Nice way to vectorize the gradient terms when working on linear regression

linearRegCostFunction.m

function [J, grad] = linearRegCostFunction(X, y, theta, lambda)
%LINEARREGCOSTFUNCTION Compute cost and gradient for regularized linear
%regression with multiple variables
%   [J, grad] = LINEARREGCOSTFUNCTION(X, y, theta, lambda) computes the
%   cost of using theta as the parameter for linear regression to fit the
%   data points in X and y. Returns the cost in J and the gradient in grad

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost and gradient of regularized linear
%               regression for a particular choice of theta.
%
%               You should set J to the cost and grad to the gradient.
%

% Cost function first
% Calculate the first term of J
sum_errors  = (1/(2*m)) * (sum( ((X * theta) - y) .^ 2));
% Notice how we DO NOT regularize the first parameter
reg_term  = (lambda/(2*m)) * sum(theta(2:end) .^ 2);
% And finally our cost function
J = sum_errors + reg_term;

% Gradient terms
% Notice how we use full vectorization here
% The trick is to compute the summatory term within the gradient function
% using a multiplication of the transpose of the input examples and
% the errors in our predictions. The transpose of X gives us all the feature
% i for all the examples in the i row and so on ...
% Also, since we DO NOT apply regularization for theta1, we use set the
% first element of a copy of theta as 0
pred     = X * theta;
grad     = ((X' * (pred - y)) / m) + ((lambda/m) * [0; theta(2:end)]);
% In the previous assignation, the term after the + operator could be
% this temp:
%temp     = theta;
%temp(1)  = 0;
%grad     = grad + ((lambda/m) * temp);

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

grad = grad(:);

end

Hey
Are you open for an online training?