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function [W, e] = lms(u, d, mu, decay, verbose) 
 
% function [W, e] = lms(u, d, mu, decay, verbose) 
% 
% lms.m - use multidimensional LMS algorithm to predict AR process 
% written for MATLAB 4.0 
% 
% Input parameters: 
%       u       : matrix of training/test points - each row is 
%                 considered a datum 
%       d       : matrix of desired outputs - each row is 
%                 considered a datum 
%       mu      : step size for update of weight vectors 
%       decay   : set to 1 for O(1/n) decay in m 
%       verbose : set to 1 for interactive processing 
 
% length of maximum number of timesteps that can be predicted 
N    = min(size(u, 1), size(d, 1)); 
 
Nin  = size(u, 2); 
Nout = size(d, 2); 
 
% initialize weight matrix and associated parameters for LMS predictor 
w = zeros(Nout, Nin); 
W = []; 
 
for n = 1:N, 
 
W = [W ; w]; 
 
% predict next sample and error 
xp(n, :) = u(n, :) * w'; 
e(n, :)  = d(n, :) - xp(n, :); 
ne(n)    = norm(e(n, :)); 
if (verbose ~= 0) 
    disp(['time step ', int2str(n), ': mag. pred. err. = ' , num2str(ne(n))]); 
end; 
% adapt weight matrix and step size 
w = w + mu * e(n, :)' * u(n, :); 
if (decay == 1) 
  mu = mu * n/(n+1); % use O(1/n) decay rate 
end; 
 
 
 
end % for n