function [Y,T]=phasespace(x,dim,tau)

%Syntax: [Y,T]=phasespace(x,dim,tau) 

%___________________________________ 

%

% The phase space reconstruction of a time series x with the Method Of Delays

% (MOD), in embedding dimension m and for time dalay tau. 

% 

% Y is the trajectory matrix in the reconstructed phase space.

% T is the phase space length.

% x is the time series. 

% dim is the embedding dimension.

% tau is the time delay.

%

%

% Reference:

% Takens F (1981): Detecting strange attractors in turbulence. Lecture notes in

% Mathematics, 898. Springer.

%

%

% Alexandros Leontitsis

% Department of Education

% University of Ioannina

% 45110 - Dourouti

% Ioannina

% Greece

%

% University e-mail: me00743@cc.uoi.gr

% Lifetime e-mail: leoaleq@yahoo.com

% Homepage: http://www.geocities.com/CapeCanaveral/Lab/1421

%

% 11 Mar 2001.

if nargin<1 || isempty(x)==1

   error('You should provide a time series.');

else

   % x must be a vector

   if min(size(x))>1

      error('Invalid time series.');

   end

   x=x(:);

   % N is the time series length

   N=length(x);

end

if nargin<2 || isempty(dim)==1

    dim=2;

else

    % dim must be scalar

    if sum(size(dim))>2

        error('dim must be scalar.');

    end

    % dim must be an integer

    if dim-round(dim)~=0

        error('dim must be an integer.');

    end

    % dim must be positive

    if dim<=0

        error('dim must be positive.');

    end

end

if nargin<3 || isempty(tau)==1

    tau=1;

else

    % tau must be scalar

    if sum(size(tau))>2

        error('tau must be scalar.');

    end

    % tau must be an integer

    if tau-round(tau)~=0

        error('tau must be an integer.');

    end

    % tau must be positive

    if tau<=0

        error('tau must be positive.');

    end

end

% Total points on phase space 

T = N - (dim-1)*tau;

% Initialize the phase space

Y = zeros (T,dim);

% Phase space reconstruction with MOD

for i = 1 : T

   Y(i,:) = x(i+(0:dim-1)*tau)';

end