% lms_AR_pred.m - use multidimensional LMS algorithm to predict AR process
% written for MATLAB 4.0
%
% Input parameters:
%                Xi       : matrix of training/test points - each row is
%                           considered a datum
%                Xi0      : initial value Xi(0) of series
%                verbose  : set to 1 for interactive processing
%                mu       : the initial value of step size
%                decay    : set to 1 for O(1/n) decay in mu

Nout = size(Xi, 2);

% length of maximum number of timesteps that can be predicted
N = size(Xi, 1);

% initialize weight matrix and associated parameters for LMS predictor
W = zeros(Nout, Nout);
Wo = [];

% compute first iteration with Xi(0) = Xi0
n	= 1;
Wo 	= [Wo W];
xp(n, :) = Xi0 * W';
e(n, :)  = Xi(n, :) - xp(n, :);
ne(n) = norm(e(n, :));
W = W + rp.mu * e(n, : )' * Xi0;

for n = 2:N,

    % save W matrix
    Wo = [Wo W];

    % predict next sample and error
    xp(n, :) = Xi(n-1, :) * W';
    e(n, :)  = Xi(n, :) - xp(n, :);
    ne(n)    = norm(e(n, :));
    if (rp.verbose ~= 0)
      disp(['time step ', int2str(n), ': mag. pred. err. = ', num2str(ne(n))]);
    end;
    % adapt weight matrix and step size
    W = W + rp.mu * e(n, :)' * Xi(n-1, :);
    if (rp.decay == 1)
      rp.mu = rp.mu  * n/(n+1); % use O(1/n) decay rate
    end;
    
 end