Logo Search packages:      
Sourcecode: octave-data-smoothing version File versions  Download package

ddmat.m

## 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

Generated by  Doxygen 1.6.0   Back to index