C++ NonbondedForce类代码示例

void NonbondedForceImpl::calcPMEParameters(const System& system, const NonbondedForce& force, double& alpha, int& xsize, int& ysize, int& zsize, bool lj) {
    if (lj)
        force.getLJPMEParameters(alpha, xsize, ysize, zsize);
    else
        force.getPMEParameters(alpha, xsize, ysize, zsize);
    if (alpha == 0.0) {
        Vec3 boxVectors[3];
        system.getDefaultPeriodicBoxVectors(boxVectors[0], boxVectors[1], boxVectors[2]);
        double tol = force.getEwaldErrorTolerance();
        alpha = (1.0/force.getCutoffDistance())*std::sqrt(-log(2.0*tol));
        if (lj) {
            xsize = (int) ceil(alpha*boxVectors[0][0]/(3*pow(tol, 0.2)));
            ysize = (int) ceil(alpha*boxVectors[1][1]/(3*pow(tol, 0.2)));
            zsize = (int) ceil(alpha*boxVectors[2][2]/(3*pow(tol, 0.2)));
        }
        else {
            xsize = (int) ceil(2*alpha*boxVectors[0][0]/(3*pow(tol, 0.2)));
            ysize = (int) ceil(2*alpha*boxVectors[1][1]/(3*pow(tol, 0.2)));
            zsize = (int) ceil(2*alpha*boxVectors[2][2]/(3*pow(tol, 0.2)));
        }
        xsize = max(xsize, 6);
        ysize = max(ysize, 6);
        zsize = max(zsize, 6);
    }
}

void testConstraints() {
    const int numParticles = 8;
    const int numConstraints = 5;
    System system;
    VariableVerletIntegrator integrator(1e-5);
    integrator.setConstraintTolerance(1e-5);
    NonbondedForce* forceField = new NonbondedForce();
    for (int i = 0; i < numParticles; ++i) {
        system.addParticle(10.0);
        forceField->addParticle((i%2 == 0 ? 0.2 : -0.2), 0.5, 5.0);
    }
    system.addConstraint(0, 1, 1.0);
    system.addConstraint(1, 2, 1.0);
    system.addConstraint(2, 3, 1.0);
    system.addConstraint(4, 5, 1.0);
    system.addConstraint(6, 7, 1.0);
    system.addForce(forceField);
    Context context(system, integrator, platform);
    vector<Vec3> positions(numParticles);
    vector<Vec3> velocities(numParticles);
    OpenMM_SFMT::SFMT sfmt;
    init_gen_rand(0, sfmt);

    for (int i = 0; i < numParticles; ++i) {
        positions[i] = Vec3(i/2, (i+1)/2, 0);
        velocities[i] = Vec3(genrand_real2(sfmt)-0.5, genrand_real2(sfmt)-0.5, genrand_real2(sfmt)-0.5);
    }
    context.setPositions(positions);
    context.setVelocities(velocities);

    // Simulate it and see whether the constraints remain satisfied.

    double initialEnergy = 0.0;
    for (int i = 0; i < 1000; ++i) {
        State state = context.getState(State::Positions | State::Energy | State::Velocities | State::Forces);
            for (int j = 0; j < numConstraints; ++j) {
                int particle1, particle2;
                double distance;
                system.getConstraintParameters(j, particle1, particle2, distance);
                Vec3 p1 = state.getPositions()[particle1];
                Vec3 p2 = state.getPositions()[particle2];
                double dist = std::sqrt((p1[0]-p2[0])*(p1[0]-p2[0])+(p1[1]-p2[1])*(p1[1]-p2[1])+(p1[2]-p2[2])*(p1[2]-p2[2]));
                ASSERT_EQUAL_TOL(distance, dist, 1e-4);
            }
        double energy = state.getKineticEnergy()+state.getPotentialEnergy();
        if (i == 1)
            initialEnergy = energy;
        else if (i > 1)
            ASSERT_EQUAL_TOL(initialEnergy, energy, 0.01);
        integrator.step(1);
    }
    double finalTime = context.getState(State::Positions).getTime();
    ASSERT(finalTime > 0.1);

    // Now try the stepTo() method.

