
/* -------------------------------------------------------------------------- *
 *                                   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.               *
 *                                                                            *
 * Portions copyright (c) 2008-2014 Stanford University and the Authors.      *
 * Authors: Peter Eastman                                                     *
 * Contributors:                                                              *
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 * Software is furnished to do so, subject to the following conditions:       *
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 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,   *
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/**
 * This tests all the different force terms in the reference implementation of CustomNonbondedForce.
 */

#ifdef WIN32
  #define _USE_MATH_DEFINES // Needed to get M_PI
#endif
#include "openmm/internal/AssertionUtilities.h"
#include "sfmt/SFMT.h"
#include "openmm/Context.h"
#include "ReferencePlatform.h"
#include "openmm/CustomNonbondedForce.h"
#include "openmm/NonbondedForce.h"
#include "openmm/System.h"
#include "openmm/VerletIntegrator.h"
#include <cmath>
#include <iostream>
#include <set>
#include <vector>

using namespace OpenMM;
using namespace std;

ReferencePlatform platform;

const double TOL = 1e-5;

void testSimpleExpression() {
    System system;
    system.addParticle(1.0);
    system.addParticle(1.0);
    VerletIntegrator integrator(0.01);
    CustomNonbondedForce* forceField = new CustomNonbondedForce("-0.1*r^3");
    forceField->addParticle(vector<double>());
    forceField->addParticle(vector<double>());
    system.addForce(forceField);
    Context context(system, integrator, platform);
    vector<Vec3> positions(2);
    positions[0] = Vec3(0, 0, 0);
    positions[1] = Vec3(2, 0, 0);
    context.setPositions(positions);
    State state = context.getState(State::Forces | State::Energy);
    const vector<Vec3>& forces = state.getForces();
    double force = 0.1*3*(2*2);
    ASSERT_EQUAL_VEC(Vec3(-force, 0, 0), forces[0], TOL);
    ASSERT_EQUAL_VEC(Vec3(force, 0, 0), forces[1], TOL);
    ASSERT_EQUAL_TOL(-0.1*(2*2*2), state.getPotentialEnergy(), TOL);
}

void testParameters() {
    System system;
    system.addParticle(1.0);
    system.addParticle(1.0);
    VerletIntegrator integrator(0.01);
    CustomNonbondedForce* forceField = new CustomNonbondedForce("scale*a*(r*b)^3; a=a1*a2; b=c+b1+b2");
    forceField->addPerParticleParameter("a");
    forceField->addPerParticleParameter("b");
    forceField->addGlobalParameter("scale", 3.0);
    forceField->addGlobalParameter("c", -1.0);
    vector<double> params(2);
    params[0] = 1.5;
    params[1] = 2.0;
    forceField->addParticle(params);
    params[0] = 2.0;
    params[1] = 3.0;
    forceField->addParticle(params);
    system.addForce(forceField);
    Context context(system, integrator, platform);
    vector<Vec3> positions(2);
    positions[0] = Vec3(0, 0, 0);
    positions[1] = Vec3(2, 0, 0);
    context.setPositions(positions);
    context.setParameter("scale", 1.0);
    context.setParameter("c", 0.0);
    State state = context.getState(State::Forces | State::Energy);
    vector<Vec3> forces = state.getForces();
    double force = -3.0*3*5.0*(10*10);
    ASSERT_EQUAL_VEC(Vec3(-force, 0, 0), forces[0], TOL);
    ASSERT_EQUAL_VEC(Vec3(force, 0, 0), forces[1], TOL);
    ASSERT_EQUAL_TOL(3.0*(10*10*10), state.getPotentialEnergy(), TOL);
    
    // Try changing the global parameters and make sure it's still correct.
    
    context.setParameter("scale", 1.5);
    context.setParameter("c", 1.0);
    state = context.getState(State::Forces | State::Energy);
    forces = state.getForces();
    force = -1.5*3.0*3*6.0*(12*12);
    ASSERT_EQUAL_VEC(Vec3(-force, 0, 0), forces[0], TOL);
    ASSERT_EQUAL_VEC(Vec3(force, 0, 0), forces[1], TOL);
    ASSERT_EQUAL_TOL(1.5*3.0*(12*12*12), state.getPotentialEnergy(), TOL);
    
    // Try changing the per-particle parameters and make sure it's still correct.
    
    params[0] = 1.6;
    params[1] = 2.1;
    forceField->setParticleParameters(0, params);
    params[0] = 1.9;
    params[1] = 2.8;
    forceField->setParticleParameters(1, params);
    forceField->updateParametersInContext(context);
    state = context.getState(State::Forces | State::Energy);
    forces = state.getForces();
    force = -1.5*1.6*1.9*3*5.9*(11.8*11.8);
    ASSERT_EQUAL_VEC(Vec3(-force, 0, 0), forces[0], TOL);
    ASSERT_EQUAL_VEC(Vec3(force, 0, 0), forces[1], TOL);
    ASSERT_EQUAL_TOL(1.5*1.6*1.9*(11.8*11.8*11.8), state.getPotentialEnergy(), TOL);
}

