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% STK_CONDITIONING produces conditioned sample paths
%
% CALL: ZSIMC = stk_conditioning (LAMBDA, ZI, ZSIM, XI_IND)
%
% produces conditioned sample paths ZSMIC from the unconditioned sample paths
% ZSIM, using the matrix of kriging weights LAMBDA. Conditioning is done with
% respect to a finite number NI of observations, located at the indices given
% in XI_IND (vector of length NI), with corresponding noiseless observed
% values ZI.
%
% The matrix LAMBDA must be of size NI x N, where N is the number of
% evaluation points for the sample paths; such a matrix is typically provided
% by stk_predict().
%
% Both ZSIM and ZSIMC have size N x NB_PATHS, where NB_PATH is the number
% sample paths to be dealt with. ZI is a column of length NI.
%
% CALL: ZSIMC = stk_conditioning (LAMBDA, ZI, ZSIM)
%
% assumes that the oberved values ZI correspond to the first NI evaluation
% points.
%
% CALL: ZSIMC = stk_conditioning (LAMBDA, ZI, ZSIM, XI_IND, NOISE_SIM)
%
% produces conditioned sample paths ZSMIC from the unconditioned sample paths
% ZSIM, using the matrix of kriging weights LAMBDA. Conditioning is done with
% respect to a finite number NI of observations, located at the indices given
% in XI_IND (vector of length NI), with corresponding noisy observed values
% ZI, using a NI x N matrix NOISE_SIM of simulated noise values.
%
% NOTE: Conditioning by kriging
%
% stk_conditioning uses the technique called "conditioning by kriging"
% (see, e.g., Chiles and Delfiner, Geostatistics: Modeling Spatial
% Uncertainty, Wiley, 1999)
%
% NOTE: Output type
%
% The output argument ZSIMC will be an stk_dataframe if either LAMBDA or ZSIM
% are stk_dataframe. In case of conflicting row names (coming from
% ZSIM.rownames on the one hand and LAMBDA.colnames on the other hand),
% ZSIMC.rownames is {}.
%
% EXAMPLE: stk_example_kb05
%
% See also stk_generate_samplepaths, stk_predict
% Copyright Notice
%
% Copyright (C) 2015, 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 zsimc = stk_conditioning (lambda, zi, z_sim, xi_ind, noise_sim)
% Are we dealing with noisy observations ?
noisy = (nargin > 4) && (~ isempty (noise_sim));
zi = double (zi);
z_sim = double (z_sim);
[ni, n] = size (lambda);
m = size (z_sim, 2);
if (nargin < 4) || (isempty (xi_ind))
xi_ind = (1:ni)';
else
xi_ind = xi_ind(:);
end
if ~ isequal (size (zi), [ni 1])
stk_error (sprintf (['Considering the size of lambda (%d x %d), zi ' ...
'should have size %d x 1'], ni, n, ni), 'IncorrectSize');
end
if ~ isequal (size (z_sim), [n m])
stk_error (sprintf (['Considering the size of lambda (%d x %d), zsim ' ...
'should have size %d x N, where N is the number of evaluation ' ...
'points for the sample paths.'], ni, n, n), 'IncorrectSize');
end
if ~ isequal (size (xi_ind), [ni 1])
stk_error (sprintf (['Considering the size of lambda (%d x %d), xi_ind ' ...
'should have size %d x 1'], ni, n, ni), 'IncorrectSize');
end
if noisy && (~ isequal (size (noise_sim), [ni m]))
stk_error (sprintf (['Considering the size of lambda (%d x %d) and the ' ...
'size of z_sim (%d x %d), noise_sim should have size %d x %d'], ni, ...
n, n, m, ni, m), 'IncorrectSize');
end
delta = bsxfun (@minus, zi, z_sim(xi_ind, :));
if noisy
delta = delta - noise_sim;
end
zsimc = z_sim + lambda' * delta;
end % function
%!shared n, m, ni, xi_ind, lambda, zsim, zi
%!
%! n = 50; m = 5; ni = 10; xi_ind = 1:ni;
%! lambda = 1/ni * ones (ni, n); % prediction == averaging
%! zsim = ones (n, m); % const unconditioned samplepaths
%! zi = zeros (ni, 1); % conditioning by zeros
%!error zsimc = stk_conditioning ();
%!error zsimc = stk_conditioning (lambda);
%!error zsimc = stk_conditioning (lambda, zi);
%!test zsimc = stk_conditioning (lambda, zi, zsim);
%!test zsimc = stk_conditioning (lambda, zi, zsim, xi_ind);
%!test
%! zsimc = stk_conditioning (lambda, zi, zsim, xi_ind);
%! assert (stk_isequal_tolabs (double (zsimc), zeros (n, m)));
%!test
%! zi = 2 * ones (ni, 1); % conditioning by twos
%! zsimc = stk_conditioning (lambda, zi, zsim, xi_ind);
%! assert (stk_isequal_tolabs (double (zsimc), 2 * ones (n, m)));
%!test
%! DIM = 1; nt = 400;
%! xt = stk_sampling_regulargrid (nt, DIM, [-1.0; 1.0]);
%!
%! NI = 6; xi_ind = [1 20 90 200 300 350];
%! xi = xt(xi_ind, 1);
%! zi = (1:NI)'; % linear response ;-)
%!
%! % Carry out the kriging prediction at points xt
%! model = stk_model ('stk_materncov52_iso');
%! model.param = log ([1.0; 2.9]);
%! [ignore_zp, lambda] = stk_predict (model, xi, [], xt);
%!
%! % Generate (unconditional) sample paths according to the model
%! NB_PATHS = 10;
%! zsim = stk_generate_samplepaths (model, xt, NB_PATHS);
%! zsimc = stk_conditioning (lambda, zi, zsim, xi_ind);
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