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% STK_MAKE_MATCOV computes a covariance matrix (and a design matrix)
%
% CALL: [K, P] = stk_make_matcov (MODEL, X0)
%
% computes the covariance matrix K and the design matrix P for the model
% MODEL at the set of points X0, which is expected to be an N x DIM
% array. As a result, a matrix K of size N x N and a matrix P of size
% N x L are obtained, where L is the number of regression functions in
% the linear part of the model.
%
% CALL: K = stk_make_matcov (MODEL, X0, X1)
%
% computes the covariance matrix K for the model MODEL between the sets
% of points X0 and X1. The resulting K matrix is of size N0 x N1, where
% N0 is the number of rows of XO and N1 the number of rows of X1.
%
% BE CAREFUL:
%
% stk_make_matcov (MODEL, X0) and stk_makematcov (MODEL, X0, X0) are NOT
% equivalent if model.lognoisevariance > - inf (in the first case, the
% noise variance is added on the diagonal of the covariance matrix).
% Copyright Notice
%
% Copyright (C) 2015, 2016, 2018 CentraleSupelec
% Copyright (C) 2011-2014 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
% (http://sourceforge.net/projects/kriging)
%
% 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, P] = stk_make_matcov (model, x0, x1, pairwise)
% Check if the covariance model contains parameters
% that should have been estimated first
if (isnumeric (model.param)) && (any (isnan (model.param)))
stk_error (['The covariance model contains undefined parameters, ' ...
'which must be estimated first.'], 'ParametersMustBeEstimated');
end
%=== process input arguments
x0 = double (x0);
if (nargin > 2) && (~ isempty (x1))
x1 = double (x1);
make_matcov_auto = false;
else
x1 = x0;
make_matcov_auto = true;
end
pairwise = (nargin > 3) && pairwise;
%=== compute the covariance matrix
K = feval (model.covariance_type, model.param, x0, x1, -1, pairwise);
if make_matcov_auto && stk_isnoisy (model)
K = K + stk_covmat_noise (model, x0, [], -1, pairwise);
end
%=== compute the regression functions
if nargout > 1
P = stk_ortho_func (model, x0);
end
end % function
%!shared model, model2, x0, x1, n0, n1, d, Ka, Kb, Kc, Pa, Pb, Pc
%! n0 = 20; n1 = 10; d = 4;
%! model = stk_model ('stk_materncov52_aniso', d);
%! model.lm = stk_lm_affine;
%! model.param = log ([1.0; 2.1; 2.2; 2.3; 2.4]);
%! model2 = model; model2.lognoisevariance = log(0.01);
%! x0 = stk_sampling_randunif (n0, d);
%! x1 = stk_sampling_randunif (n1, d);
%!error [KK, PP] = stk_make_matcov ();
%!error [KK, PP] = stk_make_matcov (model);
%!test [Ka, Pa] = stk_make_matcov (model, x0); % (1)
%!test [Kb, Pb] = stk_make_matcov (model, x0, x0); % (2)
%!test [Kc, Pc] = stk_make_matcov (model, x0, x1); % (3)
%!error [KK, PP] = stk_make_matcov (model, x0, x1, pi);
%!assert (isequal (size (Ka), [n0 n0]));
%!assert (isequal (size (Kb), [n0 n0]));
%!assert (isequal (size (Kc), [n0 n1]));
%!assert (isequal (size (Pa), [n0 d + 1]));
%!assert (isequal (size (Pb), [n0 d + 1]));
%!assert (isequal (size (Pc), [n0 d + 1]));
% In the noiseless case, (1) and (2) should give the same results
%!assert (isequal (Kb, Ka));
% In the noisy case, however...
%!test [Ka, Pa] = stk_make_matcov (model2, x0); % (1')
%!test [Kb, Pb] = stk_make_matcov (model2, x0, x0); % (2')
%!error assert (isequal (Kb, Ka));
% The second output depends on x0 only => should be the same for (1)--(3)
%!assert (isequal (Pa, Pb));
%!assert (isequal (Pa, Pc));
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