function [X] = gen_global_linear_seasonal_trigonometric_X(s,m,n)
% GEN_GLOBAL_LINEAR_SEASONAL_TRIGONOMETRIX - Gen(erate) Global Linear Seasonal Trigonometric design matrix X
%
% Input: 
%   s     : total number of seasons = seasonal indicators.
%   m     : the number of trigonometric functions to consider
%   n     : the number of data points 
% 
% Our assumed model is a globaly constant LINEAR model with "s" seasons and "m=s/2" trigonometric functions:
% 
% z_{t} = \beta_0 + \beta_1 t + \sum_{i=1}^{m} \beta_{1i} \sin( f_i t ) + \beta_{2i} \cos( f_i t ) 
% 
% See page 150 in the book by Abraham.  Note we assume that s is even.
%   
% 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.
% 
%-----

if( mod(m,2)~=0 )
  fprintf('we need m=%10d even\n',m);
  X=[];
  return; 
end

% make the part of X due to the trigonometric terms: 
f        = (2*pi/s);
fs_array = f * (1:m); 

t_array  = (1:n).';  
t_prod_f = t_array * fs_array; 
t_sin    = sin( t_prod_f ); 
t_cos    = cos( t_prod_f ); 

% make a matrix in the format of sin( f_i t ), cos( f_i t ), sin( f_{i+1} t ), cos( f_{i+1} t ) etc ... 
T1 = [];
for jj=1:m,
  T1 = [ T1, t_sin(:,jj), t_cos(:,jj) ]; 
end

% make the part of X due to the global linear piece
T2 = [ ones(n,1), (1:n).' ]; 

% form the entire matrix of regressands
X = [ T2, T1 ];