TestTriangularMatrixOperations.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: TestTriangularMatrixOperations.cpp
//
// For more information, please see: http://www.nektar.info
//
// The MIT License
//
// Copyright (c) 2006 Division of Applied Mathematics, Brown University (USA),
// Department of Aeronautics, Imperial College London (UK), and Scientific
// Computing and Imaging Institute, University of Utah (USA).
//
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included
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// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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// Description:
//
///////////////////////////////////////////////////////////////////////////////
 
#include <LibUtilities/LinearAlgebra/NekLinSys.hpp>
#include <LibUtilities/LinearAlgebra/NekMatrix.hpp>
 
#include <boost/test/tools/floating_point_comparison.hpp>
#include <boost/test/unit_test.hpp>
 
namespace Nektar::TriangularMatrixVectorMultiplicationUnitTests
{
BOOST_AUTO_TEST_CASE(TestUpperTriangularMatrixVectorMultiplication)
{
    // [1 2 3 4]
    // [0 5 6 7]
    // [0 0 8 9]
    // [0 0 0 10]
 
    NekDouble a_buf[] = {1, 2, 5, 3, 6, 8, 4, 7, 9, 10};
    NekDouble x_buf[] = {10, 20, 30, 40};
 
    NekMatrix<NekDouble, StandardMatrixTag> m(4, 4, a_buf, eUPPER_TRIANGULAR);
    NekVector<NekDouble> x(4, x_buf);
 
    NekVector<NekDouble> result = m * x;
 
    NekDouble expected_result_buf[] = {300, 560, 600, 400};
    NekVector<NekDouble> expected_result(4, expected_result_buf);
    BOOST_CHECK_EQUAL(expected_result, result);
}
 
BOOST_AUTO_TEST_CASE(TestScaledUpperTriangularMatrixVectorMultiplication)
{
    // [1 2 3 4]
    // [0 5 6 7]
    // [0 0 8 9]
    // [0 0 0 10]
 
    NekDouble a_buf[] = {1, 2, 5, 3, 6, 8, 4, 7, 9, 10};
    NekDouble x_buf[] = {10, 20, 30, 40};
 
    std::shared_ptr<NekMatrix<NekDouble, StandardMatrixTag>> m(
        new NekMatrix<NekDouble>(4, 4, a_buf, eUPPER_TRIANGULAR));
    NekMatrix<NekMatrix<NekDouble>, ScaledMatrixTag> scaled(2, m);
    NekVector<NekDouble> x(4, x_buf);
 
    NekVector<NekDouble> result = scaled * x;
 
    NekDouble expected_result_buf[] = {600, 1120, 1200, 800};
    NekVector<NekDouble> expected_result(4, expected_result_buf);
    BOOST_CHECK_EQUAL(expected_result, result);
}
 
BOOST_AUTO_TEST_CASE(TestLowerTriangularMatrixVectorMultiplication)
{
    // [1 0 0 0]
    // [2 6 0 0]
    // [5 8 7 0]
    // [3 4 9 10]
 
    NekDouble a_buf[] = {1, 2, 5, 3, 6, 8, 4, 7, 9, 10};
    NekDouble x_buf[] = {10, 20, 30, 40};
 
    NekMatrix<NekDouble, StandardMatrixTag> m(4, 4, a_buf, eLOWER_TRIANGULAR);
    NekVector<NekDouble> x(4, x_buf);
 
    NekVector<NekDouble> result = m * x;
 
    NekDouble expected_result_buf[] = {10, 140, 420, 780};
    NekVector<NekDouble> expected_result(4, expected_result_buf);
    BOOST_CHECK_EQUAL(expected_result, result);
}
 
BOOST_AUTO_TEST_CASE(TestScaledLowerTriangularMatrixVectorMultiplication)
{
    // [1 0 0 0]
    // [2 6 0 0]
    // [5 8 7 0]
    // [3 4 9 10]
 
    NekDouble a_buf[] = {1, 2, 5, 3, 6, 8, 4, 7, 9, 10};
    NekDouble x_buf[] = {10, 20, 30, 40};
 
    std::shared_ptr<NekMatrix<NekDouble, StandardMatrixTag>> m(
        new NekMatrix<NekDouble>(4, 4, a_buf, eLOWER_TRIANGULAR));
    NekMatrix<NekMatrix<NekDouble>, ScaledMatrixTag> scaled(3.0, m);
    NekVector<NekDouble> x(4, x_buf);
 