void testExclusions() {
    System system;
    VerletIntegrator integrator(0.01);
    CustomNonbondedForce* nonbonded = new CustomNonbondedForce("a*r; a=a1+a2");
    nonbonded->addPerParticleParameter("a");
    vector<double> params(1);
    vector<Vec3> positions(4);
    for (int i = 0; i < 4; i++) {
        system.addParticle(1.0);
        params[0] = i+1;
        nonbonded->addParticle(params);
        positions[i] = Vec3(i, 0, 0);
    }
    nonbonded->addExclusion(0, 1);
    nonbonded->addExclusion(1, 2);
    nonbonded->addExclusion(2, 3);
    nonbonded->addExclusion(0, 2);
    nonbonded->addExclusion(1, 3);
    system.addForce(nonbonded);
    Context context(system, integrator, platform);
    context.setPositions(positions);
    State state = context.getState(State::Forces | State::Energy);
    const vector<Vec3>& forces = state.getForces();
    ASSERT_EQUAL_VEC(Vec3(1+4, 0, 0), forces[0], TOL);
    ASSERT_EQUAL_VEC(Vec3(0, 0, 0), forces[1], TOL);
    ASSERT_EQUAL_VEC(Vec3(0, 0, 0), forces[2], TOL);
    ASSERT_EQUAL_VEC(Vec3(-(1+4), 0, 0), forces[3], TOL);
    ASSERT_EQUAL_TOL((1+4)*3.0, state.getPotentialEnergy(), TOL);
}

void testCutoff() {
    System system;
    system.addParticle(1.0);
    system.addParticle(1.0);
    system.addParticle(1.0);
    VerletIntegrator integrator(0.01);
    CustomNonbondedForce* forceField = new CustomNonbondedForce("r");
    forceField->addParticle(vector<double>());
    forceField->addParticle(vector<double>());
    forceField->addParticle(vector<double>());
    forceField->setNonbondedMethod(CustomNonbondedForce::CutoffNonPeriodic);
    forceField->setCutoffDistance(2.5);
    system.addForce(forceField);
    ASSERT(!forceField->usesPeriodicBoundaryConditions());
    ASSERT(!system.usesPeriodicBoundaryConditions());
    Context context(system, integrator, platform);
    vector<Vec3> positions(3);
    positions[0] = Vec3(0, 0, 0);
    positions[1] = Vec3(0, 2, 0);
    positions[2] = Vec3(0, 3, 0);
    context.setPositions(positions);
    State state = context.getState(State::Forces | State::Energy);
    const vector<Vec3>& forces = state.getForces();
    ASSERT_EQUAL_VEC(Vec3(0, 1, 0), forces[0], TOL);
    ASSERT_EQUAL_VEC(Vec3(0, 0, 0), forces[1], TOL);
    ASSERT_EQUAL_VEC(Vec3(0, -1, 0), forces[2], TOL);
    ASSERT_EQUAL_TOL(2.0+1.0, state.getPotentialEnergy(), TOL);
}

void testPeriodic() {
    System system;
    system.addParticle(1.0);
    system.addParticle(1.0);
    system.addParticle(1.0);
    VerletIntegrator integrator(0.01);
    CustomNonbondedForce* forceField = new CustomNonbondedForce("r");
    forceField->addParticle(vector<double>());
    forceField->addParticle(vector<double>());
    forceField->addParticle(vector<double>());
    forceField->setNonbondedMethod(CustomNonbondedForce::CutoffPeriodic);
    forceField->setCutoffDistance(2.0);
    system.setDefaultPeriodicBoxVectors(Vec3(4, 0, 0), Vec3(0, 4, 0), Vec3(0, 0, 4));
    system.addForce(forceField);
    ASSERT(forceField->usesPeriodicBoundaryConditions());
    ASSERT(system.usesPeriodicBoundaryConditions());
    Context context(system, integrator, platform);
    vector<Vec3> positions(3);
    positions[0] = Vec3(0, 0, 0);
    positions[1] = Vec3(0, 2.1, 0);
    positions[2] = Vec3(0, 3, 0);
    context.setPositions(positions);
    State state = context.getState(State::Forces | State::Energy);
    const vector<Vec3>& forces = state.getForces();
    ASSERT_EQUAL_VEC(Vec3(0, -2, 0), forces[0], TOL);
    ASSERT_EQUAL_VEC(Vec3(0, 2, 0), forces[1], TOL);
    ASSERT_EQUAL_VEC(Vec3(0, 0, 0), forces[2], TOL);
    ASSERT_EQUAL_TOL(1.9+1+0.9, state.getPotentialEnergy(), TOL);
}

void testTriclinic() {
    System system;
    system.addParticle(1.0);
    system.addParticle(1.0);
    Vec3 a(3.1, 0, 0);
    Vec3 b(0.4, 3.5, 0);
    Vec3 c(-0.1, -0.5, 4.0);
    system.setDefaultPeriodicBoxVectors(a, b, c);
    VerletIntegrator integrator(0.01);
    CustomNonbondedForce* nonbonded = new CustomNonbondedForce("r");
    nonbonded->addParticle(vector<double>());
    nonbonded->addParticle(vector<double>());
    nonbonded->setNonbondedMethod(CustomNonbondedForce::CutoffPeriodic);
    const double cutoff = 1.5;
    nonbonded->setCutoffDistance(cutoff);
    system.addForce(nonbonded);
    Context context(system, integrator, platform);
    vector<Vec3> positions(2);
    OpenMM_SFMT::SFMT sfmt;
    init_gen_rand(0, sfmt);
    for (int iteration = 0; iteration < 50; iteration++) {
        // Generate random positions for the two particles.

        positions[0] = a*genrand_real2(sfmt) + b*genrand_real2(sfmt) + c*genrand_real2(sfmt);
        positions[1] = a*genrand_real2(sfmt) + b*genrand_real2(sfmt) + c*genrand_real2(sfmt);
        context.setPositions(positions);

        // Loop over all possible periodic copies and find the nearest one.

