/* -------------------------------------------------------------------------- *
 *                                   OpenMM                                   *
 * -------------------------------------------------------------------------- *
 * 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: Peter Eastman                                                     *
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/**
 * This tests the Reference implementation of ReferenceAmoebaInPlaneAngleForce.
 */

#include "openmm/internal/AssertionUtilities.h"
//#include "AmoebaTinkerParameterFile.h"
#include "openmm/Context.h"
#include "OpenMMAmoeba.h"
#include "openmm/System.h"
#include "openmm/LangevinIntegrator.h"
#include <iostream>
#include <vector>

using namespace OpenMM;

extern "C" OPENMM_EXPORT void registerAmoebaReferenceKernelFactories();

const double TOL = 1e-5;
#define PI_M               3.141592653589
#define RADIAN            57.29577951308

/* ---------------------------------------------------------------------------------------

   Compute cross product of two 3-vectors and place in 3rd vector

   vectorZ = vectorX x vectorY

   @param vectorX             x-vector
   @param vectorY             y-vector
   @param vectorZ             z-vector

   @return vector is vectorZ

   --------------------------------------------------------------------------------------- */
     
static void crossProductVector3(double* vectorX, double* vectorY, double* vectorZ) {

    vectorZ[0]  = vectorX[1]*vectorY[2] - vectorX[2]*vectorY[1];
    vectorZ[1]  = vectorX[2]*vectorY[0] - vectorX[0]*vectorY[2];
    vectorZ[2]  = vectorX[0]*vectorY[1] - vectorX[1]*vectorY[0];

    return;
}

static double dotVector3(double* vectorX, double* vectorY) {
    return vectorX[0]*vectorY[0] + vectorX[1]*vectorY[1] + vectorX[2]*vectorY[2];
}

static void getPrefactorsGivenInPlaneAngleCosine(double cosine, double idealInPlaneAngle, double quadraticK, double cubicK,
                                                 double quarticK, double penticK, double sexticK,
                                                 double* dEdR, double* energyTerm) {

    double angle;
    if (cosine >= 1.0) {
        angle = 0.0f;
    }
    else if (cosine <= -1.0) {
        angle = RADIAN*PI_M;
    }
    else {
        angle = RADIAN*acos(cosine);
    }

    double deltaIdeal         = angle - idealInPlaneAngle;
    double deltaIdeal2        = deltaIdeal*deltaIdeal;
    double deltaIdeal3        = deltaIdeal*deltaIdeal2;
    double deltaIdeal4        = deltaIdeal2*deltaIdeal2;
 
    // deltaIdeal = r - r_0
 
    *dEdR        =  (2.0                        +
                     3.0*cubicK*  deltaIdeal    +
                     4.0*quarticK*deltaIdeal2   +
                     5.0*penticK* deltaIdeal3   +
                     6.0*sexticK* deltaIdeal4   );
 
    *dEdR       *= RADIAN*quadraticK*deltaIdeal;
 

    *energyTerm  = 1.0f + cubicK* deltaIdeal   +
                          quarticK*deltaIdeal2 +
                          penticK* deltaIdeal3 +
                          sexticK* deltaIdeal4;
    *energyTerm *= quadraticK*deltaIdeal2;

    return;
}

static void computeAmoebaInPlaneAngleForce(int bondIndex,  std::vector<Vec3>& positions, AmoebaInPlaneAngleForce& AmoebaInPlaneAngleForce,
                                                   std::vector<Vec3>& forces, double* energy) {

    int particle1, particle2, particle3, particle4;
    double idealInPlaneAngle;
    double quadraticK;
    AmoebaInPlaneAngleForce.getAngleParameters(bondIndex, particle1, particle2, particle3, particle4, idealInPlaneAngle, quadraticK);

    double cubicK         = AmoebaInPlaneAngleForce.getAmoebaGlobalInPlaneAngleCubic();
    double quarticK       = AmoebaInPlaneAngleForce.getAmoebaGlobalInPlaneAngleQuartic();
    double penticK        = AmoebaInPlaneAngleForce.getAmoebaGlobalInPlaneAnglePentic();
    double sexticK        = AmoebaInPlaneAngleForce.getAmoebaGlobalInPlaneAngleSextic();

    // T   = AD x CD
    // P   = B + T*delta
    // AP  = A - P
    // CP  = A - P
    // M   = CP x AP

    enum { AD, BD, CD, T, AP, P, CP, M, APxM, CPxM, ADxBD, BDxCD, TxCD, ADxT, dBxAD, CDxdB, LastDeltaAtomIndex };
 
