function [Y] = PickPeriodicValues( X, m, n, p, q )
% Return the sub-matrix composed of all chosen cells
% Periodic specification: m, n specify the rows; p, q specify the columns.
% If m or n contains 0, then all rows are specified.
% If p or q contains 0, then all cols are specified.
% The intersection of the row spec & col spec, is chosen.
% Example:  m=3, n=4 => The 3rd row in each group of 4 rows is specified.
%           p=2, q=6 => The 2nd col in each group of 6 cols is specified.
%           The returned matrix contains:
%           (3, 2), (3, 8), ...
%           (7, 2), (7, 8), ... etc.
%
% 15 Jan 2009 - D.Bozarth
% 16 Jan Allow m, p to be vectors.
%
if ~all(m) || ~all(n); m = 0; n = 0; end
if ~all(p) || ~all(q); p = 0; q = 0; end

Y        = [];
[h, w]   = size(X);

for j = 1:h
   % Justify the modulus operation being zero-centric,
   % .. with Matlab's starting index of 1.
   s = j; r = n;
   %r = mod(j, n);
   if mod(j, n) == 0; s = n; r = 0; end;
   
   %if j == n; r = 0; end;
   
   %if any( m == 0 ) || any( m == mod(j, n) )
   if any( m == 0 ) || any( m == mod(s, r) )      
      % The current row is specified for output.
      if p == 0
         % All columns are specified for output.
         row = [X(j, :)];
      else
         row = [];
         
         for k = 1:w
            %r = q; if j == n; r = 0; end;
            %if any( p == mod(k, r) )           
            s = k; r = q;
            if mod(k, q) == 0; s = q; r = 0; end;
            
            if any( p == mod(s, r) )
               % The current column is specified for output.
               row = [row  X(j,k)];
            end
         end
      end
            
      Y = [Y ; row];
   end
end
%
% end script