lm算法的matlab程序

下面是使用MATLAB实现lm算法的程序：

function [p, err] = lm_fit(f, p0, x, y, lambda, tol, maxiter)
% f: function handle, the function to be fitted
% p0: initial guess of the parameters
% x, y: data points to be fitted
% lambda: damping factor
% tol: tolerance for stopping criterion
% maxiter: maximum number of iterations

n = length(p0);
p = p0;
err = zeros(maxiter, 1);

for k = 1:maxiter
    % compute the Jacobian matrix
    J = zeros(length(y), n);
    for i = 1:length(y)
        for j = 1:n
            delta = 1e-5;
            p1 = p;
            p1(j) = p1(j) + delta;
            J(i,j) = (f(x(i),p1) - f(x(i),p)) / delta;
        end
    end
    
    % compute the residual vector
    r = y - f(x, p);
    
    % compute the Hessian matrix
    H = J' * J;
    
    % compute the damping factor
    mu = lambda * max(diag(H));
    
    % solve the linear system using the damped least squares method
    dp = (H + mu * eye(n)) \ (J' * r);
    
    % update the parameters
    p_new = p + dp;
    
    % compute the new residual vector
    r_new = y - f(x, p_new);
    
    % compute the new error
    err(k) = norm(r_new)^2;
    
    % check the stopping criterion
    if err(k) < tol
        break;
    end
    
    % adjust the damping factor
    if norm(dp) < 1e-6
        lambda = lambda / 10;
    else
        lambda = lambda * 10;
    end
    
    % update the parameters
    p = p_new;
end

err = err(1:k);

end

其中，f是要拟合的函数，p0是初始参数，x和y是数据点，lambda是阻尼因子，tol是停止准则，maxiter是最大迭代次数。程序返回估计的参数p和误差err。