共轭梯度算法matlab代码

以下是共轭梯度算法的MATLAB代码：

function [x, flag, relres, iter, resvec] = cg(A, b, x0, tol, maxit)
% Conjugate Gradient Method for solving Ax = b
% Input:  
%       A : the coefficient matrix of the linear system
%       b : the right-hand side vector of the linear system
%       x0: the initial guess of the solution
%       tol: the tolerance for stopping criterion
%       maxit: the maximum number of iterations
% Output: 
%       x: the solution of the linear system
%       flag: flag = 0 indicates convergence within maxit iterations
%             flag = 1 indicates no convergence within maxit iterations
%       relres: the relative residual norm(b-Ax)/norm(b)
%       iter: the number of iterations performed
%       resvec: the residual norm at each iteration

% Initialization
n = length(b);
x = x0;
r = b - A*x;
p = r;
normb = norm(b);
resvec = zeros(maxit,1);

% Iteration
for iter = 1:maxit
    Ap = A*p;
    alpha = (r'*r)/(p'*Ap);
    x = x + alpha*p;
    r_old = r;
    r = r - alpha*Ap;
    resvec(iter) = norm(r);
    relres = resvec(iter)/normb;
    
    if relres < tol
        flag = 0;
        resvec(iter+1:end) = [];
        break;
    end
    
    beta = (r'*r)/(r_old'*r_old);
    p = r + beta*p;
end

if iter == maxit
    flag = 1;
else
    flag = 0;
end
end

其中，输入参数说明如下：
- A: 系数矩阵
- b: 右手边向量
- x0: 初始解向量
- tol: 相对残量的容许误差
- maxit: 最大迭代次数

输出参数说明如下：
- x: 迭代得到的解向量
- flag: 标记是否收敛（0为收敛，1为未收敛）
- relres: 相对残量，即残量的范数除以右手边向量的范数
- iter: 迭代次数
- resvec: 每次迭代的残量的范数