Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / data-smoothing-1.3.0 / ddmat.m

diff --git a/octave_packages/data-smoothing-1.3.0/ddmat.m b/octave_packages/data-smoothing-1.3.0/ddmat.m
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+## Copyright (C) 2003 Paul H. C. Eilers <p.eilers@erasmusmc.nl>
+##
+## 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 3 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 (nargin != 2)
+    print_usage;
+  elseif ( !iscolumn (x) )
+    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 = sparse(diag(1 ./ dx));
+    D = d * V * diff(ddmat(x, d - 1));
+  endif
+endfunction