% Generates a 1D orthonormal polynomial base
% polys = legendrepoly1D_2(X,maxorder,w);
% The weighting function has not been tested extensively
% Manuel Guizar - March 10, 2009

% Copyright (c) 2016, Manuel Guizar Sicairos, James R. Fienup, University of Rochester
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function polys = legendrepoly1D_2(X,maxorder,w)

if nargin < 3
    w = 1;
end

[nc nr] = size(X);

polys = ones(nc,nr);
%%% Generation of polynomials
for ii = 0:maxorder,
    
    polys(:,:,ii+1) = (X.^(ii));   

end

%%% Normalization
for ii = 1:length(polys(1,1,:)),
%     polys(:,:,ii) = polys(:,:,ii)/sqrt(sum(sum(abs(polys(:,:,ii)).^2)));
    polys(:,:,ii) = polys(:,:,ii)/sqrt(sum(sum(w.*abs(polys(:,:,ii)).^2)));
end

%%% Orthonormalization
for ii = 2:length(polys(1,1,:)),
    for jj = 1:ii-1,
        polys(:,:,ii) = polys(:,:,ii) - sum(sum(polys(:,:,ii).*polys(:,:,jj).*w))*polys(:,:,jj);
    end
     
    polys(:,:,ii) = polys(:,:,ii)/sqrt(sum(sum(w.*polys(:,:,ii).^2)));
end
% polys(:,:,3) = polys(:,:,3) - sum(sum(polys(:,:,3).*polys(:,:,1)))*polys(:,:,1);
% polys(:,:,3) = polys(:,:,3)/sum(sum(polys(:,:,3).^2));