    // AD   0
    // BD   1
    // CD   2 
    //  T   3
    // AP   4
    //  P   5
    // CP   6
    // M    7
    // APxM, CPxM, ADxBD, BDxCD, TxCD, ADxT, dBxAD, CDxdB, LastDeltaAtomIndex

    double deltaR[LastDeltaAtomIndex][3];
    for (int ii = 0; ii < 3; ii++) {
        deltaR[AD][ii] = positions[particle1][ii] - positions[particle4][ii];
        deltaR[BD][ii] = positions[particle2][ii] - positions[particle4][ii];
        deltaR[CD][ii] = positions[particle3][ii] - positions[particle4][ii];
    }
    crossProductVector3(deltaR[AD], deltaR[CD], deltaR[T]);
 
    double rT2     = dotVector3(deltaR[T], deltaR[T]);
    double delta   = dotVector3(deltaR[T], deltaR[BD]);
         delta    *= -1.0/rT2;
 
    for (int ii = 0; ii < 3; ii++) {
       deltaR[P][ii]  = positions[particle2][ii] + deltaR[T][ii]*delta;
       deltaR[AP][ii] = positions[particle1][ii] - deltaR[P][ii];
       deltaR[CP][ii] = positions[particle3][ii] - deltaR[P][ii];
    }
 
    double rAp2 = dotVector3(deltaR[AP],  deltaR[AP]);
    double rCp2 = dotVector3(deltaR[CP],  deltaR[CP]);
    if (rAp2 <= 0.0 && rCp2 <= 0.0) {
        return;
    }

    crossProductVector3(deltaR[CP], deltaR[AP], deltaR[M]);
 
    double rm = dotVector3(deltaR[M], deltaR[M]);
         rm   = sqrt(rm);
    if (rm < 0.000001) {
       rm = 0.000001;
    }
 
    double dot     = dotVector3(deltaR[AP], deltaR[CP]);
    double cosine  = dot/sqrt(rAp2*rCp2);
 
    double dEdR;
    double energyTerm;
    getPrefactorsGivenInPlaneAngleCosine(cosine, idealInPlaneAngle, quadraticK, cubicK,
                                         quarticK, penticK, sexticK, &dEdR,  &energyTerm);
 
    double termA   = -dEdR/(rAp2*rm);
    double termC   =  dEdR/(rCp2*rm);
 
    crossProductVector3(deltaR[AP], deltaR[M], deltaR[APxM]);
    crossProductVector3(deltaR[CP], deltaR[M], deltaR[CPxM]);
 
    // forces will be gathered here
 
    enum { dA, dB, dC, dD, LastDIndex };
    double forceTerm[LastDIndex][3];
 
    for (int ii = 0; ii < 3; ii++) {
       forceTerm[dA][ii] = deltaR[APxM][ii]*termA;
       forceTerm[dC][ii] = deltaR[CPxM][ii]*termC;
       forceTerm[dB][ii] = -1.0*(forceTerm[dA][ii] + forceTerm[dC][ii]);
    }
 
    double pTrT2  = dotVector3(forceTerm[dB], deltaR[T]);
         pTrT2   /= rT2;
 
    crossProductVector3(deltaR[CD], forceTerm[dB], deltaR[CDxdB]);
    crossProductVector3(forceTerm[dB], deltaR[AD], deltaR[dBxAD]);
 
    if (fabs(pTrT2) > 1.0e-08) {
       double delta2 = delta*2.0;
 
       crossProductVector3(deltaR[BD], deltaR[CD], deltaR[BDxCD]);
       crossProductVector3(deltaR[T],  deltaR[CD], deltaR[TxCD]);
       crossProductVector3(deltaR[AD], deltaR[BD], deltaR[ADxBD]);
       crossProductVector3(deltaR[AD], deltaR[T],  deltaR[ADxT]);
       for (int ii = 0; ii < 3; ii++) {
 
          double term           = deltaR[BDxCD][ii] + delta2*deltaR[TxCD][ii];
          forceTerm[dA][ii]  += delta*deltaR[CDxdB][ii] + term*pTrT2;
 
               term           = deltaR[ADxBD][ii] + delta2*deltaR[ADxT][ii];
          forceTerm[dC][ii]  += delta*deltaR[dBxAD][ii] + term*pTrT2;
 
          forceTerm[dD][ii]  = -(forceTerm[dA][ii] + forceTerm[dB][ii] + forceTerm[dC][ii]);
       }
    }
    else {
       for (int ii = 0; ii < 3; ii++) {
 
          forceTerm[dA][ii] += delta*deltaR[CDxdB][ii];
          forceTerm[dC][ii] += delta*deltaR[dBxAD][ii];
 
          forceTerm[dD][ii]  = -(forceTerm[dA][ii] + forceTerm[dB][ii] + forceTerm[dC][ii]);
       }
    }
 
