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
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
|
########################################################################
##
## Copyright (C) 2008-2024 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## 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.
##
## Octave 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 Octave; see the file COPYING. If not, see
## <https://www.gnu.org/licenses/>.
##
########################################################################
## -*- texinfo -*-
## @deftypefn {} {ppd =} ppder (pp)
## @deftypefnx {} {ppd =} ppder (pp, m)
## Compute the piecewise @var{m}-th derivative of a piecewise polynomial
## struct @var{pp}.
##
## If @var{m} is omitted the first derivative is calculated.
## @seealso{mkpp, ppval, ppint}
## @end deftypefn
function ppd = ppder (pp, m = 1)
if (nargin < 1)
print_usage ();
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)
|
