///////////////////////////////////////////////////////////////////////////////
//
// File: testLinearSystem.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
// in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
//
// Description: Test code for NekVector
//
///////////////////////////////////////////////////////////////////////////////

#include <LibUtilities/LinearAlgebra/NekLinSys.hpp>
#include <boost/test/tools/floating_point_comparison.hpp>
#include <boost/test/unit_test.hpp>

namespace Nektar::LinearSystemUnitTests
{
BOOST_AUTO_TEST_CASE(TestLinearSystemSolveWithReturnValue)
{
    double matrix_buf[] = {10, 5, 2};

    double b_buf[] = {20, 50, 10};

    std::shared_ptr<NekMatrix<double>> A(
        new NekMatrix<double>(3, 3, matrix_buf, eDIAGONAL));
    NekVector<double> b1(3, b_buf);
    std::shared_ptr<NekVector<double>> b2(new NekVector<double>(3, b_buf));
    NekVector<double> b3(3, b_buf);
    std::shared_ptr<NekVector<double>> b4(new NekVector<double>(3, b_buf));

    LinearSystem linsys(A);

    NekVector<double> result1 = linsys.Solve(b1);
    NekVector<double> result2 = linsys.Solve(b2);
    NekVector<double> result3 = linsys.Solve(&b1);
    NekVector<double> result4 = linsys.Solve(b2.get());

    NekVector<double> result5 = linsys.Solve(b3);
    NekVector<double> result6 = linsys.Solve(b4);
    NekVector<double> result7 = linsys.Solve(&b3);
    NekVector<double> result8 = linsys.Solve(b4.get());

    double expected_result_buf[] = {2, 10, 5};
    NekVector<double> expectedResult(3, expected_result_buf);

    BOOST_CHECK_EQUAL(result1, expectedResult);
    BOOST_CHECK_EQUAL(result2, expectedResult);
    BOOST_CHECK_EQUAL(result3, expectedResult);
    BOOST_CHECK_EQUAL(result4, expectedResult);
    BOOST_CHECK_EQUAL(result5, expectedResult);
    BOOST_CHECK_EQUAL(result6, expectedResult);
    BOOST_CHECK_EQUAL(result7, expectedResult);
    BOOST_CHECK_EQUAL(result8, expectedResult);
}

BOOST_AUTO_TEST_CASE(TestLinearSystemSolveWithSoluationAsParameter)
{
    double matrix_buf[] = {10, 5, 2};

    double b_buf[] = {20, 50, 10};

    std::shared_ptr<NekMatrix<double>> A(
        new NekMatrix<double>(3, 3, matrix_buf, eDIAGONAL));
    NekVector<double> b1(3, b_buf);
    std::shared_ptr<NekVector<double>> b2(new NekVector<double>(3, b_buf));
    NekVector<double> b3(3, b_buf);
    std::shared_ptr<NekVector<double>> b4(new NekVector<double>(3, b_buf));

    NekVector<double> result1(3, 0.0);
    std::shared_ptr<NekVector<double>> result2(new NekVector<double>(3, 0.0));
    NekVector<double> result3(3, 0.0);
    std::shared_ptr<NekVector<double>> result4(new NekVector<double>(3, 0.0));

    LinearSystem linsys(A);
    double expected_result_buf[] = {2, 10, 5};
    NekVector<double> expectedResult(3, expected_result_buf);

    linsys.Solve(b1, result1);
    linsys.Solve(b2, result3);
    linsys.Solve(b3, result4);
    linsys.Solve(b4, result2);

    BOOST_CHECK_EQUAL(result1, expectedResult);
    BOOST_CHECK_EQUAL(*result2, expectedResult);
    BOOST_CHECK_EQUAL(result3, expectedResult);
    BOOST_CHECK_EQUAL(*result4, expectedResult);
}

BOOST_AUTO_TEST_CASE(TestDiagonalSystem)
{
    double matrix_buf[] = {10, 5, 2};

    double result_buf[] = {20, 50, 10};

    std::shared_ptr<NekMatrix<double>> A(
        new NekMatrix<double>(3, 3, matrix_buf, eDIAGONAL));
    std::shared_ptr<NekVector<double>> b(new NekVector<double>(3, result_buf));

    LinearSystem linsys(A);

    NekVector<double> result = linsys.Solve(b);

    double expected_result_buf[] = {2, 10, 5};
    NekVector<double> expectedResult(3, expected_result_buf);

    BOOST_CHECK_EQUAL(result, expectedResult);
    std::shared_ptr<NekVector<double>> b1 = b;
    NekVector<double> result1             = linsys.Solve(b1);
    BOOST_CHECK_EQUAL(result1, expectedResult);

    NekVector<double> result2 = linsys.SolveTranspose(b);
    BOOST_CHECK_EQUAL(expectedResult, result2);
}

