Gradient_Descent.m

clc;
clear;
syms x y;
f = (x+y)^2 + (x+1)^2 + (y+3)^2;


% 一阶导数:
fx = diff(f,x)
fy = diff(f,y)

% 做图:原始3d曲面图
x = -20:0.1:20;
y = -15:0.1:15;
[X,Y] = meshgrid(x,y); 
Z = (X+Y).^2 + (X+1).^2 + (Y+3).^2;
figure(1);
mesh(X,Y,Z);
xlabel('横坐标x'); ylabel('纵坐标y'); zlabel('空间坐标z');
hold on;
% 做图:原始点
x0 = 10; y0 = -1.5;
z0 = (x0+y0)^2 + (x0+1)^2 + (y0+3)^2;
plot3(x0,y0,z0,'r*')
hold on

% 初始化:
acc = 0.00001;     % 精度
study_step = 0.01; % 学习率
x = 10; 
y = -1.5;
k = 0; % 下降次数

% 梯度下降开始:[x1,y1] = [x0,y0] - step*( fx(x0,y0),fy(x0,y0) )
fprintf('梯度下降开始:\n');
while eval(fx)~=0 | eval(fy)~=0 
	ans_tmp = [x,y] - study_step*[eval(fx),eval(fy)];
	acc_tmp = sqrt((ans_tmp(1)-x)^2 + (ans_tmp(2)-y)^2);
	if acc_tmp <= acc
		fprintf('极值坐标为:(%.5f,%.5f,%.5f)\n',ans_tmp(1),ans_tmp(2),f_tmp);
        fprintf('迭代次数:%d\n',k);
        plot3(ans_tmp(1),ans_tmp(2),f_tmp,'r*');
        hold off
		break;
	end
	x = ans_tmp(1);
	y = ans_tmp(2);
	f_tmp = (x+y)^2 + (x+1)^2 + (y+3)^2;
    plot3(x,y,f_tmp,'r*')
    hold on;
    k = k + 1;  % 计数器
end