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#include "gmxpre.h"

#include "gromacs/mdlib/shake.h"

#include <cassert>
#include <cmath>

#include <algorithm>
#include <vector>

#include <gtest/gtest.h>

#include "gromacs/utility/arrayref.h"

#include "testutils/refdata.h"
#include "testutils/testasserts.h"

namespace gmx
{
namespace
{

/*! \brief Stride of the vector of int used to describe each SHAKE
 * constraint
 *
 * Like other such code, SHAKE is hard-wired to use t_ilist.iatoms as
 * a flat vector of tuples of general data. Here, they are triples
 * containing the index of the constraint type, and then the indices
 * of the two atoms involved. So for each constraint, we must stride
 * this vector by three to get access to its information. */
const int constraintStride = 3;

/*! \brief Compute the displacements between pairs of constrained
 * atoms described in the iatom "topology". */
std::vector<RVec> computeDisplacements(ArrayRef<const int> iatom, const std::vector<RVec>& positions)
{
    assert(0 == iatom.size() % constraintStride);
    int               numConstraints = iatom.size() / constraintStride;
    std::vector<RVec> displacements;

    for (int ll = 0; ll != numConstraints; ++ll)
    {
        int atom_i = iatom[ll * constraintStride + 1];
        int atom_j = iatom[ll * constraintStride + 2];

        displacements.push_back(positions[atom_i] - positions[atom_j]);
    }

    return displacements;
}

/*! \brief Compute half of the reduced mass of each pair of constrained
 * atoms in the iatom "topology".
 *
 * The reduced mass is m = 1/(1/m_i + 1/m_j)) */
std::vector<real> computeHalfOfReducedMasses(const std::vector<int>&  iatom,
                                             const std::vector<real>& inverseMasses)
{
    int               numConstraints = iatom.size() / constraintStride;
    std::vector<real> halfOfReducedMasses;

    for (int ll = 0; ll != numConstraints; ++ll)
    {
        int atom_i = iatom[ll * constraintStride + 1];
        int atom_j = iatom[ll * constraintStride + 2];

        halfOfReducedMasses.push_back(0.5 / (inverseMasses[atom_i] + inverseMasses[atom_j]));
    }

    return halfOfReducedMasses;
}

/*! \brief Compute the distances corresponding to the vector of displacements components */
std::vector<real> computeDistancesSquared(ArrayRef<const RVec> displacements)
{
    int               numDistancesSquared = displacements.size();
    std::vector<real> distanceSquared;

    for (int i = 0; i != numDistancesSquared; ++i)
    {
        distanceSquared.push_back(0.0);
        for (int d = 0; d != DIM; ++d)
        {
            real displacement = displacements[i][d];
            distanceSquared.back() += displacement * displacement;
        }
    }

    return distanceSquared;
}

/*! \brief Test fixture for testing SHAKE */
class ShakeTest : public ::testing::Test
{
public:
    /*! \brief Set up data for test cases to use when constructing
        their input */
    void SetUp() override
    {
        inverseMassesDatabase_.push_back(2.0);
        inverseMassesDatabase_.push_back(3.0);
        inverseMassesDatabase_.push_back(4.0);
        inverseMassesDatabase_.push_back(1.0);

        positionsDatabase_.emplace_back(2.5, -3.1, 15.7);

        positionsDatabase_.emplace_back(0.51, -3.02, 15.55);

        positionsDatabase_.emplace_back(-0.5, -3.0, 15.2);

        positionsDatabase_.emplace_back(-1.51, -2.95, 15.05);
    }

    //! Run the test
    static void runTest(size_t gmx_unused        numAtoms,
                        size_t                   numConstraints,
                        const std::vector<int>&  iatom,
                        const std::vector<real>& constrainedDistances,
                        const std::vector<real>& inverseMasses,
                        const std::vector<RVec>& positions)
    {
        // Check the test input is consistent
        assert(numConstraints * constraintStride == iatom.size());
        assert(numConstraints == constrainedDistances.size());
        assert(numAtoms == inverseMasses.size());
        assert(numAtoms == positions.size());
        for (size_t i = 0; i != numConstraints; ++i)
        {
            for (size_t j = 1; j < 3; j++)
            {
                // Check that the topology refers to atoms that have masses and positions
                assert(iatom[i * constraintStride + j] >= 0);
                assert(iatom[i * constraintStride + j] < static_cast<int>(numAtoms));
            }
        }
        std::vector<real> distanceSquaredTolerances;
        std::vector<real> lagrangianValues;
        std::vector<real> constrainedDistancesSquared;

        real coordMax = 0;
        for (size_t i = 0; i != numConstraints; ++i)
        {
            constrainedDistancesSquared.push_back(constrainedDistances[i] * constrainedDistances[i]);
            distanceSquaredTolerances.push_back(
                    0.5 / (constrainedDistancesSquared.back() * ShakeTest::tolerance_));
            lagrangianValues.push_back(0.0);

            for (size_t j = 1; j < constraintStride; j++)
            {
                for (int d = 0; d < DIM; d++)
                {
                    coordMax = std::max(coordMax, std::abs(positions[iatom[i * constraintStride + j]][d]));
                }
            }
        }
        std::vector<real> halfOfReducedMasses  = computeHalfOfReducedMasses(iatom, inverseMasses);
        std::vector<RVec> initialDisplacements = computeDisplacements(iatom, positions);

        std::vector<RVec> finalPositions = positions;
        int               numIterations  = 0;
        int               numErrors      = 0;

        cshake(iatom.data(),
               numConstraints,
               &numIterations,
               ShakeTest::maxNumIterations_,
               constrainedDistancesSquared,
               finalPositions,
               nullptr,
               initialDisplacements,
               halfOfReducedMasses,
               omega_,
               inverseMasses,
               distanceSquaredTolerances,
               lagrangianValues,
               &numErrors);

        std::vector<RVec> finalDisplacements    = computeDisplacements(iatom, finalPositions);
        std::vector<real> finalDistancesSquared = computeDistancesSquared(finalDisplacements);
        assert(numConstraints == finalDistancesSquared.size());

