function [G]=makeg(dim, m1, derivatives, sigma)
%
% Usage: G = makeg(dim, m1, derivatives, sigma)
%
% makeg will create a (dim x dim) DGT matrix with basis functions in the columns.  
% There are m1 basis functions at each location.  'derivatives' and 'sigma' are 
% length m1 vectors specifying the derivative orders of each basis function at a 
% location and the standard deviations of the Gaussians from which each derivative
% is generated.  A good basis set, with m1 = 8, is: 
%   derivatives = [ 0 3 10 21 36 53 74 99]; 
%   sigma = [3.4 3.4 3.4 3.4 3.4 3.4 3.4 3.4]'
%
% This set of m1 basis functions is then shifted to dim/m1 uniformly distributed 
% locations.

% Written by Jeffrey A Bloom.
%
% This function calls the following M-file functions:
% DG.m

%-------------------- 
% General variables
%-------------------- 

disp('  makeg called with sigma ');disp(sigma);
disp('  and orders ');disp(derivatives);

offset=(m1-1)/2;
longdim=2*dim-1;
param= [0,longdim,0,(longdim+1)/2+offset];	   % initial value
                                                % param = [n,dim,sigma,loc]
locations = (0:(dim/m1-1))*m1 + 1 + offset;

%-----------------------
% Generate the G matrix
%-----------------------
% There are m1 basis functions which are then shifted to get the rest.
% LongG are the m1 functions, doubly long to allow proper shifting

LongG = zeros(longdim,m1);
for j=1:m1
  param(3) = sigma(j);
  param(1) = derivatives(j);
  LongG(:,j) = DG(param)';
end

for j=1:m1
  for i=1:dim/m1
    start = (longdim+1)/2 - (i-1)*m1;
    G(:,(j-1)*dim/m1+i) = LongG(start:start+dim-1,j);
  end
end

%----------------------------
% Normalize the columns of G
%----------------------------

disp('  Normalizing G')
Gmax = max(G);	% This returns a row vector with each element the max of 
		% the corresponding column in G
G = G./Gmax(ones(dim,1),:)*10;	% Now all columns of G have a max of 10.

return
% end function