%% ============ Part : Compute Cost and Gradient ============

%  In this part of the exercise, you will implement the cost and gradient

%  for logistic regression. You neeed to complete the code in

%  costFunction.m

%  Setup the data matrix appropriately, and add ones for the intercept term

[m, n] = size(X);

% Add intercept term to x and X_test

X = [ones(m, ) X];

% Initialize fitting parameters

initial_theta = zeros(n + , );

% Compute and display initial cost and gradient

[cost, grad] = costFunction(initial_theta, X, y);

%% ============= Part : Optimizing using fminunc  =============

%  In this exercise, you will use a built-in function (fminunc) to find the

%  optimal parameters theta.

%  Set options for fminunc

options = optimset('GradObj', 'on', 'MaxIter', );

%  Run fminunc to obtain the optimal theta

%  This function will return theta and the cost

[theta, cost] = ...

    fminunc(@(t)(costFunction(t, X, y)), initial_theta, options);

function plotDecisionBoundary(theta, X, y)

%PLOTDECISIONBOUNDARY Plots the data points X and y into a new figure with

%the decision boundary defined by theta

%   PLOTDECISIONBOUNDARY(theta, X,y) plots the data points with + for the

%   positive examples and o for the negative examples. X is assumed to be

%   a either

%   ) Mx3 matrix, where the first column is an all-ones column for the

%      intercept.

%   ) MxN, N> matrix, where the first column is all-ones

% Plot Data

plotData(X(:,:), y);

hold on

if size(X, ) <=

    % Only need  points to define a line, so choose two endpoints

    plot_x = [min(X(:,))-,  max(X(:,))+];

    % Calculate the decision boundary line//令theta装置乘以X等于0，即可

   plot_y = (-./theta()).*(theta().*plot_x + theta());

    % Plot, and adjust axes for better viewing

    plot(plot_x, plot_y)

    % Legend, specific for the exercise

    legend('Admitted', 'Not admitted', 'Decision Boundary')

    axis([, , , ])

else

    % Here is the grid range

    u = linspace(-, 1.5, );

    v = linspace(-, 1.5, );

    z = zeros(length(u), length(v));

    % Evaluate z = theta*x over the grid

    for i = :length(u)

        for j = :length(v)

            z(i,j) = mapFeature(u(i), v(j))*theta;

        end

    end

    z = z'; % important to transpose z before calling contour

    % Plot z =

    % Notice you need to specify the range [, ]

    contour(u, v, z, [, ], 'LineWidth', )

end

hold off

end

function plotData(X, y)    //会按照真类和假类分类 画出输入的点

%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              //返回 y=1和y=0的位置，也就是行数

  pos = find(y==);        neg = find(y == );                //利用find的查找功能，把正类和负类分开，并把横纵坐标保存在pos里面

% Plot Examples

plot(X(pos, ), X(pos, ), 'k+','LineWidth', , ...

'MarkerSize', );

plot(X(neg, ), X(neg, ), 'ko', 'MarkerFaceColor', 'y', ...

'MarkerSize', );

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

hold off;

end

%% =========== Part : Regularized Logistic Regression ============

%  In this part, you are given a dataset with data points that are not

%  linearly separable. However, you would still like to use logistic

%  regression to classify the data points.

%

%  To do so, you introduce more features to use -- in particular, you add

%  polynomial features to our data matrix (similar to polynomial

%  regression).

%

% Add Polynomial Features

% Note that mapFeature also adds a column of ones for us, so the intercept

% term is handled

X = mapFeature(X(:,), X(:,));

% Initialize fitting parameters

initial_theta = zeros(size(X, ), );

% Set regularization parameter lambda to

lambda = ;

% Compute and display initial cost and gradient for regularized logistic

% regression

[cost, grad] = costFunctionReg(initial_theta, X, y, lambda);

%% ============= Part : Regularization and Accuracies =============

%  Optional Exercise:

%  In this part, you will get to try different values of lambda and

%  see how regularization affects the decision coundart

%

%  Try the following values of lambda (, , , ).

%

%  How does the decision boundary change when you vary lambda? How does

%  the training set accuracy vary?

%

% Initialize fitting parameters

initial_theta = zeros(size(X, ), );

% Set regularization parameter lambda to  (you should vary this)

lambda = ;

% Set Options

options = optimset('GradObj', 'on', 'MaxIter', );

% Optimize

[theta, J, exit_flag] = ...

    fminunc(@(t)(costFunctionReg(t, X, y, lambda)), initial_theta, options);