        EXPECT_EQ(0, numErrors);
        EXPECT_GT(numIterations, 1);
        EXPECT_LT(numIterations, ShakeTest::maxNumIterations_);
        // TODO wrap this in a Google Mock matcher if there's
        // other tests like it some time?
        for (size_t i = 0; i != numConstraints; ++i)
        {
            // We need to allow for the requested tolerance plus rounding
            // errors due to the absolute size of the coordinate values
            test::FloatingPointTolerance constraintTolerance =
                    test::absoluteTolerance(std::sqrt(constrainedDistancesSquared[i]) * ShakeTest::tolerance_
                                            + coordMax * GMX_REAL_EPS);
            // Assert that the constrained distances are within the required tolerance
            EXPECT_FLOAT_EQ_TOL(std::sqrt(constrainedDistancesSquared[i]),
                                std::sqrt(finalDistancesSquared[i]),
                                constraintTolerance);
        }
    }

    //! Tolerance for SHAKE conversion (ie. shake-tol .mdp setting)
    static const real tolerance_;
    //! Maximum number of iterations permitted in these tests
    static const int maxNumIterations_;
    //! SHAKE over-relaxation (SOR) factor
    static const real omega_;
    //! Database of inverse masses of atoms in the topology
    std::vector<real> inverseMassesDatabase_;
    //! Database of atom positions (three reals per atom)
    std::vector<RVec> positionsDatabase_;
};

const real ShakeTest::tolerance_        = 1e-5;
const int  ShakeTest::maxNumIterations_ = 30;
const real ShakeTest::omega_            = 1.0;

TEST_F(ShakeTest, ConstrainsOneBond)
{
    int numAtoms       = 2;
    int numConstraints = 1;

    std::vector<int> iatom;
    iatom.push_back(-1); // unused
    iatom.push_back(0);  // i atom index
    iatom.push_back(1);  // j atom index

    std::vector<real> constrainedDistances;
    constrainedDistances.push_back(2.0);

    std::vector<real> inverseMasses(inverseMassesDatabase_.begin(),
                                    inverseMassesDatabase_.begin() + numAtoms);
    std::vector<RVec> positions(positionsDatabase_.begin(), positionsDatabase_.begin() + numAtoms);

    runTest(numAtoms, numConstraints, iatom, constrainedDistances, inverseMasses, positions);
}

TEST_F(ShakeTest, ConstrainsTwoDisjointBonds)
{
    int numAtoms       = 4;
    int numConstraints = 2;

    std::vector<int> iatom;
    iatom.push_back(-1); // unused
    iatom.push_back(0);  // i atom index
    iatom.push_back(1);  // j atom index

    iatom.push_back(-1); // unused
    iatom.push_back(2);  // i atom index
    iatom.push_back(3);  // j atom index

    std::vector<real> constrainedDistances;
    constrainedDistances.push_back(2.0);
    constrainedDistances.push_back(1.0);

    std::vector<real> inverseMasses(inverseMassesDatabase_.begin(),
                                    inverseMassesDatabase_.begin() + numAtoms);
    std::vector<RVec> positions(positionsDatabase_.begin(), positionsDatabase_.begin() + numAtoms);

    runTest(numAtoms, numConstraints, iatom, constrainedDistances, inverseMasses, positions);
}

TEST_F(ShakeTest, ConstrainsTwoBondsWithACommonAtom)
{
    int numAtoms       = 3;
    int numConstraints = 2;

    std::vector<int> iatom;
    iatom.push_back(-1); // unused
    iatom.push_back(0);  // i atom index
    iatom.push_back(1);  // j atom index

    iatom.push_back(-1); // unused
    iatom.push_back(1);  // i atom index
    iatom.push_back(2);  // j atom index

    std::vector<real> constrainedDistances;
    constrainedDistances.push_back(2.0);
    constrainedDistances.push_back(1.0);

    std::vector<real> inverseMasses(inverseMassesDatabase_.begin(),
                                    inverseMassesDatabase_.begin() + numAtoms);
    std::vector<RVec> positions(positionsDatabase_.begin(), positionsDatabase_.begin() + numAtoms);

    runTest(numAtoms, numConstraints, iatom, constrainedDistances, inverseMasses, positions);
}

TEST_F(ShakeTest, ConstrainsThreeBondsWithCommonAtoms)
{
    int numAtoms       = 4;
    int numConstraints = 3;

    std::vector<int> iatom;
    iatom.push_back(-1); // unused
    iatom.push_back(0);  // i atom index
    iatom.push_back(1);  // j atom index

    iatom.push_back(-1); // unused
    iatom.push_back(1);  // i atom index
    iatom.push_back(2);  // j atom index

    iatom.push_back(-1); // unused
    iatom.push_back(2);  // i atom index
    iatom.push_back(3);  // j atom index

    std::vector<real> constrainedDistances;
    constrainedDistances.push_back(2.0);
    constrainedDistances.push_back(1.0);
    constrainedDistances.push_back(1.0);

    std::vector<real> inverseMasses(inverseMassesDatabase_.begin(),
                                    inverseMassesDatabase_.begin() + numAtoms);
    std::vector<RVec> positions(positionsDatabase_.begin(), positionsDatabase_.begin() + numAtoms);

    runTest(numAtoms, numConstraints, iatom, constrainedDistances, inverseMasses, positions);
}

} // namespace
} // namespace gmx
