fix embedding function to be applicable to multi-column vectors

embed.m

@@ -5,22 +5,25 @@
 %     delay T. The resulting embedding vector has length N-T*(M-1),
 %     where N is the length of the original time series.
 %
-%     Reference:
-%         Packard, N. H., Crutchfield, J. P., Farmer, J. D., 
-%         Shaw, R. S. (1980). Geometry from a time series. 
-%         Physical Review Letters 45, 712-716.
-%
 %     Example:
 %         N = 300; % length of time series
 %         x = .9*sin((1:N)*2*pi/70); % exemplary time series
 %         y = embed(x,2,17); % embed into 2 dimensions using delay 17
 %         plot(y(:,1),y(:,2))
+%
+%     Reference:
+%         Packard, N. H., Crutchfield, J. P., Farmer, J. D., 
+%         Shaw, R. S. (1980). Geometry from a time series. 
+%         Physical Review Letters 45, 712-716.
 
-% Copyright (c) 2012-2019
+% Copyright (c) 2012-2022
 % Potsdam Institute for Climate Impact Research
 % Norbert Marwan
 % http://www.pik-potsdam.de
 %
+% $Date: 2021/11/22 12:34:39 $
+% $Revision: 5.2 $
+%
 % This program is free software: you can redistribute it and/or modify it under the terms of the
 % GNU Affero General Public License as published by the Free Software Foundation, either
 % version 3 of the License, or (at your option) any later version.
@@ -36,28 +39,36 @@
 narginchk(1,3)
 nargoutchk(0,1)
 
+
 %% set default values for embedding parameters
-t = 1; m = 1;
+tau = 1; m = 1;
 
 %% get input arguments
 if nargin > 2
-    t = varargin{3};
+    tau = varargin{3};
 end
 if nargin > 1
     m = varargin{2};
 end    
 
-x = varargin{1}(:); % we expect a column vector
-Nx = length(x); % length of time series
-NX = Nx-t*(m-1); % length of embedding vector
-
+x = varargin{1}; % input vector
+N = size(x,1) - (m-1)*tau; % length of embedding vector
+if N <= 1 % check if row vector (transform it to column vector)
+   x = x(:);
+   N = length(x) - (m-1)*tau; % length of embedding vector
+end
 
-%% create embeeding vector 
-% performed using MATLAB's vectorization
-% result is an index series representing the time delay and dimension
-for i = 1:m;
-    jx(1+NX*(i-1):NX+NX*(i-1)) = 1+t*(i-1):NX+t*(i-1);
+d = size(x,2); % number of columns
+if d > N % check if long enough related to the number of columns
+   error('Number of columns should be smaller than the length of the time series.')
 end
 
-%% the final embedding vector
-y = reshape(x(jx),NX,m);
+%% create embedding vector 
+if size(x,2) == 1 % input vector is one-column time series
+    y = buffer(x,N,N-tau,'nodelay');
+else % input vector is multi-column time series
+    y = zeros(N, d*m);
+    for i = 1:d
+       y(:, (i-1)*m+[1:m] ) = buffer(x(:,i),N,N-tau,'nodelay');
+    end
+end