第二次 编程作业

function plotData(X, y)
%PLOTDATA Plots the data points X and y into a new figure 
%   PLOTDATA(x,y) plots the data points with + for the positive examples
%   and o for the negative examples. X is assumed to be a Mx2 matrix.

% Create New Figure
figure; hold on;

% ====================== YOUR CODE HERE ======================
% Instructions: Plot the positive and negative examples on a
%               2D plot, using the option 'k+' for the positive
%               examples and 'ko' for the negative examples.
%


% Find Indices of Positive and Negative Examples 
pos = find(y==1); neg = find(y == 0);
% Plot Examples 
plot(X(pos, 1), X(pos, 2), 'k+','LineWidth', 2,  'MarkerSize', 7);
plot(X(neg, 1), X(neg, 2), 'ko', 'MarkerFaceColor', 'y', 'MarkerSize', 7);

% =========================================================================
hold off;

end

function g = sigmoid(z)
%SIGMOID Compute sigmoid function
%   g = SIGMOID(z) computes the sigmoid of z.

% You need to return the following variables correctly 
g = zeros(size(z));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the sigmoid of each value of z (z can be a matrix,
%               vector or scalar).


g = 1./(1+e.^(-z));


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

end

function [J, grad] = costFunction(theta, X, y)
%COSTFUNCTION Compute cost and gradient for logistic regression
%   J = COSTFUNCTION(theta, X, y) computes the cost of using theta as the
%   parameter for logistic regression and the gradient of the cost
%   w.r.t. to the parameters.

% 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 of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta
%
% Note: grad should have the same dimensions as theta
%


h_theta = sigmoid(X * theta);
J = (-y' * log(h_theta)-(1-y)'*log(1-h_theta))/m;
grad = X'*(h_theta-y)/m;% X'才可以满足*的条件,注意运算顺序






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

end

function p = predict(theta, X)
%PREDICT Predict whether the label is 0 or 1 using learned logistic 
%regression parameters theta
%   p = PREDICT(theta, X) computes the predictions for X using a 
%   threshold at 0.5 (i.e., if sigmoid(theta'*x) >= 0.5, predict 1)

m = size(X, 1); % Number of training examples

% You need to return the following variables correctly
p = zeros(m, 1);

% ====================== YOUR CODE HERE ======================
% Instructions: Complete the following code to make predictions using
%               your learned logistic regression parameters. 
%               You should set p to a vector of 0's and 1's
%



p = sigmoid(X*theta) >=0.5;% X: m * n theta: n * 1



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


end

function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
%   theta as the parameter for regularized logistic regression and the
%   gradient of the cost w.r.t. to the parameters. 

% 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));
%Note that you should not regularize the parameter θ0. 
%In Octave/MATLAB, recall that indexing starts from 1, 
%hence, you should not be regularizing the theta(1) parameter (which corresponds to θ0) in the code. 

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta

% X: m * n theta: n * 1 h_theta: m * 1
%theta(1)就是 θ0
h_theta = sigmoid(X * theta);
J = (-y' * log(h_theta) - (1 - y)' * log(1 - h_theta)) / m +  lambda * (sum(theta.^2 )- (theta(1))^2) / (2 * m); //θ0不需要
grad = (X' * (h_theta - y) + theta * lambda) / m;
grad(1)=grad(1)-theta(1)*lambda/m;%θ0不需要


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

end