## [de8fbf]: inst / ddmat.m Maximize Restore History

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48``` ```## 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 . ## -*- texinfo -*- ##@deftypefn {Function File} {@var{D} =} ddmat (@var{x}, @var{o}) ## Compute divided differencing matrix of order @var{o} ## ## @itemize @w ## @item Input ## @itemize @w ## @item @var{x}: vector of sampling positions ## @item @var{o}: order of diffferences ## @end itemize ## @item Output ## @itemize @w ## @item @var{D}: the matrix; @var{D} * Y gives divided differences of order @var{o} ## @end itemize ## @end itemize ## ##References: Anal. Chem. (2003) 75, 3631. ## ## @end deftypefn ## corrected the recursion multiplier; JJS 2/25/08 function D = ddmat(x, d) 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)); endif endfunction ```