function [e,w] = Mmax_apa(x,d,N,M,K,w0,mu,epsilon,optsel)

%   ----------------
%   input parameters
%   ----------------
%   x : Lx1 input signal
%   d : Lx1 desired response 
%   N : filter length
%   M : number of coefficients to be updated
%   K : APA order
%   w0 : Nx1 initialization
%   mu : step-size parameter
%   epsilon : regularization parameter (to avoid divide by zero)
%   optsel : 0 for simplified coefficient selection, 1 for optimal
%   coefficient selection
%   ----------------
%   function outputs
%   ----------------
%   e : Lx1 output error vector
%   w : LxN adaptive coefficient vectors

x = x(:);
d = d(:);
w0 = w0(:);

L = length(x);
w = zeros(L,N);
e = zeros(L,1);

w(1,:) = w0';
xvec = zeros(N,1);

X = zeros(K,N);
dvec = zeros(K,1);

for i = 1:L-1
    xvec = [x(i);xvec(1:N-1)];
    X = [xvec';X(1:K-1,:)];
    e(i) = d(i)-w(i,:)*xvec;
    dvec = [d(i);dvec(1:K-1)];
    evec = dvec - X*w(i,:)';
    upd = mu*X'*inv(epsilon*eye(K)+X*X')*evec;

    if optsel == 1,
        [xs,ix] = sort(-abs(upd));          %optimal M-max selection
    else
        [xs,ix] = sort(-sum(X.^2,1));       %simplified approximation
    end

    de = zeros(1,N);
    de(ix(1:M)) = 1;
    IM = diag(de);

    upd = IM*upd;

    w(i+1,:) = w(i,:) + upd';
end
xvec = [x(L);xvec(1:N-1)];
e(L) = d(L)-w(L,:)*xvec;