    finalTime += 0.5;
    integrator.stepTo(finalTime);
    ASSERT_EQUAL(finalTime, context.getState(State::Positions).getTime());
}

void testRandomSeed() {
    const int numParticles = 8;
    const double temp = 100.0;
    const double collisionFreq = 10.0;
    System system;
    VerletIntegrator integrator(0.01);
    NonbondedForce* forceField = new NonbondedForce();
    for (int i = 0; i < numParticles; ++i) {
        system.addParticle(2.0);
        forceField->addParticle((i%2 == 0 ? 1.0 : -1.0), 1.0, 5.0);
    }
    system.addForce(forceField);
    AndersenThermostat* thermostat = new AndersenThermostat(temp, collisionFreq);
    system.addForce(thermostat);
    vector<Vec3> positions(numParticles);
    vector<Vec3> velocities(numParticles);
    for (int i = 0; i < numParticles; ++i) {
        positions[i] = Vec3((i%2 == 0 ? 2 : -2), (i%4 < 2 ? 2 : -2), (i < 4 ? 2 : -2));
        velocities[i] = Vec3(0, 0, 0);
    }

    // Try twice with the same random seed.

    thermostat->setRandomNumberSeed(5);
    Context context(system, integrator, platform);
    context.setPositions(positions);
    context.setVelocities(velocities);
    integrator.step(10);
    State state1 = context.getState(State::Positions);
    context.reinitialize();
    context.setPositions(positions);
    context.setVelocities(velocities);
    integrator.step(10);
    State state2 = context.getState(State::Positions);

    // Try twice with a different random seed.

    thermostat->setRandomNumberSeed(10);
    context.reinitialize();
    context.setPositions(positions);
    context.setVelocities(velocities);
    integrator.step(10);
    State state3 = context.getState(State::Positions);
    context.reinitialize();
    context.setPositions(positions);
    context.setVelocities(velocities);
    integrator.step(10);
    State state4 = context.getState(State::Positions);

    // Compare the results.

    for (int i = 0; i < numParticles; i++) {
        for (int j = 0; j < 3; j++) {
            ASSERT(state1.getPositions()[i][j] == state2.getPositions()[i][j]);
            ASSERT(state3.getPositions()[i][j] == state4.getPositions()[i][j]);
            ASSERT(state1.getPositions()[i][j] != state3.getPositions()[i][j]);
        }
    }
}

void testLargeSystem() {
    const int numMolecules = 50;
    const int numParticles = numMolecules*2;
    const double cutoff = 2.0;
    const double boxSize = 5.0;
    const double tolerance = 5;
    System system;
    system.setDefaultPeriodicBoxVectors(Vec3(boxSize, 0, 0), Vec3(0, boxSize, 0), Vec3(0, 0, boxSize));
    NonbondedForce* nonbonded = new NonbondedForce();
    nonbonded->setCutoffDistance(cutoff);
    nonbonded->setNonbondedMethod(NonbondedForce::CutoffPeriodic);
    system.addForce(nonbonded);

    // Create a cloud of molecules.

    OpenMM_SFMT::SFMT sfmt;
    init_gen_rand(0, sfmt);
    vector<Vec3> positions(numParticles);
    for (int i = 0; i < numMolecules; i++) {
        system.addParticle(1.0);
        system.addParticle(1.0);
        nonbonded->addParticle(-1.0, 0.2, 0.2);
        nonbonded->addParticle(1.0, 0.2, 0.2);
        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]);
        system.addConstraint(2*i, 2*i+1, 1.0);
    }

    // Minimize it and verify that the energy has decreased.
    
    ReferencePlatform platform;
    VerletIntegrator integrator(0.01);
    Context context(system, integrator, platform);
    context.setPositions(positions);
    State initialState = context.getState(State::Forces | State::Energy);
    LocalEnergyMinimizer::minimize(context, tolerance);
    State finalState = context.getState(State::Forces | State::Energy | State::Positions);
    ASSERT(finalState.getPotentialEnergy() < initialState.getPotentialEnergy());

    // Compute the force magnitude, subtracting off any component parallel to a constraint, and
    // check that it satisfies the requested tolerance.

