吴恩达机器学习I

function A = warmUpExercise()
%WARMUPEXERCISE Example function in octave
%   A = WARMUPEXERCISE() is an example function that returns the 5x5 identity matrix

A = [];

% ============= YOUR CODE HERE ==============
% Instructions: Return the 5x5 identity matrix 
%               In octave, we return values by defining which variables
%               represent the return values (at the top of the file)
%               and then set them accordingly. 
A = eye(5);
% ===========================================


end

function J = computeCost(X, y, theta)
%COMPUTECOST Compute cost for linear regression
%   J = COMPUTECOST(X, y, theta) computes the cost of using theta as the
%   parameter for linear regression to fit the data points in X and y

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

% You need to return the following variables correctly 
J = 0;

% =================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta
%               You should set J to the cost.
    f=X*theta;
    f=f-y;
    J=1/m/2*(f'*f);

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

end

function [theta, J_history] = gradientDescentMulti(X, y, theta, alpha, num_iters)
%GRADIENTDESCENTMULTI Performs gradient descent to learn theta
%   theta = GRADIENTDESCENTMULTI(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 (computeCostMulti) and gradient here.
    %
    
    hyp = X*theta;
    dJ = X'*(hyp-y);利用矩阵乘法的性质与每一个元素进行了运算
    theta  = theta - (alpha/m)*dJ;
    % ============================================================

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

end
end

mu=mean(X);
sigma=std(X);
X_norm=(X-ones(size(X,1),1)*mu)./(ones(size(X,1),1)*sigma);

function [theta] = normalEqn(X, y)
%NORMALEQN Computes the closed-form solution to linear regression 
%   NORMALEQN(X,y) computes the closed-form solution to linear 
%   regression using the normal equations.

theta = zeros(size(X, 2), 1);

% ==================== YOUR CODE HERE ======================
% Instructions: Complete the code to compute the closed form solution
%               to linear regression and put the result in theta.
%
theta = pinv(X' * X) * X' * y;


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

end