assemble_M_re.m

function out_M_re = assemble_M_re(freq, epsilon, rbf_type, der_used)

% This is the matrix of all inner products 
% of the RBF elements
std_freq = std(diff(log(1./freq)));
mean_freq = mean(diff(log(1./freq)));
out_M_re = zeros(numel(freq)+2, numel(freq)+2);
out_M_re_temp = zeros(numel(freq));
R=zeros(1,numel(freq));
C=zeros(numel(freq),1);

if std_freq/mean_freq<1  %(error in frequency difference <1% make sure that the terms are evenly distributed)
            for iter_freq_n = 1: numel(freq)
                    freq_n = freq(iter_freq_n);
                    freq_m = freq(1);
                    C(iter_freq_n, 1) = inner_prod_rbf(freq_n, freq_m, epsilon);
            end  

            for iter_freq_m = 1: numel(freq)

                    freq_n = freq(1);
                    freq_m = freq(iter_freq_m);
                    R(1, iter_freq_m) = inner_prod_rbf(freq_n, freq_m, epsilon);

            end

            out_M_re_temp = toeplitz(C,R);

        else % if the log of tau is not evenly spaced
            for iter_freq_n = 1: numel(freq)

                for iter_freq_m = 1: numel(freq)

                    freq_n = freq(iter_freq_n);
                    freq_m = freq(iter_freq_m);
                    out_M_re_temp(iter_freq_n, iter_freq_m) = inner_prod_rbf(freq_n, freq_m, epsilon);

                end
            end

        end


out_M_re(3:end, 3:end) = out_M_re_temp;

end