matlab写共轭梯度法的代码

这是一个技术问题，我可以为您提供答案。以下是用matlab编写共轭梯度法的简单示例代码：

function [x,fval,iter] = cg_descent(f,x0,tol,maxiter)
% Input: f: Objective function
% x0: Initial point
% tol: Tolerace for stopping criteria
% maxiter: Maximum number of iterations
% Output: x: Final point of optimization
% fval: Final value of objective function
% iter: Number of iterations to converge
%
% Example usage: cg_descent(@(x) x'*[1 0;0 2]*x, [2;1], 1e-4, 100)

x = x0;
g = gradient(f,x);

d = -g;
iter = 0;
while norm(g) > tol && iter < maxiter
alpha = line_search(f,x,d);
x = x + alpha*d;
g_new = gradient(f,x);
beta = dot(g_new,g_new-g)/dot(g,g);
d = -g_new + beta*d;
g = g_new;
iter = iter + 1;
end

fval = f(x);

function alpha = line_search(f,x,d)
% Input: f: Objective function
% x: Current point
% d: Search direction
% Output: alpha: Step size
%
% Backtracking line search (Boyd and Vandenberghe, Convex Optimization)
alpha = 1;
rho = 0.5;
c = 0.1;
while f(x+alpha*d) > f(x) + c*alpha*dot(gradient(f,x),d)
alpha = rho*alpha;
end

function g = gradient(f,x)
% Input: f: Objective function
% x: Point at which to calculate gradient
% Output: g: Gradient of objective function at x
%
% Calculates gradient using central difference approximation
h = 1e-8;
g = zeros(size(x));
for i = 1:length(x)
e = zeros(size(x));
e(i) = 1;
g(i) = (f(x+h*e) - f(x-h*e))/(2*h);
end

end