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## Copyright (C) 2008-2011 VZLU Prague, a.s., Czech Republic
##
## This file is part of Octave.
##
## Octave 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 software; see the file COPYING.  If not, see
## <http://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn {Function File} {ppd =} ppder (pp, m)
## Computes the piecewise @var{m}-th derivative of a piecewise polynomial
## struct @var{pp}. If @var{m} is omitted the first derivate is
## calculated.
## @seealso{mkpp, ppval, ppint}
## @end deftypefn

function ppd = ppder (pp, m)

  if ((nargin < 1) || (nargin > 2))
    print_usage ();
  elseif (nargin == 1)
    m = 1;
  endif

  if !(isstruct (pp) && strcmp (pp.form, "pp"))
    error ("ppder: PP must be a structure");
  endif

  [x, p, n, k, d] = unmkpp (pp);

  if (k - m <= 0)
    x = [x(1) x(end)];
    pd = zeros (prod (d), 1);
  else
    f = k : -1 : 1;
    ff = bincoeff (f, m + 1) .* factorial (m + 1) ./ f;
    k -= m;
    pd = p(:,1:k) * diag (ff(1:k));
  endif

  ppd = mkpp (x, pd, d);
endfunction

%!shared x,y,pp,ppd
%! x=0:8;y=[x.^2;x.^3+1];pp=spline(x,y);
%! ppd=ppder(pp);
%!assert(ppval(ppd,x),[2*x;3*x.^2],1e-14)
%!assert(ppd.order,3)
%! ppd=ppder(pp,2);
%!assert(ppval(ppd,x),[2*ones(size(x));6*x],1e-14)
%!assert(ppd.order,2)
%! ppd=ppder(pp,3);
%!assert(ppd.order,1)
%!assert(ppd.pieces,8)
%!assert(size(ppd.coefs),[16,1])
%! ppd=ppder(pp,4);
%!assert(ppd.order,1)
%!assert(ppd.pieces,1)
%!assert(size(ppd.coefs),[2,1])
%!assert(ppval(ppd,x),zeros(size(y)),1e-14)
author	John W. Eaton <jwe@octave.org>
date	Thu, 15 Sep 2011 12:51:10 -0400
parents	59e2460acae1
children	be74491c20e8