/* -------------------------------------------------------------------------- *
 *                               OpenMMAmoeba                                 *
 * -------------------------------------------------------------------------- *
 * This is part of the OpenMM molecular simulation toolkit originating from   *
 * Simbios, the NIH National Center for Physics-Based Simulation of           *
 * Biological Structures at Stanford, funded under the NIH Roadmap for        *
 * Medical Research, grant U54 GM072970. See https://simtk.org.               *
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 * Portions copyright (c) 2008-2016 Stanford University and the Authors.      *
 * Authors:                                                                   *
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#ifdef WIN32
  #define _USE_MATH_DEFINES // Needed to get M_PI
#endif
#include "openmm/internal/ContextImpl.h"
#include "openmm/internal/AmoebaVdwForceImpl.h"
#include "openmm/amoebaKernels.h"
#include <map>
#include <cmath>

using namespace OpenMM;
using namespace std;

using std::pair;
using std::vector;
using std::set;

AmoebaVdwForceImpl::AmoebaVdwForceImpl(const AmoebaVdwForce& owner) : owner(owner) {
}

AmoebaVdwForceImpl::~AmoebaVdwForceImpl() {
}

void AmoebaVdwForceImpl::initialize(ContextImpl& context) {
    const System& system = context.getSystem();

    if (owner.getNumParticles() != system.getNumParticles())
        throw OpenMMException("AmoebaVdwForce must have exactly as many particles as the System it belongs to.");

    // check that cutoff < 0.5*boxSize

    if (owner.getNonbondedMethod() == AmoebaVdwForce::CutoffPeriodic) {
        Vec3 boxVectors[3];
        system.getDefaultPeriodicBoxVectors(boxVectors[0], boxVectors[1], boxVectors[2]);
        double cutoff = owner.getCutoffDistance();
        if (cutoff > 0.5*boxVectors[0][0] || cutoff > 0.5*boxVectors[1][1] || cutoff > 0.5*boxVectors[2][2])
            throw OpenMMException("AmoebaVdwForce: The cutoff distance cannot be greater than half the periodic box size.");
    }   

    kernel = context.getPlatform().createKernel(CalcAmoebaVdwForceKernel::Name(), context);
    kernel.getAs<CalcAmoebaVdwForceKernel>().initialize(context.getSystem(), owner);
}

double AmoebaVdwForceImpl::calcForcesAndEnergy(ContextImpl& context, bool includeForces, bool includeEnergy, int groups) {
    if ((groups&(1<<owner.getForceGroup())) != 0)
        return kernel.getAs<CalcAmoebaVdwForceKernel>().execute(context, includeForces, includeEnergy);
    return 0.0;
}

double AmoebaVdwForceImpl::calcDispersionCorrection(const System& system, const AmoebaVdwForce& force) {

    // Amoeba VdW dispersion correction implemented by LPW
    // There is no dispersion correction if PBC is off or the cutoff is set to the default value of ten billion (AmoebaVdwForce.cpp)
    if (force.getNonbondedMethod() == AmoebaVdwForce::NoCutoff)
        return 0.0;

    // Identify all particle classes (defined by sigma and epsilon and reduction), and count the number of
    // particles in each class.

    map<pair<double, double>, int> classCounts;
    for (int i = 0; i < force.getNumParticles(); i++) {
        double sigma, epsilon, reduction;
        bool isAlchemical;
        // The variables reduction, ivindex and isAlchemical are not used.
        int ivindex;
        // Get the sigma and epsilon parameters, ignoring everything else.
        force.getParticleParameters(i, ivindex, sigma, epsilon, reduction, isAlchemical);
        pair<double, double> key = make_pair(sigma, epsilon);
        map<pair<double, double>, int>::iterator entry = classCounts.find(key);
        if (entry == classCounts.end())
            classCounts[key] = 1;
        else
            entry->second++;
    }