        Vec3 delta;
        double distance2 = 100.0;
        for (int i = -1; i < 2; i++)
            for (int j = -1; j < 2; j++)
                for (int k = -1; k < 2; k++) {
                    Vec3 d = positions[1]-positions[0]+a*i+b*j+c*k;
                    if (d.dot(d) < distance2) {
                        delta = d;
                        distance2 = d.dot(d);
                    }
                }
        double distance = sqrt(distance2);

        // See if the force and energy are correct.

        State state = context.getState(State::Forces | State::Energy);
        if (distance >= cutoff) {
            ASSERT_EQUAL(0.0, state.getPotentialEnergy());
            ASSERT_EQUAL_VEC(Vec3(0, 0, 0), state.getForces()[0], 0);
            ASSERT_EQUAL_VEC(Vec3(0, 0, 0), state.getForces()[1], 0);
        }
        else {
            const Vec3 force = delta/sqrt(delta.dot(delta));
            ASSERT_EQUAL_TOL(distance, state.getPotentialEnergy(), TOL);
            ASSERT_EQUAL_VEC(force, state.getForces()[0], TOL);
            ASSERT_EQUAL_VEC(-force, state.getForces()[1], TOL);
        }
    }
}

void testContinuous1DFunction() {
    System system;
    system.addParticle(1.0);
    system.addParticle(1.0);
    VerletIntegrator integrator(0.01);
    CustomNonbondedForce* forceField = new CustomNonbondedForce("fn(r)+1");
    forceField->addParticle(vector<double>());
    forceField->addParticle(vector<double>());
    vector<double> table;
    for (int i = 0; i < 21; i++)
        table.push_back(sin(0.25*i));
    forceField->addTabulatedFunction("fn", new Continuous1DFunction(table, 1.0, 6.0));
    system.addForce(forceField);
    Context context(system, integrator, platform);
    vector<Vec3> positions(2);
    positions[0] = Vec3(0, 0, 0);
    for (int i = 1; i < 30; i++) {
        double x = (7.0/30.0)*i;
        positions[1] = Vec3(x, 0, 0);
        context.setPositions(positions);
        State state = context.getState(State::Forces | State::Energy);
        const vector<Vec3>& forces = state.getForces();
        double force = (x < 1.0 || x > 6.0 ? 0.0 : -cos(x-1.0));
        double energy = (x < 1.0 || x > 6.0 ? 0.0 : sin(x-1.0))+1.0;
        ASSERT_EQUAL_VEC(Vec3(-force, 0, 0), forces[0], 0.1);
        ASSERT_EQUAL_VEC(Vec3(force, 0, 0), forces[1], 0.1);
        ASSERT_EQUAL_TOL(energy, state.getPotentialEnergy(), 0.02);
    }
    for (int i = 1; i < 20; i++) {
        double x = 0.25*i+1.0;
        positions[1] = Vec3(x, 0, 0);
        context.setPositions(positions);
        State state = context.getState(State::Energy);
        double energy = (x < 1.0 || x > 6.0 ? 0.0 : sin(x-1.0))+1.0;
        ASSERT_EQUAL_TOL(energy, state.getPotentialEnergy(), 1e-4);
    }
}

void testContinuous2DFunction() {
    const int xsize = 20;
    const int ysize = 21;
    const double xmin = 0.4;
    const double xmax = 1.5;
    const double ymin = 0.0;
    const double ymax = 2.1;
    System system;
    system.addParticle(1.0);
    system.addParticle(1.0);
    VerletIntegrator integrator(0.01);
    CustomNonbondedForce* forceField = new CustomNonbondedForce("fn(r,a)+1");
    forceField->addGlobalParameter("a", 0.0);
    forceField->addParticle(vector<double>());
    forceField->addParticle(vector<double>());
    vector<double> table(xsize*ysize);
    for (int i = 0; i < xsize; i++) {
        for (int j = 0; j < ysize; j++) {
            double x = xmin + i*(xmax-xmin)/xsize;
            double y = ymin + j*(ymax-ymin)/ysize;
            table[i+xsize*j] = sin(0.25*x)*cos(0.33*y);
        }
    }
    forceField->addTabulatedFunction("fn", new Continuous2DFunction(xsize, ysize, table, xmin, xmax, ymin, ymax));
    system.addForce(forceField);
    Context context(system, integrator, platform);
    vector<Vec3> positions(2);
    positions[0] = Vec3(0, 0, 0);
    for (double x = xmin-0.15; x < xmax+0.2; x += 0.1) {
        for (double y = ymin-0.15; y < ymax+0.2; y += 0.1) {
            positions[1] = Vec3(x, 0, 0);
            context.setParameter("a", y);
            context.setPositions(positions);
            State state = context.getState(State::Forces | State::Energy);
            const vector<Vec3>& forces = state.getForces();
            double energy = 1;
            double force = 0;
            if (x >= xmin && x <= xmax && y >= ymin && y <= ymax) {
                energy = sin(0.25*x)*cos(0.33*y)+1.0;
                force = -0.25*cos(0.25*x)*cos(0.33*y);
            }
            ASSERT_EQUAL_VEC(Vec3(-force, 0, 0), forces[0], 0.1);
            ASSERT_EQUAL_VEC(Vec3(force, 0, 0), forces[1], 0.1);
            ASSERT_EQUAL_TOL(energy, state.getPotentialEnergy(), 0.02);
        }
    }
}