    double forceNorm = 0.0;
    for (int i = 0; i < numParticles; i += 2) {
        Vec3 dir = finalState.getPositions()[i+1]-finalState.getPositions()[i];
        double distance = sqrt(dir.dot(dir));
        dir *= 1.0/distance;
        Vec3 f = finalState.getForces()[i];
        f -= dir*dir.dot(f);
        forceNorm += f.dot(f);
        f = finalState.getForces()[i+1];
        f -= dir*dir.dot(f);
        forceNorm += f.dot(f);
    }
    forceNorm = sqrt(forceNorm/(4*numMolecules));
    ASSERT(forceNorm < 3*tolerance);
}

void testArgonBox() {
    const int gridSize = 8;
    const double mass = 40.0;            // Ar atomic mass
    const double temp = 120.0;           // K
    const double epsilon = BOLTZ * temp; // L-J well depth for Ar
    const double sigma = 0.34;           // L-J size for Ar in nm
    const double density = 0.8;          // atoms / sigma^3
    double cellSize = sigma / pow(density, 0.333);
    double boxSize = gridSize * cellSize;
    double cutoff = 2.0 * sigma;

    // Create a box of argon atoms.
    
    System system;
    NonbondedForce* nonbonded = new NonbondedForce();
    vector<Vec3> positions;
    OpenMM_SFMT::SFMT sfmt;
    init_gen_rand(0, sfmt);
    const Vec3 half(0.5, 0.5, 0.5);
    for (int i = 0; i < gridSize; i++) {
        for (int j = 0; j < gridSize; j++) {
            for (int k = 0; k < gridSize; k++) {
                system.addParticle(mass);
                nonbonded->addParticle(0, sigma, epsilon);
                positions.push_back((Vec3(i, j, k) + half + Vec3(genrand_real2(sfmt), genrand_real2(sfmt), genrand_real2(sfmt))*0.1) * cellSize);
            }
        }
    }

    nonbonded->setNonbondedMethod(NonbondedForce::CutoffPeriodic);
    nonbonded->setCutoffDistance(cutoff);
    system.setDefaultPeriodicBoxVectors(Vec3(boxSize, 0, 0), Vec3(0, boxSize, 0), Vec3(0, 0, boxSize));
    system.addForce(nonbonded);

    VariableVerletIntegrator integrator(1e-5);
    Context context(system, integrator, platform);
    context.setPositions(positions);
    context.setVelocitiesToTemperature(temp);

    // Equilibrate.
    
    integrator.stepTo(1.0);

    // Simulate it and see whether energy remains constant.
    
    State state0 = context.getState(State::Energy);
    double initialEnergy = state0.getKineticEnergy() + state0.getPotentialEnergy();
    for (int i = 0; i < 20; i++) {
        double t = 1.0 + 0.05*(i+1);
        integrator.stepTo(t);
        State state = context.getState(State::Energy);
        double energy = state.getKineticEnergy() + state.getPotentialEnergy();
        ASSERT_EQUAL_TOL(initialEnergy, energy, 0.01);
    }
}

/**
 * Test an integrator that enforces constraints.
 */
void testConstraints() {
    const int numParticles = 8;
    System system;
    CustomIntegrator integrator(0.002);
    integrator.addPerDofVariable("oldx", 0);
    integrator.addComputePerDof("v", "v+dt*f/m");
    integrator.addComputePerDof("oldx", "x");
    integrator.addComputePerDof("x", "x+dt*v");
    integrator.addConstrainPositions();
    integrator.addComputePerDof("v", "(x-oldx)/dt");
    integrator.setConstraintTolerance(1e-5);
    NonbondedForce* forceField = new NonbondedForce();
    for (int i = 0; i < numParticles; ++i) {
        system.addParticle(i%2 == 0 ? 5.0 : 10.0);
        forceField->addParticle((i%2 == 0 ? 0.2 : -0.2), 0.5, 5.0);
    }
    for (int i = 0; i < numParticles-1; ++i)
        system.addConstraint(i, i+1, 1.0);
    system.addForce(forceField);
    Context context(system, integrator, platform);
    vector<Vec3> positions(numParticles);
    vector<Vec3> velocities(numParticles);
    OpenMM_SFMT::SFMT sfmt;
    init_gen_rand(0, sfmt);

    for (int i = 0; i < numParticles; ++i) {
        positions[i] = Vec3(i/2, (i+1)/2, 0);
        velocities[i] = Vec3(genrand_real2(sfmt)-0.5, genrand_real2(sfmt)-0.5, genrand_real2(sfmt)-0.5);
    }
    context.setPositions(positions);
    context.setVelocities(velocities);
    