    // accumulate forces and energy
 
    *energy                    += energyTerm;
 
    forces[particle1][0]       -= forceTerm[0][0];
    forces[particle1][1]       -= forceTerm[0][1];
    forces[particle1][2]       -= forceTerm[0][2];

    forces[particle2][0]       -= forceTerm[1][0];
    forces[particle2][1]       -= forceTerm[1][1];
    forces[particle2][2]       -= forceTerm[1][2];

    forces[particle3][0]       -= forceTerm[2][0];
    forces[particle3][1]       -= forceTerm[2][1];
    forces[particle3][2]       -= forceTerm[2][2];

    forces[particle4][0]       -= forceTerm[3][0];
    forces[particle4][1]       -= forceTerm[3][1];
    forces[particle4][2]       -= forceTerm[3][2];

}

static void computeAmoebaInPlaneAngleForces(Context& context, AmoebaInPlaneAngleForce& AmoebaInPlaneAngleForce,
                                                     std::vector<Vec3>& expectedForces, double* expectedEnergy) {

    // get positions and zero forces

    State state                 = context.getState(State::Positions);
    std::vector<Vec3> positions = state.getPositions();
    expectedForces.resize(positions.size());
    
    for (unsigned int ii = 0; ii < expectedForces.size(); ii++) {
        expectedForces[ii][0] = expectedForces[ii][1] = expectedForces[ii][2] = 0.0;
    }

    // calculates forces/energy

    *expectedEnergy = 0.0;
    for (int ii = 0; ii < AmoebaInPlaneAngleForce.getNumAngles(); ii++) {
        computeAmoebaInPlaneAngleForce(ii, positions, AmoebaInPlaneAngleForce, expectedForces, expectedEnergy);
    }
}

void compareWithExpectedForceAndEnergy(Context& context, AmoebaInPlaneAngleForce& AmoebaInPlaneAngleForce,
                                       double tolerance, const std::string& idString) {

    std::vector<Vec3> expectedForces;
    double expectedEnergy;
    computeAmoebaInPlaneAngleForces(context, AmoebaInPlaneAngleForce, expectedForces, &expectedEnergy);
   
    State state                      = context.getState(State::Forces | State::Energy);
    const std::vector<Vec3> forces   = state.getForces();

    for (unsigned int ii = 0; ii < forces.size(); ii++) {
        ASSERT_EQUAL_VEC(expectedForces[ii], forces[ii], tolerance);
    }
    ASSERT_EQUAL_TOL(expectedEnergy, state.getPotentialEnergy(), tolerance);
}

void testOneAngle() {

    System system;
    int numberOfParticles = 4;
    for (int ii = 0; ii < numberOfParticles; ii++) {
        system.addParticle(1.0);
    }

    LangevinIntegrator integrator(0.0, 0.1, 0.01);

    AmoebaInPlaneAngleForce* amoebaInPlaneAngleForce = new AmoebaInPlaneAngleForce();

    double angle      = 65.0;
    double quadraticK = 1.0;
    double cubicK     = 0.0e-01;
    double quarticK   = 0.0e-02;
    double penticK    = 0.0e-03;
    double sexticK    = 0.0e-04;
    amoebaInPlaneAngleForce->addAngle(0, 1, 2, 3, angle, quadraticK);

    amoebaInPlaneAngleForce->setAmoebaGlobalInPlaneAngleCubic(cubicK);
    amoebaInPlaneAngleForce->setAmoebaGlobalInPlaneAngleQuartic(quarticK);
    amoebaInPlaneAngleForce->setAmoebaGlobalInPlaneAnglePentic(penticK);
    amoebaInPlaneAngleForce->setAmoebaGlobalInPlaneAngleSextic(sexticK);

    system.addForce(amoebaInPlaneAngleForce);
    ASSERT(!amoebaInPlaneAngleForce->usesPeriodicBoundaryConditions());
    ASSERT(!system.usesPeriodicBoundaryConditions());
    Context context(system, integrator, Platform::getPlatformByName("Reference"));

    std::vector<Vec3> positions(numberOfParticles);

    positions[0] = Vec3(0, 1, 0);
    positions[1] = Vec3(0, 0, 0);
    positions[2] = Vec3(0, 0, 1);
    positions[3] = Vec3(1, 1, 1);

    context.setPositions(positions);
    compareWithExpectedForceAndEnergy(context, *amoebaInPlaneAngleForce, TOL, "testOneInPlaneAngle");
    
