clc;
clear;
syms x y r;
f = (x y)^2 (x 1)^2 (y 3)^2;
syms x_tmp y_tmp;
f_tmp = (x_tmp y_tmp)^2 (x_tmp 1)^2 (y_tmp 3)^2;
fx = diff(f,x);
fy = diff(f,y);
grad_f1 = [fx,fy]';
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;
x0 = 10; y0 = -1.5;
z0 = (x0 y0)^2 (x0 1)^2 (y0 3)^2;
plot3(x0,y0,z0,'r*')
hold on
acc = 0.0001;
x = 10;
y = -1.5;
k = 1;
fprintf('共轭梯度下降开始:n');
d = -eval(grad_f1);
while 1
grad_f1_down = norm(eval(grad_f1))^2;
x_tmp = x r*d(1);
y_tmp = y r*d(2);
r_result = solve(diff(eval(f_tmp)));
x = x r_result*d(1);
y = y r_result*d(2);
grad_f1_up = norm(eval(grad_f1))^2;
plot3(x,y,eval(f),'r*');
hold on
if norm(eval(grad_f1)) <= acc
fprintf('极值坐标为:(%.5f,%.5f,%.5f)n',x,y,eval(f))
fprintf('迭代次数:%dn',k)
break;
end
miu = grad_f1_up/grad_f1_down;
d = -eval(grad_f1) miu*d;
k = k 1;
end
hold off;
代码语言：javascript复制
clc;
clear;
syms x y;
f =(x y)^2 (x 1)^2 (y 3)^2;
syms x1 y1 a;
f1 = (x1 y1)^2 (x1 1)^2 (y1 3)^2;
fx = diff(f,x);
fy = diff(f,y);
fxx = diff(fx,x);
fyy = diff(fy,y);
fxy = diff(fx,y);
fyx = diff(fy,x);
grad_f1 = [fx;fy];
grad_H2 = [fxx fxy;fyx fyy];
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;
x0 = 10; y0 = -1.5;
z0 = (x0 y0)^2 (x0 1)^2 (y0 3)^2;
plot3(x0,y0,z0,'r*');
hold on
acc = 0.00001;
x = 10;
y = -1.5;
k = 0;
fprintf('阻尼牛顿下降开始:n')
while 1
ans_tmp = [x;y];
S = -eval(inv(grad_H2))*eval(grad_f1);
x1 = x a*S(1)
y1 = y a*S(2)
if diff(eval(f1),a) == 0
a_result = 0;
else
a_result = solve(diff(eval(f1)));
fprintf('第%d次迭代,当前阻尼步长为:%.5fn', k, a_result);
end
x = x a_result*S(1);
y = y a_result*S(2);
result_tmp = [x;y];
acc_tmp = sqrt( (result_tmp(1)-ans_tmp(1))^2 (result_tmp(2) - ans_tmp(2))^2 );
if acc_tmp < acc
fprintf('极值坐标为:(%.5f,%.5f,%.5f)n', x, y, eval(f));
fprintf('迭代次数:%dn',k);
plot3(x,y,eval(f),'r*');
hold off;
break;
end
plot3(x,y,eval(f),'r*');
hold on;
k = k 1;
if k >= 100
fprintf('自动结束!n');
break;
end
end