void testContinuous3DFunction() {
    const int xsize = 10;
    const int ysize = 11;
    const int zsize = 12;
    const double xmin = 0.6;
    const double xmax = 1.1;
    const double ymin = 0.0;
    const double ymax = 0.7;
    const double zmin = 0.2;
    const double zmax = 0.9;
    System system;
    system.addParticle(1.0);
    system.addParticle(1.0);
    VerletIntegrator integrator(0.01);
    CustomNonbondedForce* forceField = new CustomNonbondedForce("fn(r,a,b)+1");
    forceField->addGlobalParameter("a", 0.0);
    forceField->addGlobalParameter("b", 0.0);
    forceField->addParticle(vector<double>());
    forceField->addParticle(vector<double>());
    vector<double> table(xsize*ysize*zsize);
    for (int i = 0; i < xsize; i++) {
        for (int j = 0; j < ysize; j++) {
            for (int k = 0; k < zsize; k++) {
                double x = xmin + i*(xmax-xmin)/xsize;
                double y = ymin + j*(ymax-ymin)/ysize;
                double z = zmin + k*(zmax-zmin)/zsize;
                table[i+xsize*j+xsize*ysize*k] = sin(0.25*x)*cos(0.33*y)*(1+z);
            }
        }
    }
    forceField->addTabulatedFunction("fn", new Continuous3DFunction(xsize, ysize, zsize, table, xmin, xmax, ymin, ymax, zmin, zmax));
    system.addForce(forceField);
    Context context(system, integrator, platform);
    vector<Vec3> positions(2);
    positions[0] = Vec3(0, 0, 0);
    for (double x = xmin-0.15; x < xmax+0.2; x += 0.1) {
        for (double y = ymin-0.15; y < ymax+0.2; y += 0.1) {
            for (double z = zmin-0.15; z < zmax+0.2; z += 0.1) {
                positions[1] = Vec3(x, 0, 0);
                context.setParameter("a", y);
                context.setParameter("b", z);
                context.setPositions(positions);
                State state = context.getState(State::Forces | State::Energy);
                const vector<Vec3>& forces = state.getForces();
                double energy = 1;
                double force = 0;
                if (x >= xmin && x <= xmax && y >= ymin && y <= ymax && z >= zmin && z <= zmax) {
                    energy = sin(0.25*x)*cos(0.33*y)*(1.0+z)+1.0;
                    force = -0.25*cos(0.25*x)*cos(0.33*y)*(1.0+z);
                }
                ASSERT_EQUAL_VEC(Vec3(-force, 0, 0), forces[0], 0.1);
                ASSERT_EQUAL_VEC(Vec3(force, 0, 0), forces[1], 0.1);
                ASSERT_EQUAL_TOL(energy, state.getPotentialEnergy(), 0.05);
            }
        }
    }
}

void testDiscrete1DFunction() {
    System system;
    system.addParticle(1.0);
    system.addParticle(1.0);
    VerletIntegrator integrator(0.01);
    CustomNonbondedForce* forceField = new CustomNonbondedForce("fn(r)+1");
    forceField->addParticle(vector<double>());
    forceField->addParticle(vector<double>());
    vector<double> table;
    for (int i = 0; i < 21; i++)
        table.push_back(sin(0.25*i));
    forceField->addTabulatedFunction("fn", new Discrete1DFunction(table));
    system.addForce(forceField);
    Context context(system, integrator, platform);
    vector<Vec3> positions(2);
    positions[0] = Vec3(0, 0, 0);
    for (int i = 0; i < (int) table.size(); i++) {
        positions[1] = Vec3(i, 0, 0);
        context.setPositions(positions);
        State state = context.getState(State::Forces | State::Energy);
        const vector<Vec3>& forces = state.getForces();
        ASSERT_EQUAL_VEC(Vec3(0, 0, 0), forces[0], 1e-6);
        ASSERT_EQUAL_VEC(Vec3(0, 0, 0), forces[1], 1e-6);
        ASSERT_EQUAL_TOL(table[i]+1.0, state.getPotentialEnergy(), 1e-6);
    }
}