    // Simulate it and see whether the constraints remain satisfied.
    
    double initialEnergy = 0.0;
    for (int i = 0; i < 1000; ++i) {
        State state = context.getState(State::Positions | State::Energy);
        for (int j = 0; j < system.getNumConstraints(); ++j) {
            int particle1, particle2;
            double distance;
            system.getConstraintParameters(j, particle1, particle2, distance);
            Vec3 p1 = state.getPositions()[particle1];
            Vec3 p2 = state.getPositions()[particle2];
            double dist = std::sqrt((p1[0]-p2[0])*(p1[0]-p2[0])+(p1[1]-p2[1])*(p1[1]-p2[1])+(p1[2]-p2[2])*(p1[2]-p2[2]));
            ASSERT_EQUAL_TOL(distance, dist, 2e-5);
        }
        double energy = state.getKineticEnergy()+state.getPotentialEnergy();
        if (i == 1)
            initialEnergy = energy;
        else if (i > 1)
            ASSERT_EQUAL_TOL(initialEnergy, energy, 0.01);
        integrator.step(1);
    }
}

void testForceEnergyConsistency() {
    // Create a box of polarizable particles.
    
    const int gridSize = 3;
    const int numAtoms = gridSize*gridSize*gridSize;
    const double spacing = 0.6;
    const double boxSize = spacing*(gridSize+1);
    const double temperature = 300.0;
    const double temperatureDrude = 10.0;
    System system;
    vector<Vec3> positions;
    NonbondedForce* nonbonded = new NonbondedForce();
    DrudeForce* drude = new DrudeForce();
    system.addForce(nonbonded);
    system.addForce(drude);
    system.setDefaultPeriodicBoxVectors(Vec3(boxSize, 0, 0), Vec3(0, boxSize, 0), Vec3(0, 0, boxSize));
    nonbonded->setNonbondedMethod(NonbondedForce::PME);
    nonbonded->setCutoffDistance(1.0);
    nonbonded->setUseSwitchingFunction(true);
    nonbonded->setSwitchingDistance(0.9);
    nonbonded->setEwaldErrorTolerance(5e-5);
    for (int i = 0; i < numAtoms; i++) {
        int startIndex = system.getNumParticles();
        system.addParticle(1.0);
        system.addParticle(1.0);
        nonbonded->addParticle(1.0, 0.3, 1.0);
        nonbonded->addParticle(-1.0, 0.3, 1.0);
        nonbonded->addException(startIndex, startIndex+1, 0, 1, 0);
        drude->addParticle(startIndex+1, startIndex, -1, -1, -1, -1.0, 0.001, 1, 1);
    }
    for (int i = 0; i < gridSize; i++)
        for (int j = 0; j < gridSize; j++)
            for (int k = 0; k < gridSize; k++) {
                Vec3 pos(i*spacing, j*spacing, k*spacing);
                positions.push_back(pos);
                positions.push_back(pos);
            }
    
    // Simulate it and check that force and energy remain consistent.
    
    DrudeLangevinIntegrator integ(temperature, 50.0, temperatureDrude, 50.0, 0.001);
    Platform& platform = Platform::getPlatformByName("Reference");
    Context context(system, integ, platform);
    context.setPositions(positions);
    State prevState;
    for (int i = 0; i < 100; i++) {
        State state = context.getState(State::Energy | State::Forces | State::Positions);
        if (i > 0) {
            double expectedEnergyChange = 0;
            for (int j = 0; j < system.getNumParticles(); j++) {
                Vec3 delta = state.getPositions()[j]-prevState.getPositions()[j];
                expectedEnergyChange -= 0.5*(state.getForces()[j]+prevState.getForces()[j]).dot(delta);
            }
            ASSERT_EQUAL_TOL(expectedEnergyChange, state.getPotentialEnergy()-prevState.getPotentialEnergy(), 0.05);
        }
        prevState = state;
        integ.step(1);
    }
}