BOOST_AUTO_TEST_CASE(TestDiagonalSystemAsFullSystem)
{
    double matrix_buf[] = {10.0, 0.0, 0.0, 0.0, 5.0, 0.0, 0.0, 0.0, 2.0};

    double result_buf[] = {20, 50, 10};

    std::shared_ptr<NekMatrix<double>> A(
        new NekMatrix<double>(3, 3, matrix_buf, eFULL));
    std::shared_ptr<NekVector<double>> b(new NekVector<double>(3, result_buf));

    LinearSystem linsys(A);

    NekVector<double> result = linsys.Solve(b);

    double epsilon = 1e-14;

    BOOST_CHECK_CLOSE(result[0], 2.0, epsilon);
    BOOST_CHECK_CLOSE(result[1], 10.0, epsilon);
    BOOST_CHECK_CLOSE(result[2], 5.0, epsilon);
}

BOOST_AUTO_TEST_CASE(TestSmallFullSystem)
{

    double matrix_buf[] = {81, -5, -28, 4};

    double b_buf[] = {-941, 348};

    std::shared_ptr<NekMatrix<double>> A(
        new NekMatrix<double>(2, 2, matrix_buf, eFULL));
    std::shared_ptr<NekVector<double>> b(new NekVector<double>(2, b_buf));
    LinearSystem linsys(A);

    NekVector<double> result = linsys.Solve(b);
    double epsilon           = 1e-11;

    BOOST_CHECK_CLOSE(result[0], 32.5, epsilon);
    BOOST_CHECK_CLOSE(result[1], 127.625, epsilon);

    result = linsys.SolveTranspose(b);
    BOOST_CHECK_CLOSE(result[0], -11.0, epsilon);
    BOOST_CHECK_CLOSE(result[1], 10.0, epsilon);
}

BOOST_AUTO_TEST_CASE(TestLargeFullSystem)
{

    // Larger matrix.
    double matrix_buf[] = {
        -85, -55, -37, -35, 97,  50,  79,  56,  49,  63,  57,  -59, 45,
        -8,  -93, 92,  43,  -62, 77,  66,  54,  -5,  99,  -61, -50, -12,
        -18, 31,  -26, -62, 1,   -47, -91, -47, -61, 41,  -58, -90, 53,
        -1,  94,  83,  -86, 23,  -84, 19,  -50, 88,  -53, 85,  49,  78,
        17,  72,  -99, -85, -86, 30,  80,  72,  66,  -29, -91, -53, -19,
        -47, 68,  -72, -87, 79,  43,  -66, -53, -61, -23, -37, 31,  -34,
        -42, 88,  -76, -65, 25,  28,  -61, -60, 9,   29,  -66, -32, 78,
        39,  94,  68,  -17, -98, -36, 40,  22,  5};

    double b_buf[] = {12719, -3169, -16810, 7408, -14945,
                      -6822, 10166, 7023,   8679, -11826};

    std::shared_ptr<NekMatrix<double>> A(
        new NekMatrix<double>(10, 10, matrix_buf, eFULL));
    std::shared_ptr<NekVector<double>> b(new NekVector<double>(10, b_buf));
    LinearSystem linsys(A);

    NekVector<double> result = linsys.SolveTranspose(b);
    double epsilon           = 1e-11;
    BOOST_CHECK_CLOSE(result[0], -88.0, epsilon);
    BOOST_CHECK_CLOSE(result[1], -43.0, epsilon);
    BOOST_CHECK_CLOSE(result[2], -73.0, epsilon);
    BOOST_CHECK_CLOSE(result[3], 25.0, epsilon);
    BOOST_CHECK_CLOSE(result[4], 4.0, epsilon);
    BOOST_CHECK_CLOSE(result[5], -59.0, epsilon);
    BOOST_CHECK_CLOSE(result[6], 62.0, epsilon);
    BOOST_CHECK_CLOSE(result[7], -55.0, epsilon);
    BOOST_CHECK_CLOSE(result[8], 25.0, epsilon);
    BOOST_CHECK_CLOSE(result[9], 9.0, epsilon);
}

