function [X] = gen_global_linear_seasonal_indicator_X(s,n)
% GEN_GLOBAL_LINEAR_SEASONAL_INDICATOR - Gen(erate) Global Linear Seasonal Indicator design matrix X
%
% Input: 
%   s     : total number of seasons = seasonal indicators.
%   n     : the number of data points 
% 
% Our assumed model is a globaly constant LINEAR model with "s" seasonal indicators: 
% 
% z_{t} = \beta_0 + \beta_1 t + \sum_{i=1}^{s-1} \delta_i \mathrm{IND}_{ti} + \varepsilon_{t} 
% 
% See the book by Abraham
%   
% Written by:
% -- 
% John L. Weatherwax                2009-06-01
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

% this requirement is not nessesary but makes the code below simpleer, since we don't have to deal with any remainder terms: 
if( mod(n,s)~=0 ) 
  fprintf('we need n=%10d exactly divisable by s=%10d and n/s=%10.6f\n',n,s,n/s);
  X=[];
  return; 
end

% make blocks of size s x (s-1) representing the seasonal indicators 
IND = eye( s, s-1 ); 
ALL_IND = []; 
for t = 1:(n/s), 
  ALL_IND = [ ALL_IND; IND ]; 
end

% make the part of X due to the global linear piece
TMP = [ ones(n,1), (1:n).' ]; 

% form the entire matrix of regressands
X = [ TMP, ALL_IND ];