    // Compute the VdW tapering coefficients.  Mostly copied from amoebaCudaGpu.cpp.
    double cutoff = force.getCutoffDistance();
    double vdwTaper = 0.90; // vdwTaper is a scaling factor, it is not a distance.
    double c0 = 0.0;
    double c1 = 0.0;
    double c2 = 0.0;
    double c3 = 0.0;
    double c4 = 0.0;
    double c5 = 0.0;

    double vdwCut = cutoff;
    double vdwTaperCut = vdwTaper*cutoff;

    double vdwCut2 = vdwCut*vdwCut;
    double vdwCut3 = vdwCut2*vdwCut;
    double vdwCut4 = vdwCut2*vdwCut2;
    double vdwCut5 = vdwCut2*vdwCut3;
    double vdwCut6 = vdwCut3*vdwCut3;
    double vdwCut7 = vdwCut3*vdwCut4;

    double vdwTaperCut2 = vdwTaperCut*vdwTaperCut;
    double vdwTaperCut3 = vdwTaperCut2*vdwTaperCut;
    double vdwTaperCut4 = vdwTaperCut2*vdwTaperCut2;
    double vdwTaperCut5 = vdwTaperCut2*vdwTaperCut3;
    double vdwTaperCut6 = vdwTaperCut3*vdwTaperCut3;
    double vdwTaperCut7 = vdwTaperCut3*vdwTaperCut4;

    // get 5th degree multiplicative switching function coefficients;

    double denom = 1.0 / (vdwCut - vdwTaperCut);
    double denom2 = denom*denom;
    denom = denom * denom2*denom2;

    c0 = vdwCut * vdwCut2 * (vdwCut2 - 5.0 * vdwCut * vdwTaperCut + 10.0 * vdwTaperCut2) * denom;
    c1 = -30.0 * vdwCut2 * vdwTaperCut2*denom;
    c2 = 30.0 * (vdwCut2 * vdwTaperCut + vdwCut * vdwTaperCut2) * denom;
    c3 = -10.0 * (vdwCut2 + 4.0 * vdwCut * vdwTaperCut + vdwTaperCut2) * denom;
    c4 = 15.0 * (vdwCut + vdwTaperCut) * denom;
    c5 = -6.0 * denom;

    // Loop over all pairs of classes to compute the coefficient.
    // Copied over from TINKER - numerical integration.
    double range = 20.0;
    double cut = vdwTaperCut; // This is where tapering BEGINS
    double off = vdwCut; // This is where tapering ENDS
    int nstep = 200;
    int ndelta = int(double(nstep) * (range - cut));
    double rdelta = (range - cut) / double(ndelta);
    double offset = cut - 0.5 * rdelta;

    // Buffered-14-7 buffering constants
    double dhal = 0.07; 
    double ghal = 0.12;

    double elrc = 0.0; // This number is incremented and passed out at the end
    double e = 0.0;
    double sigma, epsilon; // The pairwise sigma and epsilon parameters.
    int i = 0, k = 0; // Loop counters.

