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// -*- C++ -*-
/**
* @brief The test file of KrigingAlgorithm class using
* StationaryFunctionalCovarianceModel
*
* Copyright 2005-2025 Airbus-EDF-IMACS-ONERA-Phimeca
*
* This library is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This library 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this library. If not, see <http://www.gnu.org/licenses/>.
*
*/
#include "openturns/OT.hxx"
#include "openturns/OTtestcode.hxx"
using namespace OT;
using namespace OT::Test;
int main(int, char *[])
{
TESTPREAMBLE;
OStream fullprint(std::cout);
try
{
// Learning data
Point levels = {8, 6};
// Define the Box
Box box(levels);
// Get the input sample
Sample inputSample( box.generate() );
// Scale each direction
inputSample *= 10;
// Define model
Description inputDescription = {"x", "y"};
Description formula = {"cos(0.5*x) + sin(y)"};
const SymbolicFunction model(inputDescription, formula);
// Build the output sample
const Sample outputSample( model(inputSample) );
// Validation
Collection<Distribution> coll(2);
coll[0] = Uniform(1.0, 9.0);
coll[1] = Uniform(1.0, 9.0);
JointDistribution dist(coll);
const Sample inputValidation(dist.getSample(10));
const Sample outputValidation(model(inputValidation));
// 2) Reimplement the squared exponential covariance model
formula[0] = "exp(-0.5* (x * x + y * y))" ;
const SymbolicFunction rho(inputDescription, formula);
const Point scale = {6.0, 2.0};
const Point amplitude = {1.5};
StationaryFunctionalCovarianceModel covarianceModel(scale, amplitude, rho);
// 3) Basis definition
Basis basis(LinearBasisFactory(2).build());
// 4) Kriging algorithm
KrigingAlgorithm algo(inputSample, outputSample, covarianceModel, basis);
Point start(inputSample.getDimension(), 50.0);
Point loglikelihood(algo.getReducedLogLikelihoodFunction()(start));
algo.setOptimizeParameters(false);
algo.run();
KrigingResult result(algo.getResult());
Function metaModel(result.getMetaModel());
assert_almost_equal(result.getConditionalMarginalVariance(inputSample),
Sample(inputSample.getSize(), 1), 1e-14, 1e-14);
// Consistency check: does the reimplementation fit the SquaredExponential class?
SquaredExponential SE(inputSample.getDimension());
SE.setScale(scale);
SE.setAmplitude(amplitude);
KrigingAlgorithm algoSE(inputSample, outputSample, SE, basis);
Point loglikelihoodSE(algoSE.getReducedLogLikelihoodFunction()(start));
assert_almost_equal(loglikelihood, loglikelihoodSE, 1e-8, 1e-8);
// High level consistency check: does the prediction fit too?
algoSE.setOptimizeParameters(false);
algoSE.run();
KrigingResult resultSE(algoSE.getResult());
Function metaModelSE(resultSE.getMetaModel());
assert_almost_equal(metaModel(inputValidation), metaModelSE(inputValidation), 1e-8, 1e-8);
// Approximation error
assert_almost_equal(outputValidation, metaModel(inputValidation), 5.0e-3, 5.0e-3);
}
catch (TestFailed & ex)
{
std::cerr << ex << std::endl;
return ExitCode::Error;
}
return ExitCode::Success;
}
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