function [gamma, m, x] = rqiter(A, s, maxiter)
% RQITER   Raylegh quotient iteration for the closest eigenvalue.
% Input:
%   A         square matrix
%   s         value close to targeted eigenvalue (complex scalar)
%   maxiter   maximal number of iterations
% Output: 
%   gamma     sequence of eigenvalue approximations (vector)
%   m         number of required iterations
%   x         final eigenvector approximation
%
    n = length(A);
    x = ones(n, 1);
    gamma = zeros(maxiter, 1);
    gamma(1) = s;
    I = eye(n);
    m = maxiter;
    for k = 2:maxiter
        s = gamma(k-1);
        B = A - s*I;
        y = B\x;
        x = y/norm(y);
        gamma(k) = x'*B*x + s;
        if (k > 3) && abs(gamma(k) - gamma(k-1)) < 1000*eps
            m = k;
            break
        end
    end 
end