//        void testSolvingBlockDiagonalMatrices()
//        {
//            //typedef NekMatrix<double, DiagonalMatrixTag, eBlock>
//            BlockMatrix;
//            //typedef BlockMatrix::InnerMatrixType InnerMatrixType;
//            //
//            //std::shared_ptr<BlockMatrix> m1(new BlockMatrix(4, 2, 2));
//            //const double m1_buf0[] = {-91, -47, 94, 83};
//            //const double m1_buf1[] = {49, 78, 80, 72};
//            //const double m1_buf2[] = {87, 79, 31, -34};
//            //const double m1_buf3[] = {9, 29, -17, -98};
//            //
//            //m1->GetBlock(0,0) = InnerMatrixType(2, 2, m1_buf0);
//            //m1->GetBlock(1,1) = InnerMatrixType(2, 2, m1_buf1);
//            //m1->GetBlock(2,2) = InnerMatrixType(2, 2, m1_buf2);
//            //m1->GetBlock(3,3) = InnerMatrixType(2, 2, m1_buf3);
//            //
//            //double b_vals[] = {-7198, 7642, 1344, 3744, -9968, 115, -2469,
//            8424};
//            //std::shared_ptr<NekVector<double> > b(new NekVector<double>(8,
//            b_vals));
//            //
//            //LinearSystem<BlockMatrix, NekVector<double> > linsys(m1, b);
//            //
//            //NekVector<double> result = linsys.Solve();
//            //double epsilon = 1e-11;
//            //BOOST_CHECK_CLOSE(result[0], 76.0, epsilon);
//            //BOOST_CHECK_CLOSE(result[1], 6.0, epsilon);
//            //BOOST_CHECK_CLOSE(result[2], 72.0, epsilon);
//            //BOOST_CHECK_CLOSE(result[3], -28.0, epsilon);
//            //BOOST_CHECK_CLOSE(result[4], -61.0, epsilon);
//            //BOOST_CHECK_CLOSE(result[5], -59.0, epsilon);
//            //BOOST_CHECK_CLOSE(result[6], 6.0, epsilon);
//            //BOOST_CHECK_CLOSE(result[7], -87.0, epsilon);
//        }

BOOST_AUTO_TEST_CASE(TestFullSystemWithWrappedVectors)
{
    // Larger matrix.
    double matrix_buf[] = {
        -85, -55, -37, -35, 97,  50,  79,  56,  49,  63,  57,  -59, 45,
        -8,  -93, 92,  43,  -62, 77,  66,  54,  -5,  99,  -61, -50, -12,
        -18, 31,  -26, -62, 1,   -47, -91, -47, -61, 41,  -58, -90, 53,
        -1,  94,  83,  -86, 23,  -84, 19,  -50, 88,  -53, 85,  49,  78,
        17,  72,  -99, -85, -86, 30,  80,  72,  66,  -29, -91, -53, -19,
        -47, 68,  -72, -87, 79,  43,  -66, -53, -61, -23, -37, 31,  -34,
        -42, 88,  -76, -65, 25,  28,  -61, -60, 9,   29,  -66, -32, 78,
        39,  94,  68,  -17, -98, -36, 40,  22,  5};

    double b_buf[]        = {12719, -3169, -16810, 7408, -14945,
                             -6822, 10166, 7023,   8679, -11826};
    double result_buf[10] = {0};

    std::shared_ptr<NekMatrix<double>> A(
        new NekMatrix<double>(10, 10, matrix_buf, eFULL));
    std::shared_ptr<NekVector<double>> b(
        new NekVector<double>(Array<OneD, double>(10, b_buf), eWrapper));
    NekVector<double> result(Array<OneD, double>(10, result_buf), eWrapper);

    LinearSystem linsys(A);

    linsys.SolveTranspose(b, result);
    double epsilon = 1e-11;
    BOOST_CHECK_CLOSE(result[0], -88.0, epsilon);
    BOOST_CHECK_CLOSE(result[1], -43.0, epsilon);
    BOOST_CHECK_CLOSE(result[2], -73.0, epsilon);
    BOOST_CHECK_CLOSE(result[3], 25.0, epsilon);
    BOOST_CHECK_CLOSE(result[4], 4.0, epsilon);
    BOOST_CHECK_CLOSE(result[5], -59.0, epsilon);
    BOOST_CHECK_CLOSE(result[6], 62.0, epsilon);
    BOOST_CHECK_CLOSE(result[7], -55.0, epsilon);
    BOOST_CHECK_CLOSE(result[8], 25.0, epsilon);
    BOOST_CHECK_CLOSE(result[9], 9.0, epsilon);
}

BOOST_AUTO_TEST_CASE(TestSymmetricMatrix)
{
    NekMatrix<double, StandardMatrixTag> m(3, 3, eSYMMETRIC);
    m.SetValue(0, 0, 3.0);
    m.SetValue(0, 1, 4.0);
    m.SetValue(0, 2, 9);
    m.SetValue(1, 1, 7);
    m.SetValue(1, 2, 2);
    m.SetValue(2, 2, 11);

    BOOST_CHECK_EQUAL(4.0, m(1, 0));

    double b_buf[] = {-20.0, 30.0, -20.0};
    NekVector<double> b(3, b_buf);

    LinearSystem linsys(m);
    NekVector<double> x  = linsys.Solve(b);
    NekVector<double> xt = linsys.SolveTranspose(b);

    double epsilon = 1e-11;
    BOOST_CHECK_CLOSE(x[0], 3.0, epsilon);
    BOOST_CHECK_CLOSE(x[1], 4.0, epsilon);
    BOOST_CHECK_CLOSE(x[2], -5.0, epsilon);
    BOOST_CHECK_CLOSE(xt[0], 3.0, epsilon);
    BOOST_CHECK_CLOSE(xt[1], 4.0, epsilon);
    BOOST_CHECK_CLOSE(xt[2], -5.0, epsilon);
}
} // namespace Nektar::LinearSystemUnitTests
