矢量化运行八度无限循环

Question

我正在尝试计算其中 h(x) = X*theta, theta is nx1 matrix and X is an mxn and y is also m x 1 矩阵。 alpha,m,theta(j) and x(j)(i) 是标量值。我正在尝试通过以下方式对其进行矢量化

    theta0 =(X*theta - y)
    theta1 = (X*theta - y).*X(:,2)
    theta0 = sum(theta0);
    theta1 = sum(theta1);
    theta0 = theta(1) - theta0*alpha/m;
    theta1 = theta(2) - theta1*alpha/m;
    theta = [theta0;theta1];

其中 num_iter=1500 和 m=length(y) 但是我的代码进入了无限循环。我的等效循环解决方案如下

     theta0 =0;
     theta1= 0;
     for i = 1:m,
        theta0 = theta0 + (sum(X(i,:)*theta) - y(i));
         theta1 = theta1 + (sum(X(i,:)*theta) - y(i))*X(i,2);
     end
     theta(1) =  theta(1) - theta0*alpha/m;
     theta(2) =  theta(2) - theta1*alpha/m;

请告诉我哪里错了

Answer 1

公式可以向量化的形式写成：

theta = theta - alpha/m * ((X*theta - y).' *X).';

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