画decision boundary(直线)
%% ============= Part 3: 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', 400); %设置一些选择项，GradObj,on:表示计算过程中需要的计算gradient;MaxIter,400表示最多迭代次数为400
% 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); %调用matlab的自带的函数fminunc, @(t)(costFunction(t, X, y))创建一个function,参数为t,调用前面写的 costFunction函数
返回求得最优解后的theta和cost
% Print theta to screen
fprintf('Cost at theta found by fminunc: %f\n', cost);
fprintf('theta: \n');
fprintf(' %f \n', theta);
% Plot Boundary
plotDecisionBoundary(theta, X, y); %调用plotDecisionBoundary函数
% Put some labels
hold on;
% Labels and Legend
xlabel('Exam 1 score')
ylabel('Exam 2 score')
% Specified in plot order
legend('Admitted', 'Not admitted')
hold off;
fprintf('\nProgram paused. Press enter to continue.\n');
pause;
plotDecisionBoundary.m
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
% 1) Mx3 matrix, where the first column is an all-ones column for the
% intercept.
% 2) MxN, N>3 matrix, where the first column is all-ones
% Plot Data
plotData(X(:,2:3), y); %调用前面写的plotData函数，参见plotData.m
hold on
if size(X, 2) <= 3 %size(X,2)表示X的列数，包括X最前面的一列1（an all-ones column for the intercept）
% Only need 2 points to define a line, so choose two endpoints % decision boundary为一条直线，画直线只需要两点就可以
plot_x = [min(X(:,2))-2, max(X(:,2))+2];
% Calculate the decision boundary line
plot_y = (-1./theta(3)).*(theta(2).*plot_x + theta(1)); %求plot_y(x2) 矩阵和标量相加减(theta(2).*plot_x + theta(1))实质是矩阵每个元素与该标量相加减
% Plot, and adjust axes for better viewing
plot(plot_x, plot_y) %调用系统的plot函数，plot_x,plot_y均为1*2矩阵
% Legend, specific for the exercise
legend('Admitted', 'Not admitted', 'Decision Boundary')
axis([30, 100, 30, 100]) %设置X轴与Y轴的范围
else %decision boundary不是一条直线(如为一个圆)时, size(X, 2) > 3
% Here is the grid range
u = linspace(-1, 1.5, 50); %linearly spaced vector.在-1到1.5之间产生50个间距相等的点(包括-1与1.5这两个点),u为行向量.
v = linspace(-1, 1.5, 50);
z = zeros(length(u), length(v));
% Evaluate z = theta*x over the grid
for i = 1:length(u)
for j = 1:length(v)
z(i,j) = mapFeature(u(i), v(j))*theta;
end
end
z = z'; % important to transpose z before calling contour
% Plot z = 0
% Notice you need to specify the range [0, 0]
contour(u, v, z, [0, 0], 'LineWidth', 2)
end
hold off
end
mapFeature.m
function out = mapFeature(X1, X2)
% MAPFEATURE Feature mapping function to polynomial features
%
% MAPFEATURE(X1, X2) maps the two input features
% to quadratic features used in the regularization exercise.
%
% Returns a new feature array with more features, comprising of
% X1, X2, X1.^2, X2.^2, X1*X2, X1*X2.^2, etc..
%
% Inputs X1, X2 must be the same size
%
degree = 6;
out = ones(size(X1(:,1)));
for i = 1:degree
for j = 0:i
out(:, end+1) = (X1.^(i-j)).*(X2.^j);
end
end
end
