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// -*- C++ -*-
/**
* @brief The test file of class LinearModelAlgorithm
*
* 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
{
{
fullprint << "Fit y ~ 3 - 2 x + 0.05 * sin(x) model using 20 points (sin(x) ~ noise)" << std::endl;
UnsignedInteger size = 20;
Sample oneSample(size, 1);
Sample twoSample(size, 1);
for (UnsignedInteger i = 0; i < size; ++i)
{
oneSample[i][0] = 7.0 * sin(-3.5 + (6.5 * i) / (size - 1.0)) + 2.0;
twoSample[i][0] = -2.0 * oneSample[i][0] + 3.0 + 0.05 * sin(oneSample[i][0]);
}
LinearModelAlgorithm test(oneSample, twoSample);
LinearModelResult result(test.getResult());
fullprint << "result = " << std::endl;
fullprint << result << std::endl;
fullprint << result.__str__() << std::endl;
fullprint << "trend coefficients = " << result.getCoefficients() << std::endl;
}
{
fullprint << "Fit y ~ 1 + 0.1 x + 10 x^2 model using 100 points" << std::endl;
UnsignedInteger size = 100;
// Define a linear grid from 0 to 10 with size points
// We use a Box experiment ==> remove 0 & 1 points
const Box experiment(Indices(1, size - 2));
Sample X(experiment.generate());
// X is defined in [0,1]
const Point scale(1, 10.0);
X *= scale;
// Stack X2
Sample X2(X);
for (UnsignedInteger i = 0; i < size; ++i)
X2(i, 0) = X(i, 0) * X(i, 0);
// Stack
X.stack(X2);
// Define y = 1 + 0.1 * x + 10 x^2 + e with e a gaussian noise
Sample Y(size, 1);
for (UnsignedInteger i = 0; i < size; ++i)
Y(i, 0) = 1.0 + 0.1 * X(i, 0) + 10.0 * X(i, 0) * X(i, 0) + 0.1 * DistFunc::rNormal();
LinearModelAlgorithm test(X, Y);
LinearModelResult result(test.getResult());
fullprint << "trend coefficients = " << result.getCoefficients() << std::endl;
// Test various attributes
const Point cook(result.getCookDistances());
const Point cook_reference = {0.0233296, 0.0360369, 0.00178903, 0.0502183, 0.0966701, 0.00562596};
Point cookFirstElements(cook_reference.getSize());
for (UnsignedInteger i = 0; i < cookFirstElements.getSize(); ++i)
cookFirstElements[i] = cook[i];
assert_almost_equal(cookFirstElements, cook_reference, 1e-5, 0.0);
const Point leverages(result.getLeverages());
const Point leverages_reference = {0.0864939, 0.0797831, 0.0735447, 0.0677578, 0.0624023, 0.0574582};
Point leverageFirstElements(leverages_reference.getSize());
for (UnsignedInteger i = 0; i < leverageFirstElements.getSize(); ++i)
leverageFirstElements[i] = leverages[i];
assert_almost_equal(leverageFirstElements, leverages_reference, 1e-6, 0.0);
LeastSquaresMethod lsMethod(result.buildMethod());
SymmetricMatrix projectionMatrix(lsMethod.getH());
assert_equal(projectionMatrix.getNbRows(), size);
assert_equal(projectionMatrix.getNbColumns(), size);
Point predictionsReference(result.getFittedSample().asPoint());
Point predictionsFromProjection(projectionMatrix * Y.asPoint());
assert_almost_equal(predictionsFromProjection, predictionsReference);
Sample residuals(result.getSampleResiduals());
assert_equal(residuals.getSize(), size);
assert_equal(residuals.getDimension(), (UnsignedInteger) 1);
Point residualsReference(Y.asPoint() - predictionsReference);
assert_almost_equal(residuals.asPoint(), residualsReference);
}
}
catch (TestFailed &ex)
{
std::cerr << ex << std::endl;
return ExitCode::Error;
}
return ExitCode::Success;
}
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