void testDiscrete2DFunction() {
    const int xsize = 10;
    const int ysize = 5;
    System system;
    system.addParticle(1.0);
    system.addParticle(1.0);
    VerletIntegrator integrator(0.01);
    CustomNonbondedForce* forceField = new CustomNonbondedForce("fn(r,a)+1");
    forceField->addGlobalParameter("a", 0.0);
    forceField->addParticle(vector<double>());
    forceField->addParticle(vector<double>());
    vector<double> table;
    for (int i = 0; i < xsize; i++)
        for (int j = 0; j < ysize; j++)
            table.push_back(sin(0.25*i)+cos(0.33*j));
    forceField->addTabulatedFunction("fn", new Discrete2DFunction(xsize, ysize, table));
    system.addForce(forceField);
    Context context(system, integrator, platform);
    vector<Vec3> positions(2);
    positions[0] = Vec3(0, 0, 0);
    for (int i = 0; i < (int) table.size(); i++) {
        positions[1] = Vec3(i%xsize, 0, 0);
        context.setPositions(positions);
        context.setParameter("a", i/xsize);
        State state = context.getState(State::Forces | State::Energy);
        const vector<Vec3>& forces = state.getForces();
        ASSERT_EQUAL_VEC(Vec3(0, 0, 0), forces[0], 1e-6);
        ASSERT_EQUAL_VEC(Vec3(0, 0, 0), forces[1], 1e-6);
        ASSERT_EQUAL_TOL(table[i]+1.0, state.getPotentialEnergy(), 1e-6);
    }
}

void testDiscrete3DFunction() {
    const int xsize = 8;
    const int ysize = 5;
    const int zsize = 6;
    System system;
    system.addParticle(1.0);
    system.addParticle(1.0);
    VerletIntegrator integrator(0.01);
    CustomNonbondedForce* forceField = new CustomNonbondedForce("fn(r,a,b)+1");
    forceField->addGlobalParameter("a", 0.0);
    forceField->addGlobalParameter("b", 0.0);
    forceField->addParticle(vector<double>());
    forceField->addParticle(vector<double>());
    vector<double> table;
    for (int i = 0; i < xsize; i++)
        for (int j = 0; j < ysize; j++)
            for (int k = 0; k < zsize; k++)
                table.push_back(sin(0.25*i)+cos(0.33*j)+0.12345*k);
    forceField->addTabulatedFunction("fn", new Discrete3DFunction(xsize, ysize, zsize, table));
    system.addForce(forceField);
    Context context(system, integrator, platform);
    vector<Vec3> positions(2);
    positions[0] = Vec3(0, 0, 0);
    for (int i = 0; i < (int) table.size(); i++) {
        positions[1] = Vec3(i%xsize, 0, 0);
        context.setPositions(positions);
        context.setParameter("a", (i/xsize)%ysize);
        context.setParameter("b", i/(xsize*ysize));
        State state = context.getState(State::Forces | State::Energy);
        const vector<Vec3>& forces = state.getForces();
        ASSERT_EQUAL_VEC(Vec3(0, 0, 0), forces[0], 1e-6);
        ASSERT_EQUAL_VEC(Vec3(0, 0, 0), forces[1], 1e-6);
        ASSERT_EQUAL_TOL(table[i]+1.0, state.getPotentialEnergy(), 1e-6);
    }
}

void testCoulombLennardJones() {
    const int numMolecules = 300;
    const int numParticles = numMolecules*2;
    const double boxSize = 20.0;

    // Create two systems: one with a NonbondedForce, and one using a CustomNonbondedForce to implement the same interaction.

    System standardSystem;
    System customSystem;
    for (int i = 0; i < numParticles; i++) {
        standardSystem.addParticle(1.0);
        customSystem.addParticle(1.0);
    }
    NonbondedForce* standardNonbonded = new NonbondedForce();
    CustomNonbondedForce* customNonbonded = new CustomNonbondedForce("4*eps*((sigma/r)^12-(sigma/r)^6)+138.935456*q/r; q=q1*q2; sigma=0.5*(sigma1+sigma2); eps=sqrt(eps1*eps2)");
    customNonbonded->addPerParticleParameter("q");
    customNonbonded->addPerParticleParameter("sigma");
    customNonbonded->addPerParticleParameter("eps");
    vector<Vec3> positions(numParticles);
    vector<Vec3> velocities(numParticles);
    OpenMM_SFMT::SFMT sfmt;
    init_gen_rand(0, sfmt);

