function [a, err, W_list, b_list]=learn_a2(P,T,Learn_b,Lumbda,mc)
%[a, err, W_list, b_list]=learn_a2(P,T,Learn_b,Lumbda,mc);
%% Adaline learning rule with TF---purelin
%% This is the on-line or incremental LMS learning algorithm.
%% P----Input pattern
%% T----Target pattern
%% Set Learn_b=1 to update bias or 0 to neglect bias learning.
%% Lumbda---Learning factor (0 to 1), i.e. 0.3.
%% mc -- Forgetting rate, a real number between 0 and 1.
%% a --- Record of NN output patterns
%% err-- Record of error between target and NN output
%% W_list and b_list: Progress lists
%%
%% [Calling example]
%t=0:0.5/600:0.5;N=length(t);
%k=0:N-1;
%s=0.1*randn(size(t))+0.2*sin(2*pi*20*(1+0.02*randn(size(t))).*t)+...
%    0.08*sin(2*pi*40*(1+0.01*randn(size(t))).*t);
%v=2.2*sin(2*pi*60*t)+0.8*randn(size(k));
%m=2*(0.23*sin(2*pi*60*t+pi/2)+0.07*randn(size(k)));
%c=s+m;
%P=[v;[0 v(1:N-1)];[0 0 v(1:N-2)];[0 0 0 v(1:N-3)];...
%        [0 0 0 0 v(1:N-4)];[0 0 0 0 0 v(1:N-5)];...
%        [0 0 0 0 0 0 v(1:N-6)];];
%[S R]=size(P);
%T=c;
%[a e w_list]=learn_a2(P,T,0,0.015,0);
%figure;subplot(211);plot(t,s,'.',t,e);axis([0 0.5 -1 1])
%title('Adaptive noise cancellation example, Signal and Restored');
%subplot(212);plot(t,s,'.',t,c);axis([0 0.5 -1 1])
%title('Signal and Contaminated signal')
%xlabel('Samples');

% Written by PenChen Chou, 2002-7-18

% Get R
[S, R]=size(P);[U, garbage]=size(T);
if R~=length(T)
    error('===>I/O sample size is not matched');
end
% Set defaults
if nargin<=4
    mc=0;
end
if nargin<=3
    Lumbda=0.3;
end
if nargin<=2
    Learn_b=0;
end
% Initiallization
W_list=[]; b_list=[]; 
% W=randn(U,S); b=randn(U,1);
% W=zeros(U,S); b=randn(U,1);
W= [1.3   2  -0.4   1   1.2    -1.7   -1.7    0.1   -1     0];
b=randn(U,1);
% Conditionally collected
W_list=W'; b_list=b; 
% Search weight W and bias b.
fprintf('\n   {Now running on-line learn_a2.} \n');
old_dw=0*W; old_db=0*b; 
if mc>=1, mc=1; end;
for i=1:R;
    n=W*P(:,i); % Get NN output
    if Learn_b
        n=n+b;
    end
    a(:,i)=n;          % It means purelin
    err(:,i)=T(:,i)-a(:,i); % Find err
    dw=mc*old_dw+(1-mc)*Lumbda*err(:,i)*[P(:,i)]';
    W=W+dw; old_dw=dw;
    if Learn_b
       db=mc*old_db+(1-mc)*Lumbda*err(:,i);
       b=b+db; old_db=db;
    end
    W_list=[W_list W'];
    b_list=[b_list b];
end

if ~Learn_b
    b_list=0*b_list;
end
% Remove the last one of W_list
[N1, N2]=size(W_list); W_list(:,N2)=[];

% Print out
Err=sum(sum(err.^2));
fprintf('     ===>Sum of squared err = %6.4f\n',Err);
fprintf('   {On-line learn_a2. execution completed} \n');
% End of this function file.