void testConstraints() {
    const int numMolecules = 10;
    const int numParticles = numMolecules*3;
    const int numConstraints = numMolecules*3;
    const double temp = 100.0;
    System system;
    LangevinIntegrator integrator(temp, 2.0, 0.001);
    integrator.setConstraintTolerance(1e-5);
    NonbondedForce* forceField = new NonbondedForce();
    for (int i = 0; i < numMolecules; ++i) {
        system.addParticle(16.0);
        system.addParticle(1.0);
        system.addParticle(1.0);
        forceField->addParticle(-0.82, 0.317, 0.65);
        forceField->addParticle(0.41, 1.0, 0.0);
        forceField->addParticle(0.41, 1.0, 0.0);
        system.addConstraint(i*3, i*3+1, 0.1);
        system.addConstraint(i*3, i*3+2, 0.1);
        system.addConstraint(i*3+1, i*3+2, 0.163);
    }
    system.addForce(forceField);
    Context context(system, integrator, platform);
    vector<Vec3> positions(numParticles);
    vector<Vec3> velocities(numParticles);
    OpenMM_SFMT::SFMT sfmt;
    init_gen_rand(0, sfmt);

    for (int i = 0; i < numMolecules; ++i) {
        positions[i*3] = Vec3((i%4)*0.4, (i/4)*0.4, 0);
        positions[i*3+1] = positions[i*3]+Vec3(0.1, 0, 0);
        positions[i*3+2] = positions[i*3]+Vec3(-0.03333, 0.09428, 0);
        velocities[i*3] = Vec3(genrand_real2(sfmt)-0.5, genrand_real2(sfmt)-0.5, genrand_real2(sfmt)-0.5);
        velocities[i*3+1] = Vec3(genrand_real2(sfmt)-0.5, genrand_real2(sfmt)-0.5, genrand_real2(sfmt)-0.5);
        velocities[i*3+2] = Vec3(genrand_real2(sfmt)-0.5, genrand_real2(sfmt)-0.5, genrand_real2(sfmt)-0.5);
    }
    context.setPositions(positions);
    context.setVelocities(velocities);

    // Simulate it and see whether the constraints remain satisfied.

    for (int i = 0; i < 1000; ++i) {
        integrator.step(1);
        State state = context.getState(State::Positions | State::Forces);
        for (int j = 0; j < numConstraints; ++j) {
            int particle1, particle2;
            double distance;
            system.getConstraintParameters(j, particle1, particle2, distance);
            Vec3 p1 = state.getPositions()[particle1];
            Vec3 p2 = state.getPositions()[particle2];
            double dist = std::sqrt((p1[0]-p2[0])*(p1[0]-p2[0])+(p1[1]-p2[1])*(p1[1]-p2[1])+(p1[2]-p2[2])*(p1[2]-p2[2]));
            ASSERT_EQUAL_TOL(distance, dist, 1e-5);
        }
    }
}

/**
 * Test getting and setting per-DOF variables.
 */
void testPerDofVariables() {
    const int numParticles = 200;
    const double boxSize = 10;
    System system;
    system.setDefaultPeriodicBoxVectors(Vec3(boxSize, 0, 0), Vec3(0, boxSize, 0), Vec3(0, 0, boxSize));
    NonbondedForce* nb = new NonbondedForce();
    system.addForce(nb);
    nb->setNonbondedMethod(NonbondedForce::CutoffNonPeriodic);
    vector<Vec3> positions(numParticles);
    OpenMM_SFMT::SFMT sfmt;
    init_gen_rand(0, sfmt);
    for (int i = 0; i < numParticles; i++) {
        system.addParticle(1.5);
        nb->addParticle(i%2 == 0 ? 1 : -1, 0.1, 1);
        bool close = true;
        while (close) {
            positions[i] = Vec3(boxSize*genrand_real2(sfmt), boxSize*genrand_real2(sfmt), boxSize*genrand_real2(sfmt));
            close = false;
            for (int j = 0; j < i; ++j) {
                Vec3 delta = positions[i]-positions[j];
                if (delta.dot(delta) < 0.1)
                    close = true;
            }
        }
    }
    CustomIntegrator integrator(0.01);
    integrator.addPerDofVariable("temp", 0);
    integrator.addPerDofVariable("pos", 0);
    integrator.addComputePerDof("v", "v+dt*f/m");
    integrator.addComputePerDof("x", "x+dt*v");
    integrator.addComputePerDof("pos", "x");
    Context context(system, integrator, platform);
    context.setPositions(positions);
    vector<Vec3> initialValues(numParticles);
    for (int i = 0; i < numParticles; i++)
        initialValues[i] = Vec3(i+0.1, i+0.2, i+0.3);
    integrator.setPerDofVariable(0, initialValues);
    
