function D = ddmat(x, d) %%function D = ddmat(x, d) %% Compute divided differencing matrix of order d %% %% Input %% x: vector of sampling positions %% d: order of diffferences %% Output %% D: the matrix; D * Y gives divided differences of order d %% %%References: Anal. Chem. (2003) 75, 3631. %% %% corrected the recursion multiplier; JJS 2/25/08 %% Copyright (C) 2003 Paul Eilers %% This program is free software; you can redistribute it and/or modify %% it under the terms of the GNU General Public License as published by %% the Free Software Foundation; either version 2 of the License, or %% (at your option) any later version. %% %% This program is distributed in the hope that it will be useful, %% but WITHOUT ANY WARRANTY; without even the implied warranty of %% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the %% GNU General Public License for more details. %% %% You should have received a copy of the GNU General Public License %% along with this program; If not, see <http://www.gnu.org/licenses/>. m = length(x); if d == 0 D = speye(m); else dx = x((d + 1):m) - x(1:(m - d)); V = spdiags(1 ./ dx, 0, m - d, m - d); D = d * V * diff(ddmat(x, d - 1)); end

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