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// -*- C++ -*-
/**
* @brief The test file of KrigingAlgorithm class
*
* 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
{
// Set Numerical precision to 3
PlatformInfo::SetNumericalPrecision(3);
{
UnsignedInteger sampleSize = 6;
UnsignedInteger dimension = 1;
// Create the function to estimate
Description input(dimension);
input[0] = "x0";
Description formulas(1);
formulas[0] = "x0 * sin(x0)";
SymbolicFunction model(input, formulas);
Sample X(sampleSize, dimension);
Sample X2(sampleSize, dimension);
for ( UnsignedInteger i = 0; i < sampleSize; ++ i )
{
X(i, 0) = 3.0 + i;
X2(i, 0) = 2.5 + i;
}
X(0, 0) = 1.0;
X(1, 0) = 3.0;
X2(0, 0) = 2.0;
X2(1, 0) = 4.0;
Sample Y(model(X));
Sample Y2(model(X2));
Basis basis(ConstantBasisFactory(dimension).build());
SquaredExponential covarianceModel(Point(1, 1e-02), Point(1, 4.50736));
KrigingAlgorithm algo(X, Y, covarianceModel, basis);
// set sensible optimization bounds and estimate hyperparameters
algo.setOptimizationBounds(Interval(X.getMin(), X.getMax()));
algo.run();
// perform an evaluation
KrigingResult result(algo.getResult());
assert_almost_equal(result.getMetaModel()(X), Y, 1e-3);
// Evaluation of the covariance on the X dataset
CovarianceMatrix covMatrix(result.getConditionalCovariance(X));
// Validation of the covariance ==> should be null on the learning set
assert_almost_equal(covMatrix, SquareMatrix(sampleSize), 0.0, 1e-13);
// Covariance per marginal & extract variance component
Collection<CovarianceMatrix> coll(result.getConditionalMarginalCovariance(X));
for(UnsignedInteger k = 0; k < coll.getSize(); ++k)
assert_almost_equal(coll[k](0, 0), 0.0, 1e-14, 1e-13);
// Validation of marginal variance
const Sample marginalVariance(result.getConditionalMarginalVariance(X));
assert_almost_equal(marginalVariance, Sample(sampleSize, 1), 1e-14, 1e-13);
// Prediction accuracy
assert_almost_equal(Y2, result.getMetaModel()(X2), 0.3, 0.0);
}
{
UnsignedInteger dimension = 2;
UnsignedInteger sampleSize = 8;
// Create the function to estimate
Description input(dimension);
input[0] = "x0";
input[1] = "x1";
Description formulas(1);
formulas[0] = "5.-x1-0.5*(x0-0.1)^2";
SymbolicFunction model(input, formulas);
Sample X(sampleSize, dimension);
X(0, 0) = -4.61611719;
X(0, 1) = -6.00099547;
X(1, 0) = 4.10469096;
X(1, 1) = 5.32782448;
X(2, 0) = 0.;
X(2, 1) = -.5;
X(3, 0) = -6.17289014;
X(3, 1) = -4.6984743;
X(4, 0) = 1.3109306;
X(4, 1) = -6.93271427;
X(5, 0) = -5.03823144;
X(5, 1) = 3.10584743;
X(6, 0) = -2.87600388;
X(6, 1) = 6.74310541;
X(7, 0) = 5.21301203;
X(7, 1) = 4.26386883;
Sample Y(model(X));
// create algorithm
Basis basis(ConstantBasisFactory(dimension).build());
Point scale(2);
scale[0] = 1e-05;
scale[1] = 18.9;
Point amplitude(1, 8.05);
SquaredExponential covarianceModel(scale, amplitude);
KrigingAlgorithm algo(X, Y, covarianceModel, basis);
algo.run();
// perform an evaluation
KrigingResult result(algo.getResult());
assert_almost_equal(result.getMetaModel()(X), Y, 1e-3);
Function metaModel(result.getMetaModel());
// Get the gradient computed by metamodel
Matrix gradientKriging(metaModel.gradient(X[1]));
// Set DF evaluation as gradient and validate
metaModel.setGradient(new CenteredFiniteDifferenceGradient(ResourceMap::GetAsScalar( "CenteredFiniteDifferenceGradient-DefaultEpsilon" ), metaModel.getEvaluation()));
// Get the gradient computed by metamodel using FD
Matrix gradientKrigingFD(metaModel.gradient(X[1]));
// Validation of the gradient
assert_almost_equal(gradientKriging, gradientKrigingFD, 1e-3, 1e-3);
// Covariance per marginal & extract variance component
Collection<CovarianceMatrix> coll(result.getConditionalMarginalCovariance(X));
for(UnsignedInteger k = 0; k < coll.getSize(); ++k)
assert_almost_equal(coll[k](0, 0), 0.0, 1e-13, 1e-13);
// Validation of marginal variance
const Sample marginalVariance(result.getConditionalMarginalVariance(X));
assert_almost_equal(marginalVariance, Sample(sampleSize, 1), 1e-13, 1e-13);
}
{
// fix https: //github.com/openturns/openturns/issues/1861
RandomGenerator::SetSeed(0);
SymbolicFunction rho("tau", "exp(-abs(tau))*cos(2*pi_*abs(tau))");
const Point scale = {1.0};
StationaryFunctionalCovarianceModel model(scale, scale, rho);
const Sample x(Normal(0, 1.0).getSample(20));
const Sample y(x + Normal(0, 0.1).getSample(20));
KrigingAlgorithm algo(x, y, model, LinearBasisFactory().build());
algo.run();
KrigingResult result(algo.getResult());
assert_almost_equal(result.getConditionalMarginalVariance(x), Sample(x.getSize(), 1), 1e-16, 1e-16);
}
}
catch (TestFailed & ex)
{
std::cerr << ex << std::endl;
return ExitCode::Error;
}
return ExitCode::Success;
}
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