    // Run a simulation, then query per-DOF values and see if they are correct.
    
    vector<Vec3> values;
    context.getState(State::Forces); // Cause atom reordering to happen before the first step
    for (int i = 0; i < 200; ++i) {
        integrator.step(1);
        State state = context.getState(State::Positions);
        integrator.getPerDofVariable(0, values);
        for (int j = 0; j < numParticles; j++)
            ASSERT_EQUAL_VEC(initialValues[j], values[j], 1e-5);
        integrator.getPerDofVariable(1, values);
        for (int j = 0; j < numParticles; j++)
            ASSERT_EQUAL_VEC(state.getPositions()[j], values[j], 1e-5);
    }
}

void testConstraints() {
    const int numParticles = 8;
    const double temp = 100.0;
    const double collisionFreq = 10.0;
    const int numSteps = 15000;
    System system;
    VerletIntegrator integrator(0.004);
    NonbondedForce* forceField = new NonbondedForce();
    for (int i = 0; i < numParticles; ++i) {
        system.addParticle(2.0);
        forceField->addParticle((i%2 == 0 ? 1.0 : -1.0), 1.0, 5.0);
    }
    system.addForce(forceField);
    system.addConstraint(0, 1, 1);
    system.addConstraint(1, 2, 1);
    system.addConstraint(2, 3, 1);
    system.addConstraint(3, 0, 1);
    system.addConstraint(4, 5, 1);
    system.addConstraint(5, 6, 1);
    system.addConstraint(6, 7, 1);
    system.addConstraint(7, 4, 1);
    AndersenThermostat* thermostat = new AndersenThermostat(temp, collisionFreq);
    system.addForce(thermostat);
    Context context(system, integrator, platform);
    vector<Vec3> positions(numParticles);
    positions[0] = Vec3(0, 0, 0);
    positions[1] = Vec3(1, 0, 0);
    positions[2] = Vec3(1, 1, 0);
    positions[3] = Vec3(0, 1, 0);
    positions[4] = Vec3(1, 0, 1);
    positions[5] = Vec3(1, 1, 1);
    positions[6] = Vec3(0, 1, 1);
    positions[7] = Vec3(0, 0, 1);
    context.setPositions(positions);
    context.setVelocitiesToTemperature(temp);

    // Let it equilibrate.

    integrator.step(5000);

    // Now run it for a while and see if the temperature is correct.

    double ke = 0.0;
    for (int i = 0; i < numSteps; ++i) {
        State state = context.getState(State::Energy);
        ke += state.getKineticEnergy();
        integrator.step(1);
    }
    ke /= numSteps;
    double expected = 0.5*(numParticles*3-system.getNumConstraints())*BOLTZ*temp;
    ASSERT_USUALLY_EQUAL_TOL(expected, ke, 0.1);
}

void testErrorTolerance(NonbondedForce::NonbondedMethod method) {
    // Create a cloud of random point charges.

    const int numParticles = 51;
    const double boxWidth = 5.0;
    System system;
    system.setDefaultPeriodicBoxVectors(Vec3(boxWidth, 0, 0), Vec3(0, boxWidth, 0), Vec3(0, 0, boxWidth));
    NonbondedForce* force = new NonbondedForce();
    system.addForce(force);
    vector<Vec3> positions(numParticles);
    OpenMM_SFMT::SFMT sfmt;
    init_gen_rand(0, sfmt);

    for (int i = 0; i < numParticles; i++) {
        system.addParticle(1.0);
        force->addParticle(-1.0+i*2.0/(numParticles-1), 1.0, 0.0);
        positions[i] = Vec3(boxWidth*genrand_real2(sfmt), boxWidth*genrand_real2(sfmt), boxWidth*genrand_real2(sfmt));
    }
    force->setNonbondedMethod(method);
    ReferencePlatform platform;

    // For various values of the cutoff and error tolerance, see if the actual error is reasonable.

