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
93
|
% STK_RBF_SPHERICAL computes the spherical correlation function
%
% CALL: K = stk_rbf_spherical (H)
%
% computes the value of the spherical correlation function at distance H:
%
% /
% | 1 - 3/2 |h| + 1/2 |h|^3 if |h| < 1,
% K = |
% | 0 otherwise.
% \
%
% CALL: K = stk_rbf_spherical (H, DIFF)
%
% computes the derivative of the spherical correlation function with
% respect the H if DIFF is equal to 1, and simply returns the value of the
% exponential correlation function if DIFF <= 0 (in which case it is
% equivalent to K = stk_rbf_spherical (H)).
%
% ADMISSIBILITY
%
% The spherical correlation is a valid correlation function in
% dimension d <= 3.
% Copyright Notice
%
% Copyright (C) 2016, 2018 CentraleSupelec
%
% Author: Julien Bect <julien.bect@centralesupelec.fr>
% Copying Permission Statement
%
% This file is part of
%
% STK: a Small (Matlab/Octave) Toolbox for Kriging
% (https://github.com/stk-kriging/stk/)
%
% STK 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.
%
% STK 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 STK. If not, see <http://www.gnu.org/licenses/>.
function k = stk_rbf_spherical (h, diff)
t = abs (h);
b = (t < 1);
k = zeros (size (h));
if (nargin < 2) || (diff <= 0)
% value of the spherical correlation at h
k(b) = ((1 - t(b)) .^ 2) .* (1 + 0.5 * t(b));
elseif diff == 1
% derivative of the spherical correlation function at h
% (convention: k'(0) = 0, even though k is not derivable at h=0)
k(b) = 1.5 * (sign (h(b))) .* (t(b) .^ 2 - 1);
else
error ('incorrect value for diff.');
end
end % function
%!shared h, diff
%! h = 1.0; diff = -1;
%!error stk_rbf_spherical ();
%!test stk_rbf_spherical (h);
%!test stk_rbf_spherical (h, diff);
%!test %% h = 0.0 => correlation = 1.0
%! x = stk_rbf_spherical (0.0);
%! assert (stk_isequal_tolrel (x, 1.0, 1e-8));
%!test %% check derivative numerically
%! h = [-1 -0.5 -0.1 0.1 0.5 1]; delta = 1e-9;
%! d1 = (stk_rbf_spherical (h + delta) - stk_rbf_spherical (h)) / delta;
%! d2 = stk_rbf_spherical (h, 1);
%! assert (stk_isequal_tolabs (d1, d2, 1e-4));
%!assert (stk_rbf_spherical (inf) == 0)
|
