共轭梯度法matlab代码

以下是共轭梯度法的MATLAB代码实现：

function [x, flag, relres, iter, resvec] = conjgrad(A, b, x0, maxiter, tol)
% Input arguments:
% A: coefficient matrix
% b: right-hand side vector
% x0: initial guess
% maxiter: maximum number of iterations
% tol: tolerance for relative residual
%
% Output arguments:
% x: solution vector
% flag: convergence flag
% relres: relative residual
% iter: number of iterations performed
% resvec: vector of residual norms at each iteration

n = length(b);
x = x0;
r = b - A*x;
p = r;
rsold = r'*r;
resvec = zeros(maxiter, 1);

for iter = 1:maxiter
    Ap = A*p;
    alpha = rsold / (p'*Ap);
    x = x + alpha*p;
    r = r - alpha*Ap;
    rsnew = r'*r;
    resvec(iter) = sqrt(rsnew);
    if sqrt(rsnew) < tol
        flag = 0;
        relres = sqrt(rsnew) / norm(b);
        resvec(iter+1:end) = [];
        return
    end
    p = r + (rsnew/rsold)*p;
    rsold = rsnew;
end

flag = 1;
relres = sqrt(rsnew) / norm(b);
resvec(iter+1:end) = [];

end

其中，输入参数`A`为系数矩阵，`b`为右手向量，`x0`为初始解向量，`maxiter`为最大迭代次数，`tol`为容忍的相对残差。输出参数`x`为求解的解向量，`flag`为收敛标志，`relres`为相对残差，`iter`为实际迭代次数，`resvec`为每次迭代的残差向量。