    // Double loop over different atom types.
    std::string sigmaCombiningRule = force.getSigmaCombiningRule();
    std::string epsilonCombiningRule = force.getEpsilonCombiningRule();
    for (auto& class1 : classCounts) {
        k = 0;
        for (auto& class2 : classCounts) { 
            // AMOEBA combining rules, copied over from the CUDA code.
            double iSigma = class1.first.first;
            double jSigma = class2.first.first;
            double iEpsilon = class1.first.second;
            double jEpsilon = class2.first.second;
            // ARITHMETIC = 1
            // GEOMETRIC  = 2
            // CUBIC-MEAN = 3
            if (sigmaCombiningRule == "ARITHMETIC") {
              sigma = iSigma + jSigma;
            } else if (sigmaCombiningRule == "GEOMETRIC") {
              sigma = 2.0f * std::sqrt(iSigma * jSigma);
            } else {
              double iSigma2 = iSigma*iSigma;
              double jSigma2 = jSigma*jSigma;
              if ((iSigma2 + jSigma2) != 0.0) {
                sigma = 2.0f * (iSigma2 * iSigma + jSigma2 * jSigma) / (iSigma2 + jSigma2);
              } else {
                sigma = 0.0;
              }
            }
            // ARITHMETIC = 1
            // GEOMETRIC  = 2
            // HARMONIC   = 3
            // W-H        = 4
            // HHG        = 5
            if (epsilonCombiningRule == "ARITHMETIC") {
              epsilon = 0.5f * (iEpsilon + jEpsilon);
            } else if (epsilonCombiningRule == "GEOMETRIC") {
              epsilon = std::sqrt(iEpsilon * jEpsilon);
            } else if (epsilonCombiningRule == "HARMONIC") {
              if ((iEpsilon + jEpsilon) != 0.0) {
                epsilon = 2.0f * (iEpsilon * jEpsilon) / (iEpsilon + jEpsilon);
              } else {
                epsilon = 0.0;
              }
            } else if (epsilonCombiningRule == "W-H") {
              double iSigma3 = iSigma * iSigma * iSigma;
              double jSigma3 = jSigma * jSigma * jSigma;
              double iSigma6 = iSigma3 * iSigma3;
              double jSigma6 = jSigma3 * jSigma3;
              double eps_s = std::sqrt(iEpsilon*jEpsilon);
              epsilon = (eps_s == 0.0 ? 0.0 : 2.0f*eps_s*iSigma3*jSigma3/(iSigma6 + jSigma6));
            } else {
              double epsilonS = std::sqrt(iEpsilon) + std::sqrt(jEpsilon);
              if (epsilonS != 0.0) {
                epsilon = 4.0f * (iEpsilon * jEpsilon) / (epsilonS * epsilonS);
              } else {
                epsilon = 0.0;
              }
            }
            int count = class1.second * class2.second;
            // Below is an exact copy of stuff from the previous block.
            double rv = sigma;
            double termik = 2.0 * M_PI * count; // termik is equivalent to 2 * pi * count.
            double rv2 = rv * rv;
            double rv6 = rv2 * rv2 * rv2;
            double rv7 = rv6 * rv;
            double etot = 0.0;
            double r2 = 0.0;
            for (int j = 1; j <= ndelta; j++) {
                double r = offset + double(j) * rdelta;
                r2 = r*r;
                double r3 = r2 * r;
                double r6 = r3 * r3;
                double r7 = r6 * r;
                // The following is for buffered 14-7 only.
                /*
                double rho = r/rv;
                double term1 = pow(((dhal + 1.0) / (dhal + rho)),7);
                double term2 = ((ghal + 1.0) / (ghal + pow(rho,7))) - 2.0;
                e = epsilon * term1 * term2;
                */
                double rho = r7 + ghal*rv7;
                double tau = (dhal + 1.0) / (r + dhal * rv);
                double tau7 = pow(tau, 7);
                e = epsilon * rv7 * tau7 * ((ghal + 1.0) * rv7 / rho - 2.0);
                double taper = 0.0;
                if (r < off) {
                    double r4 = r2 * r2;
                    double r5 = r2 * r3;
                    taper = c5 * r5 + c4 * r4 + c3 * r3 + c2 * r2 + c1 * r + c0;
                    e = e * (1.0 - taper);
                }
                etot = etot + e * rdelta * r2;
            }
            elrc = elrc + termik * etot;
            k++;
        }
        i++;
    }
    return elrc;
}

std::vector<std::string> AmoebaVdwForceImpl::getKernelNames() {
    std::vector<std::string> names;
    names.push_back(CalcAmoebaVdwForceKernel::Name());
    return names;
}

void AmoebaVdwForceImpl::updateParametersInContext(ContextImpl& context) {
    kernel.getAs<CalcAmoebaVdwForceKernel>().copyParametersToContext(context, owner);
}


