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
82
83
84
85
86
87
88
89
90
91
92
|
########################################################################
##
## 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 {} {@var{jumps} =} ppjumps (@var{pp})
## Evaluate the boundary jumps of a piecewise polynomial.
##
## If there are @math{n} intervals, and the dimensionality of @var{pp} is
## @math{d}, the resulting array has dimensions @code{[d, n-1]}.
## @seealso{mkpp}
## @end deftypefn
function jumps = ppjumps (pp)
if (nargin < 1)
print_usage ();
endif
if (! (isstruct (pp) && strcmp (pp.form, "pp")))
error ("ppjumps: PP must be a structure");
endif
## Extract info.
[x, P, n, k, d] = unmkpp (pp);
nd = length (d) + 1;
## Offsets.
dx = diff (x(1:n));
dx = repmat (dx, [prod(d), 1]);
dx = reshape (dx, [d, n-1]);
dx = shiftdim (dx, nd - 1);
## Use Horner scheme.
if (k>1)
llim = shiftdim (reshape (P(1:(n-1) * prod (d), 1), [d, n-1]), nd - 1);
endif
for i = 2 : k
llim .*= dx;
llim += shiftdim (reshape (P(1:(n-1) * prod (d), i), [d, n-1]), nd - 1);
endfor
rlim = shiftdim (ppval (pp, x(2:end-1)), nd - 1);
jumps = shiftdim (rlim - llim, 1);
endfunction
%!test
%! p = [1 6 11 6];
%! x = linspace (5, 6, 4);
%! y = polyval (p, x);
%! pp = spline (x, y);
%! jj = ppjumps (pp);
%! assert (jj, [0 0], eps);
%!test
%! breaks = [0 1 2];
%! pp1 = poly (-[1 2 3]);
%! pp2 = poly (-([1 2 3]+1));
%! pp = mkpp (breaks, [pp1;pp2]);
%! assert (ppjumps (pp), 0, eps);
%!test
%! breaks = [0 1 2];
%! pp1 = poly (-[1 2 3]);
%! pp2 = poly (([1 2 3]+1));
%! pp = mkpp (breaks, [pp1;pp2]);
%! j = - 2 * polyval (pp1, 1);
%! assert (ppjumps (pp), j, eps);
|