    vector<double> params(3);
    for (int i = 0; i < numMolecules; i++) {
        if (i < numMolecules/2) {
            standardNonbonded->addParticle(1.0, 0.2, 0.1);
            params[0] = 1.0;
            params[1] = 0.2;
            params[2] = 0.1;
            customNonbonded->addParticle(params);
            standardNonbonded->addParticle(-1.0, 0.1, 0.1);
            params[0] = -1.0;
            params[1] = 0.1;
            customNonbonded->addParticle(params);
        }
        else {
            standardNonbonded->addParticle(1.0, 0.2, 0.2);
            params[0] = 1.0;
            params[1] = 0.2;
            params[2] = 0.2;
            customNonbonded->addParticle(params);
            standardNonbonded->addParticle(-1.0, 0.1, 0.2);
            params[0] = -1.0;
            params[1] = 0.1;
            customNonbonded->addParticle(params);
        }
        positions[2*i] = Vec3(boxSize*genrand_real2(sfmt), boxSize*genrand_real2(sfmt), boxSize*genrand_real2(sfmt));
        positions[2*i+1] = Vec3(positions[2*i][0]+1.0, positions[2*i][1], positions[2*i][2]);
        velocities[2*i] = Vec3(genrand_real2(sfmt), genrand_real2(sfmt), genrand_real2(sfmt));
        velocities[2*i+1] = Vec3(genrand_real2(sfmt), genrand_real2(sfmt), genrand_real2(sfmt));
        standardNonbonded->addException(2*i, 2*i+1, 0.0, 1.0, 0.0);
        customNonbonded->addExclusion(2*i, 2*i+1);
    }
    standardNonbonded->setNonbondedMethod(NonbondedForce::NoCutoff);
    customNonbonded->setNonbondedMethod(CustomNonbondedForce::NoCutoff);
    standardSystem.addForce(standardNonbonded);
    customSystem.addForce(customNonbonded);
    ASSERT(!customNonbonded->usesPeriodicBoundaryConditions());
    ASSERT(!customSystem.usesPeriodicBoundaryConditions());
    VerletIntegrator integrator1(0.01);
    VerletIntegrator integrator2(0.01);
    Context context1(standardSystem, integrator1, platform);
    Context context2(customSystem, integrator2, platform);
    context1.setPositions(positions);
    context2.setPositions(positions);
    context1.setVelocities(velocities);
    context2.setVelocities(velocities);
    State state1 = context1.getState(State::Forces | State::Energy);
    State state2 = context2.getState(State::Forces | State::Energy);
    ASSERT_EQUAL_TOL(state1.getPotentialEnergy(), state2.getPotentialEnergy(), 1e-4);
    for (int i = 0; i < numParticles; i++) {
        ASSERT_EQUAL_VEC(state1.getForces()[i], state2.getForces()[i], 1e-4);
    }
}

void testSwitchingFunction() {
    System system;
    system.addParticle(1.0);
    system.addParticle(1.0);
    VerletIntegrator integrator(0.01);
    CustomNonbondedForce* nonbonded = new CustomNonbondedForce("10/r^2");
    vector<double> params;
    nonbonded->addParticle(params);
    nonbonded->addParticle(params);
    nonbonded->setNonbondedMethod(CustomNonbondedForce::CutoffNonPeriodic);
    nonbonded->setCutoffDistance(2.0);
    nonbonded->setUseSwitchingFunction(true);
    nonbonded->setSwitchingDistance(1.5);
    system.addForce(nonbonded);
    Context context(system, integrator, platform);
    vector<Vec3> positions(2);
    positions[0] = Vec3(0, 0, 0);
    
    // Compute the interaction at various distances.
    
    for (double r = 1.0; r < 2.5; r += 0.1) {
        positions[1] = Vec3(r, 0, 0);
        context.setPositions(positions);
        State state = context.getState(State::Forces | State::Energy);
        
        // See if the energy is correct.
        
        double expectedEnergy = 10/(r*r);
        double switchValue;
        if (r <= 1.5)
            switchValue = 1;
        else if (r >= 2.0)
            switchValue = 0;
        else {
            double t = (r-1.5)/0.5;
            switchValue = 1+t*t*t*(-10+t*(15-t*6));
        }
        ASSERT_EQUAL_TOL(switchValue*expectedEnergy, state.getPotentialEnergy(), TOL);
        
        // See if the force is the gradient of the energy.
        
        double delta = 1e-3;
        positions[1] = Vec3(r-delta, 0, 0);
        context.setPositions(positions);
        double e1 = context.getState(State::Energy).getPotentialEnergy();
        positions[1] = Vec3(r+delta, 0, 0);
        context.setPositions(positions);
        double e2 = context.getState(State::Energy).getPotentialEnergy();
        ASSERT_EQUAL_TOL((e2-e1)/(2*delta), state.getForces()[0][0], 1e-3);
    }
}

void testLongRangeCorrection() {
    // Create a box of particles.

