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% STK_RBF_MATERN52 computes the Matern correlation function of order 5/2.
%
% CALL: K = stk_rbf_matern52 (H)
%
% computes the value of the Matern correlation function of order 5/2 at
% distance H. Note that the Matern correlation function is a valid
% correlation function for all dimensions.
%
% CALL: K = stk_rbf_matern52 (H, DIFF)
%
% computes the derivative of the Matern correlation function of order 5/2, at
% distance H, with respect the distance H if DIFF is equal to 1. (If DIFF is
% equal to -1, this is the same as K = stk_rbf_matern52(H).)
%
% See also: stk_rbf_matern, stk_rbf_matern32
% Copyright Notice
%
% Copyright (C) 2016, 2018 CentraleSupelec
% Copyright (C) 2011, 2012 SUPELEC
%
% Authors: Julien Bect <julien.bect@centralesupelec.fr>
% Emmanuel Vazquez <emmanuel.vazquez@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_matern52 (h, diff)
% default: compute the value (not a derivative)
if nargin < 2,
diff = -1;
end
Nu = 5/2;
C = 2 * sqrt (Nu); % dt/dh
t = C * abs (h);
k = exp (- t);
b = (k > 0);
t = t(b);
if diff <= 0, % value of the covariance function
k(b) = (1 + t + t.^2/3) .* k(b);
elseif diff == 1, % derivative wrt h
k(b) = C * -t/3 .* (1 + t) .* k(b);
else
error ('incorrect value for diff.');
end
end % function
%!shared h, diff
%! h = 1.0; diff = -1;
%!error stk_rbf_matern52 ();
%!test stk_rbf_matern52 (h);
%!test stk_rbf_matern52 (h, diff);
%!test %% h = 0.0 => correlation = 1.0
%! x = stk_rbf_matern52 (0.0);
%! assert (stk_isequal_tolrel (x, 1.0, 1e-8));
%!test %% consistency with stk_rbf_matern: function values
%! for h = 0.1:0.1:2.0,
%! x = stk_rbf_matern (5/2, h);
%! y = stk_rbf_matern52 (h);
%! assert (stk_isequal_tolrel (x, y, 1e-8));
%! end
%!test %% consistency with stk_rbf_matern: derivatives
%! for h = 0.1:0.1:2.0,
%! x = stk_rbf_matern (5/2, h, 2);
%! y = stk_rbf_matern52 (h, 1);
%! assert (stk_isequal_tolrel (x, y, 1e-8));
%! end
%!assert (stk_rbf_matern52 (inf) == 0)
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