    NekVector<NekDouble> result = scaled * x;
 
    NekDouble expected_result_buf[] = {30, 420, 1260, 2340};
    NekVector<NekDouble> expected_result(4, expected_result_buf);
    BOOST_CHECK_EQUAL(expected_result, result);
}
 
BOOST_AUTO_TEST_CASE(TestUpperTriangularSolve)
{
    // [1 2 3 4]
    // [0 5 6 7]
    // [0 0 8 9]
    // [0 0 0 10]
 
    NekDouble a_buf[] = {1, 2, 5, 3, 6, 8, 4, 7, 9, 10};
    NekMatrix<NekDouble, StandardMatrixTag> m(4, 4, a_buf, eUPPER_TRIANGULAR);
 
    NekDouble b_buf[] = {300, 560, 600, 400};
    NekVector<NekDouble> b(4, b_buf);
 
    LinearSystem sys(m);
    NekVector<NekDouble> x = sys.Solve(b);
 
    NekDouble expected_result_buf[] = {10, 20, 30, 40};
    NekVector<NekDouble> expected_result(4, expected_result_buf);
 
    BOOST_CHECK_EQUAL(expected_result, x);
}
 
BOOST_AUTO_TEST_CASE(TestUpperTriangularTransposeSolve)
{
    // [1 2 3 4]
    // [0 5 6 7]
    // [0 0 8 9]
    // [0 0 0 10]
 
    NekDouble a_buf[] = {1, 2, 5, 3, 6, 8, 4, 7, 9, 10};
    NekMatrix<NekDouble, StandardMatrixTag> m(4, 4, a_buf, eUPPER_TRIANGULAR);
 
    NekDouble b_buf[] = {10, 120, 390, 850};
    NekVector<NekDouble> b(4, b_buf);
 
    LinearSystem sys(m);
    NekVector<NekDouble> x = sys.SolveTranspose(b);
 
    NekDouble expected_result_buf[] = {10, 20, 30, 40};
    NekVector<NekDouble> expected_result(4, expected_result_buf);
 
    BOOST_CHECK_EQUAL(expected_result, x);
}
 
BOOST_AUTO_TEST_CASE(TestLowerTriangularSolve)
{
    // [1 2 3 4]
    // [0 5 6 7]
    // [0 0 8 9]
    // [0 0 0 10]
 
    NekDouble a_buf[] = {1, 2, 5, 3, 6, 8, 4, 7, 9, 10};
    NekMatrix<NekDouble, StandardMatrixTag> m(4, 4, a_buf, eLOWER_TRIANGULAR);
 
    NekDouble b_buf[] = {10, 140, 420, 780};
    NekVector<NekDouble> b(4, b_buf);
 
    LinearSystem sys(m);
    NekVector<NekDouble> x = sys.Solve(b);
 
    NekDouble expected_result_buf[] = {10, 20, 30, 40};
    NekVector<NekDouble> expected_result(4, expected_result_buf);
 
    BOOST_CHECK_EQUAL(expected_result, x);
}
 
BOOST_AUTO_TEST_CASE(TestLowerTriangularTransposeSolve)
{
    // [1 2 3 4]
    // [0 5 6 7]
    // [0 0 8 9]
    // [0 0 0 10]
 
    NekDouble a_buf[] = {1, 2, 5, 3, 6, 8, 4, 7, 9, 10};
    NekMatrix<NekDouble, StandardMatrixTag> m(4, 4, a_buf, eLOWER_TRIANGULAR);
 
    NekDouble b_buf[] = {320, 520, 570, 400};
    NekVector<NekDouble> b(4, b_buf);
 
    LinearSystem sys(m);
    NekVector<NekDouble> x = sys.SolveTranspose(b);
 
    NekDouble expected_result_buf[] = {10, 20, 30, 40};
    NekVector<NekDouble> expected_result(4, expected_result_buf);
 
    BOOST_CHECK_EQUAL(expected_result, x);
}
} // namespace Nektar::TriangularMatrixVectorMultiplicationUnitTests