    int gridSize = 5;
    int numParticles = gridSize*gridSize*gridSize;
    double boxSize = gridSize*0.7;
    double cutoff = boxSize/3;
    System standardSystem;
    System customSystem;
    VerletIntegrator integrator1(0.01);
    VerletIntegrator integrator2(0.01);
    NonbondedForce* standardNonbonded = new NonbondedForce();
    CustomNonbondedForce* customNonbonded = new CustomNonbondedForce("4*eps*((sigma/r)^12-(sigma/r)^6); sigma=0.5*(sigma1+sigma2); eps=sqrt(eps1*eps2)");
    customNonbonded->addPerParticleParameter("sigma");
    customNonbonded->addPerParticleParameter("eps");
    vector<Vec3> positions(numParticles);
    int index = 0;
    vector<double> params1(2);
    params1[0] = 1.1;
    params1[1] = 0.5;
    vector<double> params2(2);
    params2[0] = 1;
    params2[1] = 1;
    for (int i = 0; i < gridSize; i++)
        for (int j = 0; j < gridSize; j++)
            for (int k = 0; k < gridSize; k++) {
                standardSystem.addParticle(1.0);
                customSystem.addParticle(1.0);
                if (index%2 == 0) {
                    standardNonbonded->addParticle(0, params1[0], params1[1]);
                    customNonbonded->addParticle(params1);
                }
                else {
                    standardNonbonded->addParticle(0, params2[0], params2[1]);
                    customNonbonded->addParticle(params2);
                }
                positions[index] = Vec3(i*boxSize/gridSize, j*boxSize/gridSize, k*boxSize/gridSize);
                index++;
            }
    standardNonbonded->setNonbondedMethod(NonbondedForce::CutoffPeriodic);
    customNonbonded->setNonbondedMethod(CustomNonbondedForce::CutoffPeriodic);
    standardNonbonded->setCutoffDistance(cutoff);
    customNonbonded->setCutoffDistance(cutoff);
    standardSystem.setDefaultPeriodicBoxVectors(Vec3(boxSize, 0, 0), Vec3(0, boxSize, 0), Vec3(0, 0, boxSize));
    customSystem.setDefaultPeriodicBoxVectors(Vec3(boxSize, 0, 0), Vec3(0, boxSize, 0), Vec3(0, 0, boxSize));
    standardNonbonded->setUseDispersionCorrection(true);
    customNonbonded->setUseLongRangeCorrection(true);
    standardNonbonded->setUseSwitchingFunction(true);
    customNonbonded->setUseSwitchingFunction(true);
    standardNonbonded->setSwitchingDistance(0.8*cutoff);
    customNonbonded->setSwitchingDistance(0.8*cutoff);
    standardSystem.addForce(standardNonbonded);
    customSystem.addForce(customNonbonded);

    // Compute the correction for the standard force.

    Context context1(standardSystem, integrator1, platform);
    context1.setPositions(positions);
    double standardEnergy1 = context1.getState(State::Energy).getPotentialEnergy();
    standardNonbonded->setUseDispersionCorrection(false);
    context1.reinitialize();
    context1.setPositions(positions);
    double standardEnergy2 = context1.getState(State::Energy).getPotentialEnergy();

    // Compute the correction for the custom force.

    Context context2(customSystem, integrator2, platform);
    context2.setPositions(positions);
    double customEnergy1 = context2.getState(State::Energy).getPotentialEnergy();
    customNonbonded->setUseLongRangeCorrection(false);
    context2.reinitialize();
    context2.setPositions(positions);
    double customEnergy2 = context2.getState(State::Energy).getPotentialEnergy();

    // See if they agree.

    ASSERT_EQUAL_TOL(standardEnergy1-standardEnergy2, customEnergy1-customEnergy2, 1e-4);
}

void testInteractionGroups() {
    const int numParticles = 6;
    System system;
    VerletIntegrator integrator(0.01);
    CustomNonbondedForce* nonbonded = new CustomNonbondedForce("v1+v2");
    nonbonded->addPerParticleParameter("v");
    vector<double> params(1, 0.001);
    for (int i = 0; i < numParticles; i++) {
        system.addParticle(1.0);
        nonbonded->addParticle(params);
        params[0] *= 10;
    }
    set<int> set1, set2, set3, set4;
    set1.insert(2);
    set2.insert(0);
    set2.insert(1);
    set2.insert(2);
    set2.insert(3);
    set2.insert(4);
    set2.insert(5);
    nonbonded->addInteractionGroup(set1, set2); // Particle 2 interacts with every other particle.
    set3.insert(0);
    set3.insert(1);
    set4.insert(4);
    set4.insert(5);
    nonbonded->addInteractionGroup(set3, set4); // Particles 0 and 1 interact with 4 and 5.
    nonbonded->addExclusion(1, 2); // Add an exclusion to make sure it gets skipped.
    system.addForce(nonbonded);
    Context context(system, integrator, platform);
    vector<Vec3> positions(numParticles);
    context.setPositions(positions);
    State state = context.getState(State::Energy);
    double expectedEnergy = 331.423; // Each digit is the number of interactions a particle particle is involved in.
    ASSERT_EQUAL_TOL(expectedEnergy, state.getPotentialEnergy(), TOL);
}

void testLargeInteractionGroup() {
    const int numMolecules = 300;
    const int numParticles = numMolecules*2;
    const double boxSize = 20.0;
    
    // Create a large system.
    
    System system;
    system.setDefaultPeriodicBoxVectors(Vec3(boxSize, 0, 0), Vec3(0, boxSize, 0), Vec3(0, 0, boxSize));
    for (int i = 0; i < numParticles; i++)
        system.addParticle(1.0);
    CustomNonbondedForce* nonbonded = new CustomNonbondedForce("4*eps*((sigma/r)^12-(sigma/r)^6)+138.935456*q/r; q=q1*q2; sigma=0.5*(sigma1+sigma2); eps=sqrt(eps1*eps2)");
    nonbonded->addPerParticleParameter("q");
    nonbonded->addPerParticleParameter("sigma");
    nonbonded->addPerParticleParameter("eps");
    vector<Vec3> positions(numParticles);
    OpenMM_SFMT::SFMT sfmt;
    init_gen_rand(0, sfmt);
    vector<double> params(3);
    for (int i = 0; i < numMolecules; i++) {
        if (i < numMolecules/2) {
            params[0] = 1.0;
            params[1] = 0.2;
            params[2] = 0.1;
            nonbonded->addParticle(params);
            params[0] = -1.0;
            params[1] = 0.1;
            nonbonded->addParticle(params);
        }
        else {
            params[0] = 1.0;
            params[1] = 0.2;
            params[2] = 0.2;
            nonbonded->addParticle(params);
            params[0] = -1.0;
            params[1] = 0.1;
            nonbonded->addParticle(params);
        }
        positions[2*i] = Vec3(boxSize*genrand_real2(sfmt), boxSize*genrand_real2(sfmt), boxSize*genrand_real2(sfmt));
        positions[2*i+1] = Vec3(positions[2*i][0]+1.0, positions[2*i][1], positions[2*i][2]);
        nonbonded->addExclusion(2*i, 2*i+1);
    }
    nonbonded->setNonbondedMethod(CustomNonbondedForce::CutoffPeriodic);
    system.addForce(nonbonded);
    
