function  [f, df] = regpoly2(S)%REGPOLY2  Second order polynomial regression function% Call:    f = regpoly2(S)%          [f, df] = regpoly2(S)%% S : m*n matrix with design sites% f =  [1 S S(:,1)*S S(:,2)S(:,2:n) ... S(:,n)^2]% df : Jacobian at the first point (first row in S) % hbn@imm.dtu.dk  % Last update September 4, 2002[m n] = size(S);nn = (n+1)*(n+2)/2;  % Number of columns in f  % Compute  ff = [ones(m,1) S zeros(m,nn-n-1)];j = n+1;   q = n;for  k = 1 : n  f(:,j+(1:q)) = repmat(S(:,k),1,q) .* S(:,k:n);  j = j+q;   q = q-1;endif  nargout > 1  df = [zeros(n,1)  eye(n)  zeros(n,nn-n-1)];  j = n+1;   q = n;   for  k = 1 : n    df(k,j+(1:q)) = [2*S(1,k) S(1,k+1:n)];    for i = 1 : n-k,  df(k+i,j+1+i) = S(1,k); end    j = j+q;   q = q-1;  endend