function [f,g] = linear_regression(theta, X,y)  %  % Arguments:  %   theta - A vector containing the parameter values to optimize.  %   X - The examples stored in a matrix.  %       X(i,j) is the i'th coordinate of the j'th example.  %   y - The target value for each example.  y(j) is the target for example j.  %    m=size(X,2);  n=size(X,1);  f=0;  g=zeros(size(theta));  %  % TODO:  Compute the linear regression objective by looping over the examples in X.  %        Store the objective function value in 'f'.  %  % TODO:  Compute the gradient of the objective with respect to theta by looping over  %        the examples in X and adding up the gradient for each example.  Store the  %        computed gradient in 'g'.  %%% YOUR CODE HERE %%%% Step 1 : Compute f cost functionfor i = 1:m    f = f + (theta' * X(:,i) - y(i))^2;endf = 1/2*f;% Step 2: Compute gradient for j = 1:n    for i = 1:m        g(j) = g(j) + X(j,i)*(theta' * X(:,i) - y(i));    end    end

function [f,g] = linear_regression_vec(theta, X,y)  %  % Arguments:  %   theta - A vector containing the parameter values to optimize.  %   X - The examples stored in a matrix.  %       X(i,j) is the i'th coordinate of the j'th example.  %   y - The target value for each example.  y(j) is the target for example j.  %  m=size(X,2);    % initialize objective value and gradient.  f = 0;  g = zeros(size(theta));  %  % TODO:  Compute the linear regression objective function and gradient   %        using vectorized code.  (It will be just a few lines of code!)  %        Store the objective function value in 'f', and the gradient in 'g'.  %%%% YOUR CODE HERE %%%  f = 1/2*sum((theta'*X - y).^2);    g = X*(theta'*X - y)';

function [f,g] = logistic_regression_vec(theta, X,y)  %  % Arguments:  %   theta - A column vector containing the parameter values to optimize.  %   X - The examples stored in a matrix.    %       X(i,j) is the i'th coordinate of the j'th example.  %   y - The label for each example.  y(j) is the j'th example's label.  %  m=size(X,2);    % initialize objective value and gradient.  f = 0;  g = zeros(size(theta));    %  % TODO:  Compute the logistic regression objective function and gradient   %        using vectorized code.  (It will be just a few lines of code!)  %        Store the objective function value in 'f', and the gradient in 'g'.  %%%% YOUR CODE HERE %%%f = -sum(y.*log(sigmoid(theta'*X)) + (1-y).*log(1 - sigmoid(theta'*X)));g = X*(sigmoid(theta'*X) - y)';