gradient_demo.m

梯度下降算法实现程序

clc,clear;

syms x y ; 
% f = 2*x.^2 + y.^2;   % 效果不错
f = (x-1).^4 + y.^2;
% f = (x-y) ./ (x.^2+y.^2+2); % 为什么不好使？
% [C,h]=contour(x,y,f);

% ezplot(x,y,f);  %%% error
% ezmesh(f);
figure; ezcontour(f);

lambda = 0.1;    % 步长
alpha(:,1) = [10;6];  % 初始点
dx = diff(f,x,1);
dy = diff(f,y,1);
fvalue = subs(f,{x,y},{alpha(1,1),alpha(2,1)}); % 初始点的函数值
delta_x = subs(dx,{x,y},{alpha(1,1),alpha(2,1)}); % 对x的偏导数
delta_y = subs(dy,{x,y},{alpha(1,1),alpha(2,1)}); % 对y的偏导数

hold on
plot(alpha(1,:),alpha(2,:),'r*');

flag = 0;
i = 2;
eps = 1e-4;
while ~flag        % matlab下实现do-while循环
    delta = [-double(delta_x); -double(delta_y)];  % 搜索方向（负梯度方向）
    alpha(:,i) = alpha(:,i-1) + lambda.*delta;   % 更新到新的点
    fvalue(:,i) = subs(f,{x,y},{alpha(1,i),alpha(2,i)});  %新的点函数值
    delta_x = subs(dx,{x,y},{alpha(1,i),alpha(2,i)});
    delta_y = subs(dy,{x,y},{alpha(1,i),alpha(2,i)});
    if abs(fvalue(:,i) - fvalue(:,i-1)) < eps 
        flag = 1;
    end
    arrow3(alpha(:,i-1)',alpha(:,i)','b',.2,.4);
    i = i+1;
end
plot(alpha(1,end),alpha(2,end),'r*');

hold off;