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128 lines
3.8 KiB
C++
128 lines
3.8 KiB
C++
// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
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// vi: set et ts=4 sw=4 sts=4:
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/*
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This file is part of the Open Porous Media project (OPM).
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OPM is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 2 of the License, or
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(at your option) any later version.
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OPM is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with OPM. If not, see <http://www.gnu.org/licenses/>.
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Consult the COPYING file in the top-level source directory of this
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module for the precise wording of the license and the list of
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copyright holders.
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*/
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#include "config.h"
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#define BOOST_TEST_MODULE TestLinearLeastSquares
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#include <boost/mpl/list.hpp>
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#include <boost/test/unit_test.hpp>
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#include <dune/common/dynmatrix.hh>
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#include <dune/common/dynvector.hh>
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#include <opm/models/utils/linearleastsquares.hpp>
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using namespace Opm;
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using ScalarTypes = boost::mpl::list<double, float>;
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BOOST_AUTO_TEST_CASE_TEMPLATE(SimpleOverdeterminedSystem, Scalar, ScalarTypes)
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{
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// Solve an overdetermined system Ax=b using linear least squares (i.e. normal equations)
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// Example from: https://en.wikipedia.org/wiki/Linear_least_squares
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Dune::DynamicMatrix<Scalar> A(3, 2);
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A[0][0] = 1.0;
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A[0][1] = 0.0;
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A[1][0] = 0.0;
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A[1][1] = 1.0;
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A[2][0] = 1.0;
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A[2][1] = 1.0;
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Dune::DynamicVector<Scalar> b(3);
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b[0] = 1.0;
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b[1] = 1.0;
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b[2] = 0.0;
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// Instantiate LinearLeastSquares and solve normal equations
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LinearLeastSquares<Scalar> lsq(A, b);
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lsq.solve();
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// Check results
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Dune::DynamicVector<Scalar> xExpected(2);
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xExpected[0] = 1.0 / 3.0;
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xExpected[1] = 1.0 / 3.0;
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const auto& x = lsq.x();
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BOOST_CHECK_EQUAL(x.N(), xExpected.N());
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for (std::size_t i = 0; i < x.N(); ++i) {
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BOOST_CHECK_CLOSE(x[i], xExpected[i], 1e-4);
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}
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// Check sum of squared residuals
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BOOST_CHECK_CLOSE(lsq.residualSumOfSquares(), 4.0 / 3.0, 1e-4);
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// Check total sum of squares
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BOOST_CHECK_CLOSE(lsq.totalSumOfSquares(), 2.0 / 3.0, 1e-4);
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}
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BOOST_AUTO_TEST_CASE_TEMPLATE(LinearRegression, Scalar, ScalarTypes)
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{
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// Linear regression for line: y = beta_0 + beta_1*x, with some y-data
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// Example from: https://en.wikipedia.org/wiki/Linear_least_squares#Example
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Dune::DynamicMatrix<Scalar> X(4, 2);
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X[0][0] = 1.0;
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X[0][1] = 1.0;
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X[1][0] = 1.0;
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X[1][1] = 2.0;
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X[2][0] = 1.0;
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X[2][1] = 3.0;
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X[3][0] = 1.0;
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X[3][1] = 4.0;
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Dune::DynamicVector<Scalar> y(4);
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y[0] = 6.0;
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y[1] = 5.0;
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y[2] = 7.0;
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y[3] = 10.0;
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// Solve linear least squares
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LinearLeastSquares<Scalar> lsq(X, y);
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lsq.solve();
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// Check against solution
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Dune::DynamicVector<Scalar> betaExpected(2);
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betaExpected[0] = 3.5;
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betaExpected[1] = 1.4;
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const auto& beta = lsq.x();
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BOOST_CHECK_EQUAL(beta.N(), betaExpected.N());
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for (std::size_t i = 0; i < beta.N(); ++i) {
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BOOST_CHECK_CLOSE(beta[i], betaExpected[i], 1e-4);
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}
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// Check sum of squared residuals
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BOOST_CHECK_CLOSE(lsq.residualSumOfSquares(), 4.2, 1e-4);
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// Check total sum of squares
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BOOST_CHECK_CLOSE(lsq.totalSumOfSquares(), 14.0, 1e-4);
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// Check R-squared, goodness-of-fit
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BOOST_CHECK_CLOSE(lsq.RSquared(), 0.7, 1e-4);
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// Check interpolation, i.e. y = beta^T * x for an arbitrary x
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Dune::DynamicVector<Scalar> xPred(2);
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xPred[0] = 1.0;
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xPred[1] = 5.0;
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BOOST_CHECK_CLOSE(lsq.evaluate(xPred), 10.5, 1e-4);
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}
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