下降的代码：
X是特征矩阵，已经在最左边添加了新的一列为1，theta是梯度下降要求的参数，num_iters为迭代次数。已经进行过特征缩放
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.
%
  sum1 = 0;
sum2 = 0;
sum3 = 0;
for i = 1 : m
    a=theta.';
    x = X([i],:);
    sum1 =sum1 + (a*x.'-y(i));
    sum2 =sum2 + (a*x.'-y(i))* X(i,2);
    sum3 =sum3 + (a*x.'-y(i))* X(i,3);
end

theta(1) = theta(1) - sum1 * alpha *(1/m);
theta(2) = theta(2) - sum2 * alpha *(1/m);
theta(3) = theta(3) - sum3 * alpha *(1/m);

% ============================================================

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

end

end