matlab LMS algorithm

In this article, I show the LMS algorithm in MATLAB. Following is the source codes. You  can copy it and then run it. This algrithm is invented by B Widrow and M Hoff, in 1960.

% mylms.m

% LMS algorithm


tol=0.001;
X=[[1;1;0],[1;0;1],[0;0;0],[0;1;0]];
T=[1,1,0,0];


w1=linspace(-1,2,101);w2=w1;
[w1,w2]=meshgrid(w1,w2);
for i=1:101
    for j=1:101
        E(i,j)=norm(T-[w1(i,j),w2(i,j)]*X(1:2,:)); % the error surface about W(1) and W(2), while taking W(3)=b=0
    end
end
mesh(w1,w2,E);hold on;


W=rand(1,3);  % 1 X 3
b=rand(1);
D=T-(W*X-b);
k=0;
while (norm(D)>=tol&&k<1000)   
    mu=.2;
    DW=mu*D*X.';              % least mean-square learning rule
    W=W+DW;
    Db=mu*sum(D);b=b-Db;
    D=T-(W*X-b);
    k=k+1;
    plot3(W(1),W(2),norm(T-[W(1),W(2)]*X(1:2,:)),'or');  % draw the sequence of W(1) and W(2) on the error surface
    hold on;pause(.01);
end


norm(D)