    // Compute the forces.
    
    VerletIntegrator integrator(0.01);
    Context context(system, integrator, platform);
    context.setPositions(positions);
    State state1 = context.getState(State::Forces);
    
    // Modify the force so only one particle interacts with everything else.
    
    set<int> set1, set2;
    set1.insert(151);
    for (int i = 0; i < numParticles; i++)
        set2.insert(i);
    nonbonded->addInteractionGroup(set1, set2);
    context.reinitialize();
    context.setPositions(positions);
    State state2 = context.getState(State::Forces);
    
    // The force on that one particle should be the same.
    
    ASSERT_EQUAL_VEC(state1.getForces()[151], state2.getForces()[151], 1e-4);
    
    // Modify the interaction group so it includes all interactions.  This should now reproduce the original forces
    // on all atoms.

    for (int i = 0; i < numParticles; i++)
        set1.insert(i);
    nonbonded->setInteractionGroupParameters(0, set1, set2);
    context.reinitialize();
    context.setPositions(positions);
    State state3 = context.getState(State::Forces);
    for (int i = 0; i < numParticles; i++)
        ASSERT_EQUAL_VEC(state1.getForces()[i], state3.getForces()[i], 1e-4);
}

void testInteractionGroupLongRangeCorrection() {
    const int numParticles = 10;
    const double boxSize = 10.0;
    const double cutoff = 0.5;
    System system;
    system.setDefaultPeriodicBoxVectors(Vec3(boxSize, 0, 0), Vec3(0, boxSize, 0), Vec3(0, 0, boxSize));
    CustomNonbondedForce* nonbonded = new CustomNonbondedForce("c1*c2*r^-4");
    nonbonded->addPerParticleParameter("c");
    vector<Vec3> positions(numParticles);
    vector<double> params(1);
    for (int i = 0; i < numParticles; i++) {
        system.addParticle(1.0);
        params[0] = (i%2 == 0 ? 1.1 : 2.0);
        nonbonded->addParticle(params);
        positions[i] = Vec3(0.5*i, 0, 0);
    }
    nonbonded->setNonbondedMethod(CustomNonbondedForce::CutoffPeriodic);
    nonbonded->setCutoffDistance(cutoff);
    system.addForce(nonbonded);
    
    // Setup nonbonded groups.  They involve 1 interaction of type AA,
    // 2 of type BB, and 5 of type AB.
    
    set<int> set1, set2, set3, set4, set5;
    set1.insert(0);
    set1.insert(1);
    set1.insert(2);
    nonbonded->addInteractionGroup(set1, set1);
    set2.insert(3);
    set3.insert(4);
    set3.insert(6);
    set3.insert(8);
    nonbonded->addInteractionGroup(set2, set3);
    set4.insert(5);
    set5.insert(7);
    set5.insert(9);
    nonbonded->addInteractionGroup(set4, set5);
    
    // Compute energy with and without the correction.
    
    VerletIntegrator integrator(0.01);
    Context context(system, integrator, platform);
    context.setPositions(positions);
    double energy1 = context.getState(State::Energy).getPotentialEnergy();
    nonbonded->setUseLongRangeCorrection(true);
    context.reinitialize();
    context.setPositions(positions);
    double energy2 = context.getState(State::Energy).getPotentialEnergy();
    
    // Check the result.
    
    double sum = (1.1*1.1 + 2*2.0*2.0 + 5*1.1*2.0)*2.0;
    int numPairs = (numParticles*(numParticles+1))/2;
    double expected = 2*M_PI*numParticles*numParticles*sum/(numPairs*boxSize*boxSize*boxSize);
    ASSERT_EQUAL_TOL(expected, energy2-energy1, 1e-4);
}

int main() {
    try {
        testSimpleExpression();
        testParameters();
        testExclusions();
        testCutoff();
        testPeriodic();
        testTriclinic();
        testContinuous1DFunction();
        testContinuous2DFunction();
        testContinuous3DFunction();
        testDiscrete1DFunction();
        testDiscrete2DFunction();
        testDiscrete3DFunction();
        testCoulombLennardJones();
        testSwitchingFunction();
        testLongRangeCorrection();
        testInteractionGroups();
        testLargeInteractionGroup();
        testInteractionGroupLongRangeCorrection();
    }
    catch(const exception& e) {
        cout << "exception: " << e.what() << endl;
        return 1;
    }
    cout << "Done" << endl;
    return 0;
}