    for (double cutoff = 1.0; cutoff < boxWidth/2; cutoff *= 1.2) {
        force->setCutoffDistance(cutoff);
        vector<Vec3> refForces;
        double norm = 0.0;
        for (double tol = 5e-5; tol < 1e-3; tol *= 2.0) {
            force->setEwaldErrorTolerance(tol);
            VerletIntegrator integrator(0.01);
            Context context(system, integrator, platform);
            context.setPositions(positions);
            State state = context.getState(State::Forces);
            if (refForces.size() == 0) {
                refForces = state.getForces();
                for (int i = 0; i < numParticles; i++)
                    norm += refForces[i].dot(refForces[i]);
                norm = sqrt(norm);
            }
            else {
                double diff = 0.0;
                for (int i = 0; i < numParticles; i++) {
                    Vec3 delta = refForces[i]-state.getForces()[i];
                    diff += delta.dot(delta);
                }
                diff = sqrt(diff)/norm;
                ASSERT(diff < 2*tol);
            }
        }
    }
}

void testTruncatedOctahedron() {
    const int numMolecules = 50;
    const int numParticles = numMolecules*2;
    const float cutoff = 2.0;
    Vec3 a(6.7929, 0, 0);
    Vec3 b(-2.264163559406279, 6.404455775962287, 0);
    Vec3 c(-2.264163559406279, -3.2019384603140684, 5.54658849047036);

    System system;
    system.setDefaultPeriodicBoxVectors(a, b, c);
    NonbondedForce* force = new NonbondedForce();
    OpenMM_SFMT::SFMT sfmt;
    init_gen_rand(0, sfmt);
    vector<Vec3> positions(numParticles);

    force->setCutoffDistance(cutoff);
    force->setNonbondedMethod(NonbondedForce::CutoffPeriodic);

    for (int i = 0; i < numMolecules; i++) {
        system.addParticle(1.0);
        system.addParticle(1.0);
        force->addParticle(-1, 0.2, 0.2);
        force->addParticle(1, 0.2, 0.2);
        positions[2*i] = a*(5*genrand_real2(sfmt)-2) + b*(5*genrand_real2(sfmt)-2) + c*(5*genrand_real2(sfmt)-2);
        positions[2*i+1] = positions[2*i] + Vec3(1.0, 0.0, 0.0);
        system.addConstraint(2*i, 2*i+1, 1.0);
    }
    system.addForce(force);

    VerletIntegrator integrator(0.01);
    Context context(system, integrator, Platform::getPlatformByName("Reference"));
    context.setPositions(positions);
    State initialState = context.getState(State::Positions | State::Energy, true);
    for (int i = 0; i < numMolecules; i++) {
        Vec3 center = (initialState.getPositions()[2*i]+initialState.getPositions()[2*i+1])*0.5;
        ASSERT(center[0] >= 0.0);
        ASSERT(center[1] >= 0.0);
        ASSERT(center[2] >= 0.0);
        ASSERT(center[0] <= a[0]);
        ASSERT(center[1] <= b[1]);
        ASSERT(center[2] <= c[2]);
    }
    double initialEnergy = initialState.getPotentialEnergy();

    context.setState(initialState);
    State finalState = context.getState(State::Positions | State::Energy, true);
    double finalEnergy = finalState.getPotentialEnergy();

    ASSERT_EQUAL_TOL(initialEnergy, finalEnergy, 1e-4);
}

void ValidateOpenMM::writeNonbondedForce( FILE* filePtr, const NonbondedForce & nonbondedForce ) const {

    // charge and vdw parameters

    (void) fprintf( filePtr, "NonbondedForce %d\n", nonbondedForce.getNumParticles() );
    for(int ii = 0; ii < nonbondedForce.getNumParticles(); ii++ ){
       double charge, sigma, epsilon;
       nonbondedForce.getParticleParameters( ii, charge, sigma, epsilon );
       (void) fprintf( filePtr, "%8d %14.7e %14.7e %14.7e\n", ii, charge, sigma, epsilon );
    }

    // cutoff, dielectric, Ewald tolerance

    (void) fprintf( filePtr, "CutoffDistance %14.7e\n", nonbondedForce.getCutoffDistance() );
    (void) fprintf( filePtr, "RFDielectric %14.7e\n", nonbondedForce.getReactionFieldDielectric() );
    (void) fprintf( filePtr, "EwaldRTolerance %14.7e\n", nonbondedForce.getEwaldErrorTolerance() );

