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## 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/>.
## -*- 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
## added error check that x is a column vector; JJS 4/13/09
function D = ddmat(x, d)
if ( size(x)(2) != 1 )
error("x should be a column vector")
endif
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
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