    // Try changing the angle parameters and make sure it's still correct.
    
    amoebaInPlaneAngleForce->setAngleParameters(0, 0, 1, 2, 3, 1.1*angle, 1.4*quadraticK);
    bool exceptionThrown = false;
    try {
        // This should throw an exception.
        compareWithExpectedForceAndEnergy(context, *amoebaInPlaneAngleForce, TOL, "testOneInPlaneAngle");
    }
    catch (std::exception ex) {
        exceptionThrown = true;
    }
    ASSERT(exceptionThrown);
    amoebaInPlaneAngleForce->updateParametersInContext(context);
    compareWithExpectedForceAndEnergy(context, *amoebaInPlaneAngleForce, TOL, "testOneInPlaneAngle");
}

void testPeriodic() {
    // Create a force that uses periodic boundary conditions.

    System system;
    system.setDefaultPeriodicBoxVectors(Vec3(3, 0, 0), Vec3(0, 3, 0), Vec3(0, 0, 3));
    int numberOfParticles = 4;
    for (int ii = 0; ii < numberOfParticles; ii++)
        system.addParticle(1.0);
    LangevinIntegrator integrator(0.0, 0.1, 0.01);
    AmoebaInPlaneAngleForce* amoebaInPlaneAngleForce = new AmoebaInPlaneAngleForce();
    double angle      = 65.0;
    double quadraticK = 1.0;
    double cubicK     = 0.0e-01;
    double quarticK   = 0.0e-02;
    double penticK    = 0.0e-03;
    double sexticK    = 0.0e-04;
    amoebaInPlaneAngleForce->addAngle(0, 1, 2, 3, angle, quadraticK);
    amoebaInPlaneAngleForce->setAmoebaGlobalInPlaneAngleCubic(cubicK);
    amoebaInPlaneAngleForce->setAmoebaGlobalInPlaneAngleQuartic(quarticK);
    amoebaInPlaneAngleForce->setAmoebaGlobalInPlaneAnglePentic(penticK);
    amoebaInPlaneAngleForce->setAmoebaGlobalInPlaneAngleSextic(sexticK);
    amoebaInPlaneAngleForce->setUsesPeriodicBoundaryConditions(true);
    system.addForce(amoebaInPlaneAngleForce);
    Context context(system, integrator, Platform::getPlatformByName("Reference"));

    std::vector<Vec3> positions(numberOfParticles);
    positions[0] = Vec3(0, 1, 0);
    positions[1] = Vec3(0, 0, 0);
    positions[2] = Vec3(0, 0, 1);
    positions[3] = Vec3(1, 1, 1);

    context.setPositions(positions);
    State s1 = context.getState(State::Forces | State::Energy);
    
    // Move one atom to a position that should give identical results.

    positions[2] = Vec3(0, 0, -2);
    context.setPositions(positions);
    State s2 = context.getState(State::Forces | State::Energy);
    ASSERT_EQUAL_TOL(s1.getPotentialEnergy(), s2.getPotentialEnergy(), 1e-5);
    for (int i = 0; i < numberOfParticles; i++)
        ASSERT_EQUAL_VEC(s1.getForces()[i], s2.getForces()[i], 1e-5);
}

int main(int numberOfArguments, char* argv[]) {

    try {
        std::cout << "TestReferenceAmoebaInPlaneAngleForce running test..." << std::endl;
        registerAmoebaReferenceKernelFactories();
        testOneAngle();
        testPeriodic();
    }
    catch(const std::exception& e) {
        std::cout << "exception: " << e.what() << std::endl;
        std::cout << "FAIL - ERROR.  Test failed." << std::endl;
        return 1;
    }
    //std::cout << "PASS - Test succeeded." << std::endl;
    std::cout << "Done" << std::endl;
    return 0;
}