    // cutoff mode

    std::string nonbondedForceMethod;
    switch( nonbondedForce.getNonbondedMethod() ){
        case NonbondedForce::NoCutoff:
            nonbondedForceMethod = "NoCutoff";
            break;
        case NonbondedForce::CutoffNonPeriodic:
            nonbondedForceMethod = "CutoffNonPeriodic";
            break;
        case NonbondedForce::CutoffPeriodic:
            nonbondedForceMethod = "CutoffPeriodic";
            break;
        case NonbondedForce::Ewald:
            nonbondedForceMethod = "Ewald";
            break;
        case NonbondedForce::PME:
            nonbondedForceMethod = "PME";
            break;
        default:
            nonbondedForceMethod = "Unknown";
    }
    (void) fprintf( filePtr, "NonbondedForceMethod %s\n", nonbondedForceMethod.c_str() );

    (void) fprintf( filePtr, "NonbondedForceExceptions %d\n", nonbondedForce.getNumExceptions() );
    for(int ii = 0; ii < nonbondedForce.getNumExceptions(); ii++ ){
       int particle1, particle2;
       double chargeProd, sigma, epsilon;
       nonbondedForce.getExceptionParameters( ii, particle1, particle2, chargeProd, sigma, epsilon );
       (void) fprintf( filePtr, "%8d %8d %8d %14.7e %14.7e %14.7e\n", ii, particle1, particle2, chargeProd, sigma, epsilon );
    }

}

void NonbondedForceImpl::calcEwaldParameters(const System& system, const NonbondedForce& force, double& alpha, int& kmaxx, int& kmaxy, int& kmaxz) {
    Vec3 boxVectors[3];
    system.getDefaultPeriodicBoxVectors(boxVectors[0], boxVectors[1], boxVectors[2]);
    double tol = force.getEwaldErrorTolerance();
    alpha = (1.0/force.getCutoffDistance())*std::sqrt(-log(2.0*tol));
    kmaxx = findZero(EwaldErrorFunction(boxVectors[0][0], alpha, tol), 10);
    kmaxy = findZero(EwaldErrorFunction(boxVectors[1][1], alpha, tol), 10);
    kmaxz = findZero(EwaldErrorFunction(boxVectors[2][2], alpha, tol), 10);
    if (kmaxx%2 == 0)
        kmaxx++;
    if (kmaxy%2 == 0)
        kmaxy++;
    if (kmaxz%2 == 0)
        kmaxz++;
}

void testConstraints() {
    const int numParticles = 8;
    const int numConstraints = 5;
    const double temp = 20.0;
    System system;
    BrownianIntegrator integrator(temp, 2.0, 0.001);
    integrator.setConstraintTolerance(1e-5);
    NonbondedForce* forceField = new NonbondedForce();
    for (int i = 0; i < numParticles; ++i) {
        system.addParticle(10.0);
        forceField->addParticle((i%2 == 0 ? 0.2 : -0.2), 0.5, 5.0);
    }
    system.addConstraint(0, 1, 1.0);
    system.addConstraint(1, 2, 1.0);
    system.addConstraint(2, 3, 1.0);
    system.addConstraint(4, 5, 1.0);
    system.addConstraint(6, 7, 1.0);
    system.addForce(forceField);
    Context context(system, integrator, platform);
    vector<Vec3> positions(numParticles);
    vector<Vec3> velocities(numParticles);
    OpenMM_SFMT::SFMT sfmt;
    init_gen_rand(0, sfmt);

    for (int i = 0; i < numParticles; ++i) {
        positions[i] = Vec3(i, 0, 0);
        velocities[i] = Vec3(genrand_real2(sfmt)-0.5, genrand_real2(sfmt)-0.5, genrand_real2(sfmt)-0.5);
    }
    context.setPositions(positions);
    context.setVelocities(velocities);

    // Simulate it and see whether the constraints remain satisfied.

    for (int i = 0; i < 1000; ++i) {
        State state = context.getState(State::Positions);
        for (int j = 0; j < numConstraints; ++j) {
            int particle1, particle2;
            double distance;
            system.getConstraintParameters(j, particle1, particle2, distance);
            Vec3 p1 = state.getPositions()[particle1];
            Vec3 p2 = state.getPositions()[particle2];
            double dist = std::sqrt((p1[0]-p2[0])*(p1[0]-p2[0])+(p1[1]-p2[1])*(p1[1]-p2[1])+(p1[2]-p2[2])*(p1[2]-p2[2]));
            ASSERT_EQUAL_TOL(distance, dist, 1e-4);
        }
        integrator.step(1);
    }
}