给我一个双共轭梯度法求解线性方程组的matlab参考程序

以下是一个使用双共轭梯度法求解线性方程组的Matlab参考程序：

function [x, flag, relres, iter] = bicgstab(A, b, tol, maxit)
% Biconjugate gradient stabilized method to solve Ax=b
% Input: A: matrix A
% b: column vector b
% tol: tolerance
% maxit: maximum number of iterations
% Output: x: solution
% flag: flag
% relres: relative residual
% iter: number of iterations

n = size(A,1);
x = zeros(n,1); % initial guess
r0 = b - A*x;
r = r0;
rtilde = r0;
p = zeros(n,1);
v = zeros(n,1);
s = 0;
alpha = 0;
omega = 1;

for iter = 1:maxit
rho = rtilde'*r0;
if rho == 0
flag = -1; % breakdown
relres = norm(r)/norm(r0);
return
end
if iter == 1
p = r;
else
beta = (rho/rho_old)*(alpha/omega);
p = r + beta*(p-omega*v);
end
v = A*p;
alpha = rho/(rtilde'*v);
s = r - alpha*v;
if norm(s) <= tol
x = x + alpha*p;
flag = 0; % convergence
relres = norm(s)/norm(r0);
return
end
t = A*s;
omega = (t'*s)/(t'*t);
x = x + alpha*p + omega*s;
r = s - omega*t;
rtilde = rtilde - omega*A'*t;
rho_old = rho;
relres = norm(r)/norm(r0);
if relres <= tol
flag = 0; % convergence
return
elseif isnan(relres) || isinf(relres)
flag = -2; % NaN or Inf
return
end
end
flag = 1; % maximum iterations reached
relres = norm(r)/norm(r0);

end

请注意，该程序不适用于大规模稀疏问题。如果您打算使用它来解决稀疏线性方程组，请使用专门针对稀疏矩阵的算法，例